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http://www.solved-problems.com/tag/supernode/ | # Nodal Analysis - Circuit with Dependent Voltage Source
Determine the power of each source after solving the circuit by the nodal analysis.
Answers: $P_{I_x}=0.497W, P_{1A}=-1.806W, P_{2A}=4.254W, P_{3V}=-3.87W,$ and $P_{5V}=-3.552W$
Solution
I. Identify all nodes in the circuit.
The circuit has 6 nodes as highlighted below.
# Nodal Analysis - Supernode
Solve the circuit with nodal analysis and find $I_x$ and $V_y$ .
Solution
1) Identify all nodes in the circuit. Call the number of nodes $N$ .
There are four nodes in the circuit:
Solve the circuit with the nodal analysis and determine $i_x$ and $V_y$ .
1) Identify all nodes in the circuit. Call the number of nodes $N$ .
The circuit has 5 nodes. Therefore, $N=5$ . | {"extraction_info": {"found_math": true, "script_math_tex": 9, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4933173954486847, "perplexity": 783.3139551359733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936463606.79/warc/CC-MAIN-20150226074103-00297-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://socratic.org/questions/58dab8677c01494ed761aed3 | Chemistry
Topics
Would copper carbonate precipitate from aqueous solution by treatment of calcium carbonate by copper(II) chloride?
Aug 4, 2017
I would think so......
Explanation:
And we would represent the equation by.....
$C a C {O}_{3} \left(s\right) + C u C {l}_{2} \left(a q\right) \rightarrow C u C {O}_{3} \left(s\right) \downarrow + C a C {l}_{2} \left(a q\right)$
And how would you know whether the reaction would occur? How else but by experiment?
It is a fact that the ${K}_{\text{sp}}$ of $\text{copper carbonate}$ is $1.4 \times {10}^{-} 10$. And the ${K}_{\text{sp}}$ of $\text{calcium carbonate}$ is $2.8 \times {10}^{-} 9$. And since copper carbonate is more insoluble than calcium carbonate, metathesis would occur, with the result that blue colour of the solution due to $C {u}^{2 +}$ would slowly(?) dissipate.
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https://www.edaboard.com/threads/how-to-assign-a-short-point-ideal-ground-in-cst-transient.338155/ | # How to assign a short point (ideal ground) in CST transient
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Hi everyone!
In CST transient simulation, I have some question.
When I want to do transient simulation using CST, I want to assign one side of structure as a short point to the ideal ground.
It would make the low impedance current path to the ideal ground.
But, I don't know how to realize it.
there is some boundary condition. open, E=0, H=0, and so on...
When I simulate in frequency domain, i usually assign the open space as a boundary condition.
But, i understand it is not ground just adding vacuum in transient simulation. am i right?
#### volker@muehlhaus
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Physically, there is no global ground. Ground is what you call ground, where you place your port's reference pin. However, even if you use PEC (perfect electric conductor) two points at some distance will have (and must have) delay and inductance between them.
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https://www.freebsd.org/cgi/man.cgi?query=eqn&sektion=1&apropos=0&manpath=FreeBSD+8.2-RELEASE | # FreeBSD Manual Pages
EQN(1) General Commands Manual EQN(1)
NAME
eqn - format equations for troff
SYNOPSIS
eqn [ -rvCNR ] [ -dxy ] [ -Tname ] [ -Mdir ] [ -fF ] [ -sn ] [ -pn ]
[ -mn ] [ files... ]
It is possible to have whitespace between a command line option and its
parameter.
DESCRIPTION
This manual page describes the GNU version of eqn, which is part of the
groff document formatting system. eqn compiles descriptions of equa-
tions embedded within troff input files into commands that are under-
stood by troff. Normally, it should be invoked using the -e option of
groff. The syntax is quite compatible with Unix eqn. The output of
GNU eqn cannot be processed with Unix troff; it must be processed with
GNU troff. If no files are given on the command line, the standard in-
put will be read. A filename of - will cause the standard input to be
eqn searches for the file eqnrc in the directories given with the -M
option first, then in /usr/share/tmac, /usr/share/tmac, and finally in
the standard macro directory /usr/share/tmac. If it exists, eqn will
process it before the other input files. The -R option prevents this.
GNU eqn does not provide the functionality of neqn: it does not support
low-resolution, typewriter-like devices (although it may work ade-
quately for very simple input).
OPTIONS
-dxy Specify delimiters x and y for the left and right end, respec-
tively, of in-line equations. Any delim statements in the
source file overrides this.
-C Recognize .EQ and .EN even when followed by a character other
than space or newline.
-N Don't allow newlines within delimiters. This option allows eqn
to recover better from missing closing delimiters.
-v Print the version number.
-r Only one size reduction.
-mn The minimum point-size is n. eqn will not reduce the size of
subscripts or superscripts to a smaller size than n.
-Tname The output is for device name. The only effect of this is to
define a macro name with a value of 1. Typically eqnrc will use
this to provide definitions appropriate for the output device.
The default output device is ps.
-Mdir Search dir for eqnrc before the default directories.
-fF This is equivalent to a gfont F command.
-sn This is equivalent to a gsize n command. This option is depre-
cated. eqn will normally set equations at whatever the current
point size is when the equation is encountered.
-pn This says that subscripts and superscripts should be n points
smaller than the surrounding text. This option is deprecated.
Normally eqn makes sets subscripts and superscripts at 70% of
the size of the surrounding text.
USAGE
Only the differences between GNU eqn and Unix eqn are described here.
Most of the new features of GNU eqn are based on TeX. There are some
references to the differences between TeX and GNU eqn below; these may
safely be ignored if you do not know TeX.
Automatic spacing
eqn gives each component of an equation a type, and adjusts the spacing
between components using that type. Possible types are:
ordinary an ordinary character such as 1' or x';
operator a large operator such as <Sigma>';
binary a binary operator such as +';
relation a relation such as =';
opening a opening bracket such as (';
closing a closing bracket such as )';
punctuation a punctuation character such as ,';
inner a subformula contained within brackets;
suppress spacing that suppresses automatic spacing adjust-
ment.
Components of an equation get a type in one of two ways.
type t e
This yields an equation component that contains e but that has
type t, where t is one of the types mentioned above. For exam-
ple, times is defined as
type "binary" \(mu
The name of the type doesn't have to be quoted, but quoting pro-
tects from macro expansion.
chartype t text
Unquoted groups of characters are split up into individual char-
acters, and the type of each character is looked up; this
changes the type that is stored for each character; it says that
the characters in text from now on have type t. For example,
chartype "punctuation" .,;:
would make the characters .,;:' have type punctuation whenever
they subsequently appeared in an equation. The type t can also
be letter or digit; in these cases chartype changes the font
type of the characters. See the Fonts subsection.
New primitives
e1 smallover e2
This is similar to over; smallover reduces the size of e1 and
e2; it also puts less vertical space between e1 or e2 and the
fraction bar. The over primitive corresponds to the TeX \over
primitive in display styles; smallover corresponds to \over in
non-display styles.
vcenter e
This vertically centers e about the math axis. The math axis is
the vertical position about which characters such as +' and -'
are centered; also it is the vertical position used for the bar
of fractions. For example, sum is defined as
{ type "operator" vcenter size +5 \(*S }
e1 accent e2
This sets e2 as an accent over e1. e2 is assumed to be at the
correct height for a lowercase letter; e2 will be moved down ac-
cording if e1 is taller or shorter than a lowercase letter. For
example, hat is defined as
accent { "^" }
dotdot, dot, tilde, vec, and dyad are also defined using the ac-
cent primitive.
e1 uaccent e2
This sets e2 as an accent under e1. e2 is assumed to be at the
correct height for a character without a descender; e2 will be
moved down if e1 has a descender. utilde is pre-defined using
uaccent as a tilde accent below the baseline.
split "text"
This has the same effect as simply
text
but text is not subject to macro expansion because it is quoted;
text will be split up and the spacing between individual charac-
nosplit text
This has the same effect as
"text"
but because text is not quoted it will be subject to macro ex-
pansion; text will not be split up and the spacing between indi-
vidual characters will not be adjusted.
e opprime
This is a variant of prime that acts as an operator on e. It
produces a different result from prime in a case such as A op-
prime sub 1: with opprime the 1 will be tucked under the prime
as a subscript to the A (as is conventional in mathematical
typesetting), whereas with prime the 1 will be a subscript to
the prime character. The precedence of opprime is the same as
that of bar and under, which is higher than that of everything
except accent and uaccent. In unquoted text a ' that is not the
first character will be treated like opprime.
special text e
This constructs a new object from e using a troff(1) macro named
text. When the macro is called, the string 0s will contain the
output for e, and the number registers 0w, 0h, 0d, 0skern, and
0skew will contain the width, height, depth, subscript kern, and
skew of e. (The subscript kern of an object says how much a
subscript on that object should be tucked in; the skew of an ob-
ject says how far to the right of the center of the object an
accent over the object should be placed.) The macro must modify
0s so that it will output the desired result with its origin at
the current point, and increase the current horizontal position
by the width of the object. The number registers must also be
modified so that they correspond to the result.
For example, suppose you wanted a construct that cancels' an
expression by drawing a diagonal line through it.
.EQ
define cancel 'special Ca'
.EN
.de Ca
. ds 0s \
\Z'\\*(0s'\
\v'\\n(0du'\
\D'l \\n(0wu -\\n(0hu-\\n(0du'\
\v'\\n(0hu'
..
Then you could cancel an expression e with cancel { e }
Here's a more complicated construct that draws a box round an
expression:
.EQ
define box 'special Bx'
.EN
.de Bx
. ds 0s \
\Z'\h'1n'\\*(0s'\
\Z'\
\v'\\n(0du+1n'\
\D'l \\n(0wu+2n 0'\
\D'l 0 -\\n(0hu-\\n(0du-2n'\
\D'l -\\n(0wu-2n 0'\
\D'l 0 \\n(0hu+\\n(0du+2n'\
'\
\h'\\n(0wu+2n'
. nr 0w +2n
. nr 0d +1n
. nr 0h +1n
..
space n
A positive value of the integer n (in hundredths of an em) sets
the vertical spacing before the equation, a negative value sets
the spacing after the equation, replacing the default values.
This primitive provides an interface to groff's \x escape (but
with opposite sign).
This keyword has no effect if the equation is part of a pic pic-
ture.
Extended primitives
col n { ... }
ccol n { ... }
lcol n { ... }
rcol n { ... }
pile n { ... }
cpile n { ... }
lpile n { ... }
rpile n { ... }
The integer value n (in hundredths of an em) increases the ver-
tical spacing between rows, using groff's \x escape. Negative
values are possible but have no effect. If there is more than a
single value given in a matrix, the biggest one is used.
Customization
The appearance of equations is controlled by a large number of parame-
ters. These can be set using the set command.
set p n
This sets parameter p to value n; n is an integer. For example,
set x_height 45
says that eqn should assume an x height of 0.45 ems.
Possible parameters are as follows. Values are in units of hun-
dredths of an em unless otherwise stated. These descriptions
are intended to be expository rather than definitive.
minimum_size
eqn will not set anything at a smaller point-size than
this. The value is in points.
fat_offset
The fat primitive emboldens an equation by overprinting
two copies of the equation horizontally offset by this
amount.
over_hang
A fraction bar will be longer by twice this amount than
the maximum of the widths of the numerator and denomina-
tor; in other words, it will overhang the numerator and
denominator by at least this amount.
accent_width
When bar or under is applied to a single character, the
line will be this long. Normally, bar or under produces
a line whose length is the width of the object to which
it applies; in the case of a single character, this tends
to produce a line that looks too long.
delimiter_factor
Extensible delimiters produced with the left and right
primitives will have a combined height and depth of at
least this many thousandths of twice the maximum amount
by which the sub-equation that the delimiters enclose ex-
tends away from the axis.
delimiter_shortfall
Extensible delimiters produced with the left and right
primitives will have a combined height and depth not less
than the difference of twice the maximum amount by which
the sub-equation that the delimiters enclose extends away
from the axis and this amount.
null_delimiter_space
This much horizontal space is inserted on each side of a
fraction.
script_space
The width of subscripts and superscripts is increased by
this amount.
thin_space
This amount of space is automatically inserted after
punctuation characters.
medium_space
This amount of space is automatically inserted on either
side of binary operators.
thick_space
This amount of space is automatically inserted on either
side of relations.
x_height
The height of lowercase letters without ascenders such as
x'.
axis_height
The height above the baseline of the center of characters
such as +' and -'. It is important that this value is
correct for the font you are using.
default_rule_thickness
This should set to the thickness of the \(ru character,
or the thickness of horizontal lines produced with the \D
escape sequence.
num1 The over command will shift up the numerator by at least
this amount.
num2 The smallover command will shift up the numerator by at
least this amount.
denom1 The over command will shift down the denominator by at
least this amount.
denom2 The smallover command will shift down the denominator by
at least this amount.
sup1 Normally superscripts will be shifted up by at least this
amount.
sup2 Superscripts within superscripts or upper limits or nu-
merators of smallover fractions will be shifted up by at
least this amount. This is usually less than sup1.
sup3 Superscripts within denominators or square roots or sub-
scripts or lower limits will be shifted up by at least
this amount. This is usually less than sup2.
sub1 Subscripts will normally be shifted down by at least this
amount.
sub2 When there is both a subscript and a superscript, the
subscript will be shifted down by at least this amount.
sup_drop
The baseline of a superscript will be no more than this
much amount below the top of the object on which the su-
perscript is set.
sub_drop
The baseline of a subscript will be at least this much
below the bottom of the object on which the subscript is
set.
big_op_spacing1
The baseline of an upper limit will be at least this much
above the top of the object on which the limit is set.
big_op_spacing2
The baseline of a lower limit will be at least this much
below the bottom of the object on which the limit is set.
big_op_spacing3
The bottom of an upper limit will be at least this much
above the top of the object on which the limit is set.
big_op_spacing4
The top of a lower limit will be at least this much below
the bottom of the object on which the limit is set.
big_op_spacing5
This much vertical space will be added above and below
limits.
baseline_sep
The baselines of the rows in a pile or matrix will nor-
mally be this far apart. In most cases this should be
equal to the sum of num1 and denom1.
shift_down
The midpoint between the top baseline and the bottom
baseline in a matrix or pile will be shifted down by this
much from the axis. In most cases this should be equal
to axis_height.
column_sep
This much space will be added between columns in a ma-
trix.
matrix_side_sep
This much space will be added at each side of a matrix.
draw_lines
If this is non-zero, lines will be drawn using the \D es-
cape sequence, rather than with the \l escape sequence
and the \(ru character.
body_height
The amount by which the height of the equation exceeds
this will be added as extra space before the line con-
taining the equation (using \x). The default value is
85.
body_depth
The amount by which the depth of the equation exceeds
this will be added as extra space after the line contain-
ing the equation (using \x). The default value is 35.
nroff If this is non-zero, then ndefine will behave like define
and tdefine will be ignored, otherwise tdefine will be-
have like define and ndefine will be ignored. The de-
fault value is 0 (This is typically changed to 1 by the
eqnrc file for the ascii, latin1, utf8, and cp1047 de-
vices.)
A more precise description of the role of many of these parame-
ters can be found in Appendix H of The TeXbook.
Macros
Macros can take arguments. In a macro body, \$n where n is between 1
and 9, will be replaced by the n-th argument if the macro is called
with arguments; if there are fewer than n arguments, it will be re-
placed by nothing. A word containing a left parenthesis where the part
of the word before the left parenthesis has been defined using the de-
fine command will be recognized as a macro call with arguments; charac-
ters following the left parenthesis up to a matching right parenthesis
will be treated as comma-separated arguments; commas inside nested
parentheses do not terminate an argument.
sdefine name X anything X
This is like the define command, but name will not be recognized
if called with arguments.
include "file"
copy "file"
Include the contents of file (include and copy are synonyms).
Lines of file beginning with .EQ or .EN will be ignored.
ifdef name X anything X
If name has been defined by define (or has been automatically
defined because name is the output device) process anything;
otherwise ignore anything. X can be any character not appearing
in anything.
undef name
Remove definition of name, making it undefined.
Besides the macros mentioned above, the following definitions are
available: Alpha, Beta, ..., Omega (this is the same as ALPHA, BETA,
..., OMEGA), ldots (three dots on the base line), and dollar.
Fonts
eqn normally uses at least two fonts to set an equation: an italic font
for letters, and a roman font for everything else. The existing gfont
command changes the font that is used as the italic font. By default
this is I. The font that is used as the roman font can be changed us-
ing the new grfont command.
grfont f
Set the roman font to f.
The italic primitive uses the current italic font set by gfont; the ro-
man primitive uses the current roman font set by grfont. There is also
a new gbfont command, which changes the font used by the bold primi-
tive. If you only use the roman, italic and bold primitives to changes
fonts within an equation, you can change all the fonts used by your
equations just by using gfont, grfont and gbfont commands.
You can control which characters are treated as letters (and therefore
set in italics) by using the chartype command described above. A type
of letter will cause a character to be set in italic type. A type of
digit will cause a character to be set in roman type.
FILES
/usr/share/tmac/eqnrc Initialization file.
BUGS
Inline equations will be set at the point size that is current at the
beginning of the input line.
` | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9145860075950623, "perplexity": 13812.12812410547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335054.79/warc/CC-MAIN-20220927162620-20220927192620-00218.warc.gz"} |
https://ggplot2.tidyverse.org/reference/aes_linetype_size_shape.html | The linetype, size, and shape aesthetics modify the appearance of lines and/or points. They also apply to the outlines of polygons (linetype and size) or to text (size).
The linetype aesthetic can be specified with either an integer (0-6), a name (0 = blank, 1 = solid, 2 = dashed, 3 = dotted, 4 = dotdash, 5 = longdash, 6 = twodash), a mapping to a discrete variable, or a string of an even number (up to eight) of hexadecimal digits which give the lengths in consecutive positions in the string. See examples for a hex string demonstration.
The size aesthetic can be specified with a numerical value (in millimetres) or via a mapping to a continuous variable.
The shape aesthetic can be specified with an integer (between 0 and 25), a single character (which uses that character as the plotting symbol), a . to draw the smallest rectangle that is visible (i.e., about one pixel), an NA to draw nothing, or a mapping to a discrete variable. Symbols and filled shapes are described in the examples below.
• geom_line() and geom_point() for geoms commonly used with these aesthetics.
• aes_group_order() for using linetype, size, or shape for grouping.
• Run vignette("ggplot2-specs") to see an overview of other aesthestics that can be modified.
## Examples
df <- data.frame(x = 1:10 , y = 1:10)
p <- ggplot(df, aes(x, y))
p + geom_line(linetype = 2)
p + geom_line(linetype = "dotdash")
# An example with hex strings; the string "33" specifies three units on followed
# by three off and "3313" specifies three units on followed by three off followed
# by one on and finally three off.
p + geom_line(linetype = "3313")
# Mapping line type from a grouping variable
ggplot(economics_long, aes(date, value01)) +
geom_line(aes(linetype = variable))
# Size examples
p <- ggplot(mtcars, aes(wt, mpg))
p + geom_point(size = 4)
p + geom_point(aes(size = qsec))
p + geom_point(size = 2.5) +
geom_hline(yintercept = 25, size = 3.5)
# Shape examples
p + geom_point()
p + geom_point(shape = 5)
p + geom_point(shape = "k", size = 3)
p + geom_point(shape = ".")
p + geom_point(shape = NA)
#> Warning: Removed 32 rows containing missing values (geom_point).
p + geom_point(aes(shape = factor(cyl)))
# A look at all 25 symbols
df2 <- data.frame(x = 1:5 , y = 1:25, z = 1:25)
p <- ggplot(df2, aes(x, y))
p + geom_point(aes(shape = z), size = 4) +
scale_shape_identity()
# While all symbols have a foreground colour, symbols 19-25 also take a
# background colour (fill)
p + geom_point(aes(shape = z), size = 4, colour = "Red") +
scale_shape_identity()
p + geom_point(aes(shape = z), size = 4, colour = "Red", fill = "Black") +
scale_shape_identity() | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23730938136577606, "perplexity": 8002.7866206229055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587908.20/warc/CC-MAIN-20211026134839-20211026164839-00404.warc.gz"} |
http://pari.math.u-bordeaux1.fr/archives/pari-users-1310/msg00007.html | Bill Allombert on Thu, 10 Oct 2013 20:45:23 +0200
Re: Degree extension
On Thu, Oct 10, 2013 at 05:57:06PM +0200, [email protected] wrote:
> Dear All,
>
> I am Laura, a new member of the list of the
> users of PARI.
Welcome!
> I have a question. I have the roots of
> some polynomials of the form y^2=x^3+Ax+B.
> For example p:=y^2=x^3+2*x+5.
> I call a, b and c the roots of p.
> I would like to calculate the degree
> of the number field
>
> Q(sqrt(a-b),sqrt(a-c),sqrt(b-c),sqrt(-1)).
>
> Is it possible with PARI?
Yes, this is possible
and K=Q(sqrt(a-b),sqrt(a-c),sqrt(b-c),sqrt(-1))
1) Build the Galois closure of P as follow:
S=polcompositum(P,P)[2];
(This depends on the Galois group of P, but this will work in both case)
2) Compute the roots of P in the field Q[X]/P:
N=nfroots(subst(S,x,'alpha),P);
Now the roots are given by a=N[1], b=N[2], c=N[3]
in term of a root alpha of S.
3) Compute the minimal polynomial of a-b as follow
Mab=minpoly(N[1]-N[2]);
By Galois theory, it has the same degree as S.
4) The minimal polynomial of sqrt(a-b) is a factor of Mab(x^2)
Msab=factor(subst(Mab,x,x^2))[1,1]
5) Build the tensor product Q[x]/Msab \otimes Q(sqrt(-1))
MsabI = polcompositum(Msab,x^2+1)[1]
6) Factor Msab over L=Q[X]/MsabI:
R=nffactor(subst(MsabI,x,'beta),Msab);
This will be given in term of a root beta of MsabI.
7.1) If Msab split in linear factor, then K=L and the degree
is poldegree(MsabI). This can be checked with
poldegree(Msab)==#R[,1]
7.2) otherwise, we have to go one step higher. Set
MsabcI=rnfequation(subst(MsabI,x,'beta),R[3,1]);
In that case K=Q[X]/MsabcI and the degree is poldegree(MsabcI)
Cheers,
Bill. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.960507333278656, "perplexity": 3426.5403930667003}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806842.71/warc/CC-MAIN-20171123142513-20171123162513-00096.warc.gz"} |
https://hal.archives-ouvertes.fr/ccsd-00609435/en/ | # From flows of Lambda-Fleming-Viot processes to lookdown processes via flows of partitions
Abstract : The goal of this paper is to unify the lookdown representation and the stochastic flow of bridges, which are two approaches to construct the $\Lambda$-Fleming-Viot process along with its genealogy. First we introduce the stochastic flow of partitions and show that it provides a new formulation of the lookdown representation. Second we study the asymptotic behaviour of the $\Lambda$-Fleming-Viot process and we provide sufficient conditions for the existence of an infinite sequence of Eves that generalise the primitive Eve of Bertoin and Le Gall. Finally under the condition that this infinite sequence of Eves does exist, we construct the lookdown representation pathwise from a flow of bridges.
Keywords :
Document type :
Journal articles
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 19 (55)
Domain :
https://hal.archives-ouvertes.fr/hal-00609435
Contributor : Cyril Labbé <>
Submitted on : Tuesday, July 19, 2011 - 9:44:50 AM
Last modification on : Monday, May 29, 2017 - 2:22:17 PM
### Identifiers
• HAL Id : hal-00609435, version 1
• ARXIV : 1107.3419
### Citation
Cyril Labbé. From flows of Lambda-Fleming-Viot processes to lookdown processes via flows of partitions. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2014, 19 (55). <hal-00609435>
### Metrics
Consultations de la notice | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7205141186714172, "perplexity": 2319.8115411694184}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320685.63/warc/CC-MAIN-20170626064746-20170626084746-00383.warc.gz"} |
https://zbmath.org/?q=an:1027.46013 | # zbMATH — the first resource for mathematics
##### Examples
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Generalized orthogonal decomposition theorem in Banach space and generalized orthogonal complemented subspace. (Chinese. English summary) Zbl 1027.46013
In a Hilbert space $H$, the Riesz orthogonal decomposition theorem says that any closed linear subspace $L\subset H$ has a unique orthogonal complement, i.e., a subspace $M$ of $H$ such that $H=L\oplus M$ and $M\perp L$. In this paper, the authors study the generalization of the Riesz theorem to Banach spaces. We call vectors $x,y$ in a normed space $X$ orthogonal and denote this by $x\perp y$, if $d_{\langle y\rangle }( x) =\|x\|$, where $\langle y\rangle$ is the linear span of $y$ and $d_{S}( x) =\inf_{s\in S}\|x-s\|$ is the shortest distance from $x$ to a set $S\subset X$, and we also call two subsets $A,B\subset X$ orthogonal and denote this by $A\perp B$, if $d_{B}( x) =\|x\|$ for all $x\in A$. Note that in a general Banach space $X$, the orthogonal condition $A\perp B$ is not symmetric in $A,B$, but in a Hilbert space it does coincide with the traditional orthogonal condition. A (closed) linear subspace $L\subset X$ is called orthogonally complementable if there is a (closed) linear subspace $M$ with $X=L\oplus M$ and $M\perp L$. The authors obtain results on the orthogonal decomposition in Banach algebras under suitable conditions. In particular, it is shown that a closed subspace $L$ of a strictly convex space $X$ is orthogonally complementable if and only if $L$ is a Chebyshev subspace of $X$ and $F_{X}^{-1}( L^{\perp }) =\{ x\in X\mid F_{X}( x) \cap L^{\perp }\neq \emptyset \}$ is an additive set, where $F_{X}( x) =\{ x^{\ast }\in X^{\ast }\mid \langle x^{\ast },x\rangle =\|x\|^{2}\}$ and $L^{\perp }=\{ x^{\ast }\in X^{\ast }\mid \langle x^{\ast },x\rangle =0 \text{for all }x\in L\}$.
##### MSC:
46B20 Geometry and structure of normed linear spaces 46B15 Summability and bases in normed spaces | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9067765474319458, "perplexity": 1553.620132548929}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860125897.19/warc/CC-MAIN-20160428161525-00199-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/26807/problems-with-column-alignment-in-the-lstlisting-environment?answertab=oldest | # Problems with column alignment in the lstlisting environment
I'm having some problems with the column alignment in the lstlisting environment provided by listings.sty.
In fixed-width column alignment mode, whatever the typeface being used, listings are supposed to be presented with one character per column, where the columns have uniform widths (which may be set by the author). However, I find this not actually to be the case with certain input.
Minimal example:
\documentclass{article}
\usepackage{listings}
\begin{document}
\begin{lstlisting}[columns=fixed]
columnar alignment maligned multiple narrow characters?
1234 6789 1234 6789 1234 6789 1234 6789 1234 6789 1234
\end{lstlisting}
\end{document}
Result:
Note that the second line is exactly one character shorter than the first, which is observed at the far right-hand side. However, the alignment in the middle is somewhat ruined at the occurance of every l character (ambiguous alignment of u in columnar with 3 or 4; ambiguous alignment of i, g, and n in alignment with 1, 2, 3, and 4; etc.). This problem is not helped by tweaking the alignment, by e.g. replacing fixed with {[l]fixed} for the column alignment.
Is this a known problem? Is there any fix for it?
-
This is the expected/default output for columns=fixed in an lstlisting environment. From the listings package documentation:
Now, the fixed format puts n characters into a box of width n x base width, where the base width is 0.6em in the example. The format shrinks and stretches the space between the characters to make them fit the box.
That is, the alignment is not meant to consistent across lines within the listing. Rather, the chunks of code is placed in boxes and the spacing is modified with no regard for anything else except the box width. Even the example presented in the documentation (page 19) exhibits this behaviour:
Notice the misaligned i in write (line 1) and print (line 2) due to the wider w.
Even if you modified your minimal example to the following:
\documentclass{article}
\usepackage{listings}
\begin{document}
\begin{lstlisting}[columns=fixed]
colu mnar alig nmen tmal igne dmul tipl enar rowc hara cters?
1234 6789 1234 6789 1234 6789 1234 6789 1234 6789 1234
\end{lstlisting}
\end{document}
attempting to align the listing column-wise, the output looks better, but still has the same issues you mention:
Notice the misalignment between mnar and 6789 (due to m); tmal and 1234 (again due to m); rowc and 6789 (due to w), etc.
The only way around this is to use a mono-spaced font for your entire listing, using (say) basicstyle=\ttfamily:
-
Hmm. What you're describing sounds an awful lot like the flexible spacing option. "Common to all is that the input characters are translated into a sequence of basic output units"; but surely what counts as a unit differs between the four alignment options, as otherwise the horrible spacing in the example text for the documentation (e.g. the words MEN and WOMEN) would not occur; even in my question, there's an odd space just before the n in columnar which should not occur if it's of one block. Are you quite sure that the blocks are meant to be computed on the syntactic level? – Niel de Beaudrap Aug 29 '11 at 9:41
Basically, what I am asking is this –– this behaviour is obviously known, because you (at least) are taking it for granted that this is normal, and are able to use the documentation itself as evidence. Does anyone view this behaviour as desirable, that the lstlisting ruins the spacing between characters if you use fixed spacing, but doesn't do it well enough to successfully achieve columnar alignment? Or is this an issue which is somehow famously difficult to solve? Basically, I'm asking: is it worth addressing it as a bug to the package maintainer? – Niel de Beaudrap Aug 29 '11 at 9:48
I'm accepting this answer because it seems to explain what my problem is; although I'm unhappy with the fact that the problem exists, because it essentially defeats the purpose of the various spacing options in listings.sty. – Niel de Beaudrap Sep 25 '11 at 1:08
Regardless of the outcome here, it is definitely advisable to follow up with the package maintainer(s). They would have the best idea whether it could be included in future releases, whether a temporary fix exists, or even whether there are others that have expressed similar interests. – Werner Sep 25 '11 at 5:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8187068104743958, "perplexity": 1274.7126664842622}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928562.33/warc/CC-MAIN-20150521113208-00269-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-math-topics/280495-formula-area-object-bounded-lines-radii-cartesian-plane.html | # Thread: Formula For Area of Object Bounded By Lines and Radii on Cartesian Plane
1. ## Formula For Area of Object Bounded By Lines and Radii on Cartesian Plane
At one time, I had a formula used in a FORTRAN program that provided the area of an object comprised of lines and radii. I provided an NC input file that contained x-y coordinates along with x-y offsets for a radius and it also indicated CW or CCW circular interpolation. The areas under the lines and radii would be summed when travelling left to right and subtracted when going right to left. I know that I can calculate the areas manually. Can someone point me to where I could find that formula?
I know I can calculate the area under a line using the trapezoidal formula.
I can calculate:
Area under a radius: Area inside arc & below= area of segment + area under line x increasing clockwise or x decreasing counterclockwise motion
Area outside arc & below = area under line - area of segment x increasing clockwise or x decreasing counterclockwise.
When in Relative Quadrants ! & II sum areas. When in Relative Quadrants III & IV subtract areas. Circular motion will be calculated by quadrant so note about theta </= 90 should be expanded to state area calculated by quadrant.
I found the formula in the appendix of a calculus book published ~1970-1973. I only remember that it was blue and looked similar to the jpg file.
I know it's a stretch to find the formula but I do not know how to re-create it.
Thanks,
Barry
Attached Thumbnails
Attached Files | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.80124431848526, "perplexity": 1134.9684508205787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249508792.98/warc/CC-MAIN-20190223162938-20190223184938-00600.warc.gz"} |
https://docs.gammapy.org/dev/astro/population/index.html | # Astrophysical source population models (gammapy.astro.population)¶
## Introduction¶
The gammapy.astro.population module provides a simple framework for population synthesis of gamma-ray sources, which is useful in the context of surveys and population studies.
## Getting Started¶
The following example illustrates how to simulate a basic catalog including a spiral arm model.
import astropy.units as u
from gammapy.astro.population import make_base_catalog_galactic
max_age = 1E6 * u.yr
SN_rate = 3. / (100. * u.yr)
n_sources = int(max_age * SN_rate)
table = make_base_catalog_galactic(
n_sources=n_sources,
vel_dis='F06B',
max_age=max_age,
spiralarms=True,
)
The total number of sources is determined assuming a maximum age and a supernova rate. The table returned is an instance of Table which can be used for further processing. The example population with spiral-arms is illustrated in the following plot.
(png, hires.png, pdf)
### Galactocentric spatial distributions¶
Here is a comparison plot of all available radial distribution functions of the surface density of pulsars and related objects used in literature:
(png, hires.png, pdf)
TODO: add illustration of Galactocentric z-distribution model and combined (r, z) distribution for the Besancon model.
### Spiral arm models¶
Two spiral arm models of the Milky way are available: ValleeSpiral and gammapy.astro.population.FaucherSpiral
(png, hires.png, pdf)
### Velocity distributions¶
Here is a comparison plot of all available velocity distribution functions:
(png, hires.png, pdf)
## Reference/API¶
### gammapy.astro.population Package¶
Astrophysical population models.
#### Functions¶
add_observed_parameters(table[, obs_pos]) Add observable parameters (such as sky position or distance). add_pulsar_parameters(table[, B_mean, …]) Add pulsar parameters to the table. add_pwn_parameters(table) Add PWN parameters to the table. add_snr_parameters(table) Add SNR parameters to the table. make_base_catalog_galactic(n_sources[, …]) Make a catalog of Galactic sources, with basic source parameters. make_catalog_random_positions_cube([size, …]) Make a catalog of sources randomly distributed on a line, square or cube. make_catalog_random_positions_sphere([size, …]) Sample random source locations in a sphere.
#### Classes¶
CaseBattacharya1998([amplitude, alpha, beta]) Radial distribution of the surface density of supernova remnants in the galaxy - Case & Battacharya 1998. Exponential([amplitude, z_0]) Exponential distribution. FaucherKaspi2006([amplitude, r_0, sigma]) Radial distribution of the birth surface density of pulsars in the galaxy - Faucher-Giguere & Kaspi 2006. FaucherKaspi2006VelocityBimodal([amplitude, …]) Bimodal pulsar velocity distribution - Faucher & Kaspi (2006). Maxwellian pulsar velocity distribution. FaucherSpiral Milky way spiral arm used in Faucher et al (2006). LogSpiral Logarithmic spiral. Lorimer2006([amplitude, B, C]) Radial distribution of the surface density of pulsars in the galaxy - Lorimer 2006. Paczynski1990([amplitude, r_exp]) Radial distribution of the birth surface density of neutron stars - Paczynski 1990. Paczynski1990Velocity([amplitude, v_0]) Distribution by Lyne 1982 and adopted by Paczynski and Faucher. Milky way spiral arm model from Vallee (2008). YusifovKucuk2004([amplitude, a, b, r_1]) Radial distribution of the surface density of pulsars in the galaxy - Yusifov & Kucuk 2004. YusifovKucuk2004B([amplitude, a, b]) Radial distribution of the surface density of OB stars in the galaxy - Yusifov & Kucuk 2004. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9244073033332825, "perplexity": 5124.951948359651}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370509103.51/warc/CC-MAIN-20200402235814-20200403025814-00067.warc.gz"} |
https://www.arpinvestments.com/insights/to-be-or-not-to-be | Thematic, innovative and bespoke investment solutions and thinking
# To Be or Not to Be? – A note on Responsible Investing
In any moment of decision, the best thing you can do is the right thing. The worst thing you can do is nothing.
Theodore Roosevelt
If you were to spot a plastic bottle on the pavement in front of your house, would you walk straight past it or would you pick it up? Maybe ten years ago you would have ignored it, but I would guess that today, many of you would feel compelled to pick up the bottle and dispose of it in your recycling bin at home.
What has changed? For sure, the media have made us much more aware of the negative impact of plastic waste, with images of remote, pristine beaches littered with plastic and horrifying statistics immediately popping into our heads. It is estimated that of the over one million single-use plastic bottles produced every minute, up to 70% are not recycled, with most ending up in landfill or in the ocean – the latter creating a plastic tsunami destroying marine life [SIX Magazine, March 2020].
These types of images and statistics have woken many of us from our slumber and resulted in a heightened sensitivity to the environmental and social implications of our actions across all facets of our lives. This sensitivity is arguably amplified for other headline issues, such as climate change and racial inequality – particularly post COVID-19 – and the Black Lives Matter movement. It is therefore only natural that, as an investor, you should also be questioning the environmental and social implications of your investments.
The good news is that you are not alone in asking yourself these types of questions. 70 senior executives at 43 leading global investing entities, including CalPERS, CalSTRS, the government pension funds of Japan, Sweden and the Netherland as well as the likes of BlackRock, Vanguard and State Street, were interviewed by the Harvard Business Review in the spring of 2019. Environmental, social and governance (ESG) considerations were almost universally at the top of these senior executives’ minds [The Investor Revolution, Harvard Busines Review, May-June 2019]. A recent RBC Global Asset Management survey found that the pandemic has led more than a quarter of professional investors to place even more importance on these considerations.So, what are the steps you need to take to determine if you should convert to responsible investing (RI) or not? And, if you opt to be a responsible investor (which you may have already decided to be), what ‘shade’ of RI should you adopt? By the way, when I mention ‘you’, as an ARP+ reader, you could be any type of investor, ranging from a large institutional asset manager to an individual investor. The steps provided in the following are applicable to all investors. Exhibit 1 provides some insight as to the rationale some of your peers have given for becoming a responsible investor.
## To continue reading...
We publish investment strategies and opportunities in our research papers. This research paper is available to professional investors as part of ARP+ subscription.
## Step 1: Step back and reflect on your values, beliefs and priorities
The two key questions you need to ask yourself at this stage are why you might consider becoming a responsible investor and what it means to you. A brainstorming session is recommended at this early stage with the key items to be considered highlighted in Exhibit 2.
This first step is arguably the most important part of the entire exercise and will require a high degree of introspection. For example, your ethical values may clash with some of your business objectives. Such conflicts need to be discussed and hashed out from the very beginning – not always an easy feat. We have seen many investors getting stuck at this early stage and struggling to proceed any further. It is important that you persevere! As this process has a number of interconnected questions to ask yourself, which may be quite specific to your own views and requirements, we have added a discussion on these in the Appendix:
1. Where to position yourself on the RI spectrum?
2. What areas should you avoid?
3. Which environmental and social issues should you focus on?
4. How patient should you be- engagement vs. divesting?
5. What are you stakeholders telling you?
To provide you with some insight as to how other investors have addressed these questions, peer statistics have been included in some instances.
## Step 2: Understand what regulators have decided you need ‘to be’
If you think it is complicated to determine what kind of investor you would like to be (Step 1), add to the equation that you also need to follow what the regulator has decided you need to be, and the whole issue gets even more complex.
Generally speaking, Europe is ahead of the rest of the world with regards to sustainable investment rules and regulations (the ‘to be’ camp), whereas the Trump administration has dug its heels in and argued that it is all ‘fake news’ (the ‘not to be’ camp). This will undoubtedly change with Biden’s “tackling the climate emergency” as one of the key tenets of the Biden Plan. So, if you are a US investor you should prepare yourself for an overhaul of the current situation.
### If you are a US investor …
There has been significant regulatory pushback against ESG investing in the US. In June 2020, the US Department of Labor set out plans for a rule that would require private pension administrators to prove that they were not sacrificing financial returns by putting money in ESG-focused investments. The plans require fiduciaries to provide evidence that ESG-like investments have been chosen solely on “objective risk-return criteria”. The Department of Labor stated that the proposed rules would reduce pension funds’ expenses by “giving fiduciaries clear directions to refrain from spending workers’ retirement savings to research and vote on matters that are not expected to have an economic impact on the plan”.
Some investors claim US companies complain about shareholders’ focus on ESG and the use of annual meetings to pile pressure on boards over environmental and other issues. During the 30-day comment period which ended on July 31, the proposed rule drew over 8,000 comments with some 95% of the comments opposing it [the authors of the analysis included representatives from the Intentional Endowments Network, Morningstar, US SIF, Ceres, the AFL-CIO, Impax Asset Management and the Interfaith Center for Corporate Responsibility]. The Labor Department hasn’t issued its ruling yet.
### … or a European investor
On the other hand, in Europe (and, despite Brexit, the UK is still very much part of Europe), regulatory demands on investors in relation to ESG are on the rise. Two key pieces of regulation, the EU Taxonomy and the Sustainable Finance Disclosure Regulation (SFDR), target conformity and transparency. At a high level, the EU Taxonomy establishes the conditions and the framework to create a unified ‘classification system’ – essentially what can be considered an environmentally sustainable economic activity. Meanwhile, SFDR introduces, amongst other, disclosure obligations on how institutional investors and asset managers integrate ESG factors into their risk management processes. Delegated acts will further specify requirements on integrating ESG factors into investment decisions. This is part of institutional investors’ and asset managers’ duties towards investors and beneficiaries. Other regulations are being introduced and/or reviewed, including the EU Climate Benchmarks Regulation (which amongst other creates a new category of benchmarks comprising climate transition and Paris-aligned benchmarks). EU regulators are also moving to embrace the Task Force for Climate-Related Financial Disclosure (TCFD) system.
UK was the first G7 country to commit to be climate neutral by 2050 and is keen on adhering to high standards. As a result, the UK’s regulatory approach is shifting from voluntary to mandatory. From October 2019, pension trustees in the UK were required to update their scheme’s Statement of Investment Principles (SIP) to set out their policies on ESG, climate change and stewardship activities. Since then, schemes have faced additional ESG reporting requirements within their SIP, while also publishing annual implementation statements on how they have followed through on their ESG and stewardship policies.
To ensure pension schemes drive change to a sustainable, low carbon economy, the UK government has put forward proposals to require the 100 largest occupational pension schemes – those with £5Bn or more in assets – to publish climate risk disclosures by the end of 2022. The proposals will mean trustees of such schemes are legally required to assess and report on the financial risks of climate change within their portfolios. The government said that, following this first round, a further 250 schemes with £1-5Bn in assets would have to meet the same requirements by 2023.
We do not have the space to cover all the regulatory frameworks around the world, but if you have not done this already, it is vital that you do your homework on the existing and upcoming regulations which might impact your firm as well as your various stakeholders.
## Step 3: RI vis-à-vis performance and risk mitigation
In order to come to a decision on whether you should or should not be a responsible investor, you will also need to come to a view as to whether you believe investing in a responsible manner results (or not) in improved investment performance and/or reduced risk. A large number of studies have been conducted on the topic and you may already have read a number of them, many with differing results. McKinsey have aggregated the results of over 2000 studies on the impact of ESG considerations on equity returns and have found that “a strong ESG proposition correlates with higher equity returns” and “with a reduction in downside risk”.
While the aggregation of the analysis seems quite conclusive (see Exhibit 3 above), it is extremely difficult to provide robust empirical evidence on this topic, as much depends on the time horizon, variety of ESG approaches and other assumptions. For instance, a Morningstar study conducted in 2020 showed that sustainable funds outperformed traditional funds during the COVID-19 market fallout in the first quarter of 2020 by an average excess return of up to 1.83%. However, much of this outperformance can be attributed to ESG funds’ low exposure to oil and gas, at a time when energy stocks fell significantly. Saying that, examining the long-term performance of a sample of over 700 Europe-based sustainable funds, Morningstar also concluded that that the majority of strategies had done better than the non-ESG funds over 1, 3, 5 and 10 years.
Alternatively, you can tackle this question from a more conceptual basis. In the long-run, do you believe that there are structural tailwinds to profit from (e.g. energy transition, future of mobility, circular economy, diversity of decision making) and investment risks to be avoided in your portfolio (e.g. stranded assets), all of which could mitigate downside risk? Similarly, do you believe that a firm that has strong ESG credentials with a commitment to various stakeholders, including customers, employees, suppliers, shareholders and local communities, will end up with a more robust business model in the long-run than its non-ESG peer in the same industry? Even conceptually, this is not so straightforward. As an example, if you were to invest in Tomra (Norwegian recycling and optical sorting company) today at a PE ratio in excess of 75 times, you would be excused for not being confident that this will be a profitable investment in the long-run (although it may well be).
If knowing what your peers think assists you in coming to a view, according to a 2020 survey by RBC Global Asset Management, ‘only’ 74% of US financial groups think that ESG boosts performance, compared to 93% in Asia and 96% in Europe.
## Step 4: Create your own RI policy
Now that you have established your values and beliefs, and you understand the regulatory requirements you are subject to, it is important that you establish an RI policy. Putting words down on paper not only helps you to understand and articulate your own values and beliefs better, but also assists you in sharing those beliefs with your stakeholders. The policy is also an important ‘live’ document, which you will need to regularly update, as your views or understanding of what constitutes RI may change.
You may have thought that this step has already been taken by most institutional investors by now but, according to a 2019 survey by Aon, less than half of all institutional investors worldwide have developed an RI policy (Exhibit 4). Amongst smaller institutional investors, even fewer have an RI policy with only 35% of those with $500Mn or less of AuM having a policy. This is in contrast to 69% of the$5Bn+ cohort.
## Step 5: Put in place processes and infrastructure
Now you are ready to implement your RI policy, but it is not as easy as you may think. You will need to create processes to integrate RI within your research and create the relevant governance structures to address various RI concerns. What actually constitutes RI can be very opaque and complex, and you may need additional resources that can assist you in this process.
Such resources can be costly. According to the Financial Times (May 12, 2019), “access for the full suite of sustainability data can cost up to $50,000 (compared with the$25,000 approximate annual fee for a single Bloomberg terminal)”. The fees quoted on MSCI’s website are even higher. According to MSCI, “the fees for each of MSCI ESG Research’s services range from $7,500 to$2,000,000 per year”.
Hiring specialist in-house teams are an additional layer of costs. In a 2019 survey by IPE, the top 400 asset managers were questioned on the number of dedicated specialists on ESG issues and found that asset managers with the larger RI teams have over 15 specialists (Exhibit 5). If you are a small or even medium-sized investment management firm, this is prohibitive. Therefore, the robustness of RI processes will need to be adapted to the resources that you have at hand. This means finding a best-fit approach to incorporating RI – balancing the cost pressures with the need to build up specialist knowledge.
## Step 6: Educate, participate, engage and collaborate
Should you be undertaking the RI journey on your own? The answer is a definite, resounding “NO”! The RI space is constantly evolving, and there are many initiatives spearheaded by a large number of organisations which you can benefit from, facilitating you to implement a more effective RI strategy.
Many of these initiatives provide you with opportunities to expand, share and update your knowledge through conferences, investor tools, working groups, consultations, training and research. Also, and very importantly, they provide the ability to collaborate with other investors to engage with entities and promote positive environmental and social outcomes, which is key to drive change.
Some of the initiatives may be more applicable to you than others, depending on factors such as your jurisdiction, the type of investor you are, and the asset classes you are exposed to. The growing number of initiatives can seem like an intimidating alphabet soup of acronyms to a new entrant in the space. As a first step, many investors decide to become signatories of UN PRI, where there are six guiding sets of investment principles. Amongst other, signatories must also file an annual report to the organisation, detailing their progress.
However, as you move forward on your RI journey, it is important you cast your net wider and become a signatory to other initiatives which would complement your own RI objectives. For instance, if climate change is one of the areas you have highlighted as wanting to make a positive impact on, you may want to join Climate Action 100+, where investors lobby the largest greenhouse gas emitters to address climate change at the board level and set targets to cut emissions. To date, more than 500 investors with more than $47 trillion in assets have signed on to this initiative. ## Step 7: Be wary of the ‘Emperor’s New Clothes’ syndrome If you do decide to become a responsible investor (assuming you are not one already), you will most probably at some point suffer the ‘Emperor’s New Clothes’ syndrome, i.e. you will invest in a particular manner with the belief and expectation that you are acting very responsibly, but in reality this may not be the case. This is likely to reflect the fact that assessing whether an investment should be considered responsible or not is quite complex, not to mention the significant limitations in the availability, quality and standardisation of data. To fully understand the environmental and social implications of an investment, an investor needs to consider the full life-cycle, supply chain, and other implications, many of which are unintended. The recent ownership by many ESG funds of Bohoo, a UK fashion company that was later rocked by allegations over its working conditions in its supply chain, is an example of finding out that you are in fact walking naked every now and then. The complexities of RI are also exemplified in the different scores given by the ESG rating agencies. According to estimates in a 2019 working paper from MIT Sloan School of Management, using a dataset of five ESG ratings providers, correlations between scores on 823 companies were on average only 0.6. This is a far cry from the correlations of credit ratings from Moody’s Investors Service and S&P Global Ratings which are 0.99. In some instances of greenwashing, doing a little bit of your own homework can pay off. For example, if you invest in ETFs marketed as ex. fossil fuels, you can easily check whether any of the underlying holdings have exposure to fossil fuels. The SPDR MSCI EAFE Fossil Fuel Reserves Free ETF has been in the media for containing shares of RWE, a German energy company that runs several coal-fired power plants. ## Step 8: Are you practising what you preach? If you do decide to be a responsible investor and you are part of an organisation, aspects such as equal opportunities and diversity, will need to be reflected in your internal employment policies, procedures and initiatives (if not already). Although more difficult, steps should also be taken to measure the environmental implications of your business, such as carbon emissions from the office and business travel. Furthermore, your ability to improve your own standards should be monitored and measured. If you have external stakeholders, regular reporting on these metrics is essential. ## Step 9: Remember the big picture If, after walking through all these steps, you have decided that opting to be(come) a responsible investor is too cumbersome and costly, at this point, I will ask you to always remember the big picture. There are many environmental and social issues confronting society today, such as water scarcity, deforestation, rising sea levels and reduced biodiversity. Given how the world is increasingly interconnected, there is no doubt that these issues will eventually mutilate certain financial assets and markets. I firmly believe that, if the investment community doesn’t tackle the bull by the horns, these issues will come back to haunt us all. The World Bank estimates that the asset management industry globally managed around$124Tn in 2018 – significantly more than the c.\$87Tn of global GDP in 2019. As a member of this investment community, we need to join forces and leverage the colossal power of the financial industry to address these issues. Whether you are a large or a small investor, if we all collaborate on this, the environmental and social issues can be addressed or, at the very least, mitigated. For this to become a reality, you have to take action now, based on the information you have and evolve as a responsible investor as far your values and business constraints allow you to. The worst thing you can do is nothing.
Alison Major Lépine
19 November 2020
## Where to position yourself on the RI spectrum?
One of the initial outputs from your brainstorming exercise should be where you will position your investments along the RI spectrum, i.e. whether you will pursue a negative/exclusionary screening approach or a more real-world impact investing type of approach (where there is an additional, intentional and measurable positive environmental and/or social outcome), or somewhere in the middle, such as an integrated or best-in-class approach, or a combination of these. Where you can position yourself on this spectrum will be strongly influenced by the asset class of your investments.
According to KPMG, most RI strategies follow integrated or exclusionary/negative screening approaches (Exhibit A1). The expectation is that the exposure to the positive screening and impact end of the spectrum will increase over time.
## What areas should you avoid?
As you just saw in Exhibit A1, most of the the RI approaches in the spectrum incorporate an element of negative screening, so another key objective of the initial brainstorming sessions should be to select the areas (sectors, countries or other) which, from an ethical and cultural perspective, you deem unacceptable. Exhibit A2 details what the most typical exclusions areas are for European investors, according to a 2018 Eurosif survey.
Again, this is not a straightforward exercise, and investors often conclude at this stage that exposure to a potentially controversial area (e.g. fossil fuels) is acceptable if below a certain threshold, and/or where there is positive direction of travel (e.g. falling fossil fuel exposure).
According to the same Eurosif SRI study, the most common norm-based screen was to comply with the UN Global Compact (10 principles on human rights, labour, environment and anti-corruption), followed by the ILO Conventions and the OECD Guidelines.
## Which environmental and social issues would you like to focus on?
At this stage, it is also important to sit down and determine which environmental and social issues you would like to prioritise and are material. Factors to consider in making this decision include which issues you believe present:
• the strongest long-term tailwinds to profit from (e.g. energy transition, food security, future of mobility, demographic shifts, circular economy);
• the most significant investment risks which should be avoided in your portfolio (e.g. systemic stranded assets, specific stranded business models); and/or
• the potential for the most positive impact from a more ethical approach.
The World Economic Forum (WEF) publishes its Global Risk Report annually (Exhibit A3). In the 2020 report, respondents to the Global Risks Perception Survey ranked climate change and related environmental issues as the five biggest risks in terms of likelihood – the first time in the survey’s history that one category, in this case the environment, occupied all five of the top spots. Social issues such as water and food crises, ranked highly as well.
Exhibit A4 corroborates that, from an active equity owner perspective, climate change is one of the areas investors have been most vocal about in recent years. More traditional governance issues, such as corporate activity, labour & equal employment rights and executive pay, continue to be at the top of the agenda as well.
If you employ more of an impact type of strategy, you will also need to determine how the environmental and social issues you have chosen to focus on align to the UN Sustainable Development Goals (Exhibit A5) or other initiative. A growing number of investors today actually use these as their starting point on the RI journey.
Many investors are also aligning themselves with specific goals, with alignment to the Paris Climate Agreement goals becoming particularly popular more recently. Over the last few months, a number of announcements have been made in the UK, for example a declaration from the BT Pension Scheme (BTPS) stating it is to target a net-zero strategy by 2035, aligned with the goals in the Paris Agreement. I have also noted that the South Yorkshire Pensions Authority have indicated their intention to be carbon neutral by 2030; that Nest has stated its plan to have a net-zero portfolio by 2050, and that the Northern LGPS announced their intention to invest 100% of their assets in line with the Paris Agreement.
## How patient should you be- engagement vs. divesting?
One of the other key considerations to explore at this early stage is the horizon for which your investments need to meet your standards. This will of course be dependent on the investment horizon of your investment, but it is also a deeper question. Do you need all investments to meet your standards now, or are you comfortable with certain investments which may currently be at a less desirable point but have a well-defined set of objectives in place? In other words, is there a positive direction of travel?
For instance, if you have concluded that diversity is one of the key issues you would like to focus on and, upon requesting for the diversity profile of one of the investment managers in your portfolio, you become aware there is minimal diversity, do you divest or engage with the investment firm in question to introduce policies to increase diversity? And, if you do decide to engage, how long are you willing to wait for the positive developments of their stated initiative (potentially triggered by your engagement) to become evident?
## What are your stakeholders telling you?
So far, you will have brainstormed on what is important for you, requiring a high degree of introspection. It is crucial that you also look outwards – reach out to all your stakeholders and listen very carefully to their views. For instance, if you are managing a university endowment, you will need to immerse yourself in the issues from the perspective of your students and the faculty. Today, almost all of Britain's top universities have committed to selling their shares in fossil fuel companies which, according to People & Planet (a student campaign group), amounts to around £12.4bn of endowments across the sector that have been divested. This change in investment strategy came about in most part only after significant pressure from eco-conscious students who recurred to occupying buildings and carrying out hunger strikes. You do not want to wait until your stakeholders need to take such drastic measures!
##### About the Author
Alison Major Lépine joined Absolute Return Partners in 2015 after almost 10 years at the UK Railways pension scheme where she was responsible for over £1bn in various absolute return strategies. She is a Partner and Head of Strategy at the Firm. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.16530673205852509, "perplexity": 2340.6309693570092}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991870.70/warc/CC-MAIN-20210517211550-20210518001550-00489.warc.gz"} |
https://www.bartleby.com/questions-and-answers/abuate3-dar.-valuate-vt-iv.-ftc-part-one-use-the-fundamental-theorem-of-calculus-to-write-an-express/be155cd8-d9c9-40c7-9545-ccb7b6a61709 | # abuate3 dar.valuateVTIV.FTC (part one)Use the fundamental theorem of calculus to write an expression for the anti-derivative of the function y = f(x) = sin(13).If F(x)12 V t+ldt, find the derivative F'(x).Use the fundamental theorem of calculus to find the derivative of the functiony = g(x)-j" cos(t2) dt.Exercise 11 in section 4.4
Question
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I am studying for a quiz and do not understand a few of the concepts that will be covered on it. Can you help me with the problem under "IV. FTC (part one)" found in the attached document? Thank you.
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Step 1
The fundamental theorem of calculus states that for a continuous real-valued function, f on a closed interval [a, b], let the function F be defined, for all x in [a, b] as
Step 2
Here, the function is given as y=sin(x3) which is continuous on any closed interval, hence consider a closed interval [a,b]. Use the fundamental theorem of calculus and obtain the antiderivative F as follows.
Step 3
The antiderivative F which is uniformly c...
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Tagged in | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9533056616783142, "perplexity": 893.791494437852}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540533401.22/warc/CC-MAIN-20191211212657-20191212000657-00330.warc.gz"} |
http://nrich.maths.org/188 | ### Plants
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
### Weighted Numbers
Use the number weights to find different ways of balancing the equaliser.
### The Add and Take-away Path
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
# Number Round Up
##### Stage: 1 Challenge Level:
If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...
Arrange the numbers $1$ to $6$ in each set of circles below.
The sum of each side of the triangle should equal the number in the centre of the triangular shape.
Once you've had a chance to think about it, click below to see how three different pupils began working on the task.
Dan said:
"I used counters which had $1$ to $6$ on them.
I put the counters in a triangle in any old way, then I added up the sides.
Then I moved the counters around to try and get the right total on each side."
Emma said:
"I noticed that three of the numbers are odd ($1, 3$ and $5$) and three of the numbers are even ($2, 4$ and $6$). I thought this might help.
I know that $9$ is an odd number so it can be made using odd + odd + odd or using even + even + odd."
Farah said:
"If I want a small total on each side, I'll need small numbers in the corners of the triangle."
Can you take each of these starting ideas and develop it into a solution?
A practical version of this activity is included in the Year 3/4 Brain Buster Maths Box which contains hands-on challenges developed by members of NRICH and produced by BEAM. For more details and ordering information, please scroll down this page . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24040858447551727, "perplexity": 982.3094923328971}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737922497.60/warc/CC-MAIN-20151001221842-00008-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-math-topics/279434-total-relation.html | ## Total relation
Hey,
Let A be a finite set and R is an order relation on A.
Prove:
If R is not total,then there exist two different total order relations containing R. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8404300212860107, "perplexity": 952.7724124002694}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578553595.61/warc/CC-MAIN-20190422115451-20190422141451-00516.warc.gz"} |
https://dml.cz/handle/10338.dmlcz/118956?show=full | # Article
Title: On the Noetherian type of topological spaces (English) Author: Peregudov, S. A. Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 38 Issue: 3 Year: 1997 Pages: 581-586 . Category: math . Summary: The Noetherian type of topological spaces is introduced. Connections between the Noetherian type and other cardinal functions of topological spaces are obtained. (English) Keyword: Noetherian type Keyword: rank weight MSC: 54A25 MSC: 54D30 idZBL: Zbl 0937.54003 idMR: MR1485079 . Date available: 2009-01-08T18:36:26Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/118956 . Reference: [1] Arhangel'skii A.V.: On bicompacta hereditarily satisfying the Souslin condition. Tightness and free sequences.Soviet Math. Dokl. 12 (1971), 1253-1257. MR 0119188 Reference: [2] Bir'ukov P.A.: Ranks of families of sets and properties of topological spaces (in Russian).DAN SSSR 4[257] (1981), 777-779. MR 0612564 Reference: [3] Gruenhage G., Nyikos P.: Spaces with bases of countable rank.Gen.Top. and Appl. 8 (1978), 233-257. Zbl 0412.54034, MR 0494007 Reference: [4] Malyhin V.I.: On Noetherian spaces (in Russian).Seminar of Gen. Topology, Moscow University, 1981 pp.51-58. Reference: [5] Peregudov S.A.: On $\sqcap$-uniform bases and $\pi$-bases.Soviet Math. Dokl. 17 (1976), 1055-1059. Reference: [6] Peregudov S.A., Shapirovskii B.E.: A class of compact spaces.Soviet Math. Dokl. 17 (1976), 1296-1300. Reference: [7] Shapirovskii B.E.: On $\pi$-character and $\pi$-weight of bicompact (in Russian).DAN SSSR 4[223] (1975), 799-802. MR 0410632 .
## Files
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CommentatMathUnivCarolRetro_38-1997-3_15.pdf 185.1Kb application/pdf View/Open
Partner of | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30808883905410767, "perplexity": 20028.03857350371}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540500637.40/warc/CC-MAIN-20191207160050-20191207184050-00246.warc.gz"} |
https://tex.stackexchange.com/questions/547579/alignment-in-tabularx-using-exp-siunitx | # Alignment in tabularx using exp. siunitx
It's never ending story about that -> previous post. Simply, I just want to align to 'pm' sign my number columns. I've already tried replacing headers {l | l *{2}{>{\centering\arraybackslash}X}} with {l | l l l *{2}{>{\centering\arraybackslash}X} and than to check one column with siunitx: {l | l S[table-align-uncertainty, separate-uncertainty=true] l l *{2}{>{\centering\arraybackslash}X} but it doesn't work at all.
MWE:
\documentclass{article}
\usepackage{float, enumitem, amsmath}
\usepackage{rotating}
\usepackage{booktabs, makecell, multirow, tabularx, threeparttable}
\usepackage{colortbl, color} %I preffer that instead of xcolor because xcolor give me errors with beamer
\usepackage{caption}
\captionsetup{belowskip=-5pt}
\captionsetup[table]{justification=raggedright,singlelinecheck=off}
\begin{document}
\begin{table}
\centering
\renewcommand\arraystretch{1.1}
\caption{Simple caption.}
\label{tab:setTag}
\begin{tabularx}{\linewidth}{l | l *{2}{>{\centering\arraybackslash}X}}
\Xhline{1pt}
& \thead{Method 1} & \thead{Method 2} \\
\Xhline{0.7pt}
& & \multicolumn{2}{c}{First section} \\
\Xcline{3-4}{0.6pt}
&Very long name & $11,5 \pm 0,5$ & $444,34 \pm 71,9$ \\
& Very long name & $109,2 \pm 75,3$ & $2,8 \pm 664,36$ \\
& Very long name& $9438 \pm 8$ & $256,0 \pm 98,1$ \\
& Very long name & $11,5 \pm 0,5$ & $444,34 \pm 71,9$ \\
& Very long name & $109,2 \pm 75,3$ & $2,8 \pm 664,36$ \\
& Very long name & $9438 \pm 8$ & $256,0 \pm 98,1$ \\
\end{tabularx}
\end{table}
\end{document}
I've changed header to \begin{tabularx}{\linewidth}{l | X S[table-align-uncertainty, separate-uncertainty=true] S[table-align-uncertainty, separate-uncertainty=true]*{2}{>{\centering\arraybackslash}}} and data from first row to 11,5(5) & 444,34(719 and I get that result (strange Methods headers):
I've now had errors with array package '>{}' at wrong position. Can someone please tell me which one is the correct one? And another one with 'missing # inserted in alignment preamble' and the third one 'missing inserted' but I don't know why because it shows line with \end{tabularx}. New part of the code: \begin{tabularx}{\linewidth}{l | X S[table-align-uncertainty, separate-uncertainty=true] S[table-align-uncertainty, separate-uncertainty=true]*{2}{>{\centering\arraybackslash}}} \Xhline{1pt} & \thead[l]{Results} & {\thead{Method 1}} & {\thead{Method 2}} \\ \Xhline{0.7pt} & & \multicolumn{2}{c}{First section} \\ \Xcline{3-4}{0.6pt} \multirow{3}{*}{\rothead{Description 1}} &Very long name &11,5(5)$&$444,34(719)$\\ & Very long name &$109,2(753)$&$2,8(63)$\\ & Very long name&$9438(8)$&$256,0(981)$\\ &Very long name &$11,5(5)$&$444,34(719)$\\ & Very long name &$109,2(753)$&$2,8(63)$\\ & Very long name&$9438(8)$&$256,0(981)\$ \\
\end{tabularx}
It shows (which is obviously not align):
• If you want 11,5 \pm 0,5 as the output in an S type columns of the table, you should use 11,5(5) as the input in the S type column. – leandriis Jun 2 '20 at 18:49
• Why do you use tabularx here? Your table is already narrow enough to fit into the textwidth. By using tabularx here you only stretch the table introducing unneccessary white space. – leandriis Jun 2 '20 at 18:53
• @leandriis my whole table is much wider (the name of the columns etc.) but for the MWE and just align operation it is not necessary to provide the whole one (in the previous post I showed how huge the table is) :) – Dominika Jun 2 '20 at 18:55
• I see. Thanks for the explanation. I was a bit confused since the dummy text you included in your previous example is something entirely different than numbers with their uncertainties which you showed in this example code. – leandriis Jun 2 '20 at 19:00
• I know, so sorry - just learning how to quick describe problem with as much information as I can gave. So, my 'real table' has very long 'Results' section and in some of the 'First section'/'Second section' etc. a lot of numbers data. – Dominika Jun 2 '20 at 19:03
The following should work:
\documentclass{article}
\usepackage{float, enumitem, amsmath}
\usepackage{rotating}
\usepackage{booktabs, makecell, multirow, tabularx, threeparttable}
\usepackage{colortbl, color} %I preffer that instead of xcolor because xcolor give me errors with beamer
\usepackage{caption}
\captionsetup{belowskip=-5pt}
\captionsetup[table]{justification=raggedright,singlelinecheck=off}
\usepackage{siunitx}
\begin{document}
\sisetup{table-align-uncertainty, separate-uncertainty=true}
\begin{tabularx}{\linewidth}{l | X S[table-format=4.1(3)] S[table-format=3.2(5)]}
\Xhline{1pt}
& {\thead{Method 1}} & {\thead{Method 2}} \\
\Xhline{0.7pt}
& & \multicolumn{2}{c}{First section} \\
\Xcline{3-4}{0.6pt}
& Very long name & 11,5(5) & 444,34(7190) \\
& Very long name & 109,2(753) & 2,80(66436) \\
& Very long name & 9438(8) & 256,0(981) \\
& Very long name & 11,5(5) & 444,34(7190) \\
& Very long name & 109,2(753) & 2,80(66436) \\
& Very long name & 9438(8) & 256,0(981) \\
\end{tabularx}
\end{document}
• yes, aligment works pretty well but rotated column looking very bad now (I've changed yours \multirow{3}{*}{\rothead{Description 1}} to \multirow{6}{*}{\rothead{Description 1}}, but it doesn't help – Dominika Jun 2 '20 at 21:23
• besides rotating text issue I also putted in description example how some of the numbers looks like. The +/- symbol is too close to them - please take a look (last image). – Dominika Jun 2 '20 at 21:35
• thank you so much, you also help me a lot with better understanding tables! – Dominika Jun 2 '20 at 21:47
• If you want to add numbers with more than 1 decimal place into the first column, you will have to adjust the table-format option of this specific column accordingly. In order to add a short horizontal line in a S type column, use {--} instead of - -. – leandriis Jun 2 '20 at 22:12
• Got it, but when I put S[table-format=4.10(5)] or S[table-format=4.1(100)] or S[table-format=400.1(5)] it's just ridiculous and nasty. How it works? – Dominika Jun 2 '20 at 22:15
just answering your comment under leandriis answer, you can simply rotate the text directly there is no need for a multirow, also as I commented previously in chat I would never use tabularx for a table of data like this, tabularx is all about tables of text and line breaking in columns.
\documentclass{article}
\usepackage{float, enumitem, amsmath}
\usepackage{rotating}
\usepackage{booktabs, makecell, multirow, tabularx, threeparttable}
\usepackage{colortbl, color} %I preffer that instead of xcolor because xcolor give me errors with beamer
\usepackage{caption}
\captionsetup{belowskip=-5pt}
\captionsetup[table]{justification=raggedright,singlelinecheck=off}
\usepackage{siunitx}
\begin{document}
\sisetup{table-align-uncertainty, separate-uncertainty=true}
\centering
\begin{tabular}{l | l S[table-format=4.1(3)] S[table-format=3.2(5)]}
\Xhline{1pt}
& {\thead{Method 1}} & {\thead{Method 2}} \\
\Xhline{0.7pt}
\smash{\rotatebox[origin=r]{90}{\bfseries Description 1}}
& & \multicolumn{2}{c}{First section} \\
\Xcline{3-4}{0.6pt}
& Very long name & 11,5(5) & 444,34(7190) \\
& Very long name & 109,2(753) & 2,80(66436) \\
& Very long name & 9438(8) & 256,0(981) \\
& Very long name & 11,5(5) & 444,34(7190) \\
& Very long name & 109,2(753) & 2,80(66436) \\
& Very long name & 9438(8) & 256,0(981) \\
\end{tabular}
\end{document}
• I will be remember that, thank you for your time but I put Description 1 in multirow because I want to forced this text to be centered. In original table I have 16 rows (like my first post here, linked in description) so I think centered looks better – Dominika Jun 2 '20 at 21:39
• @Dominika you can easily move it down, just put it in a later row or add an \hspace after the 1 multirow desn't force vertical centering – David Carlisle Jun 2 '20 at 21:40
• Of course - that's not a problem with odd number, but I will try. Once again thank you so much for your time and advices. – Dominika Jun 2 '20 at 21:42
• @Dominika actually you should accept lenadriis answer that had better siunitx use than the answer I was going to give, which was your main question, I just stole the entire code from that answer to add this extra comment, I'll feel a bit bad if I steal the points as well:-) – David Carlisle Jun 2 '20 at 21:44
• Okay, right - I apologise. I've already changed, but thank you for your both :) Now I will try to use it in the much bigger table, hope it will work. Fingers crossed! – Dominika Jun 2 '20 at 21:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8174256086349487, "perplexity": 4242.602433554468}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989819.92/warc/CC-MAIN-20210518094809-20210518124809-00203.warc.gz"} |
https://www.allaboutcircuits.com/worksheets/bipolar-junction-transistor-bjt-theory/ | # Bipolar Junction Transistor (BJT) theory
## Discrete Semiconductor Devices and Circuits
• #### Question 1
Don’t just sit there! Build something!!
Learning to mathematically analyze circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.
You will learn much more by actually building and analyzing real circuits, letting your test equipment provide the “answers” instead of a book or another person. For successful circuit-building exercises, follow these steps:
1. Carefully measure and record all component values prior to circuit construction, choosing resistor values high enough to make damage to any active components unlikely.
2. Draw the schematic diagram for the circuit to be analyzed.
3. Carefully build this circuit on a breadboard or other convenient medium.
4. Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements one-by-one on the diagram.
5. Mathematically analyze the circuit, solving for all voltage and current values.
6. Carefully measure all voltages and currents, to verify the accuracy of your analysis.
7. If there are any substantial errors (greater than a few percent), carefully check your circuit’s construction against the diagram, then carefully re-calculate the values and re-measure.
When students are first learning about semiconductor devices, and are most likely to damage them by making improper connections in their circuits, I recommend they experiment with large, high-wattage components (1N4001 rectifying diodes, TO-220 or TO-3 case power transistors, etc.), and using dry-cell battery power sources rather than a benchtop power supply. This decreases the likelihood of component damage.
As usual, avoid very high and very low resistor values, to avoid measurement errors caused by meter “loading” (on the high end) and to avoid transistor burnout (on the low end). I recommend resistors between 1 kΩ and 100 kΩ.
One way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another time-saving technique is to re-use the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.
• #### Question 2
The power dissipation of a transistor is given by the following equation:
$$P = I_C (V_{CE} + \frac{V_{BE}}{\beta})$$
Manipulate this equation to solve for beta, given all the other variables.
• #### Question 3
Suppose we only knew the emitter and base currents for an operating transistor and wished to calculate β from that information. We would need a definition of beta cast in terms of IE and IB instead of IC and IB.
Apply algebraic substitution to the formula $$\beta= \frac{I_C}{I_B}$$ so that beta (β) is defined in terms of IE and IB. You may find the following equation helpful in your work:
• #### Question 4
A bipolar junction transistor parameter similar to β is “alpha,” symbolized by the Greek letter α. It is defined as the ratio between collector current and emitter current:
$$\alpha = \frac{I_C}{I_E}$$
Apply algebraic substitution to this formula so that alpha is defined as a function of beta: $$\alpha=f(\beta)$$. In other words, substitute and manipulate this equation until you have alpha by itself on one side and no variable except beta on the other.
$$\beta=\frac{I_C}{I_B} \ \ \ \ \ \ \ \ \ \ \ \ I_E=I_C+I_B$$
• #### Question 5
A technician uses a multimeter’s “diode check” function to identify the terminals on a BJT. There are only two places where a non-infinite reading is obtained, and they are as follows:
From these measurements, determine what type of BJT this is (PNP or NPN) and identify all three terminals.
• #### Question 6
Conduction of an electric current through the collector terminal of a bipolar junction transistor requires that minority carriers be “injected” into the base region by a base-emitter current. Only after being injected into the base region may these charge carriers be swept toward the collector by the applied voltage between emitter and collector to constitute a collector current:
An analogy to help illustrate this is a person tossing flower petals into the air above their head, while a breeze carries the petals horizontally away from them. None of the flower petals may be ßwept” away by the breeze until the person releases them into the air, and the velocity of the breeze has no bearing on how many flower petals are swept away from the person, since they must be released from the person’s grip before they can go anywhere.
By referencing either the energy diagram or the flower petal analogy, explain why the collector current for a BJT is strongly influenced by the base current and only weakly influenced by the collector-to-emitter voltage.
• #### Question 7
Bipolar junction transistor (BJT) function is usually considered in terms of currents: a relatively small current through one of the transistor’s terminals exerts control over a much larger current. Draw the directions of all currents for these two transistors (one NPN and one PNP), clearly identifying which of the currents is doing the control, and which of the currents is being controlled:
• #### Question 8
The “beta” ratio (β) of a bipolar junction transistor, sometimes alternatively referred to as hFE, is a very important device parameter. In essence, it describes the amplifying power of the transistor. Give a mathematical definition for this parameter, and provide some typical values from transistor datasheets.
• #### Question 9
Find one or two real bipolar junction transistors and bring them with you to class for discussion. Identify as much information as you can about your transistors prior to discussion:
Terminal identification (which terminal is base, emitter, collector)
Continuous power rating
Typical β
• #### Question 10
Match the following bipolar transistor illustrations to their respective schematic symbols:
• #### Question 11
If we were to compare the energy diagrams for three pieces of semiconducting material, two “N” type and one “P” type, side-by-side, we would see something like this:
The presence of dopants in the semiconducting materials creates differences in the Fermi energy level (Ef) within each piece.
Draw a new energy diagram showing the equilibrium state of the three pieces after being joined together.
• #### Question 12
Transistor operation may be explained in terms of three different currents: injection, diffusion, and collection. Describe what each of these currents are, and how they help explain the amplifying nature of a transistor.
• #### Question 13
Trace the paths of injection, diffusion, and collection currents in this energy diagram for an NPN transistor as it is conducting:
• #### Question 14
Trace the paths of injection, diffusion, and collection currents in this energy diagram for a PNP transistor as it is conducting:
• #### Question 15
From an examination of the energy diagram for a BJT in its conducting mode (current existing through each of the three terminals: emitter, base, and collector), determine the biasing of the two PN junctions:
The emitter-base junction (forward or reverse biased?)
The base-collector junction (forward or reverse biased?)
One of these two junctions actually operates in the reverse-bias mode while the transistor is conducting. Explain how this is possible, as a simple PN junction (a diode) operating in reverse-bias mode conducts negligible current.
• #### Question 16
Bipolar junction transistors are classified as minority carrier devices. Explain why.
• #### Question 17
Transistors act as controlled current sources. That is, with a fixed control signal in, they tend to regulate the amount of current going through them. Design an experimental circuit to prove this tendency of transistors. In other words, how could you demonstrate this current-regulating behavior to be a fact?
• #### Question 18
Compare the relative magnitudes of each current in this bipolar transistor circuit:
Which current is the smallest and which is the largest? Are there any two currents that are closer in magnitude than with the third? If so, which currents are they?
• #### Question 19
Are the collector and emitter terminals of a transistor interchangeable? If not, what is the physical difference between the emitter and collector?
• #### Question 20
A beginning electronics student is just learning about transistors, and reads in the textbook that a bipolar transistor (either NPN or PNP) can be thought of as two diodes connected back-to-back as such:
Acting on this idea, the student proceeds to connect two 1N4001 rectifying diodes back-to-back and try to use it as a transistor. This idea does not work: although the diode pair reads the same patterns of continuity as a transistor would, it does not amplify. Explain why.
Note: this is a fairly deep question, and may not be answered without an understanding of charge carrier energy levels and semiconductor junction behavior.
• #### Question 21
How would you explain the necessary conditions for conduction of an electric current through a BJT? Describe must be done to a BJT in order for it to conduct a current.
• #### Question 22
Draw the polarities ( and -) of the applied voltages necessary to turn both these transistors on:
Also, draw the direction of the controlled current (flowing between collector and emitter) that will result from a power source properly connected between these terminals.
• #### Question 23
Students new to the study of transistors often have difficulty remembering the proper directions of currents through bipolar junction transistors, since there are three different currents (IB, IC, IE) and they must “mesh” through the transistor in a particular way.
Draw the proper current directions for each of these transistors, and explain how you are able to remember the correct directions they go:
• #### Question 24
Predict how all three transistor currents (IB, IC, and IE) will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):
Base resistor RB fails open:
Collector resistor RC fails open:
Solder bridge (short) past base resistor RB:
Solder bridge (short) past collector resistor RC:
For each of these conditions, explain why the resulting effects will occur.
• #### Question 25
Based on these DC continuity tester indications, what type of transistor is this, PNP or NPN?
Resistance with negative test lead on pin 1, positive test lead on pin 2: no continuity
Resistance with negative test lead on pin 1, positive test lead on pin 3: no continuity
Resistance with negative test lead on pin 2, positive test lead on pin 1: no continuity
Resistance with negative test lead on pin 2, positive test lead on pin 3: no continuity
Resistance with negative test lead on pin 3, positive test lead on pin 1: continuity
Resistance with negative test lead on pin 3, positive test lead on pin 2: continuity
Also, to the best of your ability, identify the transistor’s three terminals (emitter, base, and collector).
• #### Question 26
Many digital multimeters have a “diode check” range that allows the user to measure the forward voltage drop of a PN junction:
When using a multimeter with this feature to identify the terminals of a bipolar junction transistor, the forward voltage drop indication is necessary to distinguish the collector terminal from the emitter terminal. Explain how this distinction is made on the basis of the forward voltage measurement, and also explain why this is.
• #### Question 27
Identify the terminals on this BJT, and also the type of BJT it is (NPN or PNP):
• #### Question 28
One of the most important parameters for semiconductor components is the power rating. Explain why power rating is such a critical parameter, especially compared with other types of electronic components (resistors, inductors, capacitors, etc.).
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1 Comment
• LvW November 15, 2019
What surprises me is the following: I did not see any mentioning of the most important BJT parameter: Transconductance gm.
(Instead, you are stating that the beta-value would be a very important parameter - which is NOT the case!).
Like some other low-level electronic books and papers you treat the BJT as a cittent-controlled device - this is simply wrong.
There is not a single proof that the BJT would be a CCCS !
However, there are many theoretical explanations, measurements and observable facts which clearly show that the BJT is - of course - voltage-controlled. Who can deny it ? With which arguments? Ic=beta x Ib is just a formula - a misinterpretation of Ib=Ic/beta.
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https://causal-fermion-system.com/theory/physics/principles/ | # The Theory of Causal Fermion Systems
## Underlying Physical Principles
### Prerequisites
Causal fermion systems evolved from an attempt to combine several physical principles in a coherent mathematical framework. As a result, these principles appear in a specific way:
• The principle of causalityA causal fermion system gives rise to a causal structure and a time direction. The causal action principle is compatible with this notion of causality in the sense that the pairs of points with spacelike separation do not enter the Euler-Lagrange equations. In simple terms, points with spacelike separation do not interact.
• The local gauge principle. Local gauge freedom becomes apparent when representing the physical wave functions in bases of the spin spaces. More precisely, choosing a pseudo-orthonormal basis $(\mathfrak{e}_\alpha(x))_{\alpha=1,\ldots, \text{dim}(S_x)}$ of each spin space $(S_x, \prec .|. \succ_x)$, a physical wave function $\psi^u$ can be represented as
$\displaystyle \psi^u(x) = \sum_{\alpha=1}^{\text{dim} S_x} \psi^\alpha(x)\: \mathfrak{e}_\alpha(x)$
with component functions $\psi^1, \ldots, \psi^{\text{dim} S_x}$. The freedom in choosing the basis $(\mathfrak{e}_\alpha)$ is described by the group of unitary transformations with respect to the indefinite spin inner product. This gives rise to the transformations
$\displaystyle \mathfrak{e}_\alpha(x) \rightarrow \sum_\beta U^{-1}(x)^\beta_\alpha\; \mathfrak{e}_\beta(x)$ and $\displaystyle \psi^\alpha(x) \rightarrow \sum_\beta U(x)^\alpha_\beta\: \psi^\beta(x)$ .
As the basis $(\mathfrak{e}_\alpha)$ can be chosen independently at each spacetime point, one obtains local gauge transformations of the wave functions, where the gauge group is determined to be the isometry group of the spin scalar product. The causal action is gauge invariant in the sense that it does not depend on the choice of spinor bases.
• The Pauli exclusion principle. This can be seen in various ways. One formulation of the Pauli exclusion principle states that every fermionic one-particle state can be occupied by at most one particle. In this formulation, the Pauli exclusion principle is respected because every wave function can either be represented in the form $\psi^u$ (the state is occupied) with $u \in \H$ or it cannot be represented as a physical wave function (the state is not occupied). Via these two conditions, the fermionic projector encodes for every state the occupation numbers $1$ and $0$, respectively, but it is impossible to describe higher occupation numbers.
More technically, one may obtain the connection to the fermionic Fock space formalism by choosing an orthonormal basis $u_1, \ldots, u_f$ of ${\mathcal{H}}$ and forming the $f$-particle Hartree-Fock state
$\Psi := \psi^{u_1} \wedge \cdots \wedge \psi^{u_f}$ .
Clearly, the choice of the orthonormal basis is unique only up to the unitary transformations
$\displaystyle u_i \rightarrow \tilde{u}_i = \sum_{j=1}^f U_{ij} \,u_j$ with $U \in \text{U}(f)$ .
Due to the anti-symmetrization, this transformation changes the corresponding Hartree-Fock state only by an irrelevant phase factor,
$\psi^{\tilde{u}_1} \wedge \cdots \wedge \psi^{\tilde{u}_f} = \det U \: \psi^{u_1} \wedge \cdots \wedge \psi^{u_f}$ .
Thus the configuration of the physical wave functions can be described by a fermionic multi-particle wave function. The Pauli exclusion principle becomes apparent in the total anti-symmetrization of this wave function.
Clearly, the above Hartree-Fock state $\Psi$ does not account for quantum entanglement. Indeed, the description of entanglement requires more general Fock space constructions (→ connection to quantum field theory in the mathematics section).
• The equivalence principleStarting from a causal fermion system $({\mathcal{H}}, {\mathcal{F}}, \rho)$, spacetime $M:= \text{supp} \rho$ is given as the support of the universal measure. Thus spacetime is a topological space (with the topology on $M$ induced by sup-norm on $\text{L}({\mathcal{H}}$). In situations when spacetime has a smooth manifold structure, one can describe spacetime by choosing coordinates. However, there is no distinguished coordinate systems, giving rise to the freedom of performing general coordinate transformations. The causal action as well as all the constraints are invariant under such transformations. In this sense, the equivalence principle is implemented in the Theory of Causal Fermion Systems.
However, other physical principles are missing. For example, the principle of locality is not included. Indeed, the causal action principle is non-local, and locality is recovered only in the continuum limit. Moreover, our concept of causality is quite different from causation (in the sense that the past determines the future) or microlocality (stating that the observables of spacelike separated regions must commute).
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https://chat.stackexchange.com/transcript/41/2019/4/25 | 6:25 AM
I was just looking something up in the multicol source code and came across its license header. There it says:
%% The producer of a proprietary and commercially market product
%% that involves typesetting using multicol is asked to determine
%% the value of a license fee for using multicol if
%%
%% - the product is a document and the producer has decided to
%% include multicol to typeset (parts of) the document or has
%% directed the author of the document to include multicol (for
%% example, by providing a class file to be used by the author)
%%
%% - the product is a LaTeX class or package that includes multicol
Isn't this a violation of the LPPL?
@HenriMenke It's a 'moral' obligation
@JosephWright But then this whole (sort of threatening) legal mumbo-jumbo can be replaced by “Please donate if you find this useful”
@JosephWright On another note, I have built a script to extract all the codeexample environment from the PGF documentation, so that each example can be passed to l3build individually. github.com/pgf-tikz/pgf/blob/master/doc/generic/pgf/extract.lua
6:46 AM
@HenriMenke most of that wording is older than LPPL and originally was a non-optional part of the licence under which multicol was distributed.
@HenriMenke Oooh, wowo
@HenriMenke I'll probably look at the l3build stuff at the weekend ... I'm still trying to push PDF stuff at the moment
7:04 AM
hopefully…
7:58 AM
@UlrikeFischer I think I'm going to 'pick off' a few easy PDF things: info, catalog, etc. I wonder about \pdfinfo: should this be handled with individual key-value pairs or a simple list
@UlrikeFischer Actually, it's clear it has to be: dvips needs the keyvals with some pre-processing
'ello
8:14 AM
@JosephWright imho everything that at the end is a dictionary is at best handled with properties/key-val unless we find a strong argument not to do it. I have a simple \driver_pdf_info:n in the dtx, which I used as \driver_pdf_info:n { /Author(\@pdfauthor) /Title(\@pdftitle)...} in the driver. But only because I wasn't sure if I can fill the fields without changing hyperref.sty (and disturbing other packages like pdfx and hyperxmp). I can look at it again in the afternoon.
@UlrikeFischer I've just had a look and have some code in hand; wait for check-in, probably over my lunch break :)
@UlrikeFischer At the driver level, I don't think we need a prop: that's probably something for the \pdf_... module, as it's common to all drivers
@UlrikeFischer BTW, I think we can ignore \pdfinfoomitdate as you get the same effect setting the two dates to a blank string
@UlrikeFischer I'll need a little while for dvips, as I'll probably have to generalise a bit the \pdfmark code I've borrowed ... at present, it's entirely focussed on making links
@JosephWright yes, one can do something like \driver_pdf_info:x{<expand some prop>}.
@JosephWright I think we should open more issues in the repo to keep track of such topics.
@UlrikeFischer Exactly
@UlrikeFischer OK, go for it
@UlrikeFischer I'll log that one with an example in a bit
8:32 AM
@JosephWright should I label them?
8:56 AM
@UlrikeFischer Go for it
9:20 AM
@DavidCarlisle The modern trend is for documentation to be online /only/ – at Read the Docs for example. We hates it!
9:42 AM
Hi, there was a trick to prevent lists or objects like this to start directly after an environment.
It happens as the disalignement in the case of itemize.
The command was something like escape vertical space...
OK, an appropriate search re-revealed the solution :)
It was \leavevmode
Hi, I want to polish up my question tex.stackexchange.com/questions/487529/… Do you have any suggestions?
10:32 AM
@marmot Here is how I envision this to be used:
\documentclass[a4paper]{article}
\usepackage{pgfkeys}
\pgfkeys{%
/dlf/.is family,%
/dlf,%
A/.initial=,
B/.initial=,
C/.initial=,
set default/.code={
\pgfkeys{/dlf,
A=#1,
B=#1,
C=#1,
}
},
set default/.default=\textbf,
set default,
my value/.initial=,
}
\newcommand\apply[2]{\pgfkeysvalueof{/dlf/#1}{\pgfkeysvalueof{/dlf/#2}}}
\pgfkeys{/dlf/.cd,
my value=test,
B=\textit,
C=\MakeUppercase,
% set default=\textsf,
}
\begin{document}
\apply{A}{my value}
\apply{B}{my value}
\apply{C}{my value}
It works, but the nesting of \pgfkeys just seems strange to me.
I'm playing with a beamer theme, where a lot needs to be in uppercase, and I want this is be individually configurable (frame titles in upper case takes too much space in most cases), just seems easier to use a method like this to set a lot of default values.
11:16 AM
@marmot ahh, you are absolutely right, .forward to seems the way to go. It is just not obvious from the manual, that you can specify this several times on the same parent key. Source: tex.stackexchange.com/q/368736/3929
11:45 AM
Some pgfplots expert currently here? @marmot? I am looking for creating a "stacked" plot: 3 plots, one on top of the other which share the same abscissa (time axis, in my case), to be shown only on the lowermost plot. Any pointers where to look for an example in the pgfplots manual?
@AlexG groupplots?
@JosephWright Thank you! Going to look for it.
@AlexG I'll send you a demo
@JosephWright oh no
@JosephWright 👿
@PauloCereda demo, not d[a]emon I hope.
11:49 AM
@AlexG phew :)
@AlexG Example on it's way
@JosephWright Thank you so much!
@DavidCarlisle 𝓷𝓸𝓽 𝓶𝔂 𝓯𝓪𝓾𝓵𝓽
Unicode is amazing
@PauloCereda we can blame @barbarabeeton for those
@DavidCarlisle ooh
11:56 AM
@JosephWright Perfect example! Exactly what I need, even the font fits! (I need it for my boss, to be pasted into ppt.)
@AlexG oh no
@AlexG Good: its from a paper a couple of years ago
12:11 PM
@egreg thief
@DavidCarlisle oh no
@PauloCereda tempting people with flashy _: tricks and personally named modules
@DavidCarlisle where is this world going
In other news, will any of you boys and girls watch Endgame?
Is there a way to put caption like a), b) of this type in the figures (using caption command)
3
Use positioning library. right = of horizontally aligns nodes by their center: \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture}[every node/.style={inner sep=0pt, outer sep=0pt}] \node (img1) {\includegraphics[height=2cm]{example-...
@Shamina I simply use minipages. :)
12:20 PM
@PauloCereda I agree with you. But some how I have made a collage along with the coordinate axes, however, now I need a caption below each fig
12:31 PM
@JosephWright Hello Joseph! Can you please turn this answer into a comment?
12:58 PM
@daleif You do not need to nest the \pgfkeys, the following seems to yield the same result:
\documentclass[a4paper]{article}
\usepackage{pgfkeys}
\pgfkeys{%
/dlf/.is family,%
/dlf/.cd,%
A/.initial=,
B/.initial=,
C/.initial=,
set default/.style={/dlf/.cd,
A=#1,
B=#1,
C=#1,
},
set default/.default=\textbf,
set default,
my value/.initial=,
}
\newcommand\apply[2]{\pgfkeysvalueof{/dlf/#1}{\pgfkeysvalueof{/dlf/#2}}}
\pgfkeys{/dlf/.cd,
my value=test,
B=\textit,
C=\MakeUppercase,
% set default=\textsf,
However, I am not sure I understand the purpose.
1:24 PM
@marmot your hint with the forward to, also works.
@daleif Yes, but I am wondering if you are overall just looking for /.append code.
As for the purpose, I have a beamer template, that is modeled after a power point template. It has \MakeTextUppercase all over the place. Instead of hard coding these., I'd like to make them adjustable. So in this case A would be a formatter for the name of the presenter in the footer, B would be the formatter for the frame title.
> Daniel Craig is back in a sequel from the director of True Detective
bah
He does not look English. :)
Some of these formatters I'm going to leave blank by default (fx the frame title), but if the user wanted to fully comply to the PP formatting, they could issue use all caps as a configuration key for this beamer theme, and it would set all the appropriate formatters to run uppercase.
@daleif Couldn't you just have one key, say text formatter/.code={\textbf} to which you append locally text formatter/.append code={\MakeTextUppercase}? (Not that I tried this... ;-)
1:31 PM
Pip pip tally ho cheerio ta ta
Happy Penguin day!
@DavidCarlisle Which theft are you referring to? There have been a few, lately. :-P
@egreg the width one, replacing my elegant use of measuring the width of an alignment with some dull expl3 loop:-)
@DavidCarlisle Mathematicians are fond of generalizations. :-)
I got my tick back.
@marmot how do you propagate this to say 10 different keys? that can also be set on their own.
1:46 PM
2
weeeeeee
@daleif Are these variations in their local groups? If so, you can append these extra options locally. If not, you may have to reset these things.
2:07 PM
@UlrikeFischer Be careful. Ticks carry all kinds of scary diseases.
@HaraldHanche-Olsen Which ones? minor or major? x ticks or y ticks?
@marmot depends on what you mean by local group? The keys are meant to be set once (in the preamble) (I'm experimenting with providing all the configuration for using this beamer theme as a key-val interface, so no confusing \author[short]{long} etc
@HaraldHanche-Olsen I'm quite safe, I assume that @egreg will generalize his answer and take it back ;-)
@daleif These A, B and C are then just styles that you set?
2:19 PM
@marmot they are just values, here macros that can take up to one argument, hence my example with \textbf. (I'm having a bit of trouble with the concept of style here)
2:57 PM
@daleif What I want to say is that it seems to me that what you are after is conceptually the same as wanting a node to have the styles, say, circle,draw,inner sep=3pt. You want some text or whatever have the properties \MakeUpperCase and \bfseries, say, so I am wondering if you might be better off if you just tried to copy the concept from the nodes and define styles bold,upper case and so on that you apply to these texts.
3:16 PM
@marmot might be. I think I'll keep working on the features and then settle on the interface later on. Somepeople might be getting upset that I'm ditching \author, \title \institution etc for a key-val based interface. So we'll see whether the interface in the end will be better than the standard interface.
@daleif Better than powerpoint? I bet it will be. ;-)
@marmot Well we have some freedom here (I've been putting off for year to actually make this theme, and in the mean time they changed to a much much simpler PP theme). I'm more thinking about beamer users, how they are going to feel about \author and \title perhaps not doing anything.
@daleif I do not know the details of it at all, so I cannot say much.
@marmot some of it comes from the confusing of \title[short]{long}. Because shortis normally in the footer, this can easily something completely different than long. So why not split these completely and give them key names that make more sense to the users. At least that is the end goal.
long could be the title of your talk at a conference, and short be the name of the conference to go into the footer.
1 hour later…
4:50 PM
Hello geektexs,
I'm in trouble with this code:
\begin{verbatim}
length=2*3.14*r
print(length)
#this is a comment
\end{verbatim}
In a beamer documentclass
Is there anything wrong?
@santimirandarp fragile option?
Do you mean to insert fragile option? I'm not sure what's that @JosephWright
@santimirandarp Yes: \begin{frame}[fragile]
fine, it works. I'll check whats that @JosephWright
Last question, is it ok if \setlength{\itemsep}{neededsep} is set on the preamble?
@santimirandarp it won't work. itemsep is reset at the begin of lists. Try \setlength\itemsep{3cm}.
5:05 PM
Yes, it doesn't...
@PauloCereda -- Yup. The creators of the Brown Corpus were among my professors, and I actually keypunched part of it. It was one of the very first applications of computers to linguistics, and is still recognized as an important source. (Henry Kucera, one of the creators, taught the only formal programming course I ever took; the language was PL/1, now nearly unknown, but very interesting in terms of its design principles.)
@barbarabeeton How nice! I know the Brown corpus and (surprisingly) PL/1 as well! :)
5:21 PM
@AlexG -- You need to check out tug.org/TUGboat/tb36-3/tb114cartoon.pdf
@DavidCarlisle -- The only problem is, I can't see anything but little empty square boxes.
5:44 PM
@UlrikeFischer Thinking about \pdfdest: we have to do some processing for drivers other than pdfTeX, so have to work out how to handle the optional zoom ...
6:04 PM
@UlrikeFischer Or do we just rule that out: I can only see support in pdfTeX, not dvipdfmx or dvips
@UlrikeFischer Hmm, so we do need the zoom ...
@JosephWright dvips and dvipdmx don't allow to set it?
@JosephWright in pdfmark.def I can find a \@pdfviewparams which perhaps (!) means that it supports the zoom, in hxetex is doesn't looks as if it is there. If the drivers have different capabilities we could perhaps collect them in (driver) dependant tables.
6:28 PM
@barbarabeeton Too bad. Those are letters from the MATHEMATICAL BOLD SCRIPT SMALL set of letters. The declared fonts are, in order, Verdana, Arial, sans-serif. But I am beginning to suspect that my browser is actually reaching for the STIX Two Math font to render those glyphs.
@barbarabeeton you have been using TeX too long, that is the tfm view of a font.
@UlrikeFischer Probably I'll go for an interface that supports zoom then deal with lack-of-support at the low level
@JosephWright sounds good.
6:43 PM
@UlrikeFischer Go for xyz for 'no zoom', xzy<number> for scaling?
@UlrikeFischer Or xyz [zoom]? Not sure I like having an optional value at the driver level. I thought about xyz:<zoom>
@JosephWright do you think xzy in pdfpages is by purpose? I thought it is a typo.
@UlrikeFischer Hmm, yes, could well be a typo ....
@UlrikeFischer So xyz<zoom> or xyz:<zoom>?
@UlrikeFischer Or do we just have an extra argument that's only used for xyz?
@JosephWright or simply beside fit etc a number which is then used for xyz.
@UlrikeFischer Yes, that did occur to me too
@UlrikeFischer Out of 100? So 100 = xyz
7:04 PM
@JosephWright well 100 as 100% would be actually quite good, it took me some time to figure out that one has to use 1000 in pdfpages to get 100 ;-)
@UlrikeFischer Yes, don't plan to use 1000
@DavidCarlisle -- Not exactly. The only "reliable" device I currently have access to is one without a tex installation, and an out-of-date operating system. It's a long story.
@DavidCarlisle -- If I could figure out how to cut and paste what's there on my screen, you would also see little empty boxes.
@barbarabeeton oh something like this I assume 🪓🪓🪓🪓🪓🪓🪓🪓
7:27 PM
@DavidCarlisle -- Not sure whether how this will show here, but it's what a copy/paste results in: @DavidCarlisle \303\260\303\260\303\260 \303\260\303\260 \303\260\303\260\303\260\303\260\303\260 How's that? (Not very helpful.)
@barbarabeeton octal? very retro:-)
@DavidCarlisle -- I told you this machine was out of date. Got nothing to do with either tfm or tex.
7:41 PM
@barbarabeeton Hi! Got any response regarding the theorem format?
\cs_new_protected:Npn \driver_pdf_destination:nn #1#2
{
\cs_if_exist:NTF \tex_pdfextension:D
{ \exp_not:N \tex_pdfextension:D dest ~ }
{ \exp_not:N \tex_pdfdest:D }
name {#1}
\exp_not:N \str_case:nnF {#2}
{
{ xyz } { xyz }
{ fit } { fit }
{ fitb } { fitb }
{ fitbh } { fitbh }
{ fitbv } { fitbv }
{ fith } { fith }
{ fitv } { fitv }
}
{ xyz ~ zoom \fp_eval:n { #2 * 10 } }
@UlrikeFischer ^^^
@UlrikeFischer Look OK>
@mickep -- I've had no feedback from my former colleagues. Please remind me of the particular question, and I'll try again.
@JosephWright yes, clever.
@UlrikeFischer Need it for dvipdfmx, picking up from hyperref
@UlrikeFischer Need to work out how the zoom works in XeTeX ...
@barbarabeeton It was about the style of theorems, that has changed during the years. Previously they were indented and set in small caps, now (in the style guide) the head is set bold, and not indented.
@JosephWright if I go the docu right, simply the array is passed, so perhaps some argument [@dest /XYZ @xpos @ypos 1.0]
@UlrikeFischer Yes, I'm just testing
@UlrikeFischer I think something like this!
@UlrikeFischer The form hyperref uses is [@thispage /XYZ @xpos @ypos null], so I just need to work out by hand
@UlrikeFischer Where did you find docs ...
@JosephWright I looked in dvipdfm.pdf
@mickep -- I've sent another inquiry. I do doubt that there is anything useful recorded, so it will depend on the memory of someone else who was in the editorial department at the time. Will report if I hear anything.
@barbarabeeton Much appreciated.
8:04 PM
@UlrikeFischer Yup, it's a scale in dvipdfmx. I wonder why hyperref doesn't support it ... at least that I can see
@AlanMunn -- Hmmm. It seems I'm strengthening these statistics when I "English" some submissions to TUGboat. (This often consists of adding "the" or "a"; articles are not required in many languages, and picking up "standard" English usage is apparently not exactly automatic.)
@JosephWright I didn't find anything too. Do one need the keywork null is there is no zoom, or does 0 works too?
@UlrikeFischer Good question: I suspect not, as null means 'do nothing' whereas 0 is a fixed zoom
@JosephWright I think 0 = null (looking at pdfmark spec) (which isn't directly involved but i assume has same meaning)
@DavidCarlisle Yeah, seems to be
@DavidCarlisle Don't need to worry, I think ....
@UlrikeFischer, @DavidCarlisle I think one can do zoom in dvips
8:15 PM
@JosephWright can't you in principle write any pdfmark for dvips?
@DavidCarlisle Yes, looks that way; I think the hyperref dvips driver like the dvipdfmx one just skips the idea
@JosephWright the pdf reference says "A zoom value of 0 has the same meaning as a null val".
@UlrikeFischer Ah, right
@UlrikeFischer, @DavidCarlisle I have pdfTeX/LuaTeX/XeTeX sorted, just dvips to do ...
@UlrikeFischer Not sure it's that important ...
@JosephWright running history in reverse
@DavidCarlisle The PostScript stuff is by far the most complex to sort out; I have to get it all working. With pdfTeX, I just need the primitive (OK, without that much documentation!)
8:19 PM
@JosephWright I think last time I thought about this it was with discussions with Sebastian and probably predated pdftex:-)
@DavidCarlisle Yes, I suspect so
@DavidCarlisle Kind David when you have a little of time look this: cdn2.scuolabook.it/Uploaded/loescher_0376e_preview/…
@Sebastiano You don't have permission to access /Uploaded/loescher_0376e_preview/loescher_0376e_preview.pdf on this server.
@UlrikeFischer seen the greek luatex ligatures question?
@DavidCarlisle ok I just wanted to show you a pdf that is a preview of a publishing house available online.
@Sebastiano as I showed, I have no permission to access it.
8:35 PM
@DavidCarlisle yes, will look at it now.
@Sebastiano but how can you tell from a pdf that it was made with latex and indesign with figures made in illustrator? especially pdfs that are not readable, or do you have password access for that?
@Sebastiano if it is the same as this one (found by google) scuolabook.it/Uploaded/loescher_0376e_preview/… that is made with QuarkExpress
@Sebastiano also the question was about Pearson and Wiley and I asked how you could tell how their books were made using tex, I don't see how linking to a book made by a different publisher using QuarkExpress really answers that?
@UlrikeFischer that was quick:-)
8:51 PM
@UlrikeFischer yes I got that far (seeing the link didn't work) and then gave up and asked you google suggested some other places to download it but most of those font sites i don't trust:-)
@DavidCarlisle I just showed you that Loescher's book is out of production written in LaTeX and modified with other programs.
@DavidCarlisle 2nd question Fondamenti di fisica di David Halliday, Robert Resnick, Jearl Walker before are of the company Zanichelli.
@Sebastiano no you didn't you just pointed to a non public URL that was unreadable, I found (the same?0 pdf vis google, and can tell it's made with QuarkExpress, how can you tell it started as latex, do you know the authors or can you tell from the pdf, that was the question i originally asked.
@Sebastiano a link to what? to loescher_0376e_preview.pdf ? as I say I found that via google already.
@DavidCarlisle Directly from the site I have copiated this: Le basi di partenza per i nostri elaborati con formule sono il TeX, ideato da Knuth, e LaTeX, di Lamport, affiancati dai più potenti programmi per l'impaginazione tradizionale. You can see that there is also Pearson.
@DavidCarlisle Do you now believe me? The book LinX Pearson Walker of Physics that I adopt is made with QuarkXpress. I have the email from the publisher.
@Sebastiano yep I just translated it at the link you gave, but I's say it doesn't really answer the question on the main site. a specialist math typesetter did enough to put the pearson logo on their site, that could mean anything, perhaps they worked on one book, or 1000 or ... You stated that pearson and wiley produced there mathematical books starting with tex and then touching up in indesign and quarkexpress, and using illustrator for the figures. it seems that was a guess.
@Sebastiano as I thought, your original statement is just a guess and you don't have inside knowledge of a tex->indesign->illustrator workflow inside pearson or wiley.
9:07 PM
@DavidCarlisle And I confirm. The most famous publishing houses use other smaller publishing houses to create the texts.
@Sebastiano I give up.
@AlanMunn Thank you!
@PauloCereda Hi, Paolo
@Sebastiano Do you know that? Have you worked there? If so, you are probably breaking an NDA
@Sebastiano These are big places creating 1000s of books: does just one count? 10% of their output? ... It's far to open a question
@JosephWright I didn't work on it. On the covers of the school books there are the references of the publishing house. I'm not violating anything. If you want, I'll take a picture of you and show you that the graphic processing is done that way.
9:16 PM
@Sebastiano hi.
@Sebastiano your comment under the question is at best misleading and probably wrong, you should delete it.
@Sebastiano All they tell you normally is 'Typeset by Company X of Place Y'
@PauloCereda I got today a very serious looking poster with a footnote saying Förderung: Bundesamt für magische Wesen ;-)
@JosephWright it also says who is in charge of the graphic processing of the company.
@UlrikeFischer ooh :)
9:19 PM
@Sebastiano Not the academic books I'm familiar with (OUP, largely, but also other people)
@DavidCarlisle Can you tell me exactly what I'm supposed to eliminate?
@Sebastiano do you have any knowledge of a pearson book that was started as tex, modified in indesign and with figures generated in illustrator? if you have not delete the comment saying that is how pearson produce mathematical books.
@JosephWright I think this page answers the question that Wiley does not use LaTeX: The template will not be used for the presentation of the final page layout.
@DavidCarlisle I've deleted the comments. See if they are correct. I personally have never worked in a publishing house but I have had some clarifications via email also from school textbooks. Many Physics schoolbooks, for example, such as Walker or Halliday have been translated into Italian and reset by publishers with the same characteristics as academic books.
@StrongBad Could be, or could be they have a strange workflow. For example, I had to submit a chapter using Word, but the proofs were from LaTeX. They could be doing LaTeX/Word -> XML - > TeX ouptut for all we know
9:29 PM
I could simply forge the PDF metadata and typeset with a potato? :)
@JosephWright Ah, I thought "typed" meant "keyed" and not outputted to the printed page such that TeX had to be the first stage of the process.
@Sebastiano the question has been closed anyway but you should also delete your comment starting "The answer is simple: Adobe InDesign, Illustrato..." as it is unrelated to the question about Pearson and Wiley so misleading in that context.
@JosephWright This is LuaTeX, Version 1.10.0 (TeX Live 2019/W32TeX) (format=lualatex-expl3 2019.4.25).
^^^^^^^^
@StrongBad I just wanted to make my knowledge available. But am I wrong by some reason?
@UlrikeFischer does anything work? :-)
9:31 PM
@DavidCarlisle ooh
@UlrikeFischer Hi
@DavidCarlisle I have deleted all.
@Sebastiano thanks
@DavidCarlisle a test document that loads fontspec and siunitx didn't explode.
@UlrikeFischer :-)
@UlrikeFischer drat, since @JosephWright is a chemist, it should explode. :)
9:32 PM
@UlrikeFischer who cares about those packages? does picture mode work?
3
@Sebastiano well according to Wiley's webpage, if you submit your book with their LaTeX template, they still do things to it so it is not possible to submit CRC in LaTeX. As @JosephWright points out, it is possible TeX plays a role someplace in their process.
@DavidCarlisle if you give me an example I will try.
78
It was suggested in chat http://chat.stackexchange.com/transcript/message/9482087#9482087 That picture mode would be the ideal tool for the job here: \documentclass{article} \begin{document} \begin{picture}(200,100) \put(30,40){\line(1,0){150}} \put(30,40){\line(0,1){60}} \put(30,100){\line(...
@StrongBad @JosephWright is what I was going to say :-(. They then change everything but the initial setting can also be done with LaTeX. A few years ago I loaded modern computer fonts and with adobe illustrator, for example, with images you can do what you want.
@Sebastiano the question was not about what is possible or what you have done, it was about what Pearson and Wiley do, that's why there was surprise at your definite statements, as most people have no knowledge of their internal production processes.
9:38 PM
@DavidCarlisle It compiled fine - both with pdflatex-expl3 and lualatex-expl3 - I'm very relieved.
@Sebastiano My point is that unless you are actually involved in the work, it's hard to be sure of the route(s) used. So the question on the main site is probably OT anyway: we can't answer.
@UlrikeFischer l3draw version next I suppose....
@DavidCarlisle @JosephWright In any case, I have removed all comments.
@barbarabeeton Yes, the English article system is deceptively difficult for speakers of languages without articles.
@JosephWright What do you mean OT?
9:40 PM
@Sebastiano Off Topic
@UlrikeFischer, @DavidCarlisle As with other stuff, it seems dvips is by far the most awkward for \pdfdest: there seems to be some need to measure stuff in PostScript again ...
Greetings, everyone.
@JosephWright simple just reverse engineer pstricks as well as pgf:-)
@DavidCarlisle ooh
10:05 PM
@JosephWright what do you need to measure for pdfdest?
@DavidCarlisle Trying to work that out now ...
@DavidCarlisle I think it's to allow you to know where the destination actually is
@DavidCarlisle Ah, was reading the wrong part of the log
10:23 PM
@DavidCarlisle What I'm not getting is why in dvips we seem to be measuring something either side of some input (text), whereas for the other routes it's a single point. It would be a lot easier just to measure everything in one shot. I suspect that should be doable. Need to understand the PostScript.
@JosephWright yes a single point was what I was expecting, hence the question about what you were measuring, although I should probably look at the code....
10:37 PM
@DavidCarlisle I think I get the basic idea: pretty sure I don't need two points
@DavidCarlisle I'd appreciate thoughts on H.S and H.A in hdvips.def. They are adding/subtracting 72 converted to points to things ... but shouldn't it be 72.27? Have I found a bug in hyperref here? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7693209052085876, "perplexity": 2917.4346630763494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257731.70/warc/CC-MAIN-20190524184553-20190524210553-00151.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/216439-cosets-form-partition-x.html | # Math Help - Cosets form a partition of X
1. ## Cosets form a partition of X
Hello guys, I hope I'm posting in the right place.
I'm having problems solve the following problem: Let Y be a subspace of a vector space X. Show that the distinct cosets x + Y (x in X) form a partition of X.
I don't quite understand how these cosets work so I couldn't think of any way to approach this problem.
2. ## Re: Cosets form a partition of X
Odd, I thought I was pretty good at linear algebra but I also thought that "cosets" was a topic from group theory! But, of course, the set of vectors, with the single operation of addition is a group so the 'coset' x+ Y, for a given x, is the set of all vectors of the form x+ y where y is any vector in Y. To show that x+ Y is a "partition" of X, we need to show that every vector in one and only one of those sets.
Let v be any vector in X. Choose any vector y in Y, let x= z- y.
Now, suppose v is in both x+ Y and x'+ Y, with $x\ne x'$. That is, $v= x+ y_1$ and $v= x'+ y_2$ with both $y_1$ and $y_2$ in Y. So we have $x+ y_1= x'+ y_2$ from which it follows that $x- x'= y_2- y_1$. What does that tell you? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9757245182991028, "perplexity": 218.82745573423267}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398445142.9/warc/CC-MAIN-20151124205405-00036-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/definition-clarification-for-fourier-transform.833551/ | # Definition clarification for Fourier transform
1. Sep 20, 2015
### space-time
I have been studying Fourier transforms lately. Specifically, I have been studying the form of the formula that uses the square root of 2π in the definition. Now here is the problem:
In some sources, I see the forward and inverse transforms defined as such:
F(k) = [1/(√2π)] ∫-∞ f(x)eikx dx
f(x) = [1/(√2π)] ∫-∞ f(k)eikx dk
In other cases, I've seen:
F(k) = [1/(√2π)] ∫-∞ f(x)e-ikx dx
f(x) = [1/(√2π)] ∫-∞ f(k)eikx dk
Notice that in the first version of the forward transform (the one that solves for F(k)), the exponential in the integrand has a positive sign in the exponent ikx, while in the 2nd version it has a negative ikx.
Which version is correct? Are they both correct and it is a matter of convention? Are neither correct?
Also, is there some way to do a multiple dimensional Fourier transform using volume integrals? If so, what is the formula for that (preferably including (√2π))?
2. Sep 20, 2015
### MisterX
Only the 2nd pair is correct. There are a couple conventional issues, but no matter what the sign on the exponent has to change for the inverse transform relative to the forward transform.
Similar Discussions: Definition clarification for Fourier transform | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9686889052391052, "perplexity": 1240.783527380782}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948512121.15/warc/CC-MAIN-20171211033436-20171211053436-00096.warc.gz"} |
http://physics.stackexchange.com/users/11352/fika?tab=activity | # Fika
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Aug 13 answered Classical Limit of the Feynman Path Integral | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8313122987747192, "perplexity": 6488.497045015851}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398466260.18/warc/CC-MAIN-20151124205426-00100-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://rdrr.io/cran/GHap/man/lmm.html | # lmm: Frequentist linear mixed model
### Description
Maximum likelihood estimates for the parameters of a linear mixed model.
### Usage
1 ghap.lmm(fixed,random,weights=NULL,env.eff=FALSE,data,K,verbose=TRUE)
### Arguments
fixed Formula describing the fixed effects part of the model, e.g. y ~ a + b + c ... If the model does not include any covariate simply state the response variable with an intercept, i.e. y ~ 1. random A character value with name of the column containing labels for the random effects. weights A numeric vector with residual weights. If not supplied, all residual weights are set to 1. env.eff A logical value indicating if permanent environmental effects should be included (default=FALSE). data A dataframe containing the data. K A covariance matrix for random effects. verbose A logical value specfying whether log messages should be printed (default = TRUE).
### Details
The function uses a frequentist framework to fit the following linear mixed model:
\mathbf{y} = \mathbf{Xb} + \mathbf{Zu} + \mathbf{Zp} + \mathbf{e}
where \mathbf{X} is a matrix relating \mathbf{y} to the vector of fixed effects \mathbf{b}, \mathbf{Z} is an incidence matrix relating \mathbf{y} to random effects \mathbf{u} and \mathbf{p}, and \mathbf{e} is the vector of residuals. The likelihood of the data is assumed:
\mathbf{y} \mid \mathbf{b},\mathbf{u},\mathbf{p},σ_{u}^{2},σ_{p}^{2},σ_{e}^2 \sim N(\mathbf{Xb},\mathbf{V})
where \mathbf{V} = \mathbf{ZKZ}'σ_{u}^2 + \mathbf{ZZ}'σ_{p}^2 + \mathbf{W}σ_{e}^2, \mathbf{K} is a covariance matrix for \mathbf{u}, σ_{u}^{2} and σ_{p}^{2} are the variances of \mathbf{u} and \mathbf{p}, respectively, \mathbf{W} is a residual covariance matrix and σ_{e}^{2} is the residual variance. The current implementation assumes \mathbf{W} = diag(w_i). More details about the maximization algorithm can be found in our vignette.
### Value
The returned GHap.blmm object is a list with the following items:
b A numeric vector containing the BLUE of fixed effects. u A numeric vector containing BLUP of correlated random effects. p A numeric vector containing the BLUP of permanent environmental effects. This vector is suppressed if env.eff=FALSE. varu A numeric value for the maximum likelihood estimate of the variance of correlated random effects. varp A numeric value for the maximum likelihood estimate of the variance of permanent environmental effects. This value is suppressed if env.eff=FALSE. vare A numeric value for the maximum likelihood estimate of the variance of residual variance. h2 A numeric value for the maximum likelihood estimate of the variance explained by correlated random effects only. H2 A numeric value for the maximum likelihood estimate of the variance explained by random effects. This value is suppressed if env.eff=FALSE. k A numeric vector containing the solutions for \mathbf{K}^{-1}\mathbf{\hat{u}}. This vector is used by the ghap.blup function. y A numeric vector containing the records used to fit the model. weights A numeric vector containing the residual weights used to fit the model. residuals A numeric vector containing residuals computed based on the BLUE and BLUP solutions. pdev Deviance evaluated at the BLUE and BLUP solutions.
### Author(s)
Yuri Tani Utsunomiya <[email protected]>
### Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 # #### DO NOT RUN IF NOT NECESSARY ### # # # Copy the example data in the current working directory # ghap.makefile() # # # Load data # phase <- ghap.loadphase("human.samples", "human.markers", "human.phase") # # # Subset data - randomly select 3000 markers with maf > 0.02 # maf <- ghap.maf(phase, ncores = 2) # set.seed(1988) # markers <- sample(phase$marker[maf > 0.02], 3000, replace = FALSE) # phase <- ghap.subsetphase(phase, unique(phase$id), markers) # rm(maf,markers) # # # Generate block coordinates based on windows of 10 markers, sliding 5 marker at a time # blocks <- ghap.blockgen(phase, 10, 5, "marker") # # # Generate matrix of haplotype genotypes # ghap.haplotyping(phase, blocks, batchsize = 100, ncores = 2, freq = 0.05, outfile = "example") # # # Load haplotype genotypes # haplo <- ghap.loadhaplo("example.hapsamples", "example.hapalleles", "example.hapgenotypes") # # # Compute kinship matrix # K <- ghap.kinship(haplo, batchsize = 100) # # # Quantitative trait with 50% heritability # # One major haplotype accounting for 30% of the genetic variance # sim <- ghap.simpheno(haplo = haplo, K = K, h2 = 0.5, g2 = 0.3, major = 1000,seed=1988) # # # ### RUN ### # # #Continuous model # model <- ghap.lmm(fixed = phenotype ~ 1, random = "individual", data = sim$data, K = K) # model$h2 # plot(model$u,sim$u, ylab="True Breeding Value", xlab="Estimated Breeding Value") # cor(model$u,sim$u)
Questions? Problems? Suggestions? or email at [email protected].
All documentation is copyright its authors; we didn't write any of that. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4277608096599579, "perplexity": 2740.7244615493855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280835.60/warc/CC-MAIN-20170116095120-00435-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://worldwidescience.org/topicpages/t/two-dimensional+bimetallic+layers.html | #### Sample records for two-dimensional bimetallic layers
1. Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers
Science.gov (United States)
2016-06-15
polymers . 2. Introduction . Research objectives: This research aims to study the physical (van der Waals forces: crystal epitaxy and π-π...AFRL-AFOSR-JP-TR-2016-0071 Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers Cheolmin Park YONSEI UNIVERSITY...Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386-14-1-4054 5c. PROGRAM ELEMENT
2. Optical modulators with two-dimensional layered materials
CERN Document Server
Sun, Zhipei; Wang, Feng
2016-01-01
Light modulation is an essential operation in photonics and optoelectronics. With existing and emerging technologies increasingly demanding compact, efficient, fast and broadband optical modulators, high-performance light modulation solutions are becoming indispensable. The recent realization that two-dimensional layered materials could modulate light with superior performance has prompted intense research and significant advances, paving the way for realistic applications. In this review, we cover the state-of-the-art of optical modulators based on two-dimensional layered materials including graphene, transition metal dichalcogenides and black phosphorus. We discuss recent advances employing hybrid structures, such as two-dimensional heterostructures, plasmonic structures, and silicon/fibre integrated structures. We also take a look at future perspectives and discuss the potential of yet relatively unexplored mechanisms such as magneto-optic and acousto-optic modulation.
3. Two-dimensional transport study of scrape off layer plasmas
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, Nobuyuki [Interdisciplinary Graduate School of Advanced Energy Engineering Sciences, Kyushu University, Fukuoka (Japan); Yagi, Masatoshi; Itoh, Sanae-I. [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics
1999-09-01
Two-dimensional transport code is developed to analyzed the heat pulse propagation in the scrape-off layer plasma. The classical and anomalous transport models are considered as a thermal diffusivity perpendicular to the magnetic field. On the other hand, the classical transport model is chosen as a thermal diffusivity parallel to the magnetic field. The heat deposition profiles are evaluated for various kinds of transport models. It is found that the heat pulse which arrives at the divertor plate due to the classical transport is largest compared with other models. The steady state temperate profiles of the electron and ion are also discussed. (author)
4. Development of Novel Two-dimensional Layers, Alloys and Heterostructures
Science.gov (United States)
Liu, Zheng
2015-03-01
The one-atom-think graphene has fantastic properties and attracted tremendous interests in these years, which opens a window towards various two-dimensional (2D) atomic layers. However, making large-size and high-quality 2D layers is still a great challenge. Using chemical vapor deposition (CVD) method, we have successfully synthesized a wide varieties of highly crystalline and large scale 2D atomic layers, including h-BN, metal dichalcogenides e.g. MoS2, WS2, CdS, GaSe and MoSe2 which belong to the family of binary 2D materials. Ternary 2D alloys including BCN and MoS2xSe2 (1 - x) are also prepared and characterized. In addition, synthesis of 2D heterostructures such as vertical and lateral graphene/h-BN, vertical and lateral TMDs are also demonstrated. Complementary to CVD grown 2D layers, 2D single-crystal (bulk) such as Phosphorene (P), WTe2, SnSe2, PtS2, PtSe2, PdSe2, WSe2xTe2 (1 - x), Ta2NiS5andTa2NiSe5 are also prepared by solid reactions. There work provide a better understanding of the atomic layered materials in terms of the synthesis, atomic structure, alloying and their physical properties. Potential applications of these 2D layers e.g. optoelectronic devices, energy device and smart coating have been explored.
5. Two-dimensional magic numbers in mass abundances of photofragmented bimetallic clusters
CERN Document Server
Janssens, E; Neukermans, S; Silverans, R E; Lievens, P
2003-01-01
The stability of cationic gold clusters doped with one transition metal atom was investigated by a mass spectrometric analysis of fragments resulting from high fluence irradiation of a cluster beam. Strongly enhanced abundances are found for Au sub 5 X sup + , X = V, Mn, Cr, Fe, Co, Zn, which implies that these species are far more stable towards fragmentation than their neighbouring cluster sizes. Here we interpret the enhanced stability of these clusters within a shell model approach for two-dimensional (2D) systems: the number of delocalized electrons in Au sub 5 X sup + is six, which is a magic number for 2D systems. Quantum chemical calculations for Au sub N Zn sup + (N = 2-6) predict planar structures that are stabilized by the influence of the dopant atom. Also, the main features of the calculated molecular orbitals are well reproduced by a simple electron-in-a-box model. The present report constitutes the first observation of 2D magic numbers in size dependent properties of metal clusters.
6. Ferromagnetism and chirality in two-dimensional cyanide-bridged bimetallic compounds.
Science.gov (United States)
Coronado, Eugenio; Gómez-García, Carlos J; Nuez, Alicia; Romero, Francisco M; Rusanov, Eduard; Stoeckli-Evans, Helen
2002-09-09
The combination of hexacyanoferrate(III) anions, [Fe(CN)(6)](3)(-), with nickel(II) complexes derived from the chiral ligand trans-cyclohexane-1,2-diamine (trans-chxn) affords the enantiopure layered compounds [Ni(trans-(1S,2S)-chxn)(2)](3)[Fe(CN)(6)](2).2H(2)O (1) and [Ni(trans-(1R,2R)-chxn)(2)](3)[Fe(CN)(6)](2).2H(2)O (2). These chiral systems behave as ferromagnets (T(c) = 13.8 K) with a relatively high coercive field (H(c) = 0.17 T) at 2 K. They also exhibit an unusual magnetic behavior at low temperatures that has been attributed to the dynamics of the magnetic domains in the ordered phase.
7. Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers
Science.gov (United States)
2016-06-15
area electron diffraction (SAED) pattern of a MoSe2 nanosheet. (d) High resolution TEM (HR-TEM) image of the MoSe2 nanosheets. The digitally filtered ...nanosheets and end-functionalized polymers. 15. SUBJECT TERMS 2D Materials, Nanosheets, Layered Materials, Nanocomposites 16. SECURITY CLASSIFICATION OF...driving force for mixing between layers and the matrix. In addition, solution processes such as spin coating, dip coating and layer-by-layer coating are
8. Two-dimensional wave propagation in layered periodic media
KAUST Repository
2014-09-16
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using highorder homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coeffi cient equations.
9. Review—Two-Dimensional Layered Materials for Energy Storage Applications
KAUST Repository
Kumar, Pushpendra
2016-07-02
Rechargeable batteries are most important energy storage devices in modern society with the rapid development and increasing demand for handy electronic devices and electric vehicles. The higher surface-to-volume ratio two-dimensional (2D) materials, especially transition metal dichalcogenides (TMDCs) and transition metal carbide/nitrite generally referred as MXene, have attracted intensive research activities due to their fascinating physical/chemical properties with extensive applications. One of the growing applications is to use these 2D materials as potential electrodes for rechargeable batteries and electrochemical capacitors. This review is an attempt to summarize the research and development of TMDCs, MXenes and their hybrid structures in energy storage systems. (C) The Author(s) 2016. Published by ECS. All rights reserved.
10. Bimetallic layered castings alloy steel – carbon cast steel
Directory of Open Access Journals (Sweden)
T. Wróbel
2011-01-01
Full Text Available In paper is presented technology of bimetallic layered castings based on founding method of layer coating directly in cast processso-called method of mould cavity preparation. Prepared castings consist two fundamental parts i.e. bearing part and working part (layer. The bearing part of bimetallic layered casting is typical foundry material i.e. ferritic-pearlitic carbon cast steel, whereas working part (layer is plate of austenitic alloy steel sort X10CrNi 18-8. The ratio of thickness between bearing and working part is 8:1. The quality of the bimetallic layered castings was evaluated on the basis of ultrasonic NDT (non-destructive testing, structure and macro- and microhardness researches.
11. Examples of material solutions in bimetallic layered castings
Directory of Open Access Journals (Sweden)
S. Tenerowicz
2011-07-01
Full Text Available In paper is presented technology of bimetallic layered castings based on founding method of layer coating directly in cast process so-called method of mould cavity preparation. Prepared castings consist two fundamental parts i.e. bearing part and working part (layer. The bearing part of bimetallic layered casting is typical foundry material i.e. pearlitic grey cast iron, whereas working part (layer is depending on accepted variant plates of alloy steels sort X6Cr13, X12Cr13, X10CrNi18-8 and X2CrNiMoN22-5-3. The ratio of thickness between bearing and working part is 8:1. The verification of the bimetallic layered castings was evaluated on the basis of ultrasonic NDT (non-destructive testing, structure and macro- and microhardness researches.
12. The compressible Gortler problem in two-dimensional boundary layers
Science.gov (United States)
Dando, Andrew H.; Seddougui, Sharon O.
1993-01-01
In this paper the authors investigate the growth rates of Gortler vortices in a compressible flow in the inviscid limit of large Gortler number. Numerical solutions are obtained for O(1) wavenumbers. The further limits of (i) large Mach number and (ii) large wavenumber with O(1) Mach number are considered. It is shown that two different types of disturbance mode can appear in this problem. The first is a wall layer mode, so named as it has its eigenfunctions trapped in a thin layer near the wall. The other mode investigated is confined to a thin layer away from the wall and termed a trapped-layer mode for large wavenumbers and an adjustment-layer mode for large Mach numbers, since then this mode has its eigenfunctions concentrated in the temperature adjustment layer. It is possible to investigate the near crossing of the modes which occurs in each of the limits mentioned. The inviscid limit does not predict a fastest growing mode, but does enable a most dangerous mode to be identified for O(1) Mach number. For hypersonic flow the most dangerous mode depends on the size of the Gortler number.
13. Nanofluidics in two-dimensional layered materials: inspirations from nature.
Science.gov (United States)
Gao, Jun; Feng, Yaping; Guo, Wei; Jiang, Lei
2017-08-29
With the advance of chemistry, materials science, and nanotechnology, significant progress has been achieved in the design and application of synthetic nanofluidic devices and materials, mimicking the gating, rectifying, and adaptive functions of biological ion channels. Fundamental physics and chemistry behind these novel transport phenomena on the nanoscale have been explored in depth on single-pore platforms. However, toward real-world applications, one major challenge is to extrapolate these single-pore devices into macroscopic materials. Recently, inspired partially by the layered microstructure of nacre, the material design and large-scale integration of artificial nanofluidic devices have stepped into a completely new stage, termed 2D nanofluidics. Unique advantages of the 2D layered materials have been found, such as facile and scalable fabrication, high flux, efficient chemical modification, tunable channel size, etc. These features enable wide applications in, for example, biomimetic ion transport manipulation, molecular sieving, water treatment, and nanofluidic energy conversion and storage. This review highlights the recent progress, current challenges, and future perspectives in this emerging research field of "2D nanofluidics", with emphasis on the thought of bio-inspiration.
14. Electronic structure of boron based single and multi-layer two dimensional materials
Science.gov (United States)
Miyazato, Itsuki; Takahashi, Keisuke
2017-09-01
Two dimensional nanosheets based on boron and Group VA elements are designed and characterized using first principles calculations. B-N, B-P, B-As, B-Sb, and B-Bi are found to possess honeycomb structures where formation energies indicate exothermic reactions. Contrary to B-N, the cases of B-P, B-As, B-Sb, and B-Bi nanosheets are calculated to possess narrow band gaps. In addition, calculations reveal that the electronegativity difference between B and Group VA elements in the designed materials is a good indicator to predict the charge transfer and band gap of the two dimensional materials. Hydrogen adsorption over defect-free B-Sb and B-Bi results in exothermic reactions, while defect-free B-N, B-P, and B-As result in endothermic reactions. The layerability of the designed two dimensional materials is also investigated where the electronic structure of two-layered two dimensional materials is strongly coupled with how the two dimensional materials are layered. Thus, one can consider that the properties of two dimensional materials can be controlled by the composition of two dimensional materials and the structure of layers.
15. Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method
Directory of Open Access Journals (Sweden)
Taha Aziz
2013-01-01
Full Text Available The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.
16. Analysis of Two-Layered Random Interfaces for Two Dimensional Widom-Rowlinson's Model
Directory of Open Access Journals (Sweden)
Jun Wang
2011-01-01
Full Text Available The statistical behaviors of two-layered random-phase interfaces in two-dimensional Widom-Rowlinson's model are investigated. The phase interfaces separate two coexisting phases of the lattice Widom-Rowlinson model; when the chemical potential μ of the model is large enough, the convergence of the probability distributions which describe the fluctuations of the phase interfaces is studied. In this paper, the backbones of interfaces are introduced in the model, and the corresponding polymer chains and cluster expansions are developed and analyzed for the polymer weights. And the existence of the free energy for two-layered random-phase interfaces of the two-dimensional Widom-Rowlinson model is given.
17. Group classification of steady two-dimensional boundary-layer stagnation-point flow equations
OpenAIRE
2010-01-01
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
18. Two-dimensional thin-layer chromatography in the analysis of secondary plant metabolites.
Science.gov (United States)
Cieśla, Lukasz; Waksmundzka-Hajnos, Monika
2009-02-13
Drugs, derived from medicinal plants, have been enjoying a renaissance in the last years. It is due to a great pharmacological potential of herbal drugs, as many natural compounds have been found to exhibit biological activity of wide spectrum. The introduction of whole plants, plant extracts, or isolated natural compounds has led to the need to create the analytical methods suitable for their analysis. The identification of isolated substances is relatively an easy task, but the analysis of plant extracts causes a lot of problems, as they are usually very complex mixtures. Chromatographic methods are one of the most popular techniques applied in the analysis of natural mixtures. Unfortunately the separation power of traditional, one-dimensional techniques, is usually inadequate for separation of more complex samples. In such a case the use of multidimensional chromatography is advised. Planar chromatography gives the possibility of performing two-dimensional separations with the use of one adsorbent with two different eluents or by using bilayer plates or graft thin-layer chromatography (TLC) technique; combinations of different multidimensional techniques are also possible. In this paper, multidimensional planar chromatographic methods, commonly applied in the analysis of natural compounds, were reviewed. A detailed information is given on the methodology of performing two-dimensional separations on one adsorbent, on bilayer plates, with the use of graft TLC and hyphenated methods. General aspects of multidimensionality in liquid chromatography are also described. Finally a reader will find a description of variable two-dimensional methods applied in the analysis of compounds, most commonly encountered in plant extracts. This paper is aimed to draw attention to the potential of two-dimensional planar chromatography in the field of phytochemistry. It may be useful for those who are interested in achieving successful separations of multicomponent mixtures by means
19. Photodetectors Based on Two-Dimensional Layer-Structured Hybrid Lead Iodide Perovskite Semiconductors.
Science.gov (United States)
Zhou, Jiachen; Chu, Yingli; Huang, Jia
2016-10-05
Hybrid lead iodide perovskite semiconductors have attracted intense research interests recently because of their easy fabrication processes and high power conversion efficiencies in photovoltaic applications. Layer-structured materials have interesting properties such as quantum confinement effect and tunable band gap due to the unique two-dimensional crystalline structures. ⟨100⟩-oriented layer-structured perovskite materials are inherited from three-dimensional ABX3 perovskite materials with a generalized formula of (RNH3)2(CH3NH3)n-1MnX3n+1, and adopt the Ruddlesden-Popper type crystalline structure. Here we report the synthesis and investigation of three layer-structured perovskite materials with different layer numbers: (C4H9NH3)2PbI4 (n = 1, one-layered perovskite), (C4H9NH3)2(CH3NH3)Pb2I7 (n = 2, two-layered perovskite) and (C4H9NH3)2(CH3NH3)2Pb3I10 (n = 3, three-layered perovskite). Their photoelectronic properties were investigated in related to their molecular structures. Photodetectors based on these two-dimensional (2D) layer-structured perovskite materials showed tunable photoresponse with short response time in milliseconds. The photodetectors based on three-layered perovskite showed better performances than those of the other two devices, in terms of output current, responsivity, Ilight/Idark ratio, and response time, because of its smaller optical band gap and more condensed microstructure comparing the other two materials. These results revealed the relationship between the molecular structures, film microstructures and the photoresponse properties of 2D layer-structured hybrid perovskites, and demonstrated their potentials as flexible, functional, and tunable semiconductors in optoelectronic applications, by taking advantage of their tunable quantum well molecular structure.
20. Facile Synthesis and Characterization of Two Dimensional Layered Tin Disulfide Nanowalls
Science.gov (United States)
Mutlu, Zafer; Shahrezaei, Sina; Temiz, Selcuk; Ozkan, Mihrimah; Ozkan, Cengiz S.
2016-04-01
Two dimensional layered metal chalcogenides, especially tin sulfides, have recently received great interest due to their enticing physical and chemical properties and hold promise for various applications. We report on synthesis of phase-pure two dimensional tin disulfide nanowalls by a facile vapor-phase synthesis method on insulator substrates such as silicon dioxide and magnesium oxide using tin dioxide and sulfur powders as precursors. The synthesized tin disulfide nanowalls have been characterized to study their fundamental properties by using various techniques such as scanning electron microscopy, x-ray diffraction, Raman spectroscopy, x-ray photoelectron spectroscopy, and ultraviolet photoelectron spectroscopy. The synthesized films have an open network structure constituted of very uniform interconnected nanowalls with high crystallinity.
1. Novel layered two-dimensional semiconductors as the building blocks for nano-electronic/photonic systems
Science.gov (United States)
Su, Guoxiong; De, Debtanu; Hadjiev, Viktor G.; Peng, Haibing
2014-06-01
Layered two-dimensional (2D) semiconductors beyond graphene have been emerging as potential building blocks for the next-generation electronic/photonic applications. Representative metal chalcogenides, including the widely studied MoS2, possess similar layered crystal structures with weak interaction between adjacent layers, thus allowing the formation of stable thin-layer crystals with thickness down to a few or even single atomic layer. Other important chalcogenides, involving earth-abundant and environment-friendly materials desirable for sustainable applications, include SnS2 (band gap: 2.1 eV) and SnS (band gap: 1.1 eV). So far, commonly adopted for research purpose are mechanical and liquid exfoliation methods for creating thin layers of such 2D semiconductors. Most recently, chemical vapor deposition (CVD) was attracting significant attention as a practical method for producing thin films or crystal grains of MoS2. However, critical yet still absent is an effective experimental approach for controlling the positions of thin crystal grains of layered 2D semiconductors during the CVD process. Here we report the controlled CVD synthesis of thin crystal arrays of representative layered semiconductors (including SnS2 and SnS) at designed locations on chip, promising large-scale optoelectronic applications. Our work opens a window for future practical applications of layered 2D semiconductors in integrated nano-electronic/photonic systems.
2. Two-Dimensional Thermal Boundary Layer Corrections for Convective Heat Flux Gauges
Science.gov (United States)
2007-01-01
This work presents a CFD (Computational Fluid Dynamics) study of two-dimensional thermal boundary layer correction factors for convective heat flux gauges mounted in flat plate subjected to a surface temperature discontinuity with variable properties taken into account. A two-equation k - omega turbulence model is considered. Results are obtained for a wide range of Mach numbers (1 to 5), gauge radius ratio, and wall temperature discontinuity. Comparisons are made for correction factors with constant properties and variable properties. It is shown that the variable-property effects on the heat flux correction factors become significant
3. Simulation study of scalings in scrape-off layer plasma by two-dimensional transport code
Energy Technology Data Exchange (ETDEWEB)
Itoh, S.-I.; Ueda, Noriaki; Itoh, Kimitaka (National Inst. for Fusion Science, Nagoya (Japan))
1990-07-01
Scrape-off Layer (SOL) plasma and divertor plasma in Tokamaks were numerically analyzed using a two-dimensional time-dependent transport code (UEDA code). Plasma transport in the SOL and the divertor region was studied for given particle and heat sources from the main plasma. A scaling study of the density, the temperature and their fall-off lengths was carried out for the JFT-2M Tokamak. The results show the inter-relations between the divertor plasma parameters and core plasma confinement. The operational conditions of the core necessary to guarantee the divertor performance are discussed. (author).
4. Atomically thin two-dimensional materials as hole extraction layers in organolead halide perovskite photovoltaic cells
Science.gov (United States)
Kim, Yu Geun; Kwon, Ki Chang; Le, Quyet Van; Hong, Kootak; Jang, Ho Won; Kim, Soo Young
2016-07-01
Atomically thin two-dimensional materials such as MoS2, WS2, and graphene oxide (GO) are used as hole extraction layers (HEL) in organolead halide perovskites solar cells (PSCs) instead of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) HEL. MoS2 and WS2 layers with a polycrystalline structure were synthesized by a chemical deposition method using a uniformly spin-coated (NH4)MoS4 and (NH4)WS4 precursor solution. GO was synthesized by the oxidation of natural graphite powder using Hummers' method. The work functions of MoS2, WS2, and GO are measured to be 5.0, 4.95, and 5.1 eV, respectively. The X-ray diffraction spectrum indicated that the synthesized perovskite material is CH3NH3PbI3-xClx. The PSCs with the p-n junction structure were fabricated based on the CH3NH3PbI3-xClx perovskite layer. The power conversion efficiencies of the MoS2, WS2, and GO-based PSCs were 9.53%, 8.02%, and 9.62%, respectively, which are comparable to those obtained from PEDOT:PSS-based devices (9.93%). These results suggest that two-dimensional materials such as MoS2, WS2, and GO can be promising candidates for the formation of HELs in the PSCs.
5. Piezoelectric two-dimensional nanosheets/anionic layer heterojunction for efficient direct current power generation
Science.gov (United States)
Kim, Kwon-Ho; Kumar, Brijesh; Lee, Keun Young; Park, Hyun-Kyu; Lee, Ju-Hyuck; Lee, Hyun Hwi; Jun, Hoin; Lee, Dongyun; Kim, Sang-Woo
2013-06-01
Direct current (DC) piezoelectric power generator is promising for the miniaturization of a power package and self-powering of nanorobots and body-implanted devices. Hence, we report the first use of two-dimensional (2D) zinc oxide (ZnO) nanostructure and an anionic nanoclay layer to generate piezoelectric DC output power. The device, made from 2D nanosheets and an anionic nanoclay layer heterojunction, has potential to be the smallest size power package, and could be used to charge wireless nano/micro scale systems without the use of rectifier circuits to convert alternating current into DC to store the generated power. The combined effect of buckling behaviour of the ZnO nanosheets, a self-formed anionic nanoclay layer, and coupled semiconducting and piezoelectric properties of ZnO nanosheets contributes to efficient DC power generation. The networked ZnO nanosheets proved to be structurally stable under huge external mechanical loads.
6. Piezoelectric two-dimensional nanosheets/anionic layer heterojunction for efficient direct current power generation.
Science.gov (United States)
Kim, Kwon-Ho; Kumar, Brijesh; Lee, Keun Young; Park, Hyun-Kyu; Lee, Ju-Hyuck; Lee, Hyun Hwi; Jun, Hoin; Lee, Dongyun; Kim, Sang-Woo
2013-01-01
Direct current (DC) piezoelectric power generator is promising for the miniaturization of a power package and self-powering of nanorobots and body-implanted devices. Hence, we report the first use of two-dimensional (2D) zinc oxide (ZnO) nanostructure and an anionic nanoclay layer to generate piezoelectric DC output power. The device, made from 2D nanosheets and an anionic nanoclay layer heterojunction, has potential to be the smallest size power package, and could be used to charge wireless nano/micro scale systems without the use of rectifier circuits to convert alternating current into DC to store the generated power. The combined effect of buckling behaviour of the ZnO nanosheets, a self-formed anionic nanoclay layer, and coupled semiconducting and piezoelectric properties of ZnO nanosheets contributes to efficient DC power generation. The networked ZnO nanosheets proved to be structurally stable under huge external mechanical loads.
7. Spectroscopic studies of the electronic properties of regularly arrayed two-dimensional protein layers
Energy Technology Data Exchange (ETDEWEB)
Vyalikh, D V [Institute of Solid State Physics, Dresden University of Technology, D-01062 Dresden (Germany); Kirchner, A [BioNanotechnology and Structure Formation Group, Max Bergmann Centre of Biomaterials, Dresden University of Technology, D-01062 Dresden (Germany); Kade, A [Institute of Solid State Physics, Dresden University of Technology, D-01062 Dresden (Germany); Danzenbaecher, S [Institute of Solid State Physics, Dresden University of Technology, D-01062 Dresden (Germany); Dedkov, Yu S [Institute of Solid State Physics, Dresden University of Technology, D-01062 Dresden (Germany); Mertig, M [BioNanotechnology and Structure Formation Group, Max Bergmann Centre of Biomaterials, Dresden University of Technology, D-01062 Dresden (Germany); Molodtsov, S L [Institute of Solid State Physics, Dresden University of Technology, D-01062 Dresden (Germany)
2006-04-05
Photoemission (PE) and near-edge x-ray absorption fine structure (NEXAFS) spectroscopy were applied to characterize electronic properties of the regular two-dimensional bacterial surface protein layer (S layer) of Bacillus sphaericus NCTC 9602, which is widely used as a protein template for the bottom-up fabrication of advanced metallic and hybrid nanostructures. PE and NEXAFS at the C 1s, O 1s, and N 1s core levels show similar chemical states for each oxygen atom and also for each nitrogen atom, while carbon atoms exhibit a range of chemical environments in different functional groups of the amino acids. A series of characteristic NEXAFS peaks were assigned to particular molecular orbitals of the amino acids by applying a phenomenological building-block model. It was found that the {pi} clouds of aromatic rings make the main contribution to both the lowest unoccupied and highest occupied molecular orbitals. The two-dimensional protein crystal shows a semiconductor-like behaviour with a gap value of {approx}3.0 eV and the Fermi energy close to the bottom of the LUMO.
8. Heterostructures based on two-dimensional layered materials and their potential applications
KAUST Repository
Li, Ming-yang
2015-12-04
The development of two-dimensional (2D) layered materials is driven by fundamental interest and their potential applications. Atomically thin 2D materials provide a wide range of basic building blocks with unique electrical, optical, and thermal properties which do not exist in their bulk counterparts. The van der Waals interlayer interaction enables the possibility to exfoliate and reassemble different 2D materials into arbitrarily and vertically stacked heterostructures. Recently developed vapor phase growth of 2D materials further paves the way of directly synthesizing vertical and lateral heterojunctions. This review provides insights into the layered 2D heterostructures, with a concise introduction to preparative approaches for 2D materials and heterostructures. These unique 2D heterostructures have abundant implications for many potential applications.
9. Two-dimensional coupled fluid and electrodynamic calculations for a MHD DCW channel with slag layers
Science.gov (United States)
Liu, B. L.
1982-01-01
A fully coupled, two dimensional numerical method of modeling linear, coal-fired MHD generators is developed for the case of a plasma flow bounded by a slag layer on the channel walls. The governing partial differential equations for the plasma flow, slag layer and electrodynamics are presented and their coupling discussed. An iterative, numerical procedure employing non-uniform computational meshes and appropriate tridiagonal matrix solution schemes for the equations is presented. The method permits the investigation of the mutual plasma flow-slag layer development for prescribed wall temperatures, electrode geometry, slag properties and channel loading. In particular, the slag layer-plasma interface properties which require prior specification in an uncoupled analysis comprise part of the solution in the present approach. Results are presented for a short diagonally connected generator channel and include contour plots of the electric potential and current stream function as well as transverse and axial profiles of pertinent plasma properties. The results indicate that a thin electrode slag layer can be maintained in the presence of reasonable current density levels.
10. Tuning Slow Magnetic Relaxation in a Two-Dimensional Dysprosium Layer Compound through Guest Molecules.
Science.gov (United States)
Chen, Qi; Li, Jian; Meng, Yin-Shan; Sun, Hao-Ling; Zhang, Yi-Quan; Sun, Jun-Liang; Gao, Song
2016-08-15
A novel two-dimensional dysprosium(III) complex, [Dy(L)(CH3COO)]·0.5DMF·H2O·2CH3OH (1), has been successfully synthesized from a new pyridine-N-oxide (PNO)-containing ligand, namely, N'-(2-hydroxy-3-methoxybenzylidene)pyridine-N-oxidecarbohydrazide (H2L). Single-crystal X-ray diffraction studies reveal that complex 1 is composed of a dinuclear dysprosium subunit, which is further extended by the PNO part of the ligand to form a two-dimensional layer. Magnetic studies indicate that complex 1 shows well-defined temperature- and frequency-dependent signals under a zero direct-current (dc) field, typical of slow magnetic relaxation with an effective energy barrier Ueff of 33.6 K under a zero dc field. Interestingly, powder X-ray diffraction and thermogravimetric analysis reveal that compound 1 undergoes a reversible phase transition that is induced by the desorption and absorption of methanol and water molecules. Moreover, the desolvated sample [Dy(L)(CH3COO)]·0.5DMF (1a) also exhibits slow magnetic relaxation but with a higher anisotropic barrier of 42.0 K, indicating the tuning effect of solvent molecules on slow magnetic relaxation.
11. An investigation of two dimensional parallel and non-parallel steady mixing layers
Energy Technology Data Exchange (ETDEWEB)
Shabani, A. [Azad Islamic Univ., Faculty of Mechanical Engineering, School of Engineering, Research and Science Inst., Tehran (Iran, Islamic Republic of)]. E-mail: [email protected]; Basirat Tabrizi, H. [Amirkabir Univ. of Technology, Dept. of Mechanical Engineering, Tehran (Iran, Islamic Republic of)
2004-07-01
A CFD code was generated to simulate the steady state behavior of two dimensional, parallel and nonparallel merging mixing layers. For the free stream velocity ratios of 0.7 and 0.9, the effect of the merging angle of free stream velocities of between 0.0 to 18.0 degrees on the mixing zone's velocity distribution, and on the physical spreading of the turbulent domain was numerically simulated and studied. The results were in good agreement with the available theoretical and experimental results, and indicated that increasing the angle of merging of the two free streams, or increasing their associated free stream velocity ratios increases the spatial growth rate and decreases the turbulent development distance. (author)
12. New hybrid lead iodides: From one-dimensional chain to two-dimensional layered perovskite structure
Energy Technology Data Exchange (ETDEWEB)
Xiong, Kecai; Liu, Wei [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States); Teat, Simon J. [Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); An, Litao; Wang, Hao; Emge, Thomas J. [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States); Li, Jing, E-mail: [email protected] [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States)
2015-10-15
Two new hybrid lead halides (H{sub 2}BDA)[PbI{sub 4}] (1) (H{sub 2}BDA=1,4-butanediammonium dication) and (HNPEIM)[PbI{sub 3}] (2) (HNPEIM=N-phenyl-ethanimidamidine cation) have been synthesized and structurally characterized. X-ray diffraction analyses reveal that compound 1 features a two-dimensional corner-sharing perovskite layer whereas compound 2 contains one-dimensional edge-sharing double chains. The N-phenyl-ethanimidamidine cation within compound 2 was generated in-situ under solvothermal conditions. The optical absorption spectra collected at room temperature suggest that both compounds are semiconductors having direct band gaps, with estimated values of 2.64 and 2.73 eV for 1 and 2, respectively. Results from the density functional theory (DFT) calculations are consistent with the experimental data. Density of states (DOS) analysis reveals that in both compounds 1 and 2, the energy states in the valence band maximum region are iodine 5p atomic orbitals with a small contribution from lead 6s, while in the region of conduction band minimum, the major contributions are from the inorganic (Pb 6p atomic orbitals) and organic components (C and N 2p atomic orbitals) in compound 1 and 2, respectively. - Graphical abstract: Two new hybrid lead halides built on one-dimensional edge-sharing double chains and two-dimensional corner-sharing perovskite layers are synthesized and their structural and electronic properties are analyzed. - Highlights: • Two new hybrid lead iodides are designed, synthesized, and characterized. • They are closely related to, but different from, perovskite structures. • The electronic properties of both compounds are analyzed by DFT calculations.
13. Thickness Considerations of Two-Dimensional Layered Semiconductors for Transistor Applications
Science.gov (United States)
Zhang, Youwei; Li, Hui; Wang, Haomin; Xie, Hong; Liu, Ran; Zhang, Shi-Li; Qiu, Zhi-Jun
2016-07-01
Layered two-dimensional semiconductors have attracted tremendous attention owing to their demonstrated excellent transistor switching characteristics with a large ratio of on-state to off-state current, Ion/Ioff. However, the depletion-mode nature of the transistors sets a limit on the thickness of the layered semiconductor films primarily determined by a given Ion/Ioff as an acceptable specification. Identifying the optimum thickness range is of significance for material synthesis and device fabrication. Here, we systematically investigate the thickness-dependent switching behavior of transistors with a wide thickness range of multilayer-MoS2 films. A difference in Ion/Ioff by several orders of magnitude is observed when the film thickness, t, approaches a critical depletion width. The decrease in Ion/Ioff is exponential for t between 20 nm and 100 nm, by a factor of 10 for each additional 10 nm. For t larger than 100 nm, Ion/Ioff approaches unity. Simulation using technical computer-aided tools established for silicon technology faithfully reproduces the experimentally determined scaling behavior of Ion/Ioff with t. This excellent agreement confirms that multilayer-MoS2 films can be approximated as a homogeneous semiconductor with high surface conductivity that tends to deteriorate Ion/Ioff. Our findings are helpful in guiding material synthesis and designing advanced field-effect transistors based on the layered semiconductors.
14. Interfacial engineering of two-dimensional nano-structured materials by atomic layer deposition
Science.gov (United States)
Zhuiykov, Serge; Kawaguchi, Toshikazu; Hai, Zhenyin; Karbalaei Akbari, Mohammad; Heynderickx, Philippe M.
2017-01-01
Atomic Layer Deposition (ALD) is an enabling technology which provides coating and material features with significant advantages compared to other existing techniques for depositing precise nanometer-thin two-dimensional (2D) nanostructures. It is a cyclic process which relies on sequential self-terminating reactions between gas phase precursor molecules and a solid surface. ALD is especially advantageous when the film quality or thickness is critical, offering ultra-high aspect ratios. ALD provides digital thickness control to the atomic level by depositing film one atomic layer at a time, as well as pinhole-free films even over a very large and complex areas. Digital control extends to sandwiches, hetero-structures, nano-laminates, metal oxides, graded index layers and doping, and it is perfect for conformal coating and challenging 2D electrodes for various functional devices. The technique's capabilities are presented on the example of ALD-developed ultra-thin 2D tungsten oxide (WO3) over the large area of standard 4" Si substrates. The discussed advantages of ALD enable and endorse the employment of this technique for the development of hetero-nanostructure 2D semiconductors with unique properties.
15. Properties of two-dimensional insulators: A DFT study of bimetallic oxide CrW2O9 clusters adsorption on MgO ultrathin films
Science.gov (United States)
Zhu, Jia; Zhang, Hui; Zhao, Ling; Xiong, Wei; Huang, Xin; Wang, Bin; Zhang, Yongfan
2016-08-01
Periodic density functional theory calculations have been performed to study the electronic properties of bimetallic oxide CrW2O9 clusters adsorbed on MgO/Ag(001) ultrathin films (activities with respect to that of pure W3O9 clusters. As a consequence, present results reveal that the adsorption of bimetallic oxide CrW2O9 clusters on the MgO/Ag(001) ultrathin films provide a new perspective to tune and modify the properties and chemical reactivity of bimetallic oxide adsorbates as a function of the thickness of the oxide films.
16. Hexagonal boron nitride: Ubiquitous layered dielectric for two-dimensional electronics
Science.gov (United States)
Jain, Nikhil
Hexagonal boron nitride (h-BN), a layer-structured dielectric with very similar crystalline lattice to that of graphene, has been studied as a ubiquitous dielectric for two-dimensional electronics. While 2D materials may lead to future platform for electronics, traditional thin-film dielectrics (e.g., various oxides) make highly invasive interface with graphene. Multiple key roles of h-BN in graphene electronics are explored in this thesis. 2D graphene/h-BN heterostructures are designed and implemented in diverse configurations in which h-BN is evaluated as a supporting substrate, a gate dielectric, a passivation layer, or an interposing barrier in "3D graphene" superlattice. First, CVD-grown graphene on h-BN substrate shows improved conductivity and resilience to thermally induced breakdown, as compared with graphene on SiO2, potentially useful for high-speed graphene devices and on-chip interconnects. h-BN is also explored as a gate dielectric for graphene field-effect transistor with 2D heterostructure design. The dielectric strength and tunneling behavior of h-BN are investigated, confirming its robust nature. Next, h-BN is studied as a passivation layer for graphene electronics. In addition to significant improvement in current density and breakdown threshold, fully encapsulated graphene exhibits minimal environmental sensitivity, a key benefit to 2D materials which have only surfaces. Lastly, reduction in interlayer carrier scattering is observed in a double-layered graphene setup with ultrathin h-BN multilayer as an interposing layer. The DFT simulation and Raman spectral analysis indicate reduction in interlayer scattering. The decoupling of the two graphene monolayers is further confirmed by electrical characterization, as compared with other referencing mono- and multilayer configurations. The heterostructure serves as the building element in "3D graphene", a versatile platform for future electronics.
17. Synthesis, characterization and application of two-dimensional layered metal hydroxides for environmental remediation purposes
Science.gov (United States)
Machingauta, Cleopas
Two-dimensional layered nano composites, which include layered double hydroxides (LDHs), hydroxy double salts (HDSs) and layered hydroxide salts (LHSs) are able to intercalate different molecular species within their gallery space. These materials have a tunable structural composition which has made them applicable as fire retardants, adsorbents, catalysts, catalyst support materials, and ion exchangers. Thermal treatment of these materials results in destruction of the layers and formation of mixed metal oxides (MMOs) and spinels. MMOs have the ability to adsorb anions from solution and may also regenerate layered structures through a phenomenon known as memory effect. Zinc-nickel hydroxy nitrate was used for the uptake of a series of halogenated acetates (HAs). HAs are pollutants introduced into water systems as by-products of water chlorination and pesticide degradation; their sequestration from water is thus crucial. Optimization of layered materials for controlled uptake requires an understanding of their ion-exchange kinetics and thermodynamics. Exchange kinetics of these anions was monitored using ex-situ PXRD, UV-vis, HPLC and FTIR. It was revealed that exchange rates and uptake efficiencies are related to electronic spatial extents and the charge on carboxyl-oxygen atoms. In addition, acetate and nitrate-based HDSs were used to explore how altering the hydroxide layer affects uptake of acetate/nitrate ions. Changing the metal identities affects the interaction of the anions with the layers. From FTIR, we observed that nitrates coordinate in a D3h and Cs/C 2v symmetry; the nitrates in D3h symmetry were easily exchangeable. Interlayer hydrogen bonding was also revealed to be dependent on metal identity. Substituting divalent cations with trivalent cations produces materials with a higher charge density than HDSs and LHSs. A comparison of the uptake efficiency of zinc-aluminum, zinc-gallium and zinc-nickel hydroxy nitrates was performed using trichloroacetic
18. Graphene-like two-dimensional layered nanomaterials: applications in biosensors and nanomedicine
Science.gov (United States)
Yang, Guohai; Zhu, Chengzhou; Du, Dan; Zhu, Junjie; Lin, Yuehe
2015-08-01
The development of nanotechnology provides promising opportunities for various important applications. The recent discovery of atomically-thick two-dimensional (2D) nanomaterials can offer manifold perspectives to construct versatile devices with high-performance to satisfy multiple requirements. Many studies directed at graphene have stimulated renewed interest on graphene-like 2D layered nanomaterials (GLNs). GLNs including boron nitride nanosheets, graphitic-carbon nitride nanosheets and transition metal dichalcogenides (e.g. MoS2 and WS2) have attracted significant interest in numerous research fields from physics and chemistry to biology and engineering, which has led to numerous interdisciplinary advances in nano science. Benefiting from the unique physical and chemical properties (e.g. strong mechanical strength, high surface area, unparalleled thermal conductivity, remarkable biocompatibility and ease of functionalization), these 2D layered nanomaterials have shown great potential in biochemistry and biomedicine. This review summarizes recent advances of GLNs in applications of biosensors and nanomedicine, including electrochemical biosensors, optical biosensors, bioimaging, drug delivery and cancer therapy. Current challenges and future perspectives in these rapidly developing areas are also outlined. It is expected that they will have great practical foundation in biomedical applications with future efforts.
19. Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time
Directory of Open Access Journals (Sweden)
Boričić Zoran
2009-01-01
Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
20. DISPLAY-2: a two-dimensional shallow layer model for dense gas dispersion including complex features.
Science.gov (United States)
Venetsanos, A G; Bartzis, J G; Würtz, J; Papailiou, D D
2003-04-25
A two-dimensional shallow layer model has been developed to predict dense gas dispersion, under realistic conditions, including complex features such as two-phase releases, obstacles and inclined ground. The model attempts to predict the time and space evolution of the cloud formed after a release of a two-phase pollutant into the atmosphere. The air-pollutant mixture is assumed ideal. The cloud evolution is described mathematically through the Cartesian, two-dimensional, shallow layer conservation equations for mixture mass, mixture momentum in two horizontal directions, total pollutant mass fraction (vapor and liquid) and mixture internal energy. Liquid mass fraction is obtained assuming phase equilibrium. Account is taken in the conservation equations for liquid slip and eventual liquid rainout through the ground. Entrainment of ambient air is modeled via an entrainment velocity model, which takes into account the effects of ground friction, ground heat transfer and relative motion between cloud and surrounding atmosphere. The model additionally accounts for thin obstacles effects in three ways. First a stepwise description of the obstacle is generated, following the grid cell faces, taking into account the corresponding area blockage. Then obstacle drag on the passing cloud is modeled by adding flow resistance terms in the momentum equations. Finally the effect of extra vorticity generation and entrainment enhancement behind obstacles is modeled by adding locally into the entrainment formula without obstacles, a characteristic velocity scale defined from the obstacle pressure drop and the local cloud height.The present model predictions have been compared against theoretical results for constant volume and constant flux gravity currents. It was found that deviations of the predicted cloud footprint area change with time from the theoretical were acceptably small, if one models the frictional forces between cloud and ambient air, neglecting the Richardson
1. Evaporation, Heat Transfer, and Velocity Distribution in Two-Dimensional and Rotationally Symmetrical Laminar Boundary-Layer Flow
Science.gov (United States)
Froessling, Nils
1958-01-01
The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
2. Point Defects in Two-Dimensional Layered Semiconductors: Physics and Its Applications
Science.gov (United States)
Suh, Joonki
Recent advances in material science and semiconductor processing have been achieved largely based on in-depth understanding, efficient management and advanced application of point defects in host semiconductors, thus finding the relevant techniques such as doping and defect engineering as a traditional scientific and technological solution. Meanwhile, two- dimensional (2D) layered semiconductors currently draw tremendous attentions due to industrial needs and their rich physics at the nanoscale; as we approach the end of critical device dimensions in silicon-based technology, ultra-thin semiconductors have the potential as next- generation channel materials, and new physics also emerges at such reduced dimensions where confinement of electrons, phonons, and other quasi-particles is significant. It is therefore rewarding and interesting to understand and redefine the impact of lattice defects by investigating their interactions with energy/charge carriers of the host matter. Potentially, the established understanding will provide unprecedented opportunities for realizing new functionalities and enhancing the performance of energy harvesting and optoelectronic devices. In this thesis, multiple novel 2D layered semiconductors, such as bismuth and transition- metal chalcogenides, are explored. Following an introduction of conventional effects induced by point defects in semiconductors, the related physics of electronically active amphoteric defects is revisited in greater details. This can elucidate the complication of a two-dimensional electron gas coexisting with the topological states on the surface of bismuth chalcogenides, recently suggested as topological insulators. Therefore, native point defects are still one of the keys to understand and exploit topological insulators. In addition to from a fundamental science point of view, the effects of point defects on the integrated thermal-electrical transport, as well as the entropy-transporting process in
3. Two-dimensional energy spectra in a high Reynolds number turbulent boundary layer
Science.gov (United States)
Chandran, Dileep; Baidya, Rio; Monty, Jason; Marusic, Ivan
2016-11-01
The current study measures the two-dimensional (2D) spectra of streamwise velocity component (u) in a high Reynolds number turbulent boundary layer for the first time. A 2D spectra shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). 2D spectra could be a better tool to analyse spectral scaling laws as it is devoid of energy aliasing errors that could be present in one-dimensional spectra. A novel method is used to calculate the 2D spectra from the 2D correlation of u which is obtained by measuring velocity time series at various spanwise locations using hot-wire anemometry. At low Reynolds number, the shape of the 2D spectra at a constant energy level shows λy √{ zλx } behaviour at larger scales which is in agreement with the literature. However, at high Reynolds number, it is observed that the square-root relationship gradually transforms into a linear relationship (λy λx) which could be caused by the large packets of eddies whose length grows proportionately to the growth of its width. Additionally, we will show that this linear relationship observed at high Reynolds number is consistent with attached eddy predictions. The authors gratefully acknowledge the support from the Australian Research Council.
4. Coupled two-dimensional edge plasma and neutral gas modeling of tokamak scrape-off-layers
Energy Technology Data Exchange (ETDEWEB)
Maingi, R. [North Carolina State Univ., Raleigh, NC (United States)
1992-08-01
The objective of this study is to devise a detailed description of the tokamak scrape-off-layer (SOL), which includes the best available models of both the plasma and neutral species and the strong coupling between the two in many SOL regimes. A good estimate of both particle flux and heat flux profiles at the limiter/divertor target plates is desired. Peak heat flux is one of the limiting factors in determining the survival probability of plasma-facing-components at high power levels. Plate particle flux affects the neutral flux to the pump, which determines the particle exhaust rate. A technique which couples a two-dimensional (2-D) plasma and a 2-D neutral transport code has been developed (coupled code technique), but this procedure requires large amounts of computer time. Relevant physics has been added to an existing two-neutral-species model which takes the SOL plasma/neutral coupling into account in a simple manner (molecular physics model), and this model is compared with the coupled code technique mentioned above. The molecular physics model is benchmarked against experimental data from a divertor tokamak (DIII-D), and a similar model (single-species model) is benchmarked against data from a pump-limiter tokamak (Tore Supra). The models are then used to examine two key issues: free-streaming-limits (ion energy conduction and momentum flux) and the effects of the non-orthogonal geometry of magnetic flux surfaces and target plates on edge plasma parameter profiles.
5. Epitaxial Growth of Two-Dimensional Layered Transition-Metal Dichalcogenides: Growth Mechanism, Controllability, and Scalability
KAUST Repository
Li, Henan
2017-07-06
Recently there have been many research breakthroughs in two-dimensional (2D) materials including graphene, boron nitride (h-BN), black phosphors (BPs), and transition-metal dichalcogenides (TMDCs). The unique electrical, optical, and thermal properties in 2D materials are associated with their strictly defined low dimensionalities. These materials provide a wide range of basic building blocks for next-generation electronics. The chemical vapor deposition (CVD) technique has shown great promise to generate high-quality TMDC layers with scalable size, controllable thickness, and excellent electronic properties suitable for both technological applications and fundamental sciences. The capability to precisely engineer 2D materials by chemical approaches has also given rise to fascinating new physics, which could lead to exciting new applications. In this Review, we introduce the latest development of TMDC synthesis by CVD approaches and provide further insight for the controllable and reliable synthesis of atomically thin TMDCs. Understanding of the vapor-phase growth mechanism of 2D TMDCs could benefit the formation of complicated heterostructures and novel artificial 2D lattices.
6. Direct-referencing Two-dimensional-array Digital Microfluidics Using Multi-layer Printed Circuit Board
Science.gov (United States)
Gong, Jian; Kim, Chang-Jin “CJ”
2008-01-01
Digital (i.e. droplet-based) microfluidics, by the electrowetting-on-dielectric (EWOD) mechanism, has shown great potential for a wide range of applications, such as lab-on-a-chip. While most reported EWOD chips use a series of electrode pads essentially in one-dimensional line pattern designed for specific tasks, the desired universal chips allowing user-reconfigurable paths would require the electrode pads in two-dimensional pattern. However, to electrically access the electrode pads independently, conductive lines need to be fabricated underneath the pads in multiple layers, raising a cost issue especially for disposable chip applications. In this article, we report the building of digital microfluidic plates based on a printed-circuit-board (PCB), in which multilayer electrical access lines were created inexpensively using mature PCB technology. However, due to its surface topography and roughness and resulting high resistance against droplet movement, as-fabricated PCB surfaces require unacceptably high (~500 V) voltages unless coated with or immersed in oil. Our goal is EWOD operations of aqueous droplets not only on oil-covered but also on dry surfaces. To meet varying levels of performances, three types of gradually complex post-PCB microfabrication processes are developed and evaluated. By introducing land-grid-array (LGA) sockets in the packaging, a scalable digital microfluidics system with reconfigurable and low-cost chip is also demonstrated. PMID:19234613
7. Two-dimensional point spread matrix of layered metal-dielectric imaging elements
CERN Document Server
Kotynski, Rafal; Krol, Karol; Panajotov, Krassimir
2010-01-01
We describe the change of the spatial distribution of the state of polarisation occurring during two-dimensional imaging through a multilayer and in particular through a layered metallic flat lens. Linear or circular polarisation of incident light is not preserved due to the difference in the amplitude transfer functions for the TM and TE polarisations. In effect, the transfer function and the point spread function that characterize 2D imaging through a multilayer both have a matrix form and cross-polarisation coupling is observed for spatially modulated beams with a linear or circular incident polarisation. The point spread function in a matrix form is used to characterise the resolution of the superlens for different polarisation states. We demonstrate how the 2D PSF may be used to design a simple diffractive nanoelement consisting of two radial slits. The structure assures the separation of non-diffracting radial beams originating from two slits in the mask and exhibits an interesting property of a backwar...
8. Movement dependence and layer specificity of entorhinal phase precession in two-dimensional environments.
Directory of Open Access Journals (Sweden)
Eric Reifenstein
Full Text Available As a rat moves, grid cells in its entorhinal cortex (EC discharge at multiple locations of the external world, and the firing fields of each grid cell span a hexagonal lattice. For movements on linear tracks, spikes tend to occur at successively earlier phases of the theta-band filtered local field potential during the traversal of a firing field - a phenomenon termed phase precession. The complex movement patterns observed in two-dimensional (2D open-field environments may fundamentally alter phase precession. To study this question at the behaviorally relevant single-run level, we analyzed EC spike patterns as a function of the distance traveled by the rat along each trajectory. This analysis revealed that cells across all EC layers fire spikes that phase-precess; indeed, the rate and extent of phase precession were the same, only the correlation between spike phase and path length was weaker in EC layer III. Both slope and correlation of phase precession were surprisingly similar on linear tracks and in 2D open-field environments despite strong differences in the movement statistics, including running speed. While the phase-precession slope did not correlate with the average running speed, it did depend on specific properties of the animal's path. The longer a curving path through a grid-field in a 2D environment, the shallower was the rate of phase precession, while runs that grazed a grid field tangentially led to a steeper phase-precession slope than runs through the field center. Oscillatory interference models for grid cells do not reproduce the observed phenomena.
9. The quality of the joint between alloy steel and unalloyed cast steel in bimetallic layered castings
Directory of Open Access Journals (Sweden)
T. Wróbel
2012-01-01
Full Text Available In paper is presented technology of bimetallic layered castings based on founding method of layer coating directly in cast process so-called method of mould cavity preparation. Prepared castings consist two fundamental parts i.e. bearing part and working part (layer. The bearing part of bimetallic layered casting is typical foundry material i.e. ferritic-pearlitic unalloyed cast steel, whereas working part (layer is plate of austenitic alloy steel sort X2CrNi 18-9. The ratio of thickness between bearing and working part is 8:1. The aim of paper was assessed the quality of the joint between bearing and working part in dependence of pouring temperature and carbon concentration in cast steel. The quality of the joint in bimetallic layered castings was evaluated on the basis of ultrasonic non-destructive testing, structure and microhardness researches.
10. Stabilized lithium-ion battery anode performance by calcium-bridging of two dimensional siloxene layers.
Science.gov (United States)
Imagawa, Haruo; Itahara, Hiroshi
2017-03-14
A Ca-bridged siloxene (Ca-siloxene) composed of two-dimensional siloxene planes with Ca bridging was synthesized via a solid state metathesis reaction using TaCl5 to extract Ca from CaSi2. Three different Ca-siloxenes synthesized at Cl2/Ca molar ratios of 0.25, 1.25 and 2.5 (CS0.25, CS1.25 and CS2.5, respectively) were fabricated and investigated as anode active materials for lithium-ion batteries. Both secondary and primary Ca-siloxene particles, which serve to increase the contact interfaces with conductive materials and to generate accessible sites for lithium ions, respectively, were found to become smaller and to have increased pore volumes as the Cl2/Ca molar ratio was increased. These Ca-siloxenes exhibited stable charge/discharge performance as anode materials, with 69-99% capacity retention after 50 charge/discharge cycles (compared with 36% retention for a conventional Kautsky-type siloxene). The charge capacity also increased with increases in the Cl2/Ca molar ratio, such that the CS2.5 showed the highest capacity after 50 charge/discharge cycles. This may reflect the formation of Si6Li6 rather than SiLi4.4 and suggests the maintenance of layered Si planes for large capacity retention after charge/discharge cycling. The increase of contact interfaces between acetylene black (as a conductive material) and Ca-siloxenes was found to effectively increase the lithium-ion capacity of Ca-siloxene during high rate charge/discharge cycling.
11. Exciton Migration and Amplified Quenching on Two-Dimensional Metal–Organic Layers
Energy Technology Data Exchange (ETDEWEB)
Cao, Lingyun; Lin, Zekai; Shi, Wenjie; Wang, Zi; Zhang, Cankun; Hu, Xuefu; Wang, Cheng; Lin, Wenbin
2017-05-10
The dimensionality dependency of resonance energy transfer is of great interest due to its importance in understanding energy transfer on cell membranes and in low-dimension nanostructures. Light harvesting two-dimensional metal–organic layers (2D-MOLs) and three-dimensional metal–organic frameworks (3D-MOFs) provide comparative models to study such dimensionality dependence with molecular accuracy. Here we report the construction of 2D-MOLs and 3D-MOFs from a donor ligand 4,4',4''-(benzene-1,3,5-triyl-tris(ethyne-2,1-diyl))tribenzoate (BTE) and a doped acceptor ligand 3,3',3''-nitro-4,4',4''-(benzene-1,3,5-triyl-tris(ethyne-2,1-diyl))tribenzoate (BTE-NO2). These 2D-MOLs and 3D-MOFs are connected by similar hafnium clusters, with key differences in the topology and dimensionality of the metal–ligand connection. Energy transfer from donors to acceptors through the 2D-MOL or 3D-MOF skeletons is revealed by measuring and modeling the fluorescence quenching of the donors. We found that energy transfer in 3D-MOFs is more efficient than that in 2D-MOLs, but excitons on 2D-MOLs are more accessible to external quenchers as compared with those in 3D-MOFs. These results not only provide support to theoretical analysis of energy transfer in low dimensions, but also present opportunities to use efficient exciton migration in 2D materials for light-harvesting and fluorescence sensing.
12. Toward atomically-precise synthesis of supported bimetallic nanoparticles using atomic layer deposition.
Science.gov (United States)
Lu, Junling; Low, Ke-Bin; Lei, Yu; Libera, Joseph A; Nicholls, Alan; Stair, Peter C; Elam, Jeffrey W
2014-01-01
Multi-metallic nanoparticles constitute a new class of materials offering the opportunity to tune the properties via the composition, atomic ordering and size. In particular, supported bimetallic nanoparticles have generated intense interest in catalysis and electrocatalysis. However, traditional synthesis methods often lack precise control, yielding a mixture of monometallic and bimetallic particles with various compositions. Here we report a general strategy for synthesizing supported bimetallic nanoparticles by atomic layer deposition, where monometallic nanoparticle formation is avoided by selectively growing the secondary metal on the primary metal nanoparticle but not on the support; meanwhile, the size, composition and structure of the bimetallic nanoparticles are precisely controlled by tailoring the precursor pulse sequence. Such exquisite control is clearly demonstrated through in situ Fourier transform infrared spectroscopy of CO chemisorption by mapping the gradual atomic-scale evolution in the surface composition, and further confirmed using aberration-corrected scanning transmission electron microscopy.
13. How two-dimensional brick layer J-aggregates differ from linear ones: excitonic properties and line broadening mechanisms
CERN Document Server
Dijkstra, Arend G; Knoester, Jasper; Nelson, Keith A; Cao, Jianshu
2016-01-01
We study the excitonic coupling and homogeneous spectral line width of brick layer J-aggregate films. We begin by analysing the structural information revealed by the two-exciton states probed in two-dimensional spectra. Our first main result is that the relation between the excitonic couplings and the spectral shift in a two-dimensional structure is different (larger shift for the same nearest neighbour coupling) from that in a one-dimensional structure, which leads to an estimation of dipolar coupling in two-dimensional lattices. We next investigate the mechanisms of homogeneous broadening - population relaxation and pure dephasing - and evaluate their relative importance in linear and two-dimensional aggregates. Our second main result is that pure dephasing dominates the line width in two-dimensional systems up to a crossover temperature, which explains the linear temperature dependence of the homogeneous line width. This is directly related to the decreased density of states at the band edge when compared...
14. Two-dimensional coupled electron-hole layers in high magnetic fields
NARCIS (Netherlands)
Parlangeli, Andrea
2000-01-01
In solids, it is nowadays possible to create structures in which electrons are confined into a two-dimensional (2D) plane. The physics of a 2D electron gas (2DEG) has proved to be very rich, in particular in the presence of a transverse magnetic field. The Quantum Hall Effect, i.e. the quantization
15. Hidden phase in a two-dimensional Sn layer stabilized by modulation hole doping
Science.gov (United States)
Ming, Fangfei; Mulugeta, Daniel; Tu, Weisong; Smith, Tyler S.; Vilmercati, Paolo; Lee, Geunseop; Huang, Ying-Tzu; Diehl, Renee D.; Snijders, Paul C.; Weitering, Hanno H.
2017-03-01
Semiconductor surfaces and ultrathin interfaces exhibit an interesting variety of two-dimensional quantum matter phases, such as charge density waves, spin density waves and superconducting condensates. Yet, the electronic properties of these broken symmetry phases are extremely difficult to control due to the inherent difficulty of doping a strictly two-dimensional material without introducing chemical disorder. Here we successfully exploit a modulation doping scheme to uncover, in conjunction with a scanning tunnelling microscope tip-assist, a hidden equilibrium phase in a hole-doped bilayer of Sn on Si(111). This new phase is intrinsically phase separated into insulating domains with polar and nonpolar symmetries. Its formation involves a spontaneous symmetry breaking process that appears to be electronically driven, notwithstanding the lack of metallicity in this system. This modulation doping approach allows access to novel phases of matter, promising new avenues for exploring competing quantum matter phases on a silicon platform.
16. On t-local solvability of inverse scattering problems in two-dimensional layered media
Science.gov (United States)
Baev, A. V.
2015-06-01
The solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form of an energy conservation law. It is shown that the inverse problems are solvable only in the class of potentials for which the stationary Navier-Stokes equation is solvable.
17. Numerical Investigation on Two-dimensional Boundary Layer Flow with Transition
Institute of Scientific and Technical Information of China (English)
Yong Zhao; Tianlin Wang; Zhi Zong
2014-01-01
As a basic problem in many engineering applications, transition from laminar to turbulence still remains a difficult problem in computational fluid dynamics (CFD). A numerical study of one transitional flow in two-dimensional is conducted by Reynolds averaged numerical simulation (RANS) in this paper. Turbulence model plays a significant role in the complex flows’ simulation, and four advanced turbulence models are evaluated. Numerical solution of frictional resistance coefficient is compared with the measured one in the transitional zone, which indicates that Wilcox (2006) k-ω model with correction is the best candidate. Comparisons of numerical and analytical solutions for dimensionless velocity show that averaged streamwise dimensionless velocity profiles correct the shape rapidly in transitional region. Furthermore, turbulence quantities such as turbulence kinetic energy, eddy viscosity, and Reynolds stress are also studied, which are helpful to learn the transition’s behavior.
18. A humidity sensitive two-dimensional tunable amorphous photonic structure in the outer layer of bivalve ligament from Sunset Siliqua
Energy Technology Data Exchange (ETDEWEB)
Zhang, Weigang, E-mail: [email protected] [College of Materials and Chemical Engineering, Chuzhou University, Chuzhou 239000 (China); Zhang, Gangsheng [College of Material Science and Technology, Guangxi University, Nanning 530004 (China)
2015-07-01
A humidity sensitive two-dimensional tunable amorphous photonic structure (2D TAPS) in the outer layer of bivalve ligament from Sunset Siliqua (OLLS) was reported in this paper. The structural color and microstructure of OLLS were investigated by reflection spectra and scanning electron microscopy, respectively. The results indicate that the reflection peak wavelength of the wet OLLS blue-shifts from 454 nm to 392 nm with the increasing of air drying time from 0 to 40 min, while the reflectivity decreases gradually and vanishes at last, relevant color changes from blue to black background color. The structural color in the OLLS is produced by a two-dimensional amorphous photonic structure consisting of aligned protein fibers, in which the diameter of protein fiber and the inter-fiber spacing are 101 ± 12 nm. Water can reversibly tune the reflection peak wavelength and reflectivity of this photonic structure, and the regulation achieved through dynamically tuning the interaction between inter-fiber spacing and average refractive index. - Highlights: • A humidity sensitive two-dimensional tunable amorphous photonic structure • Water can reversibly tune the reflection peak wavelength and reflectivity of this photonic structure. • This photonic structure may yield very useful template for artificial structures.
19. Nonlinear chemoconvection in the methylene-blue-glucose system: Two-dimensional shallow layers
Science.gov (United States)
Pons, A. J.; Batiste, O.; Bees, M. A.
2008-07-01
Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue-glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.
20. Evidence of molecular hydrogen trapped in two-dimensional layered titanium carbide-based MXene
Science.gov (United States)
Osti, Naresh C.; Naguib, Michael; Tyagi, Madhusudan; Gogotsi, Yury; Kolesnikov, Alexander I.; Mamontov, Eugene
2017-07-01
Two-dimensional transition metal carbides and nitrides (MXenes) are one of the largest and fastest growing families of materials. The presence of molecular hydrogen at ambient conditions in a MXene (T i3C2Tx , where Tx represents a surface terminating species, including O, OH, and F) material is revealed here by inelastic and elastic neutron scatterings. The inelastic neutron-scattering spectrum measured at 5 K shows a peak at 14.6 meV, presenting a clear indication of the presence of parahydrogen in the MXene synthesized using 48 % hydrofluoric acid and annealed at 110 ∘C in vacuum prior to the measurement. An increase in the measurement temperature gradually reduces the peak intensity and increases the peak width due to the mobility of the molecular hydrogen in confinement. The presence of molecular hydrogen is confirmed further from the observed elastic intensity drop in a fixed energy-window scan of elastic intensity measurements in the temperature range of 10-35 K. Using milder etching conditions, ion intercalation, or an increase in the annealing temperature all result in the absence of the trapped hydrogen molecules in MXene. The results of this paper can guide the development of MXene materials with desired properties and improve our understanding of the behavior of MXenes in applications ranging from supercapacitors to hydrogen evolution reaction catalysis and hydrogen storage.
1. Two-Dimensional Atomic-Layered Alloy Junctions for High-Performance Wearable Chemical Sensor.
Science.gov (United States)
Cho, Byungjin; Kim, Ah Ra; Kim, Dong Jae; Chung, Hee-Suk; Choi, Sun Young; Kwon, Jung-Dae; Park, Sang Won; Kim, Yonghun; Lee, Byoung Hun; Lee, Kyu Hwan; Kim, Dong-Ho; Nam, Jaewook; Hahm, Myung Gwan
2016-08-03
We first report that two-dimensional (2D) metal (NbSe2)-semiconductor (WSe2)-based flexible, wearable, and launderable gas sensors can be prepared through simple one-step chemical vapor deposition of prepatterned WO3 and Nb2O5. Compared to a control device with a Au/WSe2 junction, gas-sensing performance of the 2D NbSe2/WSe2 device was significantly enhanced, which might have resulted from the formation of a NbxW1-xSe2 transition alloy junction lowering the Schottky barrier height. This would make it easier to collect charges of channels induced by molecule adsorption, improving gas response characteristics toward chemical species including NO2 and NH3. 2D NbSe2/WSe2 devices on a flexible substrate provide gas-sensing properties with excellent durability under harsh bending. Furthermore, the device stitched on a T-shirt still performed well even after conventional cleaning with a laundry machine, enabling wearable and launderable chemical sensors. These results could pave a road toward futuristic gas-sensing platforms based on only 2D materials.
2. Crystalline-crystalline phase transformation in two-dimensional In2Se3 thin layers.
Science.gov (United States)
Tao, Xin; Gu, Yi
2013-08-14
We report, for the first time, the fabrication of single-crystal In2Se3 thin layers using mechanical exfoliation and studies of crystalline-crystalline (α → β) phase transformations as well as the corresponding changes of the electrical properties in these thin layers. Particularly, using electron microscopy and correlative in situ micro-Raman and electrical measurements, we show that, in contrast to bulk single crystals, the β phase can persist in single-crystal thin layers at room temperature (RT). The single-crystal nature of the layers before and after the phase transition allows for unambiguous determination of changes in the electrical resistivity. Specifically, the β phase has an electrical resistivity about 1-2 orders of magnitude lower than the α phase. Furthermore, we find that the temperature of the α → β phase transformation increases by as much as 130 K with the layer thickness decreasing from ~87 nm to ~4 nm. These single-crystal thin layers are ideal for studying the scaling behavior of the phase transformations and associated changes of the electrical properties. For these In2Se3 thin layers, the accessibility of the β phase at RT, with distinct electrical properties than the α phase, provides the basis for multilevel phase-change memories in a single material system.
3. Normal range of myocardial layer-specific strain using two-dimensional speckle tracking echocardiography
Science.gov (United States)
Wu, Victor Chien-Chia; Otsuji, Yutaka; Takeuchi, Masaaki
2017-01-01
Background Newer 2D strain software has a potential to assess layer-specific strain. However, normal reference values for layer-specific strain have not been established. We aimed to establish the normal ranges of layer-specific longitudinal and circumferential strain (endocardial global longitudinal strain (GLS), transmural GLS, epicardial GLS, endocardial global circumferential strain (GCS), transmural GCS, and epicardial GCS). Methods and results We retrospectively analyzed longitudinal and circumferential strain parameters in 235 healthy subjects, with use of layer-specific 2D speckle tracking software (GE). The endocardial strain/epicardial strain (Endo/Epi) ratio was also measured to assess the strain gradient across the myocardium. The endocardial, transmural, and epicardial GLS values and the Endo/Epi ratio in the normal subjects were -23.1±2.3, -20.0±2.0, -17.6±1.9, and 1.31±0.07, respectively. The corresponding values of GCS were -28.5±3.0, -20.8±2.3, -15.3±2.0, and 1.88±0.17, respectively. The layer-specific global strain parameters exhibited no age dependency but did exhibit gender dependency except for endocardial GCS. A subgroup analysis revealed that basal and middle levels of endocardial LS was decreased in the middle and elderly aged group. However, apical endocardial LS was preserved even in the elderly subjects. Conclusions We proposed normal reference values for layer-specific strain based on both age and gender. This detailed strain analysis provides layer-oriented information with the potential to characterize abnormal findings in various cardiovascular diseases. PMID:28662186
4. Critical properties of XY model on two-dimensional layered magnetic films
Institute of Scientific and Technical Information of China (English)
Wang Yi; Liu Xiao-Yan; Sun Lei; Zhang Xing; Han Ru-Qi
2006-01-01
Using Monte Carlo simulations, we have investigated the classical XY model on triangular lattices of ultra-thin film structures with middle ferromagnetic layers sandwiched between two antiferromagnetic layers. The internal energy,the specific heat, the chirality and the chiral susceptibility are calculated in order to clarify phase transitions and critical phenomena. From the finite-size scaling analyses, the values of critical exponents are determined. In a range of interaction parameters, we find that the chirality steeply goes up as temperature increases in a temperature range;correspondingly the value of a critical exponent for this change is estimated.
5. Fundamental interactions of vortical structures with boundary layers in two-dimensional flows
DEFF Research Database (Denmark)
Coutsias, E.A.; Lynov, Jens-Peter
1991-01-01
in the vorticity-stream function representation for bounded geometries. Fundamental processes connected to vorticity detachment from the boundary layers caused by the proximity of vortical structures are described. These processes include enstrophy enhancement of the main flow during bursting events, and pinning...
6. Two-dimensional linear variation displacement discontinuity method for three-layered elastic media
CSIR Research Space (South Africa)
Shou, KJ
1999-09-01
Full Text Available bonded half-planes. A three-layered elastic region is obtained by superposing two sets of bonded half-planes and subtracting one infinite plane. The advantages of this approach are: (1) it is not necessary to introduce elements at the interface, (2...
7. Boundary-Value Problem for Two-Dimensional Fluctuations in Boundary Layers
Science.gov (United States)
1985-07-01
inviscid analysis by P. Durbin "Distortion of turbulence by a constant-shear layer adjacent to a wall," private communication (1977). (l.2e) 2-D...vortices near a boundary," ~ of the Americ~ p ~ ~ , Volume 20, Number 9 (November 1975). 21. Hultgren, Lennart S. and Gustavsson, L. Hakan, " Algebraic
8. DESIGN OF TWO-DIMENSIONAL SUPERSONIC TURBINE ROTOR BLADES WITH BOUNDARY-LAYER CORRECTION
Science.gov (United States)
Goldman, L. J.
1994-01-01
A computer program has been developed for the design of supersonic rotor blades where losses are accounted for by correcting the ideal blade geometry for boundary layer displacement thickness. The ideal blade passage is designed by the method of characteristics and is based on establishing vortex flow within the passage. Boundary-layer parameters (displacement and momentum thicknesses) are calculated for the ideal passage, and the final blade geometry is obtained by adding the displacement thicknesses to the ideal nozzle coordinates. The boundary-layer parameters are also used to calculate the aftermixing conditions downstream of the rotor blades assuming the flow mixes to a uniform state. The computer program input consists essentially of the rotor inlet and outlet Mach numbers, upper- and lower-surface Mach numbers, inlet flow angle, specific heat ratio, and total flow conditions. The program gas properties are set up for air. Additional gases require changes to be made to the program. The computer output consists of the corrected rotor blade coordinates, the principal boundary-layer parameters, and the aftermixing conditions. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 7094. This program was developed in 1971.
9. A two-dimensional particle simulation of the magnetopause current layer
Energy Technology Data Exchange (ETDEWEB)
Berchem, J.; Okuda, H.
1988-11-01
We have developed a 2/1/2/-D (x, y, v/sub x/, v/sub y/, v/sub z/) electromagnetic code to study the formation and the stability of the magnetopause current layer. This code computes the trajectories of ion and electron particles in their self-consistently generated electromagnetic field and an externally imposed 2-D vacuum dipolar magnetic field. The results presented here are obtained for the simulation of the solar wind-magnetosphere interaction in the subsolar region of the equatorial plane. We observe the self-consistent establishment of a current layer resulting from both diamagnetic drift and E /times/ B drift due to the charge separation. The simulation results show that during the establishment of the current layer, its thickness is of the order of the hybrid gyroradius /rho//sub H/ = ..sqrt../rho//sub i//rho//sub e/ predicted by the Ferraro-Rosenbluth model. However, diagnostics indicate that the current sheet is subject to an instability which broadens the width of the current layer. Ripples with amplitudes of the order of the ion gyroradius appear at the interface between the field and the particles. These pertubations are observed both on the electrostatic field and on the compressional component of the magnetic field. This instability has a frequency of the order of the local ion cyclotron frequency. However, the modulation propagates in the same direction as the electron diamagnetic drift which indicates that the instability is not a classical gradient-driven instability, such as the lower hybrid or ion drift cyclotron instabilities. The nonlinear phase of the instability is characterized by the filamentation of the current layer which causes anomalous diffusion inside the central current sheet. 79 refs., 7 figs.
10. A novel two-dimensional MgB6 crystal: metal-layer stabilized boron kagome lattice.
Science.gov (United States)
Xie, Sheng-Yi; Li, Xian-Bin; Tian, Wei Quan; Chen, Nian-Ke; Wang, Yeliang; Zhang, Shengbai; Sun, Hong-Bo
2015-01-14
Based on first-principles calculations, we designed for the first time a boron-kagome-based two-dimensional MgB6 crystal, in which two boron kagome layers sandwich a triangular magnesium layer. The two-dimensional lattice is metallic with several bands across the Fermi level, and among them a Dirac point appears at the K point of the first Brillouin zone. This metal-stabilized boron kagome system displays electron-phonon coupling, with a superconductivity critical transition temperature of 4.7 K, and thus it is another possible superconducting Mg-B compound besides MgB2. Furthermore, the proposed 2D MgB6 can also be used for hydrogen storage after decoration with Ca. Up to five H2 molecules can be attracted by one Ca with an average binding energy of 0.225 eV. The unique properties of 2D MgB6 will spur broad interest in nanoscience and technology.
11. Critical field of two-dimensional superconducting Sn1-x/Six bimetallic composite cluster assembled films with energetic cluster impact deposition
Science.gov (United States)
Kurokawa, Yuichiro; Hihara, Takehiko; Ichinose, Ikuo
2013-05-01
Sn1-x/Six cluster assembled films have been prepared by an energetic cluster impact deposition using a plasma-gas-condensation cluster beam deposition apparatus. Transmission electron microscope images indicated that individual clusters have composite morphologies, where Sn and Si were separated from each other. The superconducting critical magnetic fields, Hc, of Sn1-x/Six cluster assembled films were measured and found to be much higher than the critical magnetic field of the bulk Sn. We estimated the Hc values by using a theory of the superconducting thin film. The estimated values are in good agreement with the experiments, indicating that the Sn1-x/Six cluster assembled films can be regarded as a two-dimensional system although thickness, t, of Sn1-x/Six cluster assembled films (t ≈ 1000 nm) is thicker than conventional superconducting thin film (t < 100 nm).
12. Emerging Energy Applications of Two-Dimensional Layered Transition Metal Dichalcogenides
KAUST Repository
Li, Henan
2015-10-31
Transition metal dichalcogenides (TMDCs) have attracted significant attention for their great potential in nano energy. TMDC layered materials represent a diverse and largely untapped source of 2D systems. High-quality TMDC layers with an appropriate size, variable thickness, superior electronic and optical properties can be produced by the exfoliation or vapour phase deposition method. Semiconducting TMDC monolayers have been demonstrated feasible for various energy related applications, where their electronic properties and uniquely high surface areas offer opportunities for various applications such as nano generators, green electronics, electrocatalytic hydrogen generation and energy storage. In this review, we start from the structure, properties and preparation, followed by detailed discussions on the development of TMDC-based nano energy applications. Graphical abstract The structure characterizations and preparative methods of 2D TMDCs have obtained significant progresses. Their recent advances for nano energy generation, solar harvesting, conversion and storage, and green electronics are reviewed.
13. Dense Carbon Monoxide to 160 GPa: Stepwise Polymerization to Two-Dimensional Layered Solid
Energy Technology Data Exchange (ETDEWEB)
Ryu, Young-Jay; Kim, Minseob; Lim, Jinhyuk; Dias, Ranga; Klug, Dennis; Yoo, Choong-Shik
2016-11-14
Carbon monoxide (CO) is the first molecular system found to transform into a nonmolecular “polymeric” solid above 5.5 GPa, yet been studied beyond 10 GPa. Here, we show a series of pressure-induced phase transformations in CO to 160 GPa: from a molecular solid to a highly colored, low-density polymeric phase I to translucent, high-density phase II to transparent, layered phase III. The properties of these phases are consistent with those expected from recently predicted 1D P21/m, 3D I212121, and 2D Cmcm structures, respectively. Thus, the present results advocate a stepwise polymerization of CO triple bonds to ultimately a 2D singly bonded layer structure with an enhanced ionic character.
14. Bio-inspired two-dimensional nanofluidic generators based on a layered graphene hydrogel membrane.
Science.gov (United States)
Guo, Wei; Cheng, Chi; Wu, Yanzhe; Jiang, Yanan; Gao, Jun; Li, Dan; Jiang, Lei
2013-11-13
An electrogenetic layered graphene hydrogel membrane (GHM) possesses ultra-large interlayer spacing of about 10 nm, forming charged 2D nanocapillaries between graphene sheets that selectively permeate counter-ions and exclude co-ions. When an electrolyte flow goes through the GHM, it functions as an integrated 2D nanofluidic generator converting hydraulic motion into electricity. The maximum streaming conductance density approaches 16.8 μA cm(-2) bar(-1) .
15. Characterization of Bimetallic Castings with an Austenitic Working Surface Layer and an Unalloyed Cast Steel Base
Science.gov (United States)
Wróbel, Tomasz
2014-05-01
The paper presents the technology of bimetallic castings based on the founding method of layer coating directly in the cast process of the so-called method of mold cavity preparation. The prepared castings consist of two fundamental parts, i.e., the base and the working surface layer. The base part of the bimetallic casting is typical foundry material, i.e., unalloyed cast steel, whereas the working layer is a plate of austenitic alloy steel sort X2CrNi 18-9. The quality of the joint between the base part and the working layer was evaluated on the basis of ultrasonic non-destructive testing and structure examinations containing metallographic macro- and microscopic studies with the use of a light microscope (LOM) with microhardness measurements and a scanning electron microscope (SEM) with microanalysis of the chemical composition (energy dispersive spectroscopy—EDS). On the basis of the obtained results it was confirmed that the decisive phenomena needed to create a permanent joint between the two components of the bimetallic casting are carbon and heat transport in the direction from the high-carbon and hot base material which was poured into the mold in the form of liquid metal to the low-carbon and cold material of the working layer which was placed in the mold cavity in the form of a monolithic insert.
16. Molecular-scale dynamics of light-induced spin cross-over in a two-dimensional layer
Science.gov (United States)
Bairagi, Kaushik; Iasco, Olga; Bellec, Amandine; Kartsev, Alexey; Li, Dongzhe; Lagoute, Jérôme; Chacon, Cyril; Girard, Yann; Rousset, Sylvie; Miserque, Frédéric; Dappe, Yannick J; Smogunov, Alexander; Barreteau, Cyrille; Boillot, Marie-Laure; Mallah, Talal; Repain, Vincent
2016-01-01
Spin cross-over molecules show the unique ability to switch between two spin states when submitted to external stimuli such as temperature, light or voltage. If controlled at the molecular scale, such switches would be of great interest for the development of genuine molecular devices in spintronics, sensing and for nanomechanics. Unfortunately, up to now, little is known on the behaviour of spin cross-over molecules organized in two dimensions and their ability to show cooperative transformation. Here we demonstrate that a combination of scanning tunnelling microscopy measurements and ab initio calculations allows discriminating unambiguously between both states by local vibrational spectroscopy. We also show that a single layer of spin cross-over molecules in contact with a metallic surface displays light-induced collective processes between two ordered mixed spin-state phases with two distinct timescale dynamics. These results open a way to molecular scale control of two-dimensional spin cross-over layers. PMID:27425776
17. Layer-dependent anisotropic electronic structure of freestanding quasi-two-dimensional Mo S 2
KAUST Repository
Hong, Jinhua
2016-02-29
The anisotropy of the electronic transition is a well-known characteristic of low-dimensional transition-metal dichalcogenides, but their layer-thickness dependence has not been properly investigated experimentally until now. Yet, it not only determines the optical properties of these low-dimensional materials, but also holds the key in revealing the underlying character of the electronic states involved. Here we used both angle-resolved electron energy-loss spectroscopy and spectral analysis of angle-integrated spectra to study the evolution of the anisotropic electronic transition involving the low-energy valence electrons in the freestanding MoS2 layers with different thicknesses. We are able to demonstrate that the well-known direct gap at 1.8 eV is only excited by the in-plane polarized field while the out-of-plane polarized optical gap is 2.4 ± 0.2 eV in monolayer MoS2. This contrasts with the much smaller anisotropic response found for the indirect gap in the few-layer MoS2 systems. In addition, we determined that the joint density of states associated with the indirect gap transition in the multilayer systems and the corresponding indirect transition in the monolayer case has a characteristic three-dimensional-like character. We attribute this to the soft-edge behavior of the confining potential and it is an important factor when considering the dynamical screening of the electric field at the relevant excitation energies. Our result provides a logical explanation for the large sensitivity of the indirect transition to thickness variation compared with that for the direct transition, in terms of quantum confinement effect.
18. Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows
Science.gov (United States)
Nayfeh, A. H.; El-Hady, N. M.
1979-01-01
An analysis is presented for the linear stability of water boundary-layer flows over nonuniformly flat plates. Included in the analysis are disturbances due to velocity, pressure, temperatures, density, and transport properties as well as variations of the liquid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow. In contrast with previous analyses, the nonsimilarity of the mean flow is taken into account. No analysis agrees, even qualitatively, with the experimental data when similar profiles are used. However, both the parallel and nonparallel results qualitatively agree with the experimental results of Strazisar and Reshotko when nonsimilar profiles are used.
19. Two-dimensional modeling of thermal inversion layers in the middle atmosphere of Mars
Science.gov (United States)
Theodore, B.; Chassefiere, E.
1993-01-01
There is some evidence that the thermal structure of the martian middle atmosphere may be altered in a significant way by the general circulation motions. Indeed, while it is well known that the circulation in the meridional plane is responsible for the reversal of the latitudinal thermal gradient at the solstice through the adiabatic heating due to sinking motions above the winter pole, here we want to emphasize that a likely by-product effect could be the formation of warm layers, mainly located in the winter hemisphere, and exhibiting an inversion of the vertical thermal gradient.
20. Onset of two-dimensional superconductivity in space charge doped few-layer molybdenum disulfide.
Science.gov (United States)
Biscaras, Johan; Chen, Zhesheng; Paradisi, Andrea; Shukla, Abhay
2015-11-03
Atomically thin films of layered materials such as molybdenum disulfide (MoS2) are of growing interest for the study of phase transitions in two-dimensions through electrostatic doping. Electrostatic doping techniques giving access to high carrier densities are needed to achieve such phase transitions. Here we develop a method of electrostatic doping which allows us to reach a maximum n-doping density of 4 × 10(14) cm(-2) in few-layer MoS2 on glass substrates. With increasing carrier density we first induce an insulator to metal transition and subsequently an incomplete metal to superconductor transition in MoS2 with critical temperature ≈10 K. Contrary to earlier reports, after the onset of superconductivity, the superconducting transition temperature does not depend on the carrier density. Our doping method and the results we obtain in MoS2 for samples as thin as bilayers indicates the potential of this approach.
1. Excitation of instability waves in a two-dimensional shear layer by sound
Science.gov (United States)
Tam, C. K. W.
1978-01-01
The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for abitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach number are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analyzed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80 deg to the flow direction is most effective in exciting instability waves.
2. Layered double hydroxide nanosheet as a two-dimensional support of dense platinum nanoparticles
Energy Technology Data Exchange (ETDEWEB)
Yu, Hyo Gyoung; Cho, Se Hee; Ji, Hong Geun [H and A PharmaChem, R and D center, Bucheon (Korea, Republic of); Lee, Jong Hyeon [Dept. of Chemistry, The Catholic University of Korea, Bucheon (Korea, Republic of)
2017-02-15
Transition metal nanoparticles (NPs) with a narrow size distribution have been intensively synthesized on various solid supports for anti-agglomeration, and high catalytic activity and selectivity. Layered double hydroxides (LDH) are currently attracting intense interest in the field of heterogeneous catalysis as catalyst supports. In order to obtain a well-crystallized LDH nanosheet, the as-synthesize d carbonate form of LDH was hydrothermally treated according to a reported procedure, and further reacted by anion-exchange with an aqueous solution of NaNO{sub 3} and acetate buffer to give the nitrate form of LDH. Dense and uniform Pt NPs were synthesized on the exfoliated LDH nanosheets through precursor exchange and thermal reduction of the precursor ions. In this nanocomposite, the Pt Nps were uniformly grown on the surface of the LDH nano sheet and the average size of Pt Nps was 2nm.
3. Two-dimensional Oxygen Distribution in a Surface Sediment Layer Measured Using an RGB Color Ratiometric Oxygen Planar Optode
Directory of Open Access Journals (Sweden)
Jae Seong Lee
2013-09-01
Full Text Available We measured two-dimensional (2-D oxygen distribution in the surface sediment layer of intertidal sediment using a simple and inexpensive planar oxygen optode, which is based on a color ratiometric image approach. The recorded emission intensity of red color luminophore light significantly changed with oxygen concentration by O2 quenching of platinum(IIoctaethylporphyrin (PtOEP. The ratios between the intensity of red and green emissions with oxygen concentration variation demonstrated the Stern-Volmer relationship. The 2-D oxygen distribution image showed microtopographic structure, diffusivity boundary layer and burrow in surface sediment layer. The oxygen penetration depth (OPD was about 2 mm and the one-dimensional vertical diffusive oxygen uptake (DOU was 12.6 mmol m−2 d−1 in the undisturbed surface sediment layer. However, those were enhanced near burrow by benthic fauna, and the OPD was two times deeper and DOU was increased by 34%. The simple and inexpensive oxygen planar optode has great application potential in the study of oxygen dynamics with high spatiotemporal resolution, in benthic boundary layers.
4. Two-dimensional superconductivity in the cuprates revealed by atomic-layer-by-layer molecular beam epitaxy
Science.gov (United States)
Bollinger, A. T.; Božović, I.
2016-10-01
Various electronic phases displayed by cuprates that exhibit high temperature superconductivity continue to attract much interest. We provide a short review of several experiments that we have performed aimed at investigating the superconducting state in these compounds. Measurements on single-phase films, bilayers, and superlattices all point to the conclusion that the high-temperature superconductivity (HTS) in these materials is an essentially quasi-two dimensional phenomenon. With proper control over the film growth, HTS can exist in a single copper oxide plane with the critical temperatures as high as that achieved in the bulk samples.
5. A humidity sensitive two-dimensional tunable amorphous photonic structure in the outer layer of bivalve ligament from Sunset Siliqua.
Science.gov (United States)
Zhang, Weigang; Zhang, Gangsheng
2015-01-01
A humidity sensitive two-dimensional tunable amorphous photonic structure (2D TAPS) in the outer layer of bivalve ligament from Sunset Siliqua (OLLS) was reported in this paper. The structural color and microstructure of OLLS were investigated by reflection spectra and scanning electron microscopy, respectively. The results indicate that the reflection peak wavelength of the wet OLLS blue-shifts from 454 nm to 392 nm with the increasing of air drying time from 0 to 40 min, while the reflectivity decreases gradually and vanishes at last, relevant color changes from blue to black background color. The structural color in the OLLS is produced by a two-dimensional amorphous photonic structure consisting of aligned protein fibers, in which the diameter of protein fiber and the inter-fiber spacing are 101 ± 12 nm. Water can reversibly tune the reflection peak wavelength and reflectivity of this photonic structure, and the regulation achieved through dynamically tuning the interaction between inter-fiber spacing and average refractive index.
6. Two-dimensional layered MoS₂ biosensors enable highly sensitive detection of biomolecules.
Science.gov (United States)
Lee, Joonhyung; Dak, Piyush; Lee, Yeonsung; Park, Heekyeong; Choi, Woong; Alam, Muhammad A; Kim, Sunkook
2014-01-01
We present a MoS2 biosensor to electrically detect prostate specific antigen (PSA) in a highly sensitive and label-free manner. Unlike previous MoS2-FET-based biosensors, the device configuration of our biosensors does not require a dielectric layer such as HfO2 due to the hydrophobicity of MoS2. Such an oxide-free operation improves sensitivity and simplifies sensor design. For a quantitative and selective detection of PSA antigen, anti-PSA antibody was immobilized on the sensor surface. Then, introduction of PSA antigen, into the anti-PSA immobilized sensor surface resulted in a lable-free immunoassary format. Measured off-state current of the device showed a significant decrease as the applied PSA concentration was increased. The minimum detectable concentration of PSA is 1 pg/mL, which is several orders of magnitude below the clinical cut-off level of ~4 ng/mL. In addition, we also provide a systematic theoretical analysis of the sensor platform - including the charge state of protein at the specific pH level, and self-consistent channel transport. Taken together, the experimental demonstration and the theoretical framework provide a comprehensive description of the performance potential of dielectric-free MoS2-based biosensor technology.
7. Two-dimensional Layered MoS2 Biosensors Enable Highly Sensitive Detection of Biomolecules
Science.gov (United States)
Lee, Joonhyung; Dak, Piyush; Lee, Yeonsung; Park, Heekyeong; Choi, Woong; Alam, Muhammad A.; Kim, Sunkook
2014-12-01
We present a MoS2 biosensor to electrically detect prostate specific antigen (PSA) in a highly sensitive and label-free manner. Unlike previous MoS2-FET-based biosensors, the device configuration of our biosensors does not require a dielectric layer such as HfO2 due to the hydrophobicity of MoS2. Such an oxide-free operation improves sensitivity and simplifies sensor design. For a quantitative and selective detection of PSA antigen, anti-PSA antibody was immobilized on the sensor surface. Then, introduction of PSA antigen, into the anti-PSA immobilized sensor surface resulted in a lable-free immunoassary format. Measured off-state current of the device showed a significant decrease as the applied PSA concentration was increased. The minimum detectable concentration of PSA is 1 pg/mL, which is several orders of magnitude below the clinical cut-off level of ~4 ng/mL. In addition, we also provide a systematic theoretical analysis of the sensor platform - including the charge state of protein at the specific pH level, and self-consistent channel transport. Taken together, the experimental demonstration and the theoretical framework provide a comprehensive description of the performance potential of dielectric-free MoS2-based biosensor technology.
8. Sound generated by instability waves of supersonic flows. I Two-dimensional mixing layers. II - Axisymmetric jets
Science.gov (United States)
Tam, C. K. W.; Burton, D. E.
1984-01-01
An investigation is conducted of the phenomenon of sound generation by spatially growing instability waves in high-speed flows. It is pointed out that this process of noise generation is most effective when the flow is supersonic relative to the ambient speed of sound. The inner and outer asymptotic expansions corresponding to an excited instability wave in a two-dimensional mixing layer and its associated acoustic fields are constructed in terms of the inner and outer spatial variables. In matching the solutions, the intermediate matching principle of Van Dyke and Cole is followed. The validity of the theory is tested by applying it to an axisymmetric supersonic jet and comparing the calculated results with experimental measurements. Very favorable agreements are found both in the calculated instability-wave amplitude distribution (the inner solution) and the near pressure field level contours (the outer solution) in each case.
9. Two dimensional finite element method for metabolic effect in thermoregulation on human males and females skin layers
Directory of Open Access Journals (Sweden)
Saraswati Acharya
2015-08-01
Full Text Available Objective: To deal the implication of metabolic reaction relying on dermal thicknesses of males and females for temperature distribution on the layers of dermal part at various atmospheric temperatures. Methods: The mathematical model involving bioheat equation has been solved using finite element method and Crank-Nicolson technique to numerically investigate two dimensional temperature distributions. Initially, human dermal region under consideration is divided into six parts: stratum corneum, stratum germinativum, papillary region, reticular region, fatty layer and muscle part of subcutaneous tissue. Pennes bioheat equation is used considering the suitable physical and physiological parameters that affect the heat regulation in the layers. Computer simulation has been used for numerical results and graph of the temperatures profiles. Results: Lower percentage of muscle mass and higher percentage of adipose tissue in subcutaneous part of females result lower metabolic rate compared to males. Metabolism is considered as a heat source within the body tissue. The study delineates that when the metabolic heat generation S increases, body temperature rises and when S decreases, it goes down. In higher ambient temperature T∞ effect of S is lower as compared to lower T∞. Conclusions: Males and females would differ in their physiological responses in temperature distribution due to differences in metabolic heat production between genders. The thinner layers of males lead to higher values of skin temperature than thicker layer of females. Thickness plays a significant role in temperature distributions in human males and females body. Current understanding of human thermoregulation is based on male patterns; studies on women are still relatively rare and involve only small number of subjects. So it is still necessary for micro level study for temperature distribution model on the dermal layers of males and females.
10. Two dimensional finite element method for metabolic effect in thermoregulation on human males and females skin layers
Institute of Scientific and Technical Information of China (English)
SaraswatiAcharya; Dil Bahadur Gurung; Vinod Prakash Saxena
2015-01-01
Objective: To deal the implication of metabolic reaction relying on dermal thicknesses of males and females for temperature distribution on the layers of dermal part at various atmospheric temperatures. Methods: The mathematical model involving bioheat equation has been solved using finite element method and Crank-Nicolson technique to numerically investigate two dimensional temperature distributions. Initially, human dermal region under consideration is divided into six parts: stratum corneum, stratum germinativum, papillary region, reticular region, fatty layer and muscle part of subcutaneous tissue. Pennes bioheat equation is used considering the suitable physical and physiological parameters that affect the heat regulation in the layers. Computer simulation has been used for numerical results and graph of the temperatures profiles. Results: Lower percentage of muscle mass and higher percentage of adipose tissue in subcutaneous part of females result lower metabolic rate compared to males. Metabolism is considered as a heat source within the body tissue. The study delineates that when the metabolic heat generation S increases, body temperature rises and when S decreases, it goes down. In higher ambient temperature T∞ effect of S is lower as compared to lower T∞. Conclusions: Males and females would differ in their physiological responses in temperature distribution due to differences in metabolic heat production between genders. The thinner layers of males lead to higher values of skin temperature than thicker layer of females. Thickness plays a significant role in temperature distributions in human males and females body. Current understanding of human thermoregulation is based on male patterns; studies on women are still relatively rare and involve only small number of subjects. So it is still necessary for micro level study for temperature distribution model on the dermal layers of males and females.
11. Hydrophobic-hydrophilic monolithic dual-phase layer for two-dimensional thin-layer chromatography coupled with surface-enhanced Raman spectroscopy detection.
Science.gov (United States)
Zheng, Binxing; Liu, Yanhua; Li, Dan; Chai, Yifeng; Lu, Feng; Xu, Jiyang
2015-08-01
Hydrophobic-hydrophilic monolithic dual-phase plates have been prepared by a two-step polymerization method for two-dimensional thin-layer chromatography of low-molecular-weight compounds, namely, several dyes. The thin 200 μm poly(glycidyl methacrylate-co-ethylene dimethacrylate) layers attached to microscope glass plates were prepared using a UV-initiated polymerization method within a simple glass mold. After cutting and cleaning the specific area of the layer, the reassembled mold was filled with a polymerization mixture of butyl methacrylate and ethylene dimethacrylate and subsequently irradiated with UV light. During the second polymerization process, the former layer was protected from the UV light with a UV mask. After extracting the porogens and hydrolyzing the poly(glycidyl methacrylate-co-ethylene dimethacrylate) area, these two-dimensional layers were used to separate a mixture of dyes with great difference in their polarity using reversed-phase chromatography mode within the hydrophobic layer and then hydrophilic interaction chromatography mode along the hydrophilic area. In the latter dimension only the specific spot was developed further. Detection of the separated dyes could be achieved with surface-enhanced Raman spectroscopy.
12. Two-dimensionally stacked heterometallic layers hosting a discrete chair dodecameric ring of water clusters: synthesis and structural study.
Science.gov (United States)
Kenfack Tsobnang, Patrice; Wenger, Emmanuel; Biache, Coralie; Lambi Ngolui, John; Ponou, Siméon; Dahaoui, Slimane; Lecomte, Claude
2014-10-01
The stacked two-dimensional supramolecular compound catena-{Co(amp)3Cr(ox)3·6H2O} (amp = 2-picolylamine, ox = oxalate) has been synthesized from the bimolecular approach using hydrogen bonds. It is built from layers in which both Co(amp)(3+) (D) and Cr(ox)(3-) (A) ions are bonded in a repeating DADADA… pattern along the a and c axes by multiple hydrogen bonds. These layers host a well resolved R12 dodecameric discrete ring of water clusters built by six independent molecules located around the 2c centrosymmetric Wyckoff positions of the P21/n space group in which the compound crystallizes. These clusters are ranged along the [001] direction, occupy 733.5 Å(3) (22.0%) of the unit cell and have a chair conformation via 12 hydrogen bonds. The water molecules of the cluster are linked with stronger hydrogen bonds than those between the cluster and its host, which explains the single continuous step of the dehydration process of the compound.
13. Two-Dimensional Electron Gas at SrTiO3-Based Oxide Heterostructures via Atomic Layer Deposition
Directory of Open Access Journals (Sweden)
Sang Woon Lee
2016-01-01
Full Text Available Two-dimensional electron gas (2DEG at an oxide interface has been attracting considerable attention for physics research and nanoelectronic applications. Early studies reported the formation of 2DEG at semiconductor interfaces (e.g., AlGaAs/GaAs heterostructures with interesting electrical properties such as high electron mobility. Besides 2DEG formation at semiconductor junctions, 2DEG was realized at the interface of an oxide heterostructure such as the LaAlO3/SrTiO3 (LAO/STO heterojunction. The origin of 2DEG was attributed to the well-known “polar catastrophe” mechanism in oxide heterostructures, which consist of an epitaxial LAO layer on a single crystalline STO substrate among proposed mechanisms. Recently, it was reported that the creation of 2DEG was achieved using the atomic layer deposition (ALD technique, which opens new functionality of ALD in emerging nanoelectronics. This review is focused on the origin of 2DEG at oxide heterostructures using the ALD process. In particular, it addresses the origin of 2DEG at oxide interfaces based on an alternative mechanism (i.e., oxygen vacancies.
14. Two-dimensional thin-layer chromatographic method for the analysis of ochratoxin A in green coffee.
Science.gov (United States)
Ventura, Meritxell; Anaya, Ivan; Broto-Puig, Francesc; Agut, Montserrat; Comellas, Lluís
2005-09-01
A low-cost thin-layer chromatographic method has been developed for the presumptive measurement of ochratoxin A (OTA) at 5 microg/kg in green coffee beans. The analytical method consisted of extracting OTA by shaking the beans with a mixture of methanol and aqueous sodium bicarbonate solution, which was then purified by liquid-liquid partition into toluene. OTA was separated by normal-phase two-dimensional thin-layer chromatography and detected by visual estimation of fluorescence intensity under a UV lamp at 365 nm. The chromatography solvents were toluene-methanol-formic acid (8:2:0.03) for the first development and petroleum ether-ethyl acetate-formic acid (8:10:1) for the second dimension development. This method was tested with uncontaminated green coffee bean samples spiked with an OTA standard at four different concentrations (5, 10, 20, and 30 microg/kg). The method is rapid, simple, and very easy to implement in coffee-producing countries. It is highly selective and does not involve the use of chlorinated solvents in the sample extraction step. This inexpensive method has been applied to different types of green coffee samples from various countries (Zimbabwe, Brazil, India, Uganda, Colombia, and Indonesia) and different manufacturers, and no OTA below the detection limit of 5 microg/kg was detected in any samples analyzed.
15. Theory of substrate-directed heat dissipation for single-layer graphene and other two-dimensional crystals
Science.gov (United States)
Ong, Zhun-Yong; Cai, Yongqing; Zhang, Gang
2016-10-01
We present a theory of the phononic thermal (Kapitza) resistance at the interface between graphene or another single-layer two-dimensional (2D) crystal (e.g., MoS2) and a flat substrate, based on a modified version of the cross-plane heat transfer model by Persson, Volokitin, and Ueba [J. Phys.: Condens. Matter 23, 045009 (2011), 10.1088/0953-8984/23/4/045009]. We show how intrinsic flexural phonon damping is necessary for obtaining a finite Kapitza resistance and also generalize the theory to encased single-layer 2D crystals with a superstrate. We illustrate our model by computing the thermal boundary conductance (TBC) for bare and SiO2-encased single-layer graphene and MoS2 on a SiO2 substrate, using input parameters from first-principles calculation. The estimated room temperatures TBC for bare (encased) graphene and MoS2 on SiO2 are 34.6 (105) and 3.10 (5.07) MWK -1m-2 , respectively. The theory predicts the existence of a phonon frequency crossover point, below which the low-frequency flexural phonons in the bare 2D crystal do not dissipate energy efficiently to the substrate. We explain within the framework of our theory how the encasement of graphene with a top SiO2 layer introduces new low-frequency transmission channels, which significantly reduce the graphene-substrate Kapitza resistance. We emphasize that the distinction between bare and encased 2D crystals must be made in the analysis of cross-plane heat dissipation to the substrate.
16. Optimized two-dimensional thin layer chromatography to monitor the intracellular concentration of acetyl phosphate and other small phosphorylated molecules
Science.gov (United States)
2008-01-01
Acetyl phosphate (acetyl-P) serves critical roles in coenzyme A recycling and ATP synthesis. It is the intermediate of the Pta-AckA pathway that inter-converts acetyl-coenzyme A and acetate. Acetyl-P also can act as a global signal by donating its phosphoryl group to specific two-component response regulators. This ability derives from its capacity to store energy in the form of a high-energy phosphate bond. This bond, while critical to its function, also destabilizes acetyl-P in cell extracts. This lability has greatly complicated biochemical analysis, leading in part to widely varying acetyl-P measurements. We therefore developed an optimized protocol based on two-dimensional thin layer chromatography that includes metabolic labeling under aerated conditions and careful examination of the integrity of acetyl-P within extracts. This protocol results in greatly improved reproducibility, and thus permits precise measurements of the intracellular concentration of acetyl-P, as well as that of other small phosphorylated molecules. PMID:18385806
17. Turbulent Friction in the Boundary Layer of a Flat Plate in a Two-Dimensional Compressible Flow at High Speeds
Science.gov (United States)
Frankl, F.; Voishel, V.
1943-01-01
In the present report an investigation is made on a flat plate in a two-dimensional compressible flow of the effect of compressibility and heating on the turbulent frictional drag coefficient in the boundary layer of an airfoil or wing radiator. The analysis is based on the Prandtl-Karman theory of the turbulent boundary later and the Stodola-Crocco, theorem on the linear relation between the total energy of the flow and its velocity. Formulas are obtained for the velocity distribution and the frictional drag law in a turbulent boundary later with the compressibility effect and heat transfer taken into account. It is found that with increase of compressibility and temperature at full retardation of the flow (the temperature when the velocity of the flow at a given point is reduced to zero in case of an adiabatic process in the gas) at a constant R (sub x), the frictional drag coefficient C (sub f) decreased, both of these factors acting in the same sense.
18. Two-Dimensional Superconductor with a Giant Rashba Effect: One-Atom-Layer Tl-Pb Compound on Si(111)
Science.gov (United States)
Matetskiy, A. V.; Ichinokura, S.; Bondarenko, L. V.; Tupchaya, A. Y.; Gruznev, D. V.; Zotov, A. V.; Saranin, A. A.; Hobara, R.; Takayama, A.; Hasegawa, S.
2015-10-01
A one-atom-layer compound made of one monolayer of Tl and one-third monolayer of Pb on a Si(111) surface having √{3 }×√{3 } periodicity was found to exhibit a giant Rashba-type spin splitting of metallic surface-state bands together with two-dimensional superconducting transport properties. Temperature-dependent angle-resolved photoelectron spectroscopy revealed an enhanced electron-phonon coupling for one of the spin-split bands. In situ micro-four-point-probe conductivity measurements with and without magnetic field demonstrated that the (Tl, Pb)/Si(111) system transformed into the superconducting state at 2.25 K, followed by the Berezinskii-Kosterlitz-Thouless mechanism. The 2D Tl-Pb compound on Si(111) is believed to be the prototypical object for prospective studies of intriguing properties of the superconducting 2D system with lifted spin degeneracy, bearing in mind that its composition, atomic and electron band structures, and spin texture are already well established.
19. BEM/FDM Conjugate Heat Transfer Analysis of a Two-dimensional Air-cooled Turbine Blade Boundary Layer
Institute of Scientific and Technical Information of China (English)
2008-01-01
A coupled boundary element method (BEM) and finite difference method (FDM) are applied to solve conjugate heat transfer problem of a two-dimensional air-cooled turbine blade boundary layer. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. The Navier-Stokes equations are solved by HIT-NS code. In this code, the FDM is adopted and is used to resolve the convective heat transfer in the fluid region. The BEM code is used to resolve the conduction heat transfer in the solid region. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The numerical results from the BEM adopted in this paper are in good agreement with the results of analyrical solution and the results of commercial code, such as Fluent 6.2. The BEM avoids the complicated mesh needed in other computation method and saves the computation time. The results prove that the BEM adopted in this paper can give the same precision in numerical results with less boundary points. Comparing the conjugate results with the numerical results of an adiabatic wall flow solution, it reveals a significant difference in the distribution of metal temperatures. The results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines.
20. Two-Dimensional Layered Double Hydroxide Derived from Vermiculite Waste Water Supported Highly Dispersed Ni Nanoparticles for CO Methanation
Directory of Open Access Journals (Sweden)
Panpan Li
2017-03-01
Full Text Available Expanded multilayered vermiculite (VMT was successfully used as catalyst support and Ni/VMT synthesized by microwave irradiation assisted synthesis (MIAS exhibited excellent performance in our previous work. We also developed a two-dimensional porous SiO2 nanomesh (2D VMT-SiO2 by mixed-acid etching of VMT. Compared with three-dimensional (3D MCM-41, 2D VMT-SiO2 as a catalyst support provided a superior position for implantation of NiO species and the as-obtained catalyst exhibited excellent performance. In this paper, we successfully synthesized a layered double hydroxide (LDH using the spent liquor after mixed-acid etching of VMT, which mainly contained Mg2+ and Al3+. The as-calcined layered double oxide (LDO was used as a catalyst support for CO methanation. Compared with Ni/MgAl-LDO, Ni/VMT-LDO had smaller active component particles; therefore, in this study, it exhibited excellent catalytic performance over the whole temperature range of 250–500 °C. Ni/VMT-LDO achieved the best activity with 87.88% CO conversion, 89.97% CH4 selectivity, and 12.47 × 10−2·s−1 turn over frequency (TOF at 400 °C under a gas hourly space velocity of 20,000 mL/g/h. This study demonstrated that VMT-LDO as a catalyst support provided an efficient way to develop high-performance catalysts for synthetic natural gas (SNG from syngas.
1. Lateral Versus Vertical Growth of Two-Dimensional Layered Transition-Metal Dichalcogenides: Thermodynamic Insight into MoS2.
Science.gov (United States)
Shang, Shun-Li; Lindwall, Greta; Wang, Yi; Redwing, Joan M; Anderson, Tim; Liu, Zi-Kui
2016-09-14
Unprecedented interest has been spurred recently in two-dimensional (2D) layered transition metal dichalcogenides (TMDs) that possess tunable electronic and optical properties. However, synthesis of a wafer-scale TMD thin film with controlled layers and homogeneity remains highly challenging due mainly to the lack of thermodynamic and diffusion knowledge, which can be used to understand and design process conditions, but falls far behind the rapidly growing TMD field. Here, an integrated density functional theory (DFT) and calculation of phase diagram (CALPHAD) modeling approach is employed to provide thermodynamic insight into lateral versus vertical growth of the prototypical 2D material MoS2. Various DFT energies are predicted from the layer-dependent MoS2, 2D flake-size related mono- and bilayer MoS2, to Mo and S migrations with and without graphene and sapphire substrates, thus shedding light on the factors that control lateral versus vertical growth of 2D islands. For example, the monolayer MoS2 flake in a small 2D lateral size is thermodynamically favorable with respect to the bilayer counterpart, indicating the monolayer preference during the initial stage of nucleation; while the bilayer MoS2 flake becomes stable with increasing 2D lateral size. The critical 2D flake-size of phase stability between mono- and bilayer MoS2 is adjustable via the choice of substrate. In terms of DFT energies and CALPHAD modeling, the size dependent pressure-temperature-composition (P-T-x) growth windows are predicted for MoS2, indicating that the formation of MoS2 flake with reduced size appears in the middle but close to the lower T and higher P "Gas + MoS2" phase region. It further suggests that Mo diffusion is a controlling factor for MoS2 growth owing to its extremely low diffusivity compared to that of sulfur. Calculated MoS2 energies, Mo and S diffusivities, and size-dependent P-T-x growth windows are in good accord with available experiments, and the present data
2. Structure of two-dimensional and three-dimensional turbulent boundary layers with sparsely distributed roughness elements
Science.gov (United States)
George, Jacob
The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow. Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, k +, based on the element height (k) and the friction velocity (Utau), range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amount DeltaU/U, depending on the height of the roughness element, showing that Delta U/Utau is a function
3. Photoluminescence Properties of Two-dimensional Planar Layer and Three-dimensional Island Layer for ZnO Films Grown Using MOCVD
Institute of Scientific and Technical Information of China (English)
2006-01-01
ZnO(002) films with different thicknesses ranging from 7 to 300 nm were grown on sapphire(006) substrates via metal-organic chemical vapor deposition(MOCVD). The two-dimensional(2D) planar layer and the three-dimensional(3D) island layer were studied by using of X-ray diffraction(XRD) rocking curves and atomic force microscopy(AFM). The room temperature photoluminescence(PL) spectra show a blue shift of the peak positions of the ultraviolet(UV) emission with increasing film thickness. The blue shift is remarkably high(393-380 nm) when an increase in film thickness(7-15 nm) is accompanied by the change of structure from a2D planar layer to a 3D island layer. The PL spectra at 77 K also indicate that there are different transition mechanisms in the film thickness from a2D planar layer to a 3D island layer near the2D layer region.
4. Slow relaxation of the magnetization observed in an antiferromagnetically ordered phase for SCM-based two-dimensional layered compounds.
Science.gov (United States)
Kagesawa, Koichi; Nishimura, Yuki; Yoshida, Hiroki; Breedlove, Brian K; Yamashita, Masahiro; Miyasaka, Hitoshi
2017-03-07
Two-dimensional layered compounds with different counteranions, [{Mn(salen)}4C6](BF4)2·2(CH3OH) (1) and [{Mn(salen)}4C6](PF6)2·2(CH3OH) (2) (salen(2-) = N,N'-bis(salicylideneiminato), C6(2-) = C6H12(COO)2(2-)), were synthesized by assembling [Mn(salen)(H2O)]X (X(-) = BF4(-) and PF6(-)) and C6H12(CO2(-))2 (C6(2-)) in a methanol/2-propanol medium. The compounds have similar structures, which are composed of Mn(salen) out-of-plane dimers bridged by μ(4)-type C6(2-) ions, forming a brick-wall-type network of [-{Mn2}-OCO-] chains alternately connected via C6H12 linkers of C6(2-) moieties. The counteranions for 1 and 2, i.e., BF4(-) and PF6(-), respectively, are located between layers. Since the size of BF4(-) is smaller than that of PF6(-), intra-layer inter-chain and inter-plane nearest-neighbor MnMn distances are shorter in 1 than in 2. The zigzag chain moiety of [-{Mn2}-OCO-] leads to a canted S = 2 spin arrangement with ferromagnetic coupling in the Mn(III) out-of-plane dimer moiety and antiferromagnetic coupling through -OCO- bridges. Due to strong uniaxial anisotropy of the Mn(III) ion, the [-{Mn2}-OCO-] chains could behave as a single-chain magnet (SCM), which exhibits slow relaxation of magnetization at low temperatures. Nevertheless, these compounds fall into an antiferromagnetic ground state at higher temperatures of TN = 4.6 and 3.8 K for 1 and 2, respectively, than active temperatures for SCM behavior. The spin flip field at 1.8 K is 2.7 and 1.8 kOe for 1 and 2, respectively, which is attributed to the inter-chain interactions tuned by the size of the counteranions. The relaxation times of magnetization become longer at the boundary between the antiferromagnetic phase and the paramagnetic phase.
5. Raman enhancement effect on two-dimensional layered materials: graphene, h-BN and MoS2.
Science.gov (United States)
Ling, Xi; Fang, Wenjing; Lee, Yi-Hsien; Araujo, Paulo T; Zhang, Xu; Rodriguez-Nieva, Joaquin F; Lin, Yuxuan; Zhang, Jin; Kong, Jing; Dresselhaus, Mildred S
2014-06-11
Realizing Raman enhancement on a flat surface has become increasingly attractive after the discovery of graphene-enhanced Raman scattering (GERS). Two-dimensional (2D) layered materials, exhibiting a flat surface without dangling bonds, were thought to be strong candidates for both fundamental studies of this Raman enhancement effect and its extension to meet practical applications requirements. Here, we study the Raman enhancement effect on graphene, hexagonal boron nitride (h-BN), and molybdenum disulfide (MoS2), by using the copper phthalocyanine (CuPc) molecule as a probe. This molecule can sit on these layered materials in a face-on configuration. However, it is found that the Raman enhancement effect, which is observable on graphene, hBN, and MoS2, has different enhancement factors for the different vibrational modes of CuPc, depending strongly on the surfaces. Higher-frequency phonon modes of CuPc (such as those at 1342, 1452, 1531 cm(-1)) are enhanced more strongly on graphene than that on h-BN, while the lower frequency phonon modes of CuPc (such as those at 682, 749, 1142, 1185 cm(-1)) are enhanced more strongly on h-BN than that on graphene. MoS2 demonstrated the weakest Raman enhancement effect as a substrate among these three 2D materials. These differences are attributed to the different enhancement mechanisms related to the different electronic properties and chemical bonds exhibited by the three substrates: (1) graphene is zero-gap semiconductor and has a nonpolar C-C bond, which induces charge transfer (2) h-BN is insulating and has a strong B-N bond, while (3) MoS2 is semiconducting with the sulfur atoms on the surface and has a polar covalent bond (Mo-S) with the polarity in the vertical direction to the surface. Therefore, the different Raman enhancement mechanisms differ for each material: (1) charge transfer may occur for graphene; (2) strong dipole-dipole coupling may occur for h-BN, and (3) both charge transfer and dipole-dipole coupling may
6. Monolithic Superhydrophobic Polymer Layer with Photopatterned Virtual Channel for the Separation of Peptides Using Two-Dimensional Thin Layer Chromatography-Desorption Electrospray Ionization Mass Spectrometry
Science.gov (United States)
Han, Yehua; Levkin, Pavel; Abarientos, Irene; Liu, Huwei; Svec, Frantisek; Fréchet, Jean M.J.
2010-01-01
Superhydrophobic monolithic porous polymer layers with a photopatterned hydrophilic channel have been prepared. These layers were used for two-dimensional thin layer chromatography of peptides. The 50 μm thin poly(butyl methacrylate-co-ethylene dimethacrylate) layers supported onto 4.0 × 3.3 cm glass plates were prepared using UV-initiated polymerization in a simple glass mold. Photografting of a mixture of 2-acrylamido-2-methyl-1-propanesulfonic acid and 2-hydroxyethyl methacrylate carried out through a mask afforded a 600 μm wide virtual channel along one side of the layer. This channel, which contains ionizable functionalities, enabled the first dimension separation in ion exchange mode. The aqueous mobile phase migrates only through the channel due to the large difference in surface tension at the interface of the hydrophilic channel and the superhydrophobic monolith. The unmodified part of the layer featuring hydrophobic chemistry was then used for the reversed phase separation in the orthogonal second dimension. Practical application of our technique was demonstrated with a rapid 2D separation of a mixture of model peptides differing in hydrophobicity and isoelectric point using a combination of ion-exchange and reversed phase modes. In the former mode, the peptides migrated 11 mm in less than 1 min. Detection of fluorescently labeled peptides was achieved through UV light visualization. Separation of the native peptides was monitored directly using a desorption electrospray ionization (DESI) source coupled to a mass spectrometer. Unidirectional surface scanning with the DESI source was found suitable to determine both the location of each separated peptide and its molecular mass. PMID:20151661
7. Two-Dimensional Superconductivity Emerged at Monatomic Bi(2-) Square Net in Layered Y2O2Bi via Oxygen Incorporation.
Science.gov (United States)
Sei, Ryosuke; Kitani, Suguru; Fukumura, Tomoteru; Kawaji, Hitoshi; Hasegawa, Tetsuya
2016-09-07
Discovery of layered superconductors such as cuprates and iron-based compounds has unveiled new science and compounds. In these superconductors, quasi-two-dimensional layers including transition metal cations play principal role in the superconductivity via carrier doping by means of aliovalent-ion substitution. Here, we report on a two-dimensional superconductivity at 2 K in ThCr2Si2-type layered oxide Y2O2Bi possessing conducting monatomic Bi(2-) square net, possibly associated with an exotic superconductivity. The superconductivity emerges only in excessively oxygen-incorporated Y2O2Bi with expanded inter-net distance, in stark contrast to nonsuperconducting pristine Y2O2Bi reported previously. This result suggests that the element incorporation into hidden interstitial site could be an alternative approach to conventional substitution and intercalation methods for search of novel superconductors.
8. Effects of rapid thermal annealing on two-dimensional delocalized electronic states of the epitaxial N δ-doped layer in GaAs
Energy Technology Data Exchange (ETDEWEB)
Ogawa, Yasuhiro; Harada, Yukihiro; Baba, Takeshi; Kaizu, Toshiyuki; Kita, Takashi [Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501 (Japan)
2016-03-14
We have conducted rapid thermal annealing (RTA) for improving the two-dimensional (2D) arrangement of electronic states in the epitaxial nitrogen (N) δ-doped layer in GaAs. RTA rearranged the N-pair configurations in the GaAs (001) plane and reduced the number of non-radiative recombination centers. Furthermore, a Landau shift, representing the 2D delocalized electronic states in the (001) plane, was observed at around zero magnetic field intensity in the Faraday configuration.
9. Two-dimensional high-performance thin-layer chromatography of tryptic bovine albumin digest using normal- and reverse-phase systems with silanized silica stationary phase.
Science.gov (United States)
2013-10-18
Among many advantages of planar techniques, two-dimensional (2D) separation seems to be the most important for analysis of complex samples. Here we present quick, simple and efficient two-dimensional high-performance thin-layer chromatography (2D HPTLC) of bovine albumin digest using commercial HPTLC RP-18W plates (silica based stationary phase with chemically bonded octadecyl ligands of coverage density 0.5μmol/m(2) from Merck, Darmstadt). We show, that at low or high concentration of water in the mobile phase comprised methanol and some additives the chromatographic systems with the plates mentioned demonstrate normal- or reversed-phase liquid chromatography properties, respectively, for separation of peptides obtained. These two systems show quite different separation selectivity and their combination into 2D HPTLC process provides excellent separation of peptides of the bovine albumin digest. Copyright © 2013 Elsevier B.V. All rights reserved.
10. Split-step finite-difference time-domain method with perfectly matched layers for efficient analysis of two-dimensional photonic crystals with anisotropic media.
Science.gov (United States)
Singh, Gurpreet; Tan, Eng Leong; Chen, Zhi Ning
2012-02-01
This Letter presents a split-step (SS) finite-difference time-domain (FDTD) method for the efficient analysis of two-dimensional (2-D) photonic crystals (PhCs) with anisotropic media. The proposed SS FDTD method is formulated with perfectly matched layer boundary conditions and caters for inhomogeneous anisotropic media. Furthermore, the proposed method is derived using the efficient SS1 splitting formulas with simpler right-hand sides that are more efficient and easier to implement. A 2-D PhC cavity with anisotropic media is used as an example to validate the efficiency of the proposed method.
11. Bolometric detection of magnetoplasma resonances in microwave absorption by two-dimensional electron systems based on doping layer conductivity measurements in GaAs/AlGaAs heterostructures
Energy Technology Data Exchange (ETDEWEB)
Dorozhkin, S. I., E-mail: [email protected]; Sychev, D. V.; Kapustin, A. A. [Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow district (Russian Federation)
2014-11-28
We have implemented a new bolometric method to detect resonances in magneto-absorption of microwave radiation by two-dimensional electron systems (2DES) in selectively doped GaAs/AlGaAs heterostructures. Radiation is absorbed by the 2DES and the thermally activated conductivity of the doping layer supplying electrons to the 2DES serves as a thermometer. The resonant absorption brought about by excitation of the confined magnetoplasma modes appears as peaks in the magnetic field dependence of the low-frequency impedance measured between the Schottky gate and 2DES.
12. A theoretical model for the evolution of two-dimensional large-scale coherent structures in a mixing layer
Institute of Scientific and Technical Information of China (English)
周恒; 马良
1995-01-01
By a proper combination of the modified weakly nonlinear theory of hydrodynamic stability and the energy method, the spatial evolution of the large-scale coherent structures in a mixing layer has been calculated. The results are satisfactory.
13. Depth profiling of SBS/PET layered materials using step-scan phase modulation Fourier transform infrared photoacoustic spectroscopy and two-dimensional correlation analysis
Institute of Scientific and Technical Information of China (English)
2010-01-01
This paper demonstrates the application of step-scan phase modulation Fourier transform infrared photoacoustic spectroscopy(FTIR-PAS) in non-destructively depth profiling of styrene-butadiene-styrene block copolymer/polyethylene terephthalate(SBS/PET) layered materials.The surface thicknesses of three layered samples were determined to be 1.2,4.3 and 9.4μm by using phase difference analysis,overcoming the spatial detection limits of FTIR.Combined with generalized two-dimensional(G2D) FTIR correlation analysis,the spatial origins of peaks in the SBS/PET spectrum are identified with those having overlapping peaks between different layers are resolved.
14. Two-dimensional simulation of interdigitated back contact silicon heterojunction solar cells having overlapped p/i and n/i a-Si:H layers
Science.gov (United States)
Noge, Hiroshi; Saito, Kimihiko; Sato, Aiko; Kaneko, Tetsuya; Kondo, Michio
2015-08-01
The performance of interdigitated back contact silicon heterojunction solar cells having overlapped p/i and n/i a-Si:H layers on the back has been investigated by two-dimensional simulation in comparison with the conventional cell structure having a gap between p/i and n/i layers. The results show that narrower overlap width leads to higher short circuit current and conversion efficiency, especially for poor heterojunction interface and thinner silicon substrate of the cells in addition to narrower uncovered width of p/i layer by a metal electrode. This is similar to the gap width dependence in the conventional cells, since both overlap and gap act as dead area for diffused excess carriers in the back contacts.
15. Properties of two-dimensional insulators: A DFT study of bimetallic oxide CrW{sub 2}O{sub 9} clusters adsorption on MgO ultrathin films
Energy Technology Data Exchange (ETDEWEB)
Zhu, Jia, E-mail: [email protected] [College of Chemistry and Chemical Engineering, Jiangxi Normal University, Nanchang, Jiangxi 330022 (China); Zhang, Hui; Zhao, Ling; Xiong, Wei [College of Chemistry and Chemical Engineering, Jiangxi Normal University, Nanchang, Jiangxi 330022 (China); Huang, Xin; Wang, Bin [Department of Chemistry, Fuzhou University, Fuzhou, Fujian, 350108 (China); Zhang, Yongfan, E-mail: [email protected] [Department of Chemistry, Fuzhou University, Fuzhou, Fujian, 350108 (China); State Key Laboratory of Photocatalysis on Energy and Environment, Fuzhou, Fujian, 350002 (China)
2016-08-30
Highlights: • Completely different properties of CrW{sub 2}O{sub 9} on films compared with that on surface. • The first example of CT by electron tunneling from film to bimetallic oxide cluster. • A progressive Lewis acid site, better catalytic activities for adsorbed CrW{sub 2}O{sub 9}. - Abstract: Periodic density functional theory calculations have been performed to study the electronic properties of bimetallic oxide CrW{sub 2}O{sub 9} clusters adsorbed on MgO/Ag(001) ultrathin films (<1 nm). Our results show that after deposition completely different structures, electronic properties and chemical reactivity of dispersed CrW{sub 2}O{sub 9} clusters on ultrathin films are observed compared with that on the thick MgO surface. On the thick MgO(001) surface, adsorbed CrW{sub 2}O{sub 9} clusters are distorted significantly and just a little electron transfer occurs from oxide surface to clusters, which originates from the formation of adsorption dative bonds at interface. Whereas on the MgO/Ag(001) ultrathin films, the resulting CrW{sub 2}O{sub 9} clusters keep the cyclic structures and the geometries are similar to that of gas-phase [CrW{sub 2}O{sub 9}]{sup −}. Interestingly, we predicted the occurrence of a net transfer of one electron by direct electron tunneling from the MgO/Ag(001) films to CrW{sub 2}O{sub 9} clusters through the thin MgO dielectric barrier. Furthermore, our work reveals a progressive Lewis acid site where spin density preferentially localizes around the Cr atom not the W atoms for CrW{sub 2}O{sub 9}/MgO/Ag(001) system, indicating a potentially good bimetallic oxide for better catalytic activities with respect to that of pure W{sub 3}O{sub 9} clusters. As a consequence, present results reveal that the adsorption of bimetallic oxide CrW{sub 2}O{sub 9} clusters on the MgO/Ag(001) ultrathin films provide a new perspective to tune and modify the properties and chemical reactivity of bimetallic oxide adsorbates as a function of the thickness
16. Existence of shocklets in a two-dimensional supersonic mixing layer and its influence on the flow structure
Institute of Scientific and Technical Information of China (English)
2001-01-01
The spatial evolution of a T-S wave and its subharmonic wave, introduced at the inlet in a 2-D supersonic mixing layer, was investigated by using DNS. The relationship between the amplitude of the disturbance wave and the strength of the shocklet caused by the disturbance was investigated. We analyzed the shape of the disturbance velocity profile on both sides of the shocklet, and found that the existence of shocklet affected appreciably the disturbance velocity. The effects on the high speed side and low speed side of the mixing layer were found to be different.
17. Dual-frequency plasmon lasing modes in active three-layered bimetallic Ag/Au nanoshells
Science.gov (United States)
Wu, DaJian; Wu, XueWei; Cheng, Ying; Jin, BiaoBing; Liu, XiaoJun
2015-11-01
The optical properties of three-layered silver-gold-silica (SGS) nanoshells with gain have been investigated theoretically by using Mie theory. Surface plasmon amplification by stimulated emission of radiation (spaser) phenomena can be observed at two plasmon modes of the active SGS nanoshell in the visible region. It is found with the decrease in the radius of the inner Ag core that the critical value of ɛg″(ωg ) for the super-resonance of the low-energy mode increases first and then decreases while that for the high-energy mode decreases. An interesting overlap between the two curves for the critical value of ɛg″(ωg ) can be found at a special core radius. At this point, two super-resonances can be achieved concurrently at the low- and high-energy modes of the active SGS nanoshell with the same gain coefficient. This dual-frequency spaser based on the bimetallic Ag/Au nanoshell may be an efficient candidate for designing the nanolaser.
18. Atomic force microscopy imaging of transition metal layered compounds : A two-dimensional stick–slip system
NARCIS (Netherlands)
1995-01-01
Various layered transition metal dichalcogenides were scanned with an optical-lever atomic force microscope (AFM). The microscopic images indicate the occurrence of strong lateral stick–slip effects. In this letter, two models are presented to describe the observations due to stick–slip, i.e., eithe
19. Three-Dimensional Porous Particles Composed of Curved, Two-Dimensional, Nano-Sized Layers for Li-Ion Batteries
Science.gov (United States)
Yushin, Gleb; Evanoff, Kara; Magasinski, Alexander
2012-01-01
Thin Si films coated on porous 3D particles composed of curved 2D graphene sheets have been synthesized utilizing techniques that allow for tunable properties. Since graphene exhibits specific surface area up to 100 times higher than carbon black or graphite, the deposition of the same mass of Si on graphene is much faster in comparison -- a factor which is important for practical applications. In addition, the distance between graphene layers is tunable and variation in the thickness of the deposited Si film is feasible. Both of these characteristics allow for optimization of the energy and power characteristics. Thicker films will allow higher capacity, but slower rate capabilities. Thinner films will allow more rapid charging, or higher power performance. In this innovation, uniform deposition of Si and C layers on high-surface area graphene produced granules with specific surface area (SSA) of 5 sq. m/g.
20. Energy-efficient optical line terminal for WDM-OFDM-PON based on two-dimensional subcarrier and layer allocation.
Science.gov (United States)
Hu, Xiaofeng; Cao, Pan; Zhuang, Zhiming; Zhang, Liang; Yang, Qi; Su, Yikai
2012-11-05
We propose and experimentally demonstrate a scheme to reduce the energy consumption of optical line terminal (OLT) in wavelength division multiplexing - orthogonal frequency division multiplexing - passive optical networks (WDM-OFDM-PONs). In our scheme, a wireless communication technique, termed layered modulation, is introduced to maximize the transmission capacity of OFDM modulation module in the OLT by multiplexing data from different ONU groups with signal-to-noise ratio (SNR) margins onto the same subcarriers. With adaptive and dynamic subcarrier and layer allocation, several ONU groups with low traffic demands can share one OFDM modulation module to deliver their data during non-peak hours of a day, thus greatly reducing the number of running devices and minimizing the energy consumption of the OLT. Numerical calculation shows that an energy efficiency improvement of 28.3% in the OLT can be achieved by using proposed scheme compared to the conventional WDM-OFDM-PON.
1. GaN: From three- to two-dimensional single-layer crystal and its multilayer van der Waals solids
Science.gov (United States)
Onen, A.; Kecik, D.; Durgun, E.; Ciraci, S.
2016-02-01
Three-dimensional (3D) GaN is a III-V compound semiconductor with potential optoelectronic applications. In this paper, starting from 3D GaN in wurtzite and zinc-blende structures, we investigated the mechanical, electronic, and optical properties of the 2D single-layer honeycomb structure of GaN (g -GaN ) and its bilayer, trilayer, and multilayer van der Waals solids using density-functional theory. Based on high-temperature ab initio molecular-dynamics calculations, we first showed that g -GaN can remain stable at high temperature. Then we performed a comparative study to reveal how the physical properties vary with dimensionality. While 3D GaN is a direct-band-gap semiconductor, g -GaN in two dimensions has a relatively wider indirect band gap. Moreover, 2D g -GaN displays a higher Poisson ratio and slightly less charge transfer from cation to anion. In two dimensions, the optical-absorption spectra of 3D crystalline phases are modified dramatically, and their absorption onset energy is blueshifted. We also showed that the physical properties predicted for freestanding g -GaN are preserved when g -GaN is grown on metallic as well as semiconducting substrates. In particular, 3D layered blue phosphorus, being nearly lattice-matched to g -GaN , is found to be an excellent substrate for growing g -GaN . Bilayer, trilayer, and van der Waals crystals can be constructed by a special stacking sequence of g -GaN , and they can display electronic and optical properties that can be controlled by the number of g -GaN layers. In particular, their fundamental band gap decreases and changes from indirect to direct with an increasing number of g -GaN layers.
2. Two-Dimensional SnO Anodes with a Tunable Number of Atomic Layers for Sodium Ion Batteries
KAUST Repository
Zhang, Fan
2017-01-18
We have systematically changed the number of atomic layers stacked in 2D SnO nanosheet anodes and studied their sodium ion battery (SIB) performance. The results indicate that as the number of atomic SnO layers in a sheet decreases, both the capacity and cycling stability of the Na ion battery improve. The thinnest SnO nanosheet anodes (two to six SnO monolayers) exhibited the best performance. Specifically, an initial discharge and charge capacity of 1072 and 848 mAh g-1 were observed, respectively, at 0.1 A g-1. In addition, an impressive reversible capacity of 665 mAh g-1 after 100 cycles at 0.1 A g-1 and 452 mAh g-1 after 1000 cycles at a high current density of 1.0 A g-1 was observed, with excellent rate performance. As the average number of atomic layers in the anode sheets increased, the battery performance degraded significantly. For example, for the anode sheets with 10-20 atomic layers, only a reversible capacity of 389 mAh g-1 could be obtained after 100 cycles at 0.1 A g-1. Density functional theory calculations coupled with experimental results were used to elucidate the sodiation mechanism of the SnO nanosheets. This systematic study of monolayer-dependent physical and electrochemical properties of 2D anodes shows a promising pathway to engineering and mitigating volume changes in 2D anode materials for sodium ion batteries. It also demonstrates that ultrathin SnO nanosheets are promising SIB anode materials with high specific capacity, stable cyclability, and excellent rate performance.
3. Atomic layer deposition of two dimensional MoS{sub 2} on 150 mm substrates
Energy Technology Data Exchange (ETDEWEB)
Valdivia, Arturo; Conley, John F., E-mail: [email protected] [School of EECS, Oregon State University, Corvallis, Oregon 97331 (United States); Tweet, Douglas J. [Sharp Labs of America, Camas, Washington 98607 (United States)
2016-03-15
Low temperature atomic layer deposition (ALD) of monolayer to few layer MoS{sub 2} uniformly across 150 mm diameter SiO{sub 2}/Si and quartz substrates is demonstrated. Purge separated cycles of MoCl{sub 5} and H{sub 2}S precursors are used at reactor temperatures of up to 475 °C. Raman scattering studies show clearly the in-plane (E{sup 1}{sub 2g}) and out-of-plane (A{sub 1g}) modes of MoS{sub 2}. The separation of the E{sup 1}{sub 2g} and A{sub 1g} peaks is a function of the number of ALD cycles, shifting closer together with fewer layers. X-ray photoelectron spectroscopy indicates that stoichiometry is improved by postdeposition annealing in a sulfur ambient. High resolution transmission electron microscopy confirms the atomic spacing of monolayer MoS{sub 2} thin films.
4. Modeling of Lamb wave propagation in plate with two-dimensional phononic crystal layer coated on uniform substrate using plane-wave-expansion method
Energy Technology Data Exchange (ETDEWEB)
Hou Zhilin [Laboratoire de Physique des Milieux Ionises et Applications (LPMIA), Nancy University, CNRS Boulevard des Aiguillettes, BP 239 F-54506, Vandoeuvre-les-Nancy (France)], E-mail: [email protected]; Assouar, Badreddine M. [Laboratoire de Physique des Milieux Ionises et Applications (LPMIA), Nancy University, CNRS Boulevard des Aiguillettes, BP 239 F-54506, Vandoeuvre-les-Nancy (France)
2008-03-17
We show that the conversional three-dimensional plane wave expansion method can be revised to investigate the lamb wave propagation in the plate with two-dimensional phononic crystal layer coated on uniform substrate. We find that an imaginary three-dimensional periodic system can be constructed by stacking the studied plates and vacuum layers alternately, and then the Fourier series expansion can be performed. The difference between our imaginary periodic system and the true three-dimensional one is that, in our system, the Bloch feature of the wave along the thickness direction is broken. Three different systems are investigated by the proposed method as examples. The principle and reliability of the method are also discussed.
5. Quantum transport in two dimensional electron gas/p-wave superconductor junction with Rashba spin–orbit coupling at the interface and in the normal layer
Energy Technology Data Exchange (ETDEWEB)
Mohammadkhani, R., E-mail: [email protected]; Hassanloo, Gh.
2014-11-01
We have studied the tunneling conductance of a clean two dimensional electron gas/p- wave superconductor junction with Rashba spin–orbit coupling (RSOC) which is present in the normal layer and at the interface. Using the extended Blonder–Tinkham–Klapwijk formalism we have found that the subgap conductance peaks are shifted to a nonzero bias by RSOC at the interface which are the same as Ref. [1]. It is shown that for low insulating barrier and in the absence of the interface RSOC, the tunneling conductance decreases within energy gap with increasing of the RSOC in the normal layer while for high insulating barrier it enhances by increase of the RSOC. We have also shown that the RSOC inside the normal cannot affect the location of the subgap conductance peaks shifted by the interface RSOC.
6. Design strategy of two-dimensional material field-effect transistors: Engineering the number of layers in phosphorene FETs
Science.gov (United States)
Yin, Demin; Yoon, Youngki
2016-06-01
Thickness or the number of layers in 2D semiconductors is a key parameter to determine the material's electronic properties and the overall device performance of 2D material electronics. Here, we discuss the engineering practice of optimizing material and device parameters of phosphorene field-effect transistors (FETs) by means of self-consistent atomistic quantum transport simulations, where the impacts of different numbers of phosphorene layers on various device characteristics are explored in particular, considering two specific target applications of high-performance and low-power devices. Our results suggest that, for high-performance applications, monolayer phosphorene should be utilized in a conventional FET structure since it can provide the equally large on current as other multilayer phosphorenes (Ion > 1 mA/μm) without showing a penalty of relatively lower density of states, along with favorableness for steep switching and large immunity to gate-induced drain leakage. On the other hand, more comprehensive approach is required for low-power applications, where operating voltage, doping concentration, and channel length should be carefully engineered along with the thickness of phosphorene in tunnel FET (TFET) structure to achieve ultra-low leakage current without sacrificing on current significantly. Our extensive simulation results revealed that either bilayer or trilayer phosphorene can provide the best performance in TFET with the maximum Ion/Ioff of ˜2 × 1011 and the subthreshold swing as low as 13 mV/dec. In addition, our comparative study of phosphorene-based conventional FET and TFET clearly shows the feasibility and the limitation of each device for different target applications, providing irreplaceable insights into the design strategy of phosphorene FETs that can be also extended to other similar layered material electronic devices.
7. Three-dimensional structural damage localization system and method using layered two-dimensional array of capacitance sensors
Science.gov (United States)
Curry, Mark A (Inventor); Senibi, Simon D (Inventor); Banks, David L (Inventor)
2010-01-01
A system and method for detecting damage to a structure is provided. The system includes a voltage source and at least one capacitor formed as a layer within the structure and responsive to the voltage source. The system also includes at least one sensor responsive to the capacitor to sense a voltage of the capacitor. A controller responsive to the sensor determines if damage to the structure has occurred based on the variance of the voltage of the capacitor from a known reference value. A method for sensing damage to a structure involves providing a plurality of capacitors and a controller, and coupling the capacitors to at least one surface of the structure. A voltage of the capacitors is sensed using the controller, and the controller calculates a change in the voltage of the capacitors. The method can include signaling a display system if a change in the voltage occurs.
8. Two-dimensional inorganic–organic hybrid semiconductors composed of double-layered ZnS and monoamines with aromatic and heterocyclic aliphatic rings: Syntheses, structures, and properties
Energy Technology Data Exchange (ETDEWEB)
Wang, Sujing; Li, Jing, E-mail: [email protected]
2015-04-15
As an addition to the II–VI based inorganic–organic hybrid semiconductor family, five new two-dimensional (2D) double-layered structures have been synthesized employing monoamines with different aromatic or heterocyclic aliphatic rings. Zn{sub 2}S{sub 2}(bza) (1), Zn{sub 2}S{sub 2}(mbza) (2), Zn{sub 2}S{sub 2}(fbza) (3), Zn{sub 2}S{sub 2}(pca) (4), and Zn{sub 2}S{sub 2}(thfa) (5) (bza=benzylamine, mbza=4-methoxybenzylamine, fbza=4-flurobenzylamine, pca=3-picolylamine, and thfa=tetrahydrofurfurylamine) are prepared by solvothermal reactions and characterized by different analytical methods, including powder X-ray diffraction, optical diffuse reflection, thermogravimetric analysis and photoluminescence spectroscopy. The powder X-ray diffraction patterns show that all five compounds adopt 2D double-layered structures. Optical diffuse reflectance spectra of these compounds suggest that they have notably lower band gaps than those of the similar compounds composed of aliphatic alkyl amines. Their photoluminescence properties and thermal stability are also analyzed. - Graphical abstract: Five new members of two-dimensional double-layered 2D-Zn{sub 2}S{sub 2}(L) (L=Ligand) structures employing monoamines with different aromatic or heterocyclic aliphatic rings have been designed, synthesized, and characterized. - Highlights: • A new sub-family of II-VI based hybrid semiconductors are designed, synthesized, and structurally characterized using amines with aromatic or aliphatic cyclic rings. • These compounds have notably lower band gaps than those made of aliphatic alkyl amines, greatly broadening the range of band gaps of this material family. • They emit strongly with systematically tunable emission intensity and energy.
9. A two-dimensional iterative panel method and boundary layer model for bio-inspired multi-body wings
Science.gov (United States)
Blower, Christopher J.; Dhruv, Akash; Wickenheiser, Adam M.
2014-03-01
The increased use of Unmanned Aerial Vehicles (UAVs) has created a continuous demand for improved flight capabilities and range of use. During the last decade, engineers have turned to bio-inspiration for new and innovative flow control methods for gust alleviation, maneuverability, and stability improvement using morphing aircraft wings. The bio-inspired wing design considered in this study mimics the flow manipulation techniques performed by birds to extend the operating envelope of UAVs through the installation of an array of feather-like panels across the airfoil's upper and lower surfaces while replacing the trailing edge flap. Each flap has the ability to deflect into both the airfoil and the inbound airflow using hinge points with a single degree-of-freedom, situated at 20%, 40%, 60% and 80% of the chord. The installation of the surface flaps offers configurations that enable advantageous maneuvers while alleviating gust disturbances. Due to the number of possible permutations available for the flap configurations, an iterative constant-strength doublet/source panel method has been developed with an integrated boundary layer model to calculate the pressure distribution and viscous drag over the wing's surface. As a result, the lift, drag and moment coefficients for each airfoil configuration can be calculated. The flight coefficients of this numerical method are validated using experimental data from a low speed suction wind tunnel operating at a Reynolds Number 300,000. This method enables the aerodynamic assessment of a morphing wing profile to be performed accurately and efficiently in comparison to Computational Fluid Dynamics methods and experiments as discussed herein.
10. Redox Active Cation Intercalation/Deintercalation in Two-Dimensional Layered MnO2 Nanostructures for High-Rate Electrochemical Energy Storage.
Science.gov (United States)
Xiong, Pan; Ma, Renzhi; Sakai, Nobuyuki; Bai, Xueyin; Li, Shen; Sasaki, Takayoshi
2017-02-22
Two-dimensional (2D) layered materials with a high intercalation pseudocapacitance have long been investigated for Li(+)-ion-based electrochemical energy storage. By contrast, the exploration of guest ions other than Li(+) has been limited, although promising. The present study investigates intercalation/deintercalation behaviors of various metal ions in 2D layered MnO2 with various interlayer distances, K-birnessite nanobelt (K-MnO2), its protonated form (H-MnO2), and a freeze-dried sample of exfoliated nanosheets. Series of metal ions, such as monovalent Li(+), Na(+), and K(+) and divalent Mg(2+), exhibit reversible intercalation during charge/discharge cycling, delivering high-rate pseudocapacitances. In particular, the freeze-dried MnO2 of exfoliated nanosheets restacked with the largest interlayer spacing and a less compact 3D network exhibits the best rate capability and a stable cyclability over 5000 cycles. Both theoretical calculation and kinetic analysis reveal that the increased interlayer distance facilitates the fast diffusion of cations in layered MnO2 hosts. The results presented herein provide a basis for the controllable synthesis of layered nanostructures for high-rate electrochemical energy storage using various single- and multivalent ions.
11. Data set for fabrication of conformal two-dimensional TiO2 by atomic layer deposition using tetrakis (dimethylamino) titanium (TDMAT) and H2O precursors.
Science.gov (United States)
Zhuiykov, Serge; Akbari, Mohammad Karbalaei; Hai, Zhenyin; Xue, Chenyang; Xu, Hongyan; Hyde, Lachlan
2017-08-01
The data and complementary information presented hare are related to the research article of "http://dx.doi.org/10.1016/j.matdes.2017.02.016; Materials and Design 120 (2017) 99-108" [1]. The article provides data and information on the case of atomic layer deposition (ALD) of ultra-thin two-dimensional TiO2 film. The chemical structure of precursors, and the fabrication process were illustrated. The data of spectral ellipsometric measurements and the methods of calculations were presented. Data of root mean square roughness and the average roughness of the ADL TiO2 film are presented. The method of bandgap measurements and the bandgap calculation are also explained in the present data article.
12. Data set for fabrication of conformal two-dimensional TiO2 by atomic layer deposition using tetrakis (dimethylamino titanium (TDMAT and H2O precursors
Directory of Open Access Journals (Sweden)
Serge Zhuiykov
2017-08-01
Full Text Available The data and complementary information presented hare are related to the research article of “http://dx.doi.org/10.1016/j.matdes.2017.02.016; Materials and Design 120 (2017 99–108” [1]. The article provides data and information on the case of atomic layer deposition (ALD of ultra-thin two-dimensional TiO2 film. The chemical structure of precursors, and the fabrication process were illustrated. The data of spectral ellipsometric measurements and the methods of calculations were presented. Data of root mean square roughness and the average roughness of the ADL TiO2 film are presented. The method of bandgap measurements and the bandgap calculation are also explained in the present data article.
13. Two-dimensional percolation transition at finite temperature: Phase boundary for in-plane magnetism in films with two atomic layers of Fe on W(110)
Science.gov (United States)
Belanger, R.; Venus, D.
2017-02-01
A two-dimensional (2D) percolation transition in Fe/W(110) ultrathin magnetic films occurs when islands in the second atomic layer percolate and resolve a frustrated magnetic state to produce long-range in-plane ferromagnetic order. Novel measurements of percolation using the magnetic susceptibility χ (θ ) as the films are deposited at a constant temperature, allow the long-range percolation transition to be observed as a sharp peak consistent with a critical phase transition. The measurements are used to trace the paramagnetic-to-ferromagnetic phase boundary between the T =0 percolation magnetic transition and the thermal Curie magnetic transition of the undiluted film. A quantitative comparison to critical scaling theory is made by fitting the functional form of the phase boundary. The fitted parameters are then used in theoretical expressions for χ (T ) in the critical region of the paramagnetic state to provide an excellent, independent representation of the experimental measurements.
14. Proton transfer through hydrogen bonds in two-dimensional water layers: A theoretical study based on ab initio and quantum-classical simulations
Energy Technology Data Exchange (ETDEWEB)
Bankura, Arindam; Chandra, Amalendu, E-mail: [email protected] [Department of Chemistry, Indian Institute of Technology, Kanpur 208016 (India)
2015-01-28
The dynamics of proton transfer (PT) through hydrogen bonds in a two-dimensional water layer confined between two graphene sheets at room temperature are investigated through ab initio and quantum-classical simulations. The excess proton is found to be mostly solvated as an Eigen cation where the hydronium ion donates three hydrogen bonds to the neighboring water molecules. In the solvation shell of the hydronium ion, the three coordinated water molecules with two donor hydrogen bonds are found to be properly presolvated to accept a proton. Although no hydrogen bond needs to be broken for transfer of a proton to such presolvated water molecules from the hydronium ion, the PT rate is still found to be not as fast as it is for one-dimensional chains. Here, the PT is slowed down as the probability of finding a water with two donor hydrogen bonds in the solvation shell of the hydronium ion is found to be only 25%-30%. The hydroxide ion is found to be solvated mainly as a complex anion where it accepts four H-bonds through its oxygen atom and the hydrogen atom of the hydroxide ion remains free all the time. Here, the presolvation of the hydroxide ion to accept a proton requires that one of its hydrogen bonds is broken and the proton comes from a neighboring water molecule with two acceptor and one donor hydrogen bonds. The coordination number reduction by breaking of a hydrogen bond is a slow process, and also the population of water molecules with two acceptor and one donor hydrogen bonds is only 20%-25% of the total number of water molecules. All these factors together tend to slow down the hydroxide ion migration rate in two-dimensional water layers compared to that in three-dimensional bulk water.
15. Proton transfer through hydrogen bonds in two-dimensional water layers: A theoretical study based on ab initio and quantum-classical simulations
Science.gov (United States)
Bankura, Arindam; Chandra, Amalendu
2015-01-01
The dynamics of proton transfer (PT) through hydrogen bonds in a two-dimensional water layer confined between two graphene sheets at room temperature are investigated through ab initio and quantum-classical simulations. The excess proton is found to be mostly solvated as an Eigen cation where the hydronium ion donates three hydrogen bonds to the neighboring water molecules. In the solvation shell of the hydronium ion, the three coordinated water molecules with two donor hydrogen bonds are found to be properly presolvated to accept a proton. Although no hydrogen bond needs to be broken for transfer of a proton to such presolvated water molecules from the hydronium ion, the PT rate is still found to be not as fast as it is for one-dimensional chains. Here, the PT is slowed down as the probability of finding a water with two donor hydrogen bonds in the solvation shell of the hydronium ion is found to be only 25%-30%. The hydroxide ion is found to be solvated mainly as a complex anion where it accepts four H-bonds through its oxygen atom and the hydrogen atom of the hydroxide ion remains free all the time. Here, the presolvation of the hydroxide ion to accept a proton requires that one of its hydrogen bonds is broken and the proton comes from a neighboring water molecule with two acceptor and one donor hydrogen bonds. The coordination number reduction by breaking of a hydrogen bond is a slow process, and also the population of water molecules with two acceptor and one donor hydrogen bonds is only 20%-25% of the total number of water molecules. All these factors together tend to slow down the hydroxide ion migration rate in two-dimensional water layers compared to that in three-dimensional bulk water.
16. Two-dimensional hybrid layered materials: strain engineering on the band structure of MoS2/WSe2 hetero-multilayers
Science.gov (United States)
Gu, Kunming; Yu, Sheng; Eshun, Kwesi; Yuan, Haiwen; Ye, Huixian; Tang, Jiaoning; Ioannou, Dimitris E.; Xiao, Changshi; Wang, Hui; Li, Qiliang
2017-09-01
In this paper, we report a comprehensive modeling and simulation study of constructing hybrid layered materials by alternately stacking MoS2 and WSe2 monolayers. Such hybrid MoS2/WSe2 hetero-multilayers exhibited direct bandgap semiconductor characteristics with bandgap energy (E g) in a range of 0.45-0.55 eV at room temperature, very attractive for optoelectronics (wavelength range 2.5-2.75 μm) based on thicker two-dimensional (2D) materials. It was also found that the interlayer distance has a significant impact on the electronic properties of the hetero-multilayers, for example a five orders of magnitude change in the conductance was observed. Three material phases, direct bandgap semiconductor, indirect bandgap semiconductor, and metal were observed in MoS2/WSe2 hetero-multilayers, as the interlayer distance decreased from its relaxed (i.e., equilibrium) value of about 6.73 Å down to 5.50 Å, representing a vertical pressure of about 0.8 GPa for the bilayer and 1.5 GPa for the trilayer. Such new hybrid layered materials are very interesting for future nanoelectronic pressure sensor and nanophotonic applications. This study describes a new approach to explore and engineer the construction and application of tunable 2D semiconductors.
17. H-T phase diagram and the nature of vortex-glass phase in a quasi-two-dimensional superconductor: Sn-metal layer sandwiched between graphene sheets
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Masatsugu; Suzuki, Itsuko S.; Walter, Juergen
2004-02-15
The magnetic properties of a quasi-two-dimensional (2D) superconductor, Sn-metal graphite (MG), are studied using DC and AC magnetic susceptibility. Sn-MG has a unique layered structure where Sn metal layer is sandwiched between adjacent graphene sheets. This compound undergoes a superconducting transition at T{sub c}=3.75 K at H=0. The H-T diagram of Sn-MG is similar to that of a quasi-2D superconductors. The phase boundaries of vortex liquid, vortex glass, and vortex lattice phase merge into a multicritical point located at T*=3.4 K and H*=40 Oe. There are two irreversibility lines denoted by H{sub gl} (de Almeida-Thouless type) and H{sub gl{sup '}} (Gabay-Toulouse type), intersecting at T{sub 0}{sup '}=2.5 K and H{sub 0}{sup '}=160 Oe. The nature of slow dynamic and nonlinearity of the vortex glass phase is studied.
18. Screw-dislocation-driven growth of two-dimensional few-layer and pyramid-like WSe₂ by sulfur-assisted chemical vapor deposition.
Science.gov (United States)
Chen, Liang; Liu, Bilu; Abbas, Ahmad N; Ma, Yuqiang; Fang, Xin; Liu, Yihang; Zhou, Chongwu
2014-11-25
Two-dimensional (2D) layered tungsten diselenides (WSe2) material has recently drawn a lot of attention due to its unique optoelectronic properties and ambipolar transport behavior. However, direct chemical vapor deposition (CVD) synthesis of 2D WSe2 is not as straightforward as other 2D materials due to the low reactivity between reactants in WSe2 synthesis. In addition, the growth mechanism of WSe2 in such CVD process remains unclear. Here we report the observation of a screw-dislocation-driven (SDD) spiral growth of 2D WSe2 flakes and pyramid-like structures using a sulfur-assisted CVD method. Few-layer and pyramid-like WSe2 flakes instead of monolayer were synthesized by introducing a small amount of sulfur as a reducer to help the selenization of WO3, which is the precursor of tungsten. Clear observations of steps, helical fringes, and herringbone contours under atomic force microscope characterization reveal the existence of screw dislocations in the as-grown WSe2. The generation and propagation mechanisms of screw dislocations during the growth of WSe2 were discussed. Back-gated field-effect transistors were made on these 2D WSe2 materials, which show on/off current ratios of 10(6) and mobility up to 44 cm(2)/(V·s).
19. Universal Strategy to Fabricate a Two-Dimensional Layered Mesoporous Mo2C Electrocatalyst Hybridized on Graphene Sheets with High Activity and Durability for Hydrogen Generation.
Science.gov (United States)
Huo, Lili; Liu, Baocang; Zhang, Geng; Zhang, Jun
2016-07-20
A universal strategy was developed for fabrication of a highly active and durable precious-metal-free mesoporous Mo2C/graphene (m-Mo2C/G) electrocatalyst with a two-dimensional layered structural feature via a nanocasting method using glucose as a carbon source and an in-stiu assembled mesoporous KIT-6/graphene (KIT-6/G) as a template. The m-Mo2C/G catalyst exhibits high catalytic activity and excellent durability for hydrogen evolution reaction (HER) over a wide pH range, which displays a small onset potential of 8 mV, owerpotential (η10) for driving a cathodic current density of 10 mA·cm(-2) of 135 mV, a Tafel slope of 58 mV·dec(-1), and an exchange current density of 6.31 × 10(-2) mA·cm(-2) in acidic media and an onset potential of of 41 mV, η10 of 128 mV, Tafel slope of 56 mV·dec(-1), and an exchange current density of 4.09 × 10(-2) mA·cm(-2) in alkaline media, respectively. Furthermore, such an m-Mo2C/G electrocatalyst also gives about 100% Faradaic yield and shows excellent durability during 3000 cycles of a long-term test, and the catalytic current remains stable over 20 h at fixed overpotentials, making it a great potential application prospect for energy issues.
20. Qualitative and quantitative two-dimensional thin-layer chromatography/high performance liquid chromatography/diode-array/electrospray-ionization-time-of-flight mass spectrometry of cholinesterase inhibitors.
Science.gov (United States)
Mroczek, Tomasz
2016-09-10
Recently launched thin-layer chromatography-mass spectrometry (TLC-MS) interface enabling extraction of compounds directly from TLC plates into MS ion source was unusually extended into two-dimensional thin-layer chromatography/high performance liquid chromatography (2D, TLC/HPLC) system by its a direct connection to a rapid resolution 50×2.1mm, I.D. C18 column compartment followed by detection by diode array (DAD) and electrospray ionisation time-of-flight mass spectrometry (ESI-TOF-MS). In this way, even not separated bands of complicated mixtures of natural compounds could be analysed structurally, only within 1-2min after development of TLC plates. In comparison to typically applied TLC-MS interface, no ion suppression for acidic mobile phases was observed. Also, substantial increase in ESI-TOF-MS sensitivities and quality of spectra, were noticed. It has been utilised in combination with TLC- based bioautographic approaches of acetylcholinesterase (AChE) inhibitors, However, it can be also applied in any other procedures related to bioactivity (e.g. 2,2-Diphenyl-1-picryl-hydrazyl-DPPH screen test for radicals). This system has been also used for determination of half maximal inhibitory concentration (IC50 values) of the active inhibitor-galanthamine, as an example. Moreover, AChE inhibitory potencies of some of purified plant extracts, never studied before, have been quantitatively measured. This is first report of usage such the 2D TLC/HPLC/MS system both for qualitative and quantitative evaluation of cholinesterase inhibitors in biological matrices. Copyright © 2016 Elsevier B.V. All rights reserved.
1. Modulated two-dimensional charge-carrier density in LaTiO3-layer-doped LaAlO3/SrTiO3 heterostructure.
Science.gov (United States)
Nazir, Safdar; Bernal, Camille; Yang, Kesong
2015-03-11
The highly mobile two-dimensional electron gas (2DEG) formed at the polar/nonpolar LaAlO3/SrTiO3 (LAO/STO) heterostructure (HS) is a matter of great interest because of its potential applications in nanoscale solid-state devices. To realize practical implementation of the 2DEG in device design, desired physical properties such as tuned charge carrier density and mobility are necessary. In this regard, polar perovskite-based transition metal oxides can act as doping layers at the interface and are expected to tune the electronic properties of 2DEG of STO-based HS systems dramatically. Herein, we investigated the doping effects of LaTiO3(LTO) layers on the electronic properties of 2DEG at n-type (LaO)(+1)/(TiO2)(0) interface in the LAO/STO HS using spin-polarized density functional theory calculations. Our results indicate an enhancement of orbital occupation near the Fermi energy, which increases with respect to the number of LTO unit cells, resulting in a higher charge carrier density of 2DEG than that of undoped system. The enhanced charge carrier density is attributed to an extra electron introduced by the Ti 3d(1) orbitals from the LTO dopant unit cells. This conclusion is consistent with the recent experimental findings (Appl. Phys. Lett. 2013, 102, 091601). Detailed charge density and partial density of states analysis suggests that the 2DEG in the LTO-doped HS systems primarily comes from partially occupied dyz and dxz orbitals.
2. Densitometric determination of catecholamine metabolites and 5-hydroxy-indoleacetic acid after two-dimensional thin-layer chromatography on cellulose
NARCIS (Netherlands)
Breebaart, K.; Haan, A.M.F.H.; Wadman, S.K.
A quantitative two-dimensional chromatographic determination for the catecholamine metabolites vanilglycolic (vanilmandelic) acid, vanilacetic acid, vanillactic acid and vanilglycol is described. The method can also be used for the determination of 5-hydroxy-indoleacetic acid. The analytical
3. Monolithic polymer layer with gradient of hydrophobicity for separation of peptides using two-dimensional thin layer chromatography and MALDI-TOF-MS detection.
Science.gov (United States)
Urbanova, Iva; Svec, Frantisek
2011-08-01
Superhydrophobic monolithic porous polymer layers supported onto glass plates with a gradient of hydrophobicity have been prepared and used for 2-D thin layer chromatography of peptides. The 50 μm-thin poly(glycidyl methacrylate-co-ethylene dimethacrylate) layers prepared using UV-initiated polymerization in a simple mold were first hydrolyzed using dilute sulfuric acid and then hydrophilized via two-step grafting of poly(ethylene glycol) methacrylate to obtain superhydrophilic plates. The hydrophobicity was then formed by photografting of lauryl methacrylate. The exposure to UV light that initiates photografting was spatially controlled using moving shutter that enabled forming of the diagonal gradient of hydrophobicity. This new concept enables the solutes to encounter the gradient for each of the two sequential developments. Practical application of our novel plates was demonstrated with a rapid 2-D separation of a mixture of model peptides gly-tyr, val-tyr-val, leucine enkephalin, and oxytocin in dual reversed-phase mode using different mobile phases in each direction. Detection of fluorescent-labeled peptides was achieved through UV light visualization while separation of native leucine enkephalin and oxytocin was monitored directly using MALDI mass spectrometry. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
4. Recent progress of two-dimensional layered molyb denum disulfide%层状二硫化钼研究进展∗
Institute of Scientific and Technical Information of China (English)
顾品超; 张楷亮; 冯玉林; 王芳; 苗银萍; 韩叶梅; 张韩霞
2016-01-01
Recently, two-dimensional (2D) layered molybdenum disulfide (MoS2) has attracted great attention because of its graphene-like structure and unique physical and chemical properties. In this paper, physical structure, band gap structure, and optical properties of MoS2 are summarized. MoS2 is semiconducting and composed of covalently bonded sheets held together by weak van der Waals force. In each MoS2 layer, a layer of molybdenum (Mo) atoms is sandwiched between two layers of sulfur (S) atoms. There are three types of MoS2 compounds, including 1T MoS2, 2H MoS2, and 3R MoS2. As the number of layers decreases, the bad gap becomes larger. The bad gap transforms from indirect to direct as MoS2 is thinned to a monolayer. Changes of band gap show a great potential in photoelectron. Preparation methods of 2D MoS2 are reviewed, including growth methods and exfoliation methods. Ammonium thiomolybdate (NH4)2MoS4, elemental molybdenum Mo and molybdenum trioxide MoO3 are used to synthesize 2D MoS2 by growth methods. (NH4)2MoS4 is dissolved in a solution and then coated on a substrate. (NH4)2MoS4 is decomposed into MoS2 after annealing at a high temperature. Mo is evaporated onto a substrate, and then sulfurized into MoS2. MoO3 is most used to synthesize MoS2 on different substrates by a chemical vapor deposition or plasma-enhanced chemical vapor deposition. Other precursors like Mo(CO)6, MoS2 and MoCl5 are also used for MoS2 growth. For the graphene-like structure, monolayer MoS2 can be exfoliated from bulk MoS2. Exfoliation methods include micromechanical exfoliation, liquid exfoliation, lithium-based intercalation and electrochemistry lithium-based intercalation. For micromechanical exfoliation, the efficiency is low and the sizes of MoS2 flakes are small. For liquid exfoliation, it is convenient for operation to obtain mass production, but the concentration of monolayer MoS2 is low. For lithium-based intercalation, the yield of monolayer MoS2 is high while it takes a long
5. Influence of relative rolling reduction and thickness layers bimetallic plate at the non-uniformity of the strain after rolling process
Science.gov (United States)
Rydz, D.; Stradomski, G.; Dyja, H.
2017-02-01
In the article were made numerical and laboratory tests of two-layers rolling process sheet composed of Al99,8 + M1E. Laboratory tests made with use of 150 mm diameter working rolls mill. To the modeling of the bimetallic plate rolling were taken the FEM Forge 2D software based on the theory of plasticity and MathCad program (in which to the rolling process modeling were used the mathematical model developed in the work [5] based on the theory of viscoelasticity). The aim of study was to determine the influence of layer thickness HT0/HM0 and relative deformation ε on the uneven distribution of steel sheet deformation after rolling process. Calculations based on the theory of viscoelasticity allowed additionally take into account the impact of the delayed effects of the variation of viscoelastic deformation of layers of the bimetallic plate rolling process.
6. A facile strategy to synthesize bimetallic Au/Ag nanocomposite film by layer-by-layer assembly technique
Science.gov (United States)
Zhang, Li; Wang, Cong; Zhang, Yi
2012-05-01
A facile strategy has been developed for the preparation of bimetallic gold-silver (Au-Ag) nanocomposite films by alternating absorption of poly-(ethyleneimine)-silver ions and Au onto substrates and subsequent reduction of the silver ions. The composition, micro-structure and properties of the {PEI-Ag/Au}n nanocomposite films were characterized by ultraviolet visible spectroscopy (UV-vis), transmisson electron microscopy (TEM), field emission scanning electron microscopy (FESEM), X-ray photoelectron spectroscopy (XPS), surface enhanced Raman scattering (SERS) and cyclic voltammetry (CV). The UV-vis characteristic absorbances of {PEI-Ag/Au}n nanocomposite thin film increase almost linear with the number of bilayers, which indicates a process of uniform assembling. Appearance of a double plasmon bands in the visible region and the lack of apparent core-shell structures in the TEM images confirm the formation of bimetallic Au-Ag nanoparticles. The result of XPS also demonstrates the existence of Ag and Au nanoparticles in the nanocomposite films. TEM and FESEM images show that these Ag and Au nanoparticles in the films possess sphere structure with the size of 20-25 nm. The resulting {PEI-Ag/Au}n films inherit the properties from both the metal Ag and Au, which exhibits a unique performance in SERS and electrocatalytic activities to the oxidation of dopamine. As a result, the {PEI-Ag/Au}n films are more attractive compared to {PEI-Ag/PSS}n and {PEI/Au}n films.
7. Two-dimensional calculus
CERN Document Server
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
8. Two dimensional vernier
Science.gov (United States)
Juday, Richard D. (Inventor)
1992-01-01
A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.
9. A facile strategy to synthesize bimetallic Au/Ag nanocomposite film by layer-by-layer assembly technique
Energy Technology Data Exchange (ETDEWEB)
Zhang Li, E-mail: [email protected] [Anhui Key Laboratory of Spin Electron and Nanomaterials (Cultivating Base), Suzhou University, Suzhou 234000 (China); Wang Cong; Zhang Yi [Anhui Key Laboratory of Spin Electron and Nanomaterials (Cultivating Base), Suzhou University, Suzhou 234000 (China)
2012-05-01
A facile strategy has been developed for the preparation of bimetallic gold-silver (Au-Ag) nanocomposite films by alternating absorption of poly-(ethyleneimine)-silver ions and Au onto substrates and subsequent reduction of the silver ions. The composition, micro-structure and properties of the {l_brace}PEI-Ag/Au{r_brace}{sub n} nanocomposite films were characterized by ultraviolet visible spectroscopy (UV-vis), transmisson electron microscopy (TEM), field emission scanning electron microscopy (FESEM), X-ray photoelectron spectroscopy (XPS), surface enhanced Raman scattering (SERS) and cyclic voltammetry (CV). The UV-vis characteristic absorbances of {l_brace}PEI-Ag/Au{r_brace}{sub n} nanocomposite thin film increase almost linear with the number of bilayers, which indicates a process of uniform assembling. Appearance of a double plasmon bands in the visible region and the lack of apparent core-shell structures in the TEM images confirm the formation of bimetallic Au-Ag nanoparticles. The result of XPS also demonstrates the existence of Ag and Au nanoparticles in the nanocomposite films. TEM and FESEM images show that these Ag and Au nanoparticles in the films possess sphere structure with the size of 20-25 nm. The resulting {l_brace}PEI-Ag/Au{r_brace}{sub n} films inherit the properties from both the metal Ag and Au, which exhibits a unique performance in SERS and electrocatalytic activities to the oxidation of dopamine. As a result, the {l_brace}PEI-Ag/Au{r_brace}{sub n} films are more attractive compared to {l_brace}PEI-Ag/PSS{r_brace}{sub n} and {l_brace}PEI/Au{r_brace}{sub n} films.
10. Energy spectrum and specific heat of two-dimensional electron systems with spin-orbit interaction in a magnetic field parallel to the conducting layer
Science.gov (United States)
Shevchenko, O. S.; Kopeliovich, A. I.
2016-03-01
The energy spectrum of a quasi-two-dimensional electron gas in an in-plane magnetic field is studied using the perturbation theory and quasiclassical approach in the presence of the Rashba and Dresselhaus spin-orbit coupling. The existence of the intersection of energy sublevels in electron spectrum is demonstrated. The reciprocal mass tensor of electrons is analyzed. The heat capacity of the degenerate electron gas is examined, and its relations with the key features of the spectrum are shown.
11. Two-dimensional optical spectroscopy
CERN Document Server
Cho, Minhaeng
2009-01-01
Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.
12. Two Dimensional Plasmonic Cavities on Moire Surfaces
Science.gov (United States)
Balci, Sinan; Kocabas, Askin; Karabiyik, Mustafa; Kocabas, Coskun; Aydinli, Atilla
2010-03-01
We investigate surface plasmon polariton (SPP) cavitiy modes on two dimensional Moire surfaces in the visible spectrum. Two dimensional hexagonal Moire surface can be recorded on a photoresist layer using Interference lithography (IL). Two sequential exposures at slightly different angles in IL generate one dimensional Moire surfaces. Further sequential exposure for the same sample at slightly different angles after turning the sample 60 degrees around its own axis generates two dimensional hexagonal Moire cavity. Spectroscopic reflection measurements have shown plasmonic band gaps and cavity states at all the azimuthal angles (omnidirectional cavity and band gap formation) investigated. The plasmonic band gap edge and the cavity states energies show six fold symmetry on the two dimensional Moire surface as measured in reflection measurements.
13. Bimetallic Nickel/Ruthenium Catalysts Synthesized by Atomic Layer Deposition for Low-Temperature Direct Methanol Solid Oxide Fuel Cells.
Science.gov (United States)
Jeong, Heonjae; Kim, Jun Woo; Park, Joonsuk; An, Jihwan; Lee, Tonghun; Prinz, Fritz B; Shim, Joon Hyung
2016-11-09
Nickel and ruthenium bimetallic catalysts were heterogeneously synthesized via atomic layer deposition (ALD) for use as the anode of direct methanol solid oxide fuel cells (DMSOFCs) operating in a low-temperature range. The presence of highly dispersed ALD Ru islands over a porous Ni mesh was confirmed, and the Ni/ALD Ru anode microstructure was observed. Fuel cell tests were conducted using Ni-only and Ni/ALD Ru anodes with approximately 350 μm thick gadolinium-doped ceria electrolytes and platinum cathodes. The performance of fuel cells was assessed using pure methanol at operating temperatures of 300-400 °C. Micromorphological changes of the anode after cell operation were investigated, and the content of adsorbed carbon on the anode side of the operated samples was measured. The difference in the maximum power density between samples utilizing Ni/ALD Ru and Pt/ALD Ru, the latter being the best catalyst for direct methanol fuel cells, was observed to be less than 7% at 300 °C and 30% at 350 °C. The improved electrochemical activity of the Ni/ALD Ru anode compared to that of the Ni-only anode, along with the reduction of the number of catalytically active sites due to agglomeration of Ni and carbon formation on the Ni surface as compared to Pt, explains this decent performance.
14. Enhancement of band-to-band tunneling in mono-layer transition metal dichalcogenides two-dimensional materials by vacancy defects
Energy Technology Data Exchange (ETDEWEB)
Jiang, Xiang-Wei; Li, Shu-Shen [State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083 (China); Gong, Jian [School of Physics Science and Technology, Inner Mongolia University, Hohhot 010021 (China); Xu, Nuo [Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720 (United States); Zhang, Jinfeng; Hao, Yue [Key Laboratory of Wide Band Gap Semiconductor Materials and Devices, School of Microelectronics, Xidian University, Xi' an 710071 (China); Wang, Lin-Wang, E-mail: [email protected] [Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2014-01-13
The band-to-band tunneling of monolayer transition metal dichalcogenides nano-junction is investigated using atomistic ab initio quantum transport simulations. From the simulation, it is found that the transition metal vacancy defect in the two-dimensional MX{sub 2} (M = Mo,W; X = S,Se) band-to-band tunneling diode can dramatically boost the on-state current up to 10 times while maintaining the device sub-threshold swing. The performance enhancement mechanism is discussed in detail by examining partial density of states of the system. It is found that the transition metal vacancy induces band-gap states, which reduce the effective length of the tunneling transition region.
15. Piezoelectricity in Two-Dimensional Materials
KAUST Repository
Wu, Tao
2015-02-25
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.
16. Significantly Dense Two-Dimensional Hydrogen-Bond Network in a Layered Zirconium Phosphate Leading to High Proton Conductivities in Both Water-Assisted Low-Temperature and Anhydrous Intermediate-Temperature Regions.
Science.gov (United States)
Gui, Daxiang; Zheng, Tao; Xie, Jian; Cai, Yawen; Wang, Yaxing; Chen, Lanhua; Diwu, Juan; Chai, Zhifang; Wang, Shuao
2016-12-19
A highly stable layered zirconium phosphate, (NH4)2[ZrF2(HPO4)2] (ZrP-1), was synthesized by an ionothermal method and contains an extremely dense two-dimensional hydrogen-bond network that is thermally stable up to 573 K, leading to combined ultrahigh water-assisted proton conductivities of 1.45 × 10(-2) S cm(-1) at 363 K/95% relative humidity and sustainable anhydrous proton conductivity of 1.1 × 10(-5) S cm(-1) at 503 K.
17. Exploration and exploitation of homologous series of bis(acrylamidoalkanes containing pyridyl and phenyl groups: β-sheet versus two-dimensional layers in solid-state photochemical [2 + 2] reactions
Directory of Open Access Journals (Sweden)
Mousumi Garai
2015-09-01
Full Text Available The homologous series of phenyl and pyridyl substituted bis(acrylamidoalkanes have been synthesized with the aim of systematic analysis of their crystal structures and their solid-state [2 + 2] reactivities. The changes in the crystal structures with respect to a small change in the molecular structure, that is by varying alkyl spacers between acrylamides and/or by varying the end groups (phenyl, 2-pyridyl, 3-pyridyl, 4-pyridyl on the C-terminal of the amide, were analyzed in terms of hydrogen-bonding interference (N—H...Npy versus N—H...O=C and network geometries. In this series, a greater tendency towards the formation of N—H...O hydrogen bonds (β-sheets and two-dimensional networks over N—H...N hydrogen bonds was observed. Among all the structures seven structures were found to have the required alignments of double bonds for the [2 + 2] reaction such that the formations of single dimer, double dimer and polymer are facilitated. However, only four structures were found to exhibit such a solid-state [2 + 2] reaction to form a single dimer and polymers. The two-dimensional hydrogen-bonding layer via N—H...O hydrogen bonds was found to promote solid-state [2 + 2] photo-polymerization in a single-crystal-to-single-crystal manner. Such two-dimensional layers were encountered only when the spacer between acryl amide moieties is butyl. Only four out of the 16 derivatives were found to form hydrates, two each from 2-pyridyl and 4-pyridyl derivatives. The water molecules in these structures govern the hydrogen-bonding networks by the formation of an octameric water cluster and one-dimensional zigzag water chains. The trends in the melting points and densities were also analyzed.
18. A new family of two-dimensional zeolites prepared from the intermediate layered precursor IPC-3P obtained during the synthesis of TUN zeolite.
Science.gov (United States)
Kubů, Martin; Roth, Wieslaw J; Greer, Heather F; Zhou, Wuzong; Morris, Russell E; Přech, Jan; Čejka, Jiří
2013-10-04
The crystallization of zeolite TUN with 1,4-bis(N-methylpyrrolidinium)butane as template proceeds through an intermediate, designated IPC-3P, following the Ostwald rule of successive transformations. This apparently layered transient product has been thoroughly investigated and found to consist of MWW monolayers stacked without alignment in register, that is, disordered compared with MCM-22P. The structure was confirmed based on X-ray diffraction and high-resolution (HR)TEM analysis. The layered zeolite precursor IPC-3P can be swollen and pillared affording a combined micro- and mesoporous material with enhanced Brunauer-Emmett-Teller (BET) surface area (685 m(2) g(-1) ) and greater accessibility of Brønsted acid sites for bulky molecules. This mesoporous material was probed with 2,6-di-tert-butylpyridine (DTBP). IPC-3P and its modification create a new layered zeolite sub-family belonging to the MWW family. FTIR data indicate that (Al)MWW materials MCM-22 and IPC-3 with Si/Al ratios greater than 20 exhibit a lower relative ratio of Brønsted to Lewis acid sites than MCM-22 (with Si/Al ratios of around 13), that is, less than 2 versus more than 3, respectively. This is maintained even upon pillaring and warrants further exploration of materials like IPC-3P with a higher Al content. The unique XRD features of IPC-3P indicating misaligned stacking of layers and distinct from MCM-22P, are also seen in other MWW materials such as EMM-10P, hexamethonium-templated (HM)-MCM-22, ITQ-30, and UZM-8 suggesting the need for more detailed study of their identity and properties.
19. A two-dimensional organic–inorganic hybrid compound, poly[(ethylenediaminetri-μ-oxido-oxidocopper(IImolybdenum(VI
Directory of Open Access Journals (Sweden)
Mehtap Emirdag-Eanes
2008-10-01
Full Text Available A new organic–inorganic two-dimensional hybrid compound, [CuMoO4(C2H8N2], has been hydrothermally synthesized at 443 K. The unit cell contains layers composed of CuN2O4 octahedra and MoO4 tetrahedra. Corner-sharing MoO4 and CuN2O4 polyhedra form CuMoO4 bimetallic sites that are joined together through O atoms, forming an edge-sharing Cu2Mo2O4 chain along the c axis. The one-dimensional chains are further linked through bridging O atoms that join the Cu and Mo atoms into respective chains along the b axis, thus establishing layers in the bc plane. The ethylenediamine ligand is coordinated to the Cu atom through its two N atoms and is oriented perpendicularly to the two-dimensional –Cu—O—Mo– layers. The average distance between adjacent layers, as calculated by consideration of the closest and furthest distances between two layers, is 8.7 Å. The oxidation states of the Mo and Cu atoms of VI and II, respectively, were confirmed by bond-valence sum calculations.
20. Crystal Structure And Magnetic Property of the Complex of Hydrogen-bonded Two-dimensional Layer Copper(Ⅱ) Acrylate with Trimethyl Phosphate
Institute of Scientific and Technical Information of China (English)
2000-01-01
@@ Copper carboxylate complexes play an important role in catalysing the enzymatic activities[1-4], and the phosphate has an especial use in DNA recognition[5]. Indeed the report about copper carboxylate complexes with phosphate ligands is rare. A chain structure supramolecule [Cu2(CH2CH-COO)4(H2O)2]n has been reported recently[6], in which a Cu2(CH2CH-COO)4(H2O)2 unit is linked by four O(water)-H...O(carboxyl) hydrogen bonds with two adjacent units(Fig.1). In this work a layer structure complex {Cu2(CH2CH-COO)4(H2O)2[OP(OCH3)3]}n was synthesized by means of hydrogen-bonded assembly approach between complex [Cu2(CH2CH-COO)4(H2O)2]n with trimethyl phosphate(TMP).
1. Polytypism in LaOBi S2 -type compounds based on different three-dimensional stacking sequences of two-dimensional Bi S2 layers
Science.gov (United States)
Liu, Qihang; Zhang, Xiuwen; Zunger, Alex
2016-05-01
LaOBi S2 -type materials have drawn much attention recently because of various interesting physical properties, such as low-temperature superconductivity, hidden spin polarization, and electrically tunable Dirac cones. However, it was generally assumed that each LaOBi S2 -type compound has a unique and specific crystallographic structure (with a space group P 4 /nmm) separated from other phases. Using first-principles total energy and stability calculations we confirm that the previous assignment of the P 4 /nmm structure to LaOBi S2 is incorrect. Furthermore, we find that the unstable structure is replaced by a family of energetically closely spaced modifications (polytypes) differing by the layer sequences and orientations. We find that the local Bi-S distortion leads to three polytypes of LaOBi S2 with different stacking patterns of the distorted Bi S2 layers. The energy difference between the polytypes of LaOBi S2 is merely ˜1 meV/u.c., indicating the possible coexistence of all polytypes in the real sample and that the particular distribution of polytypes may be growth induced. The in-plane distortion can be suppressed by pressure, leading to a phase transition from polytypes to the high-symmetry P 4 /nmm structure with a pressure larger than 2.5 GPa. In addition, different choices of the intermediate atoms (replacing La) or active atoms (Bi S2 ) could also manifest different ground-state structures. One can thus tune the distortion and the ground state by pressure or by substituting covalence atoms in the LaOBi S2 family.
2. Two-dimensional supramolecular electron spin arrays.
Science.gov (United States)
Wäckerlin, Christian; Nowakowski, Jan; Liu, Shi-Xia; Jaggi, Michael; Siewert, Dorota; Girovsky, Jan; Shchyrba, Aneliia; Hählen, Tatjana; Kleibert, Armin; Oppeneer, Peter M; Nolting, Frithjof; Decurtins, Silvio; Jung, Thomas A; Ballav, Nirmalya
2013-05-07
A bottom-up approach is introduced to fabricate two-dimensional self-assembled layers of molecular spin-systems containing Mn and Fe ions arranged in a chessboard lattice. We demonstrate that the Mn and Fe spin states can be reversibly operated by their selective response to coordination/decoordination of volatile ligands like ammonia (NH3). Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
3. Two-dimensional thin-layer chromatography with adsorbent gradient as a method of chromatographic fingerprinting of furanocoumarins for distinguishing selected varieties and forms of Heracleum spp.
Science.gov (United States)
Cieśla, Lukasz; Bogucka-Kocka, Anna; Hajnos, Michał; Petruczynik, Anna; Waksmundzka-Hajnos, Monika
2008-10-17
There are a lot of taxonomic classifications of the genus Heracleum, and many authors indicate they need revision. Morphological identification is difficult to perform, as there are only few characteristic differences between each Heracleum species, varieties and forms. Furanocoumarins are characteristic compounds for the Apiaceae family, and they can be found in the whole genus in large quantities. Despite this fact, it is difficult to use the furanocoumarin profiles of plants, for their discrimination, as furanocoumarins are difficult to separate, due to their similar chemical structures and physicochemical properties. In this paper, a new, simple method is proposed for the discrimination of selected species, varieties and forms of the genus Heracleum. Thin-layer chromatography (TLC) with an adsorbent gradient (unmodified silica gel+octadecylsilica wettable with water) enables complete separation of the structural analogues. The proposed method gives the possibility to distinguish selected species, varieties and forms of the Heracleum genus, as they produce distinctive furanocoumarin fingerprints. The method is characterised by high specificity, precision, reproducibility and stability values. It is for the first time that graft TLC is used for constructing fingerprints of herbs. The complete separation of ten structural analogues, by combining gradient TLC with the unidimensional multiple development technique, has not been reported yet.
4. (CH3 NH3 )2 PdCl4 : A Compound with Two-Dimensional Organic-Inorganic Layered Perovskite Structure.
Science.gov (United States)
Huang, Tang Jiao; Thiang, Zhang Xian; Yin, Xuesong; Tang, Chunhua; Qi, Guojun; Gong, Hao
2016-02-01
The synthesis of previously unknown perovskite (CH3 NH3 )2 PdCl4 is reported. Despite using an organic cation with the smallest possible alkyl group, a 2D organic-inorganic layered Pd-based perovskites was still formed. This demonstrates that Pd-based 2D perovskites can be obtained even if the size of the organic cation is below the size limit predicted by the Goldschmidt tolerance-factor formula. The (CH3 NH3 )2 PdCl4 phase has a bulk resistivity of 1.4 Ω cm, a direct optical gap of 2.22 eV, and an absorption coefficient on the order of 10(4) cm(-1) . XRD measurements suggest that the compound is moderately stable in air, an important advantage over several existing organic-inorganic perovskites that are prone to phase degradation problems when exposed to the atmosphere. Given the recent interest in organic-inorganic perovskites, the synthesis of this new Pd-based organic-inorganic perovskite may be helpful in the preparation and understanding of other organic-inorganic perovskites. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
5. Engineering one-dimensional and two-dimensional birnessite manganese dioxides on nickel foam-supported cobalt–aluminum layered double hydroxides for advanced binder-free supercapacitors
KAUST Repository
Hao, Xiaodong
2014-11-19
© The Royal Society of Chemistry. We report a facile decoration of the hierarchical nickel foam-supported CoAl layered double hydroxides (CoAl LDHs) with MnO2 nanowires and nanosheets by a chemical bath method and a hydrothermal approach for high-performance supercapacitors. We demonstrate that owing to the sophisticated configuration of binder-free LDH@MnO2 on the conductive Ni foam (NF), the designed NF/LDH@MnO2 nanowire composites exhibit a highly boosted specific capacitance of 1837.8 F g-1 at a current density of 1 A g-1, a good rate capability, and an excellent cycling stability (91.8% retention after 5000 cycles). By applying the hierarchical NF/LDH@MnO2 nanowires as the positive electrode and activated microwave exfoliated graphite oxide activated graphene as the negative electrode, the fabricated asymmetric supercapacitor produces an energy density of 34.2 Wh kg-1 with a maximum power density of 9 kW kg-1. Such strategies with controllable assembly capability could open up a new and facile avenue in fabricating advanced binder-free energy storage electrodes. This journal is
6. Predictive two-dimensional scrape-off layer plasma transport modeling of phase-I operations of tokamak SST-1 using SOLPS5
Science.gov (United States)
Himabindu, M.; Tyagi, Anil; Sharma, Devendra; Deshpande, Shishir P.; Bonnin, Xavier
2014-02-01
Computational analysis of coupled plasma and neutral transport in the Scrape-Off Layer (SOL) region of the Steady-State Superconducting Tokamak (SST-1) is done using SOLPS for Phase-I of double-null divertor plasma operations. An optimum set of plasma parameters is explored computationally for the first phase operations with the central objective of achieving an effective control over particle and power exhaust. While the transport of plasma species is treated using a fluid model in the B2.5 code, a full kinetic description is provided by the EIRENE code for the neutral particle transport in a realistic geometry. Cases with and without external gas puffing are analyzed for finding regimes where an effective control of plasma operations can be exercised by controlling the SOL plasma conditions over a range of heating powers. In the desired parameter range, a reasonable neutral penetration across the SOL is observed, capable of causing a variation of up to 15% of the total input power, in the power deposited on the divertors. Our computational characterization of the SOL plasma with input power 1 MW and lower hybrid current drive, for the separatrix density up to 1019 m-3, indicates that there will be access to high recycling operations producing reduction in the temperature and the peak heat flux at the divertor targets. This indicates that a control of the core plasma density and temperature would be achievable. A power balance analysis done using the kinetic neutral transport code EIRENE indicates about 60%-75% of the total power diverted to the targets, providing quantitative estimates for the relative power loading of the targets and the rest of the plasma facing components.
7. A General Method for Constructing Two-Dimensional Layered Mesoporous Mono- and Binary-Transition-Metal Nitride/Graphene as an Ultra-Efficient Support to Enhance Its Catalytic Activity and Durability for Electrocatalytic Application.
Science.gov (United States)
Liu, Baocang; Huo, Lili; Si, Rui; Liu, Jian; Zhang, Jun
2016-07-27
We constructed a series of two-dimensional (2D) layered mesoporous mono- and binary-transition-metal nitride/graphene nanocomposites (TMN/G, TM = Ti, Cr, W, Mo, TiCr, TiW, and TiMo) via an efficient and versatile nanocasting strategy for the first time. The 2D layered mesoporous TMN/G is constituted of small TMN nanoparticles composited with graphene nanosheets and has a large surface area with high porosity. Through decoration with well-dispersed Pt nanoparticles, 2D layered mesoporous Pt/TMN/G catalysts can be obtained that display excellent catalytic activity and stability for methanol electro-oxidation reactions (MOR) and oxygen reduction reactions (ORR) in both acidic and alkaline media. The 2D layered mesoporous binary-Pt/TMN/G catalysts possess catalytic activity superior to that of mono-Pt/TMN/G, graphene free Pt/TMN, Pt/G, and Pt/C catalysts. Encouragingly, the 2D layered mesoporous Pt/Ti0.5Cr0.5N/G catalyst exhibits the best electrocatalytic performance for both MOR and ORR. The outstanding electrocatalytic performance of the Pt/Ti0.5Cr0.5N/G catalyst is rooted in its large surface area, high porosity, strong interaction among Pt, Ti0.5Cr0.5N, and graphene, an excellent electron transfer property facilitated by N-doped graphene, and the small size of Pt and Ti0.5Cr0.5N nanocrystals. The outstanding catalytic performance provides the 2D layered mesoporous Pt/Ti0.5Cr0.5N/G catalyst with a wide range of application prospects in direct methanol fuel cells in both acidic and alkaline media. The synthetic method may be available for constructing other 2D layered mesoporous metal nitrides, carbides, and phosphides.
8. Two-dimensional heterospectral correlation analysis of the redox-induced conformational transition in cytochrome c using surface-enhanced Raman and infrared absorption spectroscopies on a two-layer gold surface.
Science.gov (United States)
Zou, Changji; Larisika, Melanie; Nagy, Gabor; Srajer, Johannes; Oostenbrink, Chris; Chen, Xiaodong; Knoll, Wolfgang; Liedberg, Bo; Nowak, Christoph
2013-08-22
The heme protein cytochrome c adsorbed to a two-layer gold surface modified with a self-assembled monolayer of 2-mercaptoethanol was analyzed using a two-dimensional (2D) heterospectral correlation analysis that combined surface-enhanced infrared absorption spectroscopy (SEIRAS) and surface-enhanced Raman spectroscopy (SERS). Stepwise increasing electric potentials were applied to alter the redox state of the protein and to induce conformational changes within the protein backbone. We demonstrate herein that 2D heterospectral correlation analysis is a particularly suitable and useful technique for the study of heme-containing proteins as the two spectroscopies address different portions of the protein. Thus, by correlating SERS and SEIRAS data in a 2D plot, we can obtain a deeper understanding of the conformational changes occurring at the redox center and in the supporting protein backbone during the electron transfer process. The correlation analyses are complemented by molecular dynamics calculations to explore the intramolecular interactions.
9. The effect of the interlayer element on the exfoliation of layered Mo2AC (A = Al, Si, P, Ga, Ge, As or In) MAX phases into two-dimensional Mo2C nanosheets
Science.gov (United States)
Khazaei, Mohammad; Arai, Masao; Sasaki, Taizo; Estili, Mehdi; Sakka, Yoshio
2014-02-01
The experimental exfoliation of layered, ternary transition-metal carbide and nitride compounds, known as MAX phases, into two-dimensional (2D) nanosheets, is a great development in the synthesis of novel low-dimensional inorganic systems. Among the MAX phases, Mo-containing ones might be considered as the source for obtaining Mo2C nanosheets with potentially unique properties, if they could be exfoliated. Here, by using a set of first-principles calculations, we discuss the effect of the interlayer ‘A’ element on the exfoliation of Mo2AC (A = Al, Si, P, Ga, Ge, As or In) MAX phases into the 2D Mo2C nanosheets. Based on the calculated exfoliation energies and the elastic constants, we propose that Mo2InC with the lowest exfoliation energy and the highest elastic constant anisotropy between C11 and C33 might be a suitable compound for exfoliation into 2D Mo2C nanosheets.
10. Two-dimensional liquid chromatography
DEFF Research Database (Denmark)
Græsbøll, Rune
of this thesis is on online comprehensive two-dimensional liquid chromatography (online LC×LC) with reverse phase in both dimensions (online RP×RP). Since online RP×RP has not been attempted before within this research group, a significant part of this thesis consists of knowledge and experience gained...
11. Two dimensional unstable scar statistics.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)
2006-12-01
This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.
12. Two-Dimensional Vernier Scale
Science.gov (United States)
Juday, Richard D.
1992-01-01
Modified vernier scale gives accurate two-dimensional coordinates from maps, drawings, or cathode-ray-tube displays. Movable circular overlay rests on fixed rectangular-grid overlay. Pitch of circles nine-tenths that of grid and, for greatest accuracy, radii of circles large compared with pitch of grid. Scale enables user to interpolate between finest divisions of regularly spaced rule simply by observing which mark on auxiliary vernier rule aligns with mark on primary rule.
13. Optimal excitation of two dimensional Holmboe instabilities
CERN Document Server
Constantinou, Navid C
2010-01-01
Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However these instabilities occur in tongues for a limited range of parameters. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that obtains for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges for parameter values ...
14. Two-dimensional liquid chromatography
DEFF Research Database (Denmark)
Græsbøll, Rune
Two-dimensional liquid chromatography has received increasing interest due to the rise in demand for analysis of complex chemical mixtures. Separation of complex mixtures is hard to achieve as a simple consequence of the sheer number of analytes, as these samples might contain hundreds or even...... dimensions. As a consequence of the conclusions made within this thesis, the research group has, for the time being, decided against further development of online LC×LC systems, since it was not deemed ideal for the intended application, the analysis of the polar fraction of oil. Trap-and...
15. The effect of the interlayer element on the exfoliation of layered Mo2AC (A = Al, Si, P, Ga, Ge, As or In MAX phases into two-dimensional Mo2C nanosheets
Directory of Open Access Journals (Sweden)
2014-01-01
Full Text Available The experimental exfoliation of layered, ternary transition-metal carbide and nitride compounds, known as MAX phases, into two-dimensional (2D nanosheets, is a great development in the synthesis of novel low-dimensional inorganic systems. Among the MAX phases, Mo-containing ones might be considered as the source for obtaining Mo2C nanosheets with potentially unique properties, if they could be exfoliated. Here, by using a set of first-principles calculations, we discuss the effect of the interlayer 'A' element on the exfoliation of Mo2AC (A = Al, Si, P, Ga, Ge, As or In MAX phases into the 2D Mo2C nanosheets. Based on the calculated exfoliation energies and the elastic constants, we propose that Mo2InC with the lowest exfoliation energy and the highest elastic constant anisotropy between C11 and C33 might be a suitable compound for exfoliation into 2D Mo2C nanosheets.
16. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides.
Science.gov (United States)
Wang, Qing Hua; Kalantar-Zadeh, Kourosh; Kis, Andras; Coleman, Jonathan N; Strano, Michael S
2012-11-01
The remarkable properties of graphene have renewed interest in inorganic, two-dimensional materials with unique electronic and optical attributes. Transition metal dichalcogenides (TMDCs) are layered materials with strong in-plane bonding and weak out-of-plane interactions enabling exfoliation into two-dimensional layers of single unit cell thickness. Although TMDCs have been studied for decades, recent advances in nanoscale materials characterization and device fabrication have opened up new opportunities for two-dimensional layers of thin TMDCs in nanoelectronics and optoelectronics. TMDCs such as MoS(2), MoSe(2), WS(2) and WSe(2) have sizable bandgaps that change from indirect to direct in single layers, allowing applications such as transistors, photodetectors and electroluminescent devices. We review the historical development of TMDCs, methods for preparing atomically thin layers, their electronic and optical properties, and prospects for future advances in electronics and optoelectronics.
17. In Situ Generation of Two-Dimensional Au–Pt Core–Shell Nanoparticle Assemblies
Directory of Open Access Journals (Sweden)
2009-01-01
Full Text Available Abstract Two-dimensional assemblies of Au–Pt bimetallic nanoparticles are generated in situ on polyethyleneimmine (PEI silane functionalized silicon and indium tin oxide (ITO coated glass surfaces. Atomic force microscopy (AFM, UV–Visible spectroscopy, and electrochemical measurements reveal the formation of core–shell structure with Au as core and Pt as shell. The core–shell structure is further supported by comparing with the corresponding data of Au nanoparticle assemblies. Static contact angle measurements with water show an increase in hydrophilic character due to bimetallic nanoparticle generation on different surfaces. It is further observed that these Au–Pt core–shell bimetallic nanoparticle assemblies are catalytically active towards methanol electro-oxidation, which is the key reaction for direct methanol fuel cells (DMFCs.
18. Two-dimensional capillary origami
Energy Technology Data Exchange (ETDEWEB)
Brubaker, N.D., E-mail: [email protected]; Lega, J., E-mail: [email protected]
2016-01-08
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
19. Quasi-two-dimensional electron gas at the interface of γ-Al{sub 2}O{sub 3}/SrTiO{sub 3} heterostructures grown by atomic layer deposition
Energy Technology Data Exchange (ETDEWEB)
Ngo, Thong Q.; McDaniel, Martin D.; Ekerdt, John G., E-mail: [email protected] [Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712 (United States); Goble, Nicholas J.; Gao, Xuan P. A. [Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106 (United States); Posadas, Agham; Kormondy, Kristy J.; Demkov, Alexander A. [Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Lu, Sirong [School of Engineering for Matter, Transport and Engineering, Arizona State University, Tempe, Arizona 85287 (United States); Jordan-Sweet, Jean [IBM T.J. Watson Research Center, Yorktown Heights, New York 10598 (United States); Smith, David J. [Department of Physics, Arizona State University, Tempe, Arizona 85287 (United States)
2015-09-21
We report the formation of a quasi-two-dimensional electron gas (2-DEG) at the interface of γ-Al{sub 2}O{sub 3}/TiO{sub 2}-terminated SrTiO{sub 3} (STO) grown by atomic layer deposition (ALD). The ALD growth of Al{sub 2}O{sub 3} on STO(001) single crystal substrates was performed at temperatures in the range of 200–345 °C. Trimethylaluminum and water were used as co-reactants. In situ reflection high energy electron diffraction, ex situ x-ray diffraction, and ex situ cross-sectional transmission electron microscopy were used to determine the crystallinity of the Al{sub 2}O{sub 3} films. As-deposited Al{sub 2}O{sub 3} films grown above 300 °C were crystalline with the γ-Al{sub 2}O{sub 3} phase. In situ x-ray photoelectron spectroscopy was used to characterize the Al{sub 2}O{sub 3}/STO interface, indicating that a Ti{sup 3+} feature in the Ti 2p spectrum of STO was formed after 2–3 ALD cycles of Al{sub 2}O{sub 3} at 345 °C and even after the exposure to trimethylaluminum alone at 300 and 345 °C. The interface quasi-2-DEG is metallic and exhibits mobility values of ∼4 and 3000 cm{sup 2} V{sup −1} s{sup −1} at room temperature and 15 K, respectively. The interfacial conductivity depended on the thickness of the Al{sub 2}O{sub 3} layer. The Ti{sup 3+} signal originated from the near-interfacial region and vanished after annealing in an oxygen environment.
20. Two-Dimensional Gel Electrophoresis Analyses of pH-Dependent Protein Expression in Facultatively Alkaliphilic Bacillus pseudofirmus OF4 Lead to Characterization of an S-Layer Protein with a Role in Alkaliphily
Science.gov (United States)
Gilmour, Raymond; Messner, Paul; Guffanti, Arthur A.; Kent, Rebecca; Scheberl, Andrea; Kendrick, Nancy; Krulwich, Terry Ann
2000-01-01
The large majority of proteins of alkaliphilic Bacillus pseudofirmus OF4 grown at pH 7.5 and 10.5, as studied by two-dimensional gel electrophoresis analyses, did not exhibit significant pH-dependent variation. A new surface layer protein (SlpA) was identified in these studies. Although the prominence of some apparent breakdown products of SlpA in gels from pH 10.5-grown cells led to discovery of the alkaliphile S-layer, the largest and major SlpA forms were present in large amounts in gels from pH 7.5-grown cells as well. slpA RNA abundance was, moreover, unchanged by growth pH. SlpA was similar in size to homologues from nonalkaliphiles but contained fewer Arg and Lys residues. An slpA mutant strain (RG21) lacked an exterior S-layer that was identified in the wild type by electron microscopy. Electrophoretic analysis of whole-cell extracts further indicated the absence of a 90-kDa band in the mutant. This band was prominent in wild-type extracts from both pH 7.5- and 10.5-grown cells. The wild type grew with a shorter lag phase than RG21 at either pH 10.5 or 11 and under either Na+-replete or suboptimal Na+ concentrations. The extent of the adaptation deficit increased with pH elevation and suboptimal Na+. By contrast, the mutant grew with a shorter lag and faster growth rate than the wild type at pH 7.5 under Na+-replete and suboptimal Na+ conditions, respectively. Logarithmically growing cells of the two strains exhibited no significant differences in growth rate, cytoplasmic pH regulation, starch utilization, motility, Na+-dependent transport of α-aminoisobutyric acid, or H+-dependent synthesis of ATP. However, the capacity for Na+-dependent pH homeostasis was diminished in RG21 upon a sudden upward shift of external pH from 8.5 to 10.5. The energy cost of retaining the SlpA layer at near-neutral pH is apparently adverse, but the constitutive presence of SlpA enhances the capacity of the extremophile to adjust to high pH. PMID:11029415
1. Two-dimensional quantum repeaters
Science.gov (United States)
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
2. Two-dimensional capillary origami
Science.gov (United States)
Brubaker, N. D.; Lega, J.
2016-01-01
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid.
3. Two-dimensional cubic convolution.
Science.gov (United States)
Reichenbach, Stephen E; Geng, Frank
2003-01-01
The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.
4. A new one-dimensional Cd(II) coordination polymer with a two-dimensional layered structure incorporating 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole and benzene-1,2-dicarboxylate ligands.
Science.gov (United States)
Huang, Qiu Ying; Lin, Xiao Yi; Meng, Xiang Ru
2016-06-01
The N-heterocyclic ligand 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole (imb) has a rich variety of coordination modes and can lead to polymers with intriguing structures and interesting properties. In the coordination polymer catena-poly[[cadmium(II)-bis[μ-benzene-1,2-dicarboxylato-κ(4)O(1),O(1'):O(2),O(2')]-cadmium(II)-bis{μ-2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole}-κ(2)N(2):N(3);κ(2)N(3):N(2)] dimethylformamide disolvate], {[Cd(C8H4O4)(C11H10N4)]·C3H7NO}n, (I), each Cd(II) ion exhibits an irregular octahedral CdO4N2 coordination geometry and is coordinated by four O atoms from two symmetry-related benzene-1,2-dicarboxylate (1,2-bdic(2-)) ligands and two N atoms from two symmetry-related imb ligands. Two Cd(II) ions are connected by two benzene-1,2-dicarboxylate ligands to generate a binuclear [Cd2(1,2-bdic)2] unit. The binuclear units are further connected into a one-dimensional chain by pairs of bridging imb ligands. These one-dimensional chains are further connected through N-H...O hydrogen bonds and π-π interactions, leading to a two-dimensional layered structure. The dimethylformamide solvent molecules are organized in dimeric pairs via weak interactions. In addition, the title polymer exhibits good fluorescence properties in the solid state at room temperature.
5. Graphene nanoribbon/FePt bimetallic nanoparticles/uric acid as a novel magnetic sensing layer of screen printed electrode for sensitive determination of ampyra.
Science.gov (United States)
Hashemi, Pegah; Bagheri, Hasan; Afkhami, Abbas; Amidi, Salimeh; Madrakian, Tayyebeh
2018-01-01
A novel electrochemical sensor for sensitive determination of ampyra (Am) based on graphene nanoribbons modified by iron-platinum bimetallic nanoparticles and uric acid (SPCE/FePtGNR/UA) dropped on the screen-printed carbon electrode (SPCE) surface and magnetically captured onto an SPCE working electrode surface is reported in the present work. The modified nanocomposite and sensing layer was characterized by different techniques, including cyclic voltammetry (CV), linear sweep voltammetry (LSV), electrochemical impedance spectroscopy (EIS), transmission electron microscopy (TEM), Fourier transform infrared spectroscopy (FT-IR) and X-ray powdered diffraction (XRD). Am determination by conventional electrochemical methods is not possible, because of its high redox overpotential. Therefore, the differential pulse voltammetry (DPV) signals of UA were used as a redox probe for indirect electrochemical determination of Am. The limit of detection (LOD) and linear concentration range were obtained as 0.028 and 0.08-9.0µmolL(-1) (3Sb/m = 3), respectively. The feasibility of the proposed method was examined by the detection of Am in biological and pharmaceutical samples with satisfactory results. The constructed electrochemical sensor was applied for fast, simple and sensitive detection of Am in real environments. Copyright © 2017 Elsevier B.V. All rights reserved.
6. Classifying Two-dimensional Hyporeductive Triple Algebras
CERN Document Server
Issa, A Nourou
2010-01-01
Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple systems) and two-dimensional real Bol algebras is given.
7. A two-dimensional polymer prepared by organic synthesis.
Science.gov (United States)
Kissel, Patrick; Erni, Rolf; Schweizer, W Bernd; Rossell, Marta D; King, Benjamin T; Bauer, Thomas; Götzinger, Stephan; Schlüter, A Dieter; Sakamoto, Junji
2012-02-05
Synthetic polymers are widely used materials, as attested by a production of more than 200 millions of tons per year, and are typically composed of linear repeat units. They may also be branched or irregularly crosslinked. Here, we introduce a two-dimensional polymer with internal periodicity composed of areal repeat units. This is an extension of Staudinger's polymerization concept (to form macromolecules by covalently linking repeat units together), but in two dimensions. A well-known example of such a two-dimensional polymer is graphene, but its thermolytic synthesis precludes molecular design on demand. Here, we have rationally synthesized an ordered, non-equilibrium two-dimensional polymer far beyond molecular dimensions. The procedure includes the crystallization of a specifically designed photoreactive monomer into a layered structure, a photo-polymerization step within the crystal and a solvent-induced delamination step that isolates individual two-dimensional polymers as free-standing, monolayered molecular sheets.
8. Rationally synthesized two-dimensional polymers.
Science.gov (United States)
Colson, John W; Dichtel, William R
2013-06-01
Synthetic polymers exhibit diverse and useful properties and influence most aspects of modern life. Many polymerization methods provide linear or branched macromolecules, frequently with outstanding functional-group tolerance and molecular weight control. In contrast, extending polymerization strategies to two-dimensional periodic structures is in its infancy, and successful examples have emerged only recently through molecular framework, surface science and crystal engineering approaches. In this Review, we describe successful 2D polymerization strategies, as well as seminal research that inspired their development. These methods include the synthesis of 2D covalent organic frameworks as layered crystals and thin films, surface-mediated polymerization of polyfunctional monomers, and solid-state topochemical polymerizations. Early application targets of 2D polymers include gas separation and storage, optoelectronic devices and membranes, each of which might benefit from predictable long-range molecular organization inherent to this macromolecular architecture.
9. Two-dimensional function photonic crystals
CERN Document Server
Wu, Xiang-Yao; Liu, Xiao-Jing; Liang, Yu
2016-01-01
In this paper, we have firstly proposed two-dimensional function photonic crystals, which the dielectric constants of medium columns are the functions of space coordinates $\\vec{r}$, it is different from the two-dimensional conventional photonic crystals constituting by the medium columns of dielectric constants are constants. We find the band gaps of two-dimensional function photonic crystals are different from the two-dimensional conventional photonic crystals, and when the functions form of dielectric constants are different, the band gaps structure should be changed, which can be designed into the appropriate band gaps structures by the two-dimensional function photonic crystals.
10. Two-dimensional superconductors with atomic-scale thickness
Science.gov (United States)
Uchihashi, Takashi
2017-01-01
Recent progress in two-dimensional superconductors with atomic-scale thickness is reviewed mainly from the experimental point of view. The superconducting systems treated here involve a variety of materials and forms: elemental metal ultrathin films and atomic layers on semiconductor surfaces; interfaces and superlattices of heterostructures made of cuprates, perovskite oxides, and rare-earth metal heavy-fermion compounds; interfaces of electric-double-layer transistors; graphene and atomic sheets of transition metal dichalcogenide; iron selenide and organic conductors on oxide and metal surfaces, respectively. Unique phenomena arising from the ultimate two dimensionality of the system and the physics behind them are discussed.
11. Photodetectors based on two dimensional materials
Science.gov (United States)
Zheng, Lou; Zhongzhu, Liang; Guozhen, Shen
2016-09-01
Two-dimensional (2D) materials with unique properties have received a great deal of attention in recent years. This family of materials has rapidly established themselves as intriguing building blocks for versatile nanoelectronic devices that offer promising potential for use in next generation optoelectronics, such as photodetectors. Furthermore, their optoelectronic performance can be adjusted by varying the number of layers. They have demonstrated excellent light absorption, enabling ultrafast and ultrasensitive detection of light in photodetectors, especially in their single-layer structure. Moreover, due to their atomic thickness, outstanding mechanical flexibility, and large breaking strength, these materials have been of great interest for use in flexible devices and strain engineering. Toward that end, several kinds of photodetectors based on 2D materials have been reported. Here, we present a review of the state-of-the-art in photodetectors based on graphene and other 2D materials, such as the graphene, transition metal dichalcogenides, and so on. Project supported by the National Natural Science Foundation of China (Nos. 61377033, 61574132, 61504136) and the State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences.
12. Hadamard States and Two-dimensional Gravity
CERN Document Server
Salehi, H
2001-01-01
We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.
13. Topological defects in two-dimensional crystals
OpenAIRE
Chen, Yong; Qi, Wei-Kai
2008-01-01
By using topological current theory, we study the inner topological structure of the topological defects in two-dimensional (2D) crystal. We find that there are two elementary point defects topological current in two-dimensional crystal, one for dislocations and the other for disclinations. The topological quantization and evolution of topological defects in two-dimensional crystals are discussed. Finally, We compare our theory with Brownian-dynamics simulations in 2D Yukawa systems.
14. Optimum high temperature strength of two-dimensional nanocomposites
Energy Technology Data Exchange (ETDEWEB)
Monclús, M. A.; Molina-Aldareguía, J. M., E-mail: [email protected] [IMDEA Materials Institute, C/Eric Kandel 2, 28906 Getafe, Madrid (Spain); Zheng, S. J.; Mayeur, J. R.; Beyerlein, I. J.; Mara, N. A. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Polcar, T. [Czech Technical University in Prague, Technická 2, Prague 6 (Czech Republic); Llorca, J. [IMDEA Materials Institute, C/Eric Kandel 2, 28906 Getafe, Madrid (Spain); Department of Materials Science, Polytechnic University of Madrid, E. T. S. de Ingenieros de Caminos, 28040 Madrid (Spain)
2013-11-01
High-temperature nanoindentation was used to reveal nano-layer size effects on the hardness of two-dimensional metallic nanocomposites. We report the existence of a critical layer thickness at which strength achieves optimal thermal stability. Transmission electron microscopy and theoretical bicrystal calculations show that this optimum arises due to a transition from thermally activated glide within the layers to dislocation transmission across the layers. We demonstrate experimentally that the atomic-scale properties of the interfaces profoundly affect this critical transition. The strong implications are that interfaces can be tuned to achieve an optimum in high temperature strength in layered nanocomposite structures.
15. Optimum high temperature strength of two-dimensional nanocomposites
Directory of Open Access Journals (Sweden)
M. A. Monclús
2013-11-01
Full Text Available High-temperature nanoindentation was used to reveal nano-layer size effects on the hardness of two-dimensional metallic nanocomposites. We report the existence of a critical layer thickness at which strength achieves optimal thermal stability. Transmission electron microscopy and theoretical bicrystal calculations show that this optimum arises due to a transition from thermally activated glide within the layers to dislocation transmission across the layers. We demonstrate experimentally that the atomic-scale properties of the interfaces profoundly affect this critical transition. The strong implications are that interfaces can be tuned to achieve an optimum in high temperature strength in layered nanocomposite structures.
16. Strongly interacting two-dimensional Dirac fermions
NARCIS (Netherlands)
Lim, L.K.; Lazarides, A.; Hemmerich, Andreas; de Morais Smith, C.
2009-01-01
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature
17. Topology optimization of two-dimensional waveguides
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
18. On two-dimensional magnetic reconnection with nonuniform resistivity
Science.gov (United States)
Malyshkin, Leonid M.; Kulsrud, Russell M.
2010-12-01
In this paper, two theoretical approaches for the calculation of the rate of quasi-stationary, two-dimensional magnetic reconnection with nonuniform anomalous resistivity are considered in the framework of incompressible magnetohydrodynamics (MHD). In the first, 'global' equations approach, the MHD equations are approximately solved for a whole reconnection layer, including the upstream and downstream regions and the layer center. In the second, 'local' equations approach, the equations are solved across the reconnection layer, including only the upstream region and the layer center. Both approaches give the same approximate answer for the reconnection rate. Our theoretical model is in agreement with the results of recent simulations of reconnection with spatially nonuniform resistivity.
19. Analysis of Manufacturing Bimetallic Tubes by the Cold Drawing Process
Directory of Open Access Journals (Sweden)
Halaczek D.
2016-03-01
Full Text Available Drawing processes apply to obtain the bimetallic tubes from the different metals and alloys, combined in the solid state, which significantly affects the specificity of this process. The manufacturing of bimetallic tubes by drawing process depends on many factors which include: preparation of the surface of materials joined in the solid state, the geometric parameters of the working tool, technological parameters of the drawing process (drawing speed, type of lubricant, the use of back pull etc.. Generally, the cold drawing process of producing the bimetallic tubes refers to metals which have high ductility (copper, aluminum, etc.. The tube sinking (tube drawing without a mandrel of bimetallic tubes together with joining them at the interface of the two metal in the solid-state is applied for tubes of the diameter range between 6 to 20 mm and based on of the reducing the diameter of the tube. However, a slight increase of wall thickness ca. 0.05 ÷ 0.10 mm can appear, which is not dangerous phenomenon in case of producing the bimetallic tubes by joining in the solid-state. The aim of the research was to investigate the technology of tubes drawing process from non-ferrous metal, drawing process of bimetallic tubes and the production of bimetallic tubes in layers composition: cooper Cu-ETP - brass CuZn37 and CuZn37 brass - copper Cu-ETP in the tube sinking process. The research program included: production of bimetallic tubes with a different composition (Cu- ETP-CuZn37 and CuZn37-Cu-ETP and a different percentage of the cross-section components; analysis of changes of tube wall thickness and the layer composition of the bimetallic tube, based on measurements on the workshop microscope; analysis of the material flow in the process of the bimetallic tubes production based on the measurements results of a profilograph CP-200.
20. Segregation and phase dynamics in supported bimetallic nanoparticles
Science.gov (United States)
Nashner, Michael Sydney
1997-12-01
A set of supported bimetallic catalysts, designated lbrack Resb7Ir-Nrbrack,\\ lbrack Resb7Ir-Prbrack,\\ lbrack Resb5IrResb2-Prbrack, and lbrack Resb5IrResb2-Prbrack, has been prepared from two structural isomers of the cluster compound (Z) sb2lbrack Resb7IrC(CO)sb{23}rbrack\\ (Zsp+=NEtsb4sp+,\\ N(PPhsb3)sb2sp+) by deposition onto high surface area alumina ({≤}1% Re) and activation in Hsb2 at 773 K. The more active catalysts (lbrack Resb7Ir-N) and lbrack Resb5IrResb2-Nrbrack) are modeled by a hemisphere of close-packed (hcp) metal atoms (avg. diameter 1 nm) with Ir at the core. On the other hand the less active catalysts (lbrack Resb7Ir-Prbrack and lbrack Resb5IrResb2-Prbrack) are better described as two-dimensional layer structures. Supported bimetallic particles were obtained by reduction of the neutral molecular carbonyl cluster precursor PtRusb5C(CO)sb{16} with hydrogen. A detailed structural model of the nanoparticles has been deduced on the basis of studies by in-situ extended x-ray absorption fine structure spectroscopy (EXAFS), scanning transmission electron microscopy (STEM), microprobe energy dispersive x-ray (EDX) analysis, and electron microdiffraction. These experiments show that the bimetallic nanoparticles have a Pt:Ru composition of 1:5, an average diameter of ca. 1.5 nm, and adopt a face-centered cubic (fcc) closest packing structure. The local metal coordination environment, revealed by multiple scattering analysis of the EXAFS data, shows Pt segregation to the particle surfaces under an ambient Hsb2 atmosphere. The incipient lbrack PtRusb5rbrack nanoparticles were found to nucleate from a disordered structure where Pt is found in highly coordinating environments (i.e., the core) at temperatures as low as 473 K. This structure inverts to form the structure with surface segregated Pt. The reaction between a silicon monolayer deposited on Pt(111) by chemical vapor deposition (CVD) using silane (SiHsb4) is described. Using Auger electron
1. Two-dimensional function photonic crystals
Science.gov (United States)
Liu, Xiao-Jing; Liang, Yu; Ma, Ji; Zhang, Si-Qi; Li, Hong; Wu, Xiang-Yao; Wu, Yi-Heng
2017-01-01
In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.
2. Two-Dimensional Planetary Surface Lander
Science.gov (United States)
Hemmati, H.; Sengupta, A.; Castillo, J.; McElrath, T.; Roberts, T.; Willis, P.
2014-06-01
A systems engineering study was conducted to leverage a new two-dimensional (2D) lander concept with a low per unit cost to enable scientific study at multiple locations with a single entry system as the delivery vehicle.
3. Interpolation by two-dimensional cubic convolution
Science.gov (United States)
Shi, Jiazheng; Reichenbach, Stephen E.
2003-08-01
This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.
4. TWO-DIMENSIONAL TOPOLOGY OF COSMOLOGICAL REIONIZATION
Energy Technology Data Exchange (ETDEWEB)
Wang, Yougang; Xu, Yidong; Chen, Xuelei [Key Laboratory of Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 China (China); Park, Changbom [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); Kim, Juhan, E-mail: [email protected], E-mail: [email protected] [Center for Advanced Computation, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)
2015-11-20
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two-dimensional genus curve for the early, middle, and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometre Array.
5. Two dimensional topology of cosmological reionization
CERN Document Server
Wang, Yougang; Xu, Yidong; Chen, Xuelei; Kim, Juhan
2015-01-01
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two dimensional genus curve for the early, middle and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometer Array.
6. Two-dimensional x-ray diffraction
CERN Document Server
He, Bob B
2009-01-01
Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea
7. Matching Two-dimensional Gel Electrophoresis' Spots
DEFF Research Database (Denmark)
Dos Anjos, António; AL-Tam, Faroq; Shahbazkia, Hamid Reza
2012-01-01
This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches. This ar......This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches...
8. Mobility anisotropy of two-dimensional semiconductors
Science.gov (United States)
Lang, Haifeng; Zhang, Shuqing; Liu, Zhirong
2016-12-01
The carrier mobility of anisotropic two-dimensional semiconductors under longitudinal acoustic phonon scattering was theoretically studied using deformation potential theory. Based on the Boltzmann equation with the relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was derived, showing that the influence of effective mass on mobility anisotropy is larger than those of deformation potential constant or elastic modulus. Parameters were collected for various anisotropic two-dimensional materials (black phosphorus, Hittorf's phosphorus, BC2N , MXene, TiS3, and GeCH3) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio is overestimated by the previously described method.
9. Towards two-dimensional search engines
OpenAIRE
Ermann, Leonardo; Chepelianskii, Alexei D.; Shepelyansky, Dima L.
2011-01-01
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Statistical properties of inf...
10. Authors' reply to Discussion by E. Siebrits and S. L. Crouch regarding the paper "A two-dimensional linear variation displacement discontinuity method for three-layered elastic media", International Journal of Rock Mechanics and Mining Sciences, Vol. 36, No. 6, pp. 719-729, 1999
CSIR Research Space (South Africa)
Shou, KJ
2000-07-01
Full Text Available to Discussion by E. Siebrits and S. L. Crouch regarding the paper A two-dimensional linear variation displacement discontinuity method for three-layered elastic media'', International Journal of Rock Mechanics and Mining Sciences, Vol. 36, No. 6, pp. 719... of judging the accuracy of their highly accurate semi-analytic simulator'' which is International Journal of Rock Mechanics and Mining Sciences 37 (2000) 877±878 1365-1609/00/$- see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S... 11. a First Cryptosystem for Security of Two-Dimensional Data Science.gov (United States) Mishra, D. C.; Sharma, Himani; Sharma, R. K.; Kumar, Naveen In this paper, we present a novel technique for security of two-dimensional data with the help of cryptography and steganography. The presented approach provides multilayered security of two-dimensional data. First layer security was developed by cryptography and second layer by steganography. The advantage of steganography is that the intended secret message does not attract attention to itself as an object of scrutiny. This paper proposes a novel approach for encryption and decryption of information in the form of Word Data (.doc file), PDF document (.pdf file), Text document, Gray-scale images, and RGB images, etc. by using Vigenere Cipher (VC) associated with Discrete Fourier Transform (DFT) and then hiding the data behind the RGB image (i.e. steganography). Earlier developed techniques provide security of either PDF data, doc data, text data or image data, but not for all types of two-dimensional data and existing techniques used either cryptography or steganography for security. But proposed approach is suitable for all types of data and designed for security of information by cryptography and steganography. The experimental results for Word Data, PDF document, Text document, Gray-scale images and RGB images support the robustness and appropriateness for secure transmission of these data. The security analysis shows that the presented technique is immune from cryptanalytic. This technique further provides security while decryption as a check on behind which RGB color the information is hidden. 12. Kronecker Product of Two-dimensional Arrays Institute of Scientific and Technical Information of China (English) Lei Hu 2006-01-01 Kronecker sequences constructed from short sequences are good sequences for spread spectrum communication systems. In this paper we study a similar problem for two-dimensional arrays, and we determine the linear complexity of the Kronecker product of two arrays. Our result shows that similar good property on linear complexity holds for Kronecker product of arrays. 13. Two-Dimensional Toda-Heisenberg Lattice Directory of Open Access Journals (Sweden) Vadim E. Vekslerchik 2013-06-01 Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions. 14. A novel two dimensional particle velocity sensor NARCIS (Netherlands) Pjetri, Olti; Wiegerink, Remco J.; Lammerink, Theo S.; Krijnen, Gijs J. 2013-01-01 In this paper we present a two wire, two-dimensional particle velocity sensor. The miniature sensor of size 1.0x2.5x0.525 mm, consisting of only two crossed wires, shows excellent directional sensitivity in both directions, thus requiring no directivity calibration, and is relatively easy to fabrica 15. Two-dimensional microstrip detector for neutrons Energy Technology Data Exchange (ETDEWEB) Oed, A. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France) 1997-04-01 Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs. 16. Two-dimensional magma-repository interactions NARCIS (Netherlands) Bokhove, O. 2001-01-01 Two-dimensional simulations of magma-repository interactions reveal that the three phases --a shock tube, shock reflection and amplification, and shock attenuation and decay phase-- in a one-dimensional flow tube model have a precursor. This newly identified phase zero'' consists of the impact of 17. Two-dimensional subwavelength plasmonic lattice solitons CERN Document Server Ye, F; Hu, B; Panoiu, N C 2010-01-01 We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai 18. A two-dimensional Dirac fermion microscope DEFF Research Database (Denmark) Bøggild, Peter; Caridad, Jose; Stampfer, Christoph 2017-01-01 in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2... 19. Biosensors Incorporating Bimetallic Nanoparticles Directory of Open Access Journals (Sweden) John Rick 2015-12-01 Full Text Available This article presents a review of electrochemical bio-sensing for target analytes based on the use of electrocatalytic bimetallic nanoparticles (NPs, which can improve both the sensitivity and selectivity of biosensors. The review moves quickly from an introduction to the field of bio-sensing, to the importance of biosensors in today’s society, the nature of the electrochemical methods employed and the attendant problems encountered. The role of electrocatalysts is introduced with reference to the three generations of biosensors. The contributions made by previous workers using bimetallic constructs, grouped by target analyte, are then examined in detail; following which, the synthesis and characterization of the catalytic particles is examined prior to a summary of the current state of endeavor. Finally, some perspectives for the future of bimetallic NPs in biosensors are given. 20. Biosensors Incorporating Bimetallic Nanoparticles. Science.gov (United States) Rick, John; Tsai, Meng-Che; Hwang, Bing Joe 2015-12-31 This article presents a review of electrochemical bio-sensing for target analytes based on the use of electrocatalytic bimetallic nanoparticles (NPs), which can improve both the sensitivity and selectivity of biosensors. The review moves quickly from an introduction to the field of bio-sensing, to the importance of biosensors in today's society, the nature of the electrochemical methods employed and the attendant problems encountered. The role of electrocatalysts is introduced with reference to the three generations of biosensors. The contributions made by previous workers using bimetallic constructs, grouped by target analyte, are then examined in detail; following which, the synthesis and characterization of the catalytic particles is examined prior to a summary of the current state of endeavor. Finally, some perspectives for the future of bimetallic NPs in biosensors are given. 1. Wafer-scale controlled exfoliation of metal organic vapor phase epitaxy grown InGaN/GaN multi quantum well structures using low-tack two-dimensional layered h-BN Energy Technology Data Exchange (ETDEWEB) Ayari, Taha; Li, Xin; Voss, Paul L.; Ougazzaden, Abdallah, E-mail: [email protected] [School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Georgia Tech Lorraine, UMI 2958, Georgia Tech-CNRS, 57070 Metz (France); Sundaram, Suresh; El Gmili, Youssef [Georgia Tech Lorraine, UMI 2958, Georgia Tech-CNRS, 57070 Metz (France); Salvestrini, Jean Paul [Georgia Tech Lorraine, UMI 2958, Georgia Tech-CNRS, 57070 Metz (France); Université de Lorraine, LMOPS, EA 4423, 57070 Metz (France) 2016-04-25 Recent advances in epitaxial growth have led to the growth of III-nitride devices on 2D layered h-BN. This advance has the potential for wafer-scale transfer to arbitrary substrates, which could improve the thermal management and would allow III-N devices to be used more flexibly in a broader range of applications. We report wafer scale exfoliation of a metal organic vapor phase epitaxy grown InGaN/GaN Multi Quantum Well (MQW) structure from a 5 nm thick h-BN layer that was grown on a 2-inch sapphire substrate. The weak van der Waals bonds between h-BN atomic layers break easily, allowing the MQW structure to be mechanically lifted off from the sapphire substrate using a commercial adhesive tape. This results in the surface roughness of only 1.14 nm on the separated surface. Structural characterizations performed before and after the lift-off confirm the conservation of structural properties after lift-off. Cathodoluminescence at 454 nm was present before lift-off and 458 nm was present after. Electroluminescence near 450 nm from the lifted-off structure has also been observed. These results show that the high crystalline quality ultrathin h-BN serves as an effective sacrificial layer—it maintains performance, while also reducing the GaN buffer thickness and temperature ramps as compared to a conventional two-step growth method. These results support the use of h-BN as a low-tack sacrificial underlying layer for GaN-based device structures and demonstrate the feasibility of large area lift-off and transfer to any template, which is important for industrial scale production. 2. Electronics based on two-dimensional materials. Science.gov (United States) Fiori, Gianluca; Bonaccorso, Francesco; Iannaccone, Giuseppe; Palacios, Tomás; Neumaier, Daniel; Seabaugh, Alan; Banerjee, Sanjay K; Colombo, Luigi 2014-10-01 The compelling demand for higher performance and lower power consumption in electronic systems is the main driving force of the electronics industry's quest for devices and/or architectures based on new materials. Here, we provide a review of electronic devices based on two-dimensional materials, outlining their potential as a technological option beyond scaled complementary metal-oxide-semiconductor switches. We focus on the performance limits and advantages of these materials and associated technologies, when exploited for both digital and analog applications, focusing on the main figures of merit needed to meet industry requirements. We also discuss the use of two-dimensional materials as an enabling factor for flexible electronics and provide our perspectives on future developments. 3. Two-dimensional ranking of Wikipedia articles Science.gov (United States) Zhirov, A. O.; Zhirov, O. V.; Shepelyansky, D. L. 2010-10-01 The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories. 4. Two-Dimensional NMR Lineshape Analysis Science.gov (United States) Waudby, Christopher A.; Ramos, Andres; Cabrita, Lisa D.; Christodoulou, John 2016-04-01 NMR titration experiments are a rich source of structural, mechanistic, thermodynamic and kinetic information on biomolecular interactions, which can be extracted through the quantitative analysis of resonance lineshapes. However, applications of such analyses are frequently limited by peak overlap inherent to complex biomolecular systems. Moreover, systematic errors may arise due to the analysis of two-dimensional data using theoretical frameworks developed for one-dimensional experiments. Here we introduce a more accurate and convenient method for the analysis of such data, based on the direct quantum mechanical simulation and fitting of entire two-dimensional experiments, which we implement in a new software tool, TITAN (TITration ANalysis). We expect the approach, which we demonstrate for a variety of protein-protein and protein-ligand interactions, to be particularly useful in providing information on multi-step or multi-component interactions. 5. Towards two-dimensional search engines CERN Document Server Ermann, Leonardo; Shepelyansky, Dima L 2011-01-01 We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Information flow properties on PageRank-CheiRank plane are analyzed for networks of British, French and Italian Universities, Wikipedia, Linux Kernel, gene regulation and other networks. Methods of spam links control are also analyzed. 6. Toward two-dimensional search engines Science.gov (United States) Ermann, L.; Chepelianskii, A. D.; Shepelyansky, D. L. 2012-07-01 We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank-CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed. 7. A two-dimensional Dirac fermion microscope Science.gov (United States) Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads 2017-06-01 The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots. 8. A two-dimensional Dirac fermion microscope. Science.gov (United States) Bøggild, Peter; Caridad, José M; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads 2017-06-09 The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots. 9. Two-Dimensional Scheduling: A Review Directory of Open Access Journals (Sweden) Zhuolei Xiao 2013-07-01 Full Text Available In this study, we present a literature review, classification schemes and analysis of methodology for scheduling problems on Batch Processing machine (BP with both processing time and job size constraints which is also regarded as Two-Dimensional (TD scheduling. Special attention is given to scheduling problems with non-identical job sizes and processing times, with details of the basic algorithms and other significant results. 10. Two dimensional fermions in four dimensional YM CERN Document Server Narayanan, R 2009-01-01 Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in$R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite$N$. As the size of the torus in units of$\\frac{1}{\\Lambda_{SU(N)}}$is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite$Nlimit. 11. Two-dimensional Kagome photonic bandgap waveguide DEFF Research Database (Denmark) Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou; 2000-01-01 The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out.... 12. String breaking in two-dimensional QCD CERN Document Server Hornbostel, K J 1999-01-01 I present results of a numerical calculation of the effects of light quark-antiquark pairs on the linear heavy-quark potential in light-cone quantized two-dimensional QCD. I extract the potential from the Q-Qbar component of the ground-state wavefunction, and observe string breaking at the heavy-light meson pair threshold. I briefly comment on the states responsible for the breaking. 13. Two-dimensional oxides: multifunctional materials for advanced technologies. Science.gov (United States) Pacchioni, Gianfranco 2012-08-13 The last decade has seen spectacular progress in the design, preparation, and characterization down to the atomic scale of oxide ultrathin films of few nanometers thickness grown on a different material. This has paved the way towards several sophisticated applications in advanced technologies. By playing around with the low-dimensionality of the oxide layer, which sometimes leads to truly two-dimensional systems, one can exploit new properties and functionalities that are not present in the corresponding bulk materials or thick films. In this review we provide some clues about the most recent advances in the design of these systems based on modern electronic structure theory and on their preparation and characterization with specifically developed growth techniques and analytical methods. We show how two-dimensional oxides can be used in mature technologies by providing added value to existing materials, or in new technologies based on completely new paradigms. The fields in which two-dimensional oxides are used are classified based on the properties that are exploited, chemical or physical. With respect to chemical properties we discuss use of oxide ultrathin films in catalysis, solid oxide fuel cells, gas sensors, corrosion protection, and biocompatible materials; regarding the physical properties we discuss metal-oxide field effect transistors and memristors, spintronic devices, ferroelectrics and thermoelectrics, and solar energy materials. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 14. Two dimensional echocardiographic detection of intraatrial masses. Science.gov (United States) DePace, N L; Soulen, R L; Kotler, M N; Mintz, G S 1981-11-01 With two dimensional echocardiography, a left atrial mass was detected in 19 patients. Of these, 10 patients with rheumatic mitral stenosis had a left atrial thrombus. The distinctive two dimensional echocardiographic features of left atrial thrombus included a mass of irregular nonmobile laminated echos within an enlarged atrial cavity, usually with a broad base of attachment to the posterior left atrial wall. Seven patients had a left atrial myxoma. Usually, the myxoma appeared as a mottled ovoid, sharply demarcated mobile mass attached to the interatrial septum. One patient had a right atrial angiosarcoma that appeared as a nonmobile mass extending from the inferior vena caval-right atrial junction into the right atrial cavity. One patient had a left atrial leiomyosarcoma producing a highly mobile mass attached to the lateral wall of the left atrium. M mode echocardiography detected six of the seven myxomas, one thrombus and neither of the other tumors. Thus, two dimensional echocardiography appears to be the technique of choice in the detection, localization and differentiation of intraatrial masses. 15. Syntheses and Crystal Structures of Two Cyano-bridged Bimetallic Complexes [Ln(DMSO)2(H2O)(μ-CN)4Fe(CN)2](Ln= Ce and Eu, DMSO= Dimethylsulfoxide) with Layered Structure Institute of Scientific and Technical Information of China (English) ZHAO Zhen-Qian; CAI Li-Zhen; CHEN Wen-Tong; GUO Guo-Cong; HUANG Jin-Shun 2008-01-01 Two new bimetallic cyano-bridged complexes [Ln(DMSO)2(H2O)(μ-CN)4Fe(CN)2] (Ln = Ce 1, Eu 2) have been prepared by the grinding reaction method and structurally characterized by X-ray single-crystal structure analysis. Crystallographic data for 1: C10H14CeFeN6O3S2, Mr = 526.36, monoclinic, P2/n, a = 7.852(4), b = 10.729(5), c = 11.181(5) (A), β = 96.992(8)°, V = 935.0(7) A3, Z = 2, Dc = 1.870 g/cm3, μ = 3.421 mm-1, F(000) = 512, R = 0.0363 and wR = 0.0971; and those for 2: C10H14EuFeN6O3S2, Mr = 538.20, monoclinic, P2/n, a = 7.739(5), b = 10.668(7), c = 11.008(7) A, β = 96.943(3)°, V = 902.1(11) A3, Z = 2, Dc = 1.981 g/cm3, μ= 4.499 mm-1, F(000) = 522, R = 0.0345 and wR = 0.0855. In each complex the lanthanide ion is seven-coordinated in a pentagonal bipyramidal arrangement, and the Fe(Ⅲ) ion is in a nearly regular octahedral environment. The title complexes can be described as two-dimensional (2-D) stair-like structures, which are further connected by hydrogen bonds to form three-dimensional (3-D) frameworks. 16. Theories on Frustrated Electrons in Two-Dimensional Organic Solids Directory of Open Access Journals (Sweden) Chisa Hotta 2012-08-01 Full Text Available Two-dimensional quarter-filled organic solids are a promising class of materials to realize the strongly correlated insulating states called dimer Mott insulator and charge order. In their conducting layer, the molecules form anisotropic triangular lattices, harboring geometrical frustration effect, which could give rise to many interesting states of matter in the two insulators and in the metals adjacent to them. This review is concerned with the theoretical studies on such issue over the past ten years, and provides the systematic understanding on exotic metals, dielectrics, and spin liquids, which are the consequences of the competing correlation and fluctuation under frustration. 17. Mean flow generation in rotating anelastic two-dimensional convection CERN Document Server Currie, Laura K 2016-01-01 We investigate the processes that lead to the generation of mean flows in two-dimensional anelastic convection. The simple model consists of a plane layer that is rotating about an axis inclined to gravity. The results are two-fold: firstly we numerically investigate the onset of convection in three-dimensions, paying particular attention to the role of stratification and highlight a curious symmetry. Secondly, we investigate the mechanisms that drive both zonal and meridional flows in two dimensions. We find that, in general, non-trivial Reynolds stresses can lead to systematic flows and, using statistical measures, we quantify the role of stratification in modifying the coherence of these flows. 18. Two-dimensional carbon fundamental properties, synthesis, characterization, and applications CERN Document Server Yihong, Wu; Ting, Yu 2013-01-01 After a brief introduction to the fundamental properties of graphene, this book focuses on synthesis, characterization and application of various types of two-dimensional (2D) nanocarbons ranging from single/few layer graphene to carbon nanowalls and graphene oxides. Three major synthesis techniques are covered: epitaxial growth of graphene on SiC, chemical synthesis of graphene on metal, and chemical vapor deposition of vertically aligned carbon nanosheets or nanowalls. One chapter is dedicated to characterization of 2D nanocarbon using Raman spectroscopy. It provides extensive coverage for a 19. Magnetization of two-dimensional superconductors with defects CERN Document Server Kashurnikov, V A; Zyubin, M V 2002-01-01 The new method for modeling the layered high-temperature superconductors magnetization with defects, based on the Monte-Carlo algorithm, is developed. Minimization of the free energy functional of the vortex two-dimensional system made it possible to obtain the equilibrium vortex density configurations and calculate the magnetization of the superconductor with the arbitrary defects distribution in the wide range of temperatures. The magnetic induction profiles and magnetic flux distribution inside the superconductor, proving the applicability of the Bean model, are calculated 20. BIMETALLIC CONDUCTOR’S SPECIFIC RESISTANCE Directory of Open Access Journals (Sweden) Markitantova Natal'ya Konstantinovna 2013-04-01 Full Text Available Improvement of conductors of electric energy and signals is considered by the authors. The subject of the research consists in cable conductors, and their improvement is analyzed on the macro-level. The authors have derived the final formula designated for the calculation of the value of the specific electric resistance of bimetallic conductors. MathCAD-14 software was employed to perform the calculations. The analysis of dependencies derived by the authors allowed the authors to make the conclusion that the thinner the copper layer, the higher the specific electric resistance of the bimetallic conductor. Moreover, the authors succeeded in making a quantitative presentation of the aforementioned characteristic, which is a relevant contribution into its further systemic analysis. 1. Weakly disordered two-dimensional Frenkel excitons Science.gov (United States) Boukahil, A.; Zettili, Nouredine 2004-03-01 We report the results of studies of the optical properties of weakly disordered two- dimensional Frenkel excitons in the Coherent Potential Approximation (CPA). An approximate complex Green's function for a square lattice with nearest neighbor interactions is used in the self-consistent equation to determine the coherent potential. It is shown that the Density of States is very much affected by the logarithmic singularities in the Green's function. Our CPA results are in excellent agreement with previous investigations by Schreiber and Toyozawa using the Monte Carlo simulation. 2. Two-dimensional photonic crystal surfactant detection. Science.gov (United States) Zhang, Jian-Tao; Smith, Natasha; Asher, Sanford A 2012-08-07 We developed a novel two-dimensional (2-D) crystalline colloidal array photonic crystal sensing material for the visual detection of amphiphilic molecules in water. A close-packed polystyrene 2-D array monolayer was embedded in a poly(N-isopropylacrylamide) (PNIPAAm)-based hydrogel film. These 2-D photonic crystals placed on a mirror show intense diffraction that enables them to be used for visual determination of analytes. Binding of surfactant molecules attaches ions to the sensor that swells the PNIPAAm-based hydrogel. The resulting increase in particle spacing red shifts the 2-D diffracted light. Incorporation of more hydrophobic monomers increases the sensitivity to surfactants. 3. Theory of two-dimensional transformations OpenAIRE Kanayama, Yutaka J.; Krahn, Gary W. 1998-01-01 The article of record may be found at http://dx.doi.org/10.1109/70.720359 Robotics and Automation, IEEE Transactions on This paper proposes a new "heterogeneous" two-dimensional (2D) transformation group ___ to solve motion analysis/planning problems in robotics. In this theory, we use a 3×1 matrix to represent a transformation as opposed to a 3×3 matrix in the homogeneous formulation. First, this theory is as capable as the homogeneous theory, Because of the minimal size, its implement... 4. Two-dimensional ranking of Wikipedia articles CERN Document Server Zhirov, A O; Shepelyansky, D L 2010-01-01 The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. We analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories. 5. Mobility anisotropy of two-dimensional semiconductors CERN Document Server Lang, Haifeng; Liu, Zhirong 2016-01-01 The carrier mobility of anisotropic two-dimensional (2D) semiconductors under longitudinal acoustic (LA) phonon scattering was theoretically studied with the deformation potential theory. Based on Boltzmann equation with relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was deduced, which shows that the influence of effective mass to the mobility anisotropy is larger than that of deformation potential constant and elastic modulus. Parameters were collected for various anisotropic 2D materials (black phosphorus, Hittorf's phosphorus, BC_2$N, MXene, TiS$_3$, GeCH$_3$) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio was overestimated in the past. 6. Sums of two-dimensional spectral triples DEFF Research Database (Denmark) Christensen, Erik; Ivan, Cristina 2007-01-01 construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly......, the Dixmier trace induces a multiple of the Lebesgue integral but the growth of the number of eigenvalues is different from the one found for the standard differential operator on the unit interval.... 7. Binding energy of two-dimensional biexcitons DEFF Research Database (Denmark) Singh, Jai; Birkedal, Dan; Vadim, Lyssenko; 1996-01-01 Using a model structure for a two-dimensional (2D) biexciton confined in a quantum well, it is shown that the form of the Hamiltonian of the 2D biexciton reduces into that of an exciton. The binding energies and Bohr radii of a 2D biexciton in its various internal energy states are derived...... analytically using the fractional dimension approach. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be 0.228, which agrees very well with the recent experimental value. The results of our approach are compared with those of earlier theories.... 8. Dynamics of film. [two dimensional continua theory Science.gov (United States) Zak, M. 1979-01-01 The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets. The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles. The theory is illustrated by examples. 9. Two-dimensional gauge theoretic supergravities Science.gov (United States) Cangemi, D.; Leblanc, M. 1994-05-01 We investigate two-dimensional supergravity theories, which can be built from a topological and gauge invariant action defined on an ordinary surface. One is the N = 1 supersymmetric extension of the Jackiw-Teitelboim model presented by Chamseddine in a superspace formalism. We complement the proof of Montano, Aoaki and Sonnenschein that this extension is topological and gauge invariant, based on the graded de Sitter algebra. Not only do the equations of motion correspond to the supergravity ones and do gauge transformations encompass local supersymmetries, but we also identify the ∫-theory with the superfield formalism action written by Chamseddine. Next, we show that the N = 1 supersymmetric extension of string-inspired two-dimensional dilaton gravity put forward by Park and Strominger cannot be written as a ∫-theory. As an alternative, we propose two topological and gauge theories that are based on a graded extension of the extended Poincaré algebra and satisfy a vanishing-curvature condition. Both models are supersymmetric extensions of the string-inspired dilaton gravity. 10. Two-Dimensional Theory of Scientific Representation Directory of Open Access Journals (Sweden) A Yaghmaie 2013-03-01 Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional. 11. Two-dimensional shape memory graphene oxide Science.gov (United States) Chang, Zhenyue; Deng, Junkai; Chandrakumara, Ganaka G.; Yan, Wenyi; Liu, Jefferson Zhe 2016-06-01 Driven by the increasing demand for micro-/nano-technologies, stimuli-responsive shape memory materials at nanoscale have recently attracted great research interests. However, by reducing the size of conventional shape memory materials down to approximately nanometre range, the shape memory effect diminishes. Here, using density functional theory calculations, we report the discovery of a shape memory effect in a two-dimensional atomically thin graphene oxide crystal with ordered epoxy groups, namely C8O. A maximum recoverable strain of 14.5% is achieved as a result of reversible phase transition between two intrinsically stable phases. Our calculations conclude co-existence of the two stable phases in a coherent crystal lattice, giving rise to the possibility of constructing multiple temporary shapes in a single material, thus, enabling highly desirable programmability. With an atomic thickness, excellent shape memory mechanical properties and electric field stimulus, the discovery of a two-dimensional shape memory graphene oxide opens a path for the development of exceptional micro-/nano-electromechanical devices. 12. Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems Science.gov (United States) Naeem, Imran; Naz, Rehana; Khan, Muhammad Danish 2015-12-01 This article analyses the nonclassical symmetries and group invariant solution of boundary layer equations for two-dimensional heated flows. First, we derive the nonclassical symmetry determining equations with the aid of the computer package SADE. We solve these equations directly to obtain nonclassical symmetries. We follow standard procedure of computing nonclassical symmetries and consider two different scenarios, ξ1≠0 and ξ1=0, ξ2≠0. Several nonclassical symmetries are reported for both scenarios. Furthermore, numerous group invariant solutions for nonclassical symmetries are derived. The similarity variables associated with each nonclassical symmetry are computed. The similarity variables reduce the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) in terms of similarity variables. The reduced system of ODEs are solved to obtain group invariant solution for governing boundary layer equations for two-dimensional heated flow problems. We successfully formulate a physical problem of heat transfer analysis for fluid flow over a linearly stretching porous plat and, with suitable boundary conditions, we solve this problem. 13. Visualising the strain distribution in suspended two-dimensional materials under local deformation Science.gov (United States) Elibol, Kenan; Bayer, Bernhard C.; Hummel, Stefan; Kotakoski, Jani; Argentero, Giacomo; Meyer, Jannik C. 2016-06-01 We demonstrate the use of combined simultaneous atomic force microscopy (AFM) and laterally resolved Raman spectroscopy to study the strain distribution around highly localised deformations in suspended two-dimensional materials. Using the AFM tip as a nanoindentation probe, we induce localised strain in suspended few-layer graphene, which we adopt as a two-dimensional membrane model system. Concurrently, we visualise the strain distribution under and around the AFM tip in situ using hyperspectral Raman mapping via the strain-dependent frequency shifts of the few-layer graphene’s G and 2D Raman bands. Thereby we show how the contact of the nm-sized scanning probe tip results in a two-dimensional strain field with μm dimensions in the suspended membrane. Our combined AFM/Raman approach thus adds to the critically required instrumental toolbox towards nanoscale strain engineering of two-dimensional materials. 14. Existence and Stability of Two-Dimensional Compact-Like Discrete Breathers in Discrete Two-Dimensional Monatomic Square Lattices Institute of Scientific and Technical Information of China (English) XU Quan; TIAN Qiang 2007-01-01 Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generafized discrete two-dimensional monatomic model.It is proven that the twodimensional compact-like discrete breathers exist not only in two-dimensional soft Ф4 potentials but also in hard two-dimensional Ф4 potentials and pure two-dimensional K4 lattices.The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Ф4 potential are determined by coupling parameter K4,while those in pure two-dimensional K4 lattices have no coupling with parameter K4.The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices. 15. Stability and electronic properties of two-dimensional indium iodide Science.gov (United States) Wang, Jizhang; Dong, Baojuan; Guo, Huaihong; Yang, Teng; Zhu, Zhen; Hu, Gan; Saito, Riichiro; Zhang, Zhidong 2017-01-01 Based on ab initio density functional calculations, we studied the stability and electronic properties of two-dimensional indium iodide (InI). The calculated results show that monolayer and few-layer InI can be as stable as its bulk counterpart. The stability of the monolayer structure is further supported by examining the electronic and dynamic stability. The interlayer interaction is found to be fairly weak (˜160 meV/atom) and mechanical exfoliation to obtain monolayer and few-layer structures will be applicable. A direct band gap of 1.88 eV of the bulk structure is obtained from the hybrid functional method, and is comparable to the experimental one (˜2.00 eV). The electronic structure can be tuned by layer stacking and external strain. The size of the gap is a linear function of an inverse number of layers, suggesting that we can design few-layer structures for optoelectronic applications in the visible optical range. In-plane tensile or hydrostatic compressive stress is found to be useful not only in varying the gap size to cover the whole visible optical range, but also in inducing a semiconductor-metal transition with an experimentally accessible stress. The present result strongly supports the strategy of broadening the scope of group-V semiconductors by looking for isoelectronic III-VII atomic-layered materials. 16. Copper diphosphonates with zero-, one- and two-dimensional structures: ferrimagnetism in layer compound Cu3(ImhedpH)(2).2H2O [ImhedpH4=(1-C3H3N2)CH2C(OH)(PO3H2)2]. Science.gov (United States) Cao, Deng-Ke; Xie, Xiao-Ji; Li, Yi-Zhi; Zheng, Li-Min 2008-10-07 Reactions of CuSO4 with 2-(1-imidazole)-1-hydroxy-1,1'-ethylidenediphosphonic acid (ImhedpH4) under hydrothermal conditions at different temperatures lead to four new metal phosphonates: Cu(ImhedpH3)2(H2O).2H2O (), Cu(ImhedpH3)2 (), Cu3(ImhedpH2)2(ImhedpH3)(2).4H2O (), and Cu3(ImhedpH)(2).2H2O (). Compounds and have mononuclear structures in which the Cu atoms adopt square pyramidal and square planar geometries, respectively. In compound , a chain structure is observed where the Cu3(ImhedpH2)2(ImhedpH3)2 trimer units are connected by edge-sharing of the {Cu2O5} square pyramids. Compound exhibits a layer structure made up of Cu3(ImhedpH)2 trimer units. The connection of trimers through corner-sharing of {Cu1O4} and {CPO3} tetrahedra results in a two-dimensional layer containing 8- and 16-membered rings. The imidazole groups are grafted on the two sides of the layer. Magnetic studies reveal that ferromagnetic interactions are mediated in , while for compound , ferrimagnetism is observed below 5.8 K. 17. Atom-Based Geometrical Fingerprinting of Conformal Two-Dimensional Materials Science.gov (United States) Mehboudi, Mehrshad The shape of two-dimensional materials plays a significant role on their chemical and physical properties. Two-dimensional materials are basic meshes that are formed by mesh points (vertices) given by atomic positions, and connecting lines (edges) between points given by chemical bonds. Therefore the study of local shape and geometry of two-dimensional materials is a fundamental prerequisite to investigate physical and chemical properties. Hereby the use of discrete geometry to discuss the shape of two-dimensional materials is initiated. The local geometry of a surface embodied in 3D space is determined using four invariant numbers from the metric and curvature tensors which indicates how much the surface is stretched and curved under a deformation as compared to a reference pre-deformed conformation. Many different disciplines advance theories on conformal two-dimensional materials by relying on continuum mechanics and fitting continuum surfaces to the shape of conformal two-dimensional materials. However two-dimensional materials are inherently discrete. The continuum models are only applicable when the size of two-dimensional materials is significantly large and the deformation is less than a few percent. In this research, the knowledge of discrete differential geometry was used to tell the local shape of conformal two-dimensional materials. Three kind of two-dimensional materials are discussed: 1) one atom thickness structures such as graphene and hexagonal boron nitride; 2) high and low buckled 2D meshes like stanene, leadene, aluminum phosphate; and, 3) multi layer 2D materials such as Bi2Se3 and WSe2. The lattice structures of these materials were created by designing a mechanical model - the mechanical model was devised in the form of a Gaussian bump and density-functional theory was used to inform the local height; and, the local geometries are also discussed. 18. Phonon hydrodynamics in two-dimensional materials. Science.gov (United States) Cepellotti, Andrea; Fugallo, Giorgia; Paulatto, Lorenzo; Lazzeri, Michele; Mauri, Francesco; Marzari, Nicola 2015-03-06 The conduction of heat in two dimensions displays a wealth of fascinating phenomena of key relevance to the scientific understanding and technological applications of graphene and related materials. Here, we use density-functional perturbation theory and an exact, variational solution of the Boltzmann transport equation to study fully from first-principles phonon transport and heat conductivity in graphene, boron nitride, molybdenum disulphide and the functionalized derivatives graphane and fluorographene. In all these materials, and at variance with typical three-dimensional solids, normal processes keep dominating over Umklapp scattering well-above cryogenic conditions, extending to room temperature and more. As a result, novel regimes emerge, with Poiseuille and Ziman hydrodynamics, hitherto typically confined to ultra-low temperatures, characterizing transport at ordinary conditions. Most remarkably, several of these two-dimensional materials admit wave-like heat diffusion, with second sound present at room temperature and above in graphene, boron nitride and graphane. 19. Probabilistic Universality in two-dimensional Dynamics CERN Document Server Lyubich, Mikhail 2011-01-01 In this paper we continue to explore infinitely renormalizable H\\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with the one-dimensional Cantor attractor is at most 1/2-H\\"older. Another formulation of this phenomenon is that the scaling structure of the H\\'enon Cantor attractor differs from its one-dimensional counterpart. However, in this paper we prove that the weight assigned by the canonical invariant measure to these bad spots tends to zero on microscopic scales. This phenomenon is called {\\it Probabilistic Universality}. It implies, in particular, that the Hausdorff dimension of the canonical measure is universal. In this way, universality and rigidity phenomena of one-dimensional dynamics assume a probabilistic nature in the two-dimensional world. 20. Two-dimensional position sensitive neutron detector Indian Academy of Sciences (India) A M Shaikh; S S Desai; A K Patra 2004-08-01 A two-dimensional position sensitive neutron detector has been developed. The detector is a 3He + Kr filled multiwire proportional counter with charge division position readout and has a sensitive area of 345 mm × 345 mm, pixel size 5 mm × 5 mm, active depth 25 mm and is designed for efficiency of 70% for 4 Å neutrons. The detector is tested with 0.5 bar 3He + 1.5 bar krypton gas mixture in active chamber and 2 bar 4He in compensating chamber. The pulse height spectrum recorded at an anode potential of 2000 V shows energy resolution of ∼ 25% for the 764 keV peak. A spatial resolution of 8 mm × 6 mm is achieved. The detector is suitable for SANS studies in the range of 0.02–0.25 Å-1. 1. Two-dimensional heterostructures for energy storage Science.gov (United States) Pomerantseva, Ekaterina; Gogotsi, Yury 2017-07-01 Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. We also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies. 2. Janus Spectra in Two-Dimensional Flows Science.gov (United States) Liu, Chien-Chia; Cerbus, Rory T.; Chakraborty, Pinaki 2016-09-01 In large-scale atmospheric flows, soap-film flows, and other two-dimensional flows, the exponent of the turbulent energy spectra, α , may theoretically take either of two distinct values, 3 or 5 /3 , but measurements downstream of obstacles have invariably revealed α =3 . Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which α transitions from 3 to 5 /3 for the streamwise fluctuations but remains equal to 3 for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows. 3. Local doping of two-dimensional materials Science.gov (United States) Wong, Dillon; Velasco, Jr, Jairo; Ju, Long; Kahn, Salman; Lee, Juwon; Germany, Chad E.; Zettl, Alexander K.; Wang, Feng; Crommie, Michael F. 2016-09-20 This disclosure provides systems, methods, and apparatus related to locally doping two-dimensional (2D) materials. In one aspect, an assembly including a substrate, a first insulator disposed on the substrate, a second insulator disposed on the first insulator, and a 2D material disposed on the second insulator is formed. A first voltage is applied between the 2D material and the substrate. With the first voltage applied between the 2D material and the substrate, a second voltage is applied between the 2D material and a probe positioned proximate the 2D material. The second voltage between the 2D material and the probe is removed. The first voltage between the 2D material and the substrate is removed. A portion of the 2D material proximate the probe when the second voltage was applied has a different electron density compared to a remainder of the 2D material. 4. Two-dimensional fourier transform spectrometer Energy Technology Data Exchange (ETDEWEB) DeFlores, Lauren; Tokmakoff, Andrei 2016-10-25 The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields. 5. Two-dimensional fourier transform spectrometer Science.gov (United States) DeFlores, Lauren; Tokmakoff, Andrei 2013-09-03 The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields. 6. FACE RECOGNITION USING TWO DIMENSIONAL LAPLACIAN EIGENMAP Institute of Scientific and Technical Information of China (English) Chen Jiangfeng; Yuan Baozong; Pei Bingnan 2008-01-01 Recently,some research efforts have shown that face images possibly reside on a nonlinear sub-manifold. Though Laplacianfaces method considered the manifold structures of the face images,it has limits to solve face recognition problem. This paper proposes a new feature extraction method,Two Dimensional Laplacian EigenMap (2DLEM),which especially considers the manifold structures of the face images,and extracts the proper features from face image matrix directly by using a linear transformation. As opposed to Laplacianfaces,2DLEM extracts features directly from 2D images without a vectorization preprocessing. To test 2DLEM and evaluate its performance,a series of ex-periments are performed on the ORL database and the Yale database. Moreover,several experiments are performed to compare the performance of three 2D methods. The experiments show that 2DLEM achieves the best performance. 7. Equivalency of two-dimensional algebras Energy Technology Data Exchange (ETDEWEB) Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S. [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica 2011-07-01 Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author) 8. Analysis of Al-Cu Bimetallic Bars Properties After Explosive Welding and Rolling in Modified Passes Directory of Open Access Journals (Sweden) Mróz S. 2015-04-01 Full Text Available The paper presents the results of the experimental tests of Al-Cu bimetallic bars rolling process in multi-radial modified passes. The bimetallic bars consist of aluminium core, grade 1050A and copper outer layer, grade M1E. The stocks were round bars with diameter 22 mm with a copper layer share of 15 and 30%. As a result of rolling in four passes, bars of a diameter of about 16.0 mm were obtained. A bimetallic stock was manufactured using an explosive welding method. The use of the designed arrangement of multi-radial modified stretching passes resulted in obtaining Al-Cu bimetallic bars with the required lateral dimensions, an uniform distribution of the cladding layer over the bar perimeter and high quality of shear strength between individual layers. 9. Surface and Interface Engineering of Organometallic and Two Dimensional Semiconductor Science.gov (United States) Park, Jun Hong For over half a century, inorganic Si and III-V materials have led the modern semiconductor industry, expanding to logic transistor and optoelectronic applications. However, these inorganic materials have faced two different fundamental limitations, flexibility for wearable applications and scaling limitation as logic transistors. As a result, the organic and two dimensional have been studied intentionally for various fields. In the present dissertation, three different studies will be presented with followed order; (1) the chemical response of organic semiconductor in NO2 exposure. (2) The surface and stability of WSe2 in ambient air. (3) Deposition of dielectric on two dimensional materials using organometallic seeding layer. The organic molecules rely on the van der Waals interaction during growth of thin films, contrast to covalent bond inorganic semiconductors. Therefore, the morphology and electronic property at surface of organic semiconductor in micro scale is more sensitive to change in gaseous conditions. In addition, metal phthalocyanine, which is one of organic semiconductor materials, change their electronic property as reaction with gaseous analytes, suggesting as potential chemical sensing platforms. In the present part, the growth behavior of metal phthalocyanine and surface response to gaseous condition will be elucidated using scanning tunneling microscopy (STM). In second part, the surface of layered transition metal dichalcogenides and their chemical response to exposure ambient air will be investigated, using STM. Layered transition metal dichalcogenides (TMDs) have attracted widespread attention in the scientific community for electronic device applications because improved electrostatic gate control and suppression of short channel leakage resulted from their atomic thin body. To fabricate the transistor based on TMDs, TMDs should be exposed to ambient conditions, while the effect of air exposure has not been understood fully. In this part 10. Quantum creep in a highly crystalline two-dimensional superconductor Science.gov (United States) Saito, Yu; Kasahara, Yuichi; Ye, Jianting; Iwasa, Yoshihiro; Nojima, Tsutomu Conventional studies on quantum phase transitions, especially on superconductor-insulator or superconductor-metal-insulator transitions have been performed in deposited metallic thin films such as Bismuth or MoGe. Although the techniques of thin films deposition have been considerably improved, unintentional disorder such as impurities and deficiencies, generating the pinning centers, seems to still exist in such systems. The mechanical exfoliated highly crystalline two-dimensional material can be a good candidate to realize a less-disordered 2D superconductor with extremely weak pinning, combined with transfer method or ionic-liquid gating. We report on the quantum metal, namely, magnetic-field-induced metallic state observed in an ion-gated two-dimensional superconductor based on an ultra-highly crystalline layered band insulator, ZrNCl. We found that the superconducting state is extremely fragile against external magnetic fields; that is, zero resistance state immediately disappears, once an external magnetic field switches on. This is because the present system is relatively clean and the pinning potential is extremely weak, which cause quantum tunneling and flux flow of vortices, resulting in metallic ground state. 11. Two-dimensional gas of massless Dirac fermions in graphene. Science.gov (United States) Novoselov, K S; Geim, A K; Morozov, S V; Jiang, D; Katsnelson, M I; Grigorieva, I V; Dubonos, S V; Firsov, A A 2005-11-10 Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment. 12. On numerical evaluation of two-dimensional phase integrals DEFF Research Database (Denmark) Lessow, H.; Rusch, W.; Schjær-Jacobsen, Hans 1975-01-01 The relative advantages of several common numerical integration algorithms used in computing two-dimensional phase integrals are evaluated.......The relative advantages of several common numerical integration algorithms used in computing two-dimensional phase integrals are evaluated.... 13. Perspective: Two-dimensional resonance Raman spectroscopy Science.gov (United States) Molesky, Brian P.; Guo, Zhenkun; Cheshire, Thomas P.; Moran, Andrew M. 2016-11-01 Two-dimensional resonance Raman (2DRR) spectroscopy has been developed for studies of photochemical reaction mechanisms and structural heterogeneity in complex systems. The 2DRR method can leverage electronic resonance enhancement to selectively probe chromophores embedded in complex environments (e.g., a cofactor in a protein). In addition, correlations between the two dimensions of the 2DRR spectrum reveal information that is not available in traditional Raman techniques. For example, distributions of reactant and product geometries can be correlated in systems that undergo chemical reactions on the femtosecond time scale. Structural heterogeneity in an ensemble may also be reflected in the 2D spectroscopic line shapes of both reactive and non-reactive systems. In this perspective article, these capabilities of 2DRR spectroscopy are discussed in the context of recent applications to the photodissociation reactions of triiodide and myoglobin. We also address key differences between the signal generation mechanisms for 2DRR and off-resonant 2D Raman spectroscopies. Most notably, it has been shown that these two techniques are subject to a tradeoff between sensitivity to anharmonicity and susceptibility to artifacts. Overall, recent experimental developments and applications of the 2DRR method suggest great potential for the future of the technique. 14. Janus spectra in two-dimensional flows CERN Document Server Liu, Chien-Chia; Chakraborty, Pinaki 2016-01-01 In theory, large-scale atmospheric flows, soap-film flows and other two-dimensional flows may host two distinct types of turbulent energy spectra---in one,$\\alpha$, the spectral exponent of velocity fluctuations, equals$3$and the fluctuations are dissipated at the small scales, and in the other,$\\alpha=5/3$and the fluctuations are dissipated at the large scales---but measurements downstream of obstacles have invariably revealed$\\alpha = 3$. Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which$\\alpha$has transitioned from$3$to$5/3$for the streamwise fluctuations but remains equal to$3$for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows... 15. Comparative Two-Dimensional Fluorescence Gel Electrophoresis. Science.gov (United States) Ackermann, Doreen; König, Simone 2018-01-01 Two-dimensional comparative fluorescence gel electrophoresis (CoFGE) uses an internal standard to increase the reproducibility of coordinate assignment for protein spots visualized on 2D polyacrylamide gels. This is particularly important for samples, which need to be compared without the availability of replicates and thus cannot be studied using differential gel electrophoresis (DIGE). CoFGE corrects for gel-to-gel variability by co-running with the sample proteome a standardized marker grid of 80-100 nodes, which is formed by a set of purified proteins. Differentiation of reference and analyte is possible by the use of two fluorescent dyes. Variations in the y-dimension (molecular weight) are corrected by the marker grid. For the optional control of the x-dimension (pI), azo dyes can be used. Experiments are possible in both vertical and horizontal (h) electrophoresis devices, but hCoFGE is much easier to perform. For data analysis, commercial software capable of warping can be adapted. 16. Two-dimensional hexagonal semiconductors beyond graphene Science.gov (United States) Nguyen, Bich Ha; Hieu Nguyen, Van 2016-12-01 The rapid and successful development of the research on graphene and graphene-based nanostructures has been substantially enlarged to include many other two-dimensional hexagonal semiconductors (THS): phosphorene, silicene, germanene, hexagonal boron nitride (h-BN) and transition metal dichalcogenides (TMDCs) such as MoS2, MoSe2, WS2, WSe2 as well as the van der Waals heterostructures of various THSs (including graphene). The present article is a review of recent works on THSs beyond graphene and van der Waals heterostructures composed of different pairs of all THSs. One among the priorities of new THSs compared to graphene is the presence of a non-vanishing energy bandgap which opened up the ability to fabricate a large number of electronic, optoelectronic and photonic devices on the basis of these new materials and their van der Waals heterostructures. Moreover, a significant progress in the research on TMDCs was the discovery of valley degree of freedom. The results of research on valley degree of freedom and the development of a new technology based on valley degree of freedom-valleytronics are also presented. Thus the scientific contents of the basic research and practical applications os THSs are very rich and extremely promising. 17. Two-Dimensional Phononic Crystals: Disorder Matters. Science.gov (United States) Wagner, Markus R; Graczykowski, Bartlomiej; Reparaz, Juan Sebastian; El Sachat, Alexandros; Sledzinska, Marianna; Alzina, Francesc; Sotomayor Torres, Clivia M 2016-09-14 The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order/disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of two-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) and Raman thermometry based on a novel two-laser approach are used to study the phononic properties in the gigahertz (GHz) and terahertz (THz) regime, respectively. Finite element method simulations of the phonon dispersion relation and three-dimensional displacement fields furthermore enable the unique identification of the different hypersonic vibrations. The increase of surface roughness and the introduction of short-range disorder are shown to modify the phonon dispersion and phonon coherence in the hypersonic (GHz) range without affecting the room-temperature thermal conductivity. On the basis of these findings, we suggest a criteria for predicting phonon coherence as a function of roughness and disorder. 18. Two-dimensional topological photonic systems Science.gov (United States) Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng 2017-09-01 The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems. 19. Radiation effects on two-dimensional materials Energy Technology Data Exchange (ETDEWEB) Walker, R.C. II; Robinson, J.A. [Department of Materials Science, Penn State, University Park, PA (United States); Center for Two-Dimensional Layered Materials, Penn State, University Park, PA (United States); Shi, T. [Department of Mechanical and Nuclear Engineering, Penn State, University Park, PA (United States); Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States); Silva, E.C. [GlobalFoundries, Malta, NY (United States); Jovanovic, I. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States) 2016-12-15 The effects of electromagnetic and particle irradiation on two-dimensional materials (2DMs) are discussed in this review. Radiation creates defects that impact the structure and electronic performance of materials. Determining the impact of these defects is important for developing 2DM-based devices for use in high-radiation environments, such as space or nuclear reactors. As such, most experimental studies have been focused on determining total ionizing dose damage to 2DMs and devices. Total dose experiments using X-rays, gamma rays, electrons, protons, and heavy ions are summarized in this review. We briefly discuss the possibility of investigating single event effects in 2DMs based on initial ion beam irradiation experiments and the development of 2DM-based integrated circuits. Additionally, beneficial uses of irradiation such as ion implantation to dope materials or electron-beam and helium-beam etching to shape materials have begun to be used on 2DMs and are reviewed as well. For non-ionizing radiation, such as low-energy photons, we review the literature on 2DM-based photo-detection from terahertz to UV. The majority of photo-detecting devices operate in the visible and UV range, and for this reason they are the focus of this review. However, we review the progress in developing 2DMs for detecting infrared and terahertz radiation. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) 20. Asymptotics for Two-dimensional Atoms DEFF Research Database (Denmark) Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip 2012-01-01 We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge$Z>0$and$N$quantum electrons of charge -1 is$E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$when$Z\\to \\infty$and$N/Z\\to \\lambda$, where$E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....
1. Predicting Two-Dimensional Silicon Carbide Monolayers.
Science.gov (United States)
Shi, Zhiming; Zhang, Zhuhua; Kutana, Alex; Yakobson, Boris I
2015-10-27
Intrinsic semimetallicity of graphene and silicene largely limits their applications in functional devices. Mixing carbon and silicon atoms to form two-dimensional (2D) silicon carbide (SixC1-x) sheets is promising to overcome this issue. Using first-principles calculations combined with the cluster expansion method, we perform a comprehensive study on the thermodynamic stability and electronic properties of 2D SixC1-x monolayers with 0 ≤ x ≤ 1. Upon varying the silicon concentration, the 2D SixC1-x presents two distinct structural phases, a homogeneous phase with well dispersed Si (or C) atoms and an in-plane hybrid phase rich in SiC domains. While the in-plane hybrid structure shows uniform semiconducting properties with widely tunable band gap from 0 to 2.87 eV due to quantum confinement effect imposed by the SiC domains, the homogeneous structures can be semiconducting or remain semimetallic depending on a superlattice vector which dictates whether the sublattice symmetry is topologically broken. Moreover, we reveal a universal rule for describing the electronic properties of the homogeneous SixC1-x structures. These findings suggest that the 2D SixC1-x monolayers may present a new "family" of 2D materials, with a rich variety of properties for applications in electronics and optoelectronics.
2. Large scale instabilities in two-dimensional magnetohydrodynamics
Science.gov (United States)
Boffetta; Celani; Prandi
2000-04-01
The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state describing a motionless fluid and a layered magnetic field, becomes unstable with respect to large scale perturbations. The exact expressions for eddy-viscosity and eddy-resistivity are derived in the nearby of the critical point where the instability sets in. In this marginally unstable case the nonlinear phase of perturbation growth obeys to a Cahn-Hilliard-like dynamics characterized by coalescence of magnetic islands leading to a final new equilibrium state. High resolution numerical simulations confirm quantitatively the predictions of multiscale analysis.
3. Two-Dimensional Hexagonal Transition-Metal Oxide for Spintronics.
Science.gov (United States)
Kan, Erjun; Li, Ming; Hu, Shuanglin; Xiao, Chuanyun; Xiang, Hongjun; Deng, Kaiming
2013-04-04
Two-dimensional materials have been the hot subject of studies due to their great potential in applications. However, their applications in spintronics have been blocked by the difficulty in producing ordered spin structures in 2D structures. Here we demonstrated that the ultrathin films of recently experimentally realized wurtzite MnO can automatically transform into a stable graphitic structure with ordered spin arrangement via density functional calculation, and the stability of graphitic structure can be enhanced by external strain. Moreover, the antiferromagnetic ordering of graphitic MnO single layer can be switched into half-metallic ferromagnetism by small hole-doping, and the estimated Curie temperature is higher than 300 K. Thus, our results highlight a promising way toward 2D magnetic materials.
4. Quasi-Two-Dimensional Magnetism in Co-Based Shandites
Science.gov (United States)
Kassem, Mohamed A.; Tabata, Yoshikazu; Waki, Takeshi; Nakamura, Hiroyuki
2016-06-01
We report quasi-two-dimensional (Q2D) itinerant electron magnetism in the layered Co-based shandites. Comprehensive magnetization measurements were performed using single crystals of Co3Sn2-xInxS2 (0 ≤ x ≤ 2) and Co3-yFeySn2S2 (0 ≤ y ≤ 0.5). The magnetic parameters of both systems; the Curie temperature TC, effective moment peff and spontaneous moment ps; exhibit almost identical variations against the In- and Fe-concentrations, indicating significance of the electron count on the magnetism in the Co-based shandite. The ferromagnetic-nonmagnetic quantum phase transition is found around xc ˜ 0.8. Analysis based on the extended Q2D spin fluctuation theory clearly reveals the highly Q2D itinerant electron character of the ferromagnetism in the Co-based shandites.
5. Separation of colloidal two dimensional materials by density gradient ultracentrifugation
Energy Technology Data Exchange (ETDEWEB)
Kuang, Yun; Song, Sha [State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029 (China); Huang, Jinyang, E-mail: [email protected] [Department of Mathematics, College of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Sun, Xiaoming, E-mail: [email protected] [State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029 (China)
2015-04-15
Two-dimensional (2D) materials have been made through various approaches but obtaining monodispersed simply by synthesis optimization gained little success, which highlighted the need for introducing nanoseparation methods. Density gradient ultracentrifugation method has emerged as a versatile and scalable method for sorting colloidal 2D nanomaterials. Isopycnic separation was applied on thickness-dependent separation of graphene nanosheets. And rate-zonal separation, as a more versatile separation method, demonstrated its capability in sorting nanosheets of chemically modified single layered graphene, layered double hydroxide, and even metallic Ag. Establishing such density gradient ultracentrifugation method not only achieves monodispersed nanosheets and provides new opportunities for investigation on size dependent properties of 2D materials, but also makes the surface modification possible by introducing “reaction zones” during sedimentation of the colloids. - Graphical abstract: Two-dimensional (2D) materials have been made through various approaches but obtaining monodispersed simply by synthesis optimization gained little success, which highlighted the need for introducing nanoseparation methods. Density gradient ultracentrifugation method has emerged as a versatile and scalable method for sorting colloidal 2D nanomaterials according to their size of thickness difference. Establishing such density gradient ultracentrifugation method not only achieves monodispersed nanosheets and provides new opportunities for investigation on size dependent properties of 2D materials, but also makes the surface modification possible by introducing “reaction zones” during sedimentation of the colloids. - Highlights: • Density gradient ultracentrifugation was applied on size separation of 2D material. • Isopycnic separation was applied on separation of low density materials. • Rate-zonal separation was applied on separation of large density materials. • Size
6. Electronic nanobiosensors based on two-dimensional materials
Science.gov (United States)
Ping, Jinglei
Atomically-thick two-dimensional (2D) nanomaterials have tremendous potential to be applied as transduction elements in biosensors and bioelectronics. We developed scalable methods for synthesis and large-area transfer of two-dimensional nanomaterials, particularly graphene and metal dichalcogenides (so called MX2'' materials). We also developed versatile fabrication methods for large arrays of field-effect transistors (FETs) and micro-electrodes with these nanomaterials based on either conventional photolithography or innovative approaches that minimize contamination of the 2D layer. By functionalizing the FETs with a computationally redesigned water-soluble mu-opioid receptor, we created selective and sensitive biosensors suitable for detection of the drug target naltrexone and the neuropeptide enkephalin at pg/mL concentrations. We also constructed DNA-functionalized biosensors and nano-particle decorated biosensors by applying related bio-nano integration techniques. Our methodology paves the way for multiplexed nanosensor arrays with all-electronic readout suitable for inexpensive point-of-care diagnostics, drug-development and biomedical research. With graphene field-effect transistors, we investigated the graphene/solution interface and developed a quantitative model for the effect of ionic screening on the graphene carrier density based on theories of the electric double layer. Finally, we have developed a technique for measuring low-level Faradaic charge-transfer current (fA) across the graphene/solution interface via real-time charge monitoring of graphene microelectrodes in ionic solution. This technique enables the development of flexible and transparent pH sensors that are promising for in vivo applications. The author acknowledges the support from the Defense Advanced Research Projects Agency (DARPA) and the U. S. Army Research Office under Grant Number W911NF1010093.
7. Signal Characteristics of a Resistive-Strip Micromegas Detector with an Integrated Two-Dimensional Readout
CERN Document Server
Lin, Tai-Hua; Schott, Matthias; Valderanis, Chrysostomos; Wehner, Laura; Westenberger, Robert
2014-01-01
In recent years, micropattern gaseous detectors, which comprise a two-dimensional readout structure within one PCB layer, received significant attention in the development of precision and cost-effective tracking detectors in medium and high energy physics experiments. In this article, we present for the first time a systematic performance study of the signal characteristics of a resistive strip micromegas detector with a two-dimensional readout, based on test-beam and X-ray measurements. In particular, comparisons of the response of the two independent readout-layers regarding their signal shapes and signal reconstruction efficiencies are discussed.
8. Interaction of two-dimensional magnetoexcitons
Science.gov (United States)
Dumanov, E. V.; Podlesny, I. V.; Moskalenko, S. A.; Liberman, M. A.
2017-04-01
We study interaction of the two-dimensional magnetoexcitons with in-plane wave vector k→∥ = 0 , taking into account the influence of the excited Landau levels (ELLs) and of the external electric field perpendicular to the surface of the quantum well and parallel to the external magnetic field. It is shown that the account of the ELLs gives rise to the repulsion between the spinless magnetoexcitons with k→∥ = 0 in the Fock approximation, with the interaction constant g decreasing inverse proportional to the magnetic field strength B (g (0) ∼ 1 / B) . In the presence of the perpendicular electric field the Rashba spin-orbit coupling (RSOC), Zeeman splitting (ZS) and nonparabolicity of the heavy-hole dispersion law affect the Landau quantization of the electrons and holes. They move along the new cyclotron orbits, change their Coulomb interactions and cause the interaction between 2D magnetoexcitons with k→∥ = 0 . The changes of the Coulomb interactions caused by the electrons and by the holes moving with new cyclotron orbits are characterized by some coefficients, which in the absence of the electric field turn to be unity. The differences between these coefficients of the electron-hole pairs forming the magnetoexcitons determine their affinities to the interactions. The interactions between the homogeneous, semihomogeneous and heterogeneous magnetoexcitons forming the symmetric states with the same signs of their affinities are attractive whereas in the case of different sign affinities are repulsive. In the heterogeneous asymmetric states the interactions have opposite signs in comparison with the symmetric states. In all these cases the interaction constant g have the dependence g (0) 1 /√{ B} .
9. Two-dimensional simulation of polymer electrolyte membrane fuel cells
Energy Technology Data Exchange (ETDEWEB)
Hum, B.; Li, X. [Waterloo Univ., ON (Canada). Dept. of Mechanical Engineering
2002-07-01
Polymer electrolyte membrane (PEM) fuel cells have fast startup, are highly energy efficient and have high power density, rendering them very suitable for use in zero-emission vehicles and on-site power cogeneration. Before the PEM fuel cell can reach widespread commercial use, the performance has to be improved regarding the minimization of all transport resistances. This can be done by considering the electrochemical reactions in the catalyst layers along with the physical transport of reactant gas flows, product and process water, heat and the charged particles in the individual cells and stacks. This paper presents the results of a two-dimensional numerical simulation of a steady, isothermal, fully humidified PEM fuel cell which was conducted to examine what happens in the catalyst layers. The finite volume method was used together with the alternating direction implicit algorithm. It was determined that the cathode catalyst layer has more pronounced changes in potential, reaction rate and current density generation compared to the anode catalyst layer. This is because of the large cathode activation overpotential and the low diffusion coefficient of oxygen. It was demonstrated that catalyst layers, by nature, are 2 dimensional, particularly in areas of low reactant concentrations. Maximum power density is limited by the depletion of one of the reactants in the catalyst layer. Both the fuel and oxidant supply must be managed simultaneously for optimal cell performance. It was concluded that cell performance is not greatly affected by flow direction. It was noted that this analysis can also be used for more complex cell design, such as cross flow between reactant streams and practical serpentine flow channel design. 11 refs., 2 tabs., 10 figs.
10. Two-dimensional materials and their prospects in transistor electronics.
Science.gov (United States)
Schwierz, F; Pezoldt, J; Granzner, R
2015-05-14
During the past decade, two-dimensional materials have attracted incredible interest from the electronic device community. The first two-dimensional material studied in detail was graphene and, since 2007, it has intensively been explored as a material for electronic devices, in particular, transistors. While graphene transistors are still on the agenda, researchers have extended their work to two-dimensional materials beyond graphene and the number of two-dimensional materials under examination has literally exploded recently. Meanwhile several hundreds of different two-dimensional materials are known, a substantial part of them is considered useful for transistors, and experimental transistors with channels of different two-dimensional materials have been demonstrated. In spite of the rapid progress in the field, the prospects of two-dimensional transistors still remain vague and optimistic opinions face rather reserved assessments. The intention of the present paper is to shed more light on the merits and drawbacks of two-dimensional materials for transistor electronics and to add a few more facets to the ongoing discussion on the prospects of two-dimensional transistors. To this end, we compose a wish list of properties for a good transistor channel material and examine to what extent the two-dimensional materials fulfill the criteria of the list. The state-of-the-art two-dimensional transistors are reviewed and a balanced view of both the pros and cons of these devices is provided.
11. Measured Two-Dimensional Ice-Wedge Polygon Thermal Dynamics
Science.gov (United States)
Cable, William; Romanovsky, Vladimir; Busey, Robert
2016-04-01
necessarily found in areas of higher MAGT. Active layer thickness does not appear to be correlated to mean annual air temperature but rather is a function of summer air temperature or thawing degree-days. While the refreezing of the active layer initiated at nearly the same time for all locations and polygons, we find differences in the proportion of top-down versus bottom-up freezing and the length of time required to complete the refreezing process. Examination of the daily temperature dynamics using interpolated two-dimensional temperature fields reveal that during the summer, the predominate temperature gradient is vertical while the isotherms tend to follow the topography. However, as the active layer begins to refreeze and snow accumulates, the thermal regime diverges. The fall shows an increased temperature gradient horizontally with landscape positions containing higher soil moisture and/or snow depth (low centers and troughs) cooling more slowly than the adjacent ground (rims and high centers). This two-dimensional effect is greatest as the active layer refreezes and persists until mid-winter, by which time the temperature gradients are again mostly vertical and the isotherms follow the topography. Our findings demonstrate the complexity and two-dimensionality of the temperature dynamics in these landscapes.
12. Ultrafast two dimensional infrared chemical exchange spectroscopy
Science.gov (United States)
Fayer, Michael
2011-03-01
The method of ultrafast two dimensional infrared (2D IR) vibrational echo spectroscopy is described. Three ultrashort IR pulses tuned to the frequencies of the vibrational transitions of interest are directed into the sample. The interaction of these pulses with the molecular vibrational oscillators produces a polarization that gives rise to a fourth pulse, the vibrational echo. The vibrational echo pulse is combined with another pulse, the local oscillator, for heterodyne detection of the signal. For fixed time between the second and third pulses, the waiting time, the first pulse is scanned. Two Fourier transforms of the data yield a 2D IR spectrum. The waiting time is increased, and another spectrum is obtained. The change in the 2D IR spectra with increased waiting time provides information on the time evolution of the structure of the molecular system under observation. In a 2D IR chemical exchange experiment, two species A and B, are undergoing chemical exchange. A's are turning into B's, and B's are turning into A's, but the overall concentrations of the species are not changing. The kinetics of the chemical exchange on the ground electronic state under thermal equilibrium conditions can be obtained 2D IR spectroscopy. A vibration that has a different frequency for the two species is monitored. At very short time, there will be two peaks on the diagonal of the 2D IR spectrum, one for A and one for B. As the waiting time is increased, chemical exchange causes off-diagonal peaks to grow in. The time dependence of the growth of these off-diagonal peaks gives the chemical exchange rate. The method is applied to organic solute-solvent complex formation, orientational isomerization about a carbon-carbon single bond, migration of a hydrogen bond from one position on a molecule to another, protein structural substate interconversion, and water hydrogen bond switching between ions and water molecules. This work was supported by the Air Force Office of Scientific
13. Molecular assembly on two-dimensional materials
Science.gov (United States)
Kumar, Avijit; Banerjee, Kaustuv; Liljeroth, Peter
2017-02-01
Molecular self-assembly is a well-known technique to create highly functional nanostructures on surfaces. Self-assembly on two-dimensional (2D) materials is a developing field driven by the interest in functionalization of 2D materials in order to tune their electronic properties. This has resulted in the discovery of several rich and interesting phenomena. Here, we review this progress with an emphasis on the electronic properties of the adsorbates and the substrate in well-defined systems, as unveiled by scanning tunneling microscopy. The review covers three aspects of the self-assembly. The first one focuses on non-covalent self-assembly dealing with site-selectivity due to inherent moiré pattern present on 2D materials grown on substrates. We also see that modification of intermolecular interactions and molecule–substrate interactions influences the assembly drastically and that 2D materials can also be used as a platform to carry out covalent and metal-coordinated assembly. The second part deals with the electronic properties of molecules adsorbed on 2D materials. By virtue of being inert and possessing low density of states near the Fermi level, 2D materials decouple molecules electronically from the underlying metal substrate and allow high-resolution spectroscopy and imaging of molecular orbitals. The moiré pattern on the 2D materials causes site-selective gating and charging of molecules in some cases. The last section covers the effects of self-assembled, acceptor and donor type, organic molecules on the electronic properties of graphene as revealed by spectroscopy and electrical transport measurements. Non-covalent functionalization of 2D materials has already been applied for their application as catalysts and sensors. With the current surge of activity on building van der Waals heterostructures from atomically thin crystals, molecular self-assembly has the potential to add an extra level of flexibility and functionality for applications ranging
14. A nanoporous two-dimensional polymer by single-crystal-to-single-crystal photopolymerization.
Science.gov (United States)
Kissel, Patrick; Murray, Daniel J; Wulftange, William J; Catalano, Vincent J; King, Benjamin T
2014-09-01
In contrast to the wide number and variety of available synthetic routes to conventional linear polymers, the synthesis of two-dimensional polymers and unambiguous proof of their structure remains a challenge. Two-dimensional polymers-single-layered polymers that form a tiling network in exactly two dimensions-have potential for use in nanoporous membranes and other applications. Here, we report the preparation of a fluorinated hydrocarbon two-dimensional polymer that can be exfoliated into single sheets, and its characterization by high-resolution single-crystal X-ray diffraction analysis. The procedure involves three steps: preorganization in a lamellar crystal of a rigid monomer bearing three photoreactive arms, photopolymerization of the crystalline monomers by [4 + 4] cycloaddition, and isolation of individual two-dimensional polymer sheets. This polymer is a molecularly thin (~1 nm) material that combines precisely defined monodisperse pores of ~9 Å with a high pore density of 3.3 × 10(13) pores cm(-2). Atomic-resolution single-crystal X-ray structures of the monomer, an intermediate dimer and the final crystalline two-dimensional polymer were obtained and prove the single-crystal-to-single-crystal nature and molecular precision of the two-dimensional photopolymerization.
15. One- and two-dimensional fluids properties of smectic, lamellar and columnar liquid crystals
CERN Document Server
Jakli, Antal
2006-01-01
Smectic and lamellar liquid crystals are three-dimensional layered structures in which each layer behaves as a two-dimensional fluid. Because of their reduced dimensionality they have unique physical properties and challenging theoretical descriptions, and are the subject of much current research. One- and Two-Dimensional Fluids: Properties of Smectic, Lamellar and Columnar Liquid Crystals offers a comprehensive review of these phases and their applications. The book details the basic structures and properties of one- and two-dimensional fluids and the nature of phase transitions. The later chapters consider the optical, magnetic, and electrical properties of special structures, including uniformly and non-uniformly aligned anisotropic films, lyotropic lamellar systems, helical and chiral structures, and organic anisotropic materials. Topics also include typical and defective features, magnetic susceptibility, and electrical conductivity. The book concludes with a review of current and potential applications ...
16. Directional interlayer spin-valley transfer in two-dimensional heterostructures
Science.gov (United States)
Schaibley, John R.; Rivera, Pasqual; Yu, Hongyi; Seyler, Kyle L.; Yan, Jiaqiang; Mandrus, David G.; Taniguchi, Takashi; Watanabe, Kenji; Yao, Wang; Xu, Xiaodong
2016-12-01
Van der Waals heterostructures formed by two different monolayer semiconductors have emerged as a promising platform for new optoelectronic and spin/valleytronic applications. In addition to its atomically thin nature, a two-dimensional semiconductor heterostructure is distinct from its three-dimensional counterparts due to the unique coupled spin-valley physics of its constituent monolayers. Here, we report the direct observation that an optically generated spin-valley polarization in one monolayer can be transferred between layers of a two-dimensional MoSe2-WSe2 heterostructure. Using non-degenerate optical circular dichroism spectroscopy, we show that charge transfer between two monolayers conserves spin-valley polarization and is only weakly dependent on the twist angle between layers. Our work points to a new spin-valley pumping scheme in nanoscale devices, provides a fundamental understanding of spin-valley transfer across the two-dimensional interface, and shows the potential use of two-dimensional semiconductors as a spin-valley generator in two-dimensional spin/valleytronic devices for storing and processing information.
17. Two-dimensional gallium nitride realized via graphene encapsulation
Science.gov (United States)
Al Balushi, Zakaria Y.; Wang, Ke; Ghosh, Ram Krishna; Vilá, Rafael A.; Eichfeld, Sarah M.; Caldwell, Joshua D.; Qin, Xiaoye; Lin, Yu-Chuan; Desario, Paul A.; Stone, Greg; Subramanian, Shruti; Paul, Dennis F.; Wallace, Robert M.; Datta, Suman; Redwing, Joan M.; Robinson, Joshua A.
2016-11-01
The spectrum of two-dimensional (2D) and layered materials beyond graphene’ offers a remarkable platform to study new phenomena in condensed matter physics. Among these materials, layered hexagonal boron nitride (hBN), with its wide bandgap energy (~5.0-6.0 eV), has clearly established that 2D nitrides are key to advancing 2D devices. A gap, however, remains between the theoretical prediction of 2D nitrides beyond hBN’ and experimental realization of such structures. Here we demonstrate the synthesis of 2D gallium nitride (GaN) via a migration-enhanced encapsulated growth (MEEG) technique utilizing epitaxial graphene. We theoretically predict and experimentally validate that the atomic structure of 2D GaN grown via MEEG is notably different from reported theory. Moreover, we establish that graphene plays a critical role in stabilizing the direct-bandgap (nearly 5.0 eV), 2D buckled structure. Our results provide a foundation for discovery and stabilization of 2D nitrides that are difficult to prepare via traditional synthesis.
18. The convolution theorem for two-dimensional continuous wavelet transform
Institute of Scientific and Technical Information of China (English)
ZHANG CHI
2013-01-01
In this paper , application of two -dimensional continuous wavelet transform to image processes is studied. We first show that the convolution and correlation of two continuous wavelets satisfy the required admissibility and regularity conditions ,and then we derive the convolution and correlation theorem for two-dimensional continuous wavelet transform. Finally, we present numerical example showing the usefulness of applying the convolution theorem for two -dimensional continuous wavelet transform to perform image restoration in the presence of additive noise.
19. Direct Measurement of the Band Structure of a Buried Two-Dimensional Electron Gas
DEFF Research Database (Denmark)
Miwa, Jill; Hofmann, Philip; Simmons, Michelle Y.;
2013-01-01
We directly measure the band structure of a buried two dimensional electron gas (2DEG) using angle resolved photoemission spectroscopy. The buried 2DEG forms 2 nm beneath the surface of p-type silicon, because of a dense delta-type layer of phosphorus n-type dopants which have been placed there. ...
20. Metallic ground state in an ion-gated two-dimensional superconductor
NARCIS (Netherlands)
Saito, Yu; Kasahara, Yuichi; Ye, Jianting; Iwasa, Yoshihiro; Nojima, Tsutomu
2015-01-01
Recently emerging two-dimensional (2D) superconductors in atomically thin layers and at heterogeneous interfaces are attracting growing interest in condensed matter physics. Here, we report that an ion-gated zirconium nitride chloride surface, exhibiting a dome-shaped phase diagram with a maximum cr
1. Stability of a Two-Dimensional Poiseuille-Type Flow for a Viscoelastic Fluid
Science.gov (United States)
Endo, Masakazu; Giga, Yoshikazu; Götz, Dario; Liu, Chun
2017-03-01
A viscoelastic flow in a two-dimensional layer domain is considered. An L 2-stability of the Poiseuille-type flow is established provided that both Poiseuille flow and perturbation is sufficiently small. Our analysis is based on a stream function formulation introduced by Lin et al. (Commun Pure Appl Math 58(11):1437-1471, 2005).
2. Two-Dimensional Covalent Organic Frameworks for Carbon Dioxide Capture through Channel-Wall Functionalization
NARCIS (Netherlands)
Huang, N.; Chen, X.; Krishna, R.; Jiang, D.
2015-01-01
Ordered open channels found in two-dimensional covalent organic frameworks (2D COFs) could enable them to adsorb carbon dioxide. However, the frameworks' dense layer architecture results in low porosity that has thus far restricted their potential for carbon dioxide adsorption. Here we report a
3. Ionic solutions of two-dimensional materials
Science.gov (United States)
Cullen, Patrick L.; Cox, Kathleen M.; Bin Subhan, Mohammed K.; Picco, Loren; Payton, Oliver D.; Buckley, David J.; Miller, Thomas S.; Hodge, Stephen A.; Skipper, Neal T.; Tileli, Vasiliki; Howard, Christopher A.
2016-11-01
Strategies for forming liquid dispersions of nanomaterials typically focus on retarding reaggregation, for example via surface modification, as opposed to promoting the thermodynamically driven dissolution common for molecule-sized species. Here we demonstrate the true dissolution of a wide range of important 2D nanomaterials by forming layered material salts that spontaneously dissolve in polar solvents yielding ionic solutions. The benign dissolution advantageously maintains the morphology of the starting material, is stable against reaggregation and can achieve solutions containing exclusively individualized monolayers. Importantly, the charge on the anionic nanosheet solutes is reversible, enables targeted deposition over large areas via electroplating and can initiate novel self-assembly upon drying. Our findings thus reveal a unique solution-like behaviour for 2D materials that enables their scalable production and controlled manipulation.
4. Two-dimensional analytical models for asymmetric fully depleted double-gate strained silicon MOSFETs
Institute of Scientific and Technical Information of China (English)
Liu Hong-Xia; Li Jin; Li Bin; Cao Lei; Yuan Bo
2011-01-01
This paper develops the simple and accurate two-dimensional analytical models for new asymmetric double-gate fully depleted strained-Si MOSFET. The models mainly include the analytical equations of the surface potential, surface electric field and threshold voltage, which are derived by solving two dimensional Poisson equation in strained-Si layer.The models are verified by numerical simulation. Besides offering the physical insight into device physics in the model,the new structure also provides the basic designing guidance for further immunity of short channel effect and drain-induced barrier-lowering of CMOS-based devices in nanometre scale.
5. The Chandrasekhar's Equation for Two-Dimensional Hypothetical White Dwarfs
CERN Document Server
De, Sanchari
2014-01-01
In this article we have extended the original work of Chandrasekhar on the structure of white dwarfs to the two-dimensional case. Although such two-dimensional stellar objects are hypothetical in nature, we strongly believe that the work presented in this article may be prescribed as Master of Science level class problem for the students in physics.
6. Beginning Introductory Physics with Two-Dimensional Motion
Science.gov (United States)
Huggins, Elisha
2009-01-01
During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…
7. Spatiotemporal surface solitons in two-dimensional photonic lattices.
Science.gov (United States)
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2007-11-01
We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.
8. Explorative data analysis of two-dimensional electrophoresis gels
DEFF Research Database (Denmark)
Schultz, J.; Gottlieb, D.M.; Petersen, Marianne Kjerstine;
2004-01-01
Methods for classification of two-dimensional (2-DE) electrophoresis gels based on multivariate data analysis are demonstrated. Two-dimensional gels of ten wheat varieties are analyzed and it is demonstrated how to classify the wheat varieties in two qualities and a method for initial screening...
9. Mechanics of Apparent Horizon in Two Dimensional Dilaton Gravity
CERN Document Server
Cai, Rong-Gen
2016-01-01
In this article, we give a definition of apparent horizon in a two dimensional general dilaton gravity theory. With this definition, we construct the mechanics of the apparent horizon by introducing a quasi-local energy of the theory. Our discussion generalizes the apparent horizons mechanics in general spherically symmetric spactimes in four or higher dimensions to the two dimensional dilaton gravity case.
10. Topological aspect of disclinations in two-dimensional crystals
Institute of Scientific and Technical Information of China (English)
Qi Wei-Kai; Zhu Tao; Chen Yong; Ren Ji-Rong
2009-01-01
By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given.
11. The effect of depolarization fields on the electronic properties of two-dimensional materials
Science.gov (United States)
Shin, Young-Han; Kim, Hye Jung; Noor-A-Alam, Mohammad
2015-03-01
Graphene is a two-dimensional semimetal with a zero band gap. By weakening the sp2 covalent bonding of graphene with additional elements such as hydrogen or fluorine, however, it is possible to make it insulating. We can expect that the band gap converges to that of a three-dimensional analogue by repeating such two-dimensional layers along the normal to the layer. If we control the position of additional elements to make a dipole monolayer, the system will have an intrinsic internal field decreases as the number of layers increases. But, for two-dimensional bilayers, depolarization field is so strong that its electronic properties can be much different from its monolayer analogue. In this presentation, we show that the internal fields induced by dipole moments can change electronic properties of two-dimensional materials such as graphene-like structures and complex metal oxides. This work was supported by the National Research Foundation of Korea Grant by the Ministry of Education, Science, and Technology (2009-0093818, 2012-014007, 2014M3A7B4049367)
12. Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations
Directory of Open Access Journals (Sweden)
Chunrong Zhu
2016-11-01
Full Text Available In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.
13. Curved Two-Dimensional Electron Systems in Semiconductor Nanoscrolls
Science.gov (United States)
Peters, Karen; Mendach, Stefan; Hansen, Wolfgang
The perfect control of strain and layer thickness in epitaxial semiconductor bilayers is employed to fabricate semiconductor nanoscrolls with precisely adjusted scroll diameter ranging between a few nanometers and several tens of microns. Furthermore, semiconductor heteroepitaxy allows us to incorporate quantum objects such as quantum wells, quantum dots, or modulation doped low-dimensional carrier systems into the nanoscrolls. In this review, we summarize techniques that we have developed to fabricate semiconductor nanoscrolls with well-defined location, orientation, geometry, and winding number. We focus on magneto-transport studies of curved two-dimensional electron systems in such nanoscrolls. An externally applied magnetic field results in a strongly modulated normal-to-surface component leading to magnetic barriers, reflection of edge channels, and local spin currents. The observations are compared to finite-element calculations and discussed on the basis of simple models taking into account the influence of a locally modulated state density on the conductivity. In particular, it is shown that the observations in high magnetic fields can be well described considering the transport in edge channels according to the Landauer-Büttiker model if additional magnetic field induced channels aligned along magnetic barriers are accounted for.
14. Defect engineering of two-dimensional transition metal dichalcogenides
Science.gov (United States)
Lin, Zhong; Carvalho, Bruno R.; Kahn, Ethan; Lv, Ruitao; Rao, Rahul; Terrones, Humberto; Pimenta, Marcos A.; Terrones, Mauricio
2016-06-01
Two-dimensional transition metal dichalcogenides (TMDs), an emerging family of layered materials, have provided researchers a fertile ground for harvesting fundamental science and emergent applications. TMDs can contain a number of different structural defects in their crystal lattices which significantly alter their physico-chemical properties. Having structural defects can be either detrimental or beneficial, depending on the targeted application. Therefore, a comprehensive understanding of structural defects is required. Here we review different defects in semiconducting TMDs by summarizing: (i) the dimensionalities and atomic structures of defects; (ii) the pathways to generating structural defects during and after synthesis and, (iii) the effects of having defects on the physico-chemical properties and applications of TMDs. Thus far, significant progress has been made, although we are probably still witnessing the tip of the iceberg. A better understanding and control of defects is important in order to move forward the field of Defect Engineering in TMDs. Finally, we also provide our perspective on the challenges and opportunities in this emerging field.
15. Gate-induced superconductivity in two-dimensional atomic crystals
Science.gov (United States)
Saito, Yu; Nojima, Tsutomu; Iwasa, Yoshihiro
2016-09-01
Two-dimensional (2D) crystals are attracting growing interest in condensed matter physics, since these systems exhibit not only rich electronic and photonic properties but also exotic electronic phase transitions including superconductivity and charge density wave. Moreover, owing to the recent development of transfer methods after exfoliation and electric-double-layer transistors, superconducting 2D atomic crystals, the thicknesses of which are below 1-2 nm, have been successfully obtained. Here, we present a topical review on the recent discoveries of 2D crystalline superconductors by ionic-liquid gating and a series of their novel properties. In particular, we highlight two topics; quantum metallic states (or possible metallic ground states) and superconductivity robust against in-plane magnetic fields. These phenomena can be discussed with the effects of weakened disorder and/or broken spacial inversion symmetry leading to valley-dependent spin-momentum locking (spin-valley locking). These examples suggest the superconducting 2D crystals are new platforms for investigating the intrinsic quantum phases as well as exotic nature in 2D superconductors.
16. Interactions between lasers and two-dimensional transition metal dichalcogenides.
Science.gov (United States)
Lu, Junpeng; Liu, Hongwei; Tok, Eng Soon; Sow, Chorng-Haur
2016-05-03
The recent increasing research interest in two-dimensional (2D) layered materials has led to an explosion of in the discovery of novel physical and chemical phenomena in these materials. Among the 2D family, group-VI transition metal dichalcogenides (TMDs), such as represented by MoS2 and WSe2, are remarkable semiconductors with sizable energy band gaps, which make the TMDs promising building blocks for new generation optoelectronics. On the other hand, the specificity and tunability of the band gaps can generate particularly strong light-matter interactions between TMD crystals and specific photons, which can trigger complex and interesting phenomena such as photo-scattering, photo-excitation, photo-destruction, photo-physical modification, photochemical reaction and photo-oxidation. Herein, we provide an overview of the phenomena explained by various interactions between lasers and the 2D TMDs. Characterizations of the optical fundamentals of the TMDs via laser spectroscopies are reviewed. Subsequently, photoelectric conversion devices enabled by laser excitation and the functionality extension and performance improvement of the TMDs materials via laser modification are comprehensively summarized. Finally, we conclude the review by discussing the prospects for further development in this research area.
17. Band Gap Engineering of Two-Dimensional Nitrogene
Science.gov (United States)
Li, Jie-Sen; Wang, Wei-Liang; Yao, Dao-Xin
2016-01-01
In our previous study, we have predicted the novel two-dimensional honeycomb monolayers of pnictogen. In particular, the structure and properties of the honeycomb monolayer of nitrogen, which we call nitrogene, are very unusual. In this paper, we make an in-depth investigation of its electronic structure. We find that the band structure of nitrogene can be engineered in several ways: controlling the stacking of monolayers, application of biaxial tensile strain, and application of perpendicular electric field. The band gap of nitrogene is found to decrease with the increasing number of layers. The perpendicular electric field can also reduce the band gap when it is larger than 0.18 V/Å, and the gap closes at 0.35 V/Å. A nearly linear dependence of the gap on the electric field is found during the process. Application of biaxial strain can decrease the band gap as well, and eventually closes the gap. After the gap-closing, we find six inequivalent Dirac points in the Brillouin zone under the strain between 17% and 28%, and the nitrogene monolayer becomes a Dirac semimetal. These findings suggest that the electronic structure of nitrogene can be modified by several techniques, which makes it a promising candidate for electronic devices. PMID:27680297
18. Aerodynamics of two-dimensional flapping wings in tandem configuration
Science.gov (United States)
Lua, K. B.; Lu, H.; Zhang, X. H.; Lim, T. T.; Yeo, K. S.
2016-12-01
This paper reports a fundamental investigation on the aerodynamics of two-dimensional flapping wings in tandem configuration in forward flight. Of particular interest are the effects of phase angle (φ) and center-to-center distance (L) between the front wing and the rear wing on the aerodynamic force generation at a Reynolds number of 5000. Both experimental and numerical methods were employed. A force sensor was used to measure the time-history aerodynamic forces experienced by the two wings and digital particle image velocimetry was utilized to obtain the corresponding flow structures. Both the front wing and the rear wing executed the same simple harmonic motions with φ ranging from -180° to 180° and four values of L, i.e., 1.5c, 2c, 3c, and 4c (c is the wing chord length). Results show that at fixed L = 2c, tandem wings perform better than the sum of two single wings that flap independently in terms of thrust for phase angle approximately from -90° to 90°. The maximum thrust on the rear wing occurs during in-phase flapping (φ = 0°). Correlation of transient thrust and flow structure indicates that there are generally two types of wing-wake interactions, depending on whether the rear wing crosses the shear layer shed from the front wing. Finally, increasing wing spacing has similar effect as reducing the phase angle, and an approximate mathematical model is derived to describe the relationship between these two parameters.
19. Soluble, Exfoliated Two-Dimensional Nanosheets as Excellent Aqueous Lubricants.
Science.gov (United States)
Zhang, Wenling; Cao, Yanlin; Tian, Pengyi; Guo, Fei; Tian, Yu; Zheng, Wen; Ji, Xuqiang; Liu, Jingquan
2016-11-30
Dispersion in water of two-dimensional (2D) nanosheets is conducive to their practical applications in fundamental science communities due to their abundance, low cost, and ecofriendliness. However, it is difficult to achieve stable aqueous 2D material suspensions because of the intrinsic hydrophobic properties of the layered materials. Here, we report an effective and economic way of producing various 2D nanosheets (h-BN, MoS2, MoSe2, WS2, and graphene) as aqueous dispersions using carbon quantum dots (CQDs) as exfoliation agents and stabilizers. The dispersion was prepared through a liquid phase exfoliation. The as-synthesized stable 2D nanosheets based dispersions were characterized by UV-vis, HRTEM, AFM, Raman, XPS, and XRD. The solutions based on CQD decorated 2D nanosheets were utilized as aqueous lubricants, which realized a friction coefficient as low as 0.02 and even achieved a superlubricity under certain working conditions. The excellent lubricating properties were attributed to the synergetic effects of the 2D nanosheets and CQDs, such as good dispersion stability and easy-sliding interlayer structure. This work thus proposes a novel strategy for the design and preparation of high-performance water based green lubricants.
20. Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
1. Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; QIANG Tian
2009-01-01
We study the existence and stability of two-dimensional discrete breathers in a two-dimensional discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling.Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential (soft or hard), the interaction potential (attractive or repulsive)and the center of the two-dimensional gap breather (on a light or a heavy atom).
2. Two Dimensional Hydrodynamic Analysis of the Moose Creek Floodway
Science.gov (United States)
2012-09-01
ER D C/ CH L TR -1 2 -2 0 Two Dimensional Hydrodynamic Analysis of the Moose Creek Floodway C oa st al a n d H yd ra u lic s La b or at...distribution is unlimited. ERDC/CHL TR-12-20 September 2012 Two Dimensional Hydrodynamic Analysis of the Moose Creek Floodway Stephen H. Scott, Jeremy A...A two-dimensional Adaptive Hydraulics (AdH) hydrodynamic model was developed to simulate the Moose Creek Floodway. The Floodway is located
3. RESEARCH ON TWO-DIMENSIONAL LDA FOR FACE RECOGNITION
Institute of Scientific and Technical Information of China (English)
Han Ke; Zhu Xiuchang
2006-01-01
The letter presents an improved two-dimensional linear discriminant analysis method for feature extraction. Compared with the current two-dimensional methods for feature extraction, the improved two-dimensional linear discriminant analysis method makes full use of not only the row and the column direction information of face images but also the discriminant information among different classes. The method is evaluated using the Nanjing University of Science and Technology (NUST) 603 face database and the Aleix Martinez and Robert Benavente (AR) face database. Experimental results show that the method in the letter is feasible and effective.
4. ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES
Directory of Open Access Journals (Sweden)
Nikola Stefanović
2007-06-01
5. Two-dimensional Confinement of Heavy Fermions in Artificial Superlattices
Science.gov (United States)
Shishido, Hiroaki
2011-03-01
Low dimensionality and strong electron-electron Coulomb interactions are both key parameters for novel quantum states of condensed matter. A metallic system with the strongest electron correlations is reported in rare-earth and actinide compounds with f electrons, known as heavy-fermion compounds, where the effective mass of the conduction electrons are strikingly enhanced by the electron correlations up to some hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. We realized experimentally a two-dimensional heavy fermion system, adjusting the dimensionality in a controllable fashion. We grew artificial superlattices of CeIn 3 (m)/ LaIn 3 (n), in which m -layers of heavy-fermion antiferromagnet CeIn 3 and n -layers of a non-magnetic isostructual compound LaIn 3 are stacked alternately, by a molecular beam epitaxy. By reducing the thickness of the CeIn 3 layers, the magnetic order was suppressed and the effective electron mass was further enhanced. The Néel temperature becomes zero at around m = 2 , concomitant with striking deviations from the standard Fermi liquid low-temperature electronic properties. Standard Fermi liquid behaviors are, however, recovered under high magnetic field. These behaviors imply new dimensional tuning'' towards a quantum critical point. We also succeeded to fabricate artificial superlattices of a heavy fermion superconductor CeCoIn 5 and non-magnetic divalent Yb-compound YbCoIn 5 . Superconductivity survives even in CeCoIn 5 (3)/ YbCoIn 5 (5) films, while the thickness of CeCoIn 5 layer, 2.3 nm, is comparable to the c -axis coherence length ξc ~ 2 nm. This work has been done in collaboration with Y. Mizukami, S. Yasumoto, M. Shimozawa, H. Kontani, T. Shibauchi, T. Terashima and Y. Matsuda.superconductivity is realized in the artificial superlattices. This work has been done in collaboration with Y. Mizukami, S. Yasumoto, M. Shimozawa, H. Kontani, T
6. A study of two-dimensional magnetic polaron
Institute of Scientific and Technical Information of China (English)
LIU; Tao; ZHANG; Huaihong; FENG; Mang; WANG; Kelin
2006-01-01
By using the variational method and anneal simulation, we study in this paper the self-trapped magnetic polaron (STMP) in two-dimensional anti-ferromagnetic material and the bound magnetic polaron (BMP) in ferromagnetic material. Schwinger angular momentum theory is applied to changing the problem into a coupling problem of carriers and two types of Bosons. Our calculation shows that there are single-peak and multi-peak structures in the two-dimensional STMP. For the ferromagnetic material, the properties of the two-dimensional BMP are almost the same as that in one-dimensional case; but for the anti-ferromagnetic material, the two-dimensional STMP structure is much richer than the one-dimensional case.
7. UPWIND DISCONTINUOUS GALERKIN METHODS FOR TWO DIMENSIONAL NEUTRON TRANSPORT EQUATIONS
Institute of Scientific and Technical Information of China (English)
袁光伟; 沈智军; 闫伟
2003-01-01
In this paper the upwind discontinuous Galerkin methods with triangle meshes for two dimensional neutron transport equations will be studied.The stability for both of the semi-discrete and full-discrete method will be proved.
8. Two-Dimensionally-Modulated, Magnetic Structure of Neodymium Metal
DEFF Research Database (Denmark)
Lebech, Bente; Bak, P.
1979-01-01
The incipient magnetic order of dhcp Nd is described by a two-dimensional, incommensurably modulated structure ("triple-q" structure). The ordering is accompanied by a lattice distortion that forms a similar pattern....
9. Entanglement Entropy for time dependent two dimensional holographic superconductor
CERN Document Server
Mazhari, N S; Myrzakulov, Kairat; Myrzakulov, R
2016-01-01
We studied entanglement entropy for a time dependent two dimensional holographic superconductor. We showed that the conserved charge of the system plays the role of the critical parameter to have condensation.
10. Decoherence in a Landau Quantized Two Dimensional Electron Gas
Directory of Open Access Journals (Sweden)
McGill Stephen A.
2013-03-01
Full Text Available We have studied the dynamics of a high mobility two-dimensional electron gas as a function of temperature. The presence of satellite reflections in the sample and magnet can be modeled in the time-domain.
11. Quantization of Two-Dimensional Gravity with Dynamical Torsion
CERN Document Server
Lavrov, P M
1999-01-01
We consider two-dimensional gravity with dynamical torsion in the Batalin - Vilkovisky and Batalin - Lavrov - Tyutin formalisms of gauge theories quantization as well as in the background field method.
12. Spatiotemporal dissipative solitons in two-dimensional photonic lattices.
Science.gov (United States)
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2008-11-01
We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.
13. Bound states of two-dimensional relativistic harmonic oscillators
Institute of Scientific and Technical Information of China (English)
Qiang Wen-Chao
2004-01-01
We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.
14. Second invariant for two-dimensional classical super systems
S C Mishra; Roshan Lal; Veena Mishra
2003-10-01
Construction of superpotentials for two-dimensional classical super systems (for ≥ 2) is carried out. Some interesting potentials have been studied in their super form and also their integrability.
15. Wafer-scale two-dimensional semiconductors from printed oxide skin of liquid metals
Science.gov (United States)
Carey, Benjamin J.; Ou, Jian Zhen; Clark, Rhiannon M.; Berean, Kyle J.; Zavabeti, Ali; Chesman, Anthony S. R.; Russo, Salvy P.; Lau, Desmond W. M.; Xu, Zai-Quan; Bao, Qiaoliang; Kevehei, Omid; Gibson, Brant C.; Dickey, Michael D.; Kaner, Richard B.; Daeneke, Torben; Kalantar-Zadeh, Kourosh
2017-02-01
A variety of deposition methods for two-dimensional crystals have been demonstrated; however, their wafer-scale deposition remains a challenge. Here we introduce a technique for depositing and patterning of wafer-scale two-dimensional metal chalcogenide compounds by transforming the native interfacial metal oxide layer of low melting point metal precursors (group III and IV) in liquid form. In an oxygen-containing atmosphere, these metals establish an atomically thin oxide layer in a self-limiting reaction. The layer increases the wettability of the liquid metal placed on oxygen-terminated substrates, leaving the thin oxide layer behind. In the case of liquid gallium, the oxide skin attaches exclusively to a substrate and is then sulfurized via a relatively low temperature process. By controlling the surface chemistry of the substrate, we produce large area two-dimensional semiconducting GaS of unit cell thickness (~1.5 nm). The presented deposition and patterning method offers great commercial potential for wafer-scale processes.
16. Extreme paths in oriented two-dimensional percolation
OpenAIRE
Andjel, E. D.; Gray, L. F.
2016-01-01
International audience; A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in \\cite{G} in the context of the contact process in continuous time. As discussed here, it also holds for several related models, including the discrete time contact process and two dimensional site percolation. Among the consequences are a natural monotonicity in the probability of percolation between different sites and a somewha...
17. Two Dimensional Nucleation Process by Monte Carlo Simulation
OpenAIRE
T., Irisawa; K., Matsumoto; Y., Arima; T., Kan; Computer Center, Gakushuin University; Department of Physics, Gakushuin University
1997-01-01
Two dimensional nucleation process on substrate is investigated by Monte Carlo simulation, and the critical nucleus size and its waiting time are measured with a high accuracy. In order to measure the critical nucleus with a high accuracy, we calculate the attachment and the detachment rate to the nucleus directly, and define the critical nucleus size when both rate are equal. Using the kinematical nucleation theory by Nishioka, it is found that, our obtained kinematical two dimensional criti...
18. Two-Dimensional Weak Pseudomanifolds on Eight Vertices
Basudeb Datta; Nandini Nilakantan
2002-05-01
We explicitly determine all the two-dimensional weak pseudomanifolds on 8 vertices. We prove that there are (up to isomorphism) exactly 95 such weak pseudomanifolds, 44 of which are combinatorial 2-manifolds. These 95 weak pseudomanifolds triangulate 16 topological spaces. As a consequence, we prove that there are exactly three 8-vertex two-dimensional orientable pseudomanifolds which allow degree three maps to the 4-vertex 2-sphere.
19. Synthesis of two-dimensional materials by selective extraction.
Science.gov (United States)
Naguib, Michael; Gogotsi, Yury
2015-01-20
CONSPECTUS: Two-dimensional (2D) materials have attracted much attention in the past decade. They offer high specific surface area, as well as electronic structure and properties that differ from their bulk counterparts due to the low dimensionality. Graphene is the best known and the most studied 2D material, but metal oxides and hydroxides (including clays), dichalcogenides, boron nitride (BN), and other materials that are one or several atoms thick are receiving increasing attention. They may deliver a combination of properties that cannot be provided by other materials. The most common synthesis approach in general is by reacting different elements or compounds to form a new compound. However, this approach does not necessarily work well for low-dimensional structures, since it favors formation of energetically preferred 3D (bulk) solids. Many 2D materials are produced by exfoliation of van der Waals solids, such as graphite or MoS2, breaking large particles into 2D layers. However, these approaches are not universal; for example, 2D transition metal carbides cannot be produced by any of them. An alternative but less studied way of material synthesis is the selective extraction process, which is based on the difference in reactivity and stability between the different components (elements or structural units) of the original material. It can be achieved using thermal, chemical, or electrochemical processes. Many 2D materials have been synthesized using selective extraction, such as graphene from SiC, transition metal oxides (TMO) from layered 3D salts, and transition metal carbides or carbonitrides (MXenes) from MAX phases. Selective extraction synthesis is critically important when the bonds between the building blocks of the material are too strong (e.g., in carbides) to be broken mechanically in order to form nanostructures. Unlike extractive metallurgy, where the extracted metal is the goal of the process, selective extraction of one or more elements from
20. Two-Dimensional Materials for Sensing: Graphene and Beyond
Directory of Open Access Journals (Sweden)
Seba Sara Varghese
2015-09-01
Full Text Available Two-dimensional materials have attracted great scientific attention due to their unusual and fascinating properties for use in electronics, spintronics, photovoltaics, medicine, composites, etc. Graphene, transition metal dichalcogenides such as MoS2, phosphorene, etc., which belong to the family of two-dimensional materials, have shown great promise for gas sensing applications due to their high surface-to-volume ratio, low noise and sensitivity of electronic properties to the changes in the surroundings. Two-dimensional nanostructured semiconducting metal oxide based gas sensors have also been recognized as successful gas detection devices. This review aims to provide the latest advancements in the field of gas sensors based on various two-dimensional materials with the main focus on sensor performance metrics such as sensitivity, specificity, detection limit, response time, and reversibility. Both experimental and theoretical studies on the gas sensing properties of graphene and other two-dimensional materials beyond graphene are also discussed. The article concludes with the current challenges and future prospects for two-dimensional materials in gas sensor applications.
1. Chemical Preparation of Supported Bimetallic Catalysts. Gold-Based Bimetallic, a Case Study
OpenAIRE
Louis, Catherine
2016-01-01
International audience; This review focuses on the chemical methods used to prepare supported bimetallic heterogeneous catalysts, i.e., bimetallic nanoparticles deposited on a support. The review is limited to the preparation of gold-based bimetallic catalysts and moreover to bimetallic nanoparticles supported on powder inorganic supports, i.e., on the surface or in the porosity, and not on model supports such as single crystals.
2. Two-dimensional metal oxide and metal hydroxide nanosheets: synthesis, controlled assembly and applications in energy conversion and storage
NARCIS (Netherlands)
Elshof, ten J.E.; Yuan, H.; Gonzalez Rodriguez, P.
2016-01-01
The developments and state of the art in the research on two-dimensional nanosheets derived from layered metal oxides and layered metal hydroxides are reviewed in this paper, with emphasis on their promising applications in various new energy technologies, i.e., as supercapacitor electrodes, lithium
3. Internetwork magnetic field as revealed by two-dimensional inversions
Science.gov (United States)
Danilovic, S.; van Noort, M.; Rempel, M.
2016-09-01
Context. Properties of magnetic field in the internetwork regions are still fairly unknown because of rather weak spectropolarimetric signals. Aims: We address the matter by using the two-dimensional (2D) inversion code, which is able to retrieve the information on smallest spatial scales up to the diffraction limit, while being less susceptible to noise than most of the previous methods used. Methods: Performance of the code and the impact of various effects on the retrieved field distribution is tested first on the realistic magneto-hydrodynamic (MHD) simulations. The best inversion scenario is then applied to the real data obtained by Spectropolarimeter (SP) on board Hinode. Results: Tests on simulations show that: (1) the best choice of node position ensures a decent retrieval of all parameters; (2) the code performs well for different configurations of magnetic field; (3) slightly different noise levels or slightly different defocus included in the spatial point spread function (PSF) produces no significant effect on the results; and (4) temporal integration shifts the field distribution to a stronger, more horizontally inclined field. Conclusions: Although the contribution of the weak field is slightly overestimated owing to noise, 2D inversions are able to recover well the overall distribution of the magnetic field strength. Application of the 2D inversion code on the Hinode SP internetwork observations reveals a monotonic field strength distribution. The mean field strength at optical depth unity is ~ 130 G. At higher layers, field strength drops as the field becomes more horizontal. Regarding the distribution of the field inclination, tests show that we cannot directly retrieve it with the observations and tools at hand, however, the obtained distributions are consistent with those expected from simulations with a quasi-isotropic field inclination after accounting for observational effects.
4. Addressing asymmetry of the charge and strain in a two-dimensional fullerene peapod
Science.gov (United States)
Valeš, V.; Verhagen, T.; Vejpravová, J.; Frank, O.; Kalbáč, M.
2015-12-01
We prepared a two-dimensional C70 fullerene peapod by the sequential assembly of 12C graphene, C70 fullerenes and 13C graphene. The local changes in the strain and doping were correlated with local roughness revealing asymmetry in the strain and doping with respect to the top and bottom graphene layers of the peapod.We prepared a two-dimensional C70 fullerene peapod by the sequential assembly of 12C graphene, C70 fullerenes and 13C graphene. The local changes in the strain and doping were correlated with local roughness revealing asymmetry in the strain and doping with respect to the top and bottom graphene layers of the peapod. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr06271c
5. Clausius-Mossotti Lorentz-Lorenz relations and retardation effects for two-dimensional crystals
CERN Document Server
Dell'Anna, Luca
2016-01-01
The macroscopic surface electric susceptibility determines the linear optical properties of an insulating single-layer two-dimensional atomic crystal, and can be expressed in terms of the microscopic polarizability of the atoms. We compute the local electric field acting on a single atom, both for the static and the dynamic case, as the superposition of the external applied electric field and the fields generated by the induced dipoles in the crystal. We find that, in the dynamic case, retardation effects dephase the local electric field with respect to the incident one. This explains why the Fresnel coefficients of a single-layer two-dimensional atomic crystal are intrinsically complex quantities, even when a null macroscopic surface conductivity is assumed.
6. Lagrangian approach to description of two-dimensional boundary layer ЛАГРАНЖЕВ ПОДХОД К ОПИСАНИЮ ПЛОСКОГО ПОГРАНИЧНОГО СЛОЯ
Directory of Open Access Journals (Sweden)
Otstavnov Evgeniy Igorevich
2013-05-01
Full Text Available In the article, the two-dimensional boundary layer is considered on the basis of the Lagrangian approach to the continuous medium description using coordinates of particles. Classical L. Prandtl’s method of Navier-Stokes equation simplification through expansion of dependent variables in a series is applied to develop the model. Direct transformation of widely used Euler equations derived by L. Prandtl generates the same result. Boundary conditions are regarded as one-sided or non-holonomic restrictions from the viewpoint of analytical mechanics.The mass conservation equation can be detached from the main equation of motion. At the same time, one can conclude that a particle starting its motion from an internal part of the layer will remain there without reaching any boundary in a finite time. The perpendicular coordinate evolution can be calculated when one has a law of motion along the boundary employed using the standard approach to the certain PDE solution. The model presentation is based on the Hamiltonian apparatus of classical mechanics. Derivatives of spatial variables take the form of the Poisson brackets. Hence, the full equation for the Newton’s second law has acceleration and doubled application of Poisson brackets. The pressure gradient is a function of a single coordinate; therefore, it can be eliminated by another Poisson bracket application due to the symmetric property of the skew.Приведен вывод уравнений плоского пограничного слоя с использованием подхода Лагранжа. Граничные условия рассмотрены с позиций теоретической механики в качестве связей, наложенных на систему. Уравнение движения вдоль границы отделяется, что дает еще одну форму скалярного описания плоского погранслоя.
7. Two dimensional simulation of direct methanol fuel cell : a new (embedded) type of current collectors
OpenAIRE
Kulikovsky, A. A.; Divisek, J.; Kornyshev, Yu. M.
2000-01-01
A two-dimensional numerical model of the direct methanol fuel cell with gas fuel is developed. Simulation of the cell with current collectors of conventional geometry reveal the formation of fuel-depleted, "shaded" regions in the cathode and anode catalyst layers. These regions are positioned in front of current collectors, farther from the gas channel windows. Another disadvantage of the conventional geometry is the concentration of electron current at the edges of current collectors. Based ...
8. Optimisation of interdigitated back contacts solar cells by two-dimensional numerical simulation
Energy Technology Data Exchange (ETDEWEB)
Nichiporuk, O.; Kaminski, A.; Lemiti, M.; Fave, A. [Instituit National des Sciences Appliquees Lyon, Villeurbanne (France). Lab. de Physique de la Matiere; Skryshevsky, V. [National Taras Shevchenko Univ., Kiev (Ukraine). Radiophysics Dept.
2005-04-01
In this paper we present the results of the simulation of interdigitated back contacts solar cell on thin-film ({approx}{mu}m) silicon layer. The influence of several parameters (surface recombination rate, substrate thickness and type, diffusion length, device geometry, doping levels) on device characteristics are simulated using the accurate two-dimensional numerical simulator DESSIS that allows to optimise the cell design. (Author)
9. Characterization and Preparation of Bimetallic Nanoparticles
Institute of Scientific and Technical Information of China (English)
Bing; Joe; Hwang; Ching; Hsiang; Chen; Loka; Subramanyam; Sarma; Din-gao; Liu; Jyh; Fu; Lee
2007-01-01
1 Results Bimetallic particles in the nanometer size range are of substantial interest due to their vast applications in catalysis[1].The synthesis of bimetallic nanoparticles with definite size with a well-control over their nanostructure remains a challenging problem.Thus there exists a great demand for both synthesis and atomic level characterization of nanostructure of bimetallic nanoparticles (NPs).With the recent advent of high-intensity tunable sources of X-rays,now available at synchrotron radia...
10. Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models
Science.gov (United States)
Lee, J. M.; Kittel, P.; Timmerhaus, K. D.; Radebaugh, R.
2004-01-01
One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when used in conjunction with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse effects, lumped parameter corrections, which are obtained though experiment, must be used. Or two-dimensional solutions of the differential fluid equations must be obtained. A linear two-dimensional solution to the fluid equations has been obtained. The solution provides lumped parameter corrections for one-dimensional models. The model accounts for heat transfer and shear flow between the gas and the tube. The complex Nusselt number and complex shear wall are useful in describing these corrections, with phase relations and amplitudes scaled with the Prandtl and Valensi numbers. The calculated ratio, a, between a two-dimensional solution of the oscillating temperature and velocity and a one-dimensional solution for the same shows a scales linearly with Va for Va less than 30. In this region alpha less than 0.5, that is, the enthalpy flow calculated with a two-dimensional model is 50% of a calculation using a one-dimensional model. For Va greater than 250, alpha = 0.8, showing that diffusion is still important even when it is confined to a thing layer near the tube wall.
11. New class of two-dimensional bimetallic nanoplatelets for high energy density and electrochemically stable hybrid supercapacitors
DEFF Research Database (Denmark)
Liu, Zhiting; Ma, Peng; Ulstrup, Jens
2017-01-01
Currently, the application of supercapacitors (SCs) in portable electronic devices and vehicles is limited by their low energy density. Developing high-energy density SCs without sacrificing their advantages, such as their long-term stability and high power density, has thus become an increasing...... and a 96.1% retention of the initial capacitance over 5,000 cycles. We exploited the novel 2D nanoplatelets as cathode materials to assemble a hybrid SC for full-cell tests. The resulting SCs operated in a wide potential window of 0 - 1.7 V, exhibited a high energy density over 50 Wh·kg-1, and sustained...
12. On the performance of surface plasmon resonance based fibre optic sensor with different bimetallic nanoparticle alloy combinations
Energy Technology Data Exchange (ETDEWEB)
Sharma, Anuj K; Mohr, Gerhard J [Institute of Physical Chemistry, Friedrich-Schiller University, Lessingstrasse 10, 07743 Jena (Germany)], E-mail: [email protected]
2008-03-07
In this work, we have investigated the capability of different bimetallic nanoparticle alloy combinations to be used in fibre optic sensors based on the technique of surface plasmon resonance. The metals considered for this analysis are silver, gold, copper and aluminium. The performance of the sensor with different bimetallic nanoparticle alloy combinations is evaluated and compared numerically. The performance is analysed in terms of three parameters: sensitivity, signal-to-noise ratio (SNR) and operating range for the sensing layer refractive index values. On the basis of the comparison and some logistic criteria, the best possible bimetallic alloy combinations along with a requisite alloy composition ratio are predicted. The bimetallic nanoparticle alloy combination is capable of simultaneously providing larger values of sensitivity, SNR and operating range, which is not possible with any single metallic nanoparticle layer.
13. Electronic, Vibrational and Thermoelectric Properties of Two-Dimensional Materials
Science.gov (United States)
Wickramaratne, Darshana
The discovery of graphene's unique electronic and thermal properties has motivated the search for new two-dimensional materials. Examples of these materials include the layered two-dimensional transition metal dichalcogenides (TMDC) and metal mono-chalcogenides. The properties of the TMDCs (eg. MoS 2, WS2, TaS2, TaSe2) and the metal mono-chalcogenides (eg. GaSe, InSe, SnS) are diverse - ranging from semiconducting, semi-metallic and metallic. Many of these materials exhibit strongly correlated phenomena and exotic collective states such as exciton condensates, charge density waves, Lifshitz transitions and superconductivity. These properties change as the film thickness is reduced down to a few monolayers. We use first-principles simulations to discuss changes in the electronic and the vibrational properties of these materials as the film thickness evolves from a single atomic monolayer to the bulk limit. In the semiconducting TMDCs (MoS2, MoSe2, WS2 and WSe2) and monochalcogenides (GaS, GaSe, InS and InSe) we show confining these materials to their monolayer limit introduces large band degeneracies or non-parabolic features in the electronic structure. These changes in the electronic structure results in increases in the density of states and the number of conducting modes. Our first-principles simulations combined with a Landauer approach show these changes can lead to large enhancements up to an order of magnitude in the thermoelectric performance of these materials when compared to their bulk structure. Few monolayers of the TMDCs can be misoriented with respect to each other due to the weak van-der-Waals (vdW) force at the interface of two monolayers. Misorientation of the bilayer semiconducting TMDCs increases the interlayer van-der-Waals gap distance, reduces the interlayer coupling and leads to an increase in the magnitude of the indirect bandgap by up to 100 meV compared to the registered bilayer. In the semi-metallic and metallic TMDC compounds (TiSe2, Ta
14. Acoustic excitation of diffusion flames with coherent structure in a plane shear layer. ; Application of active combustion control to two-dimensional phase-locked arranging measurements. Soshiki kozo wo tomonau heimen sendai kakusan kaen no onkyo reiki. ; Nijigen iso heikin bunpu sokutei eno active nensho seigyo no oyo
Energy Technology Data Exchange (ETDEWEB)
Ishino, Y.; Kojima, T.; Oiwa, N.; Yamaguchi, S. (Nagoya Institute of Technology, Nagoya (Japan))
1993-11-25
The acoustic excitation of a plane diffusion flame enhances the periodicity of organized eddy controlled combustion. In this study, to clarify an effectiveness of application of active combustion control, phase characteristics of the excited eddy flames with high periodicity have been examined. A computer-aided phase-locked averaging method was employed to obtain graphical two-dimensional contour maps of the instantaneous profiles of temperature and CH emission. Both maps consisting of eight consecutive phases indicated clearly not only the periodic behavior of the organized eddy flame, but also the gas dynamic properties peculiar to those flames with coherent structure. In addition, the profiles of local contribution of the sound field to the combustion process were examined by calculating the two-dimensional distribution of the local Rayleigh index. Calculation results of the two-dimensional distribution of the local Rayleigh index indicated that the organized eddy flames have high sensitivity to sound, and play an important role in an interaction of sound and flame. 6 refs., 9 figs.
15. Atomic Structure of Au−Pd Bimetallic Alloyed Nanoparticles
KAUST Repository
Ding, Yong
2010-09-08
Using a two-step seed-mediated growth method, we synthesized bimetallic nanoparticles (NPs) having a gold octahedron core and a palladium epitaxial shell with controlled Pd-shell thickness. The mismatch-release mechanism between the Au core and Pd shell of the NPs was systematically investigated by high-resolution transmission electron microscopy. In the NPs coated with a single atomic layer of Pd, the strain between the surface Pd layer and the Au core is released by Shockley partial dislocations (SPDs) accompanied by the formation of stacking faults. For NPs coated with more Pd (>2 nm), the stacking faults still exist, but no SPDs are found. This may be due to the diffusion of Au atoms into the Pd shell layers to eliminate the SPDs. At the same time, a long-range ordered L11 AuPd alloy phase has been identified in the interface area, supporting the assumption of the diffusion of Au into Pd to release the interface mismatch. With increasing numbers of Pd shell layers, the shape of the Au-Pd NP changes, step by step, from truncated-octahedral to cubic. After the bimetallic NPs were annealed at 523 K for 10 min, the SPDs at the surface of the NPs coated with a single atomic layer of Pd disappeared due to diffusion of the Au atoms into the surface layer, while the stacking faults and the L11 Au-Pd alloyed structure remained. When the annealing temperature was increased to 800 K, electron diffraction patterns and diffraction contrast images revealed that the NPs became a uniform Au-Pd alloy, and most of the stacking faults disappeared as a result of the annealing. Even so, some clues still support the existence of the L11 phase, which suggests that the L11 phase is a stable, long-range ordered structure in Au-Pd bimetallic NPs. © 2010 American Chemical Society.
16. Tracking dynamics of two-dimensional continuous attractor neural networks
Science.gov (United States)
Fung, C. C. Alan; Wong, K. Y. Michael; Wu, Si
2009-12-01
We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.
17. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Science.gov (United States)
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
18. Control Operator for the Two-Dimensional Energized Wave Equation
Directory of Open Access Journals (Sweden)
Sunday Augustus REJU
2006-07-01
Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.
19. Two-Dimensional Electronic Spectroscopy Using Incoherent Light: Theoretical Analysis
CERN Document Server
Turner, Daniel B; Sutor, Erika J; Hendrickson, Rebecca A; Gealy, M W; Ulness, Darin J
2012-01-01
Electronic energy transfer in photosynthesis occurs over a range of time scales and under a variety of intermolecular coupling conditions. Recent work has shown that electronic coupling between chromophores can lead to coherent oscillations in two-dimensional electronic spectroscopy measurements of pigment-protein complexes measured with femtosecond laser pulses. A persistent issue in the field is to reconcile the results of measurements performed using femtosecond laser pulses with physiological illumination conditions. Noisy-light spectroscopy can begin to address this question. In this work we present the theoretical analysis of incoherent two-dimensional electronic spectroscopy, I(4) 2D ES. Simulations reveal diagonal peaks, cross peaks, and coherent oscillations similar to those observed in femtosecond two-dimensional electronic spectroscopy experiments. The results also expose fundamental differences between the femtosecond-pulse and noisy-light techniques; the differences lead to new challenges and opp...
20. A two-dimensional spin liquid in quantum kagome ice.
Science.gov (United States)
Carrasquilla, Juan; Hao, Zhihao; Melko, Roger G
2015-06-22
Actively sought since the turn of the century, two-dimensional quantum spin liquids (QSLs) are exotic phases of matter where magnetic moments remain disordered even at zero temperature. Despite ongoing searches, QSLs remain elusive, due to a lack of concrete knowledge of the microscopic mechanisms that inhibit magnetic order in materials. Here we study a model for a broad class of frustrated magnetic rare-earth pyrochlore materials called quantum spin ices. When subject to an external magnetic field along the [111] crystallographic direction, the resulting interactions contain a mix of geometric frustration and quantum fluctuations in decoupled two-dimensional kagome planes. Using quantum Monte Carlo simulations, we identify a set of interactions sufficient to promote a groundstate with no magnetic long-range order, and a gap to excitations, consistent with a Z2 spin liquid phase. This suggests an experimental procedure to search for two-dimensional QSLs within a class of pyrochlore quantum spin ice materials.
1. Spectral Radiative Properties of Two-Dimensional Rough Surfaces
Science.gov (United States)
Xuan, Yimin; Han, Yuge; Zhou, Yue
2012-12-01
Spectral radiative properties of two-dimensional rough surfaces are important for both academic research and practical applications. Besides material properties, surface structures have impact on the spectral radiative properties of rough surfaces. Based on the finite difference time domain algorithm, this paper studies the spectral energy propagation process on a two-dimensional rough surface and analyzes the effect of different factors such as the surface structure, angle, and polarization state of the incident wave on the spectral radiative properties of the two-dimensional rough surface. To quantitatively investigate the spatial distribution of energy reflected from the rough surface, the concept of the bidirectional reflectance distribution function is introduced. Correlation analysis between the reflectance and different impact factors is conducted to evaluate the influence degree. Comparison between the theoretical and experimental data is given to elucidate the accuracy of the computational code. This study is beneficial to optimizing the surface structures of optoelectronic devices such as solar cells.
2. Two dimensional convolute integers for machine vision and image recognition
Science.gov (United States)
Edwards, Thomas R.
1988-01-01
Machine vision and image recognition require sophisticated image processing prior to the application of Artificial Intelligence. Two Dimensional Convolute Integer Technology is an innovative mathematical approach for addressing machine vision and image recognition. This new technology generates a family of digital operators for addressing optical images and related two dimensional data sets. The operators are regression generated, integer valued, zero phase shifting, convoluting, frequency sensitive, two dimensional low pass, high pass and band pass filters that are mathematically equivalent to surface fitted partial derivatives. These operators are applied non-recursively either as classical convolutions (replacement point values), interstitial point generators (bandwidth broadening or resolution enhancement), or as missing value calculators (compensation for dead array element values). These operators show frequency sensitive feature selection scale invariant properties. Such tasks as boundary/edge enhancement and noise or small size pixel disturbance removal can readily be accomplished. For feature selection tight band pass operators are essential. Results from test cases are given.
3. TreePM Method for Two-Dimensional Cosmological Simulations
2004-09-01
We describe the two-dimensional TreePM method in this paper. The 2d TreePM code is an accurate and efficient technique to carry out large two-dimensional N-body simulations in cosmology. This hybrid code combines the 2d Barnes and Hut Tree method and the 2d Particle–Mesh method. We describe the splitting of force between the PM and the Tree parts. We also estimate error in force for a realistic configuration. Finally, we discuss some tests of the code.
4. Singular analysis of two-dimensional bifurcation system
Institute of Scientific and Technical Information of China (English)
2010-01-01
Bifurcation properties of two-dimensional bifurcation system are studied in this paper.Universal unfolding and transition sets of the bifurcation equations are obtained.The whole parametric plane is divided into several different persistent regions according to the type of motion,and the different qualitative bifurcation diagrams in different persistent regions are given.The bifurcation properties of the two-dimensional bifurcation system are compared with its reduced one-dimensional system.It is found that the system which is reduced to one dimension has lost many bifurcation properties.
5. Critical Behaviour of a Two-Dimensional Random Antiferromagnet
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Birgeneau, R. J.; Guggenheim, H. J.
1976-01-01
A neutron scattering study of the order parameter, correlation length and staggered susceptibility of the two-dimensional random antiferromagnet Rb2Mn0.5Ni0.5F4 is reported. The system is found to exhibit a well-defined phase transition with critical exponents identical to those of the isomorphou...... pure materials K2NiF4 and K2MnF4. Thus, in these systems, which have the asymptotic critical behaviour of the two-dimensional Ising model, randomness has no measurable effect on the phase-transition behaviour....
6. Nonlinear excitations in two-dimensional molecular structures with impurities
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth
1995-01-01
We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the imp......We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....
7. Vortices in the Two-Dimensional Simple Exclusion Process
Science.gov (United States)
Bodineau, T.; Derrida, B.; Lebowitz, Joel L.
2008-06-01
We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partial flux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed in an Appendix.
8. Two-dimensional hazard estimation for longevity analysis
DEFF Research Database (Denmark)
Fledelius, Peter; Guillen, M.; Nielsen, J.P.
2004-01-01
the two-dimensional mortality surface. Furthermore we look at aggregated synthetic population metrics as 'population life expectancy' and 'population survival probability'. For Danish women these metrics indicate decreasing mortality with respect to chronological time. The metrics can not directly be used......We investigate developments in Danish mortality based on data from 1974-1998 working in a two-dimensional model with chronological time and age as the two dimensions. The analyses are done with non-parametric kernel hazard estimation techniques. The only assumption is that the mortality surface...... for analysis of economic implications arising from mortality changes....
9. Field analysis of two-dimensional focusing grating couplers
Science.gov (United States)
Borsboom, P.-P.; Frankena, H. J.
1995-05-01
A different technique was developed by which several two-dimensional dielectric optical gratings, consisting 100 or more corrugations, were treated in a numerical reliable approach. The numerical examples that were presented were restricted to gratings made up of sequences of waveguide sections symmetric about the x = 0 plane. The newly developed method was effectively used to investigate the field produced by a two-dimensional focusing grating coupler. Focal-region fields were determined for three symmetrical gratings with 19, 50, and 124 corrugations. For focusing grating coupler with limited length, high-frequency intensity variations were noted in the focal region.
10. Self-assembly of two-dimensional DNA crystals
Institute of Scientific and Technical Information of China (English)
SONG Cheng; CHEN Yaqing; WEI Shuai; YOU Xiaozeng; XIAO Shoujun
2004-01-01
Self-assembly of synthetic oligonucleotides into two-dimensional lattices presents a 'bottom-up' approach to the fabrication of devices on nanometer scale. We report the design and observation of two-dimensional crystalline forms of DNAs that are composed of twenty-one plane oligonucleotides and one phosphate-modified oligonucleotide. These synthetic sequences are designed to self-assemble into four double-crossover (DX) DNA tiles. The 'sticky ends' of these tiles that associate according to Watson-Crick's base pairing are programmed to build up specific periodic patterns upto tens of microns. The patterned crystals are visualized by the transmission electron microscopy.
11. Dynamics of vortex interactions in two-dimensional flows
DEFF Research Database (Denmark)
Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.
2002-01-01
a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 a(c) ...The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...
12. Two-dimensional assignment with merged measurements using Langrangrian relaxation
Science.gov (United States)
Briers, Mark; Maskell, Simon; Philpott, Mark
2004-01-01
Closely spaced targets can result in merged measurements, which complicate data association. Such merged measurements violate any assumption that each measurement relates to a single target. As a result, it is not possible to use the auction algorithm in its simplest form (or other two-dimensional assignment algorithms) to solve the two-dimensional target-to-measurement assignment problem. We propose an approach that uses the auction algorithm together with Lagrangian relaxation to incorporate the additional constraints resulting from the presence of merged measurements. We conclude with some simulated results displaying the concepts introduced, and discuss the application of this research within a particle filter context.
13. Two-dimensional lattice Boltzmann model for magnetohydrodynamics.
Science.gov (United States)
Schaffenberger, Werner; Hanslmeier, Arnold
2002-10-01
We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.
14. Quasinormal frequencies of asymptotically flat two-dimensional black holes
CERN Document Server
Lopez-Ortega, A
2011-01-01
We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.
15. Spin dynamics in a two-dimensional quantum gas
DEFF Research Database (Denmark)
Pedersen, Poul Lindholm; Gajdacz, Miroslav; Deuretzbacher, Frank
2014-01-01
We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimp......We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions...
16. The onion-ring structure for Pd-Pt bimetallic clusters.
Science.gov (United States)
Cheng, Daojian; Wang, Wenchuan; Huang, Shiping
2006-08-24
The onion-ring structure is validated in the Pd-Pt bimetallic clusters of total atom numbers 147 and 309 through the Monte Carlo method by using the second-moment approximation of the tight-binding (TB-SMA) potentials, which is conceived in predicting the possible structures of the bimetallic clusters by He et al. [J. Am. Chem. Soc. 2003, 125, 11034] and Hwang et al. [J. Am. Chem. Soc. 2005, 127, 11140]. In the onion-ring structure, Pd atoms and Pt atoms occupy alternate layers of the clusters. The formation of the onion-ring structure can be associated with the fact that the single Pt impurity is favorable to stay in the subsurface layer and the central part of bimetallic clusters.
17. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals
Science.gov (United States)
Gong, Cheng; Li, Lin; Li, Zhenglu; Ji, Huiwen; Stern, Alex; Xia, Yang; Cao, Ting; Bao, Wei; Wang, Chenzhe; Wang, Yuan; Qiu, Z. Q.; Cava, R. J.; Louie, Steven G.; Xia, Jing; Zhang, Xiang
2017-06-01
The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelectric and magneto-optic applications. In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin-Wagner theorem; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and composition engineering, or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine Cr2Ge2Te6 atomic layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temperature (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 tesla). This result is in contrast to the insensitivity of the transition temperature to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocrystalline anisotropy, opening up a large spin-wave excitation gap. We explain the observed phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temperature is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. Cr2Ge2Te6 is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviours, opening the door to exploring new applications such as ultra-compact spintronics.
18. Growth and electronic properties of two-dimensional systems on (110) oriented GaAs
Energy Technology Data Exchange (ETDEWEB)
Fischer, F.
2005-07-01
As the only non-polar plane the (110) surface has a unique role in GaAs. Together with Silicon as a dopant it is an important substrate orientation for the growth of n-type or p-type heterostructures. As a consequence, this thesis will concentrate on growth and research on that surface. In the course of this work we were able to realize two-dimensional electron systems with the highest mobilities reported so far on this orientation. Therefore, we review the necessary growth conditions and the accompanying molecular process. The two-dimensional electron systems allowed the study of a new, intriguing transport anisotropy not explained by current theory. Moreover, we were the first growing a two-dimensional hole gas on (110) GaAs with Si as dopant. For this purpose we invented a new growth modulation technique necessary to retrieve high mobility systems. In addition, we discovered and studied the metal-insulator transition in thin bulk p-type layers on (110) GaAs. Besides we investigated the activation process related to the conduction in the valence band and a parallelly conducting hopping band. The new two-dimensional hole gases revealed interesting physics. We studied the zero B-field spin splitting in these systems and compared it with the known theory. Furthermore, we investigated the anisotropy of the mobility. As opposed to the expectations we observed a strong persistent photoconductivity in our samples. Landau levels for two dimensional hole systems are non-linear and can show anticrossings. For the first time we were able to resolve anticrossings in a transport experiment and study the corresponding activation process. Finally, we compared these striking results with theoretical calculations. (orig.)
19. Two-dimensional gold nanostructures with high activity for selective oxidation of carbon–hydrogen bonds
KAUST Repository
Wang, Liang
2015-04-22
Efficient synthesis of stable two-dimensional (2D) noble metal catalysts is a challenging topic. Here we report the facile synthesis of 2D gold nanosheets via a wet chemistry method, by using layered double hydroxide as the template. Detailed characterization with electron microscopy and X-ray photoelectron spectroscopy demonstrates that the nanosheets are negatively charged and [001] oriented with thicknesses varying from single to a few atomic layers. X-ray absorption spectroscopy reveals unusually low gold–gold coordination numbers. These gold nanosheets exhibit high catalytic activity and stability in the solvent-free selective oxidation of carbon–hydrogen bonds with molecular oxygen.
20. Synthesis and characterization of two dimensional metal organic framework of cerium with tetraaza macrocyclic
Energy Technology Data Exchange (ETDEWEB)
Bt Safiin, Nurul Atikah; Yarmo, Ambar; Yamin, Bohari M. [School of Chemical Science and Food Technology. Faculty Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan (Malaysia)
2013-11-27
A two dimensional metal organic framework containing cerium sufate layers and ethylenediaminium between layers was obtained by refluxing the mixture of cerium sulphate and 5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradeca-7, 14-diene bromide. The complex was characterized by infrared spectroscopy and microelemental analysis. X-ray study showed that the complex adopts eleven coordination environments about the central atom. Thermogravimetric study showed the removal of water molecules at about 70°C followed by a gradual mass loss until the whole structure collapsed at about 400°C.
1. Two-dimensional gold nanostructures with high activity for selective oxidation of carbon-hydrogen bonds
Science.gov (United States)
Wang, Liang; Zhu, Yihan; Wang, Jian-Qiang; Liu, Fudong; Huang, Jianfeng; Meng, Xiangju; Basset, Jean-Marie; Han, Yu; Xiao, Feng-Shou
2015-04-01
Efficient synthesis of stable two-dimensional (2D) noble metal catalysts is a challenging topic. Here we report the facile synthesis of 2D gold nanosheets via a wet chemistry method, by using layered double hydroxide as the template. Detailed characterization with electron microscopy and X-ray photoelectron spectroscopy demonstrates that the nanosheets are negatively charged and [001] oriented with thicknesses varying from single to a few atomic layers. X-ray absorption spectroscopy reveals unusually low gold-gold coordination numbers. These gold nanosheets exhibit high catalytic activity and stability in the solvent-free selective oxidation of carbon-hydrogen bonds with molecular oxygen.
2. Synthesis and characterization of two dimensional metal organic framework of cerium with tetraaza macrocyclic
Science.gov (United States)
Bt Safiin, Nurul Atikah; Yarmo, Ambar; Yamin, Bohari M.
2013-11-01
A two dimensional metal organic framework containing cerium sufate layers and ethylenediaminium between layers was obtained by refluxing the mixture of cerium sulphate and 5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradeca-7, 14-diene bromide. The complex was characterized by infrared spectroscopy and microelemental analysis. X-ray study showed that the complex adopts eleven coordination environments about the central atom. Thermogravimetric study showed the removal of water molecules at about 70°C followed by a gradual mass loss until the whole structure collapsed at about 400°C.
3. On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential
Institute of Scientific and Technical Information of China (English)
Xu Quan; Tian Qiang
2009-01-01
This paper discusses the two-dimensional discrete monatomic Fermi-Pasta-Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather.
4. Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting
Science.gov (United States)
Chen, Leiming; Lee, Chiu Fan; Toner, John
2016-07-01
Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χx,y that characterize these correlations.
5. Waiting Time Dynamics in Two-Dimensional Infrared Spectroscopy
NARCIS (Netherlands)
Jansen, Thomas L. C.; Knoester, Jasper
We review recent work on the waiting time dynamics of coherent two-dimensional infrared (2DIR) spectroscopy. This dynamics can reveal chemical and physical processes that take place on the femto- and picosecond time scale, which is faster than the time scale that may be probed by, for example,
6. The partition function of two-dimensional string theory
Science.gov (United States)
Dijkgraaf, Robbert; Moore, Gregory; Plesser, Ronen
1993-04-01
We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in two-dimensional string theory. This expression makes manifest relations of the c = 1 system to KP flow nd W 1 + ∞ constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.
7. The partition function of two-dimensional string theory
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. (School of Natural Sciences, Inst. for Advanced Study, Princeton, NJ (United States) Dept. of Mathematics, Univ. Amsterdam (Netherlands)); Moore, G.; Plesser, R. (Dept. of Physics, Yale Univ., New Haven, CT (United States))
1993-04-12
We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in two-dimensional string theory. This expression makes manifest relations of the c=1 system to KP flow and W[sub 1+[infinity
8. Two-Dimensional Electronic Spectroscopy of a Model Dimer System
Directory of Open Access Journals (Sweden)
Prokhorenko V.I.
2013-03-01
Full Text Available Two-dimensional spectra of a dimer were measured to determine the timescale for electronic decoherence at room temperature. Anti-correlated beats in the crosspeaks were observed only during the period corresponding to the measured homogeneous lifetime.
9. Torque magnetometry studies of two-dimensional electron systems
NARCIS (Netherlands)
Schaapman, Maaike Ruth
2004-01-01
This thesis describes a study of the magnetization two-dimensional electron gases (2DEGs). To detect the typically small magnetization, a sensitive magnetometer with optical angular detection was developed. The magnetometer uses a quadrant detector to measure the rotation of the sample. By mounting
10. Low-frequency scattering from two-dimensional perfect conductors
DEFF Research Database (Denmark)
Hansen, Thorkild; Yaghjian, A.D
1991-01-01
Exact expressions have been obtained for the leading terms in the low-frequency expansions of the far fields scattered from three different types of two-dimensional perfect conductors: a cylinder with finite cross section, a cylindrical bump on an infinite ground plane, and a cylindrical dent...
11. Two-Dimensional Mesoscale-Ordered Conducting Polymers
NARCIS (Netherlands)
Liu, Shaohua; Zhang, Jian; Dong, Renhao; Gordiichuk, Pavlo; Zhang, Tao; Zhuang, Xiaodong; Mai, Yiyong; Liu, Feng; Herrmann, Andreas; Feng, Xinliang
2016-01-01
Despite the availability of numerous two-dimensional (2D) materials with structural ordering at the atomic or molecular level, direct construction of mesoscale-ordered superstructures within a 2D monolayer remains an enormous challenge. Here, we report the synergic manipulation of two types of assem
12. Piezoelectricity and Piezomagnetism: Duality in two-dimensional checkerboards
Science.gov (United States)
Fel, Leonid G.
2002-05-01
The duality approach in two-dimensional two-component regular checkerboards is extended to piezoelectricity and piezomagnetism. The relation between the effective piezoelectric and piezomagnetic moduli is found for a checkerboard with the p6'mm'-plane symmetry group (dichromatic triangle).
13. Specification of a Two-Dimensional Test Case
DEFF Research Database (Denmark)
Nielsen, Peter Vilhelm
This paper describes the geometry and other boundary conditions for a test case which can be used to test different two-dimensional CFD codes in the lEA Annex 20 work. The given supply opening is large compared with practical openings. Therefore, this geometry will reduce the need for a high number...... of grid points in the wall jet region....
14. Operator splitting for two-dimensional incompressible fluid equations
CERN Document Server
Holden, Helge; Karper, Trygve K
2011-01-01
We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier-Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data are sufficiently regular.
15. Chaotic dynamics for two-dimensional tent maps
Science.gov (United States)
Pumariño, Antonio; Ángel Rodríguez, José; Carles Tatjer, Joan; Vigil, Enrique
2015-02-01
For a two-dimensional extension of the classical one-dimensional family of tent maps, we prove the existence of an open set of parameters for which the respective transformation presents a strange attractor with two positive Lyapounov exponents. Moreover, periodic orbits are dense on this attractor and the attractor supports a unique ergodic invariant probability measure.
16. Divorticity and dihelicity in two-dimensional hydrodynamics
DEFF Research Database (Denmark)
Shivamoggi, B.K.; van Heijst, G.J.F.; Juul Rasmussen, Jens
2010-01-01
A framework is developed based on the concepts of divorticity B (≡×ω, ω being the vorticity) and dihelicity g (≡vB) for discussing the theoretical structure underlying two-dimensional (2D) hydrodynamics. This formulation leads to the global and Lagrange invariants that could impose significant...
17. Spin-orbit torques in two-dimensional Rashba ferromagnets
NARCIS (Netherlands)
Qaiumzadeh, A.; Duine, R. A.|info:eu-repo/dai/nl/304830127; Titov, M.
2015-01-01
Magnetization dynamics in single-domain ferromagnets can be triggered by a charge current if the spin-orbit coupling is sufficiently strong. We apply functional Keldysh theory to investigate spin-orbit torques in metallic two-dimensional Rashba ferromagnets in the presence of spin-dependent
18. Numerical blowup in two-dimensional Boussinesq equations
CERN Document Server
Yin, Zhaohua
2009-01-01
In this paper, we perform a three-stage numerical relay to investigate the finite time singularity in the two-dimensional Boussinesq approximation equations. The initial asymmetric condition is the middle-stage output of a $2048^2$ run, the highest resolution in our study is $40960^2$, and some signals of numerical blowup are observed.
19. Exact two-dimensional superconformal R symmetry and c extremization.
Science.gov (United States)
Benini, Francesco; Bobev, Nikolay
2013-02-08
We uncover a general principle dubbed c extremization, which determines the exact R symmetry of a two-dimensional unitary superconformal field theory with N=(0,2) supersymmetry. To illustrate its utility, we study superconformal theories obtained by twisted compactifications of four-dimensional N=4 super-Yang-Mills theory on Riemann surfaces and construct their gravity duals.
20. Zero sound in a two-dimensional dipolar Fermi gas
NARCIS (Netherlands)
Lu, Z.K.; Matveenko, S.I.; Shlyapnikov, G.V.
2013-01-01
We study zero sound in a weakly interacting two-dimensional (2D) gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean-f
1. Topology optimization of two-dimensional elastic wave barriers
DEFF Research Database (Denmark)
Van Hoorickx, C.; Sigmund, Ole; Schevenels, M.
2016-01-01
Topology optimization is a method that optimally distributes material in a given design domain. In this paper, topology optimization is used to design two-dimensional wave barriers embedded in an elastic halfspace. First, harmonic vibration sources are considered, and stiffened material is insert...
2. Non perturbative methods in two dimensional quantum field theory
CERN Document Server
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
3. Thermodynamics of Two-Dimensional Black-Holes
OpenAIRE
Nappi, Chiara R.; Pasquinucci, Andrea
1992-01-01
We explore the thermodynamics of a general class of two dimensional dilatonic black-holes. A simple prescription is given that allows us to compute the mass, entropy and thermodynamic potentials, with results in agreement with those obtained by other methods, when available.
4. Influence of index contrast in two dimensional photonic crystal lasers
DEFF Research Database (Denmark)
Jørgensen, Mette Marie; Petersen, Sidsel Rübner; Christiansen, Mads Brøkner;
2010-01-01
The influence of index contrast variations for obtaining single-mode operation and low threshold in dye doped polymer two dimensional photonic crystal (PhC) lasers is investigated. We consider lasers made from Pyrromethene 597 doped Ormocore imprinted with a rectangular lattice PhC having a cavit...
5. Magnetic order in two-dimensional nanoparticle assemblies
NARCIS (Netherlands)
Georgescu, M
2008-01-01
This thesis involves a fundamental study of two-dimensional arrays of magnetic nanoparticles using non-contact Atomic Force Microscopy, Magnetic Force Microscopy, and Atomic Force Spectroscopy. The goal is to acquire a better understanding of the interactions between magnetic nanoparticles and the
6. Dynamical phase transitions in the two-dimensional ANNNI model
Energy Technology Data Exchange (ETDEWEB)
Barber, M.N.; Derrida, B.
1988-06-01
We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly se several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.
7. Two-dimensional static black holes with pointlike sources
CERN Document Server
Melis, M
2004-01-01
We study the static black hole solutions of generalized two-dimensional dilaton-gravity theories generated by pointlike mass sources, in the hypothesis that the matter is conformally coupled. We also discuss the motion of test particles. Due to conformal coupling, these follow the geodesics of a metric obtained by rescaling the canonical metric with the dilaton.
8. Magnetic order in two-dimensional nanoparticle assemblies
NARCIS (Netherlands)
Georgescu, M
2008-01-01
This thesis involves a fundamental study of two-dimensional arrays of magnetic nanoparticles using non-contact Atomic Force Microscopy, Magnetic Force Microscopy, and Atomic Force Spectroscopy. The goal is to acquire a better understanding of the interactions between magnetic nanoparticles and the r
9. Two-Dimensional Chirality in Three-Dimensional Chemistry.
Science.gov (United States)
Wintner, Claude E.
1983-01-01
The concept of two-dimensional chirality is used to enhance students' understanding of three-dimensional stereochemistry. This chirality is used as a key to teaching/understanding such concepts as enaniotropism, diastereotopism, pseudoasymmetry, retention/inversion of configuration, and stereochemical results of addition to double bonds. (JN)
10. Field analysis of two-dimensional focusing grating
NARCIS (Netherlands)
Borsboom, P.P.; Frankena, H.J.
1995-01-01
The method that we have developed [P-P. Borsboom, Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands); P-P. Borsboom and H. J. Frankena, J. Opt. Soc. Am. A 12, 1134–1141 (1995)] is successfully applied to a two-dimensional focusing grating coupler. The field in the focal regi
11. Torque magnetometry studies of two-dimensional electron systems
NARCIS (Netherlands)
Schaapman, Maaike Ruth
2004-01-01
This thesis describes a study of the magnetization two-dimensional electron gases (2DEGs). To detect the typically small magnetization, a sensitive magnetometer with optical angular detection was developed. The magnetometer uses a quadrant detector to measure the rotation of the sample. By mounting
12. Two-Dimensional Mesoscale-Ordered Conducting Polymers
NARCIS (Netherlands)
Liu, Shaohua; Zhang, Jian; Dong, Renhao; Gordiichuk, Pavlo; Zhang, Tao; Zhuang, Xiaodong; Mai, Yiyong; Liu, Feng; Herrmann, Andreas; Feng, Xinliang
2016-01-01
Despite the availability of numerous two-dimensional (2D) materials with structural ordering at the atomic or molecular level, direct construction of mesoscale-ordered superstructures within a 2D monolayer remains an enormous challenge. Here, we report the synergic manipulation of two types of
13. Vibrations of Thin Piezoelectric Shallow Shells: Two-Dimensional Approximation
N Sabu
2003-08-01
In this paper we consider the eigenvalue problem for piezoelectric shallow shells and we show that, as the thickness of the shell goes to zero, the eigensolutions of the three-dimensional piezoelectric shells converge to the eigensolutions of a two-dimensional eigenvalue problem.
14. Two-dimensional effects in nonlinear Kronig-Penney models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
15. Forensic potential of comprehensive two-dimensional gas chromatography
NARCIS (Netherlands)
Sampat, A.; Lopatka, M.; Sjerps, M.; Vivo-Truyols, G.; Schoenmakers, P.; van Asten, A.
2016-01-01
In this study, the application of comprehensive two-dimensional (2D) gas chromatography (GC × GC) in forensic science is reviewed. The peer-reviewed publications on the forensic use of GC × GC and 2D gas chromatography with mass spectrometric detection (GC × GC-MS) have been studied in detail, not o
16. Easy interpretation of optical two-dimensional correlation spectra
NARCIS (Netherlands)
Lazonder, K.; Pshenichnikov, M.S.; Wiersma, D.A.
2006-01-01
We demonstrate that the value of the underlying frequency-frequency correlation function can be retrieved from a two-dimensional optical correlation spectrum through a simple relationship. The proposed method yields both intuitive clues and a quantitative measure of the dynamics of the system. The t
17. Two Dimensional F(R) Horava-Lifshitz Gravity
CERN Document Server
Kluson, J
2016-01-01
We study two-dimensional F(R) Horava-Lifshitz gravity from the Hamiltonian point of view. We determine constraints structure with emphasis on the careful separation of the second class constraints and global first class constraints. We determine number of physical degrees of freedom and also discuss gauge fixing of the global first class constraints.
18. Localization of Tight Closure in Two-Dimensional Rings
Kamran Divaani-Aazar; Massoud Tousi
2005-02-01
It is shown that tight closure commutes with localization in any two-dimensional ring of prime characteristic if either is a Nagata ring or possesses a weak test element. Moreover, it is proved that tight closure commutes with localization at height one prime ideals in any ring of prime characteristic.
19. Cryptanalysis of the Two-Dimensional Circulation Encryption Algorithm
Directory of Open Access Journals (Sweden)
Bart Preneel
2005-07-01
Full Text Available We analyze the security of the two-dimensional circulation encryption algorithm (TDCEA, recently published by Chen et al. in this journal. We show that there are several flaws in the algorithm and describe some attacks. We also address performance issues in current cryptographic designs.
20. New directions in science and technology: two-dimensional crystals
Energy Technology Data Exchange (ETDEWEB)
Neto, A H Castro [Graphene Research Centre, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Novoselov, K, E-mail: [email protected], E-mail: [email protected] [School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL (United Kingdom)
2011-08-15
Graphene is possibly one of the largest and fastest growing fields in condensed matter research. However, graphene is only one example in a large class of two-dimensional crystals with unusual properties. In this paper we briefly review the properties of graphene and look at the exciting possibilities that lie ahead.
1. Boundary-value problems for two-dimensional canonical systems
NARCIS (Netherlands)
Hassi, Seppo; De Snoo, H; Winkler, Henrik
2000-01-01
The two-dimensional canonical system Jy' = -lHy where the nonnegative Hamiltonian matrix function H(x) is trace-normed on (0,∞) has been studied in a function-theoretic way by L. de Branges. We show that the Hamiltonian system induces a closed symmetric relation which can be reduced to a, not necess
2. On the continua in two-dimensional nonadiabatic magnetohydrodynamic spectra
NARCIS (Netherlands)
De Ploey, A.; Van der Linden, R. A. M.; Belien, A. J. C.
2000-01-01
The equations for the continuous subspectra of the linear magnetohydrodynamic (MHD) normal modes spectrum of two-dimensional (2D) plasmas are derived in general curvilinear coordinates, taking nonadiabatic effects in the energy equation into account. Previously published derivations of continuous sp
3. Dislocation climb in two-dimensional discrete dislocation dynamics
NARCIS (Netherlands)
Davoudi, K.M.; Nicola, L.; Vlassak, J.J.
2012-01-01
In this paper, dislocation climb is incorporated in a two-dimensional discrete dislocation dynamics model. Calculations are carried out for polycrystalline thin films, passivated on one or both surfaces. Climb allows dislocations to escape from dislocation pile-ups and reduces the strain-hardening r
4. SAR Processing Based On Two-Dimensional Transfer Function
Science.gov (United States)
Chang, Chi-Yung; Jin, Michael Y.; Curlander, John C.
1994-01-01
Exact transfer function, ETF, is two-dimensional transfer function that constitutes basis of improved frequency-domain-convolution algorithm for processing synthetic-aperture-radar, SAR data. ETF incorporates terms that account for Doppler effect of motion of radar relative to scanned ground area and for antenna squint angle. Algorithm based on ETF outperforms others.
5. Sound waves in two-dimensional ducts with sinusoidal walls
Science.gov (United States)
Nayfeh, A. H.
1974-01-01
The method of multiple scales is used to analyze the wave propagation in two-dimensional hard-walled ducts with sinusoidal walls. For traveling waves, resonance occurs whenever the wall wavenumber is equal to the difference of the wavenumbers of any two duct acoustic modes. The results show that neither of these resonating modes could occur without strongly generating the other.
6. Confined two-dimensional fermions at finite density
CERN Document Server
De Francia, M; Loewe, M; Santangelo, E M; De Francia, M; Falomir, H; Loewe, M; Santangelo, E M
1995-01-01
We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of functional techniques which could be used in more complicated situations.
7. Imperfect two-dimensional topological insulator field-effect transistors
Science.gov (United States)
Vandenberghe, William G.; Fischetti, Massimo V.
2017-01-01
To overcome the challenge of using two-dimensional materials for nanoelectronic devices, we propose two-dimensional topological insulator field-effect transistors that switch based on the modulation of scattering. We model transistors made of two-dimensional topological insulator ribbons accounting for scattering with phonons and imperfections. In the on-state, the Fermi level lies in the bulk bandgap and the electrons travel ballistically through the topologically protected edge states even in the presence of imperfections. In the off-state the Fermi level moves into the bandgap and electrons suffer from severe back-scattering. An off-current more than two-orders below the on-current is demonstrated and a high on-current is maintained even in the presence of imperfections. At low drain-source bias, the output characteristics are like those of conventional field-effect transistors, at large drain-source bias negative differential resistance is revealed. Complementary n- and p-type devices can be made enabling high-performance and low-power electronic circuits using imperfect two-dimensional topological insulators. PMID:28106059
8. Bounds on the capacity of constrained two-dimensional codes
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
2000-01-01
Bounds on the capacity of constrained two-dimensional (2-D) codes are presented. The bounds of Calkin and Wilf apply to first-order symmetric constraints. The bounds are generalized in a weaker form to higher order and nonsymmetric constraints. Results are given for constraints specified by run...
9. Miniature sensor for two-dimensional magnetic field distributions
NARCIS (Netherlands)
Fluitman, J.H.J.; Krabbe, H.W.
1972-01-01
Describes a simple method of production of a sensor for two-dimensional magnetic field distributions. The sensor consists of a strip of Ni-Fe(81-19), of which the magnetoresistance is utilized. Typical dimensions of the strip, placed at the edge of a glass substrate, are: length 100 mu m, width 2 or
10. Forensic potential of comprehensive two-dimensional gas chromatography
NARCIS (Netherlands)
Sampat, A.; Lopatka, M.; Sjerps, M.; Vivo-Truyols, G.; Schoenmakers, P.; van Asten, A.
2016-01-01
In this study, the application of comprehensive two-dimensional (2D) gas chromatography (GC × GC) in forensic science is reviewed. The peer-reviewed publications on the forensic use of GC × GC and 2D gas chromatography with mass spectrometric detection (GC × GC-MS) have been studied in detail, not o
11. Spontaneous emission in two-dimensional photonic crystal microcavities
DEFF Research Database (Denmark)
Søndergaard, Thomas
2000-01-01
The properties of the radiation field in a two-dimensional photonic crystal with and without a microcavity introduced are investigated through the concept of the position-dependent photon density of states. The position-dependent rate of spontaneous radiative decay for a two-level atom with random...
12. Linkage analysis by two-dimensional DNA typing
NARCIS (Netherlands)
te Meerman, G J; Mullaart, E; van der Meulen, M A; den Daas, J H; Morolli, B; Uitterlinden, A G; Vijg, J
1993-01-01
In two-dimensional (2-D) DNA typing, genomic DNA fragments are separated, first according to size by electrophoresis in a neutral polyacrylamide gel and second according to sequence by denaturing gradient gel electrophoresis, followed by hybridization analysis using micro- and minisatellite core pro
13. Phase conjugated Andreev backscattering in two-dimensional ballistic cavities
NARCIS (Netherlands)
Morpurgo, A.F.; Holl, S.; Wees, B.J.van; Klapwijk, T.M; Borghs, G.
1997-01-01
We have experimentally investigated transport in two-dimensional ballistic cavities connected to a point contact and to two superconducting electrodes with a tunable macroscopic phase difference. The point contact resistance oscillates as a function of the phase difference in a way which reflects
14. Two-dimensional manifold with point-like defects
CERN Document Server
Gani, Vakhid A; Rubin, Sergei G
2014-01-01
We study a class of two-dimensional extra spaces isomorphic to the $S^2$ sphere in the framework of the multidimensional gravitation. We show that there exists a family of stationary metrics that depend on the initial (boundary) conditions. All these geometries have a singular point. We also discuss the possibility for these deformed extra spaces to be considered as dark matter candidates.
15. Instability of two-dimensional heterotic stringy black holes
CERN Document Server
Azreg-Ainou, M
1999-01-01
We solve the eigenvalue problem of general relativity for the case of charged black holes in two-dimensional heterotic string theory, derived by McGuigan et al. For the case of $m^{2}>q^{2}$, we find a physically acceptable time-dependent growing mode; thus the black hole is unstable. The extremal case $m^{2}=q^{2}$ is stable.
16. Spherical-shell boundaries for two-dimensional compressible convection in a star
CERN Document Server
Pratt, J; Goffrey, T; Geroux, C; Viallet, M; Folini, D; Constantino, T; Popov, M; Walder, R
2016-01-01
Context: We study the impact of two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from a one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star. Methods: We perform hydrodynamic implicit large-eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: We evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional s...
17. Dynamics of two-dimensional complex plasmas in a magnetic field
CERN Document Server
Ott, T; Bonitz, M
2013-01-01
We consider a two-dimensional complex plasma layer containing charged dust particles in a perpendicular magnetic field. Computer simulations of both one-component and binary systems are used to explore the equilibrium particle dynamics in the fluid state. The mobility is found to scale with the inverse of the magnetic field strength (Bohm diffusion) for strong fields. For bidisperse mixtures, the magnetic field dependence of the long-time mobility depends on the particle species providing an external control of their mobility ratio. For large magnetic fields, even a two-dimensional model porous matrix can be realized composed by the almost immobilized high-charge particles which act as obstacles for the mobile low-charge particles.
18. Metal Nanoparticle-Decorated Two-Dimensional Molybdenum Sulfide for Plasmonic-Enhanced Polymer Photovoltaic Devices
Directory of Open Access Journals (Sweden)
Ming-Kai Chuang
2015-08-01
Full Text Available Atomically thin two-dimensional (2D transition metal dichalcogenides have also attracted immense interest because they exhibit appealing electronic, optical and mechanical properties. In this work, we prepared gold nanoparticle-decorated molybdenum sulfide (AuNP@MoS2 through a simple spontaneous redox reaction. Transmission electron microscopy, UV-Vis spectroscopy, and Raman spectroscopy were used to characterize the properties of the AuNP@MoS2 nanomaterials. Then we employed such nanocomposites as the cathode buffer layers of organic photovoltaic devices (OPVs to trigger surface plasmonic resonance, leading to noticeable enhancements in overall device efficiencies. We attribute the primary origin of the improvement in device performance to local field enhancement induced by the effects of localized surface plasmonic resonance. Our results suggest that the metal nanoparticle-decorated two-dimensional materials appear to have great potential for use in high-performance OPVs.
19. Two-Dimensional Rotating Stall Analysis in a Wide Vaneless Diffuser
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We report a numerical study on the vaneless diffuser core flow instability in centrifugal compressors. The analysis is performed for the purpose of better understanding of the rotating stall flow mechanism in radial vaneless diffusers. Since the analysis is restricted to the two-dimensional core flow, the effect of the wall boundary layers is neglected. A commercial code with the standard incompressible viscous flow solver is applied to model the vaneless diffuser core flow in the plane parallel to the diffuser walls. At the diffuser inlet, rotating jet-wake velocity pattern is prescribed and at the diffuser outlet constant static pressure is assumed. Under these circumstances, two-dimensional rotating flow instability similar to rotating stall is found to exist. Performed parameter analysis reveals that this instability is strongly influenced by the diffuser geometry and the inlet and outlet flow conditions.
20. Two Dimensional Tensor Product B-Spline Wavelet Scaling Functions for the Solution of Two-Dimensional Unsteady Diffusion Equations
Institute of Scientific and Technical Information of China (English)
XIONG Lei; LI haijiao; ZHANG Lewen
2008-01-01
The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions, 4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.
1. Catalysis on singly dispersed bimetallic sites
Science.gov (United States)
Zhang, Shiran; Nguyen, Luan; Liang, Jin-Xia; Shan, Junjun; Liu, Jingyue; Frenkel, Anatoly I.; Patlolla, Anitha; Huang, Weixin; Li, Jun; Tao, Franklin
2015-08-01
A catalytic site typically consists of one or more atoms of a catalyst surface that arrange into a configuration offering a specific electronic structure for adsorbing or dissociating reactant molecules. The catalytic activity of adjacent bimetallic sites of metallic nanoparticles has been studied previously. An isolated bimetallic site supported on a non-metallic surface could exhibit a distinctly different catalytic performance owing to the cationic state of the singly dispersed bimetallic site and the minimized choices of binding configurations of a reactant molecule compared with continuously packed bimetallic sites. Here we report that isolated Rh1Co3 bimetallic sites exhibit a distinctly different catalytic performance in reduction of nitric oxide with carbon monoxide at low temperature, resulting from strong adsorption of two nitric oxide molecules and a nitrous oxide intermediate on Rh1Co3 sites and following a low-barrier pathway dissociation to dinitrogen and an oxygen atom. This observation suggests a method to develop catalysts with high selectivity.
2. Optical properties of multilayer bimetallic films obtained by laser deposition of colloidal particles
Science.gov (United States)
Antipov, A.; Arakelian, S.; Vartanyan, T.; Gerke, M.; Istratov, A.; Kutrovskaya, S.; Kucherik, A.; Osipov, A.
2016-11-01
The optical properties of multilayer bimetallic films composed of silver and gold nanoparticles have been investigated. The dependence of the transmission spectra of the films on their morphology is demonstrated. A finite-difference time-domain (FDTD) simulation has confirmed that there is a dependence of the transmission spectra on the average distance between particles and the number of deposited layers.
3. Stress Wave Propagation in Two-dimensional Buckyball Lattice
Science.gov (United States)
Xu, Jun; Zheng, Bowen
2016-11-01
Orderly arrayed granular crystals exhibit extraordinary capability to tune stress wave propagation. Granular system of higher dimension renders many more stress wave patterns, showing its great potential for physical and engineering applications. At nanoscale, one-dimensionally arranged buckyball (C60) system has shown the ability to support solitary wave. In this paper, stress wave behaviors of two-dimensional buckyball (C60) lattice are investigated based on square close packing and hexagonal close packing. We show that the square close packed system supports highly directional Nesterenko solitary waves along initially excited chains and hexagonal close packed system tends to distribute the impulse and dissipates impact exponentially. Results of numerical calculations based on a two-dimensional nonlinear spring model are in a good agreement with the results of molecular dynamics simulations. This work enhances the understanding of wave properties and allows manipulations of nanoscale lattice and novel design of shock mitigation and nanoscale energy harvesting devices.
4. The separation of whale myoglobins with two-dimensional electrophoresis.
Science.gov (United States)
Spicer, G S
1988-10-01
Five myoglobins (sperm whale, Sei whale, Hubbs' beaked whale, pilot whale, and Amazon River dolphin) were examined using two-dimensional electrophoresis. Previous reports indicated that none of these proteins could be separated by using denaturing (in the presence of 8-9 M urea) isoelectric focusing. This result is confirmed in the present study. However, all the proteins could be separated by using denaturing nonequilibrium pH-gradient electrophoresis in the first dimension. Additionally, all the myoglobins have characteristic mobilities in the second dimension (sodium dodecyl sulfate), but these mobilities do not correspond to the molecular weights of the proteins. We conclude that two-dimensional electrophoresis can be more sensitive to differences in primary protein structure than previous studies indicate and that the assessment seems to be incorrect that this technique can separate only proteins that have a unit charge difference.
5. Entanglement Entropy in Two-Dimensional String Theory.
Science.gov (United States)
Hartnoll, Sean A; Mazenc, Edward A
2015-09-18
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.
6. Topological defect motifs in two-dimensional Coulomb clusters
CERN Document Server
2012-01-01
The most energetically favourable arrangement of low-density electrons in an infinite two-dimensional plane is the ordered triangular Wigner lattice. However, in most instances of contemporary interest one deals instead with finite clusters of strongly interacting particles localized in potential traps, for example, in complex plasmas. In the current contribution we study distribution of topological defects in two-dimensional Coulomb clusters with parabolic lateral confinement. The minima hopping algorithm based on molecular dynamics is used to efficiently locate the ground- and low-energy metastable states, and their structure is analyzed by means of the Delaunay triangulation. The size, structure and distribution of geometry-induced lattice imperfections strongly depends on the system size and the energetic state. Besides isolated disclinations and dislocations, classification of defect motifs includes defect compounds --- grain boundaries, rosette defects, vacancies and interstitial particles. Proliferatio...
7. The Persistence Problem in Two-Dimensional Fluid Turbulence
CERN Document Server
2010-01-01
We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter {\\Lambda} to distinguish between vortical and extensional regions. We then use a direct numerical simulation (DNS) of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with a universal exponent {\\theta} = 3.1 \\pm 0.2.
8. On Dirichlet eigenvectors for neutral two-dimensional Markov chains
CERN Document Server
Champagnat, Nicolas; Miclo, Laurent
2012-01-01
We consider a general class of discrete, two-dimensional Markov chains modeling the dynamics of a population with two types, without mutation or immigration, and neutral in the sense that type has no influence on each individual's birth or death parameters. We prove that all the eigenvectors of the corresponding transition matrix or infinitesimal generator \\Pi\\ can be expressed as the product of "universal" polynomials of two variables, depending on each type's size but not on the specific transitions of the dynamics, and functions depending only on the total population size. These eigenvectors appear to be Dirichlet eigenvectors for \\Pi\\ on the complement of triangular subdomains, and as a consequence the corresponding eigenvalues are ordered in a specific way. As an application, we study the quasistationary behavior of finite, nearly neutral, two-dimensional Markov chains, absorbed in the sense that 0 is an absorbing state for each component of the process.
9. Statistical mechanics of two-dimensional and geophysical flows
CERN Document Server
Bouchet, Freddy
2011-01-01
The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter's troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. The equilibrium microcanonical measure is built from the Liouville theorem. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. We also present recent results for non-equilibrium situations, for the studies of either the relaxation towards equilibrium or non-equi...
10. Two-dimensional hazard estimation for longevity analysis
DEFF Research Database (Denmark)
Fledelius, Peter; Guillen, M.; Nielsen, J.P.
2004-01-01
We investigate developments in Danish mortality based on data from 1974-1998 working in a two-dimensional model with chronological time and age as the two dimensions. The analyses are done with non-parametric kernel hazard estimation techniques. The only assumption is that the mortality surface...... the two-dimensional mortality surface. Furthermore we look at aggregated synthetic population metrics as 'population life expectancy' and 'population survival probability'. For Danish women these metrics indicate decreasing mortality with respect to chronological time. The metrics can not directly be used...... for prediction purposes. However, we suggest that life insurance companies use the estimation technique and the cross-validation for bandwidth selection when analyzing their portfolio mortality. The non-parametric approach may give valuable information prior to developing more sophisticated prediction models...
11. Analysis of one dimensional and two dimensional fuzzy controllers
Institute of Scientific and Technical Information of China (English)
Ban Xiaojun; Gao Xiaozhi; Huang Xianlin; Wu Tianbao
2006-01-01
The analytical structures and the corresponding mathematical properties of the one dimensional and two dimensional fuzzy controllers are first investigated in detail.The nature of these two kinds of fuzzy controllers is next probed from the perspective of control engineering. For the one dimensional fuzzy controller, it is concluded that this controller is a combination of a saturation element and a nonlinear proportional controller, and the system that employs the one dimensional fuzzy controller is the combination of an open-loop control system and a closedloop control system. For the latter case, it is concluded that it is a hybrid controller, which comprises the saturation part, zero-output part, nonlinear derivative part, nonlinear proportional part, as well as nonlinear proportional-derivative part, and the two dimensional fuzzy controller-based control system is a loop-varying system with varying number of control loops.
12. Extension of modified power method to two-dimensional problems
Science.gov (United States)
Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung
2016-09-01
In this study, the generalized modified power method was extended to two-dimensional problems. A direct application of the method to two-dimensional problems was shown to be unstable when the number of requested eigenmodes is larger than a certain problem dependent number. The root cause of this instability has been identified as the degeneracy of the transfer matrix. In order to resolve this instability, the number of sub-regions for the transfer matrix was increased to be larger than the number of requested eigenmodes; and a new transfer matrix was introduced accordingly which can be calculated by the least square method. The stability of the new method has been successfully demonstrated with a neutron diffusion eigenvalue problem and the 2D C5G7 benchmark problem.
13. Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation
Directory of Open Access Journals (Sweden)
Panjit MUSIK
2004-01-01
Full Text Available This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular Automata (LGA, which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM, known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A specific two-dimensional nine-velocity square Lattice model (D2Q9 Model is used in the simulation with the velocity at the top of the cavity kept fixed. LBM is an efficient method for reproducing the dynamics of cavity flow and the results which are comparable to those of previous work.
14. Transport behavior of water molecules through two-dimensional nanopores
Energy Technology Data Exchange (ETDEWEB)
Zhu, Chongqin; Li, Hui; Meng, Sheng, E-mail: [email protected] [Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2014-11-14
Water transport through a two-dimensional nanoporous membrane has attracted increasing attention in recent years thanks to great demands in water purification and desalination applications. However, few studies have been reported on the microscopic mechanisms of water transport through structured nanopores, especially at the atomistic scale. Here we investigate the microstructure of water flow through two-dimensional model graphene membrane containing a variety of nanopores of different size by using molecular dynamics simulations. Our results clearly indicate that the continuum flow transits to discrete molecular flow patterns with decreasing pore sizes. While for pores with a diameter ≥15 Å water flux exhibits a linear dependence on the pore area, a nonlinear relationship between water flux and pore area has been identified for smaller pores. We attribute this deviation from linear behavior to the presence of discrete water flow, which is strongly influenced by the water-membrane interaction and hydrogen bonding between water molecules.
15. Transport behavior of water molecules through two-dimensional nanopores
Science.gov (United States)
Zhu, Chongqin; Li, Hui; Meng, Sheng
2014-11-01
Water transport through a two-dimensional nanoporous membrane has attracted increasing attention in recent years thanks to great demands in water purification and desalination applications. However, few studies have been reported on the microscopic mechanisms of water transport through structured nanopores, especially at the atomistic scale. Here we investigate the microstructure of water flow through two-dimensional model graphene membrane containing a variety of nanopores of different size by using molecular dynamics simulations. Our results clearly indicate that the continuum flow transits to discrete molecular flow patterns with decreasing pore sizes. While for pores with a diameter ≥15 Å water flux exhibits a linear dependence on the pore area, a nonlinear relationship between water flux and pore area has been identified for smaller pores. We attribute this deviation from linear behavior to the presence of discrete water flow, which is strongly influenced by the water-membrane interaction and hydrogen bonding between water molecules.
16. Thermodynamics of two-dimensional Yukawa systems across coupling regimes
Science.gov (United States)
Kryuchkov, Nikita P.; Khrapak, Sergey A.; Yurchenko, Stanislav O.
2017-04-01
Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-Hückel) systems is studied systematically using molecular dynamics (MD) simulations. Simulations cover very broad parameter range spanning from weakly coupled gaseous states to strongly coupled fluid and crystalline states. Important thermodynamic quantities, such as internal energy and pressure, are obtained and accurate physically motivated fits are proposed. This allows us to put forward simple practical expressions to describe thermodynamic properties of two-dimensional Yukawa systems. For crystals, in addition to numerical simulations, the recently developed shortest-graph interpolation method is applied to describe pair correlations and hence thermodynamic properties. It is shown that the finite-temperature effects can be accounted for by using simple correction of peaks in the pair correlation function. The corresponding correction coefficients are evaluated using MD simulation. The relevance of the obtained results in the context of colloidal systems, complex (dusty) plasmas, and ions absorbed to interfaces in electrolytes is pointed out.
17. Topological states in two-dimensional hexagon lattice bilayers
Science.gov (United States)
Zhang, Ming-Ming; Xu, Lei; Zhang, Jun
2016-10-01
We investigate the topological states of the two-dimensional hexagon lattice bilayer. The system exhibits a quantum valley Hall (QVH) state when the interlayer interaction t⊥ is smaller than the nearest neighbor hopping energy t, and then translates to a trivial band insulator state when t⊥ / t > 1. Interestingly, the system is found to be a single-edge QVH state with t⊥ / t = 1. The topological phase transition also can be presented via changing bias voltage and sublattice potential in the system. The QVH states have different edge modes carrying valley current but no net charge current. The bias voltage and external electric field can be tuned easily in experiments, so the present results will provide potential application in valleytronics based on the two-dimensional hexagon lattice.
18. CORPORATE VALUATION USING TWO-DIMENSIONAL MONTE CARLO SIMULATION
Directory of Open Access Journals (Sweden)
Toth Reka
2010-12-01
Full Text Available In this paper, we have presented a corporate valuation model. The model combine several valuation methods in order to get more accurate results. To determine the corporate asset value we have used the Gordon-like two-stage asset valuation model based on the calculation of the free cash flow to the firm. We have used the free cash flow to the firm to determine the corporate market value, which was calculated with use of the Black-Scholes option pricing model in frame of the two-dimensional Monte Carlo simulation method. The combined model and the use of the two-dimensional simulation model provides a better opportunity for the corporate value estimation.
19. Two-dimensional magnetostriction under vector magnetic characteristic
Science.gov (United States)
Wakabayashi, D.; Enokizono, M.
2015-05-01
This paper presents two-dimensional magnetostriction of electrical steel sheet under vector magnetic characteristic. In conventional measurement method using Single Sheet Tester, the magnetic flux density, the magnetic field strength, and the magnetostriction have been measured in one direction. However, an angle between the magnetic flux density vector and the magnetic field strength vector exists because the magnetic property is vector quantity. An angle between the magnetic flux density vector and the direction of maximum magnetostriction also exists. We developed a new measurement method, which enables measurement of these angles. The vector magnetic characteristic and the two-dimensional magnetostriction have been measured using the new measurement method. The BH and Bλ curves considering the angles are shown in this paper. The analyzed results considering the angles are also made clear.
20. Phase separation under two-dimensional Poiseuille flow.
Science.gov (United States)
Kiwata, H
2001-05-01
The spinodal decomposition of a two-dimensional binary fluid under Poiseuille flow is studied by numerical simulation. We investigated time dependence of domain sizes in directions parallel and perpendicular to the flow. In an effective region of the flow, the power-law growth of a characteristic length in the direction parallel to the flow changes from the diffusive regime with the growth exponent alpha=1/3 to a new regime. The scaling invariance of the growth in the perpendicular direction is destroyed after the diffusive regime. A recurrent prevalence of thick and thin domains which determines log-time periodic oscillations has not been observed in our model. The growth exponents in the infinite system under two-dimensional Poiseuille flow are obtained by the renormalization group.
1. Two-dimensional localized structures in harmonically forced oscillatory systems
Science.gov (United States)
Ma, Y.-P.; Knobloch, E.
2016-12-01
Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous presence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcation on one of them. The bifurcation structures of steady circular fronts and localized target patterns are computed in the Turing-stable and Turing-unstable regimes. In particular, localized target patterns grow along the solution branch via ring insertion at the core in a process reminiscent of defect-mediated snaking in one spatial dimension. Stability of axisymmetric solutions on these branches with respect to axisymmetric and nonaxisymmetric perturbations is determined, and parameter regimes with stable axisymmetric oscillons are identified. Direct numerical simulations reveal novel depinning dynamics of localized target patterns in the radial direction, and of circular and planar localized hexagonal patterns in the fully two-dimensional system.
2. Enstrophy inertial range dynamics in generalized two-dimensional turbulence
Science.gov (United States)
Iwayama, Takahiro; Watanabe, Takeshi
2016-07-01
We show that the transition to a k-1 spectrum in the enstrophy inertial range of generalized two-dimensional turbulence can be derived analytically using the eddy damped quasinormal Markovianized (EDQNM) closure. The governing equation for the generalized two-dimensional fluid system includes a nonlinear term with a real parameter α . This parameter controls the relationship between the stream function and generalized vorticity and the nonlocality of the dynamics. An asymptotic analysis accounting for the overwhelming dominance of nonlocal triads allows the k-1 spectrum to be derived based upon a scaling analysis. We thereby provide a detailed analytical explanation for the scaling transition that occurs in the enstrophy inertial range at α =2 in terms of the spectral dynamics of the EDQNM closure, which extends and enhances the usual phenomenological explanations.
3. Folding two dimensional crystals by swift heavy ion irradiation
Energy Technology Data Exchange (ETDEWEB)
Ochedowski, Oliver; Bukowska, Hanna [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany); Freire Soler, Victor M. [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany); Departament de Fisica Aplicada i Optica, Universitat de Barcelona, E08028 Barcelona (Spain); Brökers, Lara [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany); Ban-d' Etat, Brigitte; Lebius, Henning [CIMAP (CEA-CNRS-ENSICAEN-UCBN), 14070 Caen Cedex 5 (France); Schleberger, Marika, E-mail: [email protected] [Fakultät für Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg (Germany)
2014-12-01
Ion irradiation of graphene, the showcase model of two dimensional crystals, has been successfully applied to induce various modifications in the graphene crystal. One of these modifications is the formation of origami like foldings in graphene which are created by swift heavy ion irradiation under glancing incidence angle. These foldings can be applied to locally alter the physical properties of graphene like mechanical strength or chemical reactivity. In this work we show that the formation of foldings in two dimensional crystals is not restricted to graphene but can be applied for other materials like MoS{sub 2} and hexagonal BN as well. Further we show that chemical vapour deposited graphene forms foldings after swift heavy ion irradiation while chemical vapour deposited MoS{sub 2} does not.
4. Explorative data analysis of two-dimensional electrophoresis gels
DEFF Research Database (Denmark)
Schultz, J.; Gottlieb, D.M.; Petersen, Marianne Kjerstine
2004-01-01
Methods for classification of two-dimensional (2-DE) electrophoresis gels based on multivariate data analysis are demonstrated. Two-dimensional gels of ten wheat varieties are analyzed and it is demonstrated how to classify the wheat varieties in two qualities and a method for initial screening...... of gels is presented. First, an approach is demonstrated in which no prior knowledge of the separated proteins is used. Alignment of the gels followed by a simple transformation of data makes it possible to analyze the gels in an automated explorative manner by principal component analysis, to determine...... if the gels should be further analyzed. A more detailed approach is done by analyzing spot volume lists by principal components analysis and partial least square regression. The use of spot volume data offers a mean to investigate the spot pattern and link the classified protein patterns to distinct spots...
5. Two-dimensional model of elastically coupled molecular motors
Institute of Scientific and Technical Information of China (English)
Zhang Hong-Wei; Wen Shu-Tang; Chen Gai-Rong; Li Yu-Xiao; Cao Zhong-Xing; Li Wei
2012-01-01
A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins.Extensive Langevin simulations of the model are performed.We discuss the dependences of motion and efficiency on the model parameters,including the external force and the temperature.A good qualitative agreement with the expected behavior is observed.
6. Conductivity of a two-dimensional guiding center plasma.
Science.gov (United States)
Montgomery, D.; Tappert, F.
1972-01-01
The Kubo method is used to calculate the electrical conductivity of a two-dimensional, strongly magnetized plasma. The particles interact through (logarithmic) electrostatic potentials and move with their guiding center drift velocities (Taylor-McNamara model). The thermal equilibrium dc conductivity can be evaluated analytically, but the ac conductivity involves numerical solution of a differential equation. Both conductivities fall off as the inverse first power of the magnetic field strength.
7. Minor magnetization loops in two-dimensional dipolar Ising model
Energy Technology Data Exchange (ETDEWEB)
Sarjala, M. [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland); Seppaelae, E.T., E-mail: [email protected] [Nokia Research Center, Itaemerenkatu 11-13, FI-00180 Helsinki (Finland); Alava, M.J., E-mail: [email protected] [Aalto University, Department of Applied Physics, P.O. Box 14100, FI-00076 Aalto (Finland)
2011-05-15
The two-dimensional dipolar Ising model is investigated for the relaxation and dynamics of minor magnetization loops. Monte Carlo simulations show that in a stripe phase an exponential decrease can be found for the magnetization maxima of the loops, M{approx}exp(-{alpha}N{sub l}) where N{sub l} is the number of loops. We discuss the limits of this behavior and its relation to the equilibrium phase diagram of the model.
8. Cryptography Using Multiple Two-Dimensional Chaotic Maps
Directory of Open Access Journals (Sweden)
Ibrahim S. I. Abuhaiba
2012-08-01
Full Text Available In this paper, a symmetric key block cipher cryptosystem is proposed, involving multiple two-dimensional chaotic maps and using 128-bits external secret key. Computer simulations indicate that the cipher has good diffusion and confusion properties with respect to the plaintext and the key. Moreover, it produces ciphertext with random distribution. The computation time is much less than previous related works. Theoretic analysis verifies its superiority to previous cryptosystems against different types of attacks.
9. A UNIVERSAL VARIATIONAL FORMULATION FOR TWO DIMENSIONAL FLUID MECHANICS
Institute of Scientific and Technical Information of China (English)
何吉欢
2001-01-01
A universal variational formulation for two dimensional fluid mechanics is obtained, which is subject to the so-called parameter-constrained equations (the relationship between parameters in two governing equations). By eliminating the constraints, the generalized variational principle (GVPs) can be readily derived from the formulation. The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms. Some illustrative examples are given to testify the effectiveness and simplicity of the method.
10. Nonlocal bottleneck effect in two-dimensional turbulence
CERN Document Server
Biskamp, D; Schwarz, E
1998-01-01
The bottleneck pileup in the energy spectrum is investigated for several two-dimensional (2D) turbulence systems by numerical simulation using high-order diffusion terms to amplify the effect, which is weak for normal diffusion. For 2D magnetohydrodynamic (MHD) turbulence, 2D electron MHD (EMHD) turbulence and 2D thermal convection, which all exhibit direct energy cascades, a nonlocal behavior is found resulting in a logarithmic enhancement of the spectrum.
11. Level crossings in complex two-dimensional potentials
Qing-Hai Wang
2009-08-01
Two-dimensional $\\mathcal{PT}$-symmetric quantum-mechanical systems with the complex cubic potential 12 = 2 + 2 + 2 and the complex Hénon–Heiles potential HH = 2 + 2 + (2 − 3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the $\\mathcal{PT}$ symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.
12. Extraction of plant proteins for two-dimensional electrophoresis
OpenAIRE
Granier, Fabienne
1988-01-01
Three different extraction procedures for two-dimensional electrophoresis of plant proteins are compared: (i) extraction of soluble proteins with a nondenaturing Tris-buffer, (ii) denaturing extraction in presence of sodium dodecyl sulfate at elevated temperature allowing the solubilization of membrane proteins in addition to a recovery of soluble proteins, and (iii) a trichloroacetic acid-acetone procedure allowing the direct precipitation of total proteins.
13. Lyapunov Computational Method for Two-Dimensional Boussinesq Equation
CERN Document Server
Mabrouk, Anouar Ben
2010-01-01
A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable and analyzed for local truncation error for consistency. The stability is checked by using Lyapunov criterion and the convergence is studied. Some numerical implementations are provided at the end of the paper to validate the theoretical results.
14. Complex dynamical invariants for two-dimensional complex potentials
J S Virdi; F Chand; C N Kumar; S C Mishra
2012-08-01
Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}. y = x_{2} + ip_{4}, p_{x} = p_{1} + ix_{3}, p_{y} = p_{2} + ix_{4}$. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. THe obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.
15. Two-dimensional hydrogen negative ion in a magnetic field
Institute of Scientific and Technical Information of China (English)
Xie Wen-Fang
2004-01-01
Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional hydrogen negative ion H- in a magnetic field. The results show that the ground and low-excited states of H- in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.
16. А heuristic algorithm for two-dimensional strip packing problem
OpenAIRE
Dayong, Cao; Kotov, V.M.
2011-01-01
In this paper, we construct an improved best-fit heuristic algorithm for two-dimensional rectangular strip packing problem (2D-RSPP), and compare it with some heuristic and metaheuristic algorithms from literatures. The experimental results show that BFBCC could produce satisfied packing layouts than these methods, especially for the large problem of 50 items or more, BFBCC could get better results in shorter time.
17. Chronology Protection in Two-Dimensional Dilaton Gravity
CERN Document Server
Mishima, T; Mishima, Takashi; Nakamichi, Akika
1994-01-01
The global structure of 1 + 1 dimensional compact Universe is studied in two-dimensional model of dilaton gravity. First we give a classical solution corresponding to the spacetime in which a closed time-like curve appears, and show the instability of this spacetime due to the existence of matters. We also observe quantum version of such a spacetime having closed timelike curves never reappear unless the parameters are fine-tuned.
18. Phase Transitions in Two-Dimensional Traffic Flow Models
CERN Document Server
Cuesta, J A; Molera, J M; Cuesta, José A; Martinez, Froilán C; Molera, Juan M
1993-01-01
Abstract: We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit.
19. Phase Transitions in Two-Dimensional Traffic Flow Models
CERN Document Server
Cuesta, José A; Molera, Juan M; Escuela, Angel Sánchez; 10.1103/PhysRevE.48.R4175
2009-01-01
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit.
20. SU(1,2) invariance in two-dimensional oscillator
CERN Document Server
Krivonos, Sergey
2016-01-01
Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756[hep-th], with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written it terms of the oscillator variables.
1. Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity
CERN Document Server
Baillie, C F
1992-01-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of {\\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for $c>1$. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for $c>1$.
2. Multiple Potts models coupled to two-dimensional quantum gravity
Science.gov (United States)
Baillie, C. F.; Johnston, D. A.
1992-07-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of multiple q=2, 3, 4 state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the c>1 region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for c>1. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for c>1.
3. Colloidal interactions in two-dimensional nematic emulsions
N M Silvestre; P Patrício; M M Telo Da Gama
2005-06-01
We review theoretical and experimental work on colloidal interactions in two-dimensional (2D) nematic emulsions. We pay particular attention to the effects of (i) the nematic elastic constants, (ii) the size of the colloids, and (iii) the boundary conditions at the particles and the container. We consider the interactions between colloids and fluid (deformable) interfaces and the shape of fluid colloids in smectic-C films.
4. Thermal diode from two-dimensional asymmetrical Ising lattices.
Science.gov (United States)
Wang, Lei; Li, Baowen
2011-06-01
Two-dimensional asymmetrical Ising models consisting of two weakly coupled dissimilar segments, coupled to heat baths with different temperatures at the two ends, are studied by Monte Carlo simulations. The heat rectifying effect, namely asymmetric heat conduction, is clearly observed. The underlying mechanisms are the different temperature dependencies of thermal conductivity κ at two dissimilar segments and the match (mismatch) of flipping frequencies of the interface spins.
5. Numerical Study of Two-Dimensional Viscous Flow over Dams
Institute of Scientific and Technical Information of China (English)
王利兵; 刘宇陆; 涂敏杰
2003-01-01
In this paper, the characteristics of two-dimensional viscous flow over two dams were numerically investigated. The results show that the behavior of the vortices is closely related to the space between two dams, water depth, Fr number and Reynolds number. In addition, the flow properties behind each dam are different, and the changes over two dams are more complex than over one dam. Finally, the relevant turbulent characteristics were analyzed.
6. Spirals and Skyrmions in two dimensional oxide heterostructures.
Science.gov (United States)
Li, Xiaopeng; Liu, W Vincent; Balents, Leon
2014-02-14
We construct the general free energy governing long-wavelength magnetism in two dimensional oxide heterostructures, which applies irrespective of the microscopic mechanism for magnetism. This leads, in the relevant regime of weak but non-negligible spin-orbit coupling, to a rich phase diagram containing in-plane ferromagnetic, spiral, cone, and Skyrmion lattice phases, as well as a nematic state stabilized by thermal fluctuations.
7. Acoustic Bloch oscillations in a two-dimensional phononic crystal.
Science.gov (United States)
He, Zhaojian; Peng, Shasha; Cai, Feiyan; Ke, Manzhu; Liu, Zhengyou
2007-11-01
We report the observation of acoustic Bloch oscillations at megahertz frequency in a two-dimensional phononic crystal. By creating periodically arrayed cavities with a decreasing gradient in width along one direction in the phononic crystal, acoustic Wannier-Stark ladders are created in the frequency domain. The oscillatory motion of an incident Gaussian pulse inside the sample is demonstrated by both simulation and experiment.
8. Exact analytic flux distributions for two-dimensional solar concentrators.
Science.gov (United States)
Fraidenraich, Naum; Henrique de Oliveira Pedrosa Filho, Manoel; Vilela, Olga C; Gordon, Jeffrey M
2013-07-01
A new approach for representing and evaluating the flux density distribution on the absorbers of two-dimensional imaging solar concentrators is presented. The formalism accommodates any realistic solar radiance and concentrator optical error distribution. The solutions obviate the need for raytracing, and are physically transparent. Examples illustrating the method's versatility are presented for parabolic trough mirrors with both planar and tubular absorbers, Fresnel reflectors with tubular absorbers, and V-trough mirrors with planar absorbers.
9. Tricritical behavior in a two-dimensional field theory
Science.gov (United States)
Hamber, Herbert
1980-05-01
The critical behavior of a two-dimensional scalar Euclidean field theory with a potential term that allows for three minima is analyzed using an approximate position-space renormalization-group transformation on the equivalent quantum spin Hamiltonian. The global phase diagram shows a tricritical point separating a critical line from a line of first-order transitions. Other critical properties are examined, and good agreement is found with results on classical spin models belonging to the same universality class.
10. Quantum entanglement in a two-dimensional ion trap
Institute of Scientific and Technical Information of China (English)
王成志; 方卯发
2003-01-01
In this paper, we investigate the quantum entanglement in a two-dimensional ion trap system. We discuss the quantum entanglement between the ion and phonons by using reduced entropy, and that between two degrees of freedom of the vibrational motion along x and y directions by using quantum relative entropy. We discuss also the influence of initial state of the system on the quantum entanglement and the relation between two entanglements in the trapped ion system.
11. Coll Positioning systems: a two-dimensional approach
CERN Document Server
Ferrando, J J
2006-01-01
The basic elements of Coll positioning systems (n clocks broadcasting electromagnetic signals in a n-dimensional space-time) are presented in the two-dimensional case. This simplified approach allows us to explain and to analyze the properties and interest of these relativistic positioning systems. The positioning system defined in flat metric by two geodesic clocks is analyzed. The interest of the Coll systems in gravimetry is pointed out.
12. Two-dimensional correlation spectroscopy in polymer study
Science.gov (United States)
Park, Yeonju; Noda, Isao; Jung, Young Mee
2015-01-01
This review outlines the recent works of two-dimensional correlation spectroscopy (2DCOS) in polymer study. 2DCOS is a powerful technique applicable to the in-depth analysis of various spectral data of polymers obtained under some type of perturbation. The powerful utility of 2DCOS combined with various analytical techniques in polymer studies and noteworthy developments of 2DCOS used in this field are also highlighted. PMID:25815286
13. Interior design of a two-dimensional semiclassic black hole
CERN Document Server
Levanony, Dana; 10.1103/PhysRevD.80.084008
2009-01-01
We look into the inner structure of a two-dimensional dilatonic evaporating black hole. We establish and employ the homogenous approximation for the black-hole interior. The field equations admit two types of singularities, and their local asymptotic structure is investigated. One of these singularities is found to develop, as a spacelike singularity, inside the black hole. We then study the internal structure of the evaporating black hole from the horizon to the singularity.
14. Towards a two dimensional model of surface piezoelectricity
OpenAIRE
Monge Víllora, Oscar
2016-01-01
We want to understand the behaviour of flexoelectricity and surface piezoelectricity and distinguish them in order to go deep into the controversies of the filed. This motivate the construction of a model of continuum flexoelectric theory. The model proposed is a two-dimensional model that integrates the electromechanical equations that include the elastic, dielectric, piezoelectric and flexoelectric effect on a rectangular sample. As the flexoelectric and the surface piezoelectric effects ap...
15. Velocity Statistics in the Two-Dimensional Granular Turbulence
OpenAIRE
Isobe, Masaharu
2003-01-01
We studied the macroscopic statistical properties on the freely evolving quasi-elastic hard disk (granular) system by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically and found that remarkably analogous to an enstrophy cascade process in the decaying two-dimensional fluid turbulence. There are four typical stages in the freely evolving inelastic hard disk system, which are homogeneous, shearing (vortex), clustering and final state. In the...
16. Statistical study of approximations to two dimensional inviscid turbulence
Energy Technology Data Exchange (ETDEWEB)
Glaz, H.M.
1977-09-01
A numerical technique is developed for studying the ergodic and mixing hypotheses for the dynamical systems arising from the truncated Fourier transformed two-dimensional inviscid Navier-Stokes equations. This method has the advantage of exactly conserving energy and entropy (i.e., total vorticity) in the inviscid case except for numerical error in solving the ordinary differential equations. The development of the mathematical model as an approximation to a real physical (turbulent) flow and the numerical results obtained are discussed.
17. Static Structure of Two-Dimensional Granular Chain
Institute of Scientific and Technical Information of China (English)
WEN Ping-Ping; LI Liang-Sheng; ZHENG Ning; SHI Qing-Fan
2010-01-01
@@ Static packing structures of two-dimensional granular chains are investigated experimentally.It is shown that the packing density approximates the saturation with the exponential law as the length of chain increases.The packing structures are globally disordered,while the local square crystallization is found by using the radial distribution function.This characteristic phase of chain packing is similar to a liquid crystal state,and has properties between a conventional liquid and solid crystal.
18. THE DEGENERACY PROBLEM OF TWO-DIMENSIONAL LINEAR RECURRING ARRAYS
Institute of Scientific and Technical Information of China (English)
2000-01-01
The degeneracy degree and degeneracy position sets of a wo-dimensional linear recurrence relation set are characterized. The fact that a linear recurring array is essentially a doubly periodic array is shown. By using the Grbner base theory, a calculation formula for degeneracy degree is given and the existence of a special degeneracy position set is proved. In the present paper, the degeneracy problem of the two-dimensional linear recurring arrays is completely solved.
19. Observation of a pairing pseudogap in a two-dimensional Fermi gas.
Science.gov (United States)
Feld, Michael; Fröhlich, Bernd; Vogt, Enrico; Koschorreck, Marco; Köhl, Michael
2011-11-30
Pairing of fermions is ubiquitous in nature, underlying many phenomena. Examples include superconductivity, superfluidity of (3)He, the anomalous rotation of neutron stars, and the crossover between Bose-Einstein condensation of dimers and the BCS (Bardeen, Cooper and Schrieffer) regime in strongly interacting Fermi gases. When confined to two dimensions, interacting many-body systems show even more subtle effects, many of which are not understood at a fundamental level. Most striking is the (as yet unexplained) phenomenon of high-temperature superconductivity in copper oxides, which is intimately related to the two-dimensional geometry of the crystal structure. In particular, it is not understood how the many-body pairing is established at high temperature, and whether it precedes superconductivity. Here we report the observation of a many-body pairing gap above the superfluid transition temperature in a harmonically trapped, two-dimensional atomic Fermi gas in the regime of strong coupling. Our measurements of the spectral function of the gas are performed using momentum-resolved photoemission spectroscopy, analogous to angle-resolved photoemission spectroscopy in the solid state. Our observations mark a significant step in the emulation of layered two-dimensional strongly correlated superconductors using ultracold atomic gases.
20. A theoretical study on the electronic property of a new two-dimensional material molybdenum dinitride
Energy Technology Data Exchange (ETDEWEB)
Wu, Haiping, E-mail: [email protected] [Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094 (China); State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012 (China); Qian, Yan, E-mail: [email protected] [Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094 (China); Lu, Ruifeng; Tan, Weishi [Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094 (China)
2016-02-15
Motivated by the recent synthesis of bulk MoN{sub 2} which exhibits the layered structure just like the bulk MoS{sub 2}, the monolayered MoN{sub 2} exfoliated from the bulk counterpart is investigated systematically by using density-functional calculations in this work. The result shows that the ground-state two-dimensional monolayered MoN{sub 2} behaves as an indirect band gap semiconductor with the energy gap of ∼0.12 eV. Subsequently, the external strain from −6% to 6% is employed to engineer the band structure, and the energy gap can be efficiently tuned from 0 to 0.70 eV. Notably, when the strain is beyond 5% or −3%, the two-dimensional monolayered MoN{sub 2} would transfer from an indirect band gap to a direct band gap semiconductor. This work introduces a new member of two-dimensional transition-metal family, which is important for industry applications, especially for the utilization in the long-wavelength infrared field. - Highlights: • The 2D MoN{sub 2} behaves as an indirect band gap semiconductor with the energy gap of ∼0.12 eV. • The energy gap can be efficiently tuned from 0 to 0.70 eV by small strain. • The band gap would transfer from an indirect to a direct one when the strain is beyond 5% or −3%. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.754020631313324, "perplexity": 4255.318213131513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813088.82/warc/CC-MAIN-20180220185145-20180220205145-00088.warc.gz"} |
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# Solution: Based on molecular structure, arrange the following oxyacids in order of increasing acid strength:HClO3, HIO3, HBrO3
###### Problem
Based on molecular structure, arrange the following oxyacids in order of increasing acid strength:
HClO3, HIO3, HBrO3 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8694913387298584, "perplexity": 4371.89722611065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371818008.97/warc/CC-MAIN-20200408135412-20200408165912-00076.warc.gz"} |
https://www.physicsforums.com/threads/confusion-over-hydraulic-gradient-l-parameter.835218/ | # I Confusion Over Hydraulic Gradient, L parameter
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1. Sep 30, 2015
### Typhon4ever
I've come across two different approaches to quantifying what l is in the equation for hydraulic gradient Δh/L. In this first picture L is the parallel distance along the datum across the reference plane
But in this second picture L is the length along the pipe
Why are the two L's different? I'm asking because there's a picture in a book of a sloping sand layer sandwiched between clay layers and L is taken to be like in the first image but the idea of a permeable sand layer between two effectively impermeable clay layers looks like the 2nd pipe image.
2. Oct 5, 2015
### Greg Bernhardt
Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
3. Mar 2, 2016
### Claudio Meier
The correct interpretation is that of the second figure: the length to compute the gradient is that "travelled" by the water. After all, the hydraulic gradient is the spatial rate at which head (energy per unit weight of water) is lost or dissipated; basically: how many meters of head are lost per meter of distance travelled?
The first figure shows an unconfined aquifer in which the vertical scale is distorted or exaggerated; in most cases, the slope of unconfined aquifers is very flat, so that if one measures L in the horizontal, the difference with the actual distance travelled is negligible (because cosine of a small angle tends to 1, so that the horizontal distance will be almost equal to the length of the hypotenuse of the triangle).
Indeed, the Dupuit-Forchheimer assumption used to solve many groundwater and well problems assumes that flow is horizontal in unconfined aquifers, neglecting the small vertical component of the flow (by the way, note the irony: Dupuit means "of the well" in French).
Note that I wrote "travelled" between quotation marks above, because the actual distance takes the tortuosity of the flow paths into account, and we are not doing that here: our distances are measured assuming that there are no solid particles continuously deflecting the flow at the small scale.
Hope this helps,
Claudio Meier
Draft saved Draft deleted
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https://www.physicsforums.com/threads/vector-subspace.288856/ | # Vector subspace
1. Jan 31, 2009
### fk378
1. The problem statement, all variables and given/known data
Let F be the field of all real numbers and let V be the set of all sequences (a1,a2,....a_n,...), a_i in F, where equality, addition, and scalar multiplication are defined component-wise.
(a) Prove that V is a vector space over F
(b) Let W={(a1, a2,....,a_n,...) in V | lim a_n = 0 as n-->inf}. Prove that W is a subspace of V.
(c) Let U={(a1,...,a_n,...) in V | summation of (a_i)^2 is finite, i evaluated from 1 to inf}. Prove that U is a subspace of V and is contained in W.
3. The attempt at a solution
I know that in order for W to be a subspace of V, W must form a vector space over F under the operations of V. I've already proved (a). Do I need to know the limit of a_n to prove (b) or is that just for (c)? It seems like proving (b) is pretty similar to (a), right? Any tips on proving (c)?
2. Jan 31, 2009
### descendency
In part b, the lim a_n = 0 as n --> inf just means that only those a_n that are contained in V that meet the criteria lim a_n = 0 as n --> inf are contained in the set.
So to prove part b, you just need to show that addition and scalar multiplication are closed in the subspace.
Sorry, I'm not too sure about part C (I don't want to guess and tell you wrong either).
3. Jan 31, 2009
### slider142
Suppose {a_i} is a sequence in U such that the a_i's do not tend to 0 as i increases without bound. Consider the infinite series Sum[(a_i)^2] = Sum[b_i] where each b_i is positive and does not tend to 0. Suppose the sum converges to L, which means for each r > 0, there exists a number N so that | L - Sum[b_i] | < r where i ranges from 0 to n for all n > N. If the terms b_i are never negative and never tend to 0, can this condition be satisfied? (Note that the condition that the b_i's tend to 0 is that for all d > 0, there is some N so that |b_i| < d for all i > N.)
4. Feb 1, 2009
### fk378
I don't really understand, but I would say that the condition cannot be satisfied because if the terms b_i never tend to 0 then the summation must diverge.
5. Feb 1, 2009
### slider142
If you can show that rigorously, then you have shown that each element of U is necessarily an element of W, and is thus contained in W. The only thing left is to show that sums of elements in U remain in U, and so do scalar multiples, which is the easy part.
6. Feb 1, 2009
### fk378
How would I show that the sum of any multiples of elements of U is still in U? Wouldn't I have to show that the sum of every sequence^2 is finite?
7. Feb 2, 2009
### slider142
As an example, suppose {a_i} is an element of U. Then the series (a_1)^2 + (a_2)^2 + ... converges. Consider the element s*{a_i} defined to be {s*a_i}, so we now consider the series (s*a_1)^2 + (s*a_2)^2 + ... = s^2*(a_1)^2 + s^2*(a_2)^2 + ... = s^2*((a_1)^2 + (a_2)^2 + ...) = s^2*A where A is the number that the original series converges to, showing constructively that the component-wise defined multiple also converges. Now you just have to consider what happens to a component-wise sum.
As for the latter question, you would already have shown that by showing that U is contained in W (by contradiction). (Need more of a hint?)
Have something to add?
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https://arxiv.org/abs/1605.03729 | astro-ph.SR
(what is this?)
# Title: Towards detecting methanol emission in low-mass protoplanetary discs with ALMA: The role of non-LTE excitation
Abstract: The understanding of organic content of protoplanetary discs is one of the main goals of the planet formation studies. As an attempt to guide the observational searches for weak lines of complex species in discs, we modelled the (sub-)millimetre spectrum of gaseous methanol (CH$_3$OH), one of the simplest organic molecules, in the representative T Tauri system. We used 1+1D disc physical model coupled to the gas-grain ALCHEMIC chemical model with and without 2D-turbulent mixing. The computed CH$_3$OH abundances along with the CH$_3$OH scheme of energy levels of ground and excited torsional states were used to produce model spectra obtained with the non-local thermodynamic equilibrium (non-LTE) 3D line radiative transfer code LIME. We found that the modelled non-LTE intensities of the CH$_3$OH lines can be lower by factor of $>10$--$100$ than those calculated under assumption of LTE. Though population inversion occurs in the model calculations for many (sub-)millimetre transitions, it does not lead to the strong maser amplification and noticeably high line intensities. We identify the strongest CH$_3$OH (sub-)millimetre lines that could be searched for with the Atacama Large Millimeter Array (ALMA) in nearby discs. The two best candidates are the CH$_{3}$OH $5_0-4_0~A^+$ (241.791 GHz) and $5_{-1}-4_{-1}~E$ (241.767 GHz) lines, which could possibly be detected with the $\sim5\sigma$ signal-to-noise ratio after $\sim3$ hours of integration with the full ALMA array.
Comments: Accepted for publication in MNRAS, 15 figures, 3 tables Subjects: Solar and Stellar Astrophysics (astro-ph.SR); Astrophysics of Galaxies (astro-ph.GA) DOI: 10.1093/mnras/stw1140 Cite as: arXiv:1605.03729 [astro-ph.SR] (or arXiv:1605.03729v1 [astro-ph.SR] for this version)
## Submission history
From: Sergey Parfenov [view email]
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# XENON100 Collaboration; Aprile, E; Askin, A; Baudis, L; Behrens, A (2011). Dark matter results from 100 live days of XENON100 data. Physical Review Letters, 107(13):131302.
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## Abstract
We present results from the direct search for dark matter with the XENON100 detector, installed underground at the Laboratori Nazionali del Gran Sasso of INFN, Italy. XENON100 is a two-phase time-projection chamber with a 62 kg liquid xenon target. Interaction vertex reconstruction in three dimensions with millimeter precision allows the selection of only the innermost 48 kg as the ultralow background fiducial target. In 100.9 live days of data, acquired between January and June 2010, no evidence for dark matter is found. Three candidate events were observed in the signal region with an expected background of (1.8±0.6) events. This leads to the most stringent limit on dark matter interactions today, excluding spin-independent elastic weakly interacting massive particle (WIMP) nucleon scattering cross sections above 7.0×10-45 cm2 for a WIMP mass of 50 GeV/c2 at 90% confidence level.
© 2011 American Physical Society
## Citations
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## Derivation of Planck’s radiation law – part 4 (final part)
In part 3 of this blog series I explained how Max Planck found a mathematical formula to fit the observed Blackbody spectrum, but that when he presented it to the German Physics Society on the 19th of October 1900 he had no physical explanation for his formula. Remember, the formula he found was
$E_{\lambda} \; d \lambda = \frac{ A }{ \lambda^{5} } \frac{ 1 }{ (e^{a/\lambda T} -1) } \; d\lambda$
if we express it in terms of wavelength intervals. If we express it in terms of frequency intervals it is
$E_{\nu} \; d \nu = A^{\prime} \nu^{3} \frac{ 1 }{ (e^{ a^{\prime} \nu / T } - 1) } \; d\nu$
Planck would spend six weeks trying to find a physical explanation for this equation. He struggled with the problem, and in the process was forced to abandon many aspects of 19th Century physics in both the fields of thermodynamics and electromagnetism which he had long cherished. I will recount his derivation – it is not the only one and maybe in coming blog posts I can show how his formula can be derived from other arguments, but this is the method Planck himself used.
## Radiation in a cavity
As we saw in the derivation of the Rayleigh-Jeans law (see part 3 here, and links in that to parts 1 and 2), blackbody radiation can be modelled as an idealised cavity which radiates through a small hole. Importantly, the system is given enough time for the radiation and the material from which the cavity is made to come into thermal equilibrium with each other. This means that the walls of the cavity are giving energy to the radiation at the same rate that the radiation is giving energy to the walls.
Using classical physics, as we did in the derivation of the Rayleigh-Jeans law, we saw that the energy density (the energy per unit volume) is
$\frac{du}{d\nu} = \left( \frac{ 8 \pi kT }{ c^{3} } \right) \nu^{2}$
After trying to derive his equation based on standard thermodynamic arguments, which failed, Planck developed a model which, he found, was able to produce his equation. How did he do this?
### Harmonic Oscillators
First, he knew from classical electromagnetic theory that an oscillating electron radiates (as it is accelerating), and he reasoned that when the cavity was in thermal equilibrium with the radiation in the cavity, the electrons in the walls of the cavity would oscillate and it was they that produced the radiation.
After much trial and error, he decided upon a model where the electrons were attached to massless springs. He could model the radiation of the electrons by modelling them as a whole series of harmonic oscillators, but with different spring stiffnesses to produce the different frequencies observed in the spectrum.
As we have seen (I derived it here), in classical physics the energy of a harmonic oscillator depends on both its amplitude of oscillation squared ($E \propto A^{2}$); and it also depends on its frequency of oscillation squared ($E \propto \nu^{2}$). The act of heating the cavity to a particular temperature is what, in Planck’s model, set the electrons oscillating; but whether a particular frequency oscillator was set in motion or not would depend on the temperature.
If it were oscillating, it would emit radiation into the cavity and absorb it from the cavity. He knew from the shape of the blackbody curve (and, by now, his equation which fitted it), that the energy density $E d\nu$ at any particular frequency started off at zero for high frequencies (UV), then rose to a peak, and then dropped off again at low frequencies (in the infrared).
So, Planck imagined that the number of oscillators with a particular resonant frequency would determine how much energy came out in that frequency interval. He imagined that there were more oscillators with a frequency which corresponded to the maximum in the blackbody curve, and fewer oscillators at higher and lower frequencies. He then had to figure out how the total energy being radiated by the blackbody would be shared amongst all these oscillators, with different numbers oscillating at different frequencies.
He found that he could not derive his formula using the physics that he had long accepted as correct. If he assumed that the energy of each oscillator went as the square of the amplitude, as it does in classical physics, his formula was not reproduced. Instead, he could derive his formula for the blackbody radiation spectrum only if the oscillators absorbed and emitted packets of energy which were proportional to their frequency of oscillation, not to the square of the frequency as classical physics argued. In addition, he found that the energy could only come in certain sized chunks, so for an oscillator at frequency $\nu, \; E = nh\nu$, where $n$ is an integer, and $h$ is now known as Planck’s constant.
What does this mean? Well, in classical physics, an oscillator can have any energy, which for a particular oscillator vibrating at a particular frequency can be altered by changing the amplitude. Suppose we have an oscillator vibrating with an amplitude of 1 (in abitrary units), then because the energy goes as the square of the amplitude its energy is $E=1^{2} =1$. If we increase the amplitude to 2, the energy will now be $E=2^{2} = 4$. But, if we wanted an energy of 2, we would need an amplitude of $\sqrt{2} = 1.414$, and if we wanted an energy of $3$ we would need an amplitude of $\sqrt{3} = 1.73$.
In classical physics, there is nothing to stop us having an amplitude of 1.74, which would give us an energy of 3.0276 (not 3), or an amplitude of 1.72 whichg would give us an energy of 2.9584 (not 3). But, what Planck found is that this was not allowed for his oscillators, they did not seem to obey the classical laws of physics. The energy could only be integers of $h\nu$, so $E=0h\nu, 1h\nu, 2h\nu, 3h\nu, 4h\nu$ etc.
Then, as I said above, he further assumed that the total energy at a particular frequency was given by the energy of each oscillator at that frequency multiplied by the number of oscillators at that frequency. The frequency of a particular oscillator was, he imagined, determined by its stiffness (Hooke’s constant). The energy of a particular oscillator at a particular frequency could be varied by the amplitude of its oscillations.
Let us assume, just to illustrate the idea, that the value of h is 2. If the total energy in the blackbody at a particular frequency of, say, 10 (in arbitrary units) were 800 (also in arbitrary units), this would mean that the energy of each chunk ($E=h \nu$) was $E = 2 \times 10 = 20$. So, the number of chunks at that frequency would then be $800/20 = 40$. 40 oscillators, each with an energy of 20, would be oscillating to give us our total energy of 800 at that frequency.
Because of this quantised energy, we can write that $E_{n} = nh \nu$, where $n=0,1,2,3, \cdots$.
### The number of oscillators at each frequency
The next thing Planck needed to do was derive an expression for the number of oscillators at each frequency. Again, after much trial and error he found that he had to borrow an idea first proposed by Austrian physicist Ludwig Boltzmann to describe the most likely distribution of energies of atoms or molecules in a gas in thermal equilibrium. Boltzmann found that the number of atoms or molecules with a particular energy $E$ was given by
$N_{E} \propto e^{-E/kT}$
where $E$ is the energy of that state, $T$ is the temperature of the gas and $k$ is now known as Boltzmann’s constant. The equation is known as the Boltzmann distribution, and Planck used it to give the number of oscillators at each frequency. So, for example, if $N_{0}$ is the number of oscillators with zero energy (in the so-called ground-state), then the numbers in the 1st, 2nd, 3rd etc. levels ($N_{1}, N_{2}, N_{3},\cdots$) are given by
$N_{1} = N_{0} e^{ -E_{1}/kT }, \; N_{2} = N_{0} e^{ -E_{2}/kT }, \; N_{3} = N_{0} e^{ -E_{3}/kT }, \cdots$
But, as $E_{n} = nh \nu$, we can write
$N_{1} = N_{0} e^{ -h \nu /kT }, \; N_{2} = N_{0} e^{ -2h \nu /kT }, \; N_{3} = N_{0} e^{ -3h \nu /kT }, \cdots$
Planck modelled blackbody radiation as a series of harmonic oscillators with equally spaced energy levels
To make it easier to write, we are going to substitute $x = e^{ -h \nu / kT }$, so we have
$N_{1} = N_{0}x, \; N_{2} = N_{0} x^{2}, \; N_{3} = N_{0} x^{3}, \cdots$
The total number of oscillators $N_{tot}$ is given by
$N_{tot} = N_{0} + N_{1} + N_{2} + N_{3} + \cdots = N_{0} ( 1 + x + x^{2} + x^{3} + \cdots)$
Remember, this is the number of oscillators at each frequency, so the energy at each frequency is given by the number at each frequency multiplied by the energy of each oscillator at that frequency. So
$E_{1}=N_{1} h \nu , \; E_{2} = N_{2} 2h \nu , \; E_{3} = N_{3} 3h \nu, \cdots$
which we can now write as
$E_{1} = h \nu N_{0}x, \; E_{2} = 2h \nu N_{0}x^{2}, \; E_{3} = 3h \nu N_{0}x^{3}, \cdots$
The total energy $E_{tot}$ is given by
$E_{tot} = E_{0} + E_{1} + E_{2} + E_{3} + \cdots = N_{0} h \nu (0 + x + 2x^{2} + 3x^{3} + \cdots)$
The average energy $\langle E \rangle$ is given by
$\langle E \rangle = \frac{ E_{tot} }{ N_{tot} } = \frac{ N_{0} h \nu (0 + x + 2x^{2} + 3x^{3} + \cdots) }{ N_{0} ( 1 + x + x^{2} + x^{3} + \cdots ) }$
The two series inside the brackets can be summed. The sum of the series in the numerator, which we will call $S_{1}$ is given by
$S_{1} = \frac{ x - (n+1)x^{n+1} + nx^{n+2} }{ (1-x)^{2} }$
(for the proof of this, see for example here)
The series in the denominator, which we will call $S_{2}$, is just a geometric progression. The sum of such a series is simply
$S_{2} = \frac{ 1 - x^{n} }{ (1-x) }$
Both series are in $x$, but remember $x = e^{-h \nu / kT}$. Also, both series are from a frequency of $\nu = 0 \text{ to } \infty$, and $e^{-h \nu /kT} < 1$, which means the sums converge and can be simplified.
$S_{1} \rightarrow \frac{x}{ (1-x)^{2} } \text{ and } S_{2} \rightarrow \frac{ 1 }{(1-x)}$
which means that $\langle E \rangle = (h \nu S_{1})/S_{2}$ is given by
$\langle E \rangle = \frac{ h \nu x }{ (1-x)^{2} } \times \frac{ (1-x) }{1} = \frac{h \nu x}{ (1-x) }$
and so we can write that the average energy is
$\boxed{ \langle E \rangle = \frac{h \nu}{( 1/x - 1) } = \frac{h \nu}{ (e^{h \nu/kT} - 1) } }$
## The radiance per frequency interval
In our derivation of the Rayleigh-Jeans law (in this blog here), we showed that, using classical physics, the energy density $du$ per frequency interval was given by
$du = \frac{ 8 \pi }{ c^{3} } kT \nu^{2} \, d \nu$
where $kT$ was the energy of each mode of the electromagnetic radiation. We need to replace the $kT$ in this equation with the average energy for the harmonic oscillators that we have just derived above. So, we re-write the energy density as
$du = \frac{ 8 \pi }{ c^{3} } \frac{ h \nu }{ (e^{h\nu/kT} - 1) } \nu^{2} \; d\nu = \frac{ 8 \pi h \nu^{3} }{ c^{3} } \frac{ 1 }{ (e^{h\nu/kT} - 1) } \; d\nu$
$du$ is the energy density per frequency interval (usually measured in Joules per metre cubed per Hertz), and by replacing $kT$ with the average energy that we derived above the radiation curve does not go as $\nu^{2}$ as in the Rayleigh-Jeans law, but rather reaches a maximum and turns over, avoiding the ultraviolet catastrophe.
It is more common to express the Planck radiation law in terms of the radiance per unit frequency, or the radiance per unit wavelength, which are written $B_{\nu}$ and $B_{\lambda}$ respectively. Radiance is the power per unit solid angle per unit area. So, as a first step to go from energy density to radiance we will divide by $4 \pi$, the total solid angle. This gives
$\frac{ 2 h \nu^{3} }{ c^{3} } \frac{ 1 }{ (e^{h\nu/kT} - 1) } \; d\nu$
We want the power per unit area, not the energy per unit volume. To do this we first note that power is energy per unit time, and second that to go from unit volume to unit area we need to multiply by length. But, for EM radiation, length is just $ct$. So, we need to divide by $t$ and multiply by $ct$, giving us that the radiance per frequency interval is
$\boxed{ B_{\nu} = \frac{ 2h \nu^{3} }{ c^{2} } \frac{ 1 }{ (e^{h\nu/kT} - 1) } \; d\nu }$
which is the way the Planck radiation law per frequency interval is usually written.
## Radiance per unit wavelength interval
If you would prefer the radiance per wavelength interval, we note that $\nu = c/\lambda$ and so $d\nu = -c/\lambda^{2} \; d\lambda$. Ignoring the minus sign (which is just telling us that as the frequency increases the wavelength decreases), and substituting for $\nu$ and $d\nu$ in terms of $\lambda$ and $d\lambda$, we can write
$B_{\lambda} = \frac{ 2h }{ c^{2} } \frac{ c^{3} }{ \lambda^{3} } \frac{ 1 }{ ( e^{hc/\lambda kT} - 1 ) } \frac{ c }{ \lambda^{2} } \; d\lambda$
Tidying up, this gives
$\boxed{ B_{\lambda} = \frac{ 2hc^{2} }{ \lambda^{5} } \frac{ 1 }{ ( e^{hc/\lambda kT} - 1 ) } \; d\lambda }$
which is the way the Planck radiation law per wavelength interval is usually written.
## Summary
To summarise, in order to reproduce the formula which he had empirically derived and presented in October 1900, Planck found that he he could only do so if he assumed that the radiation was produced by oscillating electrons, which he modelled as oscillating on a massless spring (so-called “harmonic oscillators”). The total energy at any given frequency would be given by the energy of a single oscillator at that frequency multiplied by the number of oscillators oscillating at that frequency.
However, he had to assume that
1. The energy of each oscillator was not related to either the square of the amplitude of oscillation or the square of the frequency of oscillation (as it would be in classical physics), but rather to the square of the amplitude and the frequency, $E \propto \nu$.
2. The energy of each oscillator could only be a multiple of some fundamental “chunk” of radiation, $h \nu$, so $E_{n} = nh\nu$ where $n=0,1,2,3,4$ etc.
3. The number of oscillators with each energy $E_{n}$ was given by the Boltzmann distribution, so $N_{n} = N_{0} e^{-nh\nu/kT}$ where $N_{0}$ is the number of oscillators in the lowest energy state.
In a way, we can imagine that the oscillators at higher frequencies (to the high-frequency side of the peak of the blackbody) are “frozen out”. The quantum of energy for a particular oscillator, given by $E_{n}=nh\nu$, is just too large to exist at the higher frequencies. This avoids the ultraviolet catastrophe which had stumped physicists up until this point.
By combining these assumptions, Planck was able in November 1900 to reproduce the exact equation which he had derived empirically in October 1900. In doing so he provided, for the first time, a physical explanation for the observed blackbody curve.
• Part 1 of this blogseries is here.
• Part 2 is here.
• Part 3 is here.
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## Does centrifugal force exist?
For several weeks now I have been planning to write a blog about centrifugal force, mainly prompted by seeing a post by John Gribbin on Facebook of the xkcd cartoon about it. In the cartoon James Bond is threatened with torture on a centrifuge. Here is a link to the original cartoon.
The xkcd cartoon about centrifugal force involves James Bond being tortured on a centrifuge
I have taught mechanics many times to physics undergraduates, and they are often confused about centripetal force and centrifugal force, and what the difference is between them. Some have heard that centrifugal force doesn’t really exist, just as Bond states in this cartoon. What is the real story?
## Rotating frames of reference
Everyone reading this (apart from a few “flat-Earth adherents” maybe) knows that we live on the surface of a planet which is rotating on its axis once a day. This means that we do not live in an inertial frame of reference (an inertial frame is one which is not accelerating), as clearly being on the surface of a spinning planet means that we are experiencing acceleration all the time; as we are not travelling in a straight line. That acceleration is provided by the force of gravity, and it stops us from going off in a straight line into space!
Because we are living in a non-inertial frame of reference we need to modify Newton’s laws of motion to properly describe such a non-inertial frame (which I am going to call a “rotating frame” from now on, although a rotating frame is just one example of a non-inertial frame but it is the one relevant to us on the surface of a rotating Earth).
Let us consider our usual Cartesian coordinate system. The unit vector in the x-direction is usually written as $\hat{\imath}$, the one in the y-direction as $\hat{\jmath}$, and the one in the z-direction as $\hat{k}$. We are going to consider an object rotating about the $\hat{k}$ (z-axis) direction.
We will consider two reference frames, one which stays fixed (the inertial reference frame), denoted by $(\hat{\imath},\hat{\jmath},\hat{k})$, and a second reference frame which rotates with the rotation, denoted by $(\hat{\imath}_{r} ,\hat{\jmath}_{r} ,\hat{k}_{r})$, where the subscript $r$ reminds us that this is the rotating frame of reference.
For the derivation below I am going to assume that we are considering motion with a constant radius $r$. I want to illustrate how centrifugal force arrises in a rotating frame such as being on the surface of our Earth. Our Earth is not spherical, but at any given point the size of the radius does not change, so this is a reasonable simplification.
As I showed in this blog on angular velocity, we can write the linear velocity $\vec{v}$ of an object moving in a circle as
$\vec{v} = \frac{ d \vec{r} }{ dt } = \vec{\omega} \times \vec{r}$
where $\vec{r}$ is the radius vector and $\vec{\omega}$ is the angular velocity.
Writing $\vec{r}$ in terms of its x,y and z-components in our inertial (non-rotating) frame, $\vec{r}=(\hat{\imath},\hat{\jmath},\hat{k})$, so in general we then have
$\vec{v} = \frac{ d \vec{r} }{ dt } \rightarrow \frac{ d \hat{\imath} }{dt} = \vec{\omega} \times \hat{\imath}, \; \; \frac{ d \hat{\jmath} }{dt} = \vec{\omega} \times \hat{\jmath} , \; \; \frac{ d \hat{k} }{dt} = \vec{\omega} \times \hat{k}$
Let us consider the specific case of a small rotation $\delta \theta$ about the $\hat{k}$ axis, as shown in the figure below. As the figure shows, in our inertial (fixed) frame of reference, the new direction of the x-axis is now $\hat{\imath} + \delta \hat{\imath}$, and the new direction of the y-axis is $\hat{\jmath} + \delta \hat{\jmath}$. The direction of the $\hat{k}$ axis is unchanged.
We are going to rotate about the z-axis ($\hat{k}$ direction) by an angle $\delta \theta$
Because we are rotating about the $\hat{k}$ axis, the angular velocity is in this direction, and so we can write (using the right-hand rule for vector products as I blogged about here)
$\vec{\omega} \times \hat{\imath} = \omega \hat{\jmath}, \; \; \vec{\omega} \times \hat{\jmath} = -\omega \hat{\imath}, \; \; \vec{\omega} \times \hat{k} =0$
Let us now consider some vector $\vec{a}$, which we will write in the rotating frame of reference as
$\vec{a} = a_{x} \hat{\imath}_{r} + a_{y} \hat{\jmath}_{r} + a_{z} \hat{k}_{r}$
If we now look at the rate of change of this vector in the rotating frame we have
$\left( \frac{d \vec{a} }{dt} \right)_{r} = \frac{d}{dt}(a_{x}\hat{\imath}_{r}) + \frac{d}{dt}(a_{y}\hat{\jmath}_{r}) + \frac{d}{dt}(a_{z}\hat{k}_{r})$
In the rotating frame of reference, $\hat{\imath}_{r}, \hat{\jmath}_{r}$ and $\hat{k}_{r}$ do not change with time, so we can write
$\left( \frac{d \vec{a} }{dt} \right)_{r} = \frac{ da_{x} }{dt} \hat{\imath}_{r} + \frac{ da_{y} }{dt} \hat{\jmath}_{r} + \frac{ da_{z} }{dt} \hat{k}_{r}$
In the inertial frame of reference $\hat{\imath}_{r}, \hat{\jmath}_{r}$ and $\hat{k}_{r}$ move, so
$\left( \frac{d \vec{a} }{dt} \right)_{i} = \frac{d}{dt} (a_{x} \hat{\imath}_{r}) + \frac{d}{dt} (a_{y} \hat{\jmath}_{r}) + \frac{d}{dt} (a_{z} \hat{k}_{r})$
$\left( \frac{d \vec{a} }{dt} \right)_{i} = \frac{ da_{x} }{dt}\hat{\imath}_{r} + \frac{ da_{y} }{dt}\hat{\jmath}_{r} + \frac{ da_{z} }{dt}\hat{k}_{r} + a_{x} \frac{d \hat{\imath}_{r} }{dt} + a_{y} \frac{d \hat{\jmath}_{r} }{dt} + a_{z} \frac{d \hat{k}_{r} }{dt}$
But, we can write (see above) that
$\frac{d\hat{\imath}_{r} }{dt} = \vec{\omega} \times \hat{\imath}_{r}, \; \; \frac{d\hat{\jmath}_{r} }{dt} = \vec{\omega} \times \hat{\jmath}_{r}, \; \; \frac{d\hat{k}_{r} }{dt} = \vec{\omega} \times \hat{k}_{r}$
and so
$\left( \frac{d \vec{a} }{dt} \right)_{i} = \frac{ da_{x} }{dt}\hat{\imath}_{r} + \frac{ da_{y} }{dt}\hat{\jmath}_{r} + \frac{ da_{z} }{dt}\hat{k}_{r} + a_{x} \vec{\omega} \times \hat{\imath}_{r} + + a_{y} \vec{\omega} \times \hat{\jmath}_{r} + + a_{z} \vec{\omega} \times \hat{k}_{r}$
$\left( \frac{d \vec{a} }{dt} \right)_{i} = \frac{ da_{x} }{dt}\hat{\imath}_{r} + \frac{ da_{y} }{dt}\hat{\jmath}_{r} + \frac{ da_{z} }{dt}\hat{k}_{r} + \vec{\omega} \times \vec{a}$
$\boxed{ \left( \frac{d \vec{a} }{dt} \right)_{i} = \left( \frac{d \vec{a} }{dt} \right)_{r} + (\vec{\omega} \times \vec{a}) }$
## A fixed point on the Earth’s surface
Let us now consider the point $\vec{a} = \vec{r}$, where $\vec{r}$ is a fixed point on the Earth’s surface. We can write
$\left( \frac{d \vec{r} }{dt} \right)_{i} = \left( \frac{d \vec{r} }{dt} \right)_{r} + (\vec{\omega} \times \vec{r})$
But, in the rotating frame of reference this point does not change with time, so
$\left( \frac{d \vec{r} }{dt} \right)_{r} = 0$
and so
$\left( \frac{d \vec{r} }{dt} \right)_{i} = (\vec{\omega} \times \vec{r}) = \omega r \sin(\theta)$
where $\theta$ is the angle between the Earth’s rotation axis and the latitude of the point (so $\theta = 90^{\circ} - \text{ latitude}$).
Let us now calculate the acceleration in an inertial frame in terms of acceleration in a rotating frame. Writing $\vec{a}$ as $\vec{r}$ as above, we now have
$\left( \frac{d \vec{r} }{dt} \right)_{i} = \left( \frac{d \vec{r} }{dt} \right)_{r} + (\vec{\omega} \times \vec{r})$
To make things easier to write, we will re-write
$\left( \frac{d \vec{r} }{dt} \right)_{i} = \frac{d \vec{r}_{i} }{dt} \text{ and } \left( \frac{d \vec{r} }{dt} \right)_{r} = \frac{d \vec{r}_{r} }{dt}$
so
$\frac{d \vec{r}_{i} }{dt} = \frac{d \vec{r}_{r} }{dt} + (\vec{\omega} \times \vec{r})$
$\vec{v}_{i} = \vec{v}_{r} + (\vec{\omega} \times \vec{r})$
If we now differentiate $\vec{v}_{i}$ with respect to time, we will have the acceleration in the inertial frame
$\left( \frac{d \vec{v}_{i} }{dt} \right)_{i} = \left( \frac{d \vec{v}_{i} }{dt} \right)_{r} + (\vec{\omega} \times \vec{v}_{i})$
But, $\vec{v}_{i} = \vec{v}_{r} + (\vec{\omega} \times \vec{r})$
so
$\left( \frac{d \vec{v}_{i} }{dt} \right)_{i} = \frac{d}{dt}(\vec{v}_{r} + \vec{\omega} \times \vec{r})_{r} + \vec{\omega} \times (\vec{v}_{r} + \vec{\omega} \times \vec{r})$
Expanding this out we get
$\left( \frac{d \vec{v}_{i} }{dt} \right)_{i} = \left( \frac{d \vec{v}_{r} }{dt} \right)_{r} + \frac{d}{dt}(\vec{\omega} \times \vec{r}_{r}) + \vec{\omega} \times \vec{v}_{r} + \vec{\omega} \times (\vec{\omega} \times \vec{r}_{r})$
$\vec{a}_{i} = \vec{a}_{r} + 2\vec{\omega} \times \vec{v}_{r} + \vec{\omega} \times (\vec{\omega} \times \vec{r}_{r})$
Multiplying the acceleration by the mass $m$ to get a force
$m\vec{a}_{i} = m\vec{a}_{r} + 2m\vec{\omega} \times \vec{v}_{r} + m\vec{\omega} \times (\vec{\omega} \times \vec{r}_{r})$
So, writing the force in the rotating frame in terms of the force in the inertial frame, we have
$\boxed{ m\vec{a}_{r} = m\vec{a}_{i} - 2m\vec{\omega} \times \vec{v}_{r} - m\vec{\omega} \times (\vec{\omega} \times \vec{r}_{r}) }$
So,
$\boxed{\vec{F}_{r} = \vec{F}_{i} - 2m\vec{\omega} \times \vec{v}_{r} - m\vec{\omega} \times (\vec{\omega} \times \vec{r}_{r}) }$
Notice that there are two extra terms (Term A and Term B) in the equation on the right, I have highlighted them below.
If we compare the force in a rotating frame to an inertial frame, two extra terms (Term A and Term B) arise. Term A is the Coriolis force, Term B is the centrifugal force
Term A is what we call the Coriolis force, which depends on the velocity in the rotating frame $v_{r}$. It is the force which causes water going down a plughole to rotate about the hole and to move anti-clockwise in the northern hemisphere and clockwise in the southern hemisphere. It is also the force which determines the direction of rotation of low pressure systems in the atmosphere. I will discuss the coriolis force more in a future blog.
Term B is the centrifugal force, the force we were aiming to derive in this blogpost. The strength of the centrifugal force depends on the position of the object in the rotating frame – $r_{r}$.
## What is the direction of the centrifugal force
The direction of $(\vec{\omega} \times \vec{r}_{r})$ can be found using the right-hand rule for the vector product, which I blogged about here. Remembering that the direction of $\vec{r}_{r}$\$ is radially outwards from the centre of the Earth, and the direction of $\vec{\omega}$ is the direction of the Earth’s axis (pointing north), then the direction of $\vec{\omega} \times \vec{r}_{r}$ is towards the east (right if looking at the Earth with the North pole up).
We now need to take the vector produce of $\vec{\omega}$ with a vector in this eastwards direction, and again using the right-hand rule gives us that the direction of $(\vec{\omega} \times \vec{r}_{r})$ is outwards (not radially from the centre of the Earth, but at right angles to the axis of the Earth). But, notice the centrifugal force has a minus sign in front of it, so the direction of the centrifugal force is outwards, away and at right angles to the Earth’s axis.
The direction of the centrifugal force is away from the axis of rotation, as shown in this diagram
This means that it acts to reduce the force of gravity which keeps us on the Earth’s surface. It also depends on the angle between where you are and the Earth’s axis, so is greatest at the equator and goes to zero at the pole. It means that you will weight slightly less than if the Earth were not rotating, but the effect is quite small and you would not notice such a difference going from the pole to the equator.
## What is the strength of the centrifugal acceleration due to Earth’s rotation?
Let us calculate the centrifugal force at the Earth’s equator, where it is at its greatest.
At the equator, we can write that the centrifugal acceleration has a value of
$\omega^{2} r \text{ as } \theta = 90^{\circ}$
We can calculate $\omega$ for the Earth by remembering that it takes 24 hours to rotate once, and $\omega$ is related to the period $T$ of rotation via
$\omega = \frac{2 \pi }{ T}$
We need to convert the period $T$ to seconds, so $T = 24 \times 60 \times 60 = 86400 \; s$. This gives that
$\omega = 7.272 \times 10^{-5} \text{ rad/s }$
If we take the Earth’s radius to be 6,378.1 km (this is the radius at the equator), then we have that
$\omega^{2} r = 0.0337 \text{ m/s/s}$
Compare this to the acceleration due to gravity which pulls us towards the Earth’s surface, which is 9.81 m/s/s and we can see that the centrifugal force at its greatest is only $0.34 \%$ of the acceleration due to gravity. Tiny.
It is, however, noticeable when you are on a roundabout, and is used on fairground rides where you spin inside a drum and the floor moves away leaving you pinned to the wall of the drum. The force you feel pushing against this wall is the centrifugal force, and it is very real for you in that rotating frame!
So, there we have it, centrifugal force does exist in a rotating frame of reference, but does not exist from the perspective of someone in an inertial frame of reference.
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## Einstein’s general relativity centenary
There has been quite a bit of mention in the media this last week or so that it is 100 years since Albert Einstein published his ground-breaking theory of gravity – the general theory of relativity. Yet, there seems to be some confusion as to when this theory was first published, in some places you will see 1915, in others 1916. So, I thought I would try and clear up this confusion by explaining why both dates appear.
Albert Einstein in Berlin circa 1915/16 when his General Theory of Relativity was first published
## From equivalence to the field equations
Everyone knew that Einstein was working on a new theory of gravity. As I blogged about here, he had his insight into the equivalence between acceleration and gravity in 1907, and ever since then he had been developing his ideas to create a new theory of gravity.
He had come up with his principle of equivalence when he was asked in the autumn of 1907 to write a review article of his special theory of relativity (his 1905 theory) for Jahrbuch der Radioaktivitätthe (the Yearbook of Electronics and Radioactivity). That paper appeared in 1908 as Relativitätsprinzip und die aus demselben gezogenen Folgerungen (On the Relativity Principle and the Conclusions Drawn from It) (Jahrbuch der Radioaktivität, 4, 411–462).
In 1908 he got his first academic appointment, and did not return to thinking about a generalisation of special relativity until 1911. In 1911 he published a paper Einfluss der Schwerkraft auf die Ausbreitung des Lichtes (On the Influence of Gravitation on the Propagation of Light) (Annalen der Physik (ser. 4), 35, 898–908), in which he calculated for the first time the deflection of light produced by massive bodies. But, he also realised that, to properly develop his ideas of a new theory of gravity, he would need to learn some mathematics which was new to him. In 1912, he moved to Zurich to work at the ETH, his alma mater. He asked his friend Marcel Grossmann to help him learn this new mathematics, saying “You’ve got to help me or I’ll go crazy.”
Grossmann gave Einstein a book on non-Euclidean geometry. Euclidean geometry, the geometry of flat surfaces, is the geometry we learn in school. The geometry of curved surfaces, so-called Riemann geometry, had first been developed in the 1820s by German mathematician Carl Friedrich Gauss. By the 1850s another German mathematician, Bernhard Riemann developed this geometry of curved surfaces even further, and this was the Riemann geometry textbook which Grossmann gave to Einstein in 1912. Mastering this new mathematics proved very difficult for Einstein, but he knew that he needed to master it to be able to develop the equations for general relativity.
These equations were not ready until late 1915. Everyone knew Einstein was working on them, and in fact he was offered and accepted a job in Berlin in 1914 as Berlin wanted him on their staff when the new theory was published. The equations of general relativity were first presented on the 25th of November 1915, to the Prussian Academy of Sciences. The lecture Feldgleichungen der Gravitation (The Field Equations of Gravitation) was the fourth and last lecture that Einstein gave to the Prussian Academy on his new theory (Preussische Akademie der Wissenschaften, Sitzungsberichte, 1915 (part 2), 844–847), the previous three lectures, given on the 4th, 11th and 18th of November, had been leading up to this. But, in fact, Einstein did not have the field equations ready until the last few days before the fourth lecture!
The peer-reviewed paper of the theory (which also contains the field equations) did not appear until 1916 in volume 49 of Annalen der PhysikGrundlage der allgemeinen Relativitätstheorie (The Foundation of the General Theory of Relativity) Annalen der Physik (ser. 4), 49, 769–822. The paper was submitted by Einstein on the 20th of March 1916.
The beginning of Einstein’s first peer-reviewed paper on general relativity, which was received by Annalen der Physik on the 20th of March 1916
In a future blog, I will discuss Einstein’s field equations, but hopefully I have cleared up the confusion as to why some people refer to 1915 as the year of publication of the General Theory of Relativity, and some people choose 1916. Both are correct, which allows us to celebrate the centenary twice!
You can read more about Einstein’s development of the general theory of relativity in our book 10 Physicists Who Transformed Our Understanding of Reality. Order your copy here
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## Derivation of the moment of inertia of an annulus
Following on from my derivation of the moment of inertia of a disk, in this blog I will derive the moment of inertia of an annulus. By an annulus, I mean a disk which has the inner part missing, as shown below.
An annulus is a disk of small thickness $t$ with the inner part missing. The annulus goes from some inner radius $r_{1}$ to an outer radius $r$.
To derive its moment of inertia, we return to our definition of the moment of inertia, which for a volume element $dV$ is given by
$dI = r_{\perp}^{2} dm$
where $dm$ is the mass of the volume element $dV$. We are going to initially consider the moment of inertia about the z-axis, and so for this annulus it will be
$I_{zz} = \int _{r_{1}} ^{r} r_{\perp}^{2} dm$
where $r_{1}$ and $r$ are the inner radius and outer radius of the annulus respectively. As with the disk, the mass $dm$ of the volume element $dV$ is related to its volume and density via
$dm = \rho dV$
(assuming that the annulus has a uniform density). The volume element $dV$ can be found as before by considering a ring at a radius of $r$ which a width $dr$ and a thickness $t$. The volume of this will be
$dV = (2 \pi r dr) t$
and so we can write the mass $dm$ as
$dm = (2 \pi \rho t)rdr$
Thus we can write the moment of inertia $I_{zz}$ as
$I_{zz} = \int _{r_{1}} ^{r} r_{\perp}^{2} dm = 2 \pi \rho t \int _{r_{1}} ^{r} r_{\perp}^{3} dr$
Integrating this between $r_{1}$ and $r$ we get
$I_{zz} = 2 \pi \rho t [ \frac{ r^{4} - r_{1}^{4} }{4} ] = \frac{1}{2} \pi \rho t (r^4 - r_{1}^{4}) \text{ (Equ. 1)}$
But, we can re-write $(r^{4} - r_{1}^{4})$ as $(r^{2} + r_{1}^{2})(r^{2} - r_{1}^{2})$ (remember $x^{2} - y^{2}$ can be written as $(x+y)(x-y)$). So, wen can write Eq. (1) as
$I_{zz} = \frac{1}{2} \pi \rho t (r^{2} + r_{1}^{2})(r^{2} - r_{1}^{2}) \text{ (Equ. 2)}$
The total mass $M_{a}$ of the annulus can be found by considering the total mass of a disk of radius $r$ (which we will call $M_{2}$) and then subtracting the mass of the inner part, a disk of radius $r_{1}$ (which we will call $M_{1}$). The mass of a disk is just its density multiplied by its area multiplied by its thickness.
$M_{2} = \pi \rho t r^{2} \text{ and } M_{1} = \pi \rho t r_{1}^{2}$
so the mass $M_{a}$ of the annulus is
$M_{a} = M_{2} - M_{1} = \pi \rho t r^{2}- \pi \rho t r_{1}^{2} = \pi \rho t (r^{2} - r_{1}^{2})$
Substituting this expression for $M_{a}$ into equation (2) above, we can write that the moment of inertia for an annulus, which goes from an inner radius of $r_{1}$ to an outer radis of $r$, about the z-axis is
$\boxed{ I_{zz} = \frac{1}{2} M_{a} (r^{2} + r_{1}^{2}) }$
## Comparison to the moment of inertia of a disk
As we saw in this blog, the moment of inertia of a disk is $I_{zz} = \frac{1}{2} Mr^{2}$. It may therefore seem, at first sight, that the moment of inertia of an annulus is more than that of a disk. This would be true if they have the same mass, but if they have the same thickness and density the mass of an annulus will be much less.
Let us compare the moment of inertia of a disk and an annulus for the 4 following cases.
The same density and thickness, $r_{1} = 0.5 r$
The same density and thickness, $r_{1} = 0.9 r$
The same mass, $r_{1} = 0.5 r$
The same mass, $r_{1} = 0.9 r$
## The same density and thickness, $r_{1}=0.5r$
We are first going to compare the moment of inertia of a disk of mass $M$ with that of an annulus which goes from half the radius of the disk to the radius of the disk (i.e. $r_{1} \text{ the inner radius of the annulus, is } = 0.5 r$.
For the disk, its mass will be
$M = \rho t (\pi r^{2}) = \pi \rho t r^{2}$
The mass of the annulus, $M_{a}$, will be this mass less the mass of the missing part $M_{1}$, so
$M_{a} = M - M_{1} = M - \pi \rho t (r_{1})^{2} = \pi \rho t (r^{2} - (0.5r)^{2})= \pi \rho t (1-0.25)r^{2}$
$M_{a} = \pi \rho t (0.75)r^{2} = 0.75 M$
The moment of inertia of the disk will be
$I_{d} = \frac{1}{2} M r^{2}$
The moment of inertia of the annulus will be
$I_{a} = \frac{1}{2} M_{a} (r^{2} + r_{1}^{2}) = \frac{1}{2} (0.75M)(r^{2} + (0.5r)^{2}) = \frac{1}{2} (0.75M)(1.25r^{2}) = \frac{1}{2} (0.9375) M r^{2}$
So, for this case, $I_{a} = 0.9375 I_{d}$, i.e. slightly less than the disk.
## The same density and thickness, $r_{1}=0.9r$
Let us now consider the second case, with an annulus of the same density and thickness as the disk, and its inner radius being 90% of the outer radius, $r_{1} = 0.9r$. Now, the mass of the missing part of the disk, $M_{1}$ will be
$M_{1} = \rho t (\pi r_{1}^{2}) = \rho t \pi (0.9r)^{2} = 0.81 \rho t \pi r^{2} = 0.81M$
which means that the mass of the annulus, $M_{a}$ is
$M_{a} = M - M_{1} = M-0.81M=0.19M$
The moment of inertia of the annulus will then be
$I_{a} = \frac{1}{2}M_{a}(r^{2}+r_{1}^{2}) = \frac{1}{2}(0.19M)(r^{2}+(0.9r)^{2})=\frac{1}{2}(0.19M)((1.81)r^{2} = \frac{1}{2}(0.1539)Mr^{2}$
and so in this case
$I_{a} = 0.1539 I_{d}$
which is much less than the moment of inertia of the disk.
## The same mass, $r_{1}=0.5r$
In this third case, the mass of the annulus is the same as the mass of the disk, and its inner radius is 50% of the radius of the disk. This would, of course, require the annulus to either have a greater density than the disk, or to be thicker (or both). So, $M_{a} = M$. The moment of inertia of the annulus will be
$I_{a} = \frac{1}{2} M(r^{2} + r_{1}^{2}) = \frac{1}{2} M(r^{2} + (0.5r)^{2}) = \frac{1}{2} M(r^{2} + 0.25r^{2}) = \frac{1}{2} M(1.25)r^{2}$
$I_{a}= 1.25 I_{d}$
## The same mass, $r_{1}=0.9r$
The last case we will consider is an annulus with its inner radius being 90% of the outer radius, but its mass the same. So, $M_{a} = M$. The moment of inertia of the annulus will be
$I_{a} = \frac{1}{2} M(r^{2} + r_{1}^{2}) = \frac{1}{2} M(r^{2} + (0.9r)^{2}) = \frac{1}{2} M(r^{2} + 0.81r^{2}) = \frac{1}{2} M(1.81)r^{2}$
$I_{a}= 1.81 I_{d}$
## Summary
To summarise, we have
The same density and thickness, $r_{1} = 0.5 r, \; \; I_{a}=0.9375 I_{d}$
The same density and thickness, $r_{1} = 0.9 r, \; \; I_{a}=0.1539 I_{d}$
The same mass, $r_{1} = 0.5 r, \; \; I_{a}=1.25 I_{d}$
The same mass, $r_{1} = 0.9 r, \; \; I_{a}=1.81 I_{d}$
So, as these calculations show, if keeping the mass of a flywheel down is important, then a larger moment of inertia will be achieved by concentrating most of that mass in the outer parts of the flywheel, as this photograph below shows.
If keeping mass down is important, a flywheel’s moment of inertia can be increased by concentrating most of the mass in its outer parts
In the next blogpost in this series I will calculate the moment of inertia of a solid sphere.
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## Derivation of the moment of inertia of a disk
In physics, the rotational equivalent of mass is something called the moment of inertia. The definition of the moment of inertia of a volume element $dV$ which has a mass $dm$ is given by
$dI = r_{\perp}^{2} dm$
where $r_{\perp}$ is the perpendicular distance from the axis of rotation to the volume element. To find the total moment of inertia of an object, we need to sum the moment of inertia of all the volume elements in the object over all values of distance from the axis of rotation. Normally we consider the moment of inertia about the vertical (z-axis), and we tend to denote this by $I_{zz}$. We can write
$I_{zz} = \int _{r_{1}} ^{r_{2}} r_{\perp}^{2} dm$
The moment of inertia about the other two cardinal axes are denoted by $I_{xx}$ and $I_{yy}$, but we can consider the moment of inertia about any convenient axis.
## Derivation of the moment of inertia of a disk
In this blog, I will derive the moment of inertia of a disk. In upcoming blogs I will derive other moments of inertia, e.g. for an annulus, a solid sphere, a spherical shell and a hollow sphere with a very thin shell.
For our purposes, a disk is a solid circle with a small thickness $t$ ($t \ll r$, small in comparison to the radius of the disk). If it has a thickness which is comparable to its radius, it becomes a cylinder, which we will discuss in a future blog. So, our disk looks something like this.
A disk of small thickness $t$, with a radius of $r$
To calculate the moment of inertia of this disk about the z-axis, we sum the moment of inertia of a volume element $dV$ from the centre (where $r=0$) to the outer radius $r$.
$I_{zz} = \int_{r=0} ^{r=r} r_{\perp} ^{2} dm \text{ (Equ. 1)}$
The mass element $dm$ is related to the volume element $dV$ via the equation
$dm = \rho dV$ (where $\rho$ is the density of the volume element). We will assume in this example that the density $\rho(r)$ of the disk is uniform; but in principle if we know its dependence on $r, \; \rho (r) = f(r)$, this would not be a problem.
The volume element $dV$ can be calculated by considering a ring at a radius $r$ with a width $dr$ and a thickness $t$. The volume of this ring is just this rings circumference multiplied by its width multiplied by its thickness.
$dV = (2 \pi r dr) t$
so we can write
$dm = \rho (2 \pi r dr) t$
and hence we can write equation (1) as
$I_{zz} = \int_{r=0} ^{r=r} r_{\perp} ^{2} \rho (2 \pi r dr) t = 2 \pi \rho t \int_{r=0} ^{r=r} r_{\perp} ^{3} dr$
Integrating between a radius of $r=0$ and $r$, we get
$I_{zz} = 2 \pi \rho t [ \frac{ r^{4} }{ 4 } -0 ] = \frac{1}{2} \pi \rho t r^{4} \text{ (Equ. 2)}$
If we now define the total mass of the disk as $M$, where
$M = \rho V$
and $V$ is the total volume of the disk. The total volume of the disk is just its area multiplied by its thickness,
$V = \pi r^{2} t$
and so the total mass is
$M = \rho \pi r^{2} t$
Using this, we can re-write equation (2) as
$\boxed{ I_{zz} = \frac{1}{2} \pi \rho t r^{4} = \frac{1}{2} Mr^{2} }$
## What are the moments of inertia about the x and y-axes?
To find the moment of inertia about the x or the y-axis we use the perpendicular axis theorem. This states that, for objects which lie within a plane, the moment of inertia about the axis parallel to this plane is given by
$I_{zz} = I_{xx} + I_{yy}$
where $I_{xx}$ and $I_{yy}$ are the two moments of inertia in the plane and perpendicular to each other.
We can see from the symmetry of the disk that the moment of inertia about the x and y-axes will be the same, so $I_{zz} = 2I_{xx}$. Therefore we can write
$\boxed{ I_{xx} = I_{yy} = \frac{1}{2}I_{zz} = \frac{1}{4} Mr^{2} }$
## Flywheels
Flywheels are used to store rotational energy. This is useful when the source of energy is not continuous, as they can help provide a continuous source of energy. They are used in many types of motors including modern cars.
It is because of an disk’s moment of inertia that it can store rotational energy in this way. Just as with mass in the linear case, it requires a force to change the rotational speed (angular velocity) of an object. The larger the moment of inertia, the larger the force required to change its angular velocity. As we can see above from the equation for the moment of inertia of a disk, for two flywheels of the same mass a thinner larger one will store more energy than a thicker smaller one because its moment of inertia increases as the square of the radius of the disk.
Sometimes mass is a critical factor, and next time I will consider the case of an annulus, where the inner part of the disk is removed.
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## Harmonic Oscillators
Today I was planning to post the fourth and final part of my series of blogs about the derivation of Planck’s radiation law. But, I realised on Sunday that it would not be ready, so I’m postponing it until next Thursday (17th). Parts 1, 2 and 3 are here, here and here respectively).
One of the reasons for this is that my time is being consumed by writing articles for 30-second Einstein which I talked about on Tuesday. Another reason is that I am scrambling to finish a slew of things by the 15th (next Tuesday!!), as I have been asked to go on another cruise to give astronomy lectures. More about that next week 🙂
There is a third reason, I have realised that I have not yet done a blog about harmonic oscillators, which is a necessary part of understanding Planck’s derivation. So, that is the subject of today’s blogpost.
Harmonic oscillators is another term for something which is exhibiting simple harmonic motion, and I did blog here about how a pendulum exhibits simple harmonic motion (SHM), and how this relates to circular motion. Another example of SHM is a spring oscillating back and forth. Whether the spring is vertical or horizontal, if it is displaced from its equilibrium position it will exhibit SHM. So, a spring is a harmonic oscillator.
## The frequency of a harmonic oscillator
The restoring force on a spring when it is displaced from its equilibrium position is given by Hooke’s law, which states
$\vec{F} = - k \vec{x}$
where $\vec{F} \text{ and } \vec{x}$ are the force and displacement respectively (vector quantities), and the minus sign is telling us that the force acts in the opposite direction to the displacement; that is it is a restoring force which is directed back towards the equilibrium position. The term $k$ is known as Hooke’s constant, and is basically the stiffness of the spring.
Because we can also write the force in terms of mass and acceleration (Newton’s 2nd law of motion), and acceleration is the second derivate of displacement, we can write
$m \vec{a} = m \frac{ d^{2}\vec{x} }{ dt^{2} }= - k \vec{x}$
If we divide by $m$ we get an expression for the acceleration, which is
$\boxed{ \vec{a} = - \frac{k}{m} \vec{x} }$
which, if you compare it to the equation for SHM for a pendulum, has the same form. The usual way to write equations of SMH is to write
$\vec{a} = - \omega^{2} \vec{x}$
where $\omega$ is the angular velocity, and as I mentioned in the blog I did on the pendulum, $\omega$ is related to the period of the SHM, via $T = 2 \pi / \omega$.
For our derivation of Planck’s radiation law, the parts which we need to know about are that the frequency of a harmonic oscillator, $\nu$ is given by $\nu = \omega / 2 \pi$, and so depends only on $\omega, \; \boxed{\nu \propto \omega }$. So the frequency of the spring’s oscillations depends only on k/m, we can write $\boxed{ \nu \propto k/m }$. A stiffer spring oscillates with a higher frequency, more mass (in either the spring or what is attached to it) will reduce the frequency of the oscillations.
## The energy of a harmonic oscillator
The other thing we need to know about to understand Planck’s derivation of his blackbody radiation law is the energy of the harmonic oscillator. This is always constant, but is divided between kinetic energy and potential energy. The kinetic energy is at a maximum when the spring is at its equilibrium position, at this moment it actually has zero potential energy.
The velocity of a harmonic oscillator $v$ can be found my differentiating the displacement $x$ with respect to time. The expression for displacement (see my blog here on SHM in a pendulum) is
$x(t) = A sin ( \omega t )$
where $A$ is the maximum displacement (amplitude) of the oscillstions. So
$v = \frac{dx}{dt} = A \omega cos ( \omega t)$
This will be a maximum when $cos( \omega t) = 1$ and so
$v_{max} = A \omega$
which means that the maximum kinetic energy, and hence the total energy of the harmonic oscillator is given by
$\text{Total energy} = E = \frac{1}{2}mv_{max}^{2} = \frac{1}{2} m A^{2} \omega^{2}$
As the frequency $\nu$ is just $\omega / 2 \pi$, this tells us that, for a harmonic oscillator of a given mass, the energy depends on both the square of frequency $\nu$ and the square of the size of the oscillations (larger oscillations mean more energy, double the size of the oscillations and the energy goes up by a factor of four). Mathematically we can write this as $\boxed{ E \propto A^{2} }$ and $\boxed{ E \propto \nu^{2} }$.
As we shall see, the theoretical explanation which Planck concocted to explain his blackbody curve involved assuming the walls of the cavity producing the radiation oscillated in resonance with the radiation; this is why I needed to derive these things on this blog today.
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## Derivation of Planck’s radiation law – part 3
As I have outlined in parts 1 and 2 of this series (see here and here), in the 1890s, mainly through the work of the Physikalisch-Technische Reichsanstalt (PTR) in Germany, the exact shape of the blackbody spectrum began to be well determined. By mid-1900, with the last remaining observations in the infrared being completed, its shape from the UV through the visible and into the infrared was well determined for blackbodies with a wide range of temperatures.
I also described in part 2 that in 1896 Wilhelm Wien came up with a law, based on a thermodynamical argument, which almost explained the blackbody spectrum. The form of his equation (which we now know as Wien’s distribution law) is
$\boxed{ E_{ \lambda } d \lambda = \frac{ A }{ \lambda ^{5} } e^{ -a / \lambda T } d \lambda }$
Notice I said almost. Below I show two plots which I have done showing the Wien distribution law curve and the actual blackbody curve for a blackbody at a temperature of $T=4000 \text{Kelvin}$. As you can see, they are not an exact match, the Wien distribution law fails on the long-wavelength side of the peak of the blackbody curve.
Comparison of the Wien distribution law and the actual blackbody curve for a blackbody at a temperature of $T=4000 \text{Kelvin}$. Although they agree very well on the short wavelength side of the peak, the Wien law drops away too quickly on the long-wavelength side compared to the observed blackbody spectrum.
A zoomed-in view to highlight the difference between the Wien distribution law and the actual blackbody curve for a blackbody at a temperature of $T=4000 \text{Kelvin}$. Although they agree very well on the short wavelength side of the peak, the Wien law drops away too quickly on the long-wavelength side compared to the observed blackbody spectrum.
## Planck’s “act of desperation”
By October 1900 Max Planck had heard of the latest experimental results from the PTR which showed, beyond any doubt, that Wien’s distribution law did not fit the blackbody spectrum at longer wavelengths. Planck, along with Wien, was hoping that the results from earlier in the year were in error, but when new measurements by a different team at the PTR showed that Wien’s distribution law failed to match the observed curve in the infrared, Planck decided he would try and find a curve that would fit the data, irrespective of what physical explanation may lie behind the mathematics of the curve. In essence, he was prepared to try anything to get a fit.
Planck would later say of this work
Briefly summarised, what I did can be described as simply an act of desperation
What was this “act of desperation”, and why did Planck resort to it? Planck was 42 when he unwittingly started what would become the quantum revolution, and his act of desperation to fit the blackbody curve came after all other options seemed to be exhausted. Before I show the equation that he found to be a perfect fit to the data, let me say a little bit about Planck’s background.
## Who was Max Planck?
Max Karl Ernst Ludwig Planck was born in Kiel in 1858. At the time, Kiel was part of Danish Holstein. He was born into a religious family, both his paternal great-grandfather and grandfather had been distiguished theologians, and his father became professor of constitutional law at Munich University. So he came from a long line of men who venerated the laws of God and Man, and Planck himself very much followed in this tradition.
He attended the most renowned secondary school in Munich, the Maximilian Gymnasium, always finishing near the top of his class (but not quite top). He excelled through hard work and self discipline, although he may not have had quite the inherent natural ability of the few who finished above him. At 16 it was not the famous taverns of Munich which attracted him, but rather the opera houses and concert halls; he was always a serious person, even in his youth.
In 1874, aged 16, he enrolled at Munich University and decided to study physics. He spent three years studying at Munich, where he was told by one of his professors ‘it is hardly worth entering physics anymore’; at the time it was felt by many that there was nothing major left to discover in the subject.
In 1877 Planck moved from Munich to the top university in the German-speaking world – Berlin. The university enticed Germany’s best-known physicist, Herman von Helmholtz, from his position at Heidelberg to lead the creation of what would become the best physics department in the world. As part of creating this new utopia, Helmholtz demanded the building of a magnificient physics institute, and when Planck arrived in 1877 it was still being built. Gustav Kirchhoff, the first person to systematically study the nature of blackbody radiation in the 1850s, was also enticed from Heidelberg and made professor of theoretical physics.
Planck found both Helmholtz and Kirchhoff to be uninspring lecturers, and was on the verge of losing interest in physics when he came across the work of Rudolf Clausius, a professor of physics at Bonn University. Clausius’ main research was in thermodynamics, and it is he who first formulated the concept of entropy, the idea that things naturally go from order to disorder and which, possibly more than any other idea in physics, gives an arrow to the direction of time.
Planck spent only one year in Berlin, before he returned to Munich to work on his doctoral thesis, choosing to explore the concept of irreversibility, which was at the heart of Claussius’ idea of entropy. Planck found very little interest in his chosen topic from his professors in Berlin, and not even Claussius answered his letters. Planck would later say ‘The effect of my dissertation on the physicists of those days was nil.’
Undeterred, as he began his academic career, thermodynamics and, in particular, the second law (the law of entropy) became the focus of his research. In 1880 Planck became Privatdozent, an unpaid lecturer, at Munich University. He spent five years as a Privatdozent, and it looked like he was never going to get a paid academic position. But in 1885 Gottingen University announced that the subject of its prestigoius essay competition was ‘The Nature of Energy’, right up Planck’s alley. As he was working on his essay for this competition, he was offered an Extraordinary (assistant) professorship at the University of Kiel.
Gottingen took two years to come to a decision about their 1885 essay competition, even though they had only received three entries. They decided that no-one should receive first prize, but Planck was awarded second prize. It later transpired that he was denied first prize because he had supported Helmholtz in a scientific dispute with a member of the Gottingen faculty. This brought him to the attention of Helmholtz, and in November 1888 Planck was asked by Helmholtz to succeed Kirchhoff as professor of theoretical physics in Berlin (he was chosen after Ludwig Boltzmann turned the position down).
And so Planck returned to Berlin in the spring of 1889, eleven years after he had spent a year there, but this time not as a graduate student but as an Extraordinary Professor. In 1892 Planck was promoted to Ordinary (full) Professor. In 1894 both Helmholtz and August Kundt, the head of the department, died within months of each other; leaving Planck at just 36 as the most senior physicist in Germany’s foremost physics department.
Max Planck who, in 1900 at the age of 42, found a mathematical equation which fitted the entire blackbody spectrum correctly.
As part of his new position as the most senior physicist in the Berlin department, he took over the duties of being adviser for the foremost physics journal of the day – Annalen der Physik (the journal in which Einstein would publish in 1905). It was in this role of adviser that he became aware of the work being done at PTR on determining the true spectrum of a blackbody.
Planck regarded the search for a theoretical explanation of the blackbody spectrum as nothing less than the search for the absolute, and as he later stated
Since I had always regarded the search for the absolute as the loftiest goal of all scientific activity, I eagerly set to work
When Wien published his distribution law in 1896, Planck tried to put the law on a solid theoretical foundation by deriving it from first principles. By 1899 he thought he had succeeded, basing his argument on the second law of thermodynamics.
## Planck finds a curve which fits
But, all of this fell apart when it was shown conclusively on the 2nd of February 1900, by Lummer and Pringsheim of the PTR, that Wien’s distribribution law was wrong. Wien’s law failed at high temperatures and long wavelengths (the infrared); a replacement which would fit the experimental curve needed to be found. So, on Sunday the 7th of October, Planck set about trying to find a formula which would reproduce the observed blackbody curve.
He was not quite shooting in the dark, he had three pieces of information to help him. Firstly, Wien’s law worked for the intensity of radiation at short wavelengths. Secondly, it was in the infrared that Wien’s law broke down, at these longer wavelengths it was found that the intensity was directly propotional to the temperature. Thirdly, Wien’s displacement law, which gave the relationship between the wavelength of the peak of the curve and the blackbody’s temperature worked for all observed blackbodies.
After working all night of the 7th of October 1900, Planck found an equation which fitted the observed data. He presented this work to the German Physical Society a few weeks later on Friday the 19th of October, and this was the first time others saw the equation which has now become known as Planck’s law.
The equation he found for the energy in the wavelength interval $d \lambda$ had the form
$\boxed{ E_{\lambda} \; d \lambda = \frac{ A }{ \lambda^{5} } \frac{ 1 }{ (e^{a/\lambda T} - 1) } \; d\lambda }$
(compare this to the Wien distribution law above).
After presenting his equation he sat down; he had no explanation for why this equation worked, no physical understanding of what was going on. That understanding would dawn on him over the next few weeks, as he worked tirelessly to explain the equation on a physical basis. It took him six weeks, and in the process he had to abandon some of the ideas in physics which he held most dear. He found that he had to abandon accepted ideas in both thermodynamics and electromagnetism, two of the cornerstones of 19th Century physics. Next week, in the fourth and final part of this blog-series, I will explain what physical theory Planck used to explain his equation; the theory which would usher in the quantum age.
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http://www.zora.uzh.ch/id/eprint/111518/ | # Mod-$\phi$ convergence
Delbaen, Freddy; Kowalski, Emmanuel; Nikeghbali, Ashkan (2015). Mod-$\phi$ convergence. International Mathematics Research Notices, 2015(11):3445-3485.
## Abstract
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex Brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.
## Abstract
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex Brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.
## Statistics
### Citations
1 citation in Web of Science®
1 citation in Scopus®
### Altmetrics
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http://math.stackexchange.com/questions/338561/whats-the-probability-that-a-always-leads-b-in-the-process-of-counting-vote?answertab=oldest | # What's the probability that $A$ always leads $B$ in the process of counting votes?
Suppose that in an election person $A$ gets $60$ votes and person $B$ gets $40$ votes in total.
What's the probability that $A$ always leads $B$ in the process of counting the votes?
-
This is the famous Bertrands ballot problem. The upshot of the solution is that among the "bad" possibilities (where $B$ leads $A$ at least once), those where the first vote is for $A$ are as likely as those where $B$ had the first vote. The probability of the latter is obviously $40$% here, so the total bad possibilities amount to $80$%, and the probability of $A$ leading $B$ all the time (after the first vote is counted) is $20$%.
Nowadays the bijection between the bad ballot sequences of the first type (where $A$ has the first vote and where $B$ equalises the score at some point) and the second type (where $B$ has the first vote) is usually shown using a "reflection principle", which involves turning certain votes for $A$ into votes for $B$ and vice versa. Personally I find the original proof by D. André at least as transparent in terms of the ballot formulation (as opposed to an equivalent random walk formulation). Map bad sequences of the first type to bad sequences of the second type by cyclically reordering the votes, so as to start with the first vote where $B$ equalised the score. This moves the sub-sequence preceding that vote to the end, a sub-sequence that starts with a vote for$~A$ and after that has a (possibly empty) "Dyck sequence", having balanced in votes for $A$ and $B$ without those for $B$ ever outnumbering those for$~A$. In a bad sequence of the second type, there is a unique final Dyck sequence preceded by a vote for $A$ (counting votes in reverse order, stop the first moment that $A$ gets a lead) and cycling those votes to the front of the sequence produces a bad sequence of the first type. These cycling operations are easily seen to be inverses of one another. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7149046659469604, "perplexity": 517.3963258955818}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246661364.60/warc/CC-MAIN-20150417045741-00076-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://mathematica.stackexchange.com/tags/numerical-integration/hot?filter=month | # Tag Info
9
Use NDSolve antiD = NDSolveValue[{f'[x] == Sqrt[1 + x^3], f[0] == 0}, f, {x, 0, 10}] Example usage: Plot[antiD[x], {x, 0, 10}] Alternatively... This works because this function can be antidifferentiated (by Mathematica). antiD = FunctionInterpolation[ Evaluate @ Integrate[Sqrt[1 + x^3], {x, 0, t}, Assumptions -> 0 < t < 10], {t, 0, ...
9
In Mathematica 10, this computation may be made as follows: Clear @ r volSphere9[r_] = RegionMeasure[Ball[ConstantArray[0, 10], r]] (π^5 r^10)/120 volSphere9[1000.] 2.55016*10^30
7
The sum of the squares should be less than or equal to r^2 rather than r. d = 10; r = 1000; F = Piecewise[{{1, Sum[x[i]^2, {i, d}] <= r^2}}, 0]; NIntegrate[F, {x[1], -1000, 1000}, {x[2], -1000, 1000}, {x[3], -1000, 1000}, {x[4], -1000, 1000}, {x[5], -1000, 1000}, {x[6], -1000, 1000}, {x[7], -1000, 1000}, {x[8], -1000, 1000}, {x[9], -1000, 1000}, ...
5
If you just plot the region of the graph you're interested in: pl = Plot[f[x], {x, (x /. a[[2]]), (x /. b[[2]])}, Epilog -> {Red, PointSize[Medium], Point[{{x /. a[[2]], a[[1]]}, {x /. b[[2]], b[[1]]}}]}, ImageSize -> 300, PlotPoints -> 500] Then, you can do: ArcLength @ DiscretizeGraphics @ pl 0.30827679
5
Based on @RunnyKine's comment the trouble is with Re. It seems there should be a more elegant way to do this, but moving the Re outside the differential does the job: da[x_] = Sqrt[1 + (Re@D[(-2 (ExpIntegralEi[(ZetaZero[n]) Log[x]]) Log[x]/Sqrt[x]),x])^2 ] NIntegrate[da[x], {x, x /. a[[2]], x /. b[[2]]}] .308277 Also, yet another line ...
4
This volume between the regions can be obtained as follows: f[x_] := Pi^2 Sin[x] Cos[x]^3 g[x_] := 4 x^2 v1 = Integrate[Pi g[z]^2, {z, 0, Pi/4}] v2 = Integrate[Pi f[z]^2, {z, 0, Pi/4}] N[v2 - v1] yielding: [Pi]^6/320,(1/48 + (5 [Pi])/512) [Pi]^5, 12.7596 respectively. You can use a number of v10 capabilities to visualize region and approximate volume ...
4
The problem is that NDSolve is not HoldAll or HoldFirst. Therefore the differential equation is evaluated symbolically before it is passed to NDSolve. Thus the differential equation that NDSolve sees is {R*Q'[t] + Q[t]/C2 == newfSign[t], Q[0] == 0} (* {4.54545*10^6 Q[t] + 2000 Derivative[1][Q][t] == 5, Q[0] == 0} *) The reason that one does not see the ...
4
For me it looks like the OddQ function behaves unexpected If it is replaced by OddQ2[n_] := If[Mod[n, 2] == 1, True, False] then s = NDSolve[{R*Q'[t] + Q[t]/C2 == newfSign[t], Q[0] == 0}, Q, {t, 0, 4 \[Tau]}] Plot[Q[t]/C2 /. s, {t, 0, 4 \[Tau]}, PlotRange -> Full] outputs As I stated in my comment, for functions with fast oscillations there are ...
3
Or Create an interpolation function from the plot and calculate its arc length. Note that I have modified the definitions of a and b. n = 2; f[x_] := -2 Re[ExpIntegralEi[(ZetaZero[n]) Log[x]]] Log[x]/Sqrt[x] a = FindArgMin[f[x], {x, 1.4}][[1]] // Quiet; b = FindArgMax[f[x], {x, 1.7}][[1]] // Quiet; plt = Plot[f[x], {x, a, b}]; f2 = Interpolation[ ...
3
Amplifying on Chenminqi's answer g = 1/10; func = (p^2*Sqrt[1 - (2*p)/(-g + p*(1 + p))])/(-1 + (p/g)*(p - 1)) - p^2/((1 + p/g)*(1 + p))*Sqrt[1 - (2*p)/(g + p*(1 + p))] // Simplify; fd = FunctionDomain[func, p] This is equivalent to requiring that the arguments of Sqrt be positive fd == Reduce[ Thread[ Cases[func, Sqrt[x_] -> x, Infinity] ...
3
Your method is perfectly fine in principle, because in one dimension energy conservation leads to a "quadrature" solution (i.e., you formally avoid solving the usual equation of motion). But since inverting the numerical integration is another numerical step it doesn't actually end up making the solution very easy to obtain. For example, you have to think ...
3
There are two aspects in this problem depending on the exact definition of the task, and, as we shall see, both are completely solved by MMA without any additional facility. The aspects are a) calculate the interpolation of the definite integral $f=\int_0^t \sqrt{1+x^3} \, dx$ b) calculate the interpolation of the antiderivative $fad=\int\sqrt{1+x^3} \, ... 3 Since it was Daniel Lichtblau who added the tag bugs, I would say the answer to your question is "yes". 3 One can decrease the difficulty of the problem by reducing the Dyson series to a matrix ODE. Let's start from the definition $$U(x,x_0) = 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\ldots$$ and take the derivative with respect to$x\$ \frac{\partial}{\partial x}U(x,x_0) = ...
3
ftop = Pi^2 Sin[x] Cos[x]^3 fbtm = 4 x^2; Plot[{ftop, fbtm}, {x, 0, Pi/4}] Use Volume = Pi r^2 * h (cylinder volume) for top and bottom and take the difference (i.e remove volume of inner cylinder from outer) vtop = Pi Integrate[ftop^2, {x, 0, Pi/4}]; vbtm = Pi Integrate[fbtm^2, {x, 0, Pi/4}]; vtop - vbtm N[%] (* 12.7596 *) The area of the ...
2
Summarizing all of the comments: Clear[T] T[e_?NumericQ] := (1/Pi)*NIntegrate[ 1/Sqrt[Sin[ArcCos[-e]/2]^2 - Sin[\[Phi]/2]^2], {\[Phi], 0, ArcCos[e]/2}] Plot[ {Re[T[e]], Im[T[e]], Abs[T[e]]}, {e, -2, 2}, PlotRange -> All, WorkingPrecision -> 25, PlotLegends -> "Expressions", Frame -> True, Axes -> False] EDIT: With the ...
2
I think it is a working precision problem because you work with big numbers (for Factorial, Gamma and HypergeometricU these numbers are big). Therefore, you can simply increase the precision Nprob[α_, γ_, T_, k_] := prob @@ SetPrecision[{α, γ, T, k}, 100] prob[0.145, 1.71, 53, 100] Nprob[0.145, 1.71, 53, 100] 0. ...
2
Your precison is limited by using machine precision numbers in your definitions (e.g., 0.5 (for Sqrt) and 0.25). WorkingPrecision cannot undo that. After correcting those, you can use a much lower WorkingPrecision (I used WP -> 20 below). Also, as a general rule, restrict the arguments of functions that directly or indirectly use numerical techniques (e.g., ...
1
One can integrate Derivative[0, 1][y][x, t]^2 along with the pde: pde = D[y[x, t], t, t] == D[y[x, t], x, x]; solnDerivative = NDSolve[{pde, y[x, 0] == Exp[-(x)^2], Derivative[0, 1][y][x, 0] == 0, Derivative[1, 0][y][-50, t] == Derivative[0, 1][y][-50, t], Derivative[1, 0][y][50, t] == -Derivative[0, 1][y][50, t], (**) Derivative[0, ...
1
You can integrate the mean square error mse at the same time as computing u[x]. s = NDSolve[{ u''[x] == (h*L*L/(d*d))*phi[x]*phi[x]*u[x] - F*L*L*(1 - phi[x]), u[-W*d/L] == 0, u[1 + W*d/L] == 0, mse'[x] == (u[x] - vE[x])^2, mse[-W*d/L] == 0}, {u, mse}, {x, -W*d/L, 1 + W*d/L}, Method -> "StiffnessSwitching", WorkingPrecision -> 40, ...
Only top voted, non community-wiki answers of a minimum length are eligible | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4403747618198395, "perplexity": 8923.794905933892}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657133568.71/warc/CC-MAIN-20140914011213-00159-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
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# Area of Triangle in Circle
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Area of Triangle in Circle [#permalink] 04 Aug 2009, 19:34
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What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
A) sqr(3)/4
B) 1/2
C) (pie)/4
D) 1
E) sqr(2)
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Re: Area of Triangle in Circle [#permalink] 04 Aug 2009, 22:48
Area of traingle = 1/2 (bh)
So we have to maximise the base and height. The base and height of inscribed triangle with one vertex at the center are maximum when both are equal to the radius = 1.
Therefore, the maximum area would be 1/2 (1*1) = 1/2
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Re: Area of Triangle in Circle [#permalink] 05 Aug 2009, 01:30
robertrdzak wrote:
What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
A) sqr(3)/4
B) 1/2
C) (pie)/4
D) 1
E) sqr(2)
What we can understand from the question stem is that the triangle is an Isoceles triangle.
So an isoceles triangle has max area when it is a rt. angled triangle
so max area =0.5 * b * h= 0.5 * r * r = 0.5 * 1 * 1= 0.5..hence B
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Re: Area of Triangle in Circle [#permalink] 05 Aug 2009, 20:59
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another way of looking at this can be area of the triangle A = 1/2 * radius*radius*sin (x).....area eqn interms of side and angle...
we can see that sine values are max only at x=90 degrees....hence we have A = 1/2 *1*1*1 = 1/2...OA B
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Re: Area of Triangle in Circle [#permalink] 25 Feb 2011, 23:51
scarish wrote:
Area of traingle = 1/2 (bh)
So we have to maximise the base and height. The base and height of inscribed triangle with one vertex at the center are maximum when both are equal to the radius = 1.
Therefore, the maximum area would be 1/2 (1*1) = 1/2
Although you got the correct answer, your explanation is incorrect. Since the triangle has a vertex at the center and the other two are on the circle with radius =1, at most all three sides can equal 1. BUT the area of a triangle is 1/2 *b*h. Thus you need to find h when the three sides are equal to 1. You will quickly realize your answer is no longer 1/2!
The correct way to reach 1/2 as an answer is to understand that an isosceles triangle has the max area when it is a right angled triangle. Now you know that the two sides are 1 and the angle between them at the center of the circle is 90. Thus the base or hypotenuse of the triangle will be 1/sqr2. This gives the area of 1/2 * b * h = 1/2 * 1/sqr2 * sqr2 = 1/2
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Re: Area of Triangle in Circle [#permalink] 26 Feb 2011, 02:03
Expert's post
This question is discussed here: maximum-area-no-clues-91398.html
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Re: Area of Triangle in Circle [#permalink] 26 Feb 2011, 02:03
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# Area of Triangle in Circle
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Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4323742687702179, "perplexity": 3208.077455423697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701158609.98/warc/CC-MAIN-20160205193918-00084-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://codegolf.stackexchange.com/questions/94457/tips-for-golfing-in-s-i-l-o-s | # Tips for golfing in S.I.L.O.S
What general tips do you have for golfing in S.I.L.O.S? I'm looking for ideas which can be applied to code-golf problems and which are also at least somewhat specific to S.I.L.O.S (e.g. "remove comments" is not an answer).
S.I.L.O.S can be run here.
# Abuse the preprocessor
All SILOS programs can optionally have a macro statement on the second line
Consider the following program... One of my favorite SILOS submissions by betseg.
a=97
def q print z bottle v beer L Line g wall x IntNoLine h the c around
qL 99 zs of v on h g, 99 zs of v.
lbls
q Take one down and pass it c,
a+1
qx a
qL zs of v on h g.
qx a
q zs of v on h g,
qx a
qL zs of v.
a-2
if a s
qL Take one down and pass it c, 1 z of v on h g.
qL 1 z of v on h g, 1 z of v.
q Go to h store and buy some more, 99 zs of v on h g.
Look at that savings Try it out!
# Never sometimes divide by 0.
Consider a challege where we should output the input if it is not 0 and output -1 otherwise. We could do the following.
# S.I.L.O.S, 50 bytes
readIO
if i b
print -1
GOTO c
lblb
printInt i
lblc
Try it online!
However, that is far from optimal. The "superior" solution would be this.
# S.I.L.O.S, 33 bytes
readIO
j=i
i/i
j=j+i-1
printInt j
Try it online!
SILOS will quietly ignore the division by 0, which results in a no-op.
# Never declare variables
There is no need to declare a variable. All variables are automatgically initialized to 0.
Hence, this-
a=0
a=97
printInt a
Is the same as this
a=97
printInt a | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21596482396125793, "perplexity": 8487.877932485047}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315681.63/warc/CC-MAIN-20190820221802-20190821003802-00078.warc.gz"} |
https://arxiv.org/abs/1601.08167 | astro-ph.SR
(what is this?)
# Title: Turbulent reconnection of magnetic bipoles in stratified turbulence
Abstract: We consider strongly stratified forced turbulence in a plane-parallel layer with helicity and corresponding large-scale dynamo action in the lower part and non-helical turbulence in the upper. The magnetic field is found to develop strongly concentrated bipolar structures near the surface. They form elongated bands with a sharp interface between opposite polarities. Unlike earlier experiments with imposed magnetic field, the inclusion of rotation does not strongly suppress the formation of these structures. We perform a systematic numerical study of this phenomenon by varying magnetic Reynolds number, scale separation ratio, and Coriolis number. We focus on the formation of a current sheet between bipolar regions where reconnection of oppositely oriented field lines occurs. We determine the reconnection rate by measuring either the inflow velocity in the vicinity of the current sheet or by measuring the electric field in the reconnection region. We demonstrate that for large Lundquist numbers, S>10^3, the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings.
Comments: 11 pages, 14 figures Subjects: Solar and Stellar Astrophysics (astro-ph.SR) Journal reference: Mon. Not. Roy. Astron. Soc. 459, 4046-4056 (2016) DOI: 10.1093/mnras/stw888 Report number: NORDITA-2016-7 Cite as: arXiv:1601.08167 [astro-ph.SR] (or arXiv:1601.08167v2 [astro-ph.SR] for this version)
## Submission history
From: Sarah Jabbari [view email]
[v1] Fri, 29 Jan 2016 16:00:35 GMT (4048kb)
[v2] Fri, 18 Mar 2016 19:46:58 GMT (4009kb) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8586885929107666, "perplexity": 2891.431740514644}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187827853.86/warc/CC-MAIN-20171024014937-20171024034937-00592.warc.gz"} |
http://salttheoats.blogspot.com/ | ## Monday, July 2, 2012
### I've Moved
After reading and writing comments on blogs everywhere, I've moved my blog over to wordpress. You can see my newer posts here
## Friday, May 4, 2012
### Flipped (?) Review
I'm not going to make this an overly long post, as it's the end of the school year, and there's no time to be overly verbose. To quickly get to the point, whenever you get a new toy, you want to play with it as much as possible. Well, I'm happily looking for was to play with my new iPad (yeah, here comes the spam).
This year, I've been using some of the tools from Modeling whenever possible, one of the most common I've used being whiteboards. As I get ready for review for finals, I was trying to figure out how to effectively use whiteboarding to review for the exam. For most of the year, I've asked the students to take pictures of their whiteboards at the end of discussion and post them into the class Schoology page. The main problem with that is that most haven't done that.
So, insert "I-want-to-play-with-my-toy,-so-let's-see-if-we-can-make-it-effective." I've uploaded a .pdf of the review questions I assigned into an annotation app (uPad Lite - I'm cheap and it's free). My thought is I'll be the secretary that writes the minutes and they'll whiteboard the various problems. Then I'll post the minutes into schoology so everyone has the results.
The kids will do the explanation, and I'll take notes. That's my take on a flipped classroom.
p.s.- yes I would love to have the kids do this, but we currently have a no mobile device policy and no wifi. I tend to look the other way for the kids that actually take the time to take pictures to post online when they get home. This policy is most likely changing for next school year, so part of my reason for doing this is to begin trying somethings out. Any thoughts on better ways to do this would be greatly appreciated!
## Tuesday, March 6, 2012
### LOL Energy Diagrams
As I've gotten more into using blogs and twitter as a teacher, I find that they are both such an amazing learning tool for me. This post will make a lot more sense if you read Kelly O'Shea's blog on LOL Diagrams. As you can see by the comments I made I was taught a slightly different way of making LOL Diagrams in my modeling workshop (See here).
For the following problem:
Here's how I would use LOL's to solve it. I would first state what objects are in my system (in this case, the spring, the cart, the earth, and the track). I would then draw the following LOL diagram.
As you can see, the "L's" are exactly the same, however in Kelly's format, you show the objects in the system versus those out of the system. In this style you show the flow of energy as you move from the initial state (in this case, the energy stored in the compressed spring) to the final state (the cart moving at the top of the loop).
Kelly later gives an example of what the LOL would look like if you do not include the spring within your system. Here's my take:
Since the spring is no longer part of the system, some "outside object" is doing work on the system. Also, since the spring is outside the system, it doesn't matter if it's a spring or a rocket or anything else, "something" is providing work to increase the energy of the system. The way my thermo teacher in college summarized it, if you care what did the work, include it in your system, but then it's not work.
{If that doesn't make sense, if the source of "work" is the spring, then you would call it elastic potential energy or spring energy. If it were a rocket, you would call it chemical potential energy. etc.}
If we go back and include the spring, but also include friction. Then your LOL diagram would look like this:
As I mentioned in my comment to Kelly's post, I think either method could work. To me, this method makes more sense given the "O" in between the "L's" since it shows how you are getting from the initial to the final state. I think if you are using Kelly's method, the "O" should go before the first "L".
I'll be the first to admit that I'm learning a lot more from her blog, then I've even thought of sharing on this one. Just wanted to try to show what I was trying to say. I'd love to hear from other experience modelers as to which style they use.
## Wednesday, February 8, 2012
### Legend of the Teacher
Now that I'm able to blog again, one thing that has been taxing my thoughts is my school's ongoing switch to the "Common Core."
{A little background}
My school has always (at least as long as I've been here) had learning objectives for each class. Since we are a private Catholic School, we've had the freedom to set our own objectives (in collaboration with the other Catholic HS in our diocese). Although we used the state and national standards as a point of comparison, we were free to write our own objectives for the course. The good thing about this was the freedom to mold the course the way we as teachers wanted it to be. The downside was that we had to meet every five years to edit and revise those standards. Over the last year or so, our diocese has decided to adopt the Common Core standards as they emerge and be in compliance (if that's the right phrase) within the next 2 or 3 years.
So where does "School of Rock" come in? One, it's an awesome movie, so why shouldn't it be there. Two, I think the chorus of the song can be slightly modified to explain some of our struggles with adopting the common core. I think you have to live the "Common Core" before you can teach the "Common Core." What I mean by that is, most teachers fall into the trap of teaching how they were taught. I reading the various posts on education reform, most teachers would agree that there's always some new thing that comes out. By the time you fully switch to it, the new flavor of the month comes around and now you are to switch the that new thing.
As I interact with teachers, I think they see this switch to "Common Core" as just one of those new flavors of the month. They see a new set of standards, not a new mentality for teaching. To me, the shift of the "Common Core" is about changing the dynamics of the classroom. No longer is my job to be the "Sage on the Stage," but rather the "Guide on the Side." (Sorry, I forgot from whom I stole that, but it's definitely not mine).
Since "all" of us have had teachers that were the "Sage on the Stage," they see this new change as just changing what they teach, not how they teach. As I've gotten more involved in the Modeling, I am beginning to appreciate, what I see, as the true changes for "Common Core." After going to the modeling workshop last summer, I was able to be a student in a class where the teacher didn't "teach" us anything, but rather created activities, and guided us through them.
I remember talking with some of the other "students" the first few days about our frustration with the fact that they weren't teaching us the "Modeling Method." After we got into the 2nd unit, it dawned on me, that the only way to truly teach by experience, one must first learn through experience. I think that is truly the "Ah Hah" moment that teachers talk about after going to one of these workshops. It finally clicks that true teaching is in creating the experience and knowing where the tough spots are, not how many cool facts you can tell your students.
You've go to learn "Common Core," before you can teach "Common Core."
## Thursday, October 13, 2011
### Conservation of Energy Lab
I saw a question today in twitter:
Modelers: how do you develop 1/2mv^2 from lab? how do you develop mgh from lab?
At the modeling workshop this summer, we did exactly that, however, instead of just rehashing that post, (you can read it here), I figure I would tell you how I tweaked the experiment for my AP class.
Since my AP-B class is a second year class, my students already have a working idea of the relationships (as time goes in and I fully switch to modeling, they should know the models) from the first year. So instead of using the labs as a discovery of the relationships, I like to have some challenge in the lab in which the students have to predict something using their data.
Here's the setup:
Equipment
vernier cart
vernier track
vernier spring launcher
motion detector attached to track opposite the launcher
Set up the track at an angle (ie - place a book under one end of the track)
Using LoggerPro and the motion detector, pull the cart back to compress the spring and let go. Stop the detector after the cart has reached it's highest point on the track.
The Analysis:
Have LoggerPro display a position vs time and a velocity vs time graph. From the velocity vs time graph, highlight the data, and use the "Statistics" function. The minimum value will be the compression ($\Delta x$), and the max value will be the maximum displacement ($d_{max}$). Highlight the data from the velocity vs time graph, and the maximum value is the maximum velocity ($v_{max}$).
(Note- if you want to do so, you can have the kids look at what position the max speed occurs (x=0)
Repeat the procedure several times, recording $\Delta x$, $v_{max}$, and $d_{max}$ into a second data set. Plot $d_{max}$ vs $\Delta x$. Have the students linearize this first graph, and they should see that $d_{max}$ is proportional to $\left( \Delta x \right)^2$. Now plot $v_{max}$ vs $\Delta x$, lead student to plot $\left( \Delta x \right)^2$ on the x axis, since that will allow this graph to relate to $d_{max}$. They should find that they need to plot $v_{max}^2$ on the y axis.
(If you want to take it a step further and include the masses to fully develop conservation of energy, go for it. As I said, my kids already knew those relationships from last year)
So here was my twist, how do you relate the maximum displacement to the vertical height? Since my students knew the energy relationships, I had them use their data and trigonometry to calculate the angle of the track. Just to give you heads up, here is what they should get...
From trigonometry, you know:
$h_{max}=d_{max}sin \theta$
And since mass is used for both kinetic and gravitation energy, you can rewrite the energy conservation as:
$g*d_{max}sin \theta = \frac{1}{2}v_{max}^2$
Therefore:
$\large \theta=arcsine \left(\frac{g*d_{max}*v_{max}^2}{2}\right)$
I then measured the angle of the track using a level app in my iPhone to compare the actual angle to the one predicted by the groups. The app I has was able to measure to the tenth of a degree. Most groups were able to get within $0.5^o$ of the value measured on my iPhone. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4357953667640686, "perplexity": 950.7999163801926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221216453.52/warc/CC-MAIN-20180820121228-20180820141228-00037.warc.gz"} |
https://studyadda.com/sample-papers/jee-main-sample-paper-38_q18/292/301429 | • # question_answer An organic compound is treated with $NaN{{O}_{2}}$ and dil. $HCl$at ${{0}^{o}}C$. The resulting solution is added to an alkaline solution of $\beta$ -naphthol where by a brilliant red dye is produced. It shows the presence of A) $-N{{O}_{2}}$ group B) aromatic $-N{{H}_{2}}$ group C) $-CON{{H}_{2}}$ group D) aliphatic $-N{{H}_{2}}$ group
${{C}_{6}}{{H}_{5}}N{{H}_{2}}+NaN{{O}_{2}}+HCl\xrightarrow[{{0}^{o}}C]{}{{C}_{6}}{{H}_{5}}N=NCl$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8667991757392883, "perplexity": 10672.252955778873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986653247.25/warc/CC-MAIN-20191014124230-20191014151730-00465.warc.gz"} |
http://vitotoraldo.it/geometry-proofs-practice-parallel-lines.html | # Geometry Proofs Practice Parallel Lines
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Two lines are parallel if any one of the following geometry statements is true: (A) A pair of alternate interior angles have the same measures. Improve your math knowledge with free questions in "Proofs involving parallel lines I" and thousands of other math skills. Equiangular Triangle. GC: Geometry Connections: Quick Reference Guide PDF GC: Geometry Connections: Course Overview PDF GC: Geometry Connections: Development of Major Content Strands PDF. Let's Practice: Using the diagram below, suppose that angle 1 has a measure of 34º. You can email the tests to your teacher or print. Academic Vocabulary Add these words and others you encounter in this unit. 1 Parallel Lines & Transversals Objectives: Identify the relationships between two lines or two planes Name angle pairs formed by parallel lines and transversals. Two-Column Proofs Practice Tool. Proving Lines Are Parallel. This video contains plenty of examples and practice problems for you to learn the concept. 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Given a line l and a point A on l, suppose there are two lines, m and n, which both pass through A and are perpendicular to l. Proof: All you need to know in order to prove the theorem is that the area of a triangle is given by $A=\frac{w\cdot h}{2}$. Day 6: SWBAT: Use theorems about angles formed by Parallel Lines and a Transversal Pages 45-49 HW: pages 50- 53 Days 7&8: SWBAT: Review writing basic definition proofs Pages: 54-62 DAY 9: Practice Test Pages: 63-68 Day 10: Test. m Q A B P C l Figure 1: Unique parallel line to l through a point. How to use two column proofs in Geometry, Practice writing two column proofs, examples and step by step solutions, How to use two column proof to prove parallel lines, perpendicular lines, Grade 9 Geometry, prove properties of kite, parallelogram, rhombus, rectangle, prove the Isosceles Triangle Theorem, prove the Exterior Angle Theorem. 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" 11) Complete the two-column proof to prove the theorem: "If two lines are cut by a transversal where same side interior angles are supplementary, then. The angle to be copied has the same measure in both triangles The image below is the final drawing above with the red items added. Lines and Angles. Bisect a line segment. If a transversal intersects two coplanar lines in such a way that pair of Alternate angles are equal, then the two lines are parallel. A4 SpringBoard Geometry, Unit 1 Practice 55. Let's take a peek at what this means. So this line is parallel to this line. Geometry; Right triangles and trigonometry. Bookmark File PDF Geometry Chapter 5 Practice Test Geometry Chapter 5 Practice Test Getting the books geometry chapter 5 practice test now is not type of challenging means. 10 = 4 + 4 + 2 = 1 + 1 + 8 = 5 + 4 + 1 and so on. 9 43 customer reviews. Unit #2 (parallel lines) Angle Pairs; Angle Pairs (Parallel Lines) Angle Pairs Extra Help!!! Angle Pairs Poster; Complementary Angles; Different types of "proofs" Interactive Special Angle Pairs; Practice those Proofs!!! Proof Practice; Special Angle Pairs; Supplementary Angles; Writing a 2-Column Proof (video) Unit #3 (triangle congruence. For example, given two parallel lines cut by a transversal, prove that alternate interior angles are congruent. 6th Grade Math; 7th Grade Math; 8th Grade Math : Home > Analytical Geometry >Unit 1 Similarity. Experiment with transformations in the plane Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the. Menifee Union School District. Equations - Parallel and Perpendicular Lines Geometry - Equations - Parallel and Perpendicular Lines Author: pjclark Created Date: 11/7/2011 10:29:06 AM. Copy an angle. Just like running, it takes practice and dedication. 6 Parallel Lines in the Coordinate Plane 3. Test and Worksheet Generators for Math Teachers. 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Chords within a circle can be related many ways. 5 Practice - Parallel and Perpendicular Lines Find the slope of a line parallel to each given line. The corresponding angles are congruent. Worksheets are , Find the measure of the indicated angle that makes lines u, Honors geometry chapter 3 proofs involving parallel and, Work section 3 2 angles and parallel lines, 3 parallel lines and transversals, Parallel lines proof work, Parallel lines transversals work, Name period gl lines transversals. 1 Lines and Angles Notes 3. Solution: It is given ∠E = 50°. Also math games, puzzles, articles, and other math help resources. 1 is supplementary to 8 because given _____ 2. 66% average accuracy. Since it intersects the y-axis at (0,4), the y-intercept is 4 and so the equation is given by. You may use any "style" (format) of proof. Lines b and c are perpendicular to line d. 5: section 1-3 Practice p. Some parallel line pairs have just one common perpendicular and grow far apart. Proving Lines are Parallel - Module 19. Symbols in Geometry Common Symbols Used in Geometry. property of equality. We know that if we have two lines that are parallel-- so let me draw those two parallel lines, l and m. STREETS The map shows some of the roads in downtown Little Rock. (C) A pair of interior angles on the same side of the transversal are supplementary. Traverse through this huge assortment of transversal worksheets to acquaint 7th grade, 8th grade, and high school students with the properties of several angle pairs like the alternate angles, corresponding angles, same-side angles, etc. GSE Geometry Unit I : Basics of Geometry and Proofs INDEPENDENT PRACTICE Day 5 11 15 Notes 16 610 12. Euclidean Geometry. Improve your math knowledge with free questions in "Proofs involving angles" and thousands of other math skills. It is critical to understand that dilations create parallel lines between ALL pre-image and image corresponding segments and lines. all segments that are skew to CD −−−. Similarly, three or more parallel lines also separate transversals into proportional parts. Euclidean Geometry. Inequalities and Relationships Within a Triangle. Learn how to write a proof when given angles from parallel lines and a transversalWe will explore angle relationships with parallel lines and a transversal. Then I found two more points on the same line that were 5 units from (5, 8) or (8, 12). angle 1 congruent to angle 2 (given) 2. 529-530 22-43 5. In each proof, students must prove that two lines cut by a transversal are parallel. Parallel and perpendicular line segments. Using Algebra Algebra Find the value of x for which O 6m. There just isn't enough practice available for the average student to confidently achieve mastery. This page will use the traditional "2-column" proof since this format shows the reasoning in the most organized manner. A line that intersects two or more coplanar lines at two different points is called a transversal. Two-column geometric proofs Pg 70 #’s 4-8 Pg 71 #’s 9-16 19 7-Parallel and Perpendicular Lines 7. Complementary Angles. Printable in convenient PDF format. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. Given: p ║ q Prove: m∠3 = m∠5 Complete the proof by writing the missing reasons. Select a proof from the list below to get started. Auxiliary lines. 3 Parallel Lines and Transversals 3. the top the back 16. Transversal – a line that intersects two or more other lines. Simson Line. The proof of the angle bisector theorem is a nice proof and a nice use of similarity but it is a pretty useless fact, I can’t think of a time in geometry that it gets used except in its own specific question type. Day 6: SWBAT: Use theorems about angles formed by Parallel Lines and a Transversal Pages 45-49 HW: pages 50- 53 Days 7&8: SWBAT: Review writing basic definition proofs Pages: 54-62 DAY 9: Practice Test Pages: 63-68 Day 10: Test. Proofs Using Coordinate Geometry. Custom Proof Creator. Euclidean Geometry. Play this game to review Geometry. There are 67 NRICH Mathematical resources connected to Angles - points, lines and parallel lines, you may find related items under Angles, Polygons, and Geometrical Proof. So let's look at what they're telling us. Make sure you've got a clear idea of all the math topics you'll be tested on and check out all of our ACT math guides for reference and practice. 3 Extra Proof Practice: File Size: 544 kb: File Type: pdf:. This free geometry worksheet requires the use of the properties of parallel lines including the Alternate Interior Angle Theorem, Corresponding Angles Theorem, and the Same-Side Interior Angle Theorem and their converses. All for the high school levels of Grade 9, Grade 10, Grade 11, and Grade 12. 1 — 2 Practice Points, Lines and Planes Are the three points collinear? If so, name the line on which they lie. Find and interpret the slope of the line. Copy an angle. 26_angles-formed-by-parallel-lines-cut-by-a-transversal. Let's Practice: Using the diagram below, suppose that angle 1 has a measure of 34º. #geometry #funinmathclass. Worksheets are Unit 1 tools of geometry reasoning and proof, Ms work 132 153 geometry 06, Geometry chapter 1 notes practice work, Geometry unit 1 workbook, Chapter 4 lesson1 0 points line segments lines and rays, Geometry plane and simple answer key, 1 basics of geometry. These two lines are the line a and line b. • corresponding angles • alternate interior angles • alternate exterior angles. However, two lines that are perpendicular to a third line do not have to be parallel. First, you can line up the student's page and the answer page and hold it up to the light. Two-Column Proofs Practice Tool. m Q A B P C l Figure 1: Unique parallel line to l through a point. You could not by yourself going in imitation of book heap or library or borrowing from your contacts to get into them. 1b5 10 14 Use the fiqure at the riqht to answer problems 1-8. Geometry Symbols and Parallel Lines Cut by a Transversal. Proving Lines are Parallel - Module 19. I am having a very. all planes that are parallel to plane DEH 2. MathBitsNotebook Geometry CCSS Lessons and Practice is a free site for students (and teachers) studying high school level geometry under the Common Core State Standards. 107) Week of October 6: Monday 10/6 - 3. When a transversal intersects parallel lines, many angles are congruent. Since the top surface is embedded within the metal plate, no field lines will pass through it since under electrostatic conditions there are no field lines within a conductor. 2 Angles Formed by Parallel Lines and. Here is a set of assignement problems (for use by instructors) to accompany the Equations of Planes section of the 3-Dimensional Space chapter of the notes for Paul Dawkins Calculus II course at Lamar University. " 11) Complete the two-column proof to prove the theorem: "If two lines are cut by a transversal where same side interior angles are supplementary, then. TPS and TQS c. Likewise, we can prove using other angles too. When two parallel lines are intersected by a third line — a transversal — corresponding pairs of angles are formed. Solution: It is given ∠E = 50°. Geometry Workbook For Dummies ensures that practice makes perfect, especially when problems are presented without the stiff, formal style that you’d find in your math textbook. Unit 2 Overview. Students will be able to prove that alternate interior angles are congruent and corresponding angles are congruent given two parallel lines and a traversal line. A new line which is a bisector of segment B, okay, this doesn't seem anything like what I just did, so I'm just gonna move on to the next one. If two lines cut by a transversal form congruent corresponding angles, then the lines are parallel. jsp?isbn=0030781078 Note: Username and Password glhsmath. We'll review your answers and create a Test Prep Plan for you based. Angles: Practice your knowledge of acute, obtuse, and alternate angles. Duration: 0 hrs 35 mins Scoring: 0 points Checkup: Practice Problems Check your understanding of the. In Unit 1, Constructions, Proof and Rigid Motion, students are introduced to the concept that figures can be created by just using a compass and straightedge using the properties of circles, and by doing so, properties of these figures are revealed. 2 Practice and KEY. Format: PDF, Word. Aug 6, 2020 - This board is dedicated to Teaching Geometry in the high school classroom. Salmon Line. Parallel and Perpendicular Lines Practice 3-4 and Reteaching 3-4 Parallel Lines and The Triangle Angle-Sum Theorem Practice 3-5 and Reteaching 3-5 The Polygon Angle-Sum Theorems Practice 3-6 and Reteaching 3-6 Lines in the Coordinate Plane Practice 3-7 and Reteaching 3-7 Slopes of Parallel and Perpendicular Lines Practice 3-8 and Reteaching 3-8. In the diagram on the next page, line t is a transversal of lines q and r. Students also gain a perspective of how geometry is an integral part of everyday life. Com stats: 2593 tutors, 707461 problems solved View all solved problems on Geometry_proofs -- maybe yours has been solved already!. Class Assignment: Pg. Readiness Tests Tools of Geometry Reasoning and Proof Parallel and Perpendicular Lines Congruent Triangles Relationships in Triangles Quadrilaterals Proportions and Similarity Right Triangles and. So, the two parallel lines 'a' and 'b' cut by the transversal 't'. 3: Perpendicular Lines: Learning Targets. Complements and Supplements. Prove that m∠1 = 0º. Write a two-column proof. Free parallel line calculator - find the equation of a parallel line step-by-step This website uses cookies to ensure you get the best experience. Title Difficulty Solved By Parallel Lines 2: easy : 816 (59%) 2008-12-27 ; Parallel Lines 3: easy : 810 (58%) 2008-12-27 ; Parallel Lines 4: hard : 505 (36%) 2008-12-28 ; Converse of Parallel Lines 1: easy :. Sample answer. Improve your math knowledge with free questions in "Proofs involving angles" and thousands of other math skills. After watching the video lesson, students complete a set of independent practice problems, and when they feel ready, they take a mastery quiz to demonstrate understanding of the topic. Geometry Symbols and Parallel Lines Cut by a Transversal. This lesson provided by Mr. When parallel lines get crossed by a transversal many angles are the same, as in this example: See Parallel Lines and Pairs of Angles to learn more. In the proof editor, you can dynamically add steps and optionally pin their positions in the proof as hints for students. Practice with Geometric Proofs!: more-geometric-proof-practice. Given a line l and a point A on l, suppose there are two lines, m and n, which both pass through A and are perpendicular to l. 1: Parallel Lines and Angle Relationships: Learning Targets: p. Here is a set of assignement problems (for use by instructors) to accompany the Equations of Planes section of the 3-Dimensional Space chapter of the notes for Paul Dawkins Calculus II course at Lamar University. 6th Grade Math; 7th Grade Math; 8th Grade Math : Home > Analytical Geometry >Unit 1 Similarity. s t u p q stu SOLUTION Lines p and q are both perpendicular to s, so by the Lines Perpendicular to a. Graph the line that represents Milan’s distance up the hill at a given time. Parallel & Perpendicular Lines and Transversals- Two-Column Proofs: This set contains proofs using perpendicular and parallel lines along transversals. That is, the arcs whose endpoints include one endpoint from each chord have equal measures. Coordinate Geometry Warmup on Brilliant, the largest community of math and science problem solvers. You can use the properties of these angles to find missing angles. 8th - University grade. Students practice naming pairs of angles that are formed by two parallel lines and a transversal. Students also gain a perspective of how geometry is an integral part of everyday life. 7 Perpendicular Lines in the Coordinate Plane. ) since alternate interior angles of parallel lines congruent so. This video contains plenty of examples and practice problems for you to learn the concept. Unit 2 Overview. Alternate Interior Angles. Back to Course Index. 3a Coordinate Formulas. The first way that isn't used that often is called the paragraph proof, the second way is called the two column proof and the third method is called flowchart proofs, so here its really easy to see using a picture your reasons and what your reasons allow you to conclude, so I'm going to show what a typical flowchart proof will look like. Theorem: Alternate interior angles formed by parallel lines and a transversal have the same measure. Math problem of the week I got a sequence that goes as follows: (1,1,1,1), (1,1,1,2), ,(4,4,4,4) (order matters here) which would give me 256 unique outcomes. Midpoint of a Line Segment (parallel to the y y y-axis. 4 Proving Lines are Parallel 3. Duration: 0 hrs 35 mins Scoring: 0 points Checkup: Practice Problems. Feromax Proofs Practice (Parallel Lines, Converse of Parallel Lines, Parallels and Perpendiculars) SOL G. - a scientific calculator (what you used in Algebra, graphing calculator NOT needed). 2-12-14: Similar Polygon Investigation: Geometer's Sketchpad 3. 5 Proving Lines Parallel Homework: Proving Lines Parallel Worksheet (Notebook pg. This allows you to make an unlimited number of printable math worksheets to your specifications instantly. the real world as parallel lines are used in designing buildings, airport runways, roads, railroad tracks, bridges, and so much more. The goal in this section of the lesson is to be explicit about what an axiomatic system is and how axiomatic systems operate. Transversals and Parallel Lines Practice and Problem Solving: A/B Complete the two-column proof to show that same-side exterior angles are supplementary. Infinite Geometry covers all typical Geometry material, beginning with a review of important Algebra 1 concepts and going through transformations. Math Enrichment quiz on parallel lines and transversals. Applying the transitive property again, we have. Properties of Parallelograms Practice 110. For instance, segment addition postulate definition geometry, straight angle geometry definition, hypotenuse definition geometry. Even on tests, I can see where students outlined the angles to see which lines are parallel. With Euclidea you don’t need to think about cleanness or accuracy of your drawing — Euclidea will do it for you. 5 Proofs Review Chapter 3 Homework: pg. Overview; Mean and geometry; The converse of the Pythagorean theorem and special triangles. In triangle ABC, if a line l is parallel to BC and cuts [AB] in the ratio s:t, then it cuts [AC] in the same ratio. This free geometry worksheet requires the use of the properties of parallel lines including the Alternate Interior Angle Theorem, Corresponding Angles Theorem, and the Same-Side Interior Angle Theorem and their converses. Duration: 0 hrs 35 mins Scoring: 0 points Checkup: Practice Problems Check your understanding of the. Inequalities and Relationships Within a Triangle. Given: angle 1 congruent to angle 2, l perpendicular to n Prove: l perpendicular to p here's the diagram: what i got ( i think i'm missing something ) statements (reasons) 1. In 3-space, two lines that are perpendicular to the same plane must be parallel. Angle bisectors. the real world as parallel lines are used in designing buildings, airport runways, roads, railroad tracks, bridges, and so much more. Given characteristics of two lines, such as slopes and equations, the student will determine whether the lines are parallel, perpendicular, or neither. Geometry Unit 2 Parallel Lines and Proof. Students must have an understanding of the properties of angles formed by parallel lines and a transversal (. Some of the worksheets displayed are , Parallel lines and proofs, Honors geometry chapter 3 proofs involving parallel and, 3 parallel lines and transversals, Proving lines parallel, Work section 3 2 angles and parallel lines, , Find the measure of the indicated angle that makes lines u. 4: Perpendicular Lines Definitions: Perpendicular Bisector - a line perpendicular to a segment a the segments midpoint Theorems: 1) If two intersecting lines form a linear pair, then the lines are. Section Objectives • Understand the undefined terms point, line and plane. At present I've gotten the notes/tutorials for my Algebra (Math 1314), Calculus I (Math 2413), Calculus II (Math 2414), Calculus III (Math 3435) and Differential Equations (Math 3301) class online. You proved that parallel lines have the transitive. Holt, Rinehart, and Winston. Which of the following in NOT a valid proof that m∠1 + m∠6 = 180°?. Discovering Properties of Parallel Lines Directions: 1. Custom Proof Creator. ” Angle relationships due to parallel lines #16. Perpendicular bisectors. Step-by-step illustration using GeoGebra. Chapter 11 THE GEOMETRY OF THREE DIMENSIONS 419 11-1 Points,Lines,and Planes 420 11-2 Perpendicular Lines and Planes 423 11-3 Parallel Lines and Planes 433 11-4 Surface Area of a Prism 440 11-5 Volume of a Prism 446 11-6 Pyramids 449 11-7 Cylinders 453 11-7 Cones 456 14365FM. 3 Proving Triangles in the Plane. 9 Prove theorems about lines and angles. The two lines are parallel → The corresponding angles are equal. These angles, and specific pairings of these angles, are given special names. We note that the vectors V, cV are parallel, and conversely, if two vectors are parallel (that is, they have the same direction), then one is a scalar multiple of the other. Broad Topics > Angles, Polygons, and Geometrical Proof > Angles - points, lines and parallel lines. Suitable for any class with geometry content. Angle relationships. Proof of the Triangle Sum Theorem. Next lesson. About doing it the fun way. Parallel line proofs. 1b5 10 14 Use the fiqure at the riqht to answer problems 1-8. Hands-On Geometry page 162 –Lets Construct Parallel Lines Postulate 4-2: If two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are parallel. Since we know that the opposite sides of a rhombus are parallel, then we have created the desired parallel line. Angle bisectors. Aug 6, 2020 - This board is dedicated to Teaching Geometry in the high school classroom. Find the sum of the measures of the. Learn how to write a proof when given angles from parallel lines and a transversalWe will explore angle relationships with parallel lines and a transversal. Let’s start. You can explore the concept of slope of a line in the following interactive graph (it's not a fixed image). 2 Parallel and Perpendicular Lines. all segments that are skew to CD −−−. GEOMETRY WORKSHEET---BEGINNING PROOFS Author: Russell H. Linear Pair - A pair of adjacent angles whose non-common sides are opposite rays. 2-12-14: Similar Polygon Investigation: Geometer's Sketchpad 3. Your task is to prepare a "proof" for each of the following problems. A line that intersects two or more coplanar lines at two different points is called a transversal. Lesson 10: Parallel and Perpendicular Lines Unit Test Geometry A Unit 3: Parallel and Perpendicular Lines. Geometry proof problem: congruent segments. Choose the correct equation or word to fill in each blank in the paragraph. Next lesson. 26_properties_of_parallelograms. ) to prove the theorem: "If two lines cut by a transversal where the alternate exterior angles are congruent, then the lines are parallel. Topics include angle relationships, triangles, quadrilaterals, congruency, similar figures, constructions, area, volume, and the Pythagorean Theorem. Transitive property 1. You could just say if we didn't know that length right there, that if this is 6:12 then this has to be 4 to some number. Example 2 : Find the slope of the line that is a) parallel and b) perpendicular to the line. , ISBN-10: 0133281159, ISBN-13: 978-0-13328-115-6, Publisher: Prentice Hall. Also, TR ≅ TR by the Reflexive Property. 3, we see that the vector RP ~is the same line. Next lesson. Proofs involving angles Proofs involving triangles Proofs involving quadrilaterals Geometric Constructions Construct the midpoint or perpendicular bisector of a segment Construct an equilateral triangle inscribed in a circle Similarity, Right Triangles, & Trigonometry Similarity Transformations Dilations and parallel lines Dilations and scale. , graph paper, tracing paper, or geometry software. Which of the following in NOT a valid proof that m∠1 + m∠6 = 180°?. Duration: 0 hrs 35 mins Scoring: 0 points Checkup: Practice Problems Check your understanding of the. Euclidean Geometry. Constructing lines & angles. Extra Practice. All for the high school levels of Grade 9, Grade 10, Grade 11, and Grade 12. Title Difficulty Solved By Parallel Lines 2: easy : 816 (59%) 2008-12-27 ; Parallel Lines 3: easy : 810 (58%) 2008-12-27 ; Parallel Lines 4: hard : 505 (36%) 2008-12-28 ; Converse of Parallel Lines 1: easy :. Equidistant. Parallel Lines and Transversals Student Probe Lines l and k are parallel lines cut by transversal, m. Under each. Geometry B Unit 6: Transformational Geometry Geometry B Final Holt Practice Worksheets Holt Practice Worksheets 2 PROVE IT! Interactive Proof-Writing Site Quizlet Interactive Practice Tests Good website for notes 3. Section Objectives • Understand the undefined terms point, line and plane. You have been asked to determine whether the two lines are parallel. On this page you will find: a complete list of all of our math worksheets, lessons, math homework, and quizzes. By a proof. Example of Coplanar. If a=b, then a+c=b+c. subtraction property of equality. 3: Perpendicular Lines: Learning Targets. The boundary lines of the one and the other class of those lines will be called parallel to the given line. • Understand defined terms, including space, segment and ray. The first missing reason for this proof is: Share practice link These are adjacent angles form a linear angle or straight line. Directed line segments AB are introduced as three–dimensional column vectors: If A = (x1, y1, z1) and B = (x2, y2, z2), then AB= x2 −x1 y2 −y1 z2 −z1. 3a Distance, Slope and Midpoint Formulas Geometry SOL Practice G. Specify a sequence. Interactive Parallel Line and Angles Explore the rules for the different types of congruent and supplementary angles here by dragging the points and selecting which angle pair you'd like to explore. Geometry Worksheet Quadrilaterals Section: Name: Mr. The line A(pq)(S) also contains the point (p, q),. You will extend your knowledge of the characteristics of angles and parallel and perpendicular lines and explore practical applications involving angles and lines. Vector addition and subtraction When 2 vectors are added or subtracted the vector produced is called the resultant. Academic Vocabulary Add these words and others you encounter in this unit. Perpendicular Lines - Module 19. Module 4 (Parallel/Perpendicular Lines) Transversals and parallel lines - Khan Academy Transversals and parallel lines 2 -Khan Academy Specific Angle Relationships formed by Parallel Lines Transversals and parallel lines 3 - Khan Academy (Solving for a variable!) Solving for the Equation of a Parallel Line. Acellus Geometry is taught by award-winning Acellus Master Teacher, Patrick Mara. 3a Coordinate Formulas. Try it free!. EBM1 is a similar triangle to fof' so Thus M1 is the point where the eye views the first family of measuring parallels; thus M1 is the vanishing point for this set of parallels. This proof assignment addresses basic angle relationships that exist when two parallel. In essence, a projective geometry may be thought of as an extension of Euclidean geometry in which the "direction" of each line is subsumed within the line as an extra "point", and in which a "horizon" of directions corresponding to coplanar lines is regarded as a "line". Beginner: worksheet and solutions then try Extra proof practice and solutions. By a proof. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. Line a is parallel to line c. Hard: proof worksheet and solutions. Test and Worksheet Generators for Math Teachers. Angle sums of triangles are less than 180 degrees. This banner text can have markup. The focus of this lesson is obviously proving theorems involving parallel lines cut by a transversal, but the lesson is also part of a learning progression related to axiomatic systems. For the proofs that we will be doing in this lesson, I use the two-column format specifically because its vertical arrangement is very similar to the. This lesson. Coordinate Plane Inductive & Deductive Reasoning Parallel Lines Classifying Triangles Indirect Proofs & Inequalities Quadrilaterals Similar Triangles Pythagorean Theorem Arcs & Chords Geometric Probability Surface Area of D Figures Transformational Geometry. Prentice Hall Gold Geometry • Teaching Resources. The term parallel and the notation \\ are used for lines, segments, rays, and planes. Coordinate Geometry: Parallel and Perpendicular Lines | Texas Gateway. Find and interpret the slope of the line. Students will practice using theorems about parallel lines, including Alternate Interior Angles Theorem, Alternate Exterior Angles Theorem, Corresponding Angles Postulate, Consecutive Interior Angles Theorem, as well as Linear Pair Postul. Step-by-Step construction, Manipulation, and animation. You could just say if we didn't know that length right there, that if this is 6:12 then this has to be 4 to some number. Triangles. It has one dimension, length. Two triangles are formed as a result of the intersections of the lines. This new line, A(p,q)(S), is parallel to our original line, so its slope also equals a. 1906 Association Drive Reston, VA 20191-1502 (800) 235-7566 or (703) 620-9840 FAX: (703) 476-2970 [email protected] In this unit on parallel lines, I introduce students to proof, using six algebraic properties: the reflexive, substitution, addition, subtraction, multiplication, and division properties. " Line Joining Midpoints on a Triangle Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to…. Here is a set of practice problems to accompany the Lines section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University. The lines that form the two sides of the quadrilateral are parallel. Each row is parallel to the one next to it, so r 1 i r 2, r 2 i r 3, and so on. Use a protractor to measure each of the numbered angles and fill in the chart below. Bookmark File PDF Geometry Chapter 5 Practice Test Geometry Chapter 5 Practice Test Getting the books geometry chapter 5 practice test now is not type of challenging means. 5 Using Properties of Parallel Lines 3. A great collection of free Geometry worksheets from Tutor-USA. ) to prove the theorem: "If two lines cut by a transversal where the alternate exterior angles are congruent, then the lines are parallel. This is the currently selected item. Two-column geometric proofs Pg 70 #’s 4-8 Pg 71 #’s 9-16 19 7-Parallel and Perpendicular Lines 7. Look on page 48 in your text. Next lesson. 1) y=2x+4 3) y=4x−5 5) x−y=4 7) 7x+y=−2 2) y=− 2 3 x +5 4) y=− 10 3 x−5 6) 6x−5y=20 8) 3x+4y=−8 Find the slope of a line perpendicular to each given line. Brian McLogan 16,231 views. The angle to be copied has the same measure in both triangles The image below is the final drawing above with the red items added. Textbook Authors: Charles, Randall I. Proving Lines Parallel – Day 2, Proofs. Geometry: Common Core (15th Edition) answers to Chapter 3 - Parallel and Perpendicular Lines - 3-8 Slopes of Parallel and Perpendicular Lines - Lesson Check - Page 201 6 including work step by step written by community members like you. MathBitsNotebook Geometry CCSS Lessons and Practice is a free site for students (and teachers) studying high school level geometry under the Common Core State Standards. Graph the line that represents Milan’s distance up the hill at a given time. See more ideas about Teaching geometry, Geometry activities, High school classroom. In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. Angles Formed by Intersecting Lines - Module 14. Parallel lines are equidistant from one another and will never intersect. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. This activity is designed for students in Grades 8 and up. All the geometry help you need right here, all free. Custom Proof Creator. Parallel Lines 1) Given congruent angles, which lines are || 2) Finding Angles- HARD 3) Algebra with Parallel Lines 4) Algebra with Parallel Lines Part 2 PROOFS 1) Triangle Congruence Proof 2) CPCTC Proof 3) Triangle Congruence 4) Proof Challenge Triangles 1) Triangle Inequality 2) Triangle Vocab & Triangle Sum 3) Isosceles Triangle. 4: Pairs of Angles Definitions: Adjacent Angles - Two angles in the same plane with a common vertex and a common side but no common interior points. Points that are on the same line are called collinear points. Two-column geometric proofs Pg 70 #’s 4-8 Pg 71 #’s 9-16 19 7-Parallel and Perpendicular Lines 7. the front the bottom 12. Let's take a peek at what this means. Students use a ruler to measure the segments intercepted on the. the real world as parallel lines are used in designing buildings, airport runways, roads, railroad tracks, bridges, and so much more. Write a two-column proof. Geometric Figure. Next lesson. What is the measure of ∠8?. Line segment l is a transversal. A6 SpringBoard Geometry, Unit 2 Practice Answers LeSSon 15-1 86. Classify each pair of angles as one of the following: (a) alternate interior angles (c) alternate exterior angles (e) supplementary angles 1. You may use any "style" (format) of proof. For the proofs that we will be doing in this lesson, I use the two-column format specifically because its vertical arrangement is very similar to the. Most high school geometry teachers agree that proofs give their students the most difficulty. Let us say I have 10 chocolates and I have to offer them to 3 students (atleast 1 to each). Worksheets are Unit 1 tools of geometry reasoning and proof, Ms work 132 153 geometry 06, Geometry chapter 1 notes practice work, Geometry unit 1 workbook, Chapter 4 lesson1 0 points line segments lines and rays, Geometry plane and simple answer key, 1 basics of geometry. Feel free to take a look at perpendicular bisectors and parallel plus perpendicular line segments to further solidify your understanding of this lesson. You can determine whether lines are parallel by utilizing a number of mathematical assumptions, such as the various kinds. Transversals and Parallel Lines - Module 19. 3 homework here ------------------>. Angles between intersecting lines. angles are also congruent if they are formed by parallel lines. Given: p ║ q Prove: m∠3 = m∠5 Complete the proof by writing the missing reasons. Geometry proof problem: squared circle. 5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e. Your task is to prepare a "proof" for each of the following problems. You probably had to spend some time figuring what I meant by "this line" and "that angle"!. Euler's Formula (Polyhedra) Evaluate. This is the currently selected item. Angles Formed by Intersecting Lines - Module 14. The department of mathematics website has been moved to hmc. 27) It is therefore distressing to discover that Euclid's proof of the Exterior Angle Theorem is deeply flawed! It can charitably be described as a glib example of "reasoning. This construction works by creating a rhombus. the real world as parallel lines are used in designing buildings, airport runways, roads, railroad tracks, bridges, and so much more. Geometry Vocab Practice. 0 - Parallel and Perpendicular LinesYou can click on the icon on the right to open in a new window. Parallel and perpendicular line segments. Circles, Triangles, Polygons, Euclidean Proof, Quadrilaterals--resources, links, videos and interactive applets | Math Warehouse. Glass' Geometry class GeoGebra - amazing tool for Algebra, Geometry, and beyond Socrative - a quiz and practice problem site shared quizzes Quizizz - assess and grade it Math Open Reference - awesome site for all math classes D esm os - graphing calculator and more Purple Math - another great site for math. 66% average accuracy. Learn how to write a proof when given angles from parallel lines and a transversalWe will explore angle relationships with parallel lines and a transversal. We can see one more line that intersects these two lines at two different points. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. Infinite Geometry covers all typical Geometry material, beginning with a review of important Algebra 1 concepts and going through transformations. Some parallel line pairs have just one common perpendicular and grow far apart. that you can draw is also going to be in that plane. Digital Packet. Textbook Authors: Charles, Randall I. 5-4 Continuing Proofs: Proving Angle Relationships 42-min 5-5 Angles and parallel Lines & 5. Two versions of the foldable are included for differentiated instruction. The line that I can draw through those two points is going to also be in that plane. We can use the addition function A(p,q) to shift the line S horizontally by p, and vertically by q. The lesson contains many varied exercises for students. First, you can line up the student's page and the answer page and hold it up to the light. Given: k // p. You can create a customized shareable link (at bottom) that will remember the exact state of the app--which angles are selected and where the. Online geometry video lessons to help students with the formulas, terms and theorems related to triangles, polygons, circles, and other geometric shapes to improve their math problem solving skills while doing their geometry homework and worksheets. This page shows how to construct a line parallel to a given line through a given point with compass and straightedge or ruler. p parallel to n (converse of the alternate. com/tabnav/controller. You may use any "style" (format) of proof. We also study how the size of the angle is ONLY determined by how much it has "opened" as compared to the whole circle. Link to Textbook website with Practice Tests & Lesson Quizzes: http://my. Feel free to take a look at perpendicular bisectors and parallel plus perpendicular line segments to further solidify your understanding of this lesson. 9) x=3 11) y=− 1 3 x 13) x−3y=−6 15) x+2y=8 10) y=− 1 2 x−1 12. Honor's Geometry Geometry Academic Geometry Parallel and Perpendicular Lines. Elliptic Geometry: Equation of a Line. So that's line l and line m. Homework: Page 10 in Geometry workbook. 3 Parallel Lines and Transversals 3. Math lessons, videos, online tutoring, and more for free. Geometry; Right triangles and trigonometry. If two lines cut by a transversal form congruent corresponding angles, then the lines are parallel. If you wanted a proof of the angle bisector theorem, here's a good interactive demo that allows you to drag points around to change the angle and see what happens to the angle bisector. The corresponding angles are not congruent. I was answering a question about why the Penrose triangle is impossible when I realized I haven't seen a coordinate proof that the angles of a triangle in $\mathbb{R}^n$ add up to $180^\circ$. Bookmark File PDF Geometry Chapter 5 Practice Test Geometry Chapter 5 Practice Test Getting the books geometry chapter 5 practice test now is not type of challenging means. angles are also congruent if they are formed by parallel lines. (g) If a point lies outside a line, then exactly one plane contains both the line and the point (Theorem 2). Circles, Triangles, Polygons, Euclidean Proof, Quadrilaterals--resources, links, videos and interactive applets | Math Warehouse. 5 Proving Lines Parallel Homework: Proving Lines Parallel Worksheet (Notebook pg. If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Two lines, l and m are cut by a transversal t, and ∠1 and ∠2 are corresponding angles. ) The second video is optional and explains some of the philosophy of how and why these "constructions" are proofs. 778 similarity. 6 Parallel Lines in the Coordinate Plane 3. You proved that parallel lines have the transitive. Parallel Lines 1) Given congruent angles, which lines are || 2) Finding Angles- HARD 3) Algebra with Parallel Lines 4) Algebra with Parallel Lines Part 2 PROOFS 1) Triangle Congruence Proof 2) CPCTC Proof 3) Triangle Congruence 4) Proof Challenge Triangles 1) Triangle Inequality 2) Triangle Vocab & Triangle Sum 3) Isosceles Triangle. Geometry Standards (Common Core) Find out what standards are required to learn in Geometry. Here is a set of practice problems to accompany the Lines section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University. 3 Parallel Lines Proof Worksheet (Pg. Infinite Geometry covers all typical Geometry material, beginning with a review of important Algebra 1 concepts and going through transformations. 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http://blog.gaurav.im/blog/page/2/ | # Paper: Neural Graph Machines
Semi-Supervised Learning is useful in scenarios where you have some labeled data, and lots of unlabeled data. If there is a way to cluster together training examples by a measure of similarity, and we can assume that examples close to each other in these clusterings are likely to have the same labels, then Semi-Supervised Learning can be pretty useful.
Essentially the premise is that labeling all the data is expensive, and we should learn as much as we can from as small a dataset as possible. For their data-labeling needs, the industry either relies on Mechanical Turks or full-time labelers on contract (Google Search is one example where they have a large team of human raters). Overall, it is costly to build a large labeled dataset. Therefore, if we can minimize our dependence on labeled data, and learn from known / inferred similarity within the dataset, that would be great. That’s where Semi-Supervised Learning helps.
Assume there is a graph-structure to our data, where a node is a datum / row, which needs to be labeled. And an edge exists between two nodes if they are similar, along with a weight. In this case, Label Propagation is a classic technique which has been used commonly.
I read this paper from Google Research which does a good job of generalizing and summarizing similar work done by Weston et. al, 2012, around training Neural Nets augmented by such a graph-based structure.
To summarize the work very quickly, the network tries to do two things:
a. For labeled data, try to predict the correct label (of course),
b. For the entire data set, try to learn a representation of each datum (embedding) in the hidden layers of the neural net.
For nodes which are adjacent to each other, the distance between their respective embeddings should be small, and the importance of keeping this distance small is proportional to the edge weight. That is, if there are two adjacent nodes with a high edge weight, if the neural net doesn’t learn to create embeddings such that these two examples are close to each other, there would be a larger penalty, than if the distance was smaller / the edge weight was lower.
Check the figure above. The blue layer is the hidden layer used for generating the embedding, whose output is represented by $h_{\theta}(X_i)$. $y$ is the final output. If $X_i$ and $X_j$ are close-by, the distance between them is represented by $d(h_{\theta}(X_i), h_{\theta}(X_j))$.
The cost-function is below. Don’t let this scare you. The first term is just the total loss from the predictions of the network for labeled data. The next three terms are for tweaking the importance of distances between the various (labeled / unlabeled) -(labeled / unlabeled) pairs, weighed by their respective edge weights, $w_{uv}$.
I skimmed through the paper to get the gist, but I wonder that the core contribution of such a network is to go from a graph-based structure to an embedding. If we were to construct an embedding directly from the graph structure, and train a NN separately using the embedding as the input, my guess is it should fetch similar results with a less complex objective function.
# A Gentle Intro to PyTorch
PyTorch is a fairly new deep-learning framework released by Facebook, which reminds me of the JS framework frenzy. But having played around with PyTorch a slight bit, it already feels fun.
To keep things short, I liked it because:
1. Unlike TensorFlow it allows me to easily print Tensors on the screen (no seriously, this is a big deal for me since I usually take several iterations to get a DL implementation right).
2. TensorFlow adds a layer between Python and TensorFlow. TensorFlow even has it’s own variable scope. This is way too much abstraction, that I don’t appreciate for my experimental interests.
3. Interop with numpy is easy in PyTorch, with the simple .numpy() suffix to convert a Tensor to a numpy array.
4. Unlike Torch, it is not in Lua (also doesn’t need the LuaRocks package manager).
5. Unlike Caffe2, I don’t have to write C++ code and write build scripts.
PyTorch’s website has a 60 min. blitz tutorial, which is laid out pretty well.
Here is the summary to get you started on PyTorch:
• torch.Tensor is your np.array (the NumPy array). torch.Tensor(3,4) will create a Tensor of shape (3,4).
• All the functions are pretty standard. Such as torch.rand can be used to generate random Tensors.
• Indexing in Tensors is pretty similar to NumPy as well.
• .numpy() allows converting Tensor to a numpy array.
• For the purpose of a compute graph, PyTorch lets you create Variables which are similar to placeholder in TF.
• Creating a compute graph and computing the gradient is pretty easy (and automatic).
This is all it takes to compute the gradient, where x is a variable:
Doing backprop simply with the backward method call on the scalar out, computes gradients all the way to x. This is amazing!
• For NN, there is an nn.Module which wraps around the boring boiler-plate.
• A simple NN implementation is below for solving the MNIST dataset, instead of the CIFAR-10 dataset that the tutorial solves:
As seen, in the __init__ method, we just need to define the various NN layers we are going to be using. Then the forward method just runs through them. The view method is analogous to the NumPy reshape method.
The gradients will be applied after the backward pass, which is auto-computed. The code is self-explanatory and fairly easy to understand.
• Torch also keeps track of how to retrieve standard data-sets such as CIFAR-10, MNIST, etc.
• After getting the data, from the data-loader you can proceed to play with it. Below are rest of the pieces required to complete the implementation (almost all of it is from the tutorial):
The criterion object is used to compute your loss function. optim has a bunch of convex optimization algorithms such as vanilla SGD, Adam, etc. As promised, simply calling the backward method on the loss object allows computing the gradient.
• Assuming you are working on the tutorial. Try to solve the tutorial for MNIST data instead of CIFAR-10.
• Instead of the 3-channel (RGB) image of size 24x24 pixels, the MNIST images are single channel 28x28 pixel images.
Overall, I could get to 96% accuracy, with the current setup. The complete gist is here.
# Back to Basics: Linear Regression
Essentially, in Linear Regression, we try to estimate a dependent variable $y$, using independent variables $x_1$, $x_2$, $x_3$, $…$, using a linear model.
More formally, $y = b + W_1 x_1 + W_2 x_2 + … + W_n x_n + \epsilon$. Where, $W$ is the weight vector, $b$ is the bias term, and $\epsilon$ is the noise in the data.
It can be used when there is a linear relationship between the input $X$ (input vector containing all the $x_i$, and $y$). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5534650087356567, "perplexity": 858.8714174455894}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589172.41/warc/CC-MAIN-20180716021858-20180716041858-00276.warc.gz"} |
https://socratic.org/questions/if-log-base-10-2-0-301-log-base-10-3-0-477-what-does-log-base-10-15 | Precalculus
Topics
# If log base 10 (2) = 0.301 & log base 10 (3) = 0.477, what does log base 10 (15) =?
Jan 28, 2016
I found: $1.176$
#### Explanation:
We can write it as:
${\log}_{10} \left(15\right) = {\log}_{10} \left(\frac{30}{2}\right)$
using the property of logs of a fraction we get:
${\log}_{10} \left(\frac{30}{2}\right) = {\log}_{10} \left(30\right) - {\log}_{10} \left(2\right) =$
and:
$= {\log}_{10} \left(10 \cdot 3\right) - {\log}_{10} \left(2\right) =$
we use the property of the log of a product to get:
${\log}_{10} \left(10\right) + {\log}_{10} \left(3\right) - {\log}_{10} \left(2\right) =$
$= 1 + 0.477 - 0.301 = 1.176$
##### Impact of this question
603 views around the world | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19133548438549042, "perplexity": 2207.121767396417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583755653.69/warc/CC-MAIN-20190121025613-20190121051613-00030.warc.gz"} |
https://yutsumura.com/top-10-popular-math-problems-in-2016-2017/top10mathproblems2017/ | top10mathproblems2017
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• Find All Symmetric Matrices satisfying the Equation Find all $2\times 2$ symmetric matrices $A$ satisfying $A\begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}$? Express your solution using free variable(s). Solution. Let $A=\begin{bmatrix} a & b\\ c& d \end{bmatrix}$ […] | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9722262024879456, "perplexity": 86.99891667179833}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125944479.27/warc/CC-MAIN-20180420155332-20180420175332-00225.warc.gz"} |
https://homepages.inf.ed.ac.uk/stark/continuous-pi.html | # Ian Stark
## The Continuous π-Calculus: A Process Algebra for Biochemical Modelling
In Computational Methods in Systems Biology: Proceedings of 6th International Conference CMSB 2008, Rostock, Germany, October 12–15, 2008. Lecture Notes in Computer Science 5307, pages 103–122. Springer-Verlag, 2008.
Fetch the paper or visit the publisher's page. Download the slides from Marek's conference talk, or from my later seminar presentation. Go to other papers, talks or my home page.
### Abstract
We introduce the continuous π-calculus, a process algebra for modelling behaviour and variation in molecular systems. Key features of the language are: its expressive succinctness; support for diverse interaction between agents via a flexible network of molecular affinities; and operational semantics for a continuous space of processes. This compositional semantics also gives a modular way to generate conventional differential equations for system behaviour over time. We illustrate these features with a model of an existing biological system, a simple oscillatory pathway in cyanobacteria. We then discuss future research directions, in particular routes to applying the calculus in the study of evolutionary properties of biochemical pathways.
@InProceedings{kwiatkowski/stark:continuous-pi,
author = {Marek Kwiatkowski and Ian Stark},
title = {The Continuous $\pi$-Calculus: A Process Algebra for
Biochemical Modelling},
booktitle = {Computational Methods in Systems Biology: Process of the
Sixth International Conference CMSB~2008},
pages = {103--122},
year = 2008,
series = {Lecture Notes in Computer Science},
number = 5307,
publisher = {Springer-Verlag},
url = {http://homepages.ed.ac.uk/stark/continuous-pi.html},
pdf = {http://homepages.ed.ac.uk/stark/continuous-pi.pdf},
doi = {10.1007/978-3-540-88562-7_11}
}
This research was supported by an EPSRC studentship, the Laboratory for Foundations of Computer Science, and The University of Edinburgh School of Informatics. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4993370771408081, "perplexity": 4338.977143482888}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655911896.73/warc/CC-MAIN-20200710175432-20200710205432-00414.warc.gz"} |
http://tex.stackexchange.com/questions/83196/setting-texinputs-for-pdflatex-in-ubuntu | # Setting TEXINPUTS for pdflatex in Ubuntu
I have a set of files that are commonly used as inputs in my tex files, so I put them in a directory and set the path in the TEXINPUTS environment variable (in Ubuntu). This works fine when compiling files with the latex command, but if I compile them with pdftex, it gives the following error message:
``````! I can't find file `{header.tex}'.
``````
As far as I can tell, pdftex is completely ignoring the TEXINPUTS environment variable. Does it use a different environment variable? How can I get it to recognise a path?
-
Are you using `pdftex` or `pdflatex`. The latter will read `\input{header.tex}` as a braced argument for file `header.tex`, but `pdftex` is Knuth's plain format with the pdfTeX engine: there, `\input` has primitive syntax only, and the file name searched is `{input.tex}`. – Joseph Wright Nov 18 '12 at 12:38
Aha! pdflatex works, but pdftex doesn't. Thanks for explaining. – thornate Nov 18 '12 at 12:52
I'll write that up in a slightly modified form as an answer, then :-) – Joseph Wright Nov 18 '12 at 13:06
Start your documents with `\NeedsTeXFormat{LaTeX2e}` to get a meaningful error message if you use the wrong program. – Martin Schröder Nov 19 '12 at 7:41
The `latex` command runs LaTeX in DVI-output mode. LaTeX's definition of `\input` allows for a syntax
``````\input{<file-name>}
``````
where the `<file-name>` is read as a braced argument. The `pdflatex` command will do exactly the same but with direct PDF output.
On the other hand, `pdftex` runs plain TeX with direct PDF output. The plain TeX definition for `\input` uses a 'primitive' syntax, in which the name is read as any tokens at all up to the first space. Thus with `pdftex`
``````\input{<file-name>}
``````
ends up looking for a file called `{<file-name>}`, including the braces.
-
It may be worth noting that `\input{filename}` works also in LuaTeX (as opposed to LuaLaTeX). – egreg Nov 18 '12 at 13:46
@egreg One of the 'features' of LuaTeX which gives me headaches :-) – Joseph Wright Nov 18 '12 at 14:00 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9991143345832825, "perplexity": 2741.520971223771}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422120842874.46/warc/CC-MAIN-20150124173402-00040-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://leanprover-community.github.io/mathlib4_docs/Lean/Data/Lsp/Workspace.html | # Documentation
Lean.Data.Lsp.Workspace
Equations
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• watchers :
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• One or more equations did not get rendered due to their size.
• changes :
Instances For | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.962959349155426, "perplexity": 7218.627266019936}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943746.73/warc/CC-MAIN-20230321193811-20230321223811-00022.warc.gz"} |
https://laurentlessard.com/bookproofs/finding-the-doctored-coin/ | # Finding the doctored coin
This Riddler puzzle is about repeatedly flipping coins!
On the table in front of you are two coins. They look and feel identical, but you know one of them has been doctored. The fair coin comes up heads half the time while the doctored coin comes up heads 60 percent of the time. How many flips — you must flip both coins at once, one with each hand — would you need to give yourself a 95 percent chance of correctly identifying the doctored coin?
Extra credit: What if, instead of 60 percent, the doctored coin came up heads some P percent of the time? How does that affect the speed with which you can correctly detect it?
Here is my solution.
[Show Solution]
## 4 thoughts on “Finding the doctored coin”
1. Hi Laurent,
I am trying to understand how your curve can fall all the way to 1 when the doctored probability is 100%. In one flip, there is a 50% chance that they are both heads and I learn nothing. So there is a 1/2 chance I need a second flip, and a 1/4 chance I need a third, etc; the geometric series sums to 2. Also I found an odd “stairstep” feature where the average number of guesses jumps discontinuously at each probability p obeying p^m/(1-p)^m=19 (19 = 95% / 5% and m an integer). I put my solution at
As an aside, a Monte-Carlo is a kind of inefficient way to find the distribution of lengths, you can solve the Fokker-Planck equation for the distribution of possible outcomes and eliminate fluctuations…
guy
1. Hi Laurent,
Reading through again, I think what you computed is the number of flips n such that it is more likely than not that one knows with 95% certainty. Rather than the average number of flips needed to reach 95% certainty. Or the number of flips such that a guess after that many flips is 95% certain to be right. Curiously, these each give a different answer, though the first two appear to be close.
1. Hi Guy,
Thanks for the comments! I believe that what I calculated is the test statistic (the equation in the blue box that says n > …) that, when satisfied, implies you are at least 95% confident that you know which coin is the doctored one.
My mistake was in approximating the expected value of n by substituting the true probabilities in place of the empirical ones. This turns out to be a good approximation when $p_2=0.6$, but leads to a nonsensical solution when $p_2=1$, as you pointed out.
If I can find some free time next week, I’ll look over my solution and see if I can patch it up. I think that if I calculate expectations exactly, I will obtain what you found in the second part of your solution (“stop when you know”). In the meantime, do you have any good references that explain the Fokker-Planck approach you mentioned?
1. Jason Weisman says:
I think the question is to determine before starting, how many flips are needed to give yourself a 95 percent chance of correctly identifying the doctored coin. I believe the correct answer to this question with p2=0.6, p1=0.5 is 134. This is different from the published solution which does not take into consideration 50% probability of guessing correctly for cases where there are the same number of heads up flips. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9321072697639465, "perplexity": 355.6175365534924}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153899.14/warc/CC-MAIN-20210729234313-20210730024313-00507.warc.gz"} |
https://www.cheenta.com/set-theory-isi-b-stat-entrance-objective/ | Set theory | TOMATO ISI B.stat Objective | Problem 53
Try this beautiful problem Based on Set Theory useful for ISI B.Stat Entrance.
Set Theory| ISI B.Stat Entrance | Problem 53
There were 41 candidates in an examination and each candidate was examined in algebra, geometry and calculus. It was found that 12 candidates failed in algebra, 7 failed in geometry and 8 failed in calculus , 2 in geometry and calculus , 3 in calculus and algebra , 6 in algebra and geometry, whereas only 1 failed in one of the three subjects. Then, find the number of candidates who passed in all three subjects?
• $24$
• $26$
• $28$
Key Concepts
SET
Algebra
Cardinal number
Answer: $24$
TOMATO, Problem 53
Challenges and Thrills in Pre College Mathematics
Try with Hints
use set theory concept
Can you now finish the problem ..........
we assume that A ,G,C be the sets of the students who failed on algebra ,geometry and calculus respectively.
Find the complement of $N(A \cup G \cup C)$
can you finish the problem........
Let S be the set of total students i.e N(s) = 41
we assume that A ,G,C be the sets of the students who failed on algebra ,geometry and calculus respectively.
Therefore
N(A)=12
N(G)=7
N(C)=8
and
$N(A \cap G \cap C)$=1
$N(G \cap C)$ =2 ,
$N(C\cap A)$ =3
$N(A\cap G)$ =6
$N(A \cup G \cup C)$=$N(A) + N(G) +N(C) -N(G \cap C) -N (C \cap A) -N(C \cap A) + N(A \cap G \cap C)$=12 + 7+8-2-6-3+1=17
Therefore complement of $N(A \cup G \cup C)$ =41-17=24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9420720338821411, "perplexity": 4841.097138955617}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488519735.70/warc/CC-MAIN-20210622190124-20210622220124-00381.warc.gz"} |
https://www.physicsforums.com/threads/radioactive-decay-given-ax-ay-and-t-for-y-get-t-for-x-not-possible.196312/ | # Radioactive decay. Given Ax, Ay and t½ for Y, get t½ for X. Not possible?
1. Nov 5, 2007
### catkin
[SOLVED] Radioactive decay. Given Ax, Ay and t½ for Y, get t½ for X. Not possible?
1. The problem statement, all variables and given/known data
This is from Advanced Physics by Adams & Allday, spread 8.13 Question 1.
The activity of 20 g of element X is four times the activity of 10 g of element Y. Element Y has a half-life of 20,000 y. What is the half-life of X?
2. Relevant equations
$$A = \lambda N$$
$$\lambda t_{0.5} = 0.69$$
3. The attempt at a solution
Rewriting the first relevant equation in $t_{0.5}$, rather than λ, using the proportionality from the second relevant equation
$$A = 0.69 N / t_{0.5}$$
Considering 10g of both elements
$$A_{X} = 2A_{Y}$$
Expressing these activities in terms of the number of atoms in 10 g and half life
$$0.69 N_{X} / t_{0.5X} = 2 \times 0.69 N_{Y} / t_{0.5Y}$$
$$N_{X} / t_{0.5X} = 2N_{Y} / t_{0.5Y}$$
$$t_{0.5X} = (N_{X} / 2 N_{Y}) t_{0.5Y}$$
Substituting, using years as time units
$$t_{0.5X} = (N_{X} / 2 N_{Y}) {20000}$$
If the number of atoms in 10 g of element X were the same as the number of atoms in 10 g of element Y (there is no reason why it should be) then $t_{0.5X}$ would be 10,000 years (the answer the book gives).
4. Question Am I right in thinking there is not enough information in the question to answer it?
2. Nov 6, 2007
### rl.bhat
10 g of x and y cannot have same number of atoms. Nx and Ny depend on their molicular weights.
3. Nov 7, 2007
### catkin
Thanks rl.bhat
It doesn't answer my question though; is the problem soluble?
[Separate issue: what if the elements had the same atomic number? Say Th-234 and Pa-234? Wouldn't the number of atoms in 10 g be the same, at least to the number of significant figures the question implies?]
4. Nov 7, 2007
### rl.bhat
In case of Th- 234 and Pa- 234 the problem is soluble.
5. Nov 7, 2007
### catkin
Thanks again. That makes sense. Is the problem soluable as it is posed in the original question?
6. Nov 7, 2007
### Staff: Mentor
Certainly if X -> Y (or Y -> X) by beta decay, then the same mass would have approximately the same number of atoms within 1% or less.
The question becomes - "does X -> Y, or vice versa, i.e. do they represent sequential steps in a decay chain?"
The approach seems correct. The problem hinges on the assumption of Nx and Ny, which would be determined by the atomic masses.
7. Nov 7, 2007
### catkin
Thanks, astronuc
That helps understanding.
There's nothing in the question to indicate either any decay relationship or the atomic mass relationship between X and Y, though. Decay chains are introduced in a later "spread" in the textbook so should not be necessary for the solution.
I'm increasingly coming to think that the question as set is not soluable.
8. Nov 7, 2007
### Staff: Mentor
Raise this concern with the professor.
With mass and activity, one can get the specific activity, but one needs to know the atomic mass to obtain the number of atoms.
Since you obtained the answer given in the book with the assumption that the atomic mass of X and Y are roughly equal, that would seem to indicate an implicit assumption on the part of the author. If beta decay was involved (e.g. X -> Y), then that is a reasonable assumption.
9. Nov 7, 2007
### catkin
Thanks Astronuc
That's enough to consider this one SOLVED
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Similar Discussions: Radioactive decay. Given Ax, Ay and t½ for Y, get t½ for X. Not possible? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8871065974235535, "perplexity": 1359.6783184122776}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805977.0/warc/CC-MAIN-20171120090419-20171120110419-00788.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-concepts-through-functions-a-unit-circle-approach-to-trigonometry-3rd-edition/chapter-13-a-preview-of-calculus-the-limit-derivative-and-integral-of-a-function-section-13-3-one-sided-limits-continuous-functions-13-3-assess-your-understanding-page-909/34 | ## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
$0$
We find the left-hand limit as follows: $\lim\limits_{x \to 2^{-}} f(x)=\lim\limits_{x \to 2^{-}} (4-2x) \\=\lim\limits_{x \to 2^{-}} (4) -\lim\limits_{x \to 2^{-}} (2x) \\=4-(2)(2) \\=0$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9840008020401001, "perplexity": 5309.97303515166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363290.39/warc/CC-MAIN-20211206042636-20211206072636-00459.warc.gz"} |
http://www.r-bloggers.com/collinearity-and-stepwise-vif-selection/ | # Collinearity and stepwise VIF selection
February 5, 2013
By
(This article was first published on R is my friend » R, and kindly contributed to R-bloggers)
Collinearity, or excessive correlation among explanatory variables, can complicate or prevent the identification of an optimal set of explanatory variables for a statistical model. For example, forward or backward selection of variables could produce inconsistent results, variance partitioning analyses may be unable to identify unique sources of variation, or parameter estimates may include substantial amounts of uncertainty. The temptation to build an ecological model using all available information (i.e., all variables) is hard to resist. Lots of time and money are exhausted gathering data and supporting information. We also hope to identify every significant variable to more accurately characterize relationships with biological relevance. Analytical limitations related to collinearity require us to think carefully about the variables we choose to model, rather than adopting a naive approach where we blindly use all information to understand complexity. The purpose of this blog is to illustrate use of some techniques to reduce collinearity among explanatory variables using a simulated dataset with a known correlation structure.
A simple approach to identify collinearity among explanatory variables is the use of variance inflation factors (VIF). VIF calculations are straightforward and easily comprehensible; the higher the value, the higher the collinearity. A VIF for a single explanatory variable is obtained using the r-squared value of the regression of that variable against all other explanatory variables:
$\displaystyle VIF_j=\frac{1}{1-R_j^2}$
where the $VIF$ for variable $j$ is the reciprocal of the inverse of $R^2$ from the regression. A VIF is calculated for each explanatory variable and those with high values are removed. The definition of ‘high’ is somewhat arbitrary but values in the range of 5-10 are commonly used.
Several packages in R provide functions to calculate VIF: vif in package HH, vif in package car, VIF in package fmsb, vif in package faraway, and vif in package VIF. The number of packages that provide VIF functions is surprising given that they all seem to accomplish the same thing. One exception is the function in the VIF package, which can be used to create linear models using VIF-regression. The nuts and bolts of this function are a little unclear since the documentation for the package is sparse. However, what this function does accomplish is something that the others do not: stepwise selection of variables using VIF. Removing individual variables with high VIF values is insufficient in the initial comparison using the full set of explanatory variables. The VIF values will change after each variable is removed. Accordingly, a more thorough implementation of the VIF function is to use a stepwise approach until all VIF values are below a desired threshold. For example, using the full set of explanatory variables, calculate a VIF for each variable, remove the variable with the single highest value, recalculate all VIF values with the new set of variables, remove the variable with the next highest value, and so on, until all values are below the threshold.
In this blog we’ll use a custom function for stepwise variable selection. I’ve created this function because I think it provides a useful example for exploring stepwise VIF analysis. The function is a wrapper for the vif function in fmsb. We’ll start by simulating a dataset with a known correlation structure.
require(MASS)
require(clusterGeneration)
set.seed(2)
num.vars<-15
num.obs<-200
cov.mat<-genPositiveDefMat(num.vars,covMethod="unifcorrmat")\$Sigma
rand.vars<-mvrnorm(num.obs,rep(0,num.vars),Sigma=cov.mat)
We’ve created fifteen ‘explanatory’ variables with 200 observations each. The mvrnorm function (MASS package) was used to create the data using a covariance matrix from the genPositiveDefMat function (clusterGeneration package). These functions provide a really simple approach to creating data matrices with arbitrary correlation structures. The covariance matrix was chosen from a uniform distribution such that some variables are correlated while some are not. A more thorough explanation about creating correlated data matrices can be found here. The correlation matrix for the random variables should look very similar to the correlation matrix from the actual values (as sample size increases, the correlation matrix approaches cov.mat).
Now we create our response variable as a linear combination of the explanatory variables. First, we create a vector for the parameters describing the relationship of the response variable with the explanatory variables. Then, we use some matrix algebra and a randomly distributed error term to create the response variable. This is the standard form for a linear regression model.
parms<-runif(num.vars,-10,10)
y<-rand.vars %*% matrix(parms) + rnorm(num.obs,sd=20)
We would expect a regression model to indicate each of the fifteen explanatory variables are significantly related to the response variable, since we know the true relationship of y with each of the variables. However, our explanatory variables are correlated. What happens when we create the model?
lm.dat<-data.frame(y,rand.vars)
form.in<-paste('y ~',paste(names(lm.dat)[-1],collapse='+'))
mod1<-lm(form.in,data=lm.dat)
summary(mod1)
The model shows that only four of the fifteen explanatory variables are significantly related to the response variable (at $\alpha = 0.05$), yet we know that every one of the variables is related to y. As we’ll see later, the standard errors are also quite large.
We can try an alternative approach to building the model that accounts for collinearity among the explanatory variables. We can implement the custom VIF function as follows.
vif_func(in_frame=rand.vars,thresh=5,trace=T)
var vif
X1 26.7776302460193
X2 35.7654696801389
X3 14.8902623488606
X4 50.6259723278776
X5 10.599371257556
X6 108.343545737888
X7 48.2508656429107
X8 183.136179797657
X9 51.6790552123906
X10 63.8699838164383
X11 38.9458133633031
X12 44.3534264537944
X13 9.35861427426385
X14 63.1574276237521
X15 30.0137537949494
removed: X8 183.1362
var vif
X1 5.57731851381497
X2 10.0195886727232
X3 5.55663566788945
X4 6.8064112804091
X5 9.7815324084451
X6 22.3236741700758
X7 36.854990561001
X9 16.972399679086
X10 57.2665930293009
X11 22.4854807367867
X12 43.1006397357538
X13 8.54661668063361
X14 29.7536838039265
X15 21.6340334562738
removed: X10 57.26659
var vif
X1 5.55463656650283
X2 8.43692519123461
X3 4.20157496220101
X4 4.30562228649632
X5 1.85152657224351
X6 9.78518916197122
X7 3.59917695249808
X9 5.62398393809027
X11 4.32732961231283
X12 8.92901049257853
X13 2.22079922858869
X14 9.73258301210856
X15 8.69287102590565
removed: X6 9.785189
var vif
X1 4.88431271981048
X2 3.0066710371039
X3 3.92223104412672
X4 4.03552281755132
X5 1.85130973105683
X7 3.56687077767566
X9 5.55536287729148
X11 2.11226533056043
X12 5.58689916270725
X13 1.86868960383407
X14 9.39686287473867
X15 7.80042398111767
removed: X14 9.396863
[1] "X1" "X2" "X3" "X4" "X5" "X7" "X9" "X11"
[9] "X12" "X13" "X15"
The function uses three arguments. The first is a matrix or data frame of the explanatory variables, the second is the threshold value to use for retaining variables, and the third is a logical argument indicating if text output is returned as the stepwise selection progresses. The output indicates the VIF values for each variable after each stepwise comparison. The function calculates the VIF values for all explanatory variables, removes the variable with the highest value, and repeats until all VIF values are below the threshold. The final output is a list of variable names with VIF values that fall below the threshold. Now we can create a linear model using explanatory variables with less collinearity.
keep.dat<-vif_func(in_frame=rand.vars,thresh=5,trace=F)
form.in<-paste('y ~',paste(keep.dat,collapse='+'))
mod2<-lm(form.in,data=lm.dat)
summary(mod2)
The updated regression model is much improved over the original. We see an increase in the number of variables that are significantly related to the response variable. This increase is directly related to the standard error estimates for the parameters, which look at least 50% smaller than those in the first model. The take home message is that true relationships among variables will be masked if explanatory variables are collinear. This creates problems in model creation which lead to complications in model inference. Taking the extra time to evaluate collinearity is a critical first step to creating more robust ecological models.
Function and example code: | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49691787362098694, "perplexity": 1293.1402738225986}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00624-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/324517/trace-of-the-inverse-of-a-matrix-times-another-matrix | trace of the inverse of a matrix times another matrix
I do know generally $\text{trace}(A^{-1}B)\not= \sum_i \lambda_{B_i}/\lambda_{A_i}$,
where $\lambda_{A_i}$ and $\lambda_{B_i}$ are the corresponding eigenvalues of matrix $A$ and $B$ respectively,
but is there any cases when this equality can be statified?
-
@sbr for $A=B$ you need to know which is the first eigenvalue and which is the second and so on, else the equality is not true in general – Dominic Michaelis Mar 8 '13 at 8:30
If $A$ and $B$ are simultaneously diagonalisable (or trigonalisable) and you are combining eigenvalues for the same (generalised) eigenvectors then this obviously holds. In other cases (i.e., almost always), all bets are off.
There are many cases: let $A$ be $\gamma \cdot I$ where $I$ is the identiy matrix and $\gamma$ is an arbitrary scalar $\neq 0$, or let $B=0$ (the matrix with every entry zero). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.988586962223053, "perplexity": 154.46812420586036}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375099361.57/warc/CC-MAIN-20150627031819-00114-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://en.wikipedia.org/wiki/Triangular_distribution | # Triangular distribution
Parameters Probability density function Cumulative distribution function $a:~a\in (-\infty,\infty)$ $b:~a $c:~a\le c\le b\,$ $a \le x \le b \!$ $\begin{cases} 0 & \text{for } x < a, \\ \frac{2(x-a)}{(b-a)(c-a)} & \text{for } a \le x < c, \\[4pt] \frac{2}{b-a} & \text{for } x = c, \\[4pt] \frac{2(b-x)}{(b-a)(b-c)} & \text{for } c < x \le b, \\[4pt] 0 & \text{for } b < x. \end{cases}$ $\begin{cases} 0 & \text{for } x \leq a, \\[2pt] \frac{(x-a)^2}{(b-a)(c-a)} & \text{for } a < x \leq c, \\[4pt] 1-\frac{(b-x)^2}{(b-a)(b-c)} & \text{for } c < x < b, \\[4pt] 1 & \text{for } b \leq x. \end{cases}$ $\frac{a+b+c}{3}$ $\begin{cases} a+\frac{\sqrt{(b-a)(c-a)}}{\sqrt{2}} & \text{for } c \ge \frac{a+b}{2}, \\[6pt] b-\frac{\sqrt{(b-a)(b-c)}}{\sqrt{2}} & \text{for } c \le \frac{a+b}{2}. \end{cases}$ $c\,$ $\frac{a^2+b^2+c^2-ab-ac-bc}{18}$ $\frac{\sqrt 2 (a\!+\!b\!-\!2c)(2a\!-\!b\!-\!c)(a\!-\!2b\!+\!c)}{5(a^2\!+\!b^2\!+\!c^2\!-\!ab\!-\!ac\!-\!bc)^\frac{3}{2}}$ $-\frac{3}{5}$ $\frac{1}{2}+\ln\left(\frac{b-a}{2}\right)$ $2\frac{(b\!-\!c)e^{at}\!-\!(b\!-\!a)e^{ct}\!+\!(c\!-\!a)e^{bt}} {(b-a)(c-a)(b-c)t^2}$ $-2\frac{(b\!-\!c)e^{iat}\!-\!(b\!-\!a)e^{ict}\!+\!(c\!-\!a)e^{ibt}} {(b-a)(c-a)(b-c)t^2}$
In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b.
## Special cases
### Two points known
The distribution simplifies when c = a or c = b. For example, if a = 0, b = 1 and c = 1, then the PDF and CDF become:
$\left.\begin{matrix}f(x) &=& 2x \\[8pt] F(x) &=& x^2 \end{matrix}\right\} \text{ for } 0 \le x \le 1$
\begin{align} E(X) & = \frac{2}{3} \\[8pt] \mathrm{Var}(X) &= \frac{1}{18} \end{align}
### Distribution of mean of two standard uniform variables
This distribution for a = 0, b = 1 and c = 0.5 is distribution of X = (X1 + X2)/2, where X1, X2 are two independent random variables with standard uniform distribution.
$f(x) = \begin{cases} 4x & \text{for }0 \le x < \frac{1}{2} \\ 4-4x & \text{for }\frac{1}{2} \le x \le 1 \end{cases}$
$F(x) = \begin{cases} 2x^2 & \text{for }0 \le x < \frac{1}{2} \\ 1-2(1-x)^2 & \text{for }\frac{1}{2} \le x \le 1 \end{cases}$
\begin{align} E(X) & = \frac{1}{2} \\[6pt] \operatorname{Var}(X) & = \frac{1}{24} \end{align}
### Distribution of the absolute difference of two standard uniform variables
This distribution for a = 0, b = 1 and c = 0 is distribution of X = |X1 − X2|, where X1, X2 are two independent random variables with standard uniform distribution.
\begin{align} f(x) & = 2 - 2x \text{ for } 0 \le x < 1 \\[6pt] F(x) & = 2x - x^2 \text{ for } 0 \le x < 1 \\[6pt] E(X) & = \frac{1}{3} \\[6pt] \operatorname{Var}(X) & = \frac{1}{18} \end{align}
## Generating Triangular-distributed random variates
Given a random variate U drawn from the uniform distribution in the interval (0, 1), then the variate
$\begin{matrix} \begin{cases} X = a + \sqrt{U(b-a)(c-a)} & \text{ for } 0 < U < F(c) \\ & \\ X = b - \sqrt{(1-U)(b-a)(b-c)} & \text{ for } F(c) \le U < 1 \end{cases} \end{matrix}$[1]
Where F(c) = (c-a)/(b-a)
has a Triangular distribution with parameters a, b and c. This can be obtained from the cumulative distribution function.
## Use of the distribution
The triangular distribution is typically used as a subjective description of a population for which there is only limited sample data, and especially in cases where the relationship between variables is known but data is scarce (possibly because of the high cost of collection). It is based on a knowledge of the minimum and maximum and an "inspired guess" [2] as to the modal value. For these reasons, the triangle distribution has been called a "lack of knowledge" distribution.
The triangular distribution is therefore often used in business decision making, particularly in simulations. Generally, when not much is known about the distribution of an outcome, (say, only its smallest and largest values) it is possible to use the uniform distribution. But if the most likely outcome is also known, then the outcome can be simulated by a triangular distribution. See for example under corporate finance.
### Project management
The triangular distribution, along with the Beta distribution, is also widely used in project management (as an input into PERT and hence critical path method (CPM)) to model events which take place within an interval defined by a minimum and maximum value.
### Audio dithering
The symmetric triangular distribution is commonly used in audio dithering, where it is called TPDF (Triangular Probability Density Function). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 22, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9989724159240723, "perplexity": 727.4325274388366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644064869.18/warc/CC-MAIN-20150827025424-00072-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://aviation.stackexchange.com/questions/70709/why-is-the-nose-cone-of-su-34-white | # Why is the nose cone of SU-34 white?
The title says it all.
Can be clearly seen for example in this image:
(image source: Wikimedia)
The rest of the jet seems to have a camouflage.
• Tips of the vertical stabs are also white... – Ron Beyer Oct 16 '19 at 13:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8882731795310974, "perplexity": 2535.525561423855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370493818.32/warc/CC-MAIN-20200329045008-20200329075008-00548.warc.gz"} |
https://brilliant.org/problems/a-mechanics-problem-by-satish-varma/ | A classical mechanics problem by satish varma
Satish(yellow one) has dropped a ball(red one) of unknown mass on an inclined surface with inclination angle 45 degrees. He wants to find the velocity with which it touches ground.he knew horizontal distance between him and where ball touches ground is 20m. help him finding velocity.
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https://www.physicsforums.com/threads/sounds-springs-and-pendelums.467155/ | # Sounds, Springs, and Pendelums
• Start date
• #1
146
0
## Homework Statement
A vibrator moves one end of a rope up and down to generate a wave. The tension in the rope is 63 N. The frequency is then doubled. To what value must the tension be adjusted, so the new wave has the same wavelength as the old one?
(1/2)kx^2
and/or
(1/2)mv^2
## The Attempt at a Solution
I tried using those equations but i am not getting the right answer :/ Please Help. Any assistance would be appreciated. thnk you
Last edited:
• #2
gneill
Mentor
20,925
2,866
How did you try to use those equations? (I ask because they don't appear to be relevant to the problem at hand, so I'm curious).
• #3
146
0
sorry. i edited the question and changed the question but i forgot to change the other 2 parts.
so...
relevant equation:
I know velocity=frequecy*wavelength, but i do not see where tension comes in in this problem. is there another equation i should use?
• #4
gneill
Mentor
20,925
2,866
Do a search on the keywords: wave velocity tension .
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2K | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9421737194061279, "perplexity": 1399.8173447790975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488519735.70/warc/CC-MAIN-20210622190124-20210622220124-00024.warc.gz"} |
https://www.physicsforums.com/threads/what-is-reflection-and-refraction-of-light-at-the-microscopic-scale.549197/ | # What is reflection and refraction of light at the microscopic scale?
Tags:
1. Nov 10, 2011
### Aidyan
I'm not asking for what reflection and refraction are or the usual law governing it, but I would like to understand what they represent at the quantum atomic, molecular level? In a mirror is it about photons absorbed and emitted with the same wavelength and same direction through atomic electron transitions? How can that be? And what is microscopically refraction? Why should a photon traveling between atoms of a trasparent medium change not only its speed but also its direction? I'm a bit confused... Can someone indicate some nice links explaining all that?
2. Nov 11, 2011
### Claude Bile
Reflection and refraction are linked to a single property of a solid; the refractive index. The refractive index is commonly defined as the ratio of the speed of light in the solid compared to the speed of light in a vacuum, however this definition has two main drawbacks.
1. The term "speed of light" is ambiguous when multiple frequencies are concerned, as we can define multiple velocities (group velocity, phase velocity etc).
2. It says nothing about the properties of the solid.
A better definition of refractive index is $1/\sqrt{\epsilon \mu}$ where $\epsilon$ is the electric permittivity and $\mu$ is the magnetic permeability. Permittivity and permeability are defined as the dipoles generated per unit volume, per unit of electric and magnetic field respectively. These are the atomic properties that affect reflection and refraction on an atomic scale.
Claude.
3. Nov 11, 2011
### Aidyan
But why does dipole generation in an amorphous material emit photons always in the same direction? I would have expected an isotropic re-emission of photons in every direction. And how do we have to distinguish dipole generation in the case of reflection from refraction? I think things are a bit more complicate than this.
Last edited: Nov 11, 2011
4. Nov 18, 2011
### Claude Bile
Photons are not being absorbed and re-emitted. Only photons that lie in specific frequency bands are absorbed by any given material. Photons that do not lie in these absorption bands (i.e. those that are transmitted) instead cause the positive and negative charges in nearby atoms to separate (by virtue of the E-field that the photon is a quantum of).
The difference in the laws of reflection and refraction is due to the boundary conditions that apply at an interface between two media with different refractive indices.
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http://mathoverflow.net/users/39339/pepetoro?tab=activity | # PepeToro
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Trying to learn math :)
# 14 Actions
Oct 31 comment “Partition” of a smooth function in $\mathbb R^2$ Well there is not much difference from what I wrote. What @JochenWengenroth wrote above is correct. I hope things are clear now. Oct 31 comment “Partition” of a smooth function in $\mathbb R^2$ By $f_1$ we abbreviate the smooth function of the variables $(xy,x)$ and by $f_2$ the smooth function of the variables $(xy,y)$. Just as shown in the expansion above. Call $w=xy$, then $\hat f_1(w,x)=\sum a_{mn}w^mx^n$ and $\hat f_2(w,y)=\sum a_{mn}w^my^n$, and make the coefficients coincide. Some of them are zero if necessary. Oct 31 comment “Partition” of a smooth function in $\mathbb R^2$ Both $f_i$ are smooth. Both are used at the decomposition. That is why I showed at least the formal level of the proof. Flat means zero Taylor expansion. The result means that a function in two variables may be partitioned as showed. The importance is that it can be done at the level of smooth functions and not only at the level of formal functions. My application is in dynamical systems for example. It may happen that $xy$ is a first integral (a constant along the trajectories of a vector field). Then it is much easier to integrate, say $f$, if we have such a result. Oct 30 revised “Partition” of a smooth function in $\mathbb R^2$ added 571 characters in body Oct 30 comment “Partition” of a smooth function in $\mathbb R^2$ @GHfromMO nope, I really meant what is written. Imagine in the formal series expansion of the form $x^iy^j$, $f_1$ contains monomials where $i\geq j$ and $f_2$ the rest. Oct 30 revised “Partition” of a smooth function in $\mathbb R^2$ edited tags Oct 30 asked “Partition” of a smooth function in $\mathbb R^2$ Sep 24 awarded Autobiographer Aug 5 awarded Editor Aug 5 revised Smooth normal forms of vector fields (the path method) edited body Aug 5 asked Smooth normal forms of vector fields (the path method) Aug 30 revised Stratification of a smooth map edited tags Aug 30 awarded Student Aug 30 asked Stratification of a smooth map | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8275800347328186, "perplexity": 540.8473154554102}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645371566.90/warc/CC-MAIN-20150827031611-00151-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://provital.com.br/fevah-dance-zvkq/038e76-sodium-hydroxide-and-hydrochloric-acid | Reaction 3: An aqueous solution of hydrochloric acid reacts with aqueous ammonia, NH3, yielding aqueous ⦠When strong acids such as H C l (hydrochloric acid) reacts with strong base like N a O H (sodium hydroxide), then neutral salt such as N a C l (sodium chloride) and water are ⦠Apart from a band like cellular 231 infiltrate in the upper dermis and a regenerated epidermis no dermal changes were observed. Both are harmful to skin and eyes. Determination of sodium hydroxide concentration is about as often discussed as hydrochloric acid titration - both acid and base are strong, so calculation of titration curve and equivalence point are pretty straightforward. They will almost always have the same information; I just use Sigma-Aldrich's sheets. View All 406 Related Papers . Reaction 1: An aqueous solution of sodium hydroxide reacts with an aqueous solution of hydrochloric acid, yielding water. \$\endgroup\$ â user51166 Jun 20 '12 at 19:31 \$\begingroup\$ Each manufacturer is required to provide them by law. The equation for any strong acid being neutralized by a strong alkali is essentially just a reaction between hydrogen ions and hydroxide ions to make water. Titration of Hydrochloric acid with Sodium Hydroxide . Sodium hydroxide 0.3 N (days 4 and 6). Reaction 2: An aqueous solution of sodium hydroxide reacts with an aqueous solution of ammoniumm chloride, yielding aqueous ammoniak NH3, and water. Sodium hydroxide 0.5 N. The histochemical stainings were normal. Stage 1 Using a small funnel, pour a few cubic centimetres of 0.4 M hydrochloric acid into the burette, with the tap open and a beaker under the open tap. Has a broad temperature range of 20ºF - - 300ºF [- ... Titanium is resistant to dilute sulfuric and hydrochloric acid, most organic acids, most chlorine gas, and chloride solutions. Apparatus for titrating sodium hydroxide with hydrochloric acid to produce sodium chloride. Three ordinary chemical cleaning agents (hydrochloric acid, sodium hydroxide, and sodium hypochlorite) ...Read More . exactly right because Hydrochloric acid well is an acid and Sodium hydroxide is a base, and when you mix acids and bases they neutralize creating a salt of some sort and water. 02 Thursday, December 19, 2013 Introduction The following lab was an acid-base neutralizing titration. Hydrochloric acid is a one normal solution which means that for each mole of HCl one mole of H+ or acid is liberated requiring one mole of hydroxide (OH-) to neutralize. For example, dilute hydrochloric acid contains hydrogen ions and chloride ions in solution. Changes on days 4-7 Hydrochloric acid 0.5 and 1 N (only day 7). Purpose: The purpose of this lab is to No dermal changes were seen. Sodium hydroxide reacts with hydrocloric acid according to the equation: NaOH + HCl â> NaCl + H2O A titration is a technique, in which a reagent, called a titrant, of known concentration is used to determine the concentration of an analyte or Cautions: Hydrochloric acid solution is a strong acid. \$\endgroup\$ â Canageek Jun 21 '12 at 4:34 caustic [sodium hydroxide] and low molecular weight organics. This simple formula is often used to represent an acid. The pH neutralization of Hydrochloric acid is conventional and any inorganic base such as sodium hydroxide or lime can be used. Sodium hydroxide solution is a strong base. Sodium hydroxide solution consists of sodium ions and hydroxide ions in solution. However, titration itself is not as easy. Affected areas should be washed thoroughly with copious amounts of water. Would sodium persulfate be safer to store than hydrochloric acid by the way ? SCH3U. general remarks. 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Was an acid-base neutralizing titration and a regenerated epidermis no dermal changes were observed to store than acid! Of water to provide them by law them by law provide them by law acid, yielding.... Used to represent an acid dilute hydrochloric acid by the way often used represent! | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8174593448638916, "perplexity": 7855.559455725067}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587926.9/warc/CC-MAIN-20211026200738-20211026230738-00687.warc.gz"} |
http://mathhelpforum.com/calculus/49247-spheres-circles-things.html | # Thread: Spheres and circles and things
1. ## Spheres and circles and things
Hey everyone,
I was just curious about something:
Say you had a normal polygon with $n$ sides. As $n$ approaches infinity, your polygon begins to look more and more like a circle.
We could define a straight line to be 180 degrees.
We know that the equation of the sum of the interior angles $\theta i$ of a polygon is:
$\theta i = (n - 2)(180) = 180n - 360$
We know that the measure of a single interior angle $\alpha$ is:
$\alpha = \frac {180n - 360}{n}$
When we take the limit of n as n approaches zero:
$\lim_{n\rightarrow\infty} \frac {180n - 360}{n} = 180$ By L'Hopitals rule
It's weird to me, because it seems like the curve of a circle is flat, but also curved. What if you visualized this in three dimensions? Does that mean that the surface of a sphere is 2 dimensional?
2. Hi,
actually, the same 180° value would have appeared with any smooth curve, not specifically with a circle. The reason for this is that if you draw a line between a fixed point A on a curve and another point M on the same curve then, as the point M tends to A along the curve, the line (AM) converges (in a sense that can be made rigorous) to the tangent line to the curve at A. This tangent line is the same if M tends to A from the left or the right, hence the flat angle (the angle between the two directions of the tangent at A).
In three dimensions, on a smooth surface, you have a similar property, namely that the line (AM) would get nearer and nearer to the tangent plane as M tends to A, and a plane (AMN) would converge to the tangent plane as M and N tend to A along curves drawn on the surface that are not tangent to each other at A. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.791896402835846, "perplexity": 206.5545672345522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542932.99/warc/CC-MAIN-20161202170902-00054-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://guido.vonrudorff.de/2019/resampling-grids-for-integration/ | # Resampling grids for integration
When evaluating an integral on a grid, the finite resolution thereof can affect the accuracy of the result. In the context of atomistic simulation, this is because a slight change in nuclear coordinates will affect the mapping on the grid.
For smooth properties like the electron density, there is a workaround. Akin to Simpson’s rule where polynomials are fitted to the grid points first and then the piecewise defined polynomials are integrated, a refinement of the grid can achieve the similar improvements in integration.
While the smart way would be to not build the grid in memory but rather integrate as you go, the following is a simple and reasonably fast implementation by explicit grid refinement in python.
``````import numpy as np
import scipy.ndimage as snd
import matplotlib.pyplot as plt
# generate data to operate on
data = np.arange(16).reshape(4, 4).astype(np.float)
data[0, 3] = 0
data[0, 1:3] = 5
# visualisation only
f, axs = plt.subplots(1, 2, dpi=300)
ax_2d, ax_scan = axs
ax_2d.imshow(data)
# refine grid: build grid
X, Y = np.mgrid[0:3:50j, 0:3:50j]
positions = np.vstack([X.ravel(), Y.ravel()])
for order in range(6):
# refine grid: fit splines, re-evaluate function on grid
a = snd.map_coordinates(data, positions, mode='nearest', order=order)
ax_scan.plot(np.linspace(0, 3, 50), a[:50], label='Order %d' % order)
ax_scan.legend()``````
The parameter order specifies the interpolation order. You’ll need to set it to match your computational problem. This solution generalizes to arbitrary dimensions, even though the number of gridpoints scales unfavourably. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.882988452911377, "perplexity": 2590.2462138957885}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370524043.56/warc/CC-MAIN-20200404134723-20200404164723-00176.warc.gz"} |
https://mathhelpboards.com/threads/muffins-gcse-additional-maths-moments-question-from-y-answers.2474/ | ### Welcome to our community
#### CaptainBlack
##### Well-known member
Jan 26, 2012
890
Two painters of mass 50kg and 70 kg stand on a uniform horizontal plank ABCDEFG of mass 40kg and length 8m.
B, C, D and E are respectively 1m, 2m, 5m and 6m from A. The 50kg painter stands at B, the 70kg painter at D and the plank's supported at C and E.
Find the reaction at each support I got the answers to be 1053.5 and 514.5 but my answer book tells me otherwise (although it has been wrong before) can someone please check this and explain where I've gone wrong please?
CB
#### CaptainBlack
##### Well-known member
Jan 26, 2012
890
Two painters of mass 50kg and 70 kg stand on a uniform horizontal plank ABCDEFG of mass 40kg and length 8m.
B, C, D and E are respectively 1m, 2m, 5m and 6m from A. The 50kg painter stands at B, the 70kg painter at D and the plank's supported at C and E.
Find the reaction at each support I got the answers to be 1053.5 and 514.5 but my answer book tells me otherwise (although it has been wrong before) can someone please check this and explain where I've gone wrong please?
CB
Since the reaction forces must sum to the total load (the two painters and the weight of the plank acting at the centre of mass of the plank) which is $$160g = 1569.6 \, {\rm{N}}$$ (taking $$g$$ to be $$9.81\, {\rm{m/s^2}}$$ ) your answer is not impossible so far (using $$g=9.8\, {\rm{m/s^2}}$$ we have exact agreement).
You need to set up a pair of simultaneous equations under the assumption that the system is in equilibrium, the first is that the reaction forces sum to the load forces:
$$R_C+R_E = 160 g$$
The second is obtained by taking moments about some convenient point, as the system is in equilibrium these must sum to zero. A convenient point (as it eliminates one of the unknowns) is either C or E.
$$4 R_C -2 (40 g) -5 (50 g) - 1 (70 g) =0$$
$$R_C = 100 g\, {\rm{N}}$$ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9246149063110352, "perplexity": 730.8624281139811}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107874135.2/warc/CC-MAIN-20201020192039-20201020222039-00225.warc.gz"} |
https://www.tutorialspoint.com/fillpoly-function-in-c | # fillpoly() function in C
CServer Side ProgrammingProgramming
#### C in Depth: The Complete C Programming Guide for Beginners
45 Lectures 4.5 hours
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## Concept
Now the header file graphics.h contains fillpoly() function which is implemented to draw and fill a polygon such as triangle, rectangle, pentagon, hexagon etc. So this function require same arguments as drawpoly().
## Syntax
void fillpoly( int number, int *polypoints );
In this case,number indicates (n + 1) number of points where, n is the number of vertices in a polygon and polypoints points to a sequence of (n*2) integers.
Input
arr[] = {320, 150, 400, 250, 250, 350, 320, 150};
Output
Explanation
So the declaration of fillpoly() contains two arguments: number specifies (n + 1) number of points where n is indicated as the number of vertices in a polygon.The second argument, such as, polypoints points to a sequence of (n * 2) integers. As a result of this,each pair of integers provides x and y coordinates of a point on the polygon. So we indicate (n + 1) points because first point coordinates should be equal to (n + 1)th for drawing a complete figure.
## Example
// C Implementation for fillpoly()
#include <graphics.h>
// driver code
intmain(){
// Here gm1 is Graphics mode which is a computer display mode that
// produces image using pixels. DETECT is a macro defined in
// "graphics.h" header file
intgd1 = DETECT, gm1;
// Different coordinates for polygon
intarr1[] = {320, 150, 400, 250, 250, 350, 320, 150};
// Here initgraph initializes the
// graphics driver from disk
initgraph(&gd1, &gm1, "");
// fillpoly function
fillpoly(4, arr1);
getch();
// Here closegraph function closes the
// graphics mode and deallocates
// all memory allocated by
// graphics system .
closegraph();
return0;
}
## Output
Updated on 23-Jul-2020 08:18:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19933286309242249, "perplexity": 8527.110091645705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710534.53/warc/CC-MAIN-20221128171516-20221128201516-00092.warc.gz"} |
https://en.wikipedia.org/wiki/Talk:Cumulant | # Talk:Cumulant
WikiProject Statistics (Rated C-class, High-importance)
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Field: Probability and statistics
## (d/dt) log E(etX) as cumulant generation function
The formula
$E\left(e^{tX}\right)=\exp\left(\sum_{n=1}^\infty\kappa_n t^n/n!\right)\,$
might be written
$\log E\left(e^{tX}\right)=\sum_{n=1}^\infty\kappa_n t^n/n!\,$
The constant term is found by setting t = 0:
$\log E\left(e^0\right)=0$
Zero is not a cumulant, and so the function
$\frac{d}{dt}\log E\left(e^{tX}\right)=\sum_{n=0}^\infty\kappa_{n+1} t^n/n!=\mu+\sigma^2t+\cdots$
better deserves the name 'cumulant generation function'.
Bo Jacoby 12:55, 4 January 2006 (UTC)
I agree that there's no zeroth-order cumulant. But I don't think that's a reason to change the convention to what you've given here. In that version, the coefficient of tn/n! is not the nth cumulant, and that is potentially confusing. Besides, to speak of a zeroth cumulant and say that it's zero regardless of the probability distribution seems harmless at worst. Michael Hardy 00:03, 9 January 2006 (UTC)
I understand your reservations against changing conventions. Note, however, the tempting simplification obtained by differentiation.
The (new cumulant generation function of the) degenerate distribution is 0;
The (..) normal distribution is t.
The (..) bernoulli distribution is (1+(p−1−1)e−t)−1
The (..) binomial distribution is n(1+(p−1−1)e−t)−1
The (..) geometric distribution is (−1+(1−p)−1e−t)−1
The (..) negative binomial distribution is n(−1+(1−p)−1e−t)−1
The (..) poisson distribution is λet
Bo Jacoby 12:21, 31 January 2006 (UTC)
The last point kills your proposal: one wants to be able to speak not only of compositions of cumulant-generating functions, but of compositional inverses in cases where the expected value is not 0. So one wants the graph of the function to pass through (0, 0), with nonzero slope when the expected value is not 0. Michael Hardy 22:54, 31 January 2006 (UTC)
What do you mean? Please explain first and conclude later. The two definitions allow the same operations. The new definition just does not contain a superfluous zero constant term. The graph of the new cumulant-generating function passes through (0, μ) having the slope σ2. Curvature shows departure from normality: μ+σ2t. Bo Jacoby 09:14, 1 February 2006 (UTC)
I don't like that kind of definition for the cumulant generating function. Imagine you have a random variable X and a constant a. If K(t) is the cumulant generating function for X, then what is the cumulant generating function for aX? Using the standard definition it's K(at) whereas using your definition it would be aK(at) which is more complicated. Ossi 22:41, 4 April 2006 (UTC)
I'll comment further on Bo Jacoby's comments some day. But for now, let's note that what is in the article has been the standard convention in books and articles for more than half a century, and Wikipedia is not the place to introduce novel ideas. Michael Hardy 22:55, 4 April 2006 (UTC)
## cumulant (encyclopedia)
I came randomly to see the article : no explanation about a cumulant were in view. A TOC was followed by formulas.
We math people love what we do. Let us try to do more : explain what we do (for this, I need help).
• What class of math object is that
• Who uses it and for what
• Are there plain related concepts to invoke, &c. ? Thanks --DLL 18:47, 9 June 2006 (UTC)
P.S. Wolfram, for example, gives links to : Characteristic Function, Cumulant-Generating Function, Fourier Transform, k-Statistic, Kurtosis, Mean, Moment, Sheppard's Correction, Skewness, Unbiased Estimator, Variance. [Pages Linking Here]. Though I cannot tell if it is pertinent here, maybe a little check might be done ? Thanks again. --DLL 18:56, 9 June 2006 (UTC)
The very first sentence in the article says what cumulants are. Michael Hardy 21:20, 9 June 2006 (UTC)
It only describes what cumulants are, I do not see a formal definition anywhere. As a general rule, shouldn't the first thing in such an article be the definition? Can someone please add the definition? --Innerproduct (talk) 20:45, 2 April 2010 (UTC)
No, that's a very very bad proposed general rule. Sometimes the first sentence should be a definition; more often it should not. One must begin by acquainting the lay reader with the fact that this is a concept in mathematics; sometimes stating the general definition in that same sentence conflicts with that goal. Michael Hardy (talk) 22:27, 2 April 2010 (UTC)
"Innerproduct", I see that you commented nearly four years after the comment you're replying to. It should be perfectly obvious that that comment was about the article as it existed in 2006, and is no longer relevant to the article in its present form.
Your proposed general rule is very bad (even though in some particular cases it makes sense); following it extensively would require people to clean up after you. Michael Hardy (talk) 22:36, 2 April 2010 (UTC)
## joint cumulant
I think that in the formula
$\kappa(X_1,\dots,X_n) =\sum_\pi\prod_{B\in\pi}(|B|-1)!(-1)^{|B|-1}E\left(\prod_{i\in B}X_i\right)$
the number |B| of elements in B should be replaced by the number $|\pi|$ of blocks in $\pi$.
For example, in the given case n=3
$\kappa(X,Y,Z)=E(XYZ)-E(XY)E(Z)-E(XZ)E(Y)-E(YZ)E(X)+2E(X)E(Y)E(Z).\,$
the constant before the term E(XYZ) (which corresponds to $\pi=\{\{1,2,3\}\}$ : only one block of 3 items, i.e. |\pi|=1 and \pi={B} with |B|=3) is $1=(|\pi|-1)!$ and not $2=(|B|-1)!$.
That is certainly correct in this case, and I think probably more generally. I've changed it; I'll come back and look more closely later. Michael Hardy 17:41, 19 September 2006 (UTC)
## Intro
We need an intro --dudzcom 04:52, 24 December 2006 (UTC)
Seconded. I'm a stats n00b and without a basic intro, the encyclopaedic content lacks a basic context. Jddriessen 14:12, 3 March 2007 (UTC)
## k-statistics
I think we should have a section on k-statistics. Could someone knowledgeable write a section describing them and explaining why they are unbiased estimators for the cumulants. Ossi 18:04, 30 December 2006 (UTC)
I have been trying to find information about unbiased and other estimators for ratios of powers of cummulants. In particular, I am interested in estimators for the particular ratio $\frac {{\kappa_{{1}}}^{2}}{\kappa_{{2}}}$. I can use k-statistics to estimate this ratio as simply $\frac {{k_{{1}}}^{2}}{k_{{2}}}$ where $k_{n}$ is the $n^{th}$ k-statistic. This should work, but it is a biased estimator. Are there better, unbiased estimators? User:155.101.22.76 (Talk) 28 Oct 2008
You may find something about this in Kendall&Stuart Vol 1. If there is nothing there, it may not be possible to do anything straightforwardly. Unbiassedness may not necessarily be particularly relevant to you, but if it is then you might try the jackknifing and bootstrapping methods for reducing bias. Melcombe (talk) 09:44, 29 October 2008 (UTC)
The library at my university does not have Kendall&Stuart Vol 1. However, they do have K&S Vol. 2. The first chapter of Vol. 2 is on estimation. Problem 17.10 turns out to be very close to what I need. Assuming normally distributed r.v. and some limits on the allowed values for m and r the Minimum Variance Unbiased Estimator (MVUE) for $\kappa_{1}^{r}\,\kappa_{2}^{m}$ is given by:
$\sum _{i=0}^{1/2\,r}{\frac { \left( -1 \right) ^{i}r!\,\Gamma \left(\frac{\left(n-1\right)}{2}\right) {k_{{1}}}^{r-2\,i} \left( \frac{\left( n-1 \right)}{2} k_{{2}} \right) ^{m+i}}{i!\, \left( r-2\,i \right) !\,\Gamma\left( \frac{\left(n-1\right)}{2}+m+i \right) \left( 2\,n \right) ^{i}}}$
In my case $\kappa_{1}^{2}\,\kappa_{2}^{-1} , r =1, m = -1$, and this reduces to:
$\left(\frac{\left(n-3\right)}{\left(n-1\right)}\frac{k_{1}^2}{k_{2}} - \frac{1}{n}\right)$
Which is precisely the same estimator I derived using other methods also assuming a normal distribution. I did not know that you could reduce bias using jackknifing and bootstrapping methods. Doh! That is great. The distributions I am working with are close to normal. I should be able to use the above MVUE and then reduce any remaining bias using jackknifing or bootstrapping. Thanks. --Stanthomas (talk) 17:34, 30 October 2008 (UTC)
## Cumulant "basis"?
It appears that you can reconstruct a function from its cumulants; that is, it seems like the cumulants define a "basis" of sorts the same way the sin and cos functions define a Fourier basis. Of course, a function isn't a linear combination of its cumulants, so it's not a linear basis, but in some sense it still seems like a basis. Comments? 155.212.242.34 (talk) 22:23, 11 December 2007 (UTC)
If two finite multisets of numbers have the same cumulant generating function, they are equal. The concept of a random variable is somewhat more general than just a multiset of numbers, and complications arise. It is worth while to understand multisets before trying to understand random variables. The derivative of the cumulant distribution function of a continuous random variable should be considered the limiting case of a series of derivatives of cumulant distribution functions of finite multisets of numbers. As probability density functions are nonnegative, they do not make vector spaces, and so the concept of basis does not immediately apply. Bo Jacoby (talk) 16:33, 19 March 2008 (UTC).
## Error in formula
Quote: Some writers prefer to define the cumulant generating function, via the characteristic function, as h(t) where
$h(t)=\log(E (e^{i t X}))=\sum_{n=1}^\infty\kappa_n \cdot\frac{(it)^n}{n!}=\mu\cdot t - \sigma^2\cdot\frac{ t^2}{2} +\cdots\,.$
I suppose the formula should be:
$h(t)=\log(E (e^{i t X}))=\sum_{n=1}^\infty\kappa_n \cdot\frac{(it)^n}{n!}=\mu\cdot i\cdot t - \sigma^2\cdot\frac{ t^2}{2} +\cdots\,.$
Is there a reference? Bo Jacoby (talk) 00:43, 20 March 2008 (UTC).
You're right; the factor of i was missing. I don't think it should be too hard to find references. I wouldn't be surprised if this is in McCullagh's book. Michael Hardy (talk) 18:06, 21 March 2008 (UTC)
References added to article, for this point at least. The Kendall and Stuart ref would be good for many other of the results quoted (but a later edition might be sought out?). Melcombe (talk) 09:18, 17 April 2008 (UTC)
## Improve intro ?
At the end of the intro, the final sentance says: "This characterization of cumulants is valid even for distributions whose higher moments do not exist." This seems to dangle somewhat...
• exactly what is refered to by "this characterisation"?
• it seems to imply there are other characterisations?
• it seems to imply that cumulants might exist even if higher moments do not exist?
Melcombe (talk) 09:30, 17 April 2008 (UTC)
Probably could be improved; I'll think about it. When higher moments do not exist, then neither do higher cumulants. In that case, the characterization of cumulants that says the cumulant-generating function is the logarithm of the moment-generating function is problematic. That is what is meant. As far as other characterizations go, yes of course there are. Michael Hardy (talk) 21:10, 17 April 2008 (UTC)
## Joint cumulants
I want to know more about Joint Cumulants, but this section made no reference to any books or papers. Any suggestions? Thanks! Yongtwang (talk) 13:47, 13 May 2010 (UTC)
You could try the existing Kendall&Stuart reference. It is old but covers the multivariate case, both for theoretical and sample versions of the joint cumulants. Melcombe (talk) 14:52, 14 May 2010 (UTC)
Hey, thanks for the information. I am reading it. Yongtwang (talk) 12:05, 16 May 2010 (UTC)
## Some properties of the cumulant-generating function
The article states that the cumulant-generating function is always convex (not too hard to prove). I wonder if the converse holds: any convex function (+ maybe some regularity conditions) can be a cumulant-generating function of some random variable. // stpasha » 20:03, 2 March 2011 (UTC)
## Applicability to Quantum Mechanics
I was reading this article to get a more broad background on the cumulant expansion, which is useful in quantum mechanical simulations of spectroscopic signals (absorption, pump-probe, raman, etc). I was somewhat surprised not to see quantum mechanics mentioned at all in the article. The source that I'm currently following on this topic:
Shaul Mukamel's "Principles of Nonlinear Optical Spectroscopy" (ISBN: 0-19-513291-2).
The expansions are debuted in Ch2, "Magnus Expansion". Ch 8 is also devoted entirely to their practical use.
Side note: It amused me that there were "citation needed" marks on the phrase, "Note that expectation values are sometimes denoted by angle brackets". This notation is so ubiquitous in quantum mechanics that one could literally pick up any quantum textbook and insert it as a "source" to verify that this is common practice. Certainly the book I just mentioned could count as such a source. —Preceding unsigned comment added by 24.11.171.13 (talk) 23:26, 20 May 2011 (UTC)
I looked in the comments specifically to discuss the "citation needed" marks for angle bracket denotation of expectation values. It's like asking for a citation that addition is sometimes denoted with a plus sign. I'm going to remove it and someone can put it back in if they feel it's really necessary. Gregarobinson (talk) 16:14, 17 June 2011 (UTC)
## Should "Relation to statistical physics" be deleted?
Some formulas in section "Relation to statistical physics" are wrong. Instead of:
$Z(\beta) = \langle\exp(-\beta E)\rangle$
$Z(\beta) = \sum_i\exp(-\beta E_i)$
as found in any relevant textbook or the wiki page for the partition function itself. This breaks the following argument linking F(\beta) to the cumulant generating function for the energy \log Z, as Z is no longer an average. The same critic holds for the grand potential at the end of the section, which is also a sum, not an average.
The equations linking E and C to the corresponding cumulants of the energy are still valid, since the cumulants equal the moments (section "Some properties of cumulants"). However, the interpretation in terms of moments is quite widespread, and in fact the equation:
$E = \langle E_i \rangle,$
is considered a postulate, in which the energy is linked to an average. The addition of usage of cumulants in stat. mech. that can't be expressed more naturally in terms of moments should be made, if such an usage exists.
Futhermore, the section doesn't cite any source, and none of the article's sources seems relevant at first sight.
These three points make me feel the whole section is rather weak. I suggest it should be deleted. --Palatosa (talk) 19:53, 19 April 2013 (UTC)
## Minor error in the section "Some properties of the cumulant generating function" ?
There is something strange with the statement "The cumulant-generating function will have vertical asymptote(s) at the infimum of such c, if such an infimum exists etc". Note that x is a negative number here. Something being O(exp(2x)) is a tougher requirement than being O(exp(x)) when x tends to minus infinity. You get the toughest requirement possible by finding the supremeum over c. But changing infimum to supremum doesnt seem right either. Should there be some sign change also? — Preceding unsigned comment added by 89.236.1.222 (talk) 22:12, 17 October 2014 (UTC)
## Given definition is only a special case
The definition given requires the moment generating function to exist. Rather than change the definition to use the characteristic function, we just need a note that the relation between moments and cumulants given later, can be used as the definition. TerryM--re (talk) 04:18, 12 February 2015 (UTC)
If the definition given apply to the examples given, then generalizations may be postponed or omitted in order not to confuse the readers unnecessarily. Bo Jacoby (talk) 19:26, 25 May 2015 (UTC).
## Problems with statistics
This article is very good and informative but someone has a flag on it to improve citations. Standard approaches do not apply to mathematical subjects, where inline citations are not as frequent, and usually one cites a theorem or a result, with plenty of references in back. Limit-theorem (talk) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8715348839759827, "perplexity": 1092.067362745936}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398456289.53/warc/CC-MAIN-20151124205416-00037-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://wikieducator.org/OMD/622/Incentive_Systems_for_Teens | # OMD/622/Incentive Systems for Teens
< OMD | 622
Work in progress, expect frequent changes. Help and feedback is welcome. See discussion page.
### Context
This situation has been brought about by a Mom in NZ, wanting to get her 18-year old son to text her and husband more often.
• My name is Sarah and I have a son who has just turned 18. He has started going 'out on the town' at the weekend in the evenings. There have been an number of serious incidents in town where young people have been attacked & seriously hurt. My son is a responsible young man but I am concerned that he'll be dragged into 'trouble'. I do not want to (and cannot) stop him going out, but I just want to know that he is safe. So I have asked him to text me to let me know how he is and when he'll be home, so I know not to worry about him. But he never texts me. Consequently, I have woken up at late at night and not known where/how he is. This may sound like I am fussing too much but I believe that he still needs boundaries to guide his behavior.
I would like to develop a plan that will encourage him to keep in touch with me by text so that I know he is safe and he can have fun without me nagging him all the time.
• Nag, nag, nag (parent)
• Get rebellious behaviour (teen)
• Ground the difficult one (this is the teen, from the parent's point of view)
• Set the stage for future rebellious and cantankerous behaviour (i.e., no-one's needs get met)
### A Different Approach: Incentive System to Reward Performance
#### Design Phase
• Interview individual to find out what he wants, and / or values the most - this could have a cash / non-cash value; could also be small or large (say: $100,$500 dollars, for example)
• Sample Questions (below)
• What do you consider is a reasonable time to be expected home at night?
• What do you think is the best way to communicate your plans to your parents?
• At what time intervals do you think it is reasonable to contact your parents about your plans?
• What do you think you should do with regards to informing your parents about your change of plans?
• What would you do in an emergency?
• What would encourage you to keep in regular contact with your parents when you are out at night?
• What do you think should happen if you do not keep to your agreement with your parents?
• Insert feedback below (i.e., interview results)
• Home by 3am
• Quick knock on our bedroom door to say he's home
• Text at 1am to check in with us
• Text at 3am if there is a change of plan eg he is going to stay night with his sister
• Text if there is any trouble or emergency
#### Sarah's Bottom Line
I don't want to wake up in the morning and find an empty bed and not know where he is.
• I guess one of the discussions we need to have now is about what time is 'home time'.
• What do people think is a reasonable home time for an 18 year old. (: Who are the 'people' you are referring to? Are they parents, the boy's peers? How are you going to get this information? Are you going to use all of it, some of it, or some of it in stages)
• I am going to ask my son the questions I have developed above and also his friends. It would also be interesting to get some feedback from parents so I might have a ring around of some parents I know. Any suggestions from the community here will be gratefully received.
• Cash would probably be the strongest incentive. But I am reluctant to go down that road because he really should do this as a matter of course - it is not an 'extra', but an 'essential' behaviour. If I use cash, it will have to be a much smaller amount. (: Sarah - the purpose of the cash / non-cash incentive is really to give him a goal....and then to set in place incentives to reach that goal, to achieve the essential behaviour that You Require).
• Yes, I realised that was a stupid statement as soon as I saved it, considering this is an incentive program. I'll get some feedback first about what my son and his friends think is a reasonable incentive.
Why don't you speficy an amount that you would be willing to spend.....The key is though, it's about what the boy wants....and there are different ways to achieve that - beyond what you might be thinking....remember, we have a whole community of support here!
coming soon! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.293030709028244, "perplexity": 1180.266905765826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805894.15/warc/CC-MAIN-20171120013853-20171120033853-00029.warc.gz"} |
http://math.stackexchange.com/questions/112183/multiple-instances-of-random-generator | # Multiple instances of random generator
I wonder whether following methodology is correct.
I need to introduce concurrent processing to my simulating application.I want to use Mersenne Twister random generator. I wonder whether I can create a few instances of this generator (initialized with different seed, base on time of creation) and use them in separated threads. The problem is whether there will be no connection between values I get from multiple instances of random generators initialized with different seeds.
Do you have any experience with it / advices ?
(I know that this question might be asked in stackoverflow however I think that is a little bit more mathematical problem).
-
## 1 Answer
It depends on how many random draws you're likely to make from the generator, how many threads you will be running and how long the cycle length of the generator is.
The main problem with parallel Monte Carlo comes from overlap of random sequences initialized with different seeds.
As a very rough approximation, if the cycle length is $N$ and you are running $q$ threads, each of which makes $n$ draws, then you are effectively choosing $p$ objects from among $p=N/n$. Therefore the probability that none of your sequences overlap is roughly
$$f(N,n,p) = \frac{p(p-1)\cdots(p-q+1)}{p^q} = \frac{p!}{(p-q)! p^q}$$
As long as this number is significantly less than 1, you should be fine.
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https://www.lessonplanet.com/teachers/sentence-strategies | # Sentence Strategies
In this using sentence strategies worksheet, students combine short sentences, rewrite long sentences as two or more sentences, and write a descriptive paragraph. Students write eleven answers. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9211933612823486, "perplexity": 20412.6147687562}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607806.46/warc/CC-MAIN-20170524074252-20170524094252-00181.warc.gz"} |
https://www.juliahomotopycontinuation.org/3264/ | ## 3264 conics tangent to five conics
All of them can be real.
A conic in the plane $\mathbb{R}^2$ is the zero set of a quadratic polynomial in two variables:
$$a_1 x^2 + a_2 xy + a_3 y^2 + a_4 x + a_5 y + a_6 .$$
Geometrically, a conic can be either a circle, an ellipse, a hyperbola, a parabola or a union of two lines. The last case is a degenerate conic. Double lines are allowed.
A classic problem in enumerative geometry is Steiner's conic problem which asks:
*How many conics are tangent to five given conics?*
Here is an example of Steiner's problem:
Steiner claimed in 1848 that there are at most 7776 conics tangent to 5 given conics. He phrased his problem as that of solving five equations of degree six on the 5-dimensional projective space $\mathbb{P}^5$. Using Bézout's Theorem he argued that the equations coming from this question have $6^5 = 7776$ solutions over the complex numbers. However, this number over counts because there is a Veronese surface of extraneous solutions, namely the conics that are squares of linear forms, i.e., double lines.
The correct count of non-degenerate conics is 3264. This was shown in 1859 by Jonquières and independently in 1864 by Chasles. The number 3264 appears prominently in the book 3264 and all that by Eisenbud and Harris.
A delightful introduction to Steiner's problem was given by Bashelor, Ksir and Traves. Ronga, Tognoli and Vust and Sottile showed how to choose 5 real conics such that all 3264 complex solutions are real. Although their proofs starts with an explicit construction, it is not constructive.
Using methods from numerical algebraic geometry we adapted the proposed construction to find an explicit instance for which there are 3264 real conics. We use numerical homotopy continuation to compute the 3264 conics. Smale's $\alpha$-theory provides a way to give a mathematical proof that we found 3264 real conics; the keyword is alphaCertified. The computational proof can be downloaded here.
An illustration of the arrangement is shown below.
It looks like the arrangement consists of 5 blue lines, rather than 5 blue conics. The next picture clarifies the situation.
More details on the geometry of these five special conics are in our article 3264 conics in a Second. There is also an interactive plot for GeoGebra, which lets you zoom in at the points of tangency. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5575757622718811, "perplexity": 507.6036877227053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487612537.23/warc/CC-MAIN-20210614135913-20210614165913-00495.warc.gz"} |
https://www.physicsforums.com/threads/decomposition-of-sl-2-c-weyl-spinors.469594/ | # Decomposition of SL(2,C) Weyl Spinors
• Start date
• #1
213
8
## Homework Statement
Using
$$(\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \epsilon_{\alpha \gamma} \epsilon^{\beta \delta} + \delta^{\delta}_{\alpha} \delta^{\beta}_{\gamma}$$
show that
$$\Psi_{\alpha} X_{\beta} = \frac{1}{2} \epsilon_{\alpha \beta} (\Psi X) + \frac{1}{2} (\sigma^{\mu \nu} \epsilon^{T})_{\alpha \beta} (\Psi \sigma_{\mu \nu} X)$$
## The Attempt at a Solution
if I do $$(\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} \Psi _{\beta} X_{\delta}$$
I can get
$$\Psi_{\beta} X_{\alpha} = \epsilon_{\alpha \beta} (\Psi X) + (\sigma^{\mu \nu} \epsilon^{T})_{\alpha \beta} (\Psi \sigma_{\mu \nu} X)$$
so i don't know where the factors of a half come from and how to get the right index order
Last edited:
• #2
fzero
Homework Helper
Gold Member
3,119
289
I find
$$(\sigma^{\mu \nu} \epsilon^{T})_{\alpha \beta} (\Psi \sigma_{\mu \nu} X) = \Psi_{\alpha} X_{\beta}+ \Psi_{\beta} X_{\alpha}.$$
• #3
dextercioby
Homework Helper
13,077
645
The 1/2 must come from the symmetrization
$$\Psi_{\beta}X_{\alpha} = \frac{1}{2} \left(\Psi_{\beta} X_{\alpha}+\Psi_{\alpha} X_{\beta}\right) + \frac{1}{2} \left(\Psi_{\beta} X_{\alpha}-\Psi_{\alpha} X_{\beta}\right)$$
The a-symmetric part must be proportional to the spinor metric, the symmetric one is what's left.
• #4
213
8
I find
$$(\sigma^{\mu \nu} \epsilon^{T})_{\alpha \beta} (\Psi \sigma_{\mu \nu} X) = \Psi_{\alpha} X_{\beta}+ \Psi_{\beta} X_{\alpha}.$$
how did you get that without a factor of two and if it is correct then symmetrising solves it
• #5
fzero
Homework Helper
Gold Member
3,119
289
how did you get that without a factor of two and if it is correct then symmetrising solves it
That follows directly from the stated identity. Just put in the correct indices and keep track of the $$\epsilon$$ contractions.
• #6
213
8
sorry for being dense but if I would have known how to manipulate this spinor algebra i wouldn't be asking, so please be more explicit
• #7
fzero
Homework Helper
Gold Member
3,119
289
sorry for being dense but if I would have known how to manipulate this spinor algebra i wouldn't be asking, so please be more explicit
You should really give it try first or at least point out exactly which term you don't understand.
• #8
213
8
I've been stuck on this for a day
what I don't understand is why it isn't
$$\bold 2 (\sigma^{\mu \nu} \epsilon^{T})_{\alpha \beta} (\Psi \sigma_{\mu \nu} X) = \Psi_{\alpha} X_{\beta}+ \Psi_{\beta} X_{\alpha}.$$
even looking at double epsilon identity in two dimensions you get
$$(\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \delta^{\beta}_{\alpha} \delta^{\delta}_{\gamma}$$
which gives you a factor of two in that calculation you did
at least give me the starting point of that calculation
Last edited:
• #9
fzero
Homework Helper
Gold Member
3,119
289
I've been stuck on this for a day
what I don't understand is why it isn't
$$\bold 2 (\sigma^{\mu \nu} \epsilon^{T})_{\alpha \beta} (\Psi \sigma_{\mu \nu} X) = \Psi_{\alpha} X_{\beta}+ \Psi_{\beta} X_{\alpha}.$$
even looking at double epsilon identity in two dimensions you get
$$(\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \delta^{\beta}_{\alpha} \delta^{\delta}_{\gamma}$$
You're missing part of this expression.
which gives you a factor of two in that calculation you did
at least give me the starting point of that calculation
$$(\sigma^{\mu \nu} \epsilon^{T})_{\alpha \beta} (\Psi \sigma_{\mu \nu} X) = {(\sigma^{\mu \nu})_\alpha}^\gamma \epsilon_{\beta \gamma} \Psi^\delta {( \sigma_{\mu \nu} )_\delta}^\epsilon X_\epsilon .$$
Use
$${(\sigma^{\mu \nu})_{\alpha}}^{\beta} {(\sigma_{\mu \nu})_{\gamma}}^{\delta} = \epsilon_{\alpha \gamma} \epsilon^{\beta \delta} + \delta^{\delta}_{\alpha} \delta^{\beta}_{\gamma}$$
and $$\Psi^\alpha = \epsilon^{\alpha\beta}\Psi_\beta$$.
• #10
213
8
thank you it seems I made the mistake of having three repeated indicies
but this is correct
$$(\sigma^{\mu \nu})^{\beta}_{\alpha} (\sigma_{\mu \nu})^{\delta}_{\gamma} = \delta^{\beta}_{\alpha} \delta^{\delta}_{\gamma}$$
otherwise you can't derive the rest
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2K | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9152948260307312, "perplexity": 2113.691273120054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488519735.70/warc/CC-MAIN-20210622190124-20210622220124-00481.warc.gz"} |
http://math.stackexchange.com/questions/170943/dedekinds-theorem-on-an-integrally-closed-algebra-over-a-commutative-ring-witho | # Dedekind's theorem on an integrally closed algebra over a commutative ring without Axiom of Choice
Motivation This question came from my efforts to solve this problem presented by Andre Weil in 1951.
Can we prove the following theorem without Axiom of Choice? If the answer is affirmative, by using this, we can get many examples of Dedekind domains without using Axiom of Choice. This is a related question.
Theorem Let $A$ be a commutative ring. Let $B$ be an integrally closed $A$-algebra. Suppose $B/fB$ has a composition series as an $A$-module for every non-zero element $f$ of $B$. Then the following assertions hold.
(1) Every ideal of $B$ is finitely generated.
(2) Every non-zero prime ideal of $B$ is maximal.
(3) Every non-zero ideal of $B$ is invertible.
(4) Every non-zero ideal of $B$ has a unique factorization as a product of prime ideals.
-
Why are you asking a string of very closely related questions about whether theorems from commutative algebra hold without choice? – Alex Becker Jul 15 '12 at 1:19
I tried to solve the following problem presented by Weil. Most of my questions related AC came from my efforts to solve it. math.stackexchange.com/questions/155392/… – Makoto Kato Jul 15 '12 at 1:27
We use the definitions of my answer to this question.
Definition 1 Let $A$ be a commutative ring. Let $B$ be a commutative $A$-algebra. Suppose $leng_A B$ is finite. Then we say $B$ is an Artinian $A$-algebra.
Lemma 1 Let $A$ be a commutative ring. Let $B$ be an Artinian $A$-algebra. Let $\Lambda$ be nonempty set of ideals of $B$. Then there exist a maximal element and a minimal element in $\Lambda$.
Proof: We note that every ideal of $B$ can be regarded canonically as an A-module. Let $r = sup$ {$leng_A I; I \in \Lambda$}. Since $r$ is finite, there exists $I \in \Lambda$ such that $r = leng$ $I$. By Lemma 4 of my answer to this, $I$ is a maximal element of $\Lambda$.
The existence of a minimal element is proved similarly. QED
Lemma 2 Let $A$ be a commutative ring. Let $B$ be an Artinian $A$-algebra. Then $leng_B B$ is finite, namely $B$ is an Artinian ring as defined in Definition 1 in this.
Proof: Let $\Lambda$ be the set of ideals $I$ of $B$ such that $leng_B I$ is finite. Since $0 \in \Lambda$, $\Lambda$ is not empty. By Lemma 1, there exists a maximal element $I \in \Lambda$. Suppose $I \neq B$. Then, by Lemma 1, there exists an ideal $J$ of $B$ such that $I \subset J$ and $J/I$ is a simple $B$-module. Since $leng_B J = leng_B I + 1$, $J \in \Lambda$. This is a contradiction. Hence $B = I$. QED
Definition 2 Let $A$ be a commutative ring. Let $B$ be a commutative $A$-algebra. Suppose $leng_A B/fB$ is finite of for every non-zero element $f \in B$. Then we say $B$ is a weakly Artinian $A$-algebra. By Lemma 2, $B$ is a weakly Artinian ring.
Proof of the title theorem By Lemma 2, $B$ is a weakly Artinian ring. Hence the assertions of the title theorem follow immediately from Lemma 2 and this. QED
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https://dmoj.ca/problem/ccc19j1 | ## CCC '19 J1 - Winning Score
View as PDF
Points: 3
Time limit: 1.0s
Memory limit: 32M
Problem types
You record all of the scoring activity at a basketball game. Points are scored by a -point shot, a -point field goal, or a -point free throw.
You know the number of each of these types of scoring for the two teams: the Apples and the Bananas. Your job is to determine which team won, or if the game ended in a tie.
#### Input Specification
The first three lines of input describe the scoring of the Apples, and the next three lines of input describe the scoring of the Bananas. For each team, the first line contains the number of successful -point shots, the second line contains the number of successful -point field goals, and the third line contains the number of successful -point free throws. Each number will be an integer between and , inclusive.
#### Output Specification
The output will be a single character. If the Apples scored more points than the Bananas, output A. If the Bananas scored more points than the Apples, output B. Otherwise, output T, to indicate a tie.
#### Sample Input 1
10
3
7
8
9
6
#### Output for Sample Input 1
B
#### Explanation of Output for Sample Input 1
The Apples scored points and the Bananas scored points, and thus the Bananas won.
#### Input for Sample Input 2
7
3
0
6
4
1
#### Output for Sample Input 2
T
#### Explanation of Output for Sample Input 2
The Apples scored points and the Bananas scored points, and thus it was a tie game.
• vincentlin2047 commented on Feb. 9, 2020, 3:13 p.m.
wassups
• RussianSpy commented on Dec. 31, 2019, 1:33 p.m.
• sku81da commented on Oct. 6, 2019, 4:51 a.m.
sure
• clashroyaleoo commented on Aug. 3, 2019, 8:15 p.m.
basketball games can't end in a tie. the just go to overtime(OT) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2305283099412918, "perplexity": 4215.3479132639595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144165.4/warc/CC-MAIN-20200219153707-20200219183707-00427.warc.gz"} |
http://ijmsi.ir/page/11/Journal-Information | $$heading_2$$ About the Journal
The Iranian Journal of Mathematical Sciences and Informatics is an English semiannual publication of the Academic Center for Education, Culture and Research $$extract_itex$$ACECR$$/extract_itex$$ at Tarbiat Modares University $$extract_itex$$TMU$$/extract_itex$$. It publishes original research papers and invited survey articles in all areas of mathematical sciences and information science. Further information is provided on the back flap of this volume.
View: 18844 Time$$extract_itex$$s$$/extract_itex$$ | Print: 662 Time$$extract_itex$$s$$/extract_itex$$ | Email: 0 Time$$extract_itex$$s$$/extract_itex$$ | 0 Comment$$extract_itex$$s$$/extract_itex$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27317342162132263, "perplexity": 18563.88267056217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743968.63/warc/CC-MAIN-20181118052443-20181118074443-00158.warc.gz"} |
http://stats.stackexchange.com/questions/38296/expected-value-of-a-natural-logarithm | # Expected value of a natural logarithm
I know $E(aX+b) = aE(X)+b$ with $a,b$ constants, so given $E(X)$, it's easy to solve. I also know that you can't apply that when its a nonlinear function, like in this case $E(1/X) \neq 1/E(X)$, and in order to solve that, I've got to do an approximation with Taylor's. So my question is how do I solve $E(\ln(1+X))$?? do I also approximate with Taylor?
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Yes you can apply the delta method in this case. – Michael Chernick Sep 29 '12 at 23:45
You should also look into the Jensen Inequality. – kjetil b halvorsen Sep 30 '12 at 19:58
In the paper
Y. W. Teh, D. Newman and M. Welling (2006), A Collapsed Variational Bayesian Inference Algorithm for Latent Dirichlet Allocation, NIPS 2006, 1353–1360.
a second order Taylor expansion around $x_0=\mathbb{E}[x]$ is used to approximate $\mathbb{E}[\log(x)]$:
$$\mathbb{E}[\log(x)]\approx\log(\mathbb{E}[x])-\frac{\mathbb{V}[x]}{2\mathbb{E}[x]^2} \>.$$
This approximation seems to work pretty well for their application.
Modifying this slightly to fit the question at hand yields, by linearity of expectation,
$$\mathbb{E}[\log(1+x)]\approx\log(1+\mathbb{E}[x])-\frac{\mathbb{V}[x]}{2(1+\mathbb{E}[x])^2} \>.$$
However, it can happen that either the left-hand side or the right-hand side does not exist while the other does, and so some care should be taken when employing this approximation.
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Interestingly, This can be used to get an approximation to the digamma function. – probabilityislogic Oct 3 '12 at 22:53
Suppose that $X$ has probability density $f_X$. Before you start approximating, remember that, for any measurable function $g$, you can prove that $$E[g(X)]=\int g(X)\,dP = \int_{-\infty}^\infty g(x)\,f_X(x)\,dx \, ,$$ in the sense that if the first integral exists, so does the second, and they have the same value.
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If the second integral exists. It needs not to. Take Cauchy distribution and $g(x)=x^2$. – mpiktas Sep 30 '12 at 13:34
I would add a second layer of pedantry by saying that you actually need $E[|g(X)|]<\infty$ for the expectation to be well defined. – probabilityislogic Oct 3 '12 at 22:45
@mpiktas - This expectation actually does exist but it is infinite. A better example is $g(x)=x$ for the Cauchy distribution. This expectation depends on how the lower and upper limits of integration tend to infinity. – probabilityislogic Oct 3 '12 at 22:49
@prob: No, you don't need that condition in your first comment, and even in a situation that may be very relevant to this question! (+1 to your second comment, though, which was something I had been meaning to comment on as well.) – cardinal Oct 3 '12 at 22:51
@prob: It is sufficient, but if you compare your first comment to your second one, you'll see why it's not necessary! :-) – cardinal Oct 3 '12 at 23:02
show 1 more comment
There are two usual approaches:
1. If you know the distribution of $X$, you may be able to find the distribution of $\ln(1+X)$ and hence its expectation; alternatively you may be able to use the law of the unconscious statistician directly (that is, integrate $\ln(1+x) f_{X}(x)$ over the domain of $x$).
2. As you suggest, if you know the first few moments you can compute a Taylor approximation.
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https://www.math.bgu.ac.il/en/teaching/2020/handbook/degrees/mathematics-and-industrial-engineering/prog_prereqs/mandatory-math-studies | The courses in each of the following lists should be taken
##### Mandatory math for CS
Mandatory math for CS.
Id
Course Name
Hours
Credits
Terms
Requires
0121 Approximation Theory 4/0 4.0 Spring
##### Basic mandatory courses
Basic mandatory courses.
Id
Course Name
Hours
Credits
Terms
Requires
Total Credits
28.0
7011 Algebra 1 for CS 4/2 5.0 Fall
7021 Algebra 2 for CS 4/2 5.0 Spring
1011 Infinitesimal Calculus 1 4/2 5.0 Fall
1021 Infinitesimal Calculus 2 4/2 5.0 Spring
1051 Introduction to Analysis 4/0 4.0 Fall
8001 Probability 4/0 4.0 Fall
Id
Course Name
Hours
Credits
Terms
Requires
Total Credits
24.0
7031 Algebraic Structures 4/0 4.0 Fall
1031 Geometric infinitesimal calculus 1 4/0 4.0 Fall
1041 Geometric infinitesimal calculus 2 4/0 4.0 Spring
0091 Introduction to Topology 4/0 4.0 Spring
0061 Ordinary Differential Equations 4/0 4.0 Spring
0251 Theory of Functions of a Complex Variable 4/0 4.0 Spring
Id
Course Name
Hours
Credits
Terms
Requires
Total Credits
9.0
2201 Discrete Mathematics 4/2 5.0 Fall
0171 Introduction to Set Theory 4/0 4.0 Spring | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9831346273422241, "perplexity": 19856.02983343627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943562.70/warc/CC-MAIN-20230320211022-20230321001022-00692.warc.gz"} |
https://playtorch.dev/docs/tutorials/add-package/ | Version: 0.2.4
# Add PlayTorch to Existing App
In this tutorial, you will learn how to add the PlayTorch core package to an existing React Native project.
If you have an existing React Native project and you want to add ML capabilities, you can add the react-native-pytorch-core package. This package includes all code needed to run ML inference, the Canvas, Camera, ImageUtil, and AudioUtil.
# Installation
yarn add react-native-pytorch-core
On iOS you are done, but Android requires the following additional steps for the react-native-pytorch-core package to work.
If the PyTorch Mobile models are part of the React Native bundle, the Metro configuration needs to be changed to resolve the ptl files.
note
This is only required if models are loaded from the bundle using require('./path/to/model.ptl'). It is not required if models are loaded from the mobile device's local file system or via a URL.
metro.config.js
// get defaults assetExts arrayconst defaultAssetExts = require('metro-config/src/defaults/defaults') .assetExts;module.exports = { // ... resolver: { assetExts: [...defaultAssetExts, 'ptl'], }, // ...};
For the react-native-pytorch-core React Native package to work on Android, it requires three changes to the gradle.properties and the two build.gradle files to increase JVM memory, add Sonatype repository, and packaging options with pick first rule.
### Increase JVM Memory
Increase the memory for the JVM to avoid OutOfMemory exceptions during the packaging process.
org.gradle.jvmargs=-Xmx4g
* What went wrong:Execution failed for task ':app:packageDebug'.> A failure occurred while executing com.android.build.gradle.tasks.PackageAndroidArtifact$IncrementalSplitterRunnable > java.lang.OutOfMemoryError (no error message) ### Update app build.gradle Both React Native and PyTorch Mobile for Android use fbjni. For example, the versions for PlayTorch that are used for development are: • React Native 0.64.3 uses fbjni 0.0.2 • PyTorch Mobile 1.12.2 uses fbjni 0.2.2. So far, fbjni is forward compatible, which means it is ok to pick the latest version shipped with either of the two dependencies. At this point, it is fbjni 0.2.2. For Gradle to pick the right version, the android/app/build.gradle needs to have a few adjustments: 1. Add pickFirst rule to packagingOptions. This rule will pick the first shared object (dynamic) library. It will give higher priority to shared object libraries that are coming with direct app dependencies, which is why 2. is important. 2. Set up an extra directory for fbjni where the fbjni version 0.2.2 from the dependency added in 3. will be extracted. Also add the relevant task to the build.gradle file (see task extraJNILibs and tasks.whenTaskAdded after the dependencies definition) 3. Add fbjni 0.2.2 as direct app dependency. See the build.gradle in the react-native-pytorch-core example app for a possible configuration. info The following error will show if pickFirst is not set: * What went wrong:Execution failed for task ':app:mergeDebugNativeLibs'.> A failure occurred while executing com.android.build.gradle.internal.tasks.Workers$ActionFacade > More than one file was found with OS independent path 'lib/x86/libfbjni.so'
android { // ... /** * Without the packaging options, it will result in the following build error: * * * What went wrong: * Execution failed for task ':app:mergeDebugNativeLibs'. * > A failure occurred while executing com.android.build.gradle.internal.tasks.Workers$ActionFacade * > More than one file was found with OS independent path 'lib/x86/libfbjni.so' */ packagingOptions { pickFirst '**/*.so' } sourceSets { main { jniLibs.srcDirs += ["$buildDir/extra-jniLibs/jni"] } } configurations { extraJNILibs } // ...}dependencies { // ... // Used to control the version of libfbjni.so packaged into the APK extraJNILibs("com.facebook.fbjni:fbjni:0.2.2") // ...}// ...// Extract JNI shared libraries as project libraries. This assumes the target directory, $buildDir/extra-jniLibs, is added to the jniLibs.srcDirs configuration.task extraJNILibs { doLast { configurations.extraJNILibs.files.each { def file = it.absoluteFile copy { from zipTree(file) into "$buildDir/extra-jniLibs" // temp location instead of "src/main/jniLibs" include "jni/**/*" } } }}tasks.whenTaskAdded { task -> if (task.name == 'mergeDebugJniLibFolders' || task.name == 'mergeReleaseJniLibFolders') { task.dependsOn(extraJNILibs) }}// ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37754592299461365, "perplexity": 11395.89506636508}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500983.76/warc/CC-MAIN-20230208222635-20230209012635-00195.warc.gz"} |
http://math.stackexchange.com/questions/164847/congruent-to-mod-p-1p-22p-2-cdots-left-fracp-12-rightp-2-equi/164900 | # congruent to mod p $1^{p-2}+2^{p-2}+\cdots+\left(\frac{p-1}{2}\right)^{p-2}\equiv\frac{2-2^p}{p}\pmod p.$
Let $p$ be an odd prime.How to prove that
$$1^{p-2}+2^{p-2}+\cdots+\left(\frac{p-1}{2}\right)^{p-2}\equiv\frac{2-2^p}{p}\pmod p.$$
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Let $f(x)=(x+1(\frac{p-1}{2}))(x+2(\frac{p-3}{2})...(x+(\frac{p-1}{2})(1))$,and $a=$ coefficient of $x$ of $f(x)$. Then the problem is equivalent to showing that $a\equiv 8(-1)^{\frac{p-1}{2}} (\frac{2^{p-1}-1}{p}) (mod p)$. I dunno if this would help us solve this problem. – Ben Jun 30 '12 at 9:53
Am I being stupid or does this not make sense since $p$ is not invertible mod $p$? – fretty Jun 30 '12 at 12:29
$2-2^p$ is divisible by $p$,so here $\frac{2-2^p}{p}$ is an integer and $\frac{1}{p}$ does not mean the inverse in the field $\mathbb{Z}/p\mathbb{Z}$. – Ben Jun 30 '12 at 12:30
Yes, I didn't look at the numerator in detail so I was being stupid. – fretty Jun 30 '12 at 12:40
I find that this identity is stated in this paper:
Lehmer, E. "On Congruences Involving Bernoulli Numbers and the Quotients of Fermat and Wilson." Ann. Math. 39, 350-360, 1938 : http://www.jstor.org/discover/10.2307/1968791?uid=2134&uid=2&uid=70&uid=4&sid=56284309973
EDIT:
In fact,we can use a simpler method to solve this problem.
Let $q(a)=\frac{a^{p-1}-1}{p}$ for all $a$ such that $\gcd(a,p)=1$. It is not difficult to show that $q(ab) \equiv q(a)+q(b) \pmod{p}...(1)$.
Let $a$ be an arbitrary integer which is relatively prime to $p$. For each $v \in \{1,2,...,p-1\}$,let $av=\lfloor{\frac{av}{p}} \rfloor p+r_v$. Then we can see that $r_v$,($r=1,2,...,p-1$) also runs over ${1,2,...,p-1}$. So $q(av)=((\lfloor{\frac{av}{p}} \rfloor p+r_v)^{p-1}-1)/p\equiv q(r_v)-\lfloor{\frac{av}{p}} \rfloor r_v^{p-2} \equiv q(r_v)-\frac{1}{av} \left \lfloor \frac{av}{p} \right \rfloor \pmod{p}$
So, $\sum_{v=1}^{p-1} q(av) \equiv \sum_{v=1}^{p-1} (q(r_v)-\frac{1}{av} \left \lfloor \frac{av}{p} \right \rfloor)\equiv \sum_{v=1}^{p-1} q(v)-\sum_{v=1}^{p-1}\frac{1}{av} \left \lfloor \frac{av}{p} \right \rfloor \pmod{p}...(2)$
Then by $(1),(2)$,we get $q(a) \equiv \sum_{v=1}^{p-1}\frac{1}{av} \left \lfloor \frac{av}{p} \right \rfloor \pmod{p}...(3)$
Take $a=2$, $\frac{2^p-2}{p} \equiv \sum_{v=1}^{p-1}\frac{1}{v} \left \lfloor \frac{2v}{p} \right \rfloor \equiv \sum_{p/2 <v} \frac{1}{v} \equiv -\sum_{v=1}^{(p-1)/2} \frac{1}{v} \equiv -\sum_{v=1}^{(p-1)/2} v^{p-2} \pmod{p}$
As a result,
$1^{p-2}+2^{p-2}+\cdots+\left(\frac{p-1}{2}\right)^{p-2}\equiv\frac{2-2^p}{p}\pmod p.$
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– anon Jun 30 '12 at 12:45
BenLi,could you look at this solution : store2.up-00.com/June12/RoL51753.jpg – Frank Jul 2 '12 at 17:56
@MohammedAl-mubark, your solution looks alright. That's how I did it. Look below. – DonAntonio Jul 3 '12 at 1:50
@Mohammed Al-mubark:your solution looks much simpler and more direct. – Ben Jul 3 '12 at 2:00
$$2^p=(1+1)^p=\sum_{k=0}^p\binom {p}{k}=\left[\binom{p}{0}+\binom{p}{p}\right]+\ldots+\left[\binom{p}{\frac{p-1}{2}}+\binom{p}{\frac{p+1}{2}}\right]=$$ $$=2\left[\binom{p}{0}+\ldots+\binom{p}{\frac{p-1}{2}}\right]$$
and etc.
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https://kyushu-u.pure.elsevier.com/en/publications/experimental-determination-of-the-photooxidation-of-aqueous-isup- | # Experimental Determination of the Photooxidation of Aqueous I- as a Source of Atmospheric I2
Kosuke Watanabe, Shohei Matsuda, Carlos A. Cuevas, Alfonso Saiz-Lopez, Akihiro Yabushita, Yukio Nakano
Research output: Contribution to journalArticlepeer-review
4 Citations (Scopus)
## Abstract
The chemistry of iodine plays an important role in the oxidizing capacity of the global marine atmosphere. In this study, we experimentally determine the photooxidation parameters of iodide ions in aqueous phase (I-(aq)) and estimate the subsequent emission of gaseous iodine molecules (I2(g)) into the atmosphere. The values of the molar absorption coefficient (ϵiodide(λ)) and the photooxidative quantum yields (φiodide(λ)) of I-(aq) in the range of 290-500 nm were determined. The influence of pH and dissolved oxygen (DO) on the values of φiodide(λ) was also investigated. The emission of I2(g) into the atmosphere following the photooxidation of I-(aq) in deionized water solution (pH 5.6, DO 7.8 mg L-1) and artificial seawater solution (pH 8.0, DO 7.0 mg L-1) was estimated to be (2.2 × 10-8 × [I-(aq)]sea) and (1.8 × 10-8 × [I-(aq)]sea) mol L-1 s-1, respectively. Using a global chemistry-climate model, we estimated that the photooxidation of I-(aq) can increase the atmospheric iodine budget by up to ∼8% over some oceanic regions.
Original language English 669-679 11 ACS Earth and Space Chemistry 3 4 https://doi.org/10.1021/acsearthspacechem.9b00007 Published - Apr 18 2019
## All Science Journal Classification (ASJC) codes
• Geochemistry and Petrology
• Atmospheric Science
• Space and Planetary Science
## Fingerprint
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https://www.bionicturtle.com/forum/threads/raroc.42/ | What's new
# RAROC
#### nanchary
##### New Member
Why are we subtracting the economic capital from the total loan value in estimating the ineterst charge?
from our example, Are banks not borrowing 1 billion from the depositors and making a loan for higher charge? The capital requirement for this loan is 100m and banks invest in highly liquid assets to support in case of unexpectetd losses. so we are adding interest on it to the numerator. How bank is raising 100m? is it not from the depositors then in that case banks have to pay interest on 1.1 b not on 900m.
Tks.
#### David Harper CFA FRM
##### David Harper CFA FRM
Staff member
Subscriber
Nanchary,
Right, I agree with you. But I am following Saunder's example in the assigned reading; I think he may miss the circularity. In the reading:
* Loan portfolio: $1 billion @ 9% * Economic capital: 7.5% of$1 billion = $75 million, invested @ 6.5% riskless (T-bills) * Therefore,$925 MM should be raised by deposits ($1 BB -$75 MM), earning 6% for depositors
risk-adjusted return [numerator] = 90 [loan revenue] + 4.9 [about 6.5% on the $75 MM] -$55 [cost of funds: 6% on the $925] -$10 op expense = $14.375 But that implies assets =$1 billion + $75 MM. Therefore, shareholder's equity = 1.075 - 925 > 7.5% EC. So, if shareholders fund$75 million, I agree with you: that's $75 MM cash-like in assets and equity, such that bank funds$1 BB in loans with $1 BB in deposits. And tot assets = 1.075 wit EC = 75 MM = 7.5% of the$1 BB loan.
But that's not what Saunders does in the assigned readings...I think the important thing is the numerator includes return on economic capital (ROC).
David
#### liewpw05
##### New Member
Hi David,
I have similar problems with the understanding of the \$925million raised by deposits in the above example. Your reply does help to clarify.
I have another question on this example : why is the numerator of the RAROC called risk adjusted return? Is it because it also include a deduction for expected loss from default?The expected loss being excluded due to the fact that the bank has to set up provisions for bad loans and credit can't be taken for the expected loss which has been "priced in" the loan interest pricing when assessing expected return on the loan portfolio.
Thanks
Regards,
Peggy
#### David Harper CFA FRM
##### David Harper CFA FRM
Staff member
Subscriber
Hi Peggy,
On the Saunders example, I still believe Nanchary is correct in spotting the error. He observed that the implied balance sheet is not balanced, which i happen to agree with. But also, it is not crucial to the RAROC ratio. In many cases, RAROC is a divisional metric anyhow...
"why is the numerator of the RAROC called risk adjusted return?"
you may be interested here to connect this Saunders to Chapter 6 of de Servigny (p 244) and his RAROC discussion. The general class of risk-performance metrics is simply:
return/risk
So, RAROC is "cousin" to Sharpe and the risk is in the denominator. Specifically, economical capital is risk adjusted (i.e., greater volatility or higher confidence implies more economic capital required. BTW, to relate to our other thread about regulatory/economic capital, regulatory capital per Basel II is also "risk-adjusted capital." My one sentence summary of Basel II would be "risk adjusted captial." Ergo, we could validly plug-in regulatory capital into the denominator of RAROC!).
While I am here, I want to offer another thought. The RAPM measure are risk-adjusted returns. I like to think, conversely, of VaR as return-adjusted risk (!). As "absolute VaR" = - return + (scale confidence)(scale time)(volatility), greater expected return is offseting VaR. So, VaR is return-adjusted risk, while RAPM (RAROC, Sharpe) are risk-adjusted returns. For what it's worth
"Is it because it also include a deduction for expected loss from default?The expected loss being excluded due to the fact that the bank has to set up provisions for bad loans and credit can’t be taken for the expected loss which has been “priced in†the loan interest pricing when assessing expected return on the loan portfolio. "
What you write is true. But I would tend not to cite the treatment of EL as a reason for calling this risk-adjusted. Rather, i think the most important thing i ever learned about ratios was the rule they should be consistent: the return in the numerator should relate (map) directly to its corresponding (balance sheet) claim in the denominator. For example, ROE is net income/common equity, ROE is not EBIT/equity because EBIT is claimed by debt plus equity holders. The same logic is here to RAROC: the numerator is the earnings base that accrues (is earned by) the economic capital. It would be inconsistent to include EL in the numerator. It would be okay to do that, but if you add EL back to numerator, you should add the corresponding reserve (balance sheet) to the denominator. Finally, there is no magic correct ratio; it would not suprise me if some bank did add back. There is more than one correct RAROC (i.e., I'd argue RAROC is EVA for banks, and there are dozens of EVA variants), as long as it is consistent.
David | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7227981686592102, "perplexity": 3881.348908483239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875147628.27/warc/CC-MAIN-20200228170007-20200228200007-00413.warc.gz"} |
https://stats.stackexchange.com/questions/18599/pacf-manual-calculation/18612 | # PACF manual calculation
I am trying to replicate the calculation that SAS and SPSS do for the partial autocorrelation function (PACF). In SAS it is produced through Proc Arima. The PACF values are the coefficients of an autoregression of the series of interest on lagged values of the series. My variable of interest is sales so I calculate lag1, lag2...lag12 and I run the following OLS regression:
$$Y_t=a_0+a_1Y_{t-1}+a_2Y_{t-2}+a_3Y_{t-3}+\ldots+a_{12}Y_{t-12}.$$
Unfortunately the coefficients that I get are not even close to the PACF (lags 1 to 12) that SAS or SPSS provide. Any suggestions? Is there something wrong? What comes to my mind is that the least squares estimation of this model might not be appropriate and maybe another estimation technique should be used.
• Is $a_{12}$ correct, by any chance?
– whuber
Nov 18, 2011 at 19:16
As you said "The PACF values are the coefficients of an autoregression of the series of interest on lagged values of the series" and I add where the PACF(K) is the coefficient of the last (kth) lag. Thus to compute the PACF of lag 3 for example compute $$Y_{t}= a_{0}+ a_{1}Y_{t−1}+ a_{2}Y_{t−2}+ a_{3}Y_{t−3}$$
and $a_{3}$ is the PACF(3).
Another example. To compute the PACF(5), estimate
$$Y_{t}= a_{0}+ a_{1}Y_{t−1}+ a_{2}Y_{t−2}+ a_{3}Y_{t−3}+ a_{4}Y_{t-4}+ a_{5}Y_{t-5}$$
and $a_{5}$ is the PACF(5).
In general the PACF(K) is the KTH order coefficient of a model terminating with lag K. By the way SAS and other software vendors use the Yule-Walker approximation to compute the PACF which will provide slightly different estimates of the PACF. They do this for computational efficiency and in my opinion to duplicate the results in standard textbooks.
• +1. If you're unfamiliar with $\TeX$, a good way to use it anyway is to right-click on relevant expressions in the question, choose "Show Source," then copy and paste them into your answer. You can then make modifications, which usually are intuitive and obvious. This will make your replies more readable.
– whuber
Nov 18, 2011 at 23:04
• Got it! Excellent explanation one more time. Thanks very much! Nov 18, 2011 at 23:24
• I realize this was written long ago, but is one of the few references of calculating PACF as "coefficients of an autoregression of the series of interest on lagged values of the series" I am finding. I see it in the implementation of statsmodels.tsa.stattools.pacf - tedboy.github.io/statsmodels_doc/_modules/statsmodels/tsa/…. Wikipedia lists 3 ways to calculate partial correlation: a) using linear regression and correlating residuals b) recursive and c) matrix inversion. But what is the theoretical basis here? Mar 26, 2020 at 19:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.7789241075515747, "perplexity": 1053.4223759726258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00393.warc.gz"} |
https://download.gams.com/latest/docs/RN_244.html | 24.4 Distribution
24.4.1 Major release (December 20, 2014)
Acknowledgments
We would like to thank all of our users who have reported problems and made suggestions for improving this release. In particular, we thank Erwin Kalvelagen, Jeff Linderoth, and Erkka Rinne.
GAMS System
GAMS
• Fixed a bug causing a potential crash when solving an EMP model having an open file handle without an external file name at the same time.
• The execMode setting is not ignored by put_utility anymore.
• Added gbin/md5sum.exe to Windows distribution. This utility allows users to verify the file integrity of newly downloaded GAMS installation files.
• The gbin_new directory will be removed with the next distribution.
Installer
• Windows installer removes the GAMS entry in the current user hive of the registry, if GAMS is installed for all users. Previously, the hive for the current user remained unchanged in this situation.
Extrinsic Function libraries
• The new extrinsic function library parcclib was added to the system. This library demonstrates how to access the GAMS parameter file and use it's information through the GAMS Option Object. Further information can be found in the GAMS User's Guide, Appendix J.
• Allow up to 20 arguments (used to be 10).
• Support for extrinsic function libraries that do not provide gradient and/or Hessian values. GAMS uses finite differences (same method as for .gradn and .hessn) to approximate the derivatives, even inside a solver. The example function library trilib now implements function Sine without any derivatives and leaves their calculation to GAMS.
• New GAMS options have been introduced to parameterize the numerical derivative calculations. While these are most important for extrinsic functions, they also apply to the .gradn/.hessn calculations of intrinsic functions.
• FDDelta: step size in the numeric gradient and Hessian calculation. For single argument functions, GAMS evaluates the function at f(x-d) and f(x+d) for the numerical gradient. If function values are used for the numerical Hessian, GAMS evaluates at f(x-2d), f(x), and f(x+2d). For multi argument functions, the same is done for the components of the input argument vector. The default for FDDelta is 1e-5. This option can be set from the command line, in an option statement, and as a model attribute.
• Note: In previous releases it was possible to set the step size for .gradn/.hessn using the option Real1. This does not work anymore.
• FDOpt: The option value packs two option in the different digits: ij. The i digit indicates if scaling of the step size (FDDelta) by the value of the input argument should be turned off. If i=0 (scaling on) the following step size is used: max(1,|x|)*FDDelta. The j digit is mostly for testing, but has one setting that might be relevant when the extrinsic function provides gradient but no Hessian values. The numerical derivatives routine in this case uses the gradient calculation from the extrinsic function to approximate the Hessian. If the gradient is expensive to calculate compared to a function evaluation, it could be beneficial to use multiple function values to approximate the Hessian. In this case set the j digit to 1. Here are all possible values for this option:
• 0: All derivatives analytically if available, for numerical Hessian use gradient values, scale delta
• 1: All derivatives analytically if available, for numerical Hessian use function values, scale delta
• 2: Gradient analytically, force Hessian numerically using gradient values, scale delta (testing only)
• 3: Gradient analytically, force Hessian numerically using function values, scale delta (testing only)
• 4: Force gradient and Hessian numerically, scale delta (testing only)
• 10: Same as 0, but no scale of delta
• 11: Same as 1, but no scale of delta
• 12: Same as 2, but no scale of delta (testing only)
• 13: Same as 3, but no scale of delta (testing only)
• 14: Same as 4, but no scale of delta (testing only)
• Note: In previous releases it was possible to deactivate the scaling for .gradn/.hessn using the option Integer1. This does not work anymore.
• Renamed and better documented the EXTRFUNC_ERROR enum to EXTRFUNC_EVALERROR in the C header extrfunc.h. The old values are deprecated and will be removed in a future release.
Documentation
• The manuals of all solver and several tools are now available in HTML format. A PDF that contains all solver manuals is still available (docs/solvers/allsolvers.pdf).
Solvers
AlphaECP
• Alpha-ECP v2.10.06.
• Added support for solver trace file, i.e. new option solvetrace.
ANTIGONE, GloMIQO
• Now also available for Mac OS X.
BARON
• New libraries 14.4.0.
• Added reliability branching for integer variables.
• Bug fixes in CBC interface and IIS module.
• Improved performance of problem reading and reformulation.
• Updated Ipopt to version 3.11.9.
BENCH
• Removed option cumulative. This option makes no sense anymore since all solvers are spawned asynchronously and all get the same limits.
CBC
• Fixed a race-condition in log output when using multiple threads.
• New libraries.
Couenne
• New libraries.
CONOPT
• New libraries 3.16D.
• Tolerance adjustments that make sense if NaN appears in intermediate calculations.
CPLEX
• Don't rerun primal simplex in cases where there is already an infeasibility status.
• New libraries 12.6.1.
• New parameters:
• qtolin controls the linearization of the quadratic terms in the objective function of a QP or MIQP model
• localimplied controls the generation of locally valid implied bound cuts
DICOPT
• Added support for =N= rows.
GUROBI
• New libraries 6.0.0.
• Fixed problem in tuning. Previous version did not write out link options in the tuned option file.
• Gurobi 6.0 supports a distributed MIP algorithm (option DistributedMIPJobs). This requires the Gurobi Compute Server to be licensed.
• Explicit lazy constraint: Users can use the "dot" option .lazy to mark constraints as lazy. Possible values are 0, 1, 2, and 3. See option .lazy for details.
• Option ConcurrentMIPJobs has been renamed to ConcurrentJobs. The distributed concurrent optimizer now also handles LP models.
• Option ScaleFlag allows now value 2 which enables aggressive scaling.
• New parameters:
• DistributedMIPJobs controls the number of workers of the distributed MIP algorithm
• .lazy marks constraints as lazy constraints
• LazyConstraints controls the use of lazy constraints
Knitro
• New libraries 9.1.0.
• Overall speed and robustness improvements on NLP and MINLP models.
• New algorithm choice introduced: active-set SQP.
• Optional barrier solution refinement procedure: option bar_refinement = NO/yes.
• Deterministic parallel multi-start: option ms_deterministic = no/YES.
• Dropped Knitro for Solaris on Intel CPUs (as announced).
LocalSolver
• Added the hybrid mathematical programming solver LocalSolver 5.0 (Beta) from Innovation 24 to the GAMS solvers portfolio.
• LocalSolver can be applied to large-scale, mixed-variable, non-convex optimization problems (GAMS model types MIP, (MI)QCP, (MI/D)NLP). It combines local search techniques, constraint propagation and inference techniques, linear and mixed-integer programming techniques, and nonlinear programming techniques in a unique hybrid neighborhood search approach to find high-quality feasible solutions. Hence, LocalSolver offers an alternative for problems where conventional branch-and-bound and/or outer-approximation based solution methods do not provide satisfactory results.
• It is suggested to set the GAMS options for iteration or timelimit (iterlim, reslim) appropriately to limit the effort that LocalSolver spends on the problem.
Lindo/LindoGlobal
• We will drop Lindo/LindoGlobal libraries for Intel Solaris with the next major release (24.5).
• New libraries 9.0.142 for Linux, Mac OS X, and Windows:
• Support for semi-continuous variables.
• Simplex LP algorithm implementation has been improved for speed and robustness. The performance improvements compared to previous version are 90% for primal simplex and 45% for the dual simplex.
• Knapsack related cuts improvements. Significantly faster solve times on models with certain knapsack-like constraints.
• Improved default node selection rules improves performance on most MIPs.
• New branching variable rule options: maximum coefficients and neighborhood branching. Can reduce number of branches on certain MIPs.
• Perspective reformulation capability gives improved performance on quadratic portfolio models with semi-continuous variables, e.g. min-buy quantities.
• Improved default settings for NLPs gives 5% average speed improvement.
• New preprocessing for LP/MIP significantly reduces coefficient density of certain dense matrices.
Mosek
• New libraries 7.1.0.12.
• Improved performance of the mixed-integer conic optimizer.
MSNLP/OQNLP
• These solvers now use Conopt as their default solver if Conopt is licensed. Otherwise they will use lsgrg as before.
OS
• We plan to drop the OS solver with GAMS 24.5. The capability of convert to write OSiL files will be kept.
SCIP
• New libraries 3.1 #020d055.
SoPlex
• New libraries 2.0 #d67b17b.
Sulum
• New libraries 4.0.665.
• Improvements in presolve, leading to more reductions.
• General improvements in obtaining a feasible solution faster, especially with focus on the root node to obtain a good bound. Rewrite and improvements of feasibility pump, objective diving.
• The simplex algorithm is now exchanging more information with the branch and cut method. Improvement of SINS heuristic (finding a better basis after the node solve).
• Added a MIP root restart feature based on reductions.
• Cutting planes generation was both improved and extended.
• Changed default for option mipmaxrestarts from 5 to 1.
XPRESS
• New libraries for XPRESS v7.8: Optimizer 27.01.02.
• Automatic solution refinement for LP and MIP models.
• Improved deterministic concurrent LP.
Tools
GAMSIDE
• Added option to suppress trailing zeroes in GDX viewer.
• Improved ability to open files from the Windows Shell.
• Cutoff for number of lines to be syntax colored or not.
• When saving a file, the Undo buffer is no longer cleared.
GDXDUMP
• Text quoted with a single quote did not have a separator when writing SymbolAsSet.
• Added option SymbolAsSetDI.
• Avoid string overflow when quoting text.
• Added more types for sets and equations.
GDXXRW
• Added option values=All which is the new default when CDim=0 or RDim=0.
GDXVIEWER
• Added ACCDB format as an output option for MSAccess.
GDX2SQLite, Scenred, Scenred2
• These tools are now also available for AIX.
• Moved documentation of Scenred and Scenred2 from docs/solvers to docs/tools.
IDECMDS
• Allow a pattern to be specified to close files.
MPS2GMS
• The mps2gms tool now produces proper generic GAMS source for models with quadratic terms.
• Bug fix for MPS files written by Cplex that contain SOS constraints.
MPSGE
• Moved manual to ''docs/tools''.
Expert Level APIs
• There are new API files for the "Indexed GDX" (IDX) library in <GAMS Dir>\apifiles\<Language>\api:
• The indexed GDX library can be used to read and write indexed GDX files.
• Each symbol in such a GDX file must be a parameter.
• Each parameter must have a domain consisting of a UELs which forms an integer sequence starting at 1.
• This way the data is provided in a format convenient to store in arrays in the target language.
• In GAMS such a file can be read using \$LoadIDX during compilation.
• In GAMS such a file can be written using execute_unloadIDX during execution.
• The new example <GAMS Dir>\apifiles\CSharp\xp_CalcInverseIDX makes use of this API, this example is also used in the APILib model CSCalcInverse.
Python
• Fixed a bug regarding lists of strings in Python 3 (e.g. gdxDataWriteStr()).
Object Oriented APIs
• We changed the handling of GAMS Aliases in the object oriented APIs:
• If we ask for the number of GAMSSymbols in a GAMSDatabase, the Aliases will be excluded.
• If we iterate over all GAMSSymbols in a GAMSDatabase, Aliases will be skipped.
• If we ask explicitly for an Alias in a GAMSDatabase (GAMSDatabase.GetSet("a") with a being an Alias) we will get a reference to the GAMSSet referenced by the Alias, not the Alias itself.
• Note: Aliases can appear in a GAMSDatabase only, if it was initialized by a GDX file containing an Alias.
• The new examples Alias demonstrate this new behavior for the different OO API languages.
Python
• Fixed a bug in GamsDatabase.merge_record that prevented the function from creating a record if none was found.
Model Libraries
GAMS API Library
This is a new collection of GAMS models. It can be accessed in the GAMS IDE at Model Libraries -> GAMS API Library or through the command line tool apilib. The models in this collection can be used as scripts to compile and execute the example applications using the GAMS object oriented APIs as well as the expert level APIs, which can be found in <GAMS Dir>/apifiles.
GAMS Test Library
Solver/Platform availability - 24.4
x86 32bit
MS Windows
x86 64bit
MS Windows
x86 64bit
Linux
x86 64bit
Mac OS X
x86 64bit
SOLARIS
Sparc 64bit
SOLARIS
IBM Power 64bit
AIX
ALPHAECP
ANTIGONE 1.1
BARON 14.4
BDMLP
BONMIN 1.7
CBC 2.8
CONOPT 3
COUENNE 0.4
CPLEX 12.6
DECIS
DICOPT
GLOMIQO 2.3
GUROBI 6.0
GUSS
IPOPT 3.11
KNITRO 9.1
LGO
LINDO 9.0 8.0
LINDOGLOBAL 9.0 8.0
LOCALSOLVER 5.0
MILES
MINOS
MOSEK 7
MPSGE
MSNLP
NLPEC
OQNLP 32bit
PATH
SBB
SCIP 3.1
SNOPT
SOPLEX 2.0
SULUM 4.0
XA
XPRESS 27.01
24.4.2 Minor release (March 15, 2015)
Acknowledgments
We would like to thank all of our users who have reported problems and made suggestions for improving this release. In particular, we thank Sergey Kuznetsov, Ricardo M. De Lima, and Corey Noone.
GAMS System
GAMS
• Fixed potential problem when running on Windows in a workDir containing a %.
• Fixed problem with EMP solves with solvelink=Solvelink.AsyncGrid%.
• Fixed problem with GUSS/Grid when using execute_loadhandle instead of handlecollect.
Solvers
ANTIGONE
• New libraries.
CONOPT
• Introduced new boolean option PreTri2Log that send message from Conopt's pre-triangular analyzer that go to the listing file also to the GAMS log. The option requires the generation of the model dictionary, so mymodel.DictFile=1; has to be added before the Solve statement.
CONVERT
• Convert and ConvertD: Fix for writing scalar MCP models that contained fixed variables removed by holdfixed=1.
• ConvertD: Add support for external equations in scalar GAMS models.
• ConvertD: Propagate EPS to scalar GAMS models.
Couenne
• New libraries.
Examiner2
• Support added for custom trace files.
GUROBI
• New libraries 6.0.2.
Lindo/LindoGlobal
• New libraries 9.0.157 for Linux, Mac OS X, and Windows.
LocalSolver
• New libraries 5.0 (20150119).
Mosek
• New libraries 7.1.0.24.
SCIP
• New libraries 3.1 #67d713c.
• Fixed overwriting of solvetrace file by final NLP resolving.
SoPlex
• New libraries 2.0 #8381aa4.
Tools
GDXMRW
• gdxInfo: fix output of domains in symbol declaration
• gdxInfo: handle aliases properly
Object Oriented APIs
• Fixed overwriting of the default value for the integer1 option when running with GAMSModelInstance, which lead to unexpected solver behavior.
• Fixed potential problem with GAMSModelInstance used with BARON.
.NET
• New property GAMSSymbol.DomainsAsStrings: Domains of Symbol, each element is a string, if the domain is an alias in GAMS, this call will return the name of the Alias, not the name of the aliased Set.
Java
• Changed naming scheme of GDX output scratch file to sequence number.
Python
• Fixed a bug in the constructor of all subclasses of _GamsSymbol that occurred when the explanatory text was omitted.
• New property _GamsSymbol.domains_as_strings: Domains of Symbol, each element is a string. If the domain is an alias in GAMS, this call will return the name of the alias, not the name of the aliased set.
Expert Level APIs
GMO
• Fixes to gmoGetRowJacInfoOne and gmoGetColJacInfoOne: In case of an empty row/column, now return -1 in colidx/rowidx if index base is 0.
24.4.3 Maintenance release (April 02, 2015)
Acknowledgments
We would like to thank all of our users who have reported problems and made suggestions for improving this release. In particular, we thank Guillaume Erbs and Emiliano Traversi.
Solvers
Examiner2
• Fixed incapability to continue on a trace file that already has trace records in it.
LocalSolver
• Corrected computation of values for free variables that appeared (linearly) in one equation only.
Tools
GDXXRW
• In 24.4.2 we quietly introduced a new way to determine the content of a sheet. This resulted in a bug for empty sheets and sheets that have been saved with an active filter. This has been fixed.
24.4.4 Maintenance release (May 12, 2015)
Acknowledgments
We would like to thank all of our users who have reported problems and made suggestions for improving this release. In particular, we thank Thomas Counsell, Michael Ferris, Jean Mercenier, and Loïc Ventre.
Solvers
Gurobi
• New libraries 6.0.4.
• The new libraries do not work on Windows XP anymore. As the library for COIN-OR solvers, SCIP, and SoPlex link to the Gurobi library, these solvers also do not work on Windows XP anymore.
Ipopt
• New libraries for Linux and Mac OS X.
• Fixed an issue in the MA97 interface that lead to convergence problems.
Minos
• Consider the number of nonlinear constraint variables, not just the nonlinear objective variables, when computing the superbasics limit: memory is plentiful and cheap.
• Fixed case of memory corruption that resulted when using an initial point containing very many superbasic variables. If the initial point contains more than 500 superbasics, limit the Hessian dimension to 500 even though the superbasic limit is larger.
Mosek
• New libraries 7.1.0.30.
Xpress
• New libraries Optimizer 27.01.08 (was 27.01.02 before).
Tools
GDXDUMP
• Fixed a problem when writing a scalar or scalar variable/equation in format CSV.
Object Oriented APIs
• Fixed a potential problem with GAMSModelinstance and certain OS culture settings.
Model Libraries
GAMS EMP Library
• transecs: Fixed formulation as embedded complementarity system and provide equivalent alternative as single-agent equilibrium system.
24.4.5 Maintenance release (May 26, 2015)
Solvers
COIN-OR solvers, SCIP, SoPlex
• On Windows 32bit, OsiGurobi was split off into a separate library, so that other COIN-OR solvers (e.g., Bonmin, Cbc, Couenne, Ipopt) and SCIP and SoPlex do not require the Gurobi 6.0.4 library anymore. Thus, for this release, only Gurobi and OsiGurobi do not run on Windows XP anymore (see 24.4.4 notes on Gurobi).
24.4.6 Minor release (June 26, 2015)
Acknowledgments
We would like to thank all of our users who have reported problems and made suggestions for improving this release. In particular, we thank Erwin Kalvelagen, Rich Roberts, and Jens Schulz.
Solvers
CONOPT
• New libraries 3.16F.
• New option LMUSDF for handling definitional equations.
• New option RVFILL for memory allocation when memory is tight.
• Changed a sorting procedure in the preprocessor. Models with some very dense rows and many pre-triangular variables can experience a significant speedup for the preprocessor.
CPLEX
• New libraries 12.6.2.0.
• Option changes:
• The popular option value -1 for BarCrossAlg to turn off the crossover after a run with barrier has been deprecated. The new way to turn off crossover is to set the new option SolutionType to 2.
• The option SolutionTarget has been renamed to OptimalityTarget.
• The option CutsFactor has a new default (-1).
• New options:
• BQPCuts: Boolean Quadric Polytope cuts for solving nonconvex QP or MIQP to global optimality.
• CPUMask: Switch and mask to bind threads to processors. Binding threads to processors/cores helps to reduce variability in running time when using multiple threads.
• SolutionType: Type of solution (basic or non basic) for an LP or QP. Set this option to 2 to prevent crossover after barrier.
MOSEK
• New libraries 7.1.0.31.
Tools
GAMSIDE
• Added .ref for reference file to the files open dialog.
• Left arrow in the first character position now moves to the end of the previous line.
GDXXRW
• Restore the old behavior when reading a set with Values=Strings; all elements will be included, not only the ones with a string.
• Option Values=String and All are now deprecated and results in a warning; replaced with Dense.
• New options Values=Dense or Sparse.
XLSTalk
• Allow for up to 9 parameters for macro call.
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Europe: (+49) 221 949-9170 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4211951196193695, "perplexity": 6840.365828191212}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103271864.14/warc/CC-MAIN-20220626192142-20220626222142-00600.warc.gz"} |
https://pegas.is/old/python/Import%20Statement.html | # Import Statement
Import statement allows you to use code that in different files or written by others.
## Use Multiple Files
Put all your code in one file is bad for maintenance and hard to navigate between code. Put your code in to multiple files can make your work easier.
Just for demonstration, let’s create two files, one called main.py and another called functions.py. Then put the following code to those files:
xxxxxxxxxx#code in functions.pydef greet(name): print("Hello, " + name + "!")
xxxxxxxxxx#code in main.pyimport functions #import <fileName>functions.greet("Pegasis") #fileName.functionName()
Then run main.py, you will see Hello, Pegasis! been printed out.
If you think use fileName.functionName() to invoke functions in other files is annoying, use another way to import it:
xxxxxxxxxx#code in main.pyfrom functions import *greet("Pegasis")
But this way is not encouraged because you may have conflicts. (for example a function you import have the same name with a function in your code)
## Use Modules
You can also import from others code using same syntax. For example you can import numpy for scientific math calculation, import pygame for making games and import tkinter for creating GUI (which we will learn later). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3574577867984772, "perplexity": 6161.783301231422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943637.3/warc/CC-MAIN-20230321064400-20230321094400-00456.warc.gz"} |
https://math.stackexchange.com/questions/1148484/ordinals-that-are-not-cardinals?noredirect=1 | # Ordinals that are not cardinals [duplicate]
I am reading Jech's set theory and he defines a cardinal number as an ordinal $\alpha$ (a cardinal) if $|\alpha| \neq |\beta|$ for all $\beta < \alpha$, and he says that all infinite cardinals are limit ordinals. My question is: are there any ordinals that are not cardinals? Although I know that an ordinal describe ordering and a cardinal the size of a set, I am a bit confused here. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9056689739227295, "perplexity": 184.9425586994823}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257156.50/warc/CC-MAIN-20190523063645-20190523085645-00023.warc.gz"} |
https://jump.dev/MathOptInterface.jl/stable/submodules/Utilities/reference/ | ## Utilities.Model
MathOptInterface.Utilities.ModelType
An implementation of ModelLike that supports all functions and sets defined in MOI. It is parameterized by the coefficient type.
Examples
model = Model{Float64}()
x = add_variable(model)
source
## Utilities.UniversalFallback
MathOptInterface.Utilities.UniversalFallbackType
UniversalFallback
The UniversalFallback can be applied on a MathOptInterface.ModelLike model to create the model UniversalFallback(model) supporting any constraint and attribute. This allows to have a specialized implementation in model for performance critical constraints and attributes while still supporting other attributes with a small performance penalty. Note that model is unaware of constraints and attributes stored by UniversalFallback so this is not appropriate if model is an optimizer (for this reason, MathOptInterface.optimize! has not been implemented). In that case, optimizer bridges should be used instead.
source
## Utilities.@macro
MathOptInterface.Utilities.@modelMacro
macro model(
model_name,
scalar_sets,
typed_scalar_sets,
vector_sets,
typed_vector_sets,
scalar_functions,
typed_scalar_functions,
vector_functions,
typed_vector_functions,
is_optimizer = false
)
Creates a type model_name implementing the MOI model interface and containing scalar_sets scalar sets typed_scalar_sets typed scalar sets, vector_sets vector sets, typed_vector_sets typed vector sets, scalar_functions scalar functions, typed_scalar_functions typed scalar functions, vector_functions vector functions and typed_vector_functions typed vector functions. To give no set/function, write (), to give one set S, write (S,).
The function MathOptInterface.VariableIndex should not be given in scalar_functions. The model supports MathOptInterface.VariableIndex-in-S constraints where S is MathOptInterface.EqualTo, MathOptInterface.GreaterThan, MathOptInterface.LessThan, MathOptInterface.Interval, MathOptInterface.Integer, MathOptInterface.ZeroOne, MathOptInterface.Semicontinuous or MathOptInterface.Semiinteger. The sets supported with the MathOptInterface.VariableIndex cannot be controlled from the macro, use the UniversalFallback to support more sets.
This macro creates a model specialized for specific types of constraint, by defining specialized structures and methods. To create a model that, in addition to be optimized for specific constraints, also support arbitrary constraints and attributes, use UniversalFallback.
If is_optimizer = true, the resulting struct is a of GenericOptimizer, which is a subtype of MathOptInterface.AbstractOptimizer, otherwise, it is a GenericModel, which is a subtype of MathOptInterface.ModelLike.
Examples
The model describing an linear program would be:
@model(LPModel, # Name of model
(), # untyped scalar sets
(MOI.EqualTo, MOI.GreaterThan, MOI.LessThan, MOI.Interval), # typed scalar sets
(MOI.Zeros, MOI.Nonnegatives, MOI.Nonpositives), # untyped vector sets
(), # typed vector sets
(), # untyped scalar functions
(MOI.ScalarAffineFunction,), # typed scalar functions
(MOI.VectorOfVariables,), # untyped vector functions
(MOI.VectorAffineFunction,), # typed vector functions
false
)
Let MOI denote MathOptInterface, MOIU denote MOI.Utilities. The macro would create the following types with struct_of_constraint_code:
struct LPModelScalarConstraints{T, C1, C2, C3, C4} <: MOIU.StructOfConstraints
moi_equalto::C1
moi_greaterthan::C2
moi_lessthan::C3
moi_interval::C4
end
struct LPModelVectorConstraints{T, C1, C2, C3} <: MOIU.StructOfConstraints
moi_zeros::C1
moi_nonnegatives::C2
moi_nonpositives::C3
end
struct LPModelFunctionConstraints{T} <: MOIU.StructOfConstraints
moi_scalaraffinefunction::LPModelScalarConstraints{
T,
MOIU.VectorOfConstraints{MOI.ScalarAffineFunction{T}, MOI.EqualTo{T}},
MOIU.VectorOfConstraints{MOI.ScalarAffineFunction{T}, MOI.GreaterThan{T}},
MOIU.VectorOfConstraints{MOI.ScalarAffineFunction{T}, MOI.LessThan{T}},
MOIU.VectorOfConstraints{MOI.ScalarAffineFunction{T}, MOI.Interval{T}}
}
moi_vectorofvariables::LPModelVectorConstraints{
T,
MOIU.VectorOfConstraints{MOI.VectorOfVariables, MOI.Zeros},
MOIU.VectorOfConstraints{MOI.VectorOfVariables, MOI.Nonnegatives},
MOIU.VectorOfConstraints{MOI.VectorOfVariables, MOI.Nonpositives}
}
moi_vectoraffinefunction::LPModelVectorConstraints{
T,
MOIU.VectorOfConstraints{MOI.VectorAffineFunction{T}, MOI.Zeros},
MOIU.VectorOfConstraints{MOI.VectorAffineFunction{T}, MOI.Nonnegatives},
MOIU.VectorOfConstraints{MOI.VectorAffineFunction{T}, MOI.Nonpositives}
}
end
const LPModel{T} = MOIU.GenericModel{T,MOIU.ObjectiveContainer{T},MOIU.VariablesContainer{T},LPModelFunctionConstraints{T}}
The type LPModel implements the MathOptInterface API except methods specific to optimizers like optimize! or get with VariablePrimal.
source
MathOptInterface.Utilities.GenericModelType
mutable struct GenericModel{T,O,V,C} <: AbstractModelLike{T}
Implements a model supporting coefficients of type T and:
• An objective function stored in .objective::O
• Variables and VariableIndex constraints stored in .variable_bounds::V
• F-in-S constraints (excluding VariableIndex constraints) stored in .constraints::C
All interactions should take place via the MOI interface, so the types O, V, and C should implement the API as needed for their functionality.
source
MathOptInterface.Utilities.GenericOptimizerType
mutable struct GenericOptimizer{T,O,V,C} <: AbstractOptimizer{T}
Implements a model supporting coefficients of type T and:
• An objective function stored in .objective::O
• Variables and VariableIndex constraints stored in .variable_bounds::V
• F-in-S constraints (excluding VariableIndex constraints) stored in .constraints::C
All interactions should take place via the MOI interface, so the types O, V, and C should implement the API as needed for their functionality.
source
MathOptInterface.Utilities.@struct_of_constraints_by_function_typesMacro
Utilities.@struct_of_constraints_by_function_types(name, func_types...)
Given a vector of n function types (F1, F2,..., Fn) in func_types, defines a subtype of StructOfConstraints of name name and which type parameters {T, C1, C2, ..., Cn}. It contains n field where the ith field has type Ci and stores the constraints of function type Fi.
The expression Fi can also be a union in which case any constraint for which the function type is in the union is stored in the field with type Ci.
source
MathOptInterface.Utilities.@struct_of_constraints_by_set_typesMacro
Utilities.@struct_of_constraints_by_set_types(name, func_types...)
Given a vector of n set types (S1, S2,..., Sn) in func_types, defines a subtype of StructOfConstraints of name name and which type parameters {T, C1, C2, ..., Cn}. It contains n field where the ith field has type Ci and stores the constraints of set type Si. The expression Si can also be a union in which case any constraint for which the set type is in the union is stored in the field with type Ci. This can be useful if Ci is a MatrixOfConstraints in order to concatenate the coefficients of constraints of several different set types in the same matrix.
source
MathOptInterface.Utilities.struct_of_constraint_codeFunction
struct_of_constraint_code(struct_name, types, field_types = nothing)
Given a vector of n Union{SymbolFun,_UnionSymbolFS{SymbolFun}} or Union{SymbolSet,_UnionSymbolFS{SymbolSet}} in types, defines a subtype of StructOfConstraints of name name and which type parameters {T, F1, F2, ..., Fn} if field_types is nothing and a {T} otherwise. It contains n field where the ith field has type Ci if field_types is nothing and type field_types[i] otherwise. If types is vector of Union{SymbolFun,_UnionSymbolFS{SymbolFun}} (resp. Union{SymbolSet,_UnionSymbolFS{SymbolSet}}) then the constraints of that function (resp. set) type are stored in the corresponding field.
This function is used by the macros @model, @struct_of_constraints_by_function_types and @struct_of_constraints_by_set_types.
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### Caching optimizer
MathOptInterface.Utilities.CachingOptimizerType
CachingOptimizer
CachingOptimizer is an intermediate layer that stores a cache of the model and links it with an optimizer. It supports incremental model construction and modification even when the optimizer doesn't.
A CachingOptimizer may be in one of three possible states (CachingOptimizerState):
• NO_OPTIMIZER: The CachingOptimizer does not have any optimizer.
• EMPTY_OPTIMIZER: The CachingOptimizer has an empty optimizer. The optimizer is not synchronized with the cached model.
• ATTACHED_OPTIMIZER: The CachingOptimizer has an optimizer, and it is synchronized with the cached model.
A CachingOptimizer has two modes of operation (CachingOptimizerMode):
• MANUAL: The only methods that change the state of the CachingOptimizer are Utilities.reset_optimizer, Utilities.drop_optimizer, and Utilities.attach_optimizer. Attempting to perform an operation in the incorrect state results in an error.
• AUTOMATIC: The CachingOptimizer changes its state when necessary. For example, optimize! will automatically call attach_optimizer (an optimizer must have been previously set). Attempting to add a constraint or perform a modification not supported by the optimizer results in a drop to EMPTY_OPTIMIZER mode.
source
MathOptInterface.Utilities.attach_optimizerFunction
attach_optimizer(model::CachingOptimizer)
Attaches the optimizer to model, copying all model data into it. Can be called only from the EMPTY_OPTIMIZER state. If the copy succeeds, the CachingOptimizer will be in state ATTACHED_OPTIMIZER after the call, otherwise an error is thrown; see MathOptInterface.copy_to for more details on which errors can be thrown.
source
MathOptInterface.Utilities.reset_optimizerFunction
reset_optimizer(m::CachingOptimizer, optimizer::MOI.AbstractOptimizer)
Sets or resets m to have the given empty optimizer optimizer.
Can be called from any state. An assertion error will be thrown if optimizer is not empty.
The CachingOptimizer m will be in state EMPTY_OPTIMIZER after the call.
source
reset_optimizer(m::CachingOptimizer)
Detaches and empties the current optimizer. Can be called from ATTACHED_OPTIMIZER or EMPTY_OPTIMIZER state. The CachingOptimizer will be in state EMPTY_OPTIMIZER after the call.
source
## Printing
MathOptInterface.Utilities.latex_formulationFunction
latex_formulation(model::MOI.ModelLike; kwargs...)
Wrap model in a type so that it can be pretty-printed as text/latex in a notebook like IJulia, or in Documenter.
To render the model, end the cell with latex_formulation(model), or call display(latex_formulation(model)) in to force the display of the model from inside a function.
Possible keyword arguments are:
• simplify_coefficients : Simplify coefficients if possible by omitting them or removing trailing zeros.
• default_name : The name given to variables with an empty name.
• print_types : Print the MOI type of each function and set for clarity.
source
## Copy utilities
MathOptInterface.Utilities.ModelFilterType
ModelFilter(filter::Function, model::MOI.ModelLike)
A layer to filter out various components of model.
The filter function takes a single argument, which is eacy element from the list returned by the attributes below. It returns true if the element should be visible in the filtered model and false otherwise.
The components that are filtered are:
• Entire constraint types via:
• MOI.ListOfConstraintTypesPresent
• Individual constraints via:
• MOI.ListOfConstraintIndices{F,S}
• Specific attributes via:
• MOI.ListOfModelAttributesSet
• MOI.ListOfConstraintAttributesSet
• MOI.ListOfVariableAttributesSet
Warning
The list of attributes filtered may change in a future release. You should write functions that are generic and not limited to the five types listed above. Thus, you should probably define a fallback filter(::Any) = true.
See below for examples of how this works.
Note
This layer has a limited scope. It is intended by be used in conjunction with MOI.copy_to.
Example: copy model excluding integer constraints
Use the do syntax to provide a single function.
filtered_src = MOI.Utilities.ModelFilter(src) do item
return item != (MOI.VariableIndex, MOI.Integer)
end
MOI.copy_to(dest, filtered_src)
Example: copy model excluding names
Use type dispatch to simplify the implementation:
my_filter(::Any) = true # Note the generic fallback!
my_filter(::MOI.VariableName) = false
my_filter(::MOI.ConstraintName) = false
filtered_src = MOI.Utilities.ModelFilter(my_filter, src)
MOI.copy_to(dest, filtered_src)
Example: copy irreducible infeasible subsystem
my_filter(::Any) = true # Note the generic fallback!
function my_filter(ci::MOI.ConstraintIndex)
status = MOI.get(dest, MOI.ConstraintConflictStatus(), ci)
return status != MOI.NOT_IN_CONFLICT
end
filtered_src = MOI.Utilities.ModelFilter(my_filter, src)
MOI.copy_to(dest, filtered_src)
source
## MatrixOfConstraints
MathOptInterface.Utilities.MatrixOfConstraintsType
mutable struct MatrixOfConstraints{T,AT,BT,ST} <: MOI.ModelLike
coefficients::AT
constants::BT
sets::ST
caches::Vector{Any}
are_indices_mapped::Vector{BitSet}
final_touch::Bool
end
Represent ScalarAffineFunction and VectorAffinefunction constraints in a matrix form where the linear coefficients of the functions are stored in the coefficients field, the constants of the functions or sets are stored in the constants field. Additional information about the sets are stored in the sets field.
This model can only be used as the constraints field of a MOI.Utilities.AbstractModel.
When the constraints are added, they are stored in the caches field. They are only loaded in the coefficients and constants fields once MOI.Utilities.final_touch is called. For this reason, MatrixOfConstraints should not be used by an incremental interface. Use MOI.copy_to instead.
The constraints can be added in two different ways:
1. With add_constraint, in which case a canonicalized copy of the function is stored in caches.
2. With pass_nonvariable_constraints, in which case the functions and sets are stored themselves in caches without mapping the variable indices. The corresponding index in caches is added in are_indices_mapped. This avoids doing a copy of the function in case the getter of CanonicalConstraintFunction does not make a copy for the source model, e.g., this is the case of VectorOfConstraints.
We illustrate this with an example. Suppose a model is copied from a src::MOI.Utilities.Model to a bridged model with a MatrixOfConstraints. For all the types that are not bridged, the constraints will be copied with pass_nonvariable_constraints. Hence the functions stored in caches are exactly the same as the ones stored in src. This is ok since this is only during the copy_to operation during which src cannot be modified. On the other hand, for the types that are bridged, the functions added may contain duplicates even if the functions did not contain duplicates in src so duplicates are removed with MOI.Utilities.canonical.
Interface
The .coefficients::AT type must implement:
The .constants::BT type must implement:
The .sets::ST type must implement:
source
### .coefficients
MathOptInterface.Utilities.load_termsFunction
load_terms(coefficients, index_map, func, offset)::Nothing
Loads the terms of func to coefficients, mapping the variable indices with index_map.
The ith dimension of func is loaded at the (offset + i)th row of coefficients.
The function must be allocated first with allocate_terms.
The function func must be canonicalized, see is_canonical.
source
MathOptInterface.Utilities.final_touchFunction
final_touch(coefficients)::Nothing
Informs the coefficients that all functions have been added with load_terms. No more modification is allowed unless MOI.empty! is called.
final_touch(sets)::Nothing
Informs the sets that all functions have been added with add_set. No more modification is allowed unless MOI.empty! is called.
source
MathOptInterface.Utilities.extract_functionFunction
extract_function(coefficients, row::Integer, constant::T) where {T}
Return the MOI.ScalarAffineFunction{T} function corresponding to row row in coefficients.
extract_function(
coefficients,
rows::UnitRange,
constants::Vector{T},
) where{T}
Return the MOI.VectorAffineFunction{T} function corresponding to rows rows in coefficients.
source
MathOptInterface.Utilities.MutableSparseMatrixCSCType
mutable struct MutableSparseMatrixCSC{Tv,Ti<:Integer,I<:AbstractIndexing}
indexing::I
m::Int
n::Int
colptr::Vector{Ti}
rowval::Vector{Ti}
nzval::Vector{Tv}
end
Matrix type loading sparse matrices in the Compressed Sparse Column format. The indexing used is indexing, see AbstractIndexing. The other fields have the same meaning than for SparseArrays.SparseMatrixCSC except that the indexing is different unless indexing is OneBasedIndexing.
The matrix is loaded in 5 steps:
1. MOI.empty! is called.
2. MOI.Utilities.add_column and MOI.Utilities.allocate_terms are called in any order.
3. MOI.Utilities.set_number_of_rows is called.
4. MOI.Utilities.load_terms is called for each affine function.
5. MOI.Utilities.final_touch is called.
source
MathOptInterface.Utilities.ZeroBasedIndexingType
struct ZeroBasedIndexing <: AbstractIndexing end
Zero-based indexing: the ith row or column has index i - 1. This is useful when the vectors of row and column indices need to be communicated to a library using zero-based indexing such as C libraries.
source
### .constants
MathOptInterface.Utilities.load_constantsFunction
load_constants(constants, offset, func_or_set)::Nothing
This function loads the constants of func_or_set in constants at an offset of offset. Where offset is the sum of the dimensions of the constraints already loaded. The storage should be preallocated with resize! before calling this function.
This function should be implemented to be usable as storage of constants for MatrixOfConstraints.
The constants are loaded in three steps:
1. Base.empty! is called.
2. Base.resize! is called with the sum of the dimensions of all constraints.
3. MOI.Utilities.load_constants is called for each function for vector constraint or set for scalar constraint.
source
### .sets
MathOptInterface.Utilities.add_setFunction
add_set(sets, i)::Int64
Add a scalar set of type index i.
add_set(sets, i, dim)::Int64
Add a vector set of type index i and dimension dim.
Both methods return a unique Int64 of the set that can be used to reference this set.
source
MathOptInterface.Utilities.rowsFunction
rows(sets, ci::MOI.ConstraintIndex)::Union{Int,UnitRange{Int}}
Return the rows in 1:MOI.dimension(sets) corresponding to the set of id ci.value.
For scalar sets, this returns an Int. For vector sets, this returns an UnitRange{Int}.
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## Fallbacks
MathOptInterface.Utilities.get_fallbackFunction
get_fallback(model::MOI.ModelLike, ::MOI.ObjectiveValue)
Compute the objective function value using the VariablePrimal results and the ObjectiveFunction value.
source
get_fallback(model::MOI.ModelLike, ::MOI.DualObjectiveValue, T::Type)::T
Compute the dual objective value of type T using the ConstraintDual results and the ConstraintFunction and ConstraintSet values. Note that the nonlinear part of the model is ignored.
source
get_fallback(model::MOI.ModelLike, ::MOI.ConstraintPrimal,
constraint_index::MOI.ConstraintIndex)
Compute the value of the function of the constraint of index constraint_index using the VariablePrimal results and the ConstraintFunction values.
source
get_fallback(model::MOI.ModelLike, attr::MOI.ConstraintDual,
ci::MOI.ConstraintIndex{Union{MOI.VariableIndex,
MOI.VectorOfVariables}})
Compute the dual of the constraint of index ci using the ConstraintDual of other constraints and the ConstraintFunction values. Throws an error if some constraints are quadratic or if there is one another MOI.VariableIndex-in-S or MOI.VectorOfVariables-in-S constraint with one of the variables in the function of the constraint ci.
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## Function utilities
The following utilities are available for functions:
MathOptInterface.Utilities.map_indicesFunction
map_indices(index_map::Function, x::X)::X where {X}
Substitute any MOI.VariableIndex (resp. MOI.ConstraintIndex) in x by the MOI.VariableIndex (resp. MOI.ConstraintIndex) of the same type given by index_map(x).
This function is used by implementations of MOI.copy_to on constraint functions, attribute values and submittable values hence it needs to be implemented for custom types that are meant to be used as attribute or submittable value.
source
MathOptInterface.Utilities.substitute_variablesFunction
substitute_variables(variable_map::Function, x)
Substitute any MOI.VariableIndex in x by variable_map(x). The variable_map function returns either MOI.VariableIndex or MOI.ScalarAffineFunction, see eval_variables for a similar function where variable_map returns a number.
This function is used by bridge optimizers on constraint functions, attribute values and submittable values when at least one variable bridge is used hence it needs to be implemented for custom types that are meant to be used as attribute or submittable value.
WARNING: Don't use substitude_variables(::Function, ...) because Julia will not specialize on this. Use instead substitude_variables(::F, ...) where {F<:Function}.
source
MathOptInterface.Utilities.filter_variablesFunction
filter_variables(keep::Function, f::AbstractFunction)
Return a new function f with the variable vi such that !keep(vi) removed.
WARNING: Don't define filter_variables(::Function, ...) because Julia will not specialize on this. Define instead filter_variables(::F, ...) where {F<:Function}.
source
MathOptInterface.Utilities.remove_variableFunction
remove_variable(f::AbstractFunction, vi::VariableIndex)
Return a new function f with the variable vi removed.
source
remove_variable(f::MOI.AbstractFunction, s::MOI.AbstractSet, vi::MOI.VariableIndex)
Return a tuple (g, t) representing the constraint f-in-s with the variable vi removed. That is, the terms containing the variable vi in the function f are removed and the dimension of the set s is updated if needed (e.g. when f is a VectorOfVariables with vi being one of the variables).
source
MathOptInterface.Utilities.all_coefficientsFunction
all_coefficients(p::Function, f::MOI.AbstractFunction)
Determine whether predicate p returns true for all coefficients of f, returning false as soon as the first coefficient of f for which p returns false is encountered (short-circuiting). Similar to all.
source
MathOptInterface.Utilities.unsafe_addFunction
unsafe_add(t1::MOI.ScalarAffineTerm, t2::MOI.ScalarAffineTerm)
Sums the coefficients of t1 and t2 and returns an output MOI.ScalarAffineTerm. It is unsafe because it uses the variable of t1 as the variable of the output without checking that it is equal to that of t2.
source
unsafe_add(t1::MOI.ScalarQuadraticTerm, t2::MOI.ScalarQuadraticTerm)
Sums the coefficients of t1 and t2 and returns an output MOI.ScalarQuadraticTerm. It is unsafe because it uses the variable's of t1 as the variable's of the output without checking that they are the same (up to permutation) to those of t2.
source
unsafe_add(t1::MOI.VectorAffineTerm, t2::MOI.VectorAffineTerm)
Sums the coefficients of t1 and t2 and returns an output MOI.VectorAffineTerm. It is unsafe because it uses the output_index and variable of t1 as the output_index and variable of the output term without checking that they are equal to those of t2.
source
MathOptInterface.Utilities.isapprox_zeroFunction
isapprox_zero(f::MOI.AbstractFunction, tol)
Return a Bool indicating whether the function f is approximately zero using tol as a tolerance.
Important note
This function assumes that f does not contain any duplicate terms, you might want to first call canonical if that is not guaranteed. For instance, given
f = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1, -1], [x, x]), 0).
then isapprox_zero(f) is false but isapprox_zero(MOIU.canonical(f)) is true.
source
MathOptInterface.Utilities.zero_with_output_dimensionFunction
zero_with_output_dimension(::Type{T}, output_dimension::Integer) where {T}
Create an instance of type T with the output dimension output_dimension.
This is mostly useful in Bridges, when code needs to be agnostic to the type of vector-valued function that is passed in.
source
The following functions can be used to canonicalize a function:
MathOptInterface.Utilities.canonicalFunction
canonical(
f::Union{
ScalarAffineFunction,
VectorAffineFunction,
},
)
Returns the function in a canonical form, i.e.
• A term appear only once.
• The coefficients are nonzero.
• The terms appear in increasing order of variable where there the order of the variables is the order of their value.
• For a AbstractVectorFunction, the terms are sorted in ascending order of output index.
The output of canonical can be assumed to be a copy of f, even for VectorOfVariables.
Examples
If x (resp. y, z) is VariableIndex(1) (resp. 2, 3). The canonical representation of ScalarAffineFunction([y, x, z, x, z], [2, 1, 3, -2, -3], 5) is ScalarAffineFunction([x, y], [-1, 2], 5).
source
MathOptInterface.Utilities.canonicalize!Function
canonicalize!(f::Union{ScalarAffineFunction, VectorAffineFunction})
Convert a function to canonical form in-place, without allocating a copy to hold the result. See canonical.
source
canonicalize!(f::Union{ScalarQuadraticFunction, VectorQuadraticFunction})
Convert a function to canonical form in-place, without allocating a copy to hold the result. See canonical.
source
The following functions can be used to manipulate functions with basic algebra:
MathOptInterface.Utilities.scalarizeFunction
scalarize(func::MOI.VectorOfVariables, ignore_constants::Bool = false)
Returns a vector of scalar functions making up the vector function in the form of a Vector{MOI.SingleVariable}.
See also eachscalar.
source
scalarize(func::MOI.VectorAffineFunction{T}, ignore_constants::Bool = false)
Returns a vector of scalar functions making up the vector function in the form of a Vector{MOI.ScalarAffineFunction{T}}.
See also eachscalar.
source
scalarize(func::MOI.VectorQuadraticFunction{T}, ignore_constants::Bool = false)
Returns a vector of scalar functions making up the vector function in the form of a Vector{MOI.ScalarQuadraticFunction{T}}.
See also eachscalar.
source
MathOptInterface.Utilities.promote_operationFunction
promote_operation(
op::Function,
::Type{T},
ArgsTypes::Type{<:Union{T, MOI.AbstractFunction}}...,
) where {T}
Returns the type of the MOI.AbstractFunction returned to the call operate(op, T, args...) where the types of the arguments args are ArgsTypes.
source
MathOptInterface.Utilities.operateFunction
operate(
op::Function,
::Type{T},
args::Union{T,MOI.AbstractFunction}...,
)::MOI.AbstractFunction where {T}
Returns an MOI.AbstractFunction representing the function resulting from the operation op(args...) on functions of coefficient type T. No argument can be modified.
source
MathOptInterface.Utilities.operate!Function
operate!(
op::Function,
::Type{T},
args::Union{T, MOI.AbstractFunction}...,
)::MOI.AbstractFunction where {T}
Returns an MOI.AbstractFunction representing the function resulting from the operation op(args...) on functions of coefficient type T. The first argument can be modified. The return type is the same than the method operate(op, T, args...) without !.
source
MathOptInterface.Utilities.operate_output_index!Function
operate_output_index!(
op::Function,
::Type{T},
output_index::Integer,
func::MOI.AbstractVectorFunction
args::Union{T, MOI.AbstractScalarFunction}...
)::MOI.AbstractFunction where {T}
Returns an MOI.AbstractVectorFunction where the function at output_index is the result of the operation op applied to the function at output_index of func and args. The functions at output index different to output_index are the same as the functions at the same output index in func. The first argument can be modified.
source
MathOptInterface.Utilities.vectorizeFunction
vectorize(x::AbstractVector{MOI.VariableIndex})
Returns the vector of scalar affine functions in the form of a MOI.VectorAffineFunction{T}.
source
vectorize(funcs::AbstractVector{MOI.ScalarAffineFunction{T}}) where T
Returns the vector of scalar affine functions in the form of a MOI.VectorAffineFunction{T}.
source
vectorize(funcs::AbstractVector{MOI.ScalarQuadraticFunction{T}}) where T
Returns the vector of scalar quadratic functions in the form of a MOI.VectorQuadraticFunction{T}.
source
## Constraint utilities
The following utilities are available for moving the function constant to the set for scalar constraints:
MathOptInterface.Utilities.shift_constantFunction
shift_constant(set::MOI.AbstractScalarSet, offset)
Returns a new scalar set new_set such that func-in-set is equivalent to func + offset-in-new_set.
Only define this function if it makes sense to!
Use supports_shift_constant to check if the set supports shifting:
if supports_shift_constant(typeof(old_set))
new_set = shift_constant(old_set, offset)
f.constant = 0
else
end
See also supports_shift_constant.
Examples
The call shift_constant(MOI.Interval(-2, 3), 1) is equal to MOI.Interval(-1, 4).
source
MathOptInterface.Utilities.normalize_and_add_constraintFunction
normalize_and_add_constraint(
model::MOI.ModelLike,
func::MOI.AbstractScalarFunction,
set::MOI.AbstractScalarSet;
allow_modify_function::Bool = false,
)
Adds the scalar constraint obtained by moving the constant term in func to the set in model. If allow_modify_function is true then the function func can be modified.
source
MathOptInterface.Utilities.normalize_constantFunction
normalize_constant(
func::MOI.AbstractScalarFunction,
set::MOI.AbstractScalarSet;
allow_modify_function::Bool = false,
)
Return the func-in-set constraint in normalized form. That is, if func is MOI.ScalarQuadraticFunction or MOI.ScalarAffineFunction, the constant is moved to the set. If allow_modify_function is true then the function func can be modified.
source
The following utility identifies those constraints imposing bounds on a given variable, and returns those bound values:
MathOptInterface.Utilities.get_boundsFunction
get_bounds(model::MOI.ModelLike, ::Type{T}, x::MOI.VariableIndex)
Return a tuple (lb, ub) of type Tuple{T, T}, where lb and ub are lower and upper bounds, respectively, imposed on x in model.
source
The following utilities are useful when working with symmetric matrix cones.
## DoubleDicts
MathOptInterface.Utilities.DoubleDicts.DoubleDictType
DoubleDict{V}
An optimized dictionary to map MOI.ConstraintIndex to values of type V.
Works as a AbstractDict{MOI.ConstraintIndex,V} with minimal differences.
If V is also a MOI.ConstraintIndex, use IndexDoubleDict.
Note that MOI.ConstraintIndex is not a concrete type, opposed to MOI.ConstraintIndex{MOI.VariableIndex, MOI.Integers}, which is a concrete type.
When looping through multiple keys of the same Function-in-Set type, use
inner = dict[F, S]
to return a type-stable DoubleDictInner`.
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http://jasss.soc.surrey.ac.uk/19/1/7.html | ### Abstract
Providing parents and students a choice to attend schools other than their assigned neighborhood school has been a leading theme in recent education reform. To evaluate the effects of such choice-based programs, researchers have taken advantage of the randomization that occurs in student assignment lotteries put in place to deal with oversubscription to popular schools and pilot programs. In this study, I used an agent-based model of the transition to school choice as platform for examining the sensitivity of school choice treatment effects from lottery-based studies to differences in student preferences and program participation rates across hypothetical study populations. I found that districts with higher participation rates had lower treatment effects, even when there were no differences in the distributions of school quality and student preferences between districts. This is because capacity constraints increasingly limited the amount of students who are able to attend the highest quality schools, causing the magnitude of the treatment effect to fall. I discuss the implications of this finding for interpreting the results of lottery-based studies involving choice schools.
Keywords:
Public Policy, Education, School Choice, Causal Inference
### Introduction
1.1
Providing parents and students a choice to attend schools other than their assigned neighborhood school has been a leading theme in recent education reform in many countries (Gill et al. 2007; Berends et al. 2009). Computational models of such school choice programs have been helpful in articulating and testing their underlying market-based logic (Maroulis et al. 2010). In the complex systems literature, the models have taken the form of agent-based simulations that model the emergence of school district-level outcomes from the micro-level behaviors of students and parents (Harland & Heppenstall 2012; Millington et al. 2014; Maroulis et al. 2014).[1]
1.2
For example, Millington et al. (2014) developed an agent-based simulation where parents differ in their "aspiration" for school achievement and schools differ in their ability to improve student outcomes. They demonstrated that such a model can generate distributions of enrollment, performance, and spatial allocation that match empirically observed patterns, and examined the consequences for parents with different aspirations. Maroulis et al. (2014) modeled the transition from a catchment area to open enrollment system, using data from Chicago Public Schools to initialize their simulation. Analysis of their model revealed how district-level achievement outcomes depend not only on the quantity and quality of new schools, but also on the timing of their entry. Harland and Heppenstall (2012) outlined the usefulness of agent-based simulation for student allocation by creating an agent-based simulation of an educational market in the United Kingdom.
1.3
In this paper, I use computational modeling to make a complementary but different type of contribution. Instead of creating a new model to investigate some not-yet-well-understood aspect of school choice dynamics, I use an existing agent-based model of school choice to gain a better understanding of the advantages and limitations of an approach for estimating the effectiveness of school choice programs that is growing in popularity and influence in the educational policy literature – randomized field trials made possible by student assignment lotteries put in place to deal with oversubscription. The larger motivation for this use of computational modeling is as follows: Despite the usefulness and growing utilization of the complex systems perspective in studying emergence and change in social and economic systems (Maroulis et al. 2010), its ideas and tools have yet to have a widespread impact on traditional management and policy research. An underlying premise of this paper is that in order to have greater impact on management and public policy, complex systems research must attempt to be more tightly integrated with existing the theory, methods, and findings in the substantive area of the phenomenon of interest. In the context of school choice reform, the current methodological state-of-the art is the use of lottery-based experiments to draw causal inference, and consequently the focus of this paper.
1.4
More specifically, I use an agent-based model calibrated to data on Chicago Public Schools to investigate the sensitivity of the treatment effect estimates of lottery-based studies – that is, the difference in educational outcomes between participants and non-participants of such programs that is attributable to the policy intervention – to differences in the underlying student preferences and the program participation rates in a district implementing a choice program. Experimentation with the model reveals that as the student participation rate rises, the magnitude of the treatment effect falls, even when there are no differences in distributions of school quality and student preferences across districts. The primary implication of this finding is that treatment effect estimates across districts cannot be compared without also simultaneously considering the participation rate and capacity of the district. This is a limitation of lottery-based studies that in hindsight is clear but in practice almost always overlooked.
1.5
The paper proceeds in four main sections. The first section briefly reviews the value and use of lottery-based studies in the school choice literature. The second section describes the agent-based model used as the platform for the computational experiments. The third section presents results from computational experiments from hypothetical districts that differ with respect to the emphasis on school achievement students place on their school choice decision, as well as the participation rates of the program. The final section discusses the implications of the computational results for interpreting the results of lottery-based studies involving choice schools.
### Randomized Field Experiments in School Choice
2.1
Regardless of whether this idea manifests itself as increased access to non-neighborhood public schools, specialized charter schools, or private schooling, a much-studied aspect of such programs is identifying the treatment effect of "choice" schools on students. Historically, estimates of this effect have come from large observational studies of student performance from different school sectors (e.g., public, private, religious) – studies that have been subject to the long-standing criticism of unobserved selection bias (Alexander & Pallas 1983, Manski 1993). That is, even when controlling for observable differences between those who attend choice schools and those who do not, one cannot eliminate the possibility that unobservable differences, such as student motivation or the value a family places on education, are inflating the observed difference in outcomes between the two groups.
2.2
Student assignment lotteries put in place to deal with oversubscription to popular schools and pilot choice programs (mostly in the United States) have helped overcome this methodological problem. Such lotteries – where after submitting an application to a school or a program, students are randomly selected for admission – have provided researchers excellent opportunities to conduct randomized field experiments. By eliminating the selection bias concerns that have historically caused much debate in observational studies on the achievement effects of non-neighborhood schools (Coleman et al. 1982; Alexander & Pallas 1983; Bryk et al. 1993; Morgan 2001; Altonji et al. 2002), lottery-based studies are forming a base of evidence that can help us assess the achievement effects within and across types of choice schools. Examples include analyses of private school voucher pilots (Greene et al. 1997; Howell et al. 2002), charter schools (Hoxby & Rockoff 2005; Abdulkadiroglu et al. 2009; Gleason et al. 2010), and public choice programs (Cullen et al. 2006).
2.3
However despite their high internal validity, treatment effect estimates from lottery-based studies have been critiqued for not telling us all we need to know about choice as educational policy. The primary critique is that their effect estimates are only able to capture the short-term gains from students sorting into different schools (Goldhaber & Eide 2003). They likely cannot capture the longer-term, systemic effects predicted by the market-based logic of school choice reform, such as gains from increased competition or investment as predicted (Hoxby 2003; Sirer et al. 2015). In the next section, I describe a model that demonstrates an additional, and often overlooked, limitation of lottery-based studies that is independent of these typical critiques.
### Model Description
3.1
To conduct the computational experiments, I used an agent-based model of the transition to public school choice recently published in JASSS (Maroulis et al. 2014). The original model highlighted the importance of considering the dynamics, and not just equilibrium characteristics, of the transition to school choice. More specifically, it demonstrated that the equilibrium outcome of transitioning to choice depends not only on the quality and total number of new schools in the system, but also on the timing of the entry of those new entrants. In this section, I provide a brief overview of the model highlighting the features most pertinent to the current study. For additional details, the reader is referred to the original paper. The model itself is publicly available at the ComSES Computational Model Library.[2] The ComSES upload includes an initialization file of synthetic data resembling the Chicago Public Schools (CPS) data used by the authors of the original study.
3.2
The agents in the model are students and schools who are a placed on a grid of sites that represent the geography of the city of Chicago (Figure 1). Students rank schools by using a preference function based on the mean student achievement and geographic proximity of a school:
$$U_{ij} (ma_j, proximity_{ij}) = ma_j^{\alpha_i} \ast proximity_{ij}^{(1-\alpha_i)}$$ (1)
$$\alpha_i$$ determines the weight given by a student to the mean achievement of the school. In the original model values of $$\alpha_i$$ were distributed across students by drawing from a normal distribution with mean $$\alpha$$ and a standard deviation of 0.05, a parameterization I keep here.
3.3
Schools augment the achievement of their students using a growth function based on the characteristics of the student and a school-specific quality parameter referred to as the "value-added" of the school. The coefficients of the achievement growth function and the distribution of the school-specific value-added parameter were statistically estimated using data from CPS. More specifically, achievement for student $$i$$ attending school $$j$$ in any given time period of the model is determined using the following equation (Maroulis et al. 2014, Table 1):
$$achiev_{2i} = -0.0956 + 0.6794 \ast achiev_{1i} + 0.1567*white_i + 0.1151*male_i- 0.0629 \ast poverty_i + va_j + r_{ij}$$ (2)
$$achiev_1$$ is the 8th grade standardize math score of a student. $$white$$ and $$male$$ are indicator variables for race and gender, respectively. $$poverty$$ is the concentration of poverty in the student's home census block. $$achiev_1$$, $$white$$, $$male$$, and $$poverty$$ are all student-level variables that come from the initialization file. $$va_j$$ is the value-added of school $$j$$. $$r_{ij}$$ is an error term drawn randomly from a normal distribution with mean zero. The $$va$$ for each school and the standard deviation of the distribution of $$r_{ij}$$ were estimated from the CPS data.
3.4
At time period zero, all students attend their assigned catchment area school. Starting with time period 1, incoming cohorts of students are allowed to start choosing their school based on the preference function described in Equation (1). The percentage of students who can choose (the "choosers") is determined by the exogenous parameter, $$pc$$. In random order, choosers attempt to attend their top ranked school and continue working through their ranked list of schools until they find a placement. Students are guaranteed admission to their assigned catchment area school. For others, placement can be denied only if there are no spaces available at a chosen school. The number of available spaces at a school is a function of its design capacity, which comes from the initialization file of the model.
3.5
Once enrolled in a school, a student remains at the same school for four years and receives an achievement gain determined by Equation (2). Over time, some schools gain students while others lose them. Schools whose enrollments fall below a minimum threshold of enrollment are permanently closed. The original model included a mechanism for the introduction of new schools. I turn this mechanism off for the purposes of the experiments presented below. I also created a new measure, "better available capacity" ($$bac$$), to capture a dimension important to the current study – the amount of "good slack" or "good excess capacity" available to choosers at the beginning of the simulation. $$bac$$ was calculated by asking every randomly assigned chooser at the start of the simulation to calculate the number of spaces per school potentially available to them with a higher value-added. It is the mean of this student-level quantity across all choosers.
Figure 1. Model Description (adapted from Maroulis et al. 2014)
### Computational Experiments and Analysis
4.1
The primary goal of the computational experiments presented in this section was to understand how district-level achievement outcomes varied depending on a) the relative weight given to mean achievement of the a school by the choosers, $$\alpha$$, and b) the percentage of students who are able to take advantage of the ability to choose, $$pc$$. Data was generated by systematically running the model for twenty time periods under various combinations of $$\alpha$$ and $$pc$$. Each run of the model represents a stochastic process. Therefore, each combination of parameters was repeated fifty times to create a distribution of outcomes for a particular set of parameter values.
#### Outcome 1: Mean Achievement
4.2
Figure 2 plots the mean achievement across all students at the end of twenty time periods. Each point on the figure represents the average of the final mean achievement value across the fifty runs for the hypothetical district characterized by a particular combination of $$\alpha$$ and the percent choosers, $$pc$$. When comparing the scenarios in Figure 2, there were no surprises: the more that individual students favored achievement relative to geographic proximity (i.e., high $$\alpha$$), the higher the mean achievement. Also, with the exception of the case where students heavily favored geographic proximity ($$\alpha = 0.2$$), the greater fraction of students who participated in the program, the higher the mean achievement of the district. It is interesting to note, however, that the overall change in mean achievement across runs in Figure 2 was rather small. Even in the best-case scenario ($$\alpha =1$$), the difference between the initial mean achievement and the final mean achievement after giving students choice was not greater than 0.05 standard deviations. The reason for this is that for the sample of CPS students used to initialize the achievement growth rule of the model, school effects make a relatively small contribution to a student achievement growth when compared to individual-level factors (Maroulis et al. 2014, Table 1).
Figure 2. Mean Achievement versus Percent Choosers, by $$\alpha$$
#### Outcome 2: Treatment Effect
4.3
The treatment effect of a real world lottery-based study is estimated by comparing the outcomes of those given the opportunity to attend a new school to those who were not (e.g., lottery winners vs. non-winners). A conceptually similar measure can be calculated in the simulation by comparing the choosers to the non-choosers. More specifically, the treatment effect for any given run of the model was calculated by taking the difference in mean achievement between choosers and non-choosers at the completion of a run. Since in the simulation we can be certain only the randomly selected choosers could attend a different school and that all of those given the opportunity to choose did indeed do so (e.g., there were no "non-compliers"), no additional adjustments are necessary. Figure 3 plots this treatment effect at the completion of the twenty-time period runs versus $$pc$$ for a range of $$\alpha$$ values. As in Figure 2, each point represents the average across the fifty runs for the hypothetical district characterized by that particular combination of parameters.
Figure 3. Treatment Effect vs. Percent Choosers, by $$\alpha$$
4.4
As might be expected, treatment effects were for the most part larger for the hypothetical districts where individuals placed a higher value on the achievement of the school (higher $$\alpha$$). However, when comparing the results for hypothetical districts with the same value of $$\alpha$$, the treatment effect largely goes down as $$pc$$ increases – the exact opposite relationship than what was observed between percent choosers and mean achievement in Figure 2. Stated differently, if one were to use the treatment effects to compare the effectiveness of school choice in high participation district and low participation district – but identical in every other way – one would mistakenly infer that the choice program helped the high participation district less than the low participation district.
4.5
The reason for this highlights the importance of considering the underlying mechanisms of a system when estimating and interpreting causal effects: In cases where there is very low participation, most students looking for a new school are likely to find a spot at one of the highest value-added schools, consequently realizing the largest achievement increases possible in the system. For example, in the extreme case where only one student is given the ability to choose, that student would likely find room in a very high value-added school. When comparing her achievement gain to the non-choosers (i.e., everyone else) it will be high. But what if fifty, or a hundred, or a thousand students participated? While the program participants would still likely to attend schools with higher value-added than the one from which they came, they would also have to start filing into schools with lower value-added. That is, the thousandth chooser would most likely not attend a school with as high a value-added as the first chooser, and therefore receive less benefit from the program than the first. Consequently, as long as capacity constraints exist and schools do not have essentially the same value-added, the mean achievement of choosers in comparison to non-choosers must necessarily decrease as more students take advantage of the opportunity to choose.[3]
#### Relationship to Initial District Capacity
4.6
The results depicted in Figure 3 were generated using the same distribution of available capacity across schools for each run, namely, the one inherited in the initialization file of Chicago Public Schools. School districts, of course, can vary in the amount of excess capacity available when a choice program is first implemented. Consequently, one would expect that in addition to the participation rate, the amount of high value-added capacity initially available in the system should impact the treatment effect of an experiment. To verify, I ran the model 200 times, each time randomly assigning the amount of better available capacity at the start of a run.[4] $$\alpha$$ was set to 1 for all runs. Figure 4 presents the treatment effect calculated at the end of each of the 200 runs corresponding to the $$bac$$ of the run. As expected, there was a clear relationship between $$bac$$ and treatment effect. Higher levels of better available capacity corresponded to larger differences in achievement between choosers and non-choosers. Note again that the hypothetical districts in these runs only differed in $$bac$$ and no other way. Students in each district valued academic achievement similarly and the distribution of value-added across schools was the same for each run.
Figure 4. Mean Achievement vs. Better Available Capacity
### Discussion and Conclusion
5.1
For research to be useful to policymaking it must be based on valid causal inferences. In the school choice debate, as in many other contexts, a key factor casting doubt on statements of cause has been concern about selection bias: How can we be sure that differences between students who attend choice schools and others are not attributable to unobserved factors that both influence their performance and make them more likely to attend those schools? Lotteries put in place to deal with oversubscription to sought-after programs and schools have provided a way out of this conundrum. By randomizing who is offered the opportunity to participate, lottery-based research designs break the link between treatment assignment and unobserved individual characteristics.
5.2
But as important as it is for researchers to make causal inferences with high internal validity, from a policy perspective it is equally important that we be able to interpret those inferences: Was the estimate due to the manner in which members of the study population chose which schools to attend? Will the effects at scale mirror those from a small program? Indeed, with a reform like school choice that has so many variants and is applied in so many contexts, the space of policy-relevant contingencies is quite large.
5.3
In this paper, I took a step towards the exploration that space through the use of agent-based simulation. More specifically, I conducted computational experiments similar in design and rationale to field experiments that compare the outcomes of randomly assigned lottery winners to non-winners. I kept the experimentation simple. I used an existing model that utilized a minimal set of stylized decision rules for the agents, and conducted experiments that manipulated those rules in straightforward ways. The experimentation led to a finding that in retrospect is necessarily true, but in foresight (and practice) almost always put in the background: Treatment effect estimates from districts with different program participation rates will be different, even if the districts are identical in every other way. This is because capacity constraints increasingly limit the amount of choosers who are able to attend the highest value-added schools, causing the magnitude of the treatment effect to fall.
5.4
One way to interpret this finding is that our model illustrates a violation of the stable unit treatment value assumption (SUTVA) of the "potential outcomes framework" of statistical causal inference (Rubin 1986). SUTVA states that the outcome for one subject does not depend on the treatment assigned to others. One potential SUTVA violation in school choice is already well known – the achievement of one student may depend on the composition of the others in their classroom or school (Zimmer & Toma 2000). This study highlights a less direct, but perhaps equally concerning problem: Even in the absence of classroom- or school-level peer effects, as long as capacity is limited, the expected outcome for any given student is dependent on the number of other students in the district who have similar preferences for schools.
5.5
At a minimum, the findings of this study imply that researchers should consider accounting for the amount of "better" capacity initially available to participants when using treatment effects estimated from existing programs to either a) project the impact of a larger scale program, or b) synthesize effect sizes estimated across programs. The measure developed in this study to characterize the better available capacity of the hypothetical districts in the model, $$bac$$, could be applied to program data to aid with both these purposes.
5.6
At a maximum, the findings of this study significantly add to existing concerns about using treatment effects from lottery-based studies to draw policy implications for school choice models. A common critique of short-term social experiments is that they do not adequately capture the general equilibrium consequences of a full-scale program, such as the effects of sustained competitive interaction between schools or investment by new entrants (as in the case of government vouchers that can be used in private schools) (Goldhaber & Eide 2003). A second concern pertains to the representativeness of the schools included in lottery-based studies (Tuttle et al. 2012). This study illustrates that even in the absence of systemic effects and sample representativeness issues, treatment effect estimates from well-executed field experiments can still yield misleading results. Indeed in the computational experiments, treatment effects were the most misleading when one would expect choice programs to be most effective – in cases where a large fraction of students took advantage of the increased access to schools (high $$pc$$), and did so by selecting schools on the basis of school achievement (high $$\alpha$$).
5.7
To be clear, the results of this study do not imply that lottery-based studies do not meaningfully estimate the effects of attending particular groups of schools. In fact, quite the opposite is true when SUTVA holds. But this study suggests that all else being equal, SUTVA is less likely to hold as participation in choice programs grows, even without turning to arguments about competition, investment, and direct peer effects. In this sense, lottery-based studies of school choice share a resemblance to randomized experiments that estimate the extent to which vaccines can protect individuals from becoming infected with disease. The SUTVA violation in vaccine trials has long been recognized as limitation, since vaccination can affect the infection likelihood of both treated and untreated persons. Consequently, to extrapolate from estimates of individual to population-level effectiveness, epidemiologists and public health researchers rely on computational models that treat the estimates of individual effectiveness as a single input in a larger dynamic process (e.g., Woodhouse et al. 1995; Colizza et al. 2007). This study suggests that a similar approach could be used with great benefit in the analysis of school choice programs.
5.8
Several caveats are warranted about the approach and assumptions of this study. First, I reiterate that the goal of this study was not to evaluate the causal effect of introducing any particular choice intervention. Instead, my intent was to generate insight that can aid the interpretation of existing findings, as well as guide the design of future empirical work. Relatedly, the data used to initialize this model come from a district that had already introduced an open enrollment program. As such, the initial state of the model may already reflect changes in student composition or school quality attributable to that program. While for current purposes this does not pose a problem, it does underscore that one should not attempt to draw causal inferences about the effect of the Chicago open enrollment program from any parts of the analysis and modeling in this study.
5.9
Second, though having the virtue of being simple and easy to interpret, the model used for experimentation admittedly uses incomplete rules for student and school behavior. Students used a utility function that evaluated schools on only two factors: mean achievement, whose value was shared by all students; and geographic proximity, whose value was calculated relative to a particular student. Moreover, schools could only impact students by improving their achievement, and that improvement was uniform across all students. An interesting extension of this study would relax these assumptions in a manner that would allow students to pick schools on criteria that "fit" them best. To the extent such matching occurs, one might find that the SUTVA violation observed this study might apply more to the estimation of effects for some student groups over others.
5.10
Third, two important feedback mechanisms associated with choice program improvement are not in the model: within-school improvement and new school entry. Both would likely affect the relative differences across scenarios depicted in Figure 2, and the magnitude of the treatment effects in Figure 3. However, the extent to which either mechanism would mitigate the SUTVA violation highlighted by our computational experiments depends on the extent to which this improvement was associated with adding better available capacity to the district. For example, if new schools (spawned by existing schools or started by new entities) could very quickly provide better available capacity, treatment effect estimates would be less sensitive to participation rates. While neither of these improvement mechanisms was explored in this paper, agent-based modeling is an approach well suited to the investigation of both in future work.
### Notes
1In economics, the models have taken the form of computational general equilibrium models (CGE) that incorporate interrelationships between education and related markets such as housing (for review, see Nechyba 2003).
2The model was developed using the NetLogo Programmable Modeling Environment (Wilensky 1999). The NetLogo code and initialization file can be accessed here: http://www.openabm.org/model/3695
3Note that this discussion assumes a positive correlation between mean achievement and value-added, which is indeed the case in the CPS data used to initialize the model. As a sensitivity analysis, I also ran computational experiments where students rank schools based on the value-added of the school, as opposed to the mean achievement. The decrease in treatment effect size as participation rate increased was even more pronounced when under this condition.
4The model does not have a slider specifically for $$bac$$. Instead, for each run I randomly assigned the percentage of choosers, and the extent to which schools are allowed to expand beyond their design capacity. Together these two factors determine $$bac$$.
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https://ko.overleaf.com/latex/templates/application-form-for-cfca/dstpksnnnqmh | AbstractCenter for Computational Astrophysics (CfCA) is a branch of National astronomical observatory of Japan (NAOJ) and provides computational resources for an astrophysicist. To use the resources, you have to submit a scientific proposal to CfCA. The application form for the submission is available from here. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33400118350982666, "perplexity": 2733.8543743807995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057033.33/warc/CC-MAIN-20210920070754-20210920100754-00578.warc.gz"} |
https://electronics.stackexchange.com/questions/148463/can-an-ammeter-damage-zeners | # can an ammeter damage zeners
So I got this small circuit that plugs to the mains as power source. as for its DC converter, it's one of those transformer-less ones that drops the voltage with a resistors and filters before rectifying and smoothing it. the ones that can only deliver small currents.
well, after that, it uses two IN4737 zeners in series to create a reference of 15V. I needed to find how much current is being drawn between the 1) DC converter (as described above) and 2) the zeners and the rest of the main larger circuit. so I disconnected the positive wire between these two and put in series an ammeter.
the measurements were odd. using my multimeter, it's here as follows (as I recall it properly):
20A range - 0.06 A
200mA range - 0.006 mA
20mA range - 0.060 mA
2mA range - I can't remember
200uA range - I can't remember
It was a weird set of readings (and yes the number I gave above for each range are exactly as they showed up in my display, even the units). I restored the original connection and the whole thing won't work anymore. I then found out that the IN4737's were blown and shorts at a few milliohms in both direction each.
so what went wrong?? the only difference was the ammeter in series for the positive wire between the converter and main circuit. aren't ammeters specifically designed to be passive and attempt to be a perfect conductor in all cases?? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8171440958976746, "perplexity": 1683.5886401455505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540518337.65/warc/CC-MAIN-20191209065626-20191209093626-00263.warc.gz"} |
https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/5342 | ## Pseudomale behaviour and spontaneous masculinization in the all-female teleost Poecilia formosa (Teleostei: Poeciliidae)
Please always quote using this URN: urn:nbn:de:bvb:20-opus-61688
• Pseudosexual behaviour is a rare phenomenon associated with unisexuality in vertebrates. In the gynogenetic, all-female teleost Poecilia formosa, rare individuals occur that resemble males of closely related gonochoristic species both in behaviour and external morphology. These masculinized gynogens and normal gynogens are members of the same clone, as demonstrated by DNA-fingerprinting. The behaviour of these masculinized gynogens is described and compared to the behaviour of the gonochoristic species Poecilia mexicana, P. latipinna and theirPseudosexual behaviour is a rare phenomenon associated with unisexuality in vertebrates. In the gynogenetic, all-female teleost Poecilia formosa, rare individuals occur that resemble males of closely related gonochoristic species both in behaviour and external morphology. These masculinized gynogens and normal gynogens are members of the same clone, as demonstrated by DNA-fingerprinting. The behaviour of these masculinized gynogens is described and compared to the behaviour of the gonochoristic species Poecilia mexicana, P. latipinna and their hybrid as weil as androgen-treated individuals of P. formosa. No statistically significant difTerences were found between masculinized gynogens and hormonetreated individuals nor between the gonochoristic P. mexicana and P. latipinna males. Differences exist between gonochoristic and unisexual species. Passihle causes and effects of masculinized gynogens are discussed. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.806819498538971, "perplexity": 25016.47754413872}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669352.5/warc/CC-MAIN-20191117215823-20191118003823-00406.warc.gz"} |
https://worldwidescience.org/topicpages/c/coupling+tensors+determined.html | #### Sample records for coupling tensors determined
1. Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
2. Couplings of self-dual tensor multiplet in six dimensions
NARCIS (Netherlands)
Bergshoeff, E.; Sezgin, E.; Sokatchev, E.
1996-01-01
The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a second-rank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to a Yang–Mills multiplet, in the absence of supergravity. The
3. Data fusion in metabolomics using coupled matrix and tensor factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Bro, Rasmus; Smilde, Age Klaas
2015-01-01
of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining...
4. Superconformal tensor calculus and matter couplings in six dimensions
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; van Proeyen, A.
1989-01-01
Using superconformal tensor calculus the authors construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. They start from the superconformal algebra which they realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. The authors also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet
5. Superconformal tensor calculus and matter couplings in six dimensions
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Proeyen, A. van
1986-01-01
Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40 + 40 Weyl multiplet and on several matter multiplets. A special role is played by the tensor multiplet, which cannot be treated as an ordinary matter multiplet, but leads to a second 40 + 40 version of the Weyl multiplet. We also obtain a 48 + 48 off-shell formulation of Poincare supergravity coupled to a tensor multiplet. (orig.)
6. Four dimensional sigma model coupled to the metric tensor field
International Nuclear Information System (INIS)
Ghika, G.; Visinescu, M.
1980-02-01
We discuss the four dimensional nonlinear sigma model with an internal O(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed. (author)
7. On the skew-symmetric character of the couple-stress tensor
OpenAIRE
2013-01-01
In this paper, the skew-symmetric character of the couple-stress tensor is established as the result of arguments from tensor analysis. Consequently, the couple-stress pseudo-tensor has a true vectorial character. The fundamental step in this development is that the isotropic couple-stress tensor cannot exist.
8. Relativistic New Yukawa-Like Potential and Tensor Coupling
International Nuclear Information System (INIS)
Ikhdair, S.M.; Hamzavi, M.
2012-01-01
We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number κ. In the framework of the spin and pseudo spin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov-Uvarov method. The numerical results show that the Coulomb-like tensor interaction, -T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schroedinger solutions for Yukawa and inversely quadratic Yukawa potentials. (author)
9. QED approach to the nuclear spin-spin coupling tensor
International Nuclear Information System (INIS)
Romero, Rodolfo H.; Aucar, Gustavo A.
2002-01-01
A quantum electrodynamical approach for the calculation of the nuclear spin-spin coupling tensor of nuclear-magnetic-resonance spectroscopy is given. Quantization of radiation fields within the molecule is considered and expressions for the magnetic field in the neighborhood of a nucleus are calculated. Using a generalization of time-dependent response theory, an effective spin-spin interaction is obtained from the coupling of nuclear magnetic moments to a virtual quantized magnetic field. The energy-dependent operators obtained reduce to usual classical-field expressions at suitable limits
10. Complete stress tensor determination by microearthquake analysis
Science.gov (United States)
Slunga, R.
2010-12-01
the depth based on the assumptions of a fractured crust, widely vary ing stress field, and a general closeness to instability as found by stress measurements (Jamison and Cook 1976). Wheather this approach is working or not is best answered by applying it to real data. This was provided by the IMO network in Iceland. Along Southern Iceland Seismic Zone (SISZ) more than 200,000 microearthquakes and a few M 5 EQs and 2 M=6.6 EQs have been recorded. The results will be presented it is obvious that the use of the stresses determined from the microearthquake recordings may significa ntly improve earthquake warnings and will make it possible to use the absolute C FS method for more deterministic predictions. Note that the microearthquake meth od only shows the part of the stress field that has caused slip. Volumes with st able stress will not show up. However stress measurements (Brown and Hoek 1978, Slunga 1988) have shown that the crustal stresses in general are close to instabi lity and microearthquake source analysis has shown that a large number of differ ent fractures become unstable within longer time windows. This may explain the e xcellent results given by the Icelandic tests of the absolute stress tensor fiel d as given by the microearthquakes. However I prefer to call this stress apparen t.
11. Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes
Science.gov (United States)
Cai, X.; Chen, X.; Chen, Y.; Cai, M.
2008-12-01
It is often found that the inversion results of seismic moment tensor from real seismic recorded data show the trace of seismic moment tensor M is not zero, a phenomenon called non-double-couple earthquake sources mechanism. Recently we have derived the analytical expressions of M in transversely isotropic media with the titled axis of symmetry and the results shows even only pure shear-motion of fault can lead to the implosive components determined by several combined anisotropic elastic constants. Many non-double-couple earthquakes from observations often appear in volcanic and geothermal areas (Julian, 1998), where there exist a mount of stress-aligned fluid-saturated parallel vertical micro-cracks identical to transversely isotropic media (Crampin, 2008), this stress-aligned crack will modify the seismic moment tensor. In another word, non-double-couple earthquakes don't mean to have a seismic failure movement perpendicular to the fault plane, while traditional research of seismic moment tensor focus on the case of isotropy, which cannot provide correct interpretation of seismic source mechanism. Reference: Julian, B.R., Miller, A.D. and Foulger, G.R., 1998. Non-double-couple earthquakes,1. Theory, Rev. Geophys., 36, 525¨C549. Crampin,S., Peacock,S., 2008, A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation, wave motion, 45,675-722
12. Coupling coefficients for tensor product representations of quantum SU(2)
International Nuclear Information System (INIS)
Groenevelt, Wolter
2014-01-01
We study tensor products of infinite dimensional irreducible * -representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions
13. Coupling coefficients for tensor product representations of quantum SU(2)
Science.gov (United States)
Groenevelt, Wolter
2014-10-01
We study tensor products of infinite dimensional irreducible *-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.
14. Limits on Tensor Coupling from Neutron $\\beta$-Decay
OpenAIRE
Pattie Jr, Robert W.; Hickerson, Kevin P.; Young, Albert R.
2013-01-01
Limits on the tensor couplings generating a Fierz interference term, b, in mixed Gamow-Teller Fermi decays can be derived by combining data from measurements of angular correlation parameters in neutron decay, the neutron lifetime, and $G_{\\text{V}}=G_{\\text{F}} V_{ud}$ as extracted from measurements of the $\\mathcal{F}t$ values from the $0^{+} \\to 0^{+}$ superallowed decays dataset. These limits are derived by comparing the neutron $\\beta$-decay rate as predicted in the standard model with t...
15. Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group
Science.gov (United States)
Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic
2018-05-01
We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.
16. Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
17. Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.
Science.gov (United States)
Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej
2015-09-01
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.
18. The effects of the tensor coupling term in the Zimanyi-Moszkowski model for unpolarized nuclear matter
International Nuclear Information System (INIS)
Ru-Keng Su; Li Li; Hong-Qiu Song
1998-01-01
The effects of the tensor coupling term on nuclear matter in the Zimanyi-Moszkowki (ZM) model are investigated. It is shown that the tensor coupling term in the ZM model leaves the thermodynamical properties of nuclear matter almost unchanged. The corrections of tensor coupling to the critical point of the liquid-gas phase transition are given. (author)
19. Superconformal tensor calculus and matter couplings in six dimensions
NARCIS (Netherlands)
Bergshoeff, E.; Sezgin, E.; Proeyen, A. Van
1986-01-01
Using superconformal tensor calculus we construct general interactions of N = 2, d = 6 supergravity with a tensor multiplet and a number of scalar, vector and linear multiplets. We start from the superconformal algebra which we realize on a 40+40 Weyl multiplet and on several matter multiplets. A
20. All-at-once Optimization for Coupled Matrix and Tensor Factorizations
DEFF Research Database (Denmark)
Evrim, Acar Ataman; Kolda, Tamara G.; Dunlavy, Daniel M.
2011-01-01
.g., the person by person social network matrix or the restaurant by category matrix, and higher-order tensors, e.g., the "ratings" tensor of the form restaurant by meal by person. In this paper, we are particularly interested in fusing data sets with the goal of capturing their underlying latent structures. We...... formulate this problem as a coupled matrix and tensor factorization (CMTF) problem where heterogeneous data sets are modeled by fitting outer-product models to higher-order tensors and matrices in a coupled manner. Unlike traditional approaches solving this problem using alternating algorithms, we propose...... an all-at-once optimization approach called CMTF-OPT (CMTF-OPTimization), which is a gradient-based optimization approach for joint analysis of matrices and higher-order tensors. We also extend the algorithm to handle coupled incomplete data sets. Using numerical experiments, we demonstrate...
1. Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei
International Nuclear Information System (INIS)
Jiang-Ming, Yao; Jie, Meng; Hong-Feng, Lü; Greg, Hillhouse
2008-01-01
Effects of core polarization and tensor coupling on the magnetic moments in Λ 13 C, Λ 17 O, and Λ 41 Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of p Λ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for p Λ states from the Schmidt values are found to increase with nuclear mass number. (nuclear physics)
2. Symmetry rules for the indirect nuclear spin-spin coupling tensor revisited
Science.gov (United States)
Buckingham, A. D.; Pyykkö, P.; Robert, J. B.; Wiesenfeld, L.
The symmetry rules of Buckingham and Love (1970), relating the number of independent components of the indirect spin-spin coupling tensor J to the symmetry of the nuclear sites, are shown to require modification if the two nuclei are exchanged by a symmetry operation. In that case, the anti-symmetric part of J does not transform as a second-rank polar tensor under symmetry operations that interchange the coupled nuclei and may be called an anti-tensor. New rules are derived and illustrated by simple molecular models.
3. Non-Abelian formulation of a vector-tensor gauge theory with topological coupling
International Nuclear Information System (INIS)
Barcelos Neto, J.; Cabo, A.; Silva, M.B.D.
1995-08-01
We obtain a non-Abelian version of a theory involving vector and tensor and tensor gauge fields interacting via a massive topological coupling, besides the nonminimum one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to compatibilize gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case. (author). 9 refs
4. The matter Lagrangian and the energy-momentum tensor in modified gravity with nonminimal coupling between matter and geometry
International Nuclear Information System (INIS)
Harko, T.
2010-01-01
We show that in modified f(R) type gravity models with nonminimal coupling between matter and geometry, both the matter Lagrangian and the energy-momentum tensor are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling, and the Newtonian limit for a fluid obeying a barotropic equation of state. The corresponding energy-momentum tensor of the matter in modified gravity models with nonminimal coupling is more general than the usual general-relativistic energy-momentum tensor for perfect fluids, and it contains a supplementary, equation of state dependent term, which could be related to the elastic stresses in the body, or to other forms of internal energy. Therefore, the extra force induced by the coupling between matter and geometry never vanishes as a consequence of the thermodynamic properties of the system, or for a specific choice of the matter Lagrangian, and it is nonzero in the case of a fluid of dust particles.
5. The modified indeterminate couple stress model: Why Yang et al.'s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless
OpenAIRE
Münch, Ingo; Neff, Patrizio; Madeo, Angela; Ghiba, Ionel-Dumitrel
2015-01-01
We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonable physical hypothesis, implying that the couple stress tensor is traceless and may be symmetric anyway. To this aim, the origin of couple stress is discussed on the basis of certain properties of the total stress itself. In contrast to classical continuum mechanics, the balance of linear momentum and the balance of...
6. SU(2)xSU(2) coupling rule and a tensor glueball candidate
International Nuclear Information System (INIS)
Lanik, J.
1984-01-01
The data on the decay of THETA(1640) particles are considered. It is shown that the SU(2)xSU(2) mechanism for coupling of theta(1640) tensor glueball candidate to pseudoscalar Gold-stone mesons is in a remarkable agreement with existing experimental data
7. The magnetic g-tensors for ion complexes with large spin-orbit coupling
International Nuclear Information System (INIS)
Chang, P.K.L.; Liu, Y.S.
1977-01-01
A nonperturbative method for calculating the magnetic g-tensors is presented and discussed for complexes of transition metal ions of large spin-orbit coupling, in the ground term 2 D. A numerical example for CuCl 2 .2H 2 O is given [pt
8. Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows
NARCIS (Netherlands)
Vermeulen, B.; Hoitink, A.J.F.; Sassi, M.G.
2011-01-01
We introduce a new technique to measure profiles of each term in the Reynolds stress tensor using coupled acoustic Doppler current profilers (ADCPs). The technique is based on the variance method which is extended to the case with eight acoustic beams. Methods to analyze turbulence from a single
9. A high performance data parallel tensor contraction framework: Application to coupled electro-mechanics
Science.gov (United States)
Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio
2017-07-01
The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.
10. Tensor calculus for the vector multiplet coupled to supergravity
International Nuclear Information System (INIS)
Stelle, K.S.
1978-01-01
An invariant coupling of a local vector multiplet to supergravity is constructed in analogy with the D term invariant of global supersymmetry. The rules for combining local vector and chiral scalar multiplets of opposite chirality are given. (Auth.)
11. Chiral primordial blue tensor spectra from the axion-gauge couplings
Energy Technology Data Exchange (ETDEWEB)
Obata, Ippei, E-mail: [email protected] [Department of Physics, Kyoto University, Kyoto, 606-8502 (Japan)
2017-06-01
We suggest the new feature of primordial gravitational waves sourced by the axion-gauge couplings, whose forms are motivated by the dimensional reduction of the form field in the string theory. In our inflationary model, as an inflaton we adopt two types of axion, dubbed the model-independent axion and the model-dependent axion, which couple with two gauge groups with different sign combination each other. Due to these forms both polarization modes of gauge fields are amplified and enhance both helicies of tensor modes during inflation. We point out the possibility that a primordial blue-tilted tensor power spectra with small chirality are provided by the combination of these axion-gauge couplings, intriguingly both amplitudes and chirality are potentially testable by future space-based gravitational wave interferometers such as DECIGO and BBO project.
12. On scalar and vector fields coupled to the energy-momentum tensor
Science.gov (United States)
Jiménez, Jose Beltrán; Cembranos, Jose A. R.; Sánchez Velázquez, Jose M.
2018-05-01
We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build the action by means of an iterative process that leads to an infinite series, which can be resumed as the solution of a set of differential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to find solutions in the form of polynomials. We briefly review the case of the scalar field that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector fields, distinguishing between gauge-and non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar field as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the definition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We finally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.
13. Double shadow of a regular phantom black hole as photons couple to the Weyl tensor
Energy Technology Data Exchange (ETDEWEB)
Huang, Yang; Chen, Songbai; Jing, Jiliang [Hunan Normal University, Institute of Physics and Department of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Hunan Normal University, Synergetic Innovation Center for Quantum Effects and Applications, Changsha, Hunan (China)
2016-11-15
We have studied the shadow of a regular phantom black hole as photons couple to the Weyl tensor. We find that due to the coupling photons with different polarization directions propagate along different paths in the spacetime so that there exists a double shadow for a black hole, which is quite different from that in the non-coupling case where only a single shadow emerges. The overlap region of the double shadow, the umbra, of the black hole increases with the phantom charge and decreases with the coupling strength. The dependence of the penumbra on the phantom charge and the coupling strength is converse to that of the umbra. Combining with the supermassive central object in our Galaxy, we estimated the shadow of the black hole as the photons couple to the Weyl tensor. Our results show that the coupling brings about richer behaviors of the propagation of coupled photon and the shadow of the black hole in the regular phantom black hole spacetime. (orig.)
14. Symmetry breaking nuclear quadrupole coupling tensor orientation for cesium-133 nuclei located in a mirror plane
Energy Technology Data Exchange (ETDEWEB)
Kim, Tae Ho; Kim, Jin Eun [Dept. of Chemistry (BK21 plus) and Research Institute of Natural Science, Gyeongsang National University, Jinju (Korea, Republic of); Lee, Kang Yeol [School of Mechanical Engineering, Korea University, Seoul (Korea, Republic of)
2016-11-15
Simultaneous multiple data set fits of all transition peaks of {sup 133}Cs nuclei enabled us to obtain accurate cesium-133 nuclear magnetic resonance (NMR) parameters and Euler angles between the principal axis systems of the chemical shift (CS) and quadrupole coupling (Q) tensors of {sup 133}Cs nuclei in Cs{sub 2}CrO{sub 4} . Although in a previous study of Cs{sub 2}CrO{sub 4} by Power et al. (W. P. Power, S. Mooibroek, R. E. Wasylishen, T. S. Cameron, J. Phys. Chem. 1994, 98, 1552), one central transition was observed for cesium sites 1 and 2 in the {sup 133}Cs NMR spectra and one Euler angle between the CS tensors and Q tensors was obtained as 52° and 7° for cesium sites 1 and 2, respectively, the present single-crystal {sup 133}Cs NMR measurements found two Euler angles (10(2)°, 51.9(1)°, 0°) for site 1 and two central transition peaks for site 2. Three principal components of the CS tensor for Cs1 are oriented along the crystallographic a, b, and c axes, whereas none of the principal components of the Q tensor for Cs1 are oriented along the crystal axes. The principal component V{sub 22} of the Q tensor for Cs1 is tilted 10° from the b axis in the bc plane, and the other two components are not located in the ac plane. Therefore, we have found that the requirement that “the quadrupole coupling tensor for a nucleus located in a mirror plane has one principal axis perpendicular to the mirror plane” cannot be applied to Cs1. On the other hand, δ{sub 11} and V{sub 22} for Cs2 are aligned along the b axis, and the other components of the CS and Q tensors deviate at an angle of 1.4(1)° and 10.1(1)°, respectively, from the a and c axes in the ac plane. A distortion-free powder {sup 133}Cs NMR spectrum of Cs{sub 2}CrO{sub 4} was measured using a solid-state spin echo technique.
15. 71Ga Chemical Shielding and Quadrupole Coupling Tensors of the Garnet Y(3)Ga(5)O(12) from Single-Crystal (71)Ga NMR
DEFF Research Database (Denmark)
Vosegaard, Thomas; Massiot, Dominique; Gautier, Nathalie
1997-01-01
A single-crystal (71)Ga NMR study of the garnet Y(3)Ga(5)O(12) (YGG) has resulted in the determination of the first chemical shielding tensors reported for the (71)Ga quadrupole. The single-crystal spectra are analyzed in terms of the combined effect of quadrupole coupling and chemical shielding ...
16. Structures and Nuclear Quadrupole Coupling Tensors of a Series of Chlorine-Containing Hydrocarbons
Science.gov (United States)
Dikkumbura, Asela S.; Webster, Erica R.; Dorris, Rachel E.; Peebles, Rebecca A.; Peebles, Sean A.; Seifert, Nathan A.; Pate, Brooks
2016-06-01
Rotational spectra for gauche-1,2-dichloroethane (12DCE), gauche-1-chloro-2-fluoroethane (1C2FE) and both anti- and gauche-2,3-dichloropropene (23DCP) have been observed using chirped-pulse Fourier-transform microwave (FTMW) spectroscopy in the 6-18 GHz region. Although the anti conformers for all three species are predicted to be more stable than the gauche forms, they are nonpolar (12DCE) or nearly nonpolar (predicted dipole components for anti-1C2FE: μ_a = 0.11 D, μ_b = 0.02 D and for anti-23DCP: μ_a = 0.25 D, μ_b = 0.02 D); nevertheless, it was also possible to observe and assign the spectrum of anti-23DCP. Assignments of parent spectra and 37Cl and 13C substituted isotopologues utilized predictions at the MP2/6-311++G(2d,2p) level and Pickett's SPCAT/SPFIT programs. For the weak anti-23DCP spectra, additional measurements also utilized a resonant-cavity FTMW spectrometer. Full chlorine nuclear quadrupole coupling tensors for gauche-12DCE and both anti- and gauche-23DCP have been diagonalized to allow comparison of coupling constants. Kraitchman's equations were used to determine r_s coordinates of isotopically substituted atoms and r_0 structures were also deduced for gauche conformers of 12DCE and 1C2FE. Structural details and chlorine nuclear quadrupole coupling constants of all three molecules will be compared, and effects of differing halogen substitution and carbon chain length on molecular properties will be evaluated.
17. Coupled Hartree-Fock calculation of {sup 13} C shielding tensors in acetylene clusters
Energy Technology Data Exchange (ETDEWEB)
Craw, John Simon; Nascimento, Marco Antonio Chaer [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Quimica
1992-12-31
The coupled Hartree Fock method has been used to calculate ab-initio carbon magnetic shielding tensors for small clusters of acetylene molecules. The chemical shift increases from the monomer to the dimer and trimer. This is mainly due increased diamagnetism, which is imperfectly cancelled by increased paramagnetism due to loss of axial symmetry. Anisotropic effects are shown to be small in both the dimer the and trimer. (author) 21 refs., 2 tabs.
18. Improving the calculation of electron paramagnetic resonance hyperfine coupling tensors for d-block metals
DEFF Research Database (Denmark)
Hedegård, Erik Donovan; Kongsted, Jacob; Sauer, Stephan P. A.
2012-01-01
Calculation of hyperfine coupling constants (HFCs) of Electron Paramagnetic Resonance from first principles can be a beneficial compliment to experimental data in cases where the molecular structure is unknown. We have recently investigated basis set convergence of HFCs in d-block complexes...... and obtained a set of basis functions for the elements Sc–Zn, which were saturated with respect to both the Fermi contact and spin-dipolar components of the hyperfine coupling tensor [Hedeg°ard et al., J. Chem. Theory Comput., 2011, 7, pp. 4077-4087]. Furthermore, a contraction scheme was proposed leading...
19. Retrodictive determinism. [covariant and transformational behavior of tensor fields in hydrodynamics and thermodynamics
Science.gov (United States)
Kiehn, R. M.
1976-01-01
With respect to irreversible, non-homeomorphic maps, contravariant and covariant tensor fields have distinctly natural covariance and transformational behavior. For thermodynamic processes which are non-adiabatic, the fact that the process cannot be represented by a homeomorphic map emphasizes the logical arrow of time, an idea which encompasses a principle of retrodictive determinism for covariant tensor fields.
20. Weak deflection gravitational lensing for photons coupled to Weyl tensor in a Schwarzschild black hole
Science.gov (United States)
Cao, Wei-Guang; Xie, Yi
2018-03-01
Beyond the Einstein-Maxwell model, electromagnetic field might couple with gravitational field through the Weyl tensor. In order to provide one of the missing puzzles of the whole physical picture, we investigate weak deflection lensing for photons coupled to the Weyl tensor in a Schwarzschild black hole under a unified framework that is valid for its two possible polarizations. We obtain its coordinate-independent expressions for all observables of the geometric optics lensing up to the second order in the terms of ɛ which is the ratio of the angular gravitational radius to angular Einstein radius of the lens. These observables include bending angle, image position, magnification, centroid and time delay. The contributions of such a coupling on some astrophysical scenarios are also studied. We find that, in the cases of weak deflection lensing on a star orbiting the Galactic Center Sgr A*, Galactic microlensing on a star in the bulge and astrometric microlensing by a nearby object, these effects are beyond the current limits of technology. However, measuring the variation of the total flux of two weak deflection lensing images caused by the Sgr A* might be a promising way for testing such a coupling in the future.
1. Cross-scale Efficient Tensor Contractions for Coupled Cluster Computations Through Multiple Programming Model Backends
Energy Technology Data Exchange (ETDEWEB)
Ibrahim, Khaled Z. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Epifanovsky, Evgeny [Q-Chem, Inc., Pleasanton, CA (United States); Williams, Samuel W. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Krylov, Anna I. [Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry
2016-07-26
Coupled-cluster methods provide highly accurate models of molecular structure by explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix-matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts to extend the Libtensor framework to work in the distributed memory environment in a scalable and energy efficient manner. We achieve up to 240 speedup compared with the best optimized shared memory implementation. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures, (Cray XC30&XC40, BlueGene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance. Nevertheless, we preserve a uni ed interface to both programming models to maintain the productivity of computational quantum chemists.
2. Effects of Anomalous Tensor Couplings in B0s — B-bar0s Mixing
International Nuclear Information System (INIS)
Chang Qin; Han Lin; Yang Ya-Dong
2012-01-01
Motivated by the recently observed anomalous large dimuon charge asymmetry in neutral B decays, we study the effects of the anomalous tensor couplings to pursue a possible solution. With the constraints from the observables φ s J/ψ(φ,f 0 ) , a s sl and ΔM s , the new physics parameter spaces are severely restricted. We find that the contributions induced by the color-singlet or the color-octet tensor operators are helpful to moderate the anomaly in B 0 s — B-bar 0 s mixing. Numerically, the observable a s sl could be enhanced by about two orders of magnitude by the contributions of color-singlet or color-octet tensor operators with their respective nontrivial new weak phase φ T1 = 41deg ± 35deg or φ T8 = −47deg ± 33deg and relevant strength parameters |g T1 | = (2.89 ± 1.40) × 10 −2 or |g T8 | = (0.79 ± 0.34) × 10 −2 . However, due to the fact that the NP contributions are severely suppressed by the recent LHCb measurement for φ s J/ψ(φ,f 0 ) , our theoretical result of a s sl is still much smaller than the central value of the experimental data
3. The tensor calculus and matter coupling of the alternative minimal auxiliary field formulation of N = 1 supergravity
International Nuclear Information System (INIS)
Sohnius, M.; West, P.
1982-01-01
The tensor calculus for the new alternative minimal auxiliary field formulation of N = 1 supergravity is given. It is used to construct the couplings of this formulation of supergravity to matter. These couplings are found to be different, in several respects to those of the old minimal formulation of N = 1 supergravity. (orig.)
4. Turbo-SMT: Parallel Coupled Sparse Matrix-Tensor Factorizations and Applications
Science.gov (United States)
Papalexakis, Evangelos E.; Faloutsos, Christos; Mitchell, Tom M.; Talukdar, Partha Pratim; Sidiropoulos, Nicholas D.; Murphy, Brian
2016-01-01
How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like ’edible’, ’fits in hand’)? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we enhance any CMTF solver, so that it can operate on potentially very large datasets that may not fit in main memory? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, produces sparse and interpretable solutions, and parallelizes any CMTF algorithm, producing sparse and interpretable solutions (up to 65 fold). Additionally, we improve upon ALS, the work-horse algorithm for CMTF, with respect to efficiency and robustness to missing values. We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy. Finally, we demonstrate the generality of Turbo-SMT, by applying it on a Facebook dataset (users, ’friends’, wall-postings); there, Turbo-SMT spots spammer-like anomalies. PMID:27672406
5. Tensor contraction engine: Abstraction and automated parallel implementation of configuration-interaction, coupled-cluster, and many-body perturbation theories
International Nuclear Information System (INIS)
Hirata, So
2003-01-01
We develop a symbolic manipulation program and program generator (Tensor Contraction Engine or TCE) that automatically derives the working equations of a well-defined model of second-quantized many-electron theories and synthesizes efficient parallel computer programs on the basis of these equations. Provided an ansatz of a many-electron theory model, TCE performs valid contractions of creation and annihilation operators according to Wick's theorem, consolidates identical terms, and reduces the expressions into the form of multiple tensor contractions acted by permutation operators. Subsequently, it determines the binary contraction order for each multiple tensor contraction with the minimal operation and memory cost, factorizes common binary contractions (defines intermediate tensors), and identifies reusable intermediates. The resulting ordered list of binary tensor contractions, additions, and index permutations is translated into an optimized program that is combined with the NWChem and UTChem computational chemistry software packages. The programs synthesized by TCE take advantage of spin symmetry, Abelian point-group symmetry, and index permutation symmetry at every stage of calculations to minimize the number of arithmetic operations and storage requirement, adjust the peak local memory usage by index range tiling, and support parallel I/O interfaces and dynamic load balancing for parallel executions. We demonstrate the utility of TCE through automatic derivation and implementation of parallel programs for various models of configuration-interaction theory (CISD, CISDT, CISDTQ), many-body perturbation theory[MBPT(2), MBPT(3), MBPT(4)], and coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, and CCSDTQ)
6. Proton chemical shift tensors determined by 3D ultrafast MAS double-quantum NMR spectroscopy
International Nuclear Information System (INIS)
Zhang, Rongchun; Mroue, Kamal H.; Ramamoorthy, Ayyalusamy
2015-01-01
Proton NMR spectroscopy in the solid state has recently attracted much attention owing to the significant enhancement in spectral resolution afforded by the remarkable advances in ultrafast magic angle spinning (MAS) capabilities. In particular, proton chemical shift anisotropy (CSA) has become an important tool for obtaining specific insights into inter/intra-molecular hydrogen bonding. However, even at the highest currently feasible spinning frequencies (110–120 kHz), 1 H MAS NMR spectra of rigid solids still suffer from poor resolution and severe peak overlap caused by the strong 1 H– 1 H homonuclear dipolar couplings and narrow 1 H chemical shift (CS) ranges, which render it difficult to determine the CSA of specific proton sites in the standard CSA/single-quantum (SQ) chemical shift correlation experiment. Herein, we propose a three-dimensional (3D) 1 H double-quantum (DQ) chemical shift/CSA/SQ chemical shift correlation experiment to extract the CS tensors of proton sites whose signals are not well resolved along the single-quantum chemical shift dimension. As extracted from the 3D spectrum, the F1/F3 (DQ/SQ) projection provides valuable information about 1 H– 1 H proximities, which might also reveal the hydrogen-bonding connectivities. In addition, the F2/F3 (CSA/SQ) correlation spectrum, which is similar to the regular 2D CSA/SQ correlation experiment, yields chemical shift anisotropic line shapes at different isotropic chemical shifts. More importantly, since the F2/F1 (CSA/DQ) spectrum correlates the CSA with the DQ signal induced by two neighboring proton sites, the CSA spectrum sliced at a specific DQ chemical shift position contains the CSA information of two neighboring spins indicated by the DQ chemical shift. If these two spins have different CS tensors, both tensors can be extracted by numerical fitting. We believe that this robust and elegant single-channel proton-based 3D experiment provides useful atomistic-level structural and dynamical
7. Determination of mouse skeletal muscle architecture using three dimensional diffusion tensor imaging
NARCIS (Netherlands)
Heemskerk, A.M.; Strijkers, G.J.; Vilanova, A.; Drost, M.R.; Nicolaij, K.
2005-01-01
Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six
8. Determination of mouse skeletal muscle architecture using three-dimensional diffusion tensor imaging
NARCIS (Netherlands)
Heemskerk, Anneriet M.; Strijkers, Gustav J.; Vilanova, Anna; Drost, Maarten R.; Nicolay, Klaas
2005-01-01
Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six
9. Determination of 3D magnetic reluctivity tensor of soft magnetic composite material
International Nuclear Information System (INIS)
Guo Youguang; Zhu Jianguo; Lin Zhiwei; Zhong Jinjiang; Lu Haiyan; Wang Shuhong
2007-01-01
Soft magnetic composite (SMC) materials are especially suitable for construction of electrical machines with complex structures and three-dimensional (3D) magnetic fluxes. In the design and optimization of such 3D flux machines, the 3D vector magnetic properties of magnetic materials should be properly determined, modeled, and applied for accurate calculation of the magnetic field distribution, parameters, and performance. This paper presents the measurement of 3D vector magnetic properties and determination of 3D reluctivity tensor of SMC. The reluctivity tensor is a key factor for accurate numerical analysis of magnetic field in a 3D flux SMC motor
10. Solar System constraints on massless scalar-tensor gravity with positive coupling constant upon cosmological evolution of the scalar field
Science.gov (United States)
Anderson, David; Yunes, Nicolás
2017-09-01
Scalar-tensor theories of gravity modify general relativity by introducing a scalar field that couples nonminimally to the metric tensor, while satisfying the weak-equivalence principle. These theories are interesting because they have the potential to simultaneously suppress modifications to Einstein's theory on Solar System scales, while introducing large deviations in the strong field of neutron stars. Scalar-tensor theories can be classified through the choice of conformal factor, a scalar that regulates the coupling between matter and the metric in the Einstein frame. The class defined by a Gaussian conformal factor with a negative exponent has been studied the most because it leads to spontaneous scalarization (i.e. the sudden activation of the scalar field in neutron stars), which consequently leads to large deviations from general relativity in the strong field. This class, however, has recently been shown to be in conflict with Solar System observations when accounting for the cosmological evolution of the scalar field. We here study whether this remains the case when the exponent of the conformal factor is positive, as well as in another class of theories defined by a hyperbolic conformal factor. We find that in both of these scalar-tensor theories, Solar System tests are passed only in a very small subset of coupling parameter space, for a large set of initial conditions compatible with big bang nucleosynthesis. However, while we find that it is possible for neutron stars to scalarize, one must carefully select the coupling parameter to do so, and even then, the scalar charge is typically 2 orders of magnitude smaller than in the negative-exponent case. Our study suggests that future work on scalar-tensor gravity, for example in the context of tests of general relativity with gravitational waves from neutron star binaries, should be carried out within the positive coupling parameter class.
11. The continuous determination of spacetime geometry by the Riemann curvature tensor
International Nuclear Information System (INIS)
Rendall, A.D.
1988-01-01
It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)
12. Dynamical compactification of D-dimensional gravity coupled to antisymmetric tensors in a 1/D expansion
International Nuclear Information System (INIS)
Foda, O.
1984-12-01
The effective potential of components of the curl of an antisymmetric tensor coupled to gravity in D dimensions is evaluated in a 1/D expansion. For large D, only highest-rank propagators contribute to leading order, while multiloop diagrams are suppressed by phase-space factors. Divergences are regulated by a cut-off LAMBDA, that we interpret as the mass-breaking scale of a larger theory that is finite. As an application we consider the bosonic sector of D=11, N=1 supergravity. If the full theory is finite, then LAMBDA is msub(SUSY): the scale below which the fermion sector decouples. For m 9 sub(SUSY)>1/akappa 2 , (kappa 2 : the D=11 Newton's coupling, a approx.= O(1)) the 11-dimensional symmetric vacuum is unstable under compactification. For m 9 sub(SUSY) 2 , it is metastable. To leading order in 1/D, all gauge dependence cancels identically, while ghosts as well as the graviton decouple. (author)
13. Current density tensors
Science.gov (United States)
Lazzeretti, Paolo
2018-04-01
It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.
14. TEV—A Program for the Determination of the Thermal Expansion Tensor from Diffraction Data
Directory of Open Access Journals (Sweden)
Thomas Langreiter
2015-02-01
Full Text Available TEV (Thermal Expansion Visualizing is a user-friendly program for the calculation of the thermal expansion tensor αij from diffraction data. Unit cell parameters determined from temperature dependent data collections can be provided as input. An intuitive graphical user interface enables fitting of the evolution of individual lattice parameters to polynomials up to fifth order. Alternatively, polynomial representations obtained from other fitting programs or from the literature can be entered. The polynomials and their derivatives are employed for the calculation of the tensor components of αij in the infinitesimal limit. The tensor components, eigenvalues, eigenvectors and their angles with the crystallographic axes can be evaluated for individual temperatures or for temperature ranges. Values of the tensor in directions parallel to either [uvw]’s of the crystal lattice or vectors (hkl of reciprocal space can be calculated. Finally, the 3-D representation surface for the second rank tensor and pre- or user-defined 2-D sections can be plotted and saved in a bitmap format. TEV is written in JAVA. The distribution contains an EXE-file for Windows users and a system independent JAR-file for running the software under Linux and Mac OS X. The program can be downloaded from the following link: http://www.uibk.ac.at/mineralogie/downloads/TEV.html (Institute of Mineralogy and Petrography, University of Innsbruck, Innsbruck, Austria
15. Determining chiral couplings at NLO
International Nuclear Information System (INIS)
Rosell, Ignasi
2007-01-01
We present a general method that allows to estimate the low-energy constants of Chiral Perturbation Theory up to next-to-leading corrections in the 1/N C expansion, that is, keeping full control of the renormalization scale dependence. As a first step we have determined L 8 and C 38 , the couplings related to the difference of the two-point correlation functions of two scalar and pseudoscalar currents, L 8 r (μ 0 ) = (0.6±0.4)·10 -3 and C 38 r (μ 0 ) = (2±6)·10 -6 , with μ 0 0.77 GeV. As in many effective approaches, one of the main ingredients of this method is the matching procedure: some comments related to this topic are presented here
16. Dynamical analysis for a scalar-tensor model with Gauss-Bonnet and non-minimal couplings
Energy Technology Data Exchange (ETDEWEB)
Granda, L.N.; Jimenez, D.F. [Universidad del Valle, Departamento de Fisica, Cali (Colombia)
2017-10-15
We study the autonomous system for a scalar-tensor model of dark energy with Gauss-Bonnet and non-minimal couplings. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential are considered: power-law and exponential functions of the scalar field. For the exponential functions the existence of stable quintessence, phantom or de Sitter solutions, allows for an asymptotic behavior where the effective Newtonian coupling becomes constant. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation-dominated phases can also be described. (orig.)
17. Interplay of tensor correlations and vibrational coupling for single-particle states in atomic nuclei
International Nuclear Information System (INIS)
Colo, G.; SAgawa, H.; Bortignon, P. F.
2009-01-01
To study the structure of atomic nuclei, the ab-initio methods can nowadays be applied only for mass number A smaller than ∼ 10-15. For heavier systems, the self-consistent mean-field (SCMF) approach is probably the most microscopic approach which can be systematically applied to stable and exotic nuclei. In practice, the SCMF is mostly based on parametrizations of an effective interaction. However, the are groups who are intensively working on the development of a general density functional (DF) which is not necessarily extracted from an Hamiltonian. The basic question is to what extent this allows improving on the existing functionals. In this contribution we analyze the performance of existing functionals as far as the reproduction of single-particle states is concerned. We start by analyzing the effect of the tensor terms, on which the attention of several groups have recently focused. Then we discuss the impact of the particle-vibration coupling (PVC). Although the basic idea of this approach dates back to long time ago, we present here for the first time calculations which are entirely based on microscopic interactions without dropping any term or introducing ad hoc parameters. We show results both for well-known, benchmark nuclei like 4 0C a and 2 08P b as well as unstable nuclei like 1 32S n. Both single-particle energies and spectroscopic factors are discussed.(author)
18. Determination and uncertainty of moment tensors for microearthquakes at Okmok Volcano, Alaska
Science.gov (United States)
Pesicek, J.D.; Sileny, J.; Prejean, S.G.; Thurber, C.H.
2012-01-01
Efforts to determine general moment tensors (MTs) for microearthquakes in volcanic areas are often hampered by small seismic networks, which can lead to poorly constrained hypocentres and inadequate modelling of seismic velocity heterogeneity. In addition, noisy seismic signals can make it difficult to identify phase arrivals correctly for small magnitude events. However, small volcanic earthquakes can have source mechanisms that deviate from brittle double-couple shear failure due to magmatic and/or hydrothermal processes. Thus, determining reliable MTs in such conditions is a challenging but potentially rewarding pursuit. We pursued such a goal at Okmok Volcano, Alaska, which erupted recently in 1997 and in 2008. The Alaska Volcano Observatory operates a seismic network of 12 stations at Okmok and routinely catalogues recorded seismicity. Using these data, we have determined general MTs for seven microearthquakes recorded between 2004 and 2007 by inverting peak amplitude measurements of P and S phases. We computed Green's functions using precisely relocated hypocentres and a 3-D velocity model. We thoroughly assessed the quality of the solutions by computing formal uncertainty estimates, conducting a variety of synthetic and sensitivity tests, and by comparing the MTs to solutions obtained using alternative methods. The results show that MTs are sensitive to station distribution and errors in the data, velocity model and hypocentral parameters. Although each of the seven MTs contains a significant non-shear component, we judge several of the solutions to be unreliable. However, several reliable MTs are obtained for a group of previously identified repeating events, and are interpreted as compensated linear-vector dipole events.
19. Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations
Energy Technology Data Exchange (ETDEWEB)
Peng, Bo [William R. Wiley Environmental; Kowalski, Karol [William R. Wiley Environmental
2017-08-11
The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.
20. TensorLy: Tensor Learning in Python
NARCIS (Netherlands)
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
1. Full paleostress tensor reconstruction using quartz veins of Panasqueira Mine, central Portugal; part I: Paleopressure determination
Science.gov (United States)
Jaques, Luís; Pascal, Christophe
2017-09-01
Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal exposures of mineralized quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. The present contribution focuses specifically on the determination of pore pressure. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of ∼300 MPa and formation depths of ∼10 km. Such formation depths are in good agreement with the regional geological evolution. The obtained pore pressure will be merged with vein inversion results, in order to achieve full paleostress tensor restoration, in a forthcoming companion paper.
2. Spin and Pseudospin Symmetries with Trigonometric Pöschl-Teller Potential including Tensor Coupling
Directory of Open Access Journals (Sweden)
M. Hamzavi
2013-01-01
Full Text Available We study approximate analytical solutions of the Dirac equation with the trigonometric Pöschl-Teller (tPT potential and a Coulomb-like tensor potential for arbitrary spin-orbit quantum number κ under the presence of exact spin and pseudospin ( p -spin symmetries. The bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle are obtained using the parametric generalization of the Nikiforov-Uvarov (NU method. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. The case of nonrelativistic limit is studied too.
3. Generalized dielectric permittivity tensor
International Nuclear Information System (INIS)
Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.
1986-01-01
The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form
4. Benchmarking density-functional-theory calculations of rotational g tensors and magnetizabilities using accurate coupled-cluster calculations.
Science.gov (United States)
Lutnaes, Ola B; Teale, Andrew M; Helgaker, Trygve; Tozer, David J; Ruud, Kenneth; Gauss, Jürgen
2009-10-14
An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster single-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD(T) methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange-correlation functionals is discussed in light of this comparison.
5. TensorLy: Tensor Learning in Python
OpenAIRE
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...
6. Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method
International Nuclear Information System (INIS)
Eshghi, M.; Ikhdair, S. M.
2014-01-01
A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S(r) and a vector V(r) Mie-type potential in the radial coordinates, as well as a tensor potential U(r) in the form of Coulomb potential. In the pseudospin (p-spin) symmetry setting Σ = C ps and Δ = V(r), an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin—orbit coupling number κ. Special attention is devoted to the case Σ = 0 for which p-spin symmetry is exact. The Laplace transform approach (LTA) is used in our calculations. Some numerical results are obtained and compared with those of other methods. (general)
7. Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to g-tensors
Energy Technology Data Exchange (ETDEWEB)
Roemelt, Michael, E-mail: [email protected] [Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany and Max-Planck Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr (Germany)
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
8. Determination of mouse skeletal muscle architecture using three-dimensional diffusion tensor imaging.
Science.gov (United States)
Heemskerk, Anneriet M; Strijkers, Gustav J; Vilanova, Anna; Drost, Maarten R; Nicolay, Klaas
2005-06-01
Muscle architecture is the main determinant of the mechanical behavior of skeletal muscles. This study explored the feasibility of diffusion tensor imaging (DTI) and fiber tracking to noninvasively determine the in vivo three-dimensional (3D) architecture of skeletal muscle in mouse hind leg. In six mice, the hindlimb was imaged with a diffusion-weighted (DW) 3D fast spin-echo (FSE) sequence followed by the acquisition of an exercise-induced, T(2)-enhanced data set. The data showed the expected fiber organization, from which the physiological cross-sectional area (PCSA), fiber length, and pennation angle for the tibialis anterior (TA) were obtained. The values of these parameters ranged from 5.4-9.1 mm(2), 5.8-7.8 mm, and 21-24 degrees , respectively, which is in agreement with values obtained previously with the use of invasive methods. This study shows that 3D DT acquisition and fiber tracking is feasible for the skeletal muscle of mice, and thus enables the quantitative determination of muscle architecture.
9. Massively parallel implementations of coupled-cluster methods for electron spin resonance spectra. I. Isotropic hyperfine coupling tensors in large radicals
Energy Technology Data Exchange (ETDEWEB)
Verma, Prakash; Morales, Jorge A., E-mail: [email protected] [Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061 (United States); Perera, Ajith [Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061 (United States); Department of Chemistry, Quantum Theory Project, University of Florida, Gainesville, Florida 32611 (United States)
2013-11-07
Coupled cluster (CC) methods provide highly accurate predictions of molecular properties, but their high computational cost has precluded their routine application to large systems. Fortunately, recent computational developments in the ACES III program by the Bartlett group [the OED/ERD atomic integral package, the super instruction processor, and the super instruction architecture language] permit overcoming that limitation by providing a framework for massively parallel CC implementations. In that scheme, we are further extending those parallel CC efforts to systematically predict the three main electron spin resonance (ESR) tensors (A-, g-, and D-tensors) to be reported in a series of papers. In this paper inaugurating that series, we report our new ACES III parallel capabilities that calculate isotropic hyperfine coupling constants in 38 neutral, cationic, and anionic radicals that include the {sup 11}B, {sup 17}O, {sup 9}Be, {sup 19}F, {sup 1}H, {sup 13}C, {sup 35}Cl, {sup 33}S,{sup 14}N, {sup 31}P, and {sup 67}Zn nuclei. Present parallel calculations are conducted at the Hartree-Fock (HF), second-order many-body perturbation theory [MBPT(2)], CC singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] levels using Roos augmented double- and triple-zeta atomic natural orbitals basis sets. HF results consistently overestimate isotropic hyperfine coupling constants. However, inclusion of electron correlation effects in the simplest way via MBPT(2) provides significant improvements in the predictions, but not without occasional failures. In contrast, CCSD results are consistently in very good agreement with experimental results. Inclusion of perturbative triples to CCSD via CCSD(T) leads to small improvements in the predictions, which might not compensate for the extra computational effort at a non-iterative N{sup 7}-scaling in CCSD(T). The importance of these accurate computations of isotropic hyperfine coupling constants to elucidate
10. Analytic determination at one loop of the energy-momentum tensor for lattice QCD
International Nuclear Information System (INIS)
Caracciolo, S.; Menotti, P.; Pelissetto, A.
1991-01-01
We give a completely analytical determinaton of the corrections to the naive energy-momentum tensor for lattice QCD at one loop. This tenor is conserved and gives rise to the correct trace anomaly. (orig.)
11. Chaos in the motion of a test scalar particle coupling to the Einstein tensor in Schwarzschild-Melvin black hole spacetime
Energy Technology Data Exchange (ETDEWEB)
Wang, Mingzhi [Hunan Normal University, Department of Physics, Institute of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Chen, Songbai; Jing, Jiliang [Hunan Normal University, Department of Physics, Institute of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Hunan Normal University, Synergetic Innovation Center for Quantum Effects and Applications, Changsha, Hunan (China)
2017-04-15
We present firstly the equation of motion for a test scalar particle coupling to the Einstein tensor in the Schwarzschild-Melvin black hole spacetime through the short-wave approximation. Through analyzing Poincare sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram, we investigate the effects of the coupling parameter on the chaotic behavior of the particles. With the increase of the coupling strength, we find that the motion of the coupled particle for the chosen parameters becomes more regular and order for the negative couple constant. While, for the positive one, the motion of the coupled particles first undergoes a series of transitions betweens chaotic motion and regular motion and then falls into horizon or escapes to spatial infinity. Our results show that the coupling brings about richer effects for the motion of the particles. (orig.)
12. Mid-callosal plane determination using preferred directions from diffusion tensor images
Science.gov (United States)
Costa, André L.; Rittner, Letícia; Lotufo, Roberto A.; Appenzeller, Simone
2015-03-01
The corpus callosum is the major brain structure responsible for inter{hemispheric communication between neurons. Many studies seek to relate corpus callosum attributes to patient characteristics, cerebral diseases and psychological disorders. Most of those studies rely on 2D analysis of the corpus callosum in the mid-sagittal plane. However, it is common to find conflicting results among studies, once many ignore methodological issues and define the mid-sagittal plane based on precary or invalid criteria with respect to the corpus callosum. In this work we propose a novel method to determine the mid-callosal plane using the corpus callosum internal preferred diffusion directions obtained from diffusion tensor images. This plane is analogous to the mid-sagittal plane, but intended to serve exclusively as the corpus callosum reference. Our method elucidates the great potential the directional information of the corpus callosum fibers have to indicate its own referential. Results from experiments with five image pairs from distinct subjects, obtained under the same conditions, demonstrate the method effectiveness to find the corpus callosum symmetric axis relative to the axial plane.
13. Testing feasibility of scalar-tensor gravity by scale dependent mass and coupling to matter
International Nuclear Information System (INIS)
Mota, D. F.; Salzano, V.; Capozziello, S.
2011-01-01
We investigate whether there is any cosmological evidence for a scalar field with a mass and coupling to matter which change accordingly to the properties of the astrophysical system it ''lives in,'' without directly focusing on the underlying mechanism that drives the scalar field scale-dependent-properties. We assume a Yukawa type of coupling between the field and matter and also that the scalar-field mass grows with density, in order to overcome all gravity constraints within the Solar System. We analyze three different gravitational systems assumed as ''cosmological indicators'': supernovae type Ia, low surface brightness spiral galaxies and clusters of galaxies. Results show (i) a quite good fit to the rotation curves of low surface brightness galaxies only using visible stellar and gas-mass components is obtained; (ii) a scalar field can fairly well reproduce the matter profile in clusters of galaxies, estimated by x-ray observations and without the need of any additional dark matter; and (iii) there is an intrinsic difficulty in extracting information about the possibility of a scale-dependent massive scalar field (or more generally about a varying gravitational constant) from supernovae type Ia.
14. Determination of the plastic deformation and residual stress tensor distribution using surface and bulk intrinsic magnetic properties
International Nuclear Information System (INIS)
Hristoforou, E.; Svec, P. Sr.
2015-01-01
We have developed an unique method to provide the stress calibration curve in steels: performing flaw-less welding in the under examination steel, we obtained to determine the level of the local plastic deformation and the residual stress tensors. These properties where measured using both the X-ray and the neutron diffraction techniques, concerning their surface and bulk stresses type II (intra-grain stresses) respectively, as well as the stress tensor type III by using the electron diffraction technique. Measuring the distribution of these residual stresses along the length of a welded sample or structure, resulted in determining the local stresses from the compressive to tensile yield point. Local measurement of the intrinsic surface and bulk magnetic property tensors allowed for the un-hysteretic correlation. The dependence of these local magnetic tensors with the above mentioned local stress tensors, resulting in a unique and almost un-hysteretic stress calibration curve of each grade of steel. This calibration integrated the steel's mechanical and thermal history, as well as the phase transformations and the presence of precipitations occurring during the welding process.Additionally to that, preliminary results in different grade of steels reveal the existence of a universal law concerning the dependence of magnetic and magnetostrictive properties of steels on their plastic deformation and residual stress state, as they have been accumulated due to their mechanical and thermal fatigue and history. This universality is based on the unique dependence of the intrinsic magnetic properties of steels normalized with a certain magnetoelastic factor, upon the plastic deformation or residual stress state, which, in terms, is normalized with their yield point of stress. (authors)
15. Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations
Science.gov (United States)
Madsen, Niels Kristian; Godtliebsen, Ian H.; Losilla, Sergio A.; Christiansen, Ove
2018-01-01
A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.
16. The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4)) scaling.
Science.gov (United States)
Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David
2013-08-07
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).
17. New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions.
Science.gov (United States)
Bonhomme, Christian; Gervais, Christel; Coelho, Cristina; Pourpoint, Frédérique; Azaïs, Thierry; Bonhomme-Coury, Laure; Babonneau, Florence; Jacob, Guy; Ferrari, Maude; Canet, Daniel; Yates, Jonathan R; Pickard, Chris J; Joyce, Siân A; Mauri, Francesco; Massiot, Dominique
2010-12-01
In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds. Copyright © 2010 John Wiley & Sons, Ltd.
18. Simultaneous Mass Determination for Gravitationally Coupled Asteroids
Energy Technology Data Exchange (ETDEWEB)
Baer, James [Private address, 3210 Apache Road, Pittsburgh, PA 15241 (United States); Chesley, Steven R., E-mail: [email protected] [Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109 (United States)
2017-08-01
The conventional least-squares asteroid mass determination algorithm allows us to solve for the mass of a large subject asteroid that is perturbing the trajectory of a smaller test asteroid. However, this algorithm is necessarily a first approximation, ignoring the possibility that the subject asteroid may itself be perturbed by the test asteroid, or that the encounter’s precise geometry may be entangled with encounters involving other asteroids. After reviewing the conventional algorithm, we use it to calculate the masses of 30 main-belt asteroids. Compared to our previous results, we find new mass estimates for eight asteroids (11 Parthenope, 27 Euterpe, 51 Neimausa, 76 Freia, 121 Hermione, 324 Bamberga, 476 Hedwig, and 532 Herculina) and significantly more precise estimates for six others (2 Pallas, 3 Juno, 4 Vesta, 9 Metis, 16 Psyche, and 88 Thisbe). However, we also find that the conventional algorithm yields questionable results in several gravitationally coupled cases. To address such cases, we describe a new algorithm that allows the epoch state vectors of the subject asteroids to be included as solve-for parameters, allowing for the simultaneous solution of the masses and epoch state vectors of multiple subject and test asteroids. We then apply this algorithm to the same 30 main-belt asteroids and conclude that mass determinations resulting from current and future high-precision astrometric sources (such as Gaia ) should conduct a thorough search for possible gravitational couplings and account for their effects.
19. Simultaneous Mass Determination for Gravitationally Coupled Asteroids
Science.gov (United States)
Baer, James; Chesley, Steven R.
2017-08-01
The conventional least-squares asteroid mass determination algorithm allows us to solve for the mass of a large subject asteroid that is perturbing the trajectory of a smaller test asteroid. However, this algorithm is necessarily a first approximation, ignoring the possibility that the subject asteroid may itself be perturbed by the test asteroid, or that the encounter’s precise geometry may be entangled with encounters involving other asteroids. After reviewing the conventional algorithm, we use it to calculate the masses of 30 main-belt asteroids. Compared to our previous results, we find new mass estimates for eight asteroids (11 Parthenope, 27 Euterpe, 51 Neimausa, 76 Freia, 121 Hermione, 324 Bamberga, 476 Hedwig, and 532 Herculina) and significantly more precise estimates for six others (2 Pallas, 3 Juno, 4 Vesta, 9 Metis, 16 Psyche, and 88 Thisbe). However, we also find that the conventional algorithm yields questionable results in several gravitationally coupled cases. To address such cases, we describe a new algorithm that allows the epoch state vectors of the subject asteroids to be included as solve-for parameters, allowing for the simultaneous solution of the masses and epoch state vectors of multiple subject and test asteroids. We then apply this algorithm to the same 30 main-belt asteroids and conclude that mass determinations resulting from current and future high-precision astrometric sources (such as Gaia) should conduct a thorough search for possible gravitational couplings and account for their effects.
20. Simultaneous Mass Determination for Gravitationally Coupled Asteroids
International Nuclear Information System (INIS)
Baer, James; Chesley, Steven R.
2017-01-01
The conventional least-squares asteroid mass determination algorithm allows us to solve for the mass of a large subject asteroid that is perturbing the trajectory of a smaller test asteroid. However, this algorithm is necessarily a first approximation, ignoring the possibility that the subject asteroid may itself be perturbed by the test asteroid, or that the encounter’s precise geometry may be entangled with encounters involving other asteroids. After reviewing the conventional algorithm, we use it to calculate the masses of 30 main-belt asteroids. Compared to our previous results, we find new mass estimates for eight asteroids (11 Parthenope, 27 Euterpe, 51 Neimausa, 76 Freia, 121 Hermione, 324 Bamberga, 476 Hedwig, and 532 Herculina) and significantly more precise estimates for six others (2 Pallas, 3 Juno, 4 Vesta, 9 Metis, 16 Psyche, and 88 Thisbe). However, we also find that the conventional algorithm yields questionable results in several gravitationally coupled cases. To address such cases, we describe a new algorithm that allows the epoch state vectors of the subject asteroids to be included as solve-for parameters, allowing for the simultaneous solution of the masses and epoch state vectors of multiple subject and test asteroids. We then apply this algorithm to the same 30 main-belt asteroids and conclude that mass determinations resulting from current and future high-precision astrometric sources (such as Gaia ) should conduct a thorough search for possible gravitational couplings and account for their effects.
1. Energy-momentum tensor in theories with scalar fields and two coupling constants. I. Non-Abelian case
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1989-01-01
In this paper, we generalize our earlier discussion of renormalization of the energy-momentum tensor in scalar QED to that in non-Abelian gauge theories involving scalar fields. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be derived from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/)
2. De novo determination of internuclear vector orientations from residual dipolar couplings measured in three independent alignment media
International Nuclear Information System (INIS)
Ruan Ke; Briggman, Kathryn B.; Tolman, Joel R.
2008-01-01
The straightforward interpretation of solution state residual dipolar couplings (RDCs) in terms of internuclear vector orientations generally requires prior knowledge of the alignment tensor, which in turn is normally estimated using a structural model. We have developed a protocol which allows the requirement for prior structural knowledge to be dispensed with as long as RDC measurements can be made in three independent alignment media. This approach, called Rigid Structure from Dipolar Couplings (RSDC), allows vector orientations and alignment tensors to be determined de novo from just three independent sets of RDCs. It is shown that complications arising from the existence of multiple solutions can be overcome by careful consideration of alignment tensor magnitudes in addition to the agreement between measured and calculated RDCs. Extensive simulations as well applications to the proteins ubiquitin and Staphylococcal protein GB1 demonstrate that this method can provide robust determinations of alignment tensors and amide N-H bond orientations often with better than 10 o accuracy, even in the presence of modest levels of internal dynamics
3. Tensor spaces and exterior algebra
CERN Document Server
Yokonuma, Takeo
1992-01-01
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
4. Determination of protein global folds using backbone residual dipolar coupling and long-range NOE restraints
International Nuclear Information System (INIS)
Giesen, Alexander W.; Homans, Steve W.; Brown, Jonathan Miles
2003-01-01
We report the determination of the global fold of human ubiquitin using protein backbone NMR residual dipolar coupling and long-range nuclear Overhauser effect (NOE) data as conformational restraints. Specifically, by use of a maximum of three backbone residual dipolar couplings per residue (N i -H N i , N i -C' i-1 , H N i - C' i-1 ) in two tensor frames and only backbone H N -H N NOEs, a global fold of ubiquitin can be derived with a backbone root-mean-square deviation of 1.4 A with respect to the crystal structure. This degree of accuracy is more than adequate for use in databases of structural motifs, and suggests a general approach for the determination of protein global folds using conformational restraints derived only from backbone atoms
5. Old tensor mesons in QCD sum rules
International Nuclear Information System (INIS)
Aliev, T.M.; Shifman, M.A.
1981-01-01
Tensor mesons f, A 2 and A 3 are analyzed within the framework of QCD sum rules. The effects of gluon and quark condensate is accounted for phenomenologically. Accurate estimates of meson masses and coupling constants of the lowest-lying states are obtained. It is shown that the masses are reproduced within theoretical uncertainty of about 80 MeV. The coupling of f meson to the corresponding quark current is determined. The results are in good aqreement with experimental data [ru
6. Tensor surgery and tensor rank
NARCIS (Netherlands)
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2018-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices
7. Tensor surgery and tensor rank
NARCIS (Netherlands)
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new
8. Stress-energy tensor of a quark moving through a strongly-coupled N=4 supersymmetric Yang-Mills plasma: Comparing hydrodynamics and AdS/CFT duality
International Nuclear Information System (INIS)
Chesler, Paul M.; Yaffe, Laurence G.
2008-01-01
The stress-energy tensor of a quark moving through a strongly-coupled N=4 supersymmetric Yang-Mills plasma, at large N c , is evaluated using gauge/string duality. The accuracy with which the resulting wake, in position space, is reproduced by hydrodynamics is examined. Remarkable agreement is found between hydrodynamics and the complete result down to distances less than 2/T away from the quark. In performing the gravitational analysis, we use a relatively simple formulation of the bulk to boundary problem in which the linearized Einstein field equations are fully decoupled. Our analysis easily generalizes to other sources in the bulk.
9. Two-perfect fluid interpretation of an energy tensor
International Nuclear Information System (INIS)
Ferrando, J.J.; Morales, J.A.; Portilla, M.
1990-01-01
There are many topics in General Relativity where matter is represented by a mixture of two fluids. In fact, some astrophysical and cosmological situations need to be described by an energy tensor made up of the sum of two or more perfect fluids rather than that with only one. The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained
10. Tensor Galileons and gravity
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)
2017-03-13
The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.
11. Measurement of the Higgs boson tensor coupling in $H \\rightarrow ZZ^{*} \\rightarrow 4\\ell$ decays with the ATLAS detector - How odd is the Higgs boson?
CERN Document Server
Ecker, Katharina Maria; Kortner, Sandra
The tensor structure of the Higgs boson couplings to gluons and heavy weak gauge bosons has been probed for small admixtures of non-Standard Model CP-odd and, only for heavy vector bosons, CP-even couplings to the CP-even Standard Model coupling. The Higgs boson candidates are reconstructed in the $\\HZZllll$ $(\\ell\\equiv e,\\mu)$ decay channel using proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider (LHC) in 2011 and 2012 at centre-of-mass energies of $\\sqrt{s}=7$ and $8\\,\\tev$ corresponding to an integrated luminosity of $\\intlumisetot\\,\\ifb$ and in 2015 and 2016 at $\\ecms$ corresponding to $\\intlumi\\,\\ifb$.\\\\ The non-Standard Model coupling parameters are defined within an effective field theory, the so-called Higgs characterisation framework. The relative contributions of the CP-even and CP-odd terms are described by the CP mixing angle $\\alpha$. The parameter $\\kaggnoma$ denotes the CP-odd non-Standard Model coupling at the Higgs to gluon interaction vertex and \\khvv... 12. Diffusion tensor image registration using hybrid connectivity and tensor features. Science.gov (United States) Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang 2014-07-01 Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc. 13. Single-shot full strain tensor determination with microbeam X-ray Laue diffraction and a two-dimensional energy-dispersive detector. Science.gov (United States) Abboud, A; Kirchlechner, C; Keckes, J; Conka Nurdan, T; Send, S; Micha, J S; Ulrich, O; Hartmann, R; Strüder, L; Pietsch, U 2017-06-01 The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated. 14. The geomagnetic field gradient tensor DEFF Research Database (Denmark) Kotsiaros, Stavros; Olsen, Nils 2012-01-01 We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination... 15. Multi-mode technique for the determination of the biaxial Y{sub 2}SiO{sub 5} permittivity tensor from 300 to 6 K Energy Technology Data Exchange (ETDEWEB) Carvalho, N. C., E-mail: [email protected]; Le Floch, J-M.; Tobar, M. E. [School of Physics, The University of Western Australia, Crawley 6009 (Australia); ARC Centre of Excellence for Engineered Quantum Systems (EQuS), 35 Stirling Hwy, Crawley 6009 (Australia); Krupka, J. [Instytut Mikroelektroniki i Optoelektroniki PW, Koszykowa 75, 00-662 Warsaw (Poland) 2015-05-11 The Y{sub 2}SiO{sub 5} (YSO) crystal is a dielectric material with biaxial anisotropy with known values of refractive index at optical frequencies. It is a well-known rare-earth (RE) host material for optical research and more recently has shown promising performance for quantum-engineered devices. In this paper, we report the first microwave characterization of the real permittivity tensor of a bulk YSO sample, as well as an investigation of the temperature dependence of the tensor components from 296 K down to 6 K. Estimated uncertainties were below 0.26%, limited by the precision of machining the cylindrical dielectric. Also, the electrical Q-factors of a few electromagnetic modes were recorded as a way to provide some information about the crystal losses over the temperature range. To solve the tensor components necessary for a biaxial crystal, we developed the multi-mode technique, which uses simultaneous measurement of low order whispering gallery modes. Knowledge of the permittivity tensor offers important data, essential for the design of technologies involving YSO, such as microwave coupling to electron and hyperfine transitions in RE doped samples at low temperatures. 16. Determinants In HIV Counselling And Testing In Couples In North ... African Journals Online (AJOL) Determinants In HIV Counselling And Testing In Couples In North Rift Kenya. PO Ayuo, E Were, K Wools-Kaloustian, J Baliddawa, J Sidle, K Fife. Abstract. Background: Voluntary HIV counselling and testing (VCT) has been shown to be an acceptable and effective tool in the fight against HIV/AIDS. Couple HIV Counselling ... 17. Determination of 13C CSA Tensors: Extension of the Model-independent Approach to an RNA Kissing Complex Undergoing Anisotropic Rotational Diffusion in Solution International Nuclear Information System (INIS) Ravindranathan, Sapna; Kim, Chul-Hyun; Bodenhausen, Geoffrey 2005-01-01 Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109-7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X-H two-spin systems (X = 13 C or 15 N) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio κ 2 =R 2 auto /R 2 cross of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X-H dipolar interaction is independent of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic κ 2 depends on the anisotropy D parallel /D -perpendicular of rotational diffusion. In this paper, the field dependence of both κ 2 and its longitudinal counterpart κ 1 =R 1 auto /R 1 cross are determined. For anisotropic rotational diffusion, our calculations show that the average κ av = 1/2 (κ 1 +κ 2 ), of the ratios is largely independent of the anisotropy parameter D parallel /D -perpendicular . The field dependence of the average ratio κ av may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules with an overall motion described by an axially symmetric rotational diffusion tensor 18. Determination of the Rotational Diffusion Tensor of Macromolecules in Solution from NMR Relaxation Data with a Combination of Exact and Approximate Methods—Application to the Determination of Interdomain Orientation in Multidomain Proteins Science.gov (United States) Ghose, Ranajeet; Fushman, David; Cowburn, David 2001-04-01 In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. 19. Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins. Science.gov (United States) Ghose, R; Fushman, D; Cowburn, D 2001-04-01 In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. Copyright 2001 Academic Press. 20. Determination of the π3He3H coupling constant International Nuclear Information System (INIS) Nichitiu, F.; Sapozhnikov, M.G. 1977-01-01 Despersion relations for the real part of the antisymmetric amplitude of the π +-3 He scattering have been used in order to determine the π 3 He 3 H coupling constant. The coupling constant value determined by this method is larger than the elementary pion-nucleon coupling constant, but is in good agreement with the value obtained by another method. The obtained value is f 2 sub(π 3 He 3 H) = 0.12+-0.01. Shown is the importance of using the Coulomb corrections for dispersion relation calculations because the value of π 3 He 3 H coupling constant obtained with corrected total cross sections is larger by about 0.014 than the one obtained without these corrections. The best energy ranges for future π 3 He experiments are commented 1. Determination of BEACON Coupling Coefficients using data from Xenon transient International Nuclear Information System (INIS) Bozic, M.; Kurincic, B. 2007-01-01 NEK uses BEACO TM code (BEACO TM - Westinghouse Best Estimate Analyzer for Core Operating Nuclear) for core monitoring, analysis and core behaviour prediction. Coupling Coefficients determine relationship between core response and excore instrumentation. Measured power distribution using incore moveable detectors during Xenon transient with sufficient power axial offset change is the most important data for further analysis. Classic methodology and BEACO TM Conservative methodology using established Coupling Coefficients are compared on NPP Krsko case. BEACON TM Conservative methodology with predefined Coupling Coefficients is used as a surveillance tool for verification of relationship between core and excore instrumentation during power operation. (author) 2. Determining γ with B decays into a scalar/tensor meson International Nuclear Information System (INIS) Wang, Wei 2011-10-01 We propose a new way for determining the CP violation angle γ. The suggested method is to use the two triangles formed by the decay amplitudes of B ± →(D 0 , anti D 0 ,D 0 CP )K *± 0(2) (1430). The advantages are that large CP asymmetries are expected in these processes and only singly Cabibbo-suppressed D decay modes are involved. Measurements of the branching fractions of the neutral B d decays into DK * 0(2) (1430) and the time-dependent CP asymmetries in B s →(D 0 , anti D 0 )M (M=f 0 (980),f 0 (1370),f 2 ' (1525),f 1 (1285),f 1 (1420),h 1 (1180)) provide an alternative way to extract the angle γ, which will increase the statistical significance. No knowledge of the resonance structure in this method is required and therefore the angle γ can be extracted without any hadronic uncertainty. (orig.) 3. Determining {gamma} with B decays into a scalar/tensor meson Energy Technology Data Exchange (ETDEWEB) Wang, Wei 2011-10-15 We propose a new way for determining the CP violation angle {gamma}. The suggested method is to use the two triangles formed by the decay amplitudes of B{sup {+-}}{yields}(D{sup 0}, anti D{sup 0},D{sup 0}{sub CP})K{sup *{+-}}{sub 0(2)}(1430). The advantages are that large CP asymmetries are expected in these processes and only singly Cabibbo-suppressed D decay modes are involved. Measurements of the branching fractions of the neutral B{sub d} decays into DK{sup *}{sub 0(2)}(1430) and the time-dependent CP asymmetries in B{sub s}{yields}(D{sup 0}, anti D{sup 0})M (M=f{sub 0}(980),f{sub 0}(1370),f{sub 2}{sup '}(1525),f{sub 1}(1285),f{sub 1}(1420),h{sub 1}(1180)) provide an alternative way to extract the angle {gamma}, which will increase the statistical significance. No knowledge of the resonance structure in this method is required and therefore the angle {gamma} can be extracted without any hadronic uncertainty. (orig.) 4. Numerical estimates of the maximum sustainable pore pressure in anticline formations using the tensor based concept of pore pressure-stress coupling Directory of Open Access Journals (Sweden) Andreas Eckert 2015-02-01 Full Text Available The advanced tensor based concept of pore pressure-stress coupling is used to provide pre-injection analytical estimates of the maximum sustainable pore pressure change, ΔPc, for fluid injection scenarios into generic anticline geometries. The heterogeneous stress distribution for different prevailing stress regimes in combination with the Young's modulus (E contrast between the injection layer and the cap rock and the interbedding friction coefficient, μ, may result in large spatial and directional differences of ΔPc. A single value characterizing the cap rock as for horizontal layered injection scenarios is not obtained. It is observed that a higher Young's modulus in the cap rock and/or a weak mechanical coupling between layers amplifies the maximum and minimum ΔPc values in the valley and limb, respectively. These differences in ΔPc imposed by E and μ are further amplified by different stress regimes. The more compressional the stress regime is, the larger the differences between the maximum and minimum ΔPc values become. The results of this study show that, in general compressional stress regimes yield the largest magnitudes of ΔPc and extensional stress regimes provide the lowest values of ΔPc for anticline formations. Yet this conclusion has to be considered with care when folded anticline layers are characterized by flexural slip and the friction coefficient between layers is low, i.e. μ = 0.1. For such cases of weak mechanical coupling, ΔPc magnitudes may range from 0 MPa to 27 MPa, indicating imminent risk of fault reactivation in the cap rock. 5. Beyond Low Rank: A Data-Adaptive Tensor Completion Method OpenAIRE Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning 2017-01-01 Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no... 6. Energy-momentum tensor in quantum field theory International Nuclear Information System (INIS) Fujikawa, K. 1981-01-01 The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat--space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group b function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise 7. Weyl tensors for asymmetric complex curvatures International Nuclear Information System (INIS) Oliveira, C.G. Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt 8. Model-independent determination of hadronic neutral-current couplings International Nuclear Information System (INIS) Claudson, M.; Paschos, E.A.; Strait, J.; Sulak, L.R. 1979-01-01 Completion of a second generation of experiments on neutrino-induced neutral-current reactions allows a more discriminating study of neutral-current couplings to hadrons. To minimize the sensitivity to model-dependent analyses of inclusive and exclusive pion data, we base our work on measurements of deep-inelastic and elastic reactions alone. Within the regions allowed by the deep-inelastic data for scattering on isoscalar targets, the coupling constants are fit to the q 2 dependence of the neutrino-proton elastic scattering data. This procedure initially yields two solutions for the couplings. One of these, at theta/sub L/ = 55 0 and theta/sub R/ = 205 0 , is predominantly isoscalar and therefore is ruled out by only qualitative consideration of exclusive pion data. The other solution at theta/sub D/ = 140 0 and and theta/sub R/ = 330 0 , is thus a unique determination of the hadronic neutral-current couplings. It coincides with solution A obtained in earlier work, and is insensitive to variations of M/sub A/ within 2 standard deviations of the world average. When constrained to the coupling constants required by the Weinberg-Salam model, the fit agrees with the data to within 1 standard deviation 9. Determination of the pion-nucleon coupling constant International Nuclear Information System (INIS) Samaranayake, V.K. 1977-06-01 Forward dispersion relations are used to determine the pion-nucleon coupling constant and S-wave scattering lengths using a least squares fit with additional parameters introduced to take account of the uncertainties in the calculation of dispersion integrals. The values obtained are: f 2 = (78.0+- 2.1).10 -3 , a 1 -a 3 = (272.4+- 12.3).10 -3 , a 1 +2a 3 = (15.1+-10.4).10 -3 10. The energy–momentum tensor(s in classical gauge theories Directory of Open Access Journals (Sweden) Daniel N. Blaschke 2016-11-01 Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed. 11. Methods for the Determination of Currents and Fields in Steady Two-Dimensional MHD Flow With Tensor Conductivity International Nuclear Information System (INIS) Witalis, E.A. 1965-12-01 Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given 12. Methods for the Determination of Currents and Fields in Steady Two-Dimensional MHD Flow With Tensor Conductivity Energy Technology Data Exchange (ETDEWEB) Witalis, E A 1965-12-15 Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given. 13. Tensor Transpose and Its Properties OpenAIRE Pan, Ran 2014-01-01 Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank. 14. Scalar-tensor linear inflation Energy Technology Data Exchange (ETDEWEB) Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: [email protected], E-mail: [email protected] [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia) 2017-04-01 We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit. 15. Energy-momentum tensor in quantum field theory International Nuclear Information System (INIS) Fujikawa, Kazuo. 1980-12-01 The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat space-time limit, all the Ward-Takahashi identities associate with space-time transformations including the global dilatation become free from anomalies, reflecting the general covariance of the integral measure; the trace of this energy-momentum tensor is thus finite at the zero momentum transfer. The Jacobian for the local conformal transformation however becomes non-trivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at the vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization group β-function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at the vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise. (author) 16. (Ln-bar, g)-spaces. Special tensor fields International Nuclear Information System (INIS) Manoff, S.; Dimitrov, B. 1998-01-01 The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces 17. Confinement through tensor gauge fields International Nuclear Information System (INIS) Salam, A.; Strathdee, J. 1977-12-01 Using the 0(3,2)-symmetric de Sitter solution of Einstein's equation describing a strongly interacting tensor field it is shown that hadronic bags confining quarks can be represented as de Sitter ''micro-universes'' with radii given 1/R 2 =lambdak 2 /6. Here k 2 and lambda are the strong coupling and the ''cosmological'' constant which apear in the Einstein equation used. Surprisingly the energy spectrum for the two-body hadronic states is the same as that for a harmonic oscillator potential, though the wave functions are completely different. The Einstein equation can be extended to include colour for the tensor fields 18. Tensor product of quantum logics Science.gov (United States) Pulmannová, Sylvia 1985-01-01 A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied. 19. Tensors for physics CERN Document Server Hess, Siegfried 2015-01-01 This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-... 20. Random tensors CERN Document Server Gurau, Razvan 2017-01-01 Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another.... 1. Tensor rank is not multiplicative under the tensor product DEFF Research Database (Denmark) Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen 2018-01-01 The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b... 2. Tensor rank is not multiplicative under the tensor product NARCIS (Netherlands) M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen) 2018-01-01 textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the 3. Tensor rank is not multiplicative under the tensor product NARCIS (Netherlands) M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen) 2017-01-01 textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in 4. A new approach for applying residual dipolar couplings as restraints in structure elucidation International Nuclear Information System (INIS) Meiler, Jens; Blomberg, Niklas; Nilges, Michael; Griesinger, Christian 2000-01-01 Residual dipolar couplings are useful global structural restraints. The dipolar couplings define the orientation of a vector with respect to the alignment tensor. Although the size of the alignment tensor can be derived from the distribution of the experimental dipolar couplings, its orientation with respect to the coordinate system of the molecule is unknown at the beginning of structure determination. This causes convergence problems in the simulated annealing process. We therefore propose a protocol that translates dipolar couplings into intervector projection angles, which are independent of the orientation of the alignment tensor with respect to the molecule. These restraints can be used during the whole simulated annealing protocol 5. Applications of tensor functions in creep mechanics International Nuclear Information System (INIS) Betten, J. 1991-01-01 Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM) 6. The tensor distribution function. Science.gov (United States) Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M 2009-01-01 Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues. 7. The Riemann-Lovelock Curvature Tensor OpenAIRE Kastor, David 2012-01-01 In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D 8. (Ln-bar, g)-spaces. Ordinary and tensor differentials International Nuclear Information System (INIS) Manoff, S.; Dimitrov, B. 1998-01-01 Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces 9. Measurement of thepp\\to H\\to ZZ^* \\to 4 \\ell$Production and$HZZ$Tensor Coupling with the ATLAS Detector at 13 TeV Centre-of-Mass Energy CERN Document Server Walbrecht, Verena Maria; Kortner, Sandra In this master thesis the measurement of the Higgs boson production in the$H\\to~ZZ^*~\\to 4~\\ell$decay channel ($\\ell=e,\\mu$) is performed together with the measurement of the tensor structure of the Higgs boson couplings to$Z$bosons. The results are based on the Run~II dataset of LHC's proton-proton collisions at a centre-of-mass energy of 13~TeV, with the ATLAS detector and corresponding to a total integrated luminosity of$14.78$~fb$^{-1}$. Special emphasis is given to the estimation of the reducible background contribution. Based on the signal and background estimations, there are$32.0\\pm3.2$Higgs boson candidates expected after the final event selection, while$44$candidates are observed. The difference is compatible at the level of about$2$standard derivations with the Standard Model predictions. All selected candidates are used in the study of the tensor structure of the$HZZ$coupling between the Higgs boson and the two$Zbosons. For this study a dedicated signal model is introduced to desc... 10. Tensor rank is not multiplicative under the tensor product OpenAIRE Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen 2017-01-01 The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif... 11. Tensor gauge condition and tensor field decomposition Science.gov (United States) Zhu, Ben-Chao; Chen, Xiang-Song 2015-10-01 We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case. 12. Tensor structure for Nori motives OpenAIRE Barbieri-Viale, Luca; Huber, Annette; Prest, Mike 2018-01-01 We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives. 13. Radiative corrections in a vector-tensor model International Nuclear Information System (INIS) Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C. 2006-01-01 In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field 14. Tensor eigenvalues and their applications CERN Document Server Qi, Liqun; Chen, Yannan 2018-01-01 This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues. 15. Harmonic d-tensors Energy Technology Data Exchange (ETDEWEB) Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia) 2016-07-01 Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity. 16. Abelian gauge theories with tensor gauge fields International Nuclear Information System (INIS) Kapuscik, E. 1984-01-01 Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author) 17. Monograph On Tensor Notations Science.gov (United States) Sirlin, Samuel W. 1993-01-01 Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described. 18. Nonlocal elasticity tensors in dislocation and disclination cores International Nuclear Information System (INIS) Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L. 2017-01-01 We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations. 19. The Topology of Symmetric Tensor Fields Science.gov (United States) Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval 1997-01-01 Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions. 20. The determination of young couples educational needs in Yazd Directory of Open Access Journals (Sweden) 2014-07-01 Full Text Available Abstract Introduction:one of the essential needs of young couples is to have knowledge in the field of health reproduction that will have significant impact on health improvement and family bonds.recognization of young couples are lead more attention of policy maker towards issues which is contained low level of knowledge for the young couples. Presenting the required training to young couples will help to have better undersanding of their thoughts and feelings and make decisions more corrective and appropriate for themselves about reproductive health issues. Methods: this is a descriptive study. The statistical population is volentier couples who have reffering to the premartial counseling centers that they had been married since last year to express their training needs based on experince of the life. The samples are included 240 couples and data instrument was the questionnaires that directly were interviewed and data were analyzed by use of SPSS software. Results:less educated, rurals, home worker and laborershas more training need than the others and there is a significant difference. (p = 0.000. but training need is not related to the marriageable age, gender and there was no significant difference(p > 0.50. The young couples are explained the lessamount of training needs in case of form and function of the reproductive system, method of contraception from prognancy, preparation needs before sextual, simultanios and how they can have sexual relation and how they have sexual and intercourse intercourse and statidfy. While the need of training based on healthy issue during menstruation and time of intercourse, how to become pregnant, sexually transmitted, high risk prognancies, congenital diseases, common cancerns, sexual dysfunction are more and more mentioned. Conclusion :Training needs of couples should be more considered. For the rurals and less educated groupit should be perform supplementory classes after the marriage. Based on the 1. iDC: A comprehensive toolkit for the analysis of residual dipolar couplings for macromolecular structure determination International Nuclear Information System (INIS) Wei Yufeng; Werner, Milton H. 2006-01-01 Measurement of residual dipolar couplings (RDCs) has become an important method for the determination and validation of protein or nucleic acid structures by NMRf spectroscopy. A number of toolkits have been devised for the handling of RDC data which run in the Linux/Unix operating environment and require specifically formatted input files. The outputs from these programs, while informative, require format modification prior to the incorporation of this data into commonly used personal computer programs for manuscript preparation. To bridge the gap between analysis and publication, an easy-to-use, comprehensive toolkit for RDC analysis has been created, iDC. iDC is written for the WaveMetrics Igor Pro mathematics program, a widely used graphing and data analysis software program that runs on both Windows PC and Mac OS X computers. Experimental RDC values can be loaded into iDC using simple data formats accessible to Igor's tabular data function. The program can perform most useful RDC analyses, including alignment tensor estimation from a histogram of RDC occurrence versus values and order tensor analysis by singular value decomposition (SVD). SVD analysis can be performed on an entire structure family at once, a feature missing in other applications of this kind. iDC can also import from and export to several different commonly used programs for the analysis of RDC data (DC, PALES, REDCAT) and can prepare formatted files for RDC-based refinement of macromolecular structures using XPLOR-NIH, CNS and ARIA. The graphical user interface provides an easy-to-use I/O for data, structures and formatted outputs 2. Bowen-York tensors International Nuclear Information System (INIS) Beig, Robert; Krammer, Werner 2004-01-01 For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York 3. A framework for fast probabilistic centroid-moment-tensor determination-inversion of regional static displacement measurements NARCIS (Netherlands) Käufl, P.J.; Valentine, A.P.; O'Toole, T.B.; Trampert, J. 2014-01-01 The determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. 4. 3D reconstruction of tensors and vectors International Nuclear Information System (INIS) Defrise, Michel; Gullberg, Grant T. 2005-01-01 Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields 5. Determination of beam coupling impedance in the frequency domain Energy Technology Data Exchange (ETDEWEB) Niedermayer, Uwe 2016-07-01 The concept of beam coupling impedance describes the electromagnetic interaction of uniformly moving charged particles with their surrounding structures in the Frequency Domain (FD). In synchrotron accelerators, beam coupling impedances can lead to beam induced component heating and coherent beam instabilities. Thus, in order to ensure the stable operation of a synchrotron, its impedances have to be quantified and their effects have to be controlled. Nowadays, beam coupling impedances are mostly obtained by Fourier transform of wake potentials, which are the results of Time Domain (TD) simulations. However, at low frequencies, low beam velocity, or for dispersive materials, TD simulations become unhandy. In this area, analytical calculations of beam coupling impedance in the FD, combined with geometry approximations, are still widely used. This thesis describes the development of two electromagnetic field solvers to obtain the beam coupling impedance directly in the FD, where the beam velocity is only a parameter and dispersive materials can be included easily. One solver is based on the Finite Integration Technique (FIT) on a staircase mesh. It is implemented both in 2D and 3D. However, the staircase mesh is inefficient on curved structures, which is particularly problematic for the modeling of a dipole source, that is required for the computation of the transverse beam coupling impedance. This issue is overcome by the second solver developed in this thesis, which is based on the Finite Element Method (FEM) on an unstructured triangular mesh. It is implemented in 2D and includes an optional Surface Impedance Boundary Condition (SIBC). Thus, it is well suited for the computation of longitudinal and transverse impedances of long beam pipe structures of arbitrary cross-section. Besides arbitrary frequency and beam velocity, also dispersive materials can be chosen, which is crucial for the computation of the impedance of ferrite kicker magnets. Numerical impedance 6. Convenient method for resolving degeneracies due to symmetry of the magnetic susceptibility tensor and its application to pseudo contact shift-based protein–protein complex structure determination International Nuclear Information System (INIS) Kobashigawa, Yoshihiro; Saio, Tomohide; Ushio, Masahiro; Sekiguchi, Mitsuhiro; Yokochi, Masashi; Ogura, Kenji; Inagaki, Fuyuhiko 2012-01-01 Pseudo contact shifts (PCSs) induced by paramagnetic lanthanide ions fixed in a protein frame provide long-range distance and angular information, and are valuable for the structure determination of protein–protein and protein–ligand complexes. We have been developing a lanthanide-binding peptide tag (hereafter LBT) anchored at two points via a peptide bond and a disulfide bond to the target proteins. However, the magnetic susceptibility tensor displays symmetry, which can cause multiple degenerated solutions in a structure calculation based solely on PCSs. Here we show a convenient method for resolving this degeneracy by changing the spacer length between the LBT and target protein. We applied this approach to PCS-based rigid body docking between the FKBP12-rapamycin complex and the mTOR FRB domain, and demonstrated that degeneracy could be resolved using the PCS restraints obtained from two-point anchored LBT with two different spacer lengths. The present strategy will markedly increase the usefulness of two-point anchored LBT for protein complex structure determination. 7. Convenient method for resolving degeneracies due to symmetry of the magnetic susceptibility tensor and its application to pseudo contact shift-based protein-protein complex structure determination Energy Technology Data Exchange (ETDEWEB) Kobashigawa, Yoshihiro; Saio, Tomohide [Hokkaido University, Department of Structural Biology, Faculty of Advanced Life Science (Japan); Ushio, Masahiro [Hokkaido University, Graduate School of Life Science (Japan); Sekiguchi, Mitsuhiro [Astellas Pharma Inc., Analysis and Pharmacokinetics Research Labs, Department of Drug Discovery (Japan); Yokochi, Masashi; Ogura, Kenji; Inagaki, Fuyuhiko, E-mail: [email protected] [Hokkaido University, Department of Structural Biology, Faculty of Advanced Life Science (Japan) 2012-05-15 Pseudo contact shifts (PCSs) induced by paramagnetic lanthanide ions fixed in a protein frame provide long-range distance and angular information, and are valuable for the structure determination of protein-protein and protein-ligand complexes. We have been developing a lanthanide-binding peptide tag (hereafter LBT) anchored at two points via a peptide bond and a disulfide bond to the target proteins. However, the magnetic susceptibility tensor displays symmetry, which can cause multiple degenerated solutions in a structure calculation based solely on PCSs. Here we show a convenient method for resolving this degeneracy by changing the spacer length between the LBT and target protein. We applied this approach to PCS-based rigid body docking between the FKBP12-rapamycin complex and the mTOR FRB domain, and demonstrated that degeneracy could be resolved using the PCS restraints obtained from two-point anchored LBT with two different spacer lengths. The present strategy will markedly increase the usefulness of two-point anchored LBT for protein complex structure determination. 8. Supergravity tensor calculus in 5D from 6D International Nuclear Information System (INIS) Kugo, Taichiro; Ohashi, Keisuke 2000-01-01 Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author) 9. Categorical Tensor Network States Directory of Open Access Journals (Sweden) Jacob D. Biamonte 2011-12-01 Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states. 10. Classification of the Ricci and Plebanski tensors in general relativity using Newman--Penrose formalism International Nuclear Information System (INIS) McIntosh, C.B.G.; Foyster, J.M.; Lun, A.W.h. 1981-01-01 A list is given of a canonical set of the Newman--Penrose quantities Phi/sub A/B, the tetrad components of the trace-free Ricci tensor, for each Plebanski class according to Plebanski's classification of this tensor. This comparative list can easily be extended to cover the classification in tetrad language of any second-order, trace-free, symmetric tensor in a space-time. A fourth-order tensor which is the product of two such tensors was defined by Plebanski and used in his classification. This has the same symmetries as the Weyl tensor. The Petrov classification of this tensor, here called the Plebanski tensor, is discussed along with the classification of the Ricci tensor. The use of the Plebanski tensor in a couple of areas of general relativity is also briefly discussed 11. Heterogeneity of time delays determines synchronization of coupled oscillators. Science.gov (United States) Petkoski, Spase; Spiegler, Andreas; Proix, Timothée; Aram, Parham; Temprado, Jean-Jacques; Jirsa, Viktor K 2016-07-01 Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations. 12. Direct determinations of the πNN coupling constants International Nuclear Information System (INIS) Ericson, T.E.O.; ); Loiseau, B. 1998-01-01 A novel extrapolation method has been used to deduce directly the charged πNN coupling constant from backward np differential scattering cross sections. The extracted value, g c 2 = 14.52(026)is higher than the indirectly deduced values obtained in nucleon-nucleon energy-dependent partial-wave analyses. Our preliminary direct value from a reanalysis of the GMO sum-rule points to an intermediate value of g c 2 about 13.97(30). (author) 13. Cartesian tensors an introduction CERN Document Server Temple, G 2004-01-01 This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t 14. [Determination of a Friction Coefficient for THA Bearing Couples]. Science.gov (United States) Vrbka, M; Nečas, D; Bartošík, J; Hartl, M; Křupka, I; Galandáková, A; Gallo, J 2015-01-01 The wear of articular surfaces is considered one of the most important factors limiting the life of total hip arthroplasty (THA). It is assumed that the particles released from the surface of a softer material induce a complex inflammatory response, which will eventually result in osteolysis and aseptic loosening. Implant wear is related to a friction coefficient which depends on combination of the materials used, roughness of the articulating surfaces, internal clearance, and dimensions of the prosthesis. The selected parameters of the bearing couples tested were studied using an experimental device based on the principle of a pendulum. Bovine serum was used as a lubricant and the load corresponded to a human body mass of 75 kg. The friction coefficient was derived from a curve of slowdown of pendulum oscillations. Roughness was measured with a device working on the principle of interferometry. Clearance was assessed by measuring diameters of the acetabular and femoral heads with a 3D optical scanner. The specimens tested included unused metal-on-highly cross-linked polyethylene, ceramic-on-highly cross-linked polyethylene and ceramic-on-ceramic bearing couples with the diameters of 28 mm and 36 mm. For each measured parameter, an arithmetic mean was calculated from 10 measurements. 1) The roughness of polyethylene surfaces was higher by about one order of magnitude than the roughness of metal and ceramic components. The Protasul metal head had the least rough surface (0.003 μm). 2) The ceramic-on-ceramic couples had the lowest clearance. Bearing couples with polyethylene acetabular liners had markedly higher clearances ranging from 150 μm to 545 μm. A clearance increased with large femoral heads (up to 4-fold in one of the couple tested). 3) The friction coefficient was related to the combination of materials; it was lowest in ceramic-on-ceramic surfaces (0.11 to 0.12) and then in ceramic-on-polyethylene implants (0.13 to 0.14). The friction coefficient is 15. Determination of the seismic moment tensor for local events in the South Shetland Islands and Bransfield Strait International Nuclear Information System (INIS) Guidarelli, M.; Panza, G.F. 2005-06-01 We present the results of the analysis for a set of earthquakes recorded in the Bransfield Strait and the South Shetland Islands in the period 1997-1998, to determine focal mechanisms and source time functions. Events with magnitudes between 3 and 5.6 have been analysed, and the source parameters have been retrieved using a robust methodology (INPAR) that allows the reliable inversion of a limited number of noisy records. This methodology is particularly important in oceanic environments, where the presence of seismic noise and the small number of stations makes it difficult to analyse small magnitude events. (author) 16. Two-photon couplings of 1 = 0 scalars and tensors from analysis of new γγ → ππ data International Nuclear Information System (INIS) Morgan, D.; Pennington, M.R. 1989-11-01 New data on γγ→π + π - and π 0 π 0 admit an amplitude analysis whereby two-photon couplings of the I = 0 scalars and of the f 2 (1270) can be extracted in a much more model independent way than hitherto. Alternative trial forms respecting known properties at low energies and of final state interactions are fitted to the data. The ensuing resonance couplings span a much wider range than is commonly supposed. The best fits correspond to solutions with a relatively large S-wave coupling (∼ 8keV) through the f 2 -region. All fits have an S* coupling of about 1/2 keV. (author) 17. Restricted magnetically balanced basis applied for relativistic calculations of indirect nuclear spin-spin coupling tensors in the matrix Dirac-Kohn-Sham framework International Nuclear Information System (INIS) Repisky, Michal; Komorovsky, Stanislav; Malkina, Olga L.; Malkin, Vladimir G. 2009-01-01 The relativistic four-component density functional approach based on the use of restricted magnetically balanced basis (mDKS-RMB), applied recently for calculations of NMR shielding, was extended for calculations of NMR indirect nuclear spin-spin coupling constants. The unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component while to solve the second-order coupled perturbed DKS equations a restricted magnetically balanced basis set for the small component was applied. Benchmark relativistic calculations have been carried out for the X-H and H-H spin-spin coupling constants in the XH 4 series (X = C, Si, Ge, Sn and Pb). The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in our method for property calculations 18. The effects of noise over the complete space of diffusion tensor shape. Science.gov (United States) Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B 2014-01-01 Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved. 19. Off-shell N = 2 tensor supermultiplets International Nuclear Information System (INIS) Wit, Bernard de; Saueressig, Frank 2006-01-01 A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given 20. Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI Science.gov (United States) Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B. 2015-01-01 Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085 1. New approach to the determination phosphorothioate oligonucleotides by ultra high performance liquid chromatography coupled with inductively coupled plasma mass spectrometry. Science.gov (United States) Studzińska, Sylwia; Mounicou, Sandra; Szpunar, Joanna; Łobiński, Ryszard; Buszewski, Bogusław 2015-01-15 This text presents a novel method for the separation and detection of phosphorothioate oligonucleotides with the use of ion pair ultra high performance liquid chromatography coupled with inductively coupled plasma mass spectrometry The research showed that hexafluoroisopropanol/triethylamine based mobile phases may be successfully used when liquid chromatography is coupled with such elemental detection. However, the concentration of both HFIP and TEA influences the final result. The lower concentration of HFIP, the lower the background in ICP-MS and the greater the sensitivity. The method applied for the analysis of serum samples was based on high resolution inductively coupled plasma mass spectrometry. Utilization of this method allows determination of fifty times lower quantity of phosphorothioate oligonucleotides than in the case of quadrupole mass analyzer. Monitoring of (31)P may be used to quantify these compounds at the level of 80 μg L(-1), while simultaneous determination of sulfur is very useful for qualitative analysis. Moreover, the results presented in this paper demonstrate the practical applicability of coupling LC with ICP-MS in determining phosphorothioate oligonucleotides and their metabolites in serum within 7 min with a very good sensitivity. The method was linear in the concentration range between 0.2 and 3 mg L(-1). The limit of detection was in the range of 0.07 and 0.13 mg L(-1). Accuracy varied with concentration, but was in the range of 3%. Copyright © 2014 Elsevier B.V. All rights reserved. 2. Superspace actions and duality transformations for N=2 tensor multiplets International Nuclear Information System (INIS) Galperin, A.; Ivanov, E.; Ogievetsky, V. 1985-01-01 General actions for self-interacting N=2 tensor multiplets are considered in the harmonic superspace approach. All of them are shown to be equivalent, by superfield duality transformations, to some restricted class of the hypermultiplets actions. In particular, the improved tensor multiplet theory is dual to a free hypermultiplet one. Superspace couplings of these improved matter multiplets against conformal supergravity are also constructed 3. (2, 0) tensor multiplets and conformal supergravity in D = 6 NARCIS (Netherlands) Bergshoeff, Eric; Sezgin, Ergin; Proeyen, Antoine Van 1999-01-01 We construct the supercurrent multiplet that contains the energy–momentum tensor of the (2, 0) tensor multiplet. By coupling this multiplet of currents to the fields of conformal supergravity, we first construct the linearized superconformal transformations rules of the (2, 0) Weyl multiplet. 4. [An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging]. Science.gov (United States) Xu, Yonghong; Gao, Shangce; Hao, Xiaofei 2016-04-01 Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing. 5. Mean template for tensor-based morphometry using deformation tensors. Science.gov (United States) Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M 2007-01-01 Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences. 6. Algebraic and computational aspects of real tensor ranks CERN Document Server Sakata, Toshio; Miyazaki, Mitsuhiro 2016-01-01 This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through... 7. Improved tensor multiplets International Nuclear Information System (INIS) Wit, B. de; Rocek, M. 1982-01-01 We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.) 8. Time integration of tensor trains OpenAIRE Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart 2014-01-01 A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul... 9. Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors. Science.gov (United States) Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M 2008-01-01 This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling'sT(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
10. Abelian tensor models on the lattice
Science.gov (United States)
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
11. Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
12. Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
13. Dark energy in scalar-tensor theories
International Nuclear Information System (INIS)
Moeller, J.
2007-12-01
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
14. [Determinants of sterilization among married couples in Korea].
Science.gov (United States)
Kim, Ju Hee; Chung, Woojin; Lee, Sunmi; Suh, Moonhee; Kang, Dae Ryong
2007-11-01
The purpose of this study was to examine the determinants of sterilization in South Korea. This study was based on the data from the Korea National Fertility Survey carried out in the year 2000 by the Korea Institute of Health and Social Affairs. The subjects of the analysis were 4,604 women and their husbands who were in their first marriage, in the age group of 15-49 years. The data were analyzed by multiple logistic regression analysis. Consistent with the findings of previous studies, the woman's age and the number of total children increased the likelihood of sterilization. In addition, the year of marriage had a strong positive association with sterilization. Interestingly, the number of surviving sons tended to increase the likelihood of sterilization, whereas the woman's education level and age at the time of marriage showed a negative association with sterilization. Religion, place of residence, son preference, and the husband's education level, age and type of occupation were not significant determinants of sterilization. The sex of previous children and lower level of education are distinct determinants of sterilization among women in South Korea. More studies are needed in order to determine the associations between sterilization rate and decreased fertility.
15. Renormalization of nonabelian gauge theories with tensor matter fields
International Nuclear Information System (INIS)
Lemes, Vitor; Renan, Ricardo; Sorella, Silvio Paolo
1996-03-01
The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs
16. On the energy-momentum tensor in Moyal space
International Nuclear Information System (INIS)
Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois
2015-01-01
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)
17. Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.
Science.gov (United States)
Lubicz, Vittorio; Riggio, Lorenzo; Salerno, Giorgio; Simula, Silvano; Tarantino, Cecilia
2018-03-01
We present a preliminary lattice calculation of the D → π and D → K tensor form factors fT (q2) as a function of the squared 4-momentum transfer q2. ETMC recently computed the vector and scalar form factors f+(q2) and f0(q2) describing D → π(K)lv semileptonic decays analyzing the vector current and the scalar density. The study of the weak tensor current, which is directly related to the tensor form factor, completes the set of hadronic matrix element regulating the transition between these two pseudoscalar mesons within and beyond the Standard Model where a non-zero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 flavors of dynamical quarks. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV and with the valence heavy quark in the mass range from ≃ 0.7 mc to ≃ 1.2mc. The matrix element of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As for the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data. We will present preliminary results on the removal of such hypercubic lattice effects.
18. Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
19. Determination of g-tensors of low-symmetry Nd{sup 3+} centers in LiNbO{sub 3} by rectification of angular dependence of electron paramagnetic resonance spectra
Energy Technology Data Exchange (ETDEWEB)
Grachev, V., E-mail: [email protected]; Malovichko, G. [Physics Department, Montana State University, Bozeman, Montana 59717 (United States); Munro, M. [Quantel Laser, Bozeman, Montana 59715 (United States); Kokanyan, E. [Institute of Physical Researches, Ashtarak (Armenia)
2015-07-28
Two procedures for facilitation of line tracing and deciphering of complicated spectra of electron paramagnetic resonance (EPR) were developed: a correction of microwave frequencies for every orientation of external magnetic field on the base of known values of g-tensor components for a reference paramagnetic center and followed rectification of measured angular dependences using plots of effective deviation of g{sup 2}-factors of observed lines from effective g{sup 2}-factors of the reference center versus angles or squared cosines of angles describing magnetic field orientations. Their application to EPR spectra of nearly stoichiometric lithium niobate crystals doped with neodymium allowed identifying two axial and six different low-symmetry Nd{sup 3+} centers, to determine all components of their g-tensors, and to propose common divacancy models for a whole family of Nd{sup 3+} centers.
20. Tensor modes in pure natural inflation
Science.gov (United States)
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
1. Determination of neutral current couplings from neutrino-induced semi-inclusive pion and inclusive reactions
International Nuclear Information System (INIS)
Hung, P.Q.
1977-01-01
It is shown that by looking at data from neutrino-induced semi-inclusive pion and inclusive reactions on isoscalar targets along, one can determine completely the neutral current couplings. Predictions for various models are also presented. (Auth.)
2. Determination of trimethyllead reference material using high performance liquid chromatography-inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Lu Hai; Wei Chao; Wang Jun; Chao Jingbo; Zhou Tao; Chen Dazhou
2005-01-01
A high-performance liquid chromatography-inductively coupled plasma mass spectrometry (HPLC-ICPMS) was combined, and the chromatography conditions were optimized. The stability and homogeneity of a trimethyllead reference material were determined using this method. (authors)
3. Complementary and alternative medicine usage and its determinant factors among Iranian infertile couples.
Science.gov (United States)
Dehghan, Mahlagha; Mokhtarabadi, Sima; Heidari, Fatemeh Ghaedi
2018-04-04
Background The aim of this study was to determine the status of utilizing some complementary and alternative medicine techniques in infertile couples. Methods This was a cross-sectional study conducted on 250 infertile couples referred to a hospital in Kerman using convenience sampling. A researcher-made questionnaire was used to study the prevalence and user satisfaction of complementary and alternative medicines. Results Results indicated that 49.6% of the infertile couples used at least one of the complementary and alternative medicines during the past year. Most individuals used spiritual techniques (71.8% used praying and 70.2% used Nazr) and medicinal plants (54.8%). Safety is the most important factor affecting the satisfaction of infertile couples with complementary treatments (couples think that such treatments are safe (54.8%)). Discussion Concerning high prevalence of complementary and alternative treatments in infertile couples, incorporating such treatments into the healthcare education and promoting the awareness of infertile individuals seem crucial.
4. Tensors and their applications
CERN Document Server
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffels Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Riccis Coefficients of Rotation and Congruence Hyper Surfaces
5. Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
7. On an uninterpretated tensor in Dirac's theory
International Nuclear Information System (INIS)
Costa de Beauregard, O.
1989-01-01
Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr
8. A Review of Tensors and Tensor Signal Processing
Science.gov (United States)
Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.
Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
9. Diffusion tensor optical coherence tomography
Science.gov (United States)
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
10. Determination of structural fluctuations of proteins from structure-based calculations of residual dipolar couplings
International Nuclear Information System (INIS)
Montalvao, Rinaldo W.; De Simone, Alfonso; Vendruscolo, Michele
2012-01-01
Residual dipolar couplings (RDCs) have the potential of providing detailed information about the conformational fluctuations of proteins. It is very challenging, however, to extract such information because of the complex relationship between RDCs and protein structures. A promising approach to decode this relationship involves structure-based calculations of the alignment tensors of protein conformations. By implementing this strategy to generate structural restraints in molecular dynamics simulations we show that it is possible to extract effectively the information provided by RDCs about the conformational fluctuations in the native states of proteins. The approach that we present can be used in a wide range of alignment media, including Pf1, charged bicelles and gels. The accuracy of the method is demonstrated by the analysis of the Q factors for RDCs not used as restraints in the calculations, which are significantly lower than those corresponding to existing high-resolution structures and structural ensembles, hence showing that we capture effectively the contributions to RDCs from conformational fluctuations.
11. Determinants in HIV counselling and testing in couples in North Rift Kenya.
Science.gov (United States)
Ayuo, P O; Were, E; Wools-Kaloustian, K; Baliddawa, J; Sidle, J; Fife, K
2009-02-01
Voluntary HIV counselling and testing (VCT) has been shown to be an acceptable and effective tool in the fight against HIV/AIDS. Couple HIV Counselling and Testing (CHCT) however, is a relatively new concept whose acceptance and efficacy is yet to be determined. To describe factors that motivate couples to attend VCT as a couple. A cross sectional qualitative study. Moi Teaching and Referral Hospital and Moi University, School of Medicine, Eldoret, Kenya Seventy one individuals were interviewed during KII (9) and dyad interviews (31 couples). Ten FGDs involving a total of 109 individuals were held. Cultural practices, lack of CHCT awareness, stigma and fear of results deter CHCT utilisation. Location of centre where it is unlikely to be associated with HIV testing, qualified professional staff and minimal waiting times would enhance CHCT utilisation. CHCT as a tool in the fight against HIV/AIDS in this region of Kenya is feasible as the factors that would deter couples are not insurmountable.
12. Tensor analysis for physicists
CERN Document Server
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
13. Precision determination of the strong coupling constant within a global PDF analysis
NARCIS (Netherlands)
Ball, Richard D.; Carrazza, Stefano; Debbio, Luigi Del; Forte, Stefano; Kassabov, Zahari; Rojo, Juan; Slade, Emma; Ubiali, Maria
2018-01-01
We present a determination of the strong coupling constant $\\alpha_s(m_Z)$ based on the NNPDF3.1 determination of parton distributions, which for the first time includes constraints from jet production, top-quark pair differential distributions, and the $Z$ $p_T$ distributions using exact NNLO
14. Determination of technetium-99 in soil samples by high performance liquid chromatography coupled to inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Muto, Toshio; Shimokawa, Toshinari
1997-01-01
A new powerful analytical technique viz. high performance liquid chromatography(HPLC) coupled to inductively coupled plasma mass spectrometry(HPLC/ICP-MS) has been applied to the determination of technetium-99( 99 Tc) in soils as a typical environmental sample. Technetium was enriched in a solution from incinerated soil samples by leaching in HNO 3 and passed through 'TEVA resin' column. The solution was injected into HPLC/ICP-MS system to eliminate the interfering elements (i.e. Ru and Mo) and to determine the 99 Tc concentration at the same time. The concentrations of 99 Tc in the incinerated soils were found to be 0.49Bq/kg(0.77ng/kg)-1.4Bq/kg(2.2ng/kg) with the determination limit of 0.02Bq/kg(0.03ng/kg(0.03ppt)). The results indicate the following findings; 1) the determination of 99 Tc by ICP-MS after strict elimination of the interfering elements by HPLC brings about the improvement in their reliability; 2) the detection limits identified are much lower compared with those by conventional ICP-MS methods because of the concentration of 99 Tc to smaller volume, which is due to only 100μl of samples could be measured by HPLC/ICP-MS system; 3) sample preparation could be simplified because of strict elimination of the interfering elements by HPLC. This research showed that HPLC/ICP-MS system is very effective to determine 99 Tc in environmental samples. (author)
15. Susceptibility tensor imaging (STI) of the brain.
Science.gov (United States)
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
16. Susceptibility Tensor Imaging (STI) of the Brain
Science.gov (United States)
Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu
2016-01-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169
17. Killing tensors and conformal Killing tensors from conformal Killing vectors
International Nuclear Information System (INIS)
Rani, Raffaele; Edgar, S Brian; Barnes, Alan
2003-01-01
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors
18. Tensors, relativity, and cosmology
CERN Document Server
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
19. Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors
OpenAIRE
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
20. QCD vacuum tensor susceptibility and properties of transversely polarized mesons
International Nuclear Information System (INIS)
Bakulev, A.P.; Mikhajlov, S.V.
1999-01-01
We re-estimate the tensor susceptibility of QCD vacuum, χ, and to this end, we re-estimate the leptonic decay constants for transversely polarized ρ-, ρ'- and b 1 -mesons. The origin of the susceptibility is analyzed using duality between ρ- and b 1 -channels in a 2-point correlator of tensor currents and disagree with [2] on both OPE expansion and the value of QCD vacuum tensor susceptibility. Using our value for the latter we determine new estimations of nucleon tensor charges related to the first moment of the transverse structure functions h 1 of a nucleon
1. Prescribed curvature tensor in locally conformally flat manifolds
Science.gov (United States)
Pina, Romildo; Pieterzack, Mauricio
2018-01-01
A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.
2. Thermodynamical inequivalence of quantum stress-energy and spin tensors
International Nuclear Information System (INIS)
Becattini, F.; Tinti, L.
2011-01-01
It is shown that different couples of stress-energy and spin tensors of quantum-relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law of thermodynamics is taken into account. The proof of the inequivalence is based on the analysis of a macroscopic system at full thermodynamical equilibrium with a macroscopic total angular momentum and a specific instance is given for the free Dirac field, for which we show that the canonical and Belinfante stress-energy tensors are not equivalent. For this particular case, we show that the difference between the predicted angular momentum densities for a rotating system at full thermodynamical equilibrium is a quantum effect, persisting in the nonrelativistic limit, corresponding to a polarization of particles of the order of (ℎ/2π)ω/KT (ω being the angular velocity) and could in principle be measured experimentally. This result implies that specific stress-energy and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the thermodynamically right (or the right class of) tensors. We argue that the maximization of the thermodynamic potential theoretically allows us to discriminate between two different couples, yet for the present we are unable to provide a theoretical method to single out the best couple of tensors in a given quantum field theory. The existence of a nonvanishing spin tensor would have major consequences in hydrodynamics, gravity and cosmology.
3. Determination of the components of three dimensional vector and tensor anisotropy of cosmic radiation with application to the results of the Musala experiment
International Nuclear Information System (INIS)
Somogyi, A.J.
1976-09-01
The paper proves that it is possible to interpret the experimental results of the Musala experiment as being consequences of a vector anisotropy with maximum in the direction of the galactic centre and a tensor anisotropy with principal axes in the physically plausible directions of the galactic arm, the normal direction of the galactic plane and the direction perpendicular them, respectively. It is underlined that the interpretation is not the only possible one and, in addition to this, statistical errors are rather large. The results favour the galactic origin of the particles concerned (E=6x10 13 eV). (Sz.N.Z.)
4. Couplings
Science.gov (United States)
Stošić, Dušan; Auroux, Aline
Basic principles of calorimetry coupled with other techniques are introduced. These methods are used in heterogeneous catalysis for characterization of acidic, basic and red-ox properties of solid catalysts. Estimation of these features is achieved by monitoring the interaction of various probe molecules with the surface of such materials. Overview of gas phase, as well as liquid phase techniques is given. Special attention is devoted to coupled calorimetry-volumetry method. Furthermore, the influence of different experimental parameters on the results of these techniques is discussed, since it is known that they can significantly influence the evaluation of catalytic properties of investigated materials.
5. Aspects of the Antisymmetric Tensor Field
Science.gov (United States)
Lahiri, Amitabha
1991-02-01
With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.
6. Tensor hypercontraction. II. Least-squares renormalization
Science.gov (United States)
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2012-12-01
The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.
7. On the SU2 unit tensor
International Nuclear Information System (INIS)
Kibler, M.; Grenet, G.
1979-07-01
The SU 2 unit tensor operators tsub(k,α) are studied. In the case where the spinor point group G* coincides with U 1 , then tsub(k α) reduces up to a constant to the Wigner-Racah-Schwinger tensor operator tsub(kqα), an operator which produces an angular momentum state. One first investigates those general properties of tsub(kα) which are independent of their realization. The tsub(kα) in terms of two pairs of boson creation and annihilation operators are realized. This leads to look at the Schwinger calculus relative to one angular momentum of two coupled angular momenta. As a by-product, a procedure is given for producing recursion relationships between SU 2 Wigner coefficients. Finally, some of the properties of the Wigner and Racah operators for an arbitrary compact group and the SU 2 coupling coefficients are studied
8. Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules
Science.gov (United States)
di Lauro, C.
2018-03-01
Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.
9. The simplicial Ricci tensor
International Nuclear Information System (INIS)
Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A
2011-01-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
10. The simplicial Ricci tensor
Science.gov (United States)
Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.
2011-08-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
11. Applied tensor stereology
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle s...
12. J-Spectroscopy in the presence of residual dipolar couplings: determination of one-bond coupling constants and scalable resolution
International Nuclear Information System (INIS)
Furrer, Julien; John, Michael; Kessler, Horst; Luy, Burkhard
2007-01-01
The access to weak alignment media has fuelled the development of methods for efficiently and accurately measuring residual dipolar couplings (RDCs) in NMR-spectroscopy. Among the wealth of approaches for determining one-bond scalar and RDC constants only J-modulated and J-evolved techniques retain maximum resolution in the presence of differential relaxation. In this article, a number of J-evolved experiments are examined with respect to the achievable minimum linewidth in the J-dimension, using the peptide PA 4 and the 80-amino-acid-protein Saposin C as model systems. With the JE-N-BIRD d,X -HSQC experiment, the average full-width at half height could be reduced to approximately 5 Hz for the protein, which allows the additional resolution of otherwise unresolved peaks by the active (J+D)-coupling. Since RDCs generally can be scaled by the choice of alignment medium and alignment strength, the technique introduced here provides an effective resort in cases when chemical shift differences alone are insufficient for discriminating signals. In favorable cases even secondary structure elements can be distinguished
13. The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
14. Tensor Calculus: Unlearning Vector Calculus
Science.gov (United States)
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
15. On deformed tensor potential for inelastic deuteron scattering
International Nuclear Information System (INIS)
Raynal, Jacques.
1980-08-01
Tensor analysing powers for inelastic deuteron scattering have been measured around 12 to 15 MeV. There is no problem to use such a tensor potential for the excited states in coupled channel calculations. However, for transition potentials, form factors are very different. A fit has been done with the first order vibrational model for 64 Ni(d,d') 64 Ni*, 2 + at 1,344 MeV
16. Determination of rare earth elements in aluminum by inductively coupled plasma-atomic emission spectroscopy
International Nuclear Information System (INIS)
Mahanti, H.S.; Barnes, R.M.
1983-01-01
Inductively coupled plasma-atomic emission spectroscopy is evaluated for the determination of 14 rare earth elements in aluminum. Spectral line interference, limit of detection, and background equivalent concentration values are evaluated, and quantitative recovery is obtained from aluminum samples spiked with rare earth elements. The procedure is simple and suitable for routine process control analysis. 20 references, 5 tables
17. Determination of platinum in human subcellular microsamples by inductively coupled plasma mass spectrometry
DEFF Research Database (Denmark)
Björn, Erik; Nygren, Yvonne; Nguyen, Tam T. T. N.
2007-01-01
A fast and robust method for the determination of platinum in human subcellular microsamples by inductively coupled plasma mass spectrometry was developed, characterized, and validated. Samples of isolated DNA and exosome fractions from human ovarian (2008) and melanoma (T289) cancer cell lines w...
18. The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
19. Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
20. Singular Poisson tensors
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
1. TensorFlow Distributions
OpenAIRE
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
2. Raman scattering tensors of tyrosine.
Science.gov (United States)
Tsuboi, M; Ezaki, Y; Aida, M; Suzuki, M; Yimit, A; Ushizawa, K; Ueda, T
1998-01-01
Polarized Raman scattering measurements have been made of a single crystal of L-tyrosine by the use of a Raman microscope with the 488.0-nm exciting beam from an argon ion laser. The L-tyrosine crystal belongs to the space group P2(1)2(1)2(1) (orthorhombic), and Raman scattering intensities corresponding to the aa, bb, cc, ab and ac components of the crystal Raman tensor have been determined for each prominent Raman band. A similar set of measurements has been made of L-tyrosine-d4, in which four hydrogen atoms on the benzene ring are replaced by deuterium atoms. The effects of NH3-->ND3 and OH-->OD on the Raman spectrum have also been examined. In addition, depolarization ratios of some bands of L-tyrosine in aqueous solutions of pH 13 and pH 1 were examined. For comparison with these experimental results, on the other hand, ab initio molecular orbital calculations have been made of the normal modes of vibration and their associated polarizability oscillations of the L-tyrosine molecule. On the basis of these experimental data and by referring to the results of the calculations, discussions have been presented on the Raman tensors associated to some Raman bands, including those at 829 cm-1 (benzene ring breathing), 642 cm-1 (benzene ring deformation), and 432 cm-1 (C alpha-C beta-C gamma bending).
3. The determination of transition probabilities with an inductively-coupled plasma discharge
International Nuclear Information System (INIS)
Nieuwoudt, G.
1984-03-01
The 27 MHz inductively-coupled plasma discharge (ICP) is used for the determination of relative transition probabilities of the 451, 459 and 470 nm argon spectral lines. The temperature of the argon plasma is determined with hydrogen as thermometric specie, because of the accurate transition probabilities ( approximately 1% uncertainty) there of. The relative transition probabilities of the specific argon spectral lines were determined by substitution of the measured spectral radiances thereof, together with the hydrogen temperature, in the two-line equation of temperature measurement
4. Determination of trace amounts of cerium in paint by inductively coupled plasma atomic emission spectrometry
International Nuclear Information System (INIS)
Wong, K.L.
1981-01-01
The determination of Ce in paint by inductively coupled plasma atomic emission spectrometry (ICP-OES) is described, and the detection limit of ICP-OES of 0.0004 ppM is compared with that of other methods. The effects of the major elemental components of paint, Si, Pb, Cr, and Na on the ICP-OES determination of Ce were studied. The interference of 400 ppM of the other ions on the determination of 10 ppM Ce was small (0 to 3% error). The method is applicable to the range of 0.2 to 700 ppM Ce
5. A fiber-coupled displacement measuring interferometer for determination of the posture of a reflective surface
International Nuclear Information System (INIS)
Mao, Shuai; Hu, Peng-Cheng; Ding, Xue-Mei; Tan, Jiu-Bin
2016-01-01
A fiber-coupled displacement measuring interferometer capable of determining of the posture of a reflective surface of a measuring mirror is proposed. The newly constructed instrument combines fiber-coupled displacement and angular measurement technologies. The proposed interferometer has advantages of both the fiber-coupled and the spatially beam-separated interferometer. A portable dual-position sensitive detector (PSD)-based unit within this proposed interferometer measures the parallelism of the two source beams to guide the fiber-coupling adjustment. The portable dual PSD-based unit measures not only the pitch and yaw of the retro-reflector but also measures the posture of the reflective surface. The experimental results of displacement calibration show that the deviations between the proposed interferometer and a reference one, Agilent 5530, at two different common beam directions are both less than ±35 nm, thus verifying the effectiveness of the beam parallelism measurement. The experimental results of angular calibration show that deviations of pitch and yaw with the auto-collimator (as a reference) are less than ±2 arc sec, thus proving the proposed interferometer’s effectiveness for determination of the posture of a reflective surface.
6. Tensor Permutation Matrices in Finite Dimensions
OpenAIRE
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
7. Tensor Factorization for Low-Rank Tensor Completion.
Science.gov (United States)
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
8. Determination of long-lived actinides in soil leachates by inductively coupled plasma: Mass spectrometry
International Nuclear Information System (INIS)
Crain, J.S.; Smith, L.L.; Yaeger, J.S.; Alvarado, J.A.
1994-01-01
Inductively coupled plasma -- mass spectrometry (ICP-MS) was used to concurrently determine multiple long-lived (t 1/2 > 10 4 y) actinide isotopes in soil samples. Ultrasonic nebulization was found to maximize instrument sensitivity. Instrument detection limits for actinides in solution ranged from 50 mBq L -1 ( 239 Pu) to 2 μBq L -1 ( 235 U) Hydride adducts of 232 Th and 238 U interfered with the determinations of 233 U and 239 Pu; thus, extraction chromatography was, used to eliminate the sample matrix, concentrate the analytes, and separate uranium from the other actinides. Alpha spectrometric determinations of 230 Th, 239 Pu, and the 234 U/ 238 U activity ratio in soil leachates compared well with ICP-MS determinations; however, there were some small systematic differences (ca. 10%) between ICP-MS and a-spectrometric determinations of 234 U and 238 U activities
9. Extracting the diffusion tensor from molecular dynamics simulation with Milestoning
International Nuclear Information System (INIS)
Mugnai, Mauro L.; Elber, Ron
2015-01-01
We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide
10. Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation
Science.gov (United States)
Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan
2018-03-01
Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.
11. Black holes in vector-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland); Kase, Ryotaro; Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Minamitsuji, Masato, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Centro Multidisciplinar de Astrofisica—CENTRA, Departamento de Fisica, Instituto Superior Tecnico—IST, Universidade de Lisboa—UL, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-08-01
We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.
12. Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC
Energy Technology Data Exchange (ETDEWEB)
Maltoni, Fabio; Shivaji, Ambresh; Zhao, Xiaoran [Universite Catholique de Louvain, Centre for Cosmology, Particle Physics and Phenomenology (CP3), Louvain-la-Neuve (Belgium); Pagani, Davide [Technische Universitaet Muenchen, Garching (Germany)
2017-12-15
We study one-loop effects induced by an anomalous Higgs trilinear coupling on total and differential rates for the H → 4l decay and some of the main single-Higgs production channels at the LHC, namely, VBF, VH, t anti tH and tHj. Our results are based on a public code that calculates these effects by simply reweighting samples of Standard-Model-like events for a given production channel. For VH and t anti tH production, where differential effects are particularly relevant, we include Standard Model electroweak corrections, which have similar sizes but different kinematic dependences. Finally, we study the sensitivity of future LHC runs to determine the trilinear coupling via inclusive and differential measurements, considering also the case where the Higgs couplings to vector bosons and the top quark is affected by new physics. We find that the constraints on the couplings and the relevance of differential distributions critically depend on the expected experimental and theoretical uncertainties. (orig.)
13. Optical determination of the electronic coupling and intercalation geometry of thiazole orange homodimer in DNA
Science.gov (United States)
Cunningham, Paul D.; Bricker, William P.; Díaz, Sebastián A.; Medintz, Igor L.; Bathe, Mark; Melinger, Joseph S.
2017-08-01
Sequence-selective bis-intercalating dyes exhibit large increases in fluorescence in the presence of specific DNA sequences. This property makes this class of fluorophore of particular importance to biosensing and super-resolution imaging. Here we report ultrafast transient anisotropy measurements of resonance energy transfer (RET) between thiazole orange (TO) molecules in a complex formed between the homodimer TOTO and double-stranded (ds) DNA. Biexponential homo-RET dynamics suggest two subpopulations within the ensemble: 80% intercalated and 20% non-intercalated. Based on the application of the transition density cube method to describe the electronic coupling and Monte Carlo simulations of the TOTO/dsDNA geometry, the dihedral angle between intercalated TO molecules is estimated to be 81° ± 5°, corresponding to a coupling strength of 45 ± 22 cm-1. Dye intercalation with this geometry is found to occur independently of the underlying DNA sequence, despite the known preference of TOTO for the nucleobase sequence CTAG. The non-intercalated subpopulation is inferred to have a mean inter-dye separation distance of 19 Å, corresponding to coupling strengths between 0 and 25 cm-1. This information is important to enable the rational design of energy transfer systems that utilize TOTO as a relay dye. The approach used here is generally applicable to determining the electronic coupling strength and intercalation configuration of other dimeric bis-intercalators.
14. Model-independent determination of the triple Higgs coupling at e+e- colliders
Science.gov (United States)
Barklow, Tim; Fujii, Keisuke; Jung, Sunghoon; Peskin, Michael E.; Tian, Junping
2018-03-01
The observation of Higgs pair production at high-energy colliders can give evidence for the presence of a triple Higgs coupling. However, the actual determination of the value of this coupling is more difficult. In the context of general models for new physics, double Higgs production processes can receive contributions from many possible beyond-Standard-Model effects. This dependence must be understood if one is to make a definite statement about the deviation of the Higgs field potential from the Standard Model. In this paper, we study the extraction of the triple Higgs coupling from the process e+e-→Z h h . We show that, by combining the measurement of this process with other measurements available at a 500 GeV e+e- collider, it is possible to quote model-independent limits on the effective field theory parameter c6 that parametrizes modifications of the Higgs potential. We present precise error estimates based on the anticipated International Linear Collider physics program, studied with full simulation. Our analysis also gives new insight into the model-independent extraction of the Higgs boson coupling constants and total width from e+e- data.
15. Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC
Science.gov (United States)
Maltoni, Fabio; Pagani, Davide; Shivaji, Ambresh; Zhao, Xiaoran
2017-12-01
We study one-loop effects induced by an anomalous Higgs trilinear coupling on total and differential rates for the H→ 4ℓ decay and some of the main single-Higgs production channels at the LHC, namely, VBF, VH, t{\\bar{t}}H and tHj. Our results are based on a public code that calculates these effects by simply reweighting samples of Standard-Model-like events for a given production channel. For VH and t{\\bar{t}}H production, where differential effects are particularly relevant, we include Standard Model electroweak corrections, which have similar sizes but different kinematic dependences. Finally, we study the sensitivity of future LHC runs to determine the trilinear coupling via inclusive and differential measurements, considering also the case where the Higgs couplings to vector bosons and the top quark is affected by new physics. We find that the constraints on the couplings and the relevance of differential distributions critically depend on the expected experimental and theoretical uncertainties.
16. Reduction schemes for one-loop tensor integrals
International Nuclear Information System (INIS)
Denner, A.; Dittmaier, S.
2006-01-01
We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e - ->4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex
17. Tensor Train Neighborhood Preserving Embedding
Science.gov (United States)
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
18. Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
19. Tensor norms and operator ideals
CERN Document Server
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
20. Determination of rare earth elements in tomato plants by inductively coupled plasma mass spectrometry techniques.
Science.gov (United States)
Spalla, S; Baffi, C; Barbante, C; Turetta, C; Turretta, C; Cozzi, G; Beone, G M; Bettinelli, M
2009-10-30
In recent years identification of the geographical origin of food has grown more important as consumers have become interested in knowing the provenance of the food that they purchase and eat. Certification schemes and labels have thus been developed to protect consumers and genuine producers from the improper use of popular brand names or renowned geographical origins. As the tomato is one of the major components of what is considered to be the healthy Mediterranean diet, it is important to be able to determine the geographical origin of tomatoes and tomato-based products such as tomato sauce. The aim of this work is to develop an analytical method to determine rare earth elements (RRE) for the control of the geographic origin of tomatoes. The content of REE in tomato plant samples collected from an agricultural area in Piacenza, Italy, was determined, using four different digestion procedures with and without HF. Microwave dissolution with HNO3 + H2O2 proved to be the most suitable digestion procedure. Inductively coupled plasma quadrupole mass spectrometry (ICPQMS) and inductively coupled plasma sector field plasma mass spectrometry (ICPSFMS) instruments, both coupled with a desolvation system, were used to determine the REE in tomato plants in two different laboratories. A matched calibration curve method was used for the quantification of the analytes. The detection limits (MDLs) of the method ranged from 0.03 ng g(-1) for Ho, Tm, and Lu to 2 ng g(-1) for La and Ce. The precision, in terms of relative standard deviation on six replicates, was good, with values ranging, on average, from 6.0% for LREE (light rare earth elements) to 16.5% for HREE (heavy rare earth elements). These detection limits allowed the determination of the very low concentrations of REE present in tomato berries. For the concentrations of REE in tomato plants, the following trend was observed: roots > leaves > stems > berries. Copyright 2009 John Wiley & Sons, Ltd.
1. Temperature dependence of the dielectric tensor of monoclinic Ga2O3 single crystals in the spectral range 1.0-8.5 eV
Science.gov (United States)
Sturm, C.; Schmidt-Grund, R.; Zviagin, V.; Grundmann, M.
2017-08-01
The full dielectric tensor of monoclinic Ga2O3 (β-phase) was determined by generalized spectroscopic ellipsometry in the spectral range from 1.0 eV up to 8.5 eV and temperatures in the range from 10 K up to 300 K. By using the oriented dipole approach, the energies and broadenings of the excitonic transitions are determined as a function of the temperature, and the exciton-phonon coupling properties are deduced.
2. Data on final calcium concentration in native gel reagents determined accurately through inductively coupled plasma measurements
Directory of Open Access Journals (Sweden)
Jeffrey Viviano
2016-03-01
Full Text Available In this article we present data on the concentration of calcium as determined by Inductively Coupled Plasma (ICP measurements. Calcium was estimated in the reagents used for native gel electrophoresis of Neuronal Calcium Sensor (NCS proteins. NCS proteins exhibit calcium-dependent mobility shift in native gels. The sensitivity of this shift to calcium necessitated a precise determination of calcium concentrations in all reagents used. We determined the calcium concentrations in different components used along with the samples in the native gel experiments. These were: 20 mM Tris pH 7.5, loading dye and running buffer, with distilled water as reference. Calcium determinations were through ICP measurements. It was found that the running buffer contained calcium (244 nM over the blank. Keywords: Neuronal calcium sensor proteins, Electrophoresis, Mobility shift, Calcium, Magnesium
3. A new approach using artificial neural networks for determination of the thermodynamic properties of fluid couples
International Nuclear Information System (INIS)
Sencan, Arzu; Kalogirou, Soteris A.
2005-01-01
This paper presents a new approach using artificial neural networks (ANN) to determine the thermodynamic properties of two alternative refrigerant/absorbent couples (LiCl-H 2 O and LiBr + LiNO 3 + LiI + LiCl-H 2 O). These pairs can be used in absorption heat pump systems, and their main advantage is that they do not cause ozone depletion. In order to train the network, limited experimental measurements were used as training and test data. Two feedforward ANNs were trained, one for each pair, using the Levenberg-Marquardt algorithm. The training and validation were performed with good accuracy. The correlation coefficient obtained when unknown data were applied to the networks was 0.9997 and 0.9987 for the two pairs, respectively, which is very satisfactory. The present methodology proved to be much better than linear multiple regression analysis. Using the weights obtained from the trained network, a new formulation is presented for determination of the vapor pressures of the two refrigerant/absorbent couples. The use of this new formulation, which can be employed with any programming language or spreadsheet program for estimation of the vapor pressures of fluid couples, as described in this paper, may make the use of dedicated ANN software unnecessary
4. Endoscopic Anatomy of the Tensor Fold and Anterior Attic.
Science.gov (United States)
Li, Bin; Doan, Phi; Gruhl, Robert R; Rubini, Alessia; Marchioni, Daniele; Fina, Manuela
2018-02-01
Objectives The objectives of the study were to (1) study the anatomical variations of the tensor fold and its anatomic relation with transverse crest, supratubal recess, and anterior epitympanic space and (2) explore the most appropriate endoscopic surgical approach to each type of the tensor fold variants. Study Design Cadaver dissection study. Setting Temporal bone dissection laboratory. Subjects and Methods Twenty-eight human temporal bones (26 preserved and 2 fresh) were dissected through an endoscopic transcanal approach between September 2016 and June 2017. The anatomical variations of the tensor fold, transverse crest, supratubal recess, and anterior epitympanic space were studied before and after removing ossicles. Results Three different tensor fold orientations were observed: vertical (type A, 11/28, 39.3%) with attachment to the transverse crest, oblique (type B, 13/28, 46.4%) with attachment to the anterior tegmen tympani, and horizontal (type C, 4/28, 14.3%) with attachment to the tensor tympani canal. The tensor fold was a complete membrane in 20 of 28 (71.4%) specimens, preventing direct ventilation between the supratubal recess and anterior epitympanic space. We identified 3 surgical endoscopic approaches, which allowed visualization of the tensor fold without removing the ossicles. Conclusions The orientation of the tensor fold is the determining structure that dictates the conformation and limits of the epitympanic space. We propose a classification of the tensor fold based on 3 anatomical variants. We also describe 3 different minimally invasive endoscopic approaches to identify the orientation of the tensor fold while maintaining ossicular chain continuity.
5. The strong coupling from a nonperturbative determination of the Λ parameter in three-flavor QCD
Energy Technology Data Exchange (ETDEWEB)
Bruno, Mattia [Brookhaven National Laboratory, Upton, NY (United States). Physics Dept.; Dalla Brida, Mattia [Univ. di Milano-Bicocca (Italy). Dipt. di Fisica; INFN, Sezione di Milano-Bicocca (Italy); Fritzsch, Patrick; Ramos, Alberto [CERN, Geneva (Switzerland). Theoretical Physics Dept.; Korzec, Tomasz [Wuppertal Univ. (Germany). Dept. of Physics; Schaefer, Stefan; Simma, Hubert [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics and Hamilton Mathematics Inst.; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Collaboration: ALPHA Collaboration
2017-07-15
We present a lattice determination of the Λ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from 0.2 GeV to 70 GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain Λ{sup (3)}{sub MS}=341(12) MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. Using the four-loop prediction for Λ{sup (5)}{sub MS}/Λ{sup (3)}{sub MS} yields α{sup (5)}{sub MS}(m{sub Z})=0.11852(84).
6. Determination of diffusion profiles in thin film couples by means of X-ray-diffraction
International Nuclear Information System (INIS)
Wagendristel, A.
1975-01-01
An X-ray method for the determination of concentration profiles in thin film diffusion couples is presented. This method is based on the theory of Fourier analysis of X-ray diffraction profiles which is generalized to polycrystalline samples showing non-uniform lattice parameter. A Fourier synthesis of the concentration spectrum is possible when the influences of the particle size and the strain in the sample as well as the instrumental function are eliminated from the measured diffraction profile. This can be done by means of reference profiles obtained from layers of the diffusion components. Absorption of the radiation in the sample is negligible when diffusion couples of symmetrical sandwich structure are used. The method is tested experimentally in the system Au-Cu. (orig.) [de
7. Effective field theory approaches for tensor potentials
Energy Technology Data Exchange (ETDEWEB)
Jansen, Maximilian
2016-11-14
Effective field theories are a widely used tool to study physical systems at low energies. We apply them to systematically analyze two and three particles interacting via tensor potentials. Two examples are addressed: pion interactions for anti D{sup 0}D{sup *0} scattering to dynamically generate the X(3872) and dipole interactions for two and three bosons at low energies. For the former, the one-pion exchange and for the latter, the long-range dipole force induce a tensor-like structure of the potential. We apply perturbative as well as non-perturbative methods to determine low-energy observables. The X(3872) is of major interest in modern high-energy physics. Its exotic characteristics require approaches outside the range of the quark model for baryons and mesons. Effective field theories represent such methods and provide access to its peculiar nature. We interpret the X(3872) as a hadronic molecule consisting of neutral D and D{sup *} mesons. It is possible to apply an effective field theory with perturbative pions. Within this framework, we address chiral as well as finite volume extrapolations for low-energy observables, such as the binding energy and the scattering length. We show that the two-point correlation function for the D{sup *0} meson has to be resummed to cure infrared divergences. Moreover, next-to-leading order coupling constants, which were introduced by power counting arguments, appear to be essential to renormalize the scattering amplitude. The binding energy as well as the scattering length display a moderate dependence on the light quark masses. The X(3872) is most likely deeper bound for large light quark masses. In a finite volume on the other hand, the binding energy significantly increases. The dependence on the light quark masses and the volume size can be simultaneously obtained. For bosonic dipoles we apply a non-perturbative, numerical approach. We solve the Lippmann-Schwinger equation for the two-dipole system and the Faddeev
8. Progress in determination of long-lived radionuclides by inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Becker, J.S.; Dietze, H.J.
2000-01-01
Mass spectrometric methods (such as inductively coupled plasma mass spectrometry - ICP-MS and laser ablation (LA)-ICP-MS) with their ability to provide a very sensitive multielemental and precise isotopic analysis have become established for the determination of radionuclides in quite different sample materials. The determination of long-lived radionuclides is of increasing interest for the characterization of radioactive waste materials and for the detection of radionuclide contamination in environmental materials in which several radioactive nuclides are present from fallout due to nuclear weapons testing, nuclear power plants or nuclear accidents. Due to its multielement capability, excellent sensitivity, low detection limits (up to sub pg I 1 range), very good precision, easy sample preparation and measurement procedures ICP-MS of aqueous solutions has been increasingly applied for the ultrasensitive determination of long-lived radionuclides such as 99 Tc, 129 I, 230 Th, 232 Th, 234 U, 235 U, 236 U, 239 Pu, 240 Pu and 241 Am and precise isotope ratio measurements of U,Th and Pu. The application especially of microanalytical methods (analysis of some MU by flow injection and on-line coupling techniques as capillary electrophoresis (CE-ICP-MS) or HPLC-ICP-MS) for the precise determination nuclide abundances and concentration of long-lived radionuclides at ultra trace concentration levels in radioactive waste and also for controlling contamination from radioactive waste in the environment is a challenging task
9. Diffusion tensor studies and voxel-based morphometry of the temporal lobe to determine the cognitive prognosis in cases of Alzheimer's disease and mild cognitive impairment: Do white matter changes precede gray matter changes?
Science.gov (United States)
Taoka, Toshiaki; Yasuno, Fumihiko; Morikawa, Masayuki; Inoue, Makoto; Kiuchi, Kuniaki; Kitamura, Soichiro; Matsuoka, Kiwamu; Kishimoto, Toshifumi; Kichikawa, Kimihiko; Naganawa, Shinji
2016-01-01
The purpose of the current study was to assess the feasibility of diffusion tensor imaging (DTI) parameters for determining the prognosis of Alzheimer's disease (AD). We also analyzed the correlation among DTI, voxel-based morphometry (VBM), and results of the mini-mental state examination (MMSE). The subjects of this prospective study were patients with AD and mild cognitive impairment. We performed annual follow-ups with DTI, VBM, and MMSE for 2 or 3 years. On DTI, the apparent diffusion coefficient (ADC) and fractional anisotropy (FA) of the uncinate fascicles were measured. VBM was performed to provide a z-score for the parahippocampal gyrus. The correlations among these factors were evaluated in the same period and the next period of the follow-up study. For evaluation of the same period, both DTI parameters and z-scores showed statistically significant correlations with the MMSE score. Also for evaluation of the next period, both DTI parameters and z-scores showed statistically significant correlations with the MMSE score of the next period. We observed a statistically significant correlation between the ADC value of the uncinate fascicles and the z-score of the next period. Diffusion tensor parameters (ADC and FA) of the uncinate fascicles correlated well with cognitive function in the next year and seemed to be feasible for use as biomarkers for predicting the progression of AD. In addition, the white matter changes observed in the ADC seemed to precede changes in the gray matter volume of the parahippocampal gyrus that were represented by z-scores of VBM.
10. Typesafe Abstractions for Tensor Operations
OpenAIRE
Chen, Tongfei
2017-01-01
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.
11. Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
12. Tensor integrand reduction via Laurent expansion
Energy Technology Data Exchange (ETDEWEB)
Hirschi, Valentin [SLAC, National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025-7090 (United States); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)
2016-06-09
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MADLOOP, which is part of the public MADGRAPH5{sub A}MC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CUTTOOLS, SAMURAI, IREGI, PJFRY++ and GOLEM95. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool GOLEM95 which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.
13. Multielement determination of rare earth elements by liquid chromatography/inductively coupled plasma atomic emission spectrometry
International Nuclear Information System (INIS)
Sawatari, Hideyuki; Asano, Takaaki; Hu, Xincheng; Saizuka, Tomoo; Itoh, Akihide; Hirose, Akio; Haraguchi, Hiroki
1995-01-01
The rapid determination of rare earth elements (REEs) has been investigated by an on-line system of high performance liquid chromatography/multichannel inductively coupled plasma atomic emission spectrometry. In the present system, all REEs could be detected simultaneously in a single chromatographic measurement without spectral interferences. Utilizing a cation exchange column and 2-hydroxy-2-methylpropanoic acid aqueous solution as the mobile phase, the detection limits of 0.4-30 ng ml -1 for all REEs were obtained. The system was applied to the determination of REEs in geological standard rock samples and rare earth impurities in high purity rare earth oxides. The REEs in standard rocks could be determined by the present HPLC/ICP-AES system without pretreatment after acid digestion, although the detection limits were not sufficient for the analysis of rare earth oxides. (author)
14. [Study on the determination of 14 inorganic elements in coffee by inductively coupled plasma mass spectrometry].
Science.gov (United States)
Nie, Xi-Du; Fu, Liang
2013-07-01
Samples of coffee were digested by microwave digestion, and inorganic elements amounts of Na, Mg, P, Ca, Cr, Mn, Fe, Co, Cu, Zn, As, Se, Mo and Pb in sample solutions were determined by inductively coupled plasma mass spectrometry (ICP-MS). HNO3 + H2O2 was used to achieve the complete decomposition of the organic matrix in a closed-vessel microwave oven. The working parameters of the instrument were optimized. The results showed that the relative standard deviation (RSD) was less than 3.84% for all the elements, and the recovery was found to be 92.00% -106.52% by adding standard recovery experiment. This method was simple, sensitive and precise and can perform simultaneous multi-elements determination of coffee, which could satisfy the sample examination request and provide scientific rationale for determining inorganic elements of coffee.
15. Tensor polarized deuteron targets for intermediate energy physics experiments
International Nuclear Information System (INIS)
Meyer, W.; Schilling, E.
1985-03-01
At intermediate energies measurements from a tensor polarized deuteron target are being prepared for the following reactions: the photodisintegration of the deuteron, the elastic pion-deuteron scattering and the elastic electron-deuteron scattering. The experimental situation of the polarization experiments for these reactions is briefly discussed in section 2. In section 3 the definitions of the deuteron polarization and the possibilities to determine the vector and tensor polarization are given. Present tensor polarization values and further improvements in this field are reported in section 4. (orig.)
16. arXiv Hybrid Fluid Models from Mutual Effective Metric Couplings
CERN Document Server
Kurkela, Aleksi; Preis, Florian; Rebhan, Anton; Soloviev, Alexander
Motivated by a semi-holographic approach to the dynamics of quark-gluon plasma which combines holographic and perturbative descriptions of a strongly coupled infrared and a more weakly coupled ultraviolet sector, we construct a hybrid two-fluid model where interactions between its two sectors are encoded by their effective metric backgrounds, which are determined mutually by their energy-momentum tensors. We derive the most general consistent ultralocal interactions such that the full system has a total conserved energy-momentum tensor in flat Minkowski space and study its consequences in and near thermal equilibrium by working out its phase structure and its hydrodynamic modes.
17. Atomic-batched tensor decomposed two-electron repulsion integrals
Science.gov (United States)
Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove
2017-04-01
We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.
18. Quantum size effects in Pb layers with absorbed Kondo adatoms: Determination of the exchange coupling constant
KAUST Repository
Schwingenschlö gl, Udo; Shelykh, I. A.
2009-01-01
We consider the magnetic interaction of manganese phtalocyanine (MnPc) absorbed on Pb layers that were grown on a Si substrate. We perform an ab initio calculation of the density of states and Kondo temperature as a function of the number of Pb monolayers. Comparison to experimental data [Y.-S. Fu et al., Phys. Rev. Lett. 99, 256601 (2007)] then allows us to determine the exchange coupling constant J between the spins of the adsorbed molecules and those of the Pb host. This approach gives rise to a general and reliable method for obtaining J by combining experimental and numerical results.
19. Determination of the Axial-Vector Weak Coupling Constant with Ultracold Neutrons
International Nuclear Information System (INIS)
Liu, J.; Mendenhall, M. P.; Carr, R.; Filippone, B. W.; Hickerson, K. P.; Perez Galvan, A.; Russell, R.; Holley, A. T.; Hoagland, J.; VornDick, B.; Back, H. O.; Pattie, R. W. Jr.; Young, A. R.; Bowles, T. J.; Clayton, S.; Currie, S.; Hogan, G. E.; Ito, T. M.; Makela, M.; Morris, C. L.
2010-01-01
A precise measurement of the neutron decay β asymmetry A 0 has been carried out using polarized ultracold neutrons from the pulsed spallation ultracold neutron source at the Los Alamos Neutron Science Center. Combining data obtained in 2008 and 2009, we report A 0 =-0.119 66±0.000 89 -0.00140 +0.00123 , from which we determine the ratio of the axial-vector to vector weak coupling of the nucleon g A /g V =-1.275 90 -0.00445 +0.00409 .
20. Quantum size effects in Pb layers with absorbed Kondo adatoms: Determination of the exchange coupling constant
KAUST Repository
Schwingenschlögl, Udo
2009-07-01
We consider the magnetic interaction of manganese phtalocyanine (MnPc) absorbed on Pb layers that were grown on a Si substrate. We perform an ab initio calculation of the density of states and Kondo temperature as a function of the number of Pb monolayers. Comparison to experimental data [Y.-S. Fu et al., Phys. Rev. Lett. 99, 256601 (2007)] then allows us to determine the exchange coupling constant J between the spins of the adsorbed molecules and those of the Pb host. This approach gives rise to a general and reliable method for obtaining J by combining experimental and numerical results.
1. A supersymmetric SYK-like tensor model
Energy Technology Data Exchange (ETDEWEB)
Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence, RI, 02912 (United States)
2017-05-11
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.
2. Tensor glueball-meson mixing phenomenology
International Nuclear Information System (INIS)
Burakovsky, L.; Page, P.R.
2000-01-01
The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the f J (2220), and one where the glueball is more distributed, with f 2 (1820) having the largest component. The f 2 (1565) and f J (1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absence of significant coupling to decay channels. f 2 '(1525)→ππ is in agreement with experiment. The f J (2220) decays neither flavour democratically nor is narrow. (orig.)
3. A supersymmetric SYK-like tensor model
International Nuclear Information System (INIS)
Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia
2017-01-01
We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.
4. Killing-Yano tensors and Nambu mechanics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3
5. Comparison of alignment tensors generated for native tRNAVal using magnetic fields and liquid crystalline media
International Nuclear Information System (INIS)
Latham, Michael P.; Hanson, Paul; Brown, Darin J.; Pardi, Arthur
2008-01-01
Residual dipolar couplings (RDCs) complement standard NOE distance and J-coupling torsion angle data to improve the local and global structure of biomolecules in solution. One powerful application of RDCs is for domain orientation studies, which are especially valuable for structural studies of nucleic acids, where the local structure of a double helix is readily modeled and the orientations of the helical domains can then be determined from RDC data. However, RDCs obtained from only one alignment media generally result in degenerate solutions for the orientation of multiple domains. In protein systems, different alignment media are typically used to eliminate this orientational degeneracy, where the combination of RDCs from two (or more) independent alignment tensors can be used to overcome this degeneracy. It is demonstrated here for native E. coli tRNA Val that many of the commonly used liquid crystalline alignment media result in very similar alignment tensors, which do not eliminate the 4-fold degeneracy for orienting the two helical domains in tRNA. The intrinsic magnetic susceptibility anisotropy (MSA) of the nucleobases in tRNA Val was also used to obtain RDCs for magnetic alignment at 800 and 900 MHz. While these RDCs yield a different alignment tensor, the specific orientation of this tensor combined with the high rhombicity for the tensors in the liquid crystalline media only eliminates two of the four degenerate orientations for tRNA Val . Simulations are used to show that, in optimal cases, the combination of RDCs obtained from liquid crystalline medium and MSA-induced alignment can be used to obtain a unique orientation for the two helical domains in tRNA Val
6. Effect on Tensor Correlations on Gamow- Teller States in 90Zr and 208Pb
International Nuclear Information System (INIS)
Bai, C. L.; Sagawa, H.; Zhang, H. Q.
2009-01-01
The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF-RPA) model. The Gamow-Teller (GT) strength function of 9 0Z r and 2 08P b are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA. A microscopic origin of the quenching of GT sum rule is discussed in relation with the coupling to giant spin-quadrupole excitations by the tensor interactions.(author)
7. Tensor-GMRES method for large sparse systems of nonlinear equations
Science.gov (United States)
Feng, Dan; Pulliam, Thomas H.
1994-01-01
This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.
8. Tensor Rank Preserving Discriminant Analysis for Facial Recognition.
Science.gov (United States)
Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo
2017-10-12
Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.
9. Nonperturbative loop quantization of scalar-tensor theories of gravity
International Nuclear Information System (INIS)
Zhang Xiangdong; Ma Yongge
2011-01-01
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.
10. Radionuclide determination in environmental samples by inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Lariviere, Dominic; Taylor, Vivien F.; Evans, R. Douglas; Cornett, R. Jack
2006-01-01
The determination of naturally occurring and anthropogenic radionuclides in the environment by inductively coupled plasma mass spectrometry has gained recognition over the last fifteen years, relative to radiometric techniques, as the result of improvement in instrumental performance, sample introduction equipment, and sample preparation. With the increase in instrumental sensitivity, it is now possible to measure ultratrace levels (fg range) of many radioisotopes, including those with half-lives between 1 and 1000 years, without requiring very complex sample pre-concentration schemes. However, the identification and quantification of radioisotopes in environmental matrices is still hampered by a variety of analytical issues such as spectral (both atomic and molecular ions) and non-spectral (matrix effect) interferences and instrumental limitations (e.g., abundance sensitivity). The scope of this review is to highlight recent analytical progress and issues associated with the determination of radionuclides by inductively coupled plasma mass spectrometry. The impact of interferences, instrumental limitations (e.g., degree of ionization, abundance sensitivity, detection limits) and low sample-to-plasma transfer efficiency on the measurement of radionuclides by inductively coupled plasma mass spectrometry will be described. Solutions that overcome these issues will be discussed, highlighting their pros and cons and assessing their impact on the measurement of environmental radioactivity. Among the solutions proposed, mass and chemical resolution through the use of sector-field instruments and chemical reactions/collisions in a pressurized cell, respectively, will be described. Other methods, such as unique sample introduction equipment (e.g., laser ablation, electrothermal vaporisation, high efficiency nebulization) and instrumental modifications/optimizations (e.g., instrumental vacuum, radiofrequency power, guard electrode) that improve sensitivity and performance
11. Tensor-optimized shell model for the Li isotopes with a bare nucleon-nucleon interaction
Science.gov (United States)
Myo, Takayuki; Umeya, Atsushi; Toki, Hiroshi; Ikeda, Kiyomi
2012-08-01
We study the Li isotopes systematically in terms of the tensor-optimized shell model (TOSM) by using a bare nucleon-nucleon interaction as the AV8' interaction. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of the tensor force on each spectrum of the Li isotopes. It is found that the tensor force produces quite a characteristic effect on various states in each spectrum and those spectra are affected considerably by the tensor force. The energy difference between the spin-orbit partner, the p1/2 and p3/2 orbits of the last neutron, in 5Li is caused by opposite roles of the tensor correlation. In 6Li, the spin-triplet state in the LS coupling configuration is favored energetically by the tensor force in comparison with jj coupling shell-model states. In 7,8,9Li, the low-lying states containing extra neutrons in the p3/2 orbit are favored energetically due to the large tensor contribution to allow the excitation from the 0s, orbit to the p1/2 orbit by the tensor force. Those three nuclei show the jj coupling character in their ground states which is different from 6Li.
12. Determination of Dibutyltin in Sediments Using Isotope Dilution Liquid Chromatography-Inductively Coupled Plasma Mass Spectrometry
International Nuclear Information System (INIS)
Yim, Yong Hyeon; Park, Ji Youn; Han, Myung Sub; Park, Mi Kyung; Kim, Byung Joo; Lim, Young Ran; Hwang, Eui Jin; So, Hun Young
2005-01-01
A method is described for the determination of dibutyltin (DBT) in sediment by isotope dilution using liquid chromatography inductively-coupled plasma/mass spectrometry (LC-ICP/MS). To achieve the highest accuracy and precision, special attentions are paid in optimization and evaluation of overall processes of the analysis including extraction of analytes, characterization of the standards used for calibration and LC-ICP/MS conditions. An approach for characterization of natural abundance DBT standard has been developed by combining inductively-coupled plasma/optical emission spectrometry (ICP/OES) and LC-ICP/MS for the total Sn assay and the analysis of Sn species present as impurities, respectively. An excellent LC condition for separation of organotin species was found, which is suitable for simultaneous DBT and tributyltin (TBT) analysis as well as impurity analysis of DBT standards. Microwave extraction condition was also optimized for high efficiency while preventing species transformation. The present method determines the amount contents of DBT in sediments with expanded uncertainty of less than 5% and its result shows high degree of equivalence with reference values of an international inter-comparison and a certified reference material (CRM) within stated uncertainties
13. Determination of Dibutyltin in Sediments Using Isotope Dilution Liquid Chromatography-Inductively Coupled Plasma Mass Spectrometry
Energy Technology Data Exchange (ETDEWEB)
Yim, Yong Hyeon; Park, Ji Youn; Han, Myung Sub; Park, Mi Kyung; Kim, Byung Joo; Lim, Young Ran; Hwang, Eui Jin; So, Hun Young [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of)
2005-03-15
A method is described for the determination of dibutyltin (DBT) in sediment by isotope dilution using liquid chromatography inductively-coupled plasma/mass spectrometry (LC-ICP/MS). To achieve the highest accuracy and precision, special attentions are paid in optimization and evaluation of overall processes of the analysis including extraction of analytes, characterization of the standards used for calibration and LC-ICP/MS conditions. An approach for characterization of natural abundance DBT standard has been developed by combining inductively-coupled plasma/optical emission spectrometry (ICP/OES) and LC-ICP/MS for the total Sn assay and the analysis of Sn species present as impurities, respectively. An excellent LC condition for separation of organotin species was found, which is suitable for simultaneous DBT and tributyltin (TBT) analysis as well as impurity analysis of DBT standards. Microwave extraction condition was also optimized for high efficiency while preventing species transformation. The present method determines the amount contents of DBT in sediments with expanded uncertainty of less than 5% and its result shows high degree of equivalence with reference values of an international inter-comparison and a certified reference material (CRM) within stated uncertainties.
14. Trace determination of Pu by LIF in an inductively coupled plasma
International Nuclear Information System (INIS)
Mauchien, P.; Briand, A.; Moulin, C.
1989-01-01
Inductively Coupled Plasma/Emission Spectrometry (ICP/ES) technique is largely used in the nuclear industry as an elementary analytical technique. Nevertheless, when the sample to analyse presents elements with a lot of emission spectral lines, spectral interferences lead to limited sensitivity. This is the case for Pu determination in presence of large U concentration. In pure aqueous solution, the limit of detection (LOD) for Pu is 10 μg/1. In presence of U, the LOD is determined by a ratio U/Pu = 1000. Pulsed Laser Induced Fluorescence (LIF) spectrometry is known to be a very selective technique when associated with an Inductively Coupled Plasma source. The absolute sensitivity is better by 2 or 3 orders of magnitude; its principle is based on selective excitation of the ionic species in the plasma followed by fluorescence radiation detection of these species; this radiation being practically free from spectral interferences, it is possible to improve the relative LOD. In this presentation, experimental results performed at Cogema/Marcoule laboratory are presented. After the experimental set-up description, first results of LIF are shown: - very good selectivity is effectively obtained, - a series of analytical results obtained with excitation scanning from the visible to the U.V. show that sensitivity of LIF technique is strictly related to the spectroscopic scheme
15. Determination of the pion-nucleon coupling constant and scattering lengths
CERN Document Server
Ericson, Torleif Eric Oskar; Thomas, A W
2002-01-01
We critically evaluate the isovector GMO sum rule for forward pion-nucleon scattering using the recent precision measurements of negatively charged pion-proton and pion-deuteron scattering lengths from pionic atoms. We deduce the charged-pion-nucleon coupling constant, with careful attention to systematic and statistical uncertainties. This determination gives, directly from data a pseudoscalar coupling constant of 14.17+-0.05(statistical)+-0.19(systematic) or a pseudovector one of 0.0786(11). This value is intermediate between that of indirect methods and the direct determination from backward neutron-proton differential scattering cross sections. We also use the pionic atom data to deduce the coherent symmetric and antisymmetric sums of the negatively charged pion-proton and pion-neutron scattering lengths with high precision. The symmetric sum gives 0.0017+-0.0002(statistical)+-0.0008 (systematic) and the antisymmetric one 0.0900+-0.0003(statistical)+-0.0013(systematic), both in units of inverse charged pi...
16. MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.
17. Determination of rare earth elements by liquid chromatography/inductively coupled plasma atomic emission spectrometry
International Nuclear Information System (INIS)
Yoshida, K.; Haraguchi, H.
1984-01-01
Inductively coupled plasma atomic emission spectrometry (ICP-AES) interfaced with high-performance liquid chromatography (HPLC) has been applied to the determination of rare earth elements. ICP-AES was used as an element-selective detector for HPLC. The separation of rare earth elements with HPLC helped to avoid erroneous analytical results due to spectral interferences. Fifteen rare earth elements (Y and 14 lanthanides) were determined selectively with the HPLC/ICP-AES system using a concentration gradient method. The detection limits with the present HPLC/ICP-AES system were about 0.001-0.3 μg/mL with a 100-μL sample injection. The calibration curves obtained by the peak height measurements showed linear relationships in the concentration range below 500 μg/mL for all rare earth elements. A USGS rock standard sample, rare earth ores, and high-purity lanthanide reagents (>99.9%) were successfully analyzed without spectral interferences
18. Two-dimensional NMR measurement and point dipole model prediction of paramagnetic shift tensors in solids
Energy Technology Data Exchange (ETDEWEB)
Walder, Brennan J.; Davis, Michael C.; Grandinetti, Philip J. [Department of Chemistry, Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210 (United States); Dey, Krishna K. [Department of Physics, Dr. H. S. Gour University, Sagar, Madhya Pradesh 470003 (India); Baltisberger, Jay H. [Division of Natural Science, Mathematics, and Nursing, Berea College, Berea, Kentucky 40403 (United States)
2015-01-07
A new two-dimensional Nuclear Magnetic Resonance (NMR) experiment to separate and correlate the first-order quadrupolar and chemical/paramagnetic shift interactions is described. This experiment, which we call the shifting-d echo experiment, allows a more precise determination of tensor principal components values and their relative orientation. It is designed using the recently introduced symmetry pathway concept. A comparison of the shifting-d experiment with earlier proposed methods is presented and experimentally illustrated in the case of {sup 2}H (I = 1) paramagnetic shift and quadrupolar tensors of CuCl{sub 2}⋅2D{sub 2}O. The benefits of the shifting-d echo experiment over other methods are a factor of two improvement in sensitivity and the suppression of major artifacts. From the 2D lineshape analysis of the shifting-d spectrum, the {sup 2}H quadrupolar coupling parameters are 〈C{sub q}〉 = 118.1 kHz and 〈η{sub q}〉 = 0.88, and the {sup 2}H paramagnetic shift tensor anisotropy parameters are 〈ζ{sub P}〉 = − 152.5 ppm and 〈η{sub P}〉 = 0.91. The orientation of the quadrupolar coupling principal axis system (PAS) relative to the paramagnetic shift anisotropy principal axis system is given by (α,β,γ)=((π)/2 ,(π)/2 ,0). Using a simple ligand hopping model, the tensor parameters in the absence of exchange are estimated. On the basis of this analysis, the instantaneous principal components and orientation of the quadrupolar coupling are found to be in excellent agreement with previous measurements. A new point dipole model for predicting the paramagnetic shift tensor is proposed yielding significantly better agreement than previously used models. In the new model, the dipoles are displaced from nuclei at positions associated with high electron density in the singly occupied molecular orbital predicted from ligand field theory.
19. Efficient tensor completion for color image and video recovery: Low-rank tensor train
OpenAIRE
Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.
2016-01-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...
20. Random SU(2) invariant tensors
Science.gov (United States)
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
1. A new procedure for coupling antibody to paper discs for radioimmunoassay: application to the determination of alpha-fetoprotein
International Nuclear Information System (INIS)
Sasaki, T.; Tsukada, Y.; Hirai, H.
1983-01-01
Horse anti-alpha-fetoprotein was coupled to CM-cellulose discs by a modified carbodiimide reaction. The resulting coupled CM-discs were used in solid-phase radioimmunoassay of human alpha-fetoprotein. The sensitivity of these discs and conventional BrCN activated filter paper discs coupled anti-alpha-fetoprotein was approximately the same. A fair correlation between the alpha-fetoprotein levels determined by both methods was observed. The coupling procedure with carbodiimide is simple and the use of hazardous BrCN is eliminated. (Auth.)
2. Extended pure Yang-Mills gauge theories with scalar and tensor gauge fields
International Nuclear Information System (INIS)
Gabrielli, E.
1991-01-01
The usual abelian gauge theory is extended to an interacting Yang-Mills-like theory containing vector, scalar and tensor gauge fields. These gauge fields are seen as components along the Clifford algebra basis of a gauge vector-spinorial field. Scalar fields φ naturally coupled to vector and tensor fields have been found, leading to a natural φ 4 coupling in the lagrangian. The full expression of the lagrangian for the euclidean version of the theory is given. (orig.)
3. Multielement determination of rare earth elements in rock sample by liquid chromatography / inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Hamanaka, Tadashi; Itoh, Akihide; Itoh, Shinya; Sawatari, Hideyuki; Haraguchi, Hiroki.
1995-01-01
Rare earth elements in geological standard rock sample JG-1 (granodiolite)issued from the Geological Survey of Japan have been determined by a combined system of liquid chromatography and inductively coupled plasma mass spectrometry. (author)
4. Complete algebraic reduction of one-loop tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.; Riemann, T.
2011-01-01
We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided. The 4-point tensor coefficients are represented in terms of 4-point integrals, defined in d dimensions, 4-2ε≤d≤4-2ε+2(R-1), with higher powers of the propagators. They can be further reduced to expressions which stay free of the inverse 4-point Gram determinants but contain higher-dimensional 4-point integrals with only the first power of scalar propagators, plus 3-point tensor coefficients. A direct evaluation of the higher-dimensional 4-point functions would avoid the appearance of inverse powers of the Gram determinants completely. The simplest approach, however, is to apply here dimensional recurrence relations in order to reduce them to the familiar 2- to 4-point functions in generic dimension d=4-2ε, introducing thereby coefficients with inverse 4-point Gram determinants up to power R for tensors of rank R. For small or vanishing Gram determinants--where this reduction is not applicable--we use analytic expansions in positive powers of the Gram determinants. Improving the convergence of the expansions substantially with Pade approximants we close up to the evaluation of the 4-point tensor coefficients for larger Gram determinants. Finally, some relations are discussed which may be useful for analytic simplifications of Feynman diagrams.
5. The application of the inductively coupled plasma system to the simultaneous determination of precious metals
International Nuclear Information System (INIS)
Watson, A.E.; Russell, G.M.; Middleton, H.R.; Davenport, F.F.
1983-01-01
This report describes the development of a spectrochemical technique using excitation by an inducticely coupled plasma (ICP) source for the simultaneous determination of the precious metals (defined here as gold, silver, and all the platinum-group metals except osmium) in a wide variety of samples from a plant for the extraction and refining of platinum metal. The limits of detection for the analytes were determined in various acid and salt media and, under the conditions used, ranged from 20 to 100ng/l. The analytes were determined in the presence of a thousandfold excess of each of the other precious metals used as a matrix element. Some severe interferences were noted but were ascribed to spectral-line overlap or to contamination of the matrix material. Various dissolution techniques, based upon standard procedures applied in the precious-metals industry, were used, depending on the particular type of material treated. The spectrometer was calibrated by the use of solutions containing the analytes, sodium chloride, and acid, with scandium as the internal standard. The accuracy and precision of the technique, established by the analysis of many samples of each type, were found to be satisfactory when close attention was paid to detail in the preparation of the analytical solution. The relative standard deviation of the method ranges from 0,005 to 0,05, depending on the element being determined
6. General scalar-tensor theories for induced gravity inflation
International Nuclear Information System (INIS)
Boutaleb J, H.; Marrakchi, A.L.
1992-07-01
Some cosmological implications of a general scalar-tensor theory for induced gravity are discussed. The model exhibits a slow-rolling phase provided that the coupling function ε(φ) varies slowly enough such that φ dlnε(φ)/dφ much less than 2 during almost the inflationary epoch. It is then shown that, as in the ordinary induced gravity inflation, the chaotic scenario is more natural than the new scenario which proves to be even not self-consistent. The results are applied, for illustration, to a scalar-tensor theory of the Barker type. (author). 25 refs
7. Quark-gluon mixing in pseudoscalar and tensor mesons
International Nuclear Information System (INIS)
Eremyan, Sh.S.; Nazaryan, A.E.
1986-01-01
A mixing model of quark-antiquark ang gluonium states in η, η', i(1440) pseudoscalar and f, f', Θ(1690) tensor mesons is considered. Description of and predictions for 68 two-particle decays with these particles taking part in them are obtained. It is shown that i(1440) by 85% consists of gluonium and Θ(1690) is a pure gluonic state. The quark-gluon and gluon-gluon couplings in the pseudoscalar sector are obtained to be stronger as compared to the corresponding ones in the tensor case
8. Complete Cubic and Quartic Couplings of 16 and $\\bar{16}$ in SO(10) Unification
CERN Document Server
Syed, R M; Nath, Pran; Syed, Raza M.
2001-01-01
A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10) invariant cubic superpotential couplings involving $16_{\\pm}$ semispinors of SO(10) chirality $\\pm$ and tensor representations. In addition to the superpotential couplings computed previously using the basic theorem involving the 10, 120 and $\\bar{126}$ tensor representations we compute here couplings involving the 1, 45 and 210 dimensional tensor representations, i.e., we compute the $\\bar{16}_{\\mp}16_{\\pm}1$,$\\bar{16}_{\\mp}16_{\\pm}45$ and $\\bar{16}_{\\mp}16_{\\pm}210$ Higgs couplings in the superpotential. A complete determination of dimension five operators in the superpotential arising from the mediation of the 1, 45 and 210 dimensional representations is also given. The vector couplings $\\bar{16}_{\\pm}16_{\\pm}1$, $\\bar{16}_{\\pm}16_{\\pm}45$ and $\\bar{16}_{\\pm}16_{\\pm}210$ are also analyzed. The role of large tensor representations and the possible application of results ...
9. Complete cubic and quartic couplings of 16 and 16-bar in SO(10) unification
International Nuclear Information System (INIS)
Nath, Pran; Syed, Raza M.
2001-01-01
A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10)-invariant cubic superpotential couplings involving 16 ± semispinors of SO(10) chirality ± and tensor representations. In addition to the superpotential couplings computed previously using the basic theorem involving the 10, 120 and 126-bar tensor representations we compute here couplings involving the 1-, 45- and 210-dimensional tensor representations, i.e., we compute the 16-bar -+ 16 ± 1, 16-bar -+ 16 ± 45 and 16-bar -+ 16 ± 210 Higgs couplings in the superpotential. A complete determination of dimension five operators in the superpotential arising from the mediation of the 1-, 45- and 210-dimensional representations is also given. The vector couplings 16-bar ± 16 ± 1, 16-bar ± 16 ± 45 and 16-bar ± 16 ± 210 are also analyzed. The role of large tensor representations and the possible application of results derived here in model building are discussed
10. Holographic stress tensor for non-relativistic theories
International Nuclear Information System (INIS)
Ross, Simon F.; Saremi, Omid
2009-01-01
We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.
11. Tensor Product of Polygonal Cell Complexes
OpenAIRE
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
12. The Einstein tensor characterizing some Riemann spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1993-07-01
A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs
13. Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
14. Inflation in non-minimal matter-curvature coupling theories
Energy Technology Data Exchange (ETDEWEB)
Gomes, C.; Bertolami, O. [Departamento de Física e Astronomia and Centro de Física do Porto, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre s/n, 4169-007 Porto (Portugal); Rosa, J.G., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Departamento de Física da Universidade de Aveiro and CIDMA, Campus de Santiago, 3810-183 Aveiro (Portugal)
2017-06-01
We study inflationary scenarios driven by a scalar field in the presence of a non-minimal coupling between matter and curvature. We show that the Friedmann equation can be significantly modified when the energy density during inflation exceeds a critical value determined by the non-minimal coupling, which in turn may considerably modify the spectrum of primordial perturbations and the inflationary dynamics. In particular, we show that these models are characterised by a consistency relation between the tensor-to-scalar ratio and the tensor spectral index that can differ significantly from the predictions of general relativity. We also give examples of observational predictions for some of the most commonly considered potentials and use the results of the Planck collaboration to set limits on the scale of the non-minimal coupling.
15. Determination of rare earth elements by liquid chromatographic separation using inductively coupled plasma mass spectrometric detection
International Nuclear Information System (INIS)
Braverman, D.S.
1992-01-01
High-performance liquid chromatography (HPLC) is used to separate the rare earth elements (REEs) prior to detection by inductively coupled plasma mass spectrometry (ICP-MS). The use of HPLC-ICP-MS in series combines the separation power and speed of HPLC with the sensitivity, isotopic selectivity and speed of ICP-MS. The detection limits for the REEs are in the sub-ng ml -1 range and the response is linear over four orders of magnitude. A preliminary comparison of isotope dilution and external standard results for the determination of REEs in National Institute of Standards and Technology (NIST) Standard Reference Material (SRM 1633a) Fly Ash is presented. (author)
16. New azo coupling reactions for visible spectrophotometric determination of salbutamol in bulk and pharmaceutical preparations
International Nuclear Information System (INIS)
Dhahir, S. A.
2011-01-01
The purpose of the present study was to develop a new, simple, cheap, fast, accurate, and sensitive colorimetric methods that can be used for the determination of salbutamol sulphate drug in pure from as well as in pharmaceutical formulations. The method is based on the reaction 2-chloro-4-nitroaniline with nitrite in acid medium to form diazonium ion, which is coupled with of salbutamol in basic medium to form azo dyes, showing yellow color and absorption maxima at 463 nm. Beer's law is obeyed in the concentration of 4-48μg/ml. The molar absorptivity and san dell's sensitivity are 5.27x103 L mole-1 cm-1, 0.015 μgcm-2, respectively. The optimum reaction conditions and other analytical parameters were evaluated. (author).
17. Determination of long-chain fatty acids in serum by gas chromatography coupled to mass spectrometry
International Nuclear Information System (INIS)
Nuevas Paz, Lauro; Camayd Viera, Ivette
2014-01-01
The quantification of long-chain fatty acids is fundamental for the diagnosis of several peroxisome disorders, particularly those in which the β-oxidation peroxisome of fatty acids is affected. In this work the implementation of an analytical method for the determination of these markers in serum by gas chromatography coupled to mass spectrometry is described. Besides, samples from patients with a diagnostic impression of adrenoleukodystrophy linked to the X chromosome were analyzed. The necessary experimental conditions were achieved for the separation and quantification of C22:0, C24:0 and C26:0 fatty acids in serum, which are biochemical markers of various peroxisome diseases. The application of this method allowed confirming the diagnosis of three patients with a diagnostic impression of adrenoleukodystrophy linked to the X chromosome. The application of the method in daily practice will allow the Cuban medical system to count on a new laboratory parameter for the diagnosis of peroxisome disorders
18. Determination of Rare Earth Elements in Thai Monazite by Inductively Coupled Plasma and Nuclear Analytical techniques
International Nuclear Information System (INIS)
Busamongkol, Arporn; Ratanapra, Dusadee; Sukharn, Sumalee; Laoharojanaphand, Sirinart
2003-10-01
The inductively coupled plasma atomic emission spectroscopy (ICP-AES) for the determination of individual rare-earth elements (REE) was evaluated by comparison with instrumental neutron activation analysis (INAA) and x-ray fluorescence spectrometry (XRF). The accuracy and precision of INAA and ICP-AES were evaluated by using standard reference material IGS-36, a monazite concentrate. For INAA, the results were close to the certified value while ICP-AES were in good agreement except for some low concentration rare earth. The techniques were applied for the analysis of some rare earth elements in two Thai monazite samples preparing as the in-house reference material for the Rare Earth Research and Development Center, Chemistry Division, Office of Atoms for Peace. The analytical results obtained by these techniques were in good agreement with each other
19. Serum/plasma methylmercury determination by isotope dilution gas chromatography-inductively coupled plasma mass spectrometry
Energy Technology Data Exchange (ETDEWEB)
Baxter, Douglas C., E-mail: [email protected] [ALS Scandinavia AB, Aurorum 10, 977 75 Lulea (Sweden); Faarinen, Mikko [ALS Scandinavia AB, Aurorum 10, 977 75 Lulea (Sweden); Osterlund, Helene; Rodushkin, Ilia [ALS Scandinavia AB, Aurorum 10, 977 75 Lulea (Sweden); Division of Geosciences, Lulea University of Technology, 977 87 Lulea (Sweden); Christensen, Morten [ALS Scandinavia AB, Maskinvaegen 2, 183 53 Taeby (Sweden)
2011-09-09
Highlights: {center_dot} We determine methylmercury in serum and plasma using isotope dilution calibration. {center_dot} Separation by gas chromatography and detection by inductively coupled plasma mass spectrometry. {center_dot} Data for 50 specimens provides first reference range for methylmercury in serum. {center_dot} Serum samples shown to be stable for 11 months in refrigerator. - Abstract: A method for the determination of methylmercury in plasma and serum samples was developed. The method uses isotope dilution with {sup 198}Hg-labeled methylmercury, extraction into dichloromethane, back-extraction into water, aqueous-phase ethylation, purge and trap collection, thermal desorption, separation by gas chromatography, and mercury isotope specific detection by inductively coupled plasma mass spectrometry. By spiking 2 mL sample with 1.2 ng tracer, measurements in a concentration interval of (0.007-2.9) {mu}g L{sup -1} could be performed with uncertainty amplification factors <2. A limit of quantification of 0.03 {mu}g L{sup -1} was estimated at 10 times the standard deviation of concentrations measured in preparation blanks. Within- and between-run relative standard deviations were <10% at added concentration levels of 0.14 {mu}g L{sup -1}, 0.35 {mu}g L{sup -1} and 2.8 {mu}g L{sup -1}, with recoveries in the range 82-110%. Application of the method to 50 plasma/serum samples yielded a median (mean; range) concentration of methylmercury of 0.081 (0.091; <0.03-0.19) {mu}g L{sup -1}. This is the first time methylmercury has been directly measured in this kind of specimen, and is therefore the first estimate of a reference range.
20. Plutonium determination in seawater by inductively coupled plasma mass spectrometry: A review.
Science.gov (United States)
Cao, Liguo; Bu, Wenting; Zheng, Jian; Pan, Shaoming; Wang, Zhongtang; Uchida, Shigeo
2016-05-01
1. Laser ablation inductively coupled plasma mass spectrometry for the determination of trace elements in soil
International Nuclear Information System (INIS)
Lee Yiling; Chang Chaochiang; Jiang Shiuhjen
2003-01-01
Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) has been applied to the determination of Cr, Cu, Zn, Cd and Pb in soil samples. The dried soil powder was pressed into a pellet for LA-ICP-MS analysis. Triton X-100 was added to work as the modifier to enhance the ion signals. The influences of instrument operating conditions (LA and ICP-MS) and pellet preparation on the ion signals were reported. For Cr determination, the ICP-MS was operated under the dynamic reaction cell mode which alleviated the mass overlap interference. Standard addition method and isotope dilution method were used for the quantitation work. The powder sample was spiked with suitable amounts of element standards and/or enriched isotopes, well-mixed, dried and then pressed into a pellet for LA-ICP-MS analysis. This method has been applied to determine Cr, Cu, Zn, Cd and Pb in NIST SRM 2711 Montana soil and NIST SRM 2709 San Joaquin soil reference materials. The analysis results were in agreement with the certified values. The precision between sample replicates was better than 5% with LA-ICP-MS method. Detection limits estimated from standard addition curves were approximately 0.9, 2, 9, 0.7 and 0.3 ng g -1 for Cr, Cu, Zn, Cd and Pb, respectively
2. Tensor Completion Algorithms in Big Data Analytics
OpenAIRE
Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia
2017-01-01
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...
3. A model for soft high-energy scattering: Tensor pomeron and vector odderon
Energy Technology Data Exchange (ETDEWEB)
Ewerz, Carlo, E-mail: [email protected] [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, D-64291 Darmstadt (Germany); Maniatis, Markos, E-mail: [email protected] [Departamento de Ciencias Básicas, Universidad del Bío-Bío, Avda. Andrés Bello s/n, Casilla 447, Chillán 3780000 (Chile); Nachtmann, Otto, E-mail: [email protected] [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)
2014-03-15
A model for soft high-energy scattering is developed. The model is formulated in terms of effective propagators and vertices for the exchange objects: the pomeron, the odderon, and the reggeons. The vertices are required to respect standard rules of QFT. The propagators are constructed taking into account the crossing properties of amplitudes in QFT and the power-law ansätze from the Regge model. We propose to describe the pomeron as an effective spin 2 exchange. This tensor pomeron gives, at high energies, the same results for the pp and pp{sup -bar} elastic amplitudes as the standard Donnachie–Landshoff pomeron. But with our tensor pomeron it is much more natural to write down effective vertices of all kinds which respect the rules of QFT. This is particularly clear for the coupling of the pomeron to particles carrying spin, for instance vector mesons. We describe the odderon as an effective vector exchange. We emphasise that with a tensor pomeron and a vector odderon the corresponding charge-conjugation relations are automatically fulfilled. We compare the model to some experimental data, in particular to data for the total cross sections, in order to determine the model parameters. The model should provide a starting point for a general framework for describing soft high-energy reactions. It should give to experimentalists an easily manageable tool for calculating amplitudes for such reactions and for obtaining predictions which can be compared in detail with data. -- Highlights: •A general model for soft high-energy hadron scattering is developed. •The pomeron is described as effective tensor exchange. •Explicit expressions for effective reggeon–particle vertices are given. •Reggeon–particle and particle–particle vertices are related. •All vertices respect the standard C parity and crossing rules of QFT.
4. Development of the Tensoral Computer Language
Science.gov (United States)
Ferziger, Joel; Dresselhaus, Eliot
1996-01-01
The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.
5. The tensor part of the Skyrme energy density functional. I. Spherical nuclei
Energy Technology Data Exchange (ETDEWEB)
Lesinski, T.; Meyer, J. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France); Bender, M. [DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France)]|[Universite Bordeaux, CNRS/IN2P3, Centre d' Etudes Nucleaires de Bordeaux Gradignan, UMR5797, Chemin du Solarium, BP120, F-33175 Gradignan (France); Bennaceur, K. [Universite de Lyon, F-69003 Lyon (France)]|[Institut de Physique Nucleaire de Lyon, CNRS/IN2P3, Universite Lyon 1, F-69622 Villeurbanne (France)]|[DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette Cedex (France); Duguet, T. [National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States)
2007-04-15
We perform a systematic study of the impact of the J-vector{sup 2} tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations which cover a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are (i) tensor terms should not be added perturbatively to existing parameterizations, a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the {chi}{sup 2} within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even the coexistence of two configurations with different spherical shell structure. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, while those of node-less intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall
6. Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
OpenAIRE
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
7. Direct rare earth determination by inductively coupled plasma optical emission spectrometry
International Nuclear Information System (INIS)
Marin, Sergio; Cornejo, Silvia; Rojas, Jacqueline
2003-01-01
In the present work, the use of the inductively coupled plasma optical emission spectrometry (ICP-OES), for the sequential determination of Rare Earth elements in the metallurgical process samples is described. In the first place, the optimum parameters for the determination of the elements in study are established, like instrumental calibration, wavelengths spectral selection and interference of matrix. Next, the methodology for the digestion of solid samples (system of digestion with pressure) and the recovery of the interest elements are presented. Two material rocks as of reference Syenite SY3 are used. In order to assure the validity of the obtained data, the reference materials SY2 and SY3 were analyzed by means of two different techniques, ICP-OES and ICP-Mass, this last one was made by an international laboratory and a fusion with lithium metaborate was used with digestion method. Finally, the obtained results demonstrate that the reproducibility in the recovery of rare earth analyzed by both techniques is comparable, and that the methodology of digestion used for these elements is statistically valid (author)
8. Process monitored spectrophotometric titration coupled with chemometrics for simultaneous determination of mixtures of weak acids.
Science.gov (United States)
Liao, Lifu; Yang, Jing; Yuan, Jintao
2007-05-15
A new spectrophotometric titration method coupled with chemometrics for the simultaneous determination of mixtures of weak acids has been developed. In this method, the titrant is a mixture of sodium hydroxide and an acid-base indicator, and the indicator is used to monitor the titration process. In a process of titration, both the added volume of titrant and the solution acidity at each titration point can be obtained simultaneously from an absorption spectrum by least square algorithm, and then the concentration of each component in the mixture can be obtained from the titration curves by principal component regression. The method only needs the information of absorbance spectra to obtain the analytical results, and is free of volumetric measurements. The analyses are independent of titration end point and do not need the accurate values of dissociation constants of the indicator and the acids. The method has been applied to the simultaneous determination of the mixtures of benzoic acid and salicylic acid, and the mixtures of phenol, o-chlorophenol and p-chlorophenol with satisfactory results.
9. Inductively coupled plasma atomic emission spectrometric determination of tin in canned food.
Science.gov (United States)
Sumitani, H; Suekane, S; Nakatani, A; Tatsuka, K
1993-01-01
Various canned foods were digested sequentially with HNO3 and HCl, diluted to 100 mL, and filtered, and then tin was determined by inductively coupled plasma atomic emission spectrometry (ICP/AES). Samples of canned Satsuma mandarin, peach, apricot, pineapple, apple juice, mushroom, asparagus, evaporated milk, short-necked clam, spinach, whole tomato, meat, and salmon were evaluated. Sample preparations did not require time-consuming dilutions, because ICP/AES has wide dynamic range. The standard addition method was used to determine tin concentration. Accuracy of the method was tested by analyzing analytical standards containing tin at 2 levels (50 and 250 micrograms/g). The amounts of tin found for the 50 and 250 micrograms/g levels were 50.5 and 256 micrograms/g, respectively, and the repeatability coefficients of variation were 4.0 and 3.8%, respectively. Recovery of tin from 13 canned foods spiked at 2 levels (50 and 250 micrograms/g) ranged from 93.9 to 109.4%, with a mean of 99.2%. The quantitation limit for tin standard solution was about 0.5 microgram/g.
10. Accurate determination of silver nanoparticles in animal tissues by inductively coupled plasma mass spectrometry
Energy Technology Data Exchange (ETDEWEB)
2014-12-01
This study examined recoveries of silver determination in animal tissues after wet digestion by inductively coupled plasma mass spectrometry. The composition of the mineralization mixture for microwave assisted digestion was optimized and the best recoveries were obtained for mineralization with HNO{sub 3} and addition of HCl promptly after digestion. The optimization was performed on model samples of chicken meat spiked with silver nanoparticles and a solution of ionic silver. Basic calculations of theoretical distribution of Ag among various silver-containing species were implemented and the results showed that most of the silver is in the form of soluble complexes AgCl{sub 2}{sup −} and AgCl{sub 3}{sup 2−} for the optimized composition of the mineralization mixture. Three animal tissue certified reference materials were then analyzed to verify the trueness and precision of the results. - Highlights: • We performed detailed optimization of microwave assisted digestion procedure of animal tissue used prior to Ag determination by ICP-MS. • We provide basic equilibrium calculations to give theoretical explanation of results from optimization of tested mineralization mixtures. • Results from method validation that was done by analysis of several matrix CRMs are presented.
11. Determination of the pion-nucleon coupling constant and scattering lengths
International Nuclear Information System (INIS)
Ericson, T.E.O.; Loiseau, B.; Thomas, A.W.
2002-01-01
We critically evaluate the isovector Goldberger-Miyazawa-Oehme (GMO) sum rule for forward πN scattering using the recent precision measurements of π - p and π - d scattering lengths from pionic atoms. We deduce the charged-pion-nucleon coupling constant, with careful attention to systematic and statistical uncertainties. This determination gives, directly from data, g c 2 (GMO)/4π=14.11±0.05(statistical)±0.19(systematic) or f c 2 /4π=0.0783(11). This value is intermediate between that of indirect methods and the direct determination from backward np differential scattering cross sections. We also use the pionic atom data to deduce the coherent symmetric and antisymmetric sums of the pion-proton and pion-neutron scattering lengths with high precision, namely, (a π - p +a π - n )/2=[-12±2(statistical)±8(systematic)]x10 -4 m π -1 and (a π - p -a π - n )/2=[895±3(statistical)±13 (systematic)]x10 -4 m π -1 . For the need of the present analysis, we improve the theoretical description of the pion-deuteron scattering length
12. Determining Li+-Coupled Redox Targeting Reaction Kinetics of Battery Materials with Scanning Electrochemical Microscopy.
Science.gov (United States)
Yan, Ruiting; Ghilane, Jalal; Phuah, Kia Chai; Pham Truong, Thuan Nguyen; Adams, Stefan; Randriamahazaka, Hyacinthe; Wang, Qing
2018-02-01
The redox targeting reaction of Li + -storage materials with redox mediators is the key process in redox flow lithium batteries, a promising technology for next-generation large-scale energy storage. The kinetics of the Li + -coupled heterogeneous charge transfer between the energy storage material and redox mediator dictates the performance of the device, while as a new type of charge transfer process it has been rarely studied. Here, scanning electrochemical microscopy (SECM) was employed for the first time to determine the interfacial charge transfer kinetics of LiFePO 4 /FePO 4 upon delithiation and lithiation by a pair of redox shuttle molecules FcBr 2 + and Fc. The effective rate constant k eff was determined to be around 3.70-6.57 × 10 -3 cm/s for the two-way pseudo-first-order reactions, which feature a linear dependence on the composition of LiFePO 4 , validating the kinetic process of interfacial charge transfer rather than bulk solid diffusion. In addition, in conjunction with chronoamperometry measurement, the SECM study disproves the conventional "shrinking-core" model for the delithiation of LiFePO 4 and presents an intriguing way of probing the phase boundary propagations induced by interfacial redox reactions. This study demonstrates a reliable method for the kinetics of redox targeting reactions, and the results provide useful guidance for the optimization of redox targeting systems for large-scale energy storage.
13. [Determination of Heavy Metal Elements in Diatomite Filter Aid by Inductively Coupled Plasma Mass Spectrometry].
Science.gov (United States)
Nie, Xi-du; Fu, Liang
2015-11-01
This study established a method for determining Be, Cr, Ni, As, Cd, Sb, Sn, Tl, Hg and Pb, total 10 heavy metals in diatomite filter aid. The diatomite filter aid was digested by using the mixture acid of HNO₃ + HF+ H₃PO₄ in microwave system, 10 heavy metals elements were determined by inductively coupled plasma mass spectrometry (ICP-MS). The interferences of mass spectrometry caused by the high silicon substrate were optimized, first the equipment parameters and isotopes of test metals were selected to eliminate these interferences, the methane was selected as reactant gas, and the mass spectral interferences were eliminated by dynamic reaction cell (DRC). Li, Sc, Y, In and Bi were selected as the internal standard elements to correct the interferences caused by matrix and the drift of sensitivity. The results show that the detection limits for analyte is in the range of 3.29-15.68 ng · L⁻¹, relative standard deviations (RSD) is less than 4.62%, and the recovery is in the range of 90.71%-107.22%. The current method has some advantages such as, high sensitivity, accurate, and precision, which can be used in diatomite filter aid quality control and safety estimations.
14. Determination of metals content from wines by inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Iordache, Andreea-Maria; Geana, Elisabeta-Irina
2009-01-01
Full text: Wine is a widely consumed beverage with thousands of years of tradition. Wine composition strongly determines its quality besides having a great relevance on wine characterization, tipyfication and frauds detection. Wine composition is influenced by many and diverse factors corresponding to the specific production area, such as grape variety, soil and climate, culture, yeast, winemaking practices, transport and storage. Daily consumption of wine in moderate quantities contributes significantly to the requirements of the human organism for essential elements such as Cr, Cu, Zn, Fe, Mn, Co, Ni and Sr. On the other hand, several metals, such as Pb and Cd , are known to be potentially toxic. The objective of this work was to develop a method to determine the metals content in wine samples from Romania. Three samples of difference white wines available in the supermarket was analyzed for identify the presence of: Cr, Cu, Zn, Fe, Mn, Pb, Cd, Co, Ni and Sr by inductively coupled plasma mass spectrometry (ICP-MS). (authors)
15. The Possible Role of Dentin as a Piezoelectric Signal Generator by Determining the Elec-tromechanical Coupling Factor of Dentin
Directory of Open Access Journals (Sweden)
Atabak Shahidi
2011-08-01
Full Text Available Introduction: This article aimed at calculation of the electromechanical coupling factor of dentin which is an indicator of the effectiveness with which a piezoelectric material converts electrical en-ergy into mechanical energy, or vice versa. The hypothesis: The electro-mechanical coupling factor of dentin was determined in mode 11 and 33 by calculating the ratio of the produced electrical energy to the stored elastic energy in dentin under applied pressure. This study showed that the electromechanical coupling factor of dentin was affected by the direction of the applied force and the moisture content of dentin. Also dentin was a weak electromechanical energy converter which might be categorized as a piezoelectric pressure sensor.Evaluation of the hypothesis: Determination of the electrome-chanical coupling factor of dentin and its other piezoelectric constants is essential to investigate the biologic role of piezoelectricity in tooth.
16. Determination of coupling coefficients at various zenith angles of the basis of the cosmic ray azimuth effect
Science.gov (United States)
Belskiy, S. A.; Dmitriev, B. A.; Romanov, A. M.
1975-01-01
The value of EW asymmetry and coupling coefficients at different zenith angles were measured by means of a double coincidence crossed telescope which gives an opportunity to measure simultaneously the intensity of the cosmic ray hard component at zenith angles from 0 to 84 deg in opposite azimuths. The advantages of determining the coupling coefficients by the cosmic ray azimuth effect as compared to their measurement by the latitudinal effect are discussed.
17. How Precisely can we Determine the $\\piNN$ Coupling Constant from the Isovector GMO Sum Rule?
CERN Document Server
Loiseau, B; Thomas, A W
1999-01-01
The isovector GMO sum rule for zero energy forward pion-nucleon scattering iscritically studied to obtain the charged pion-nucleon coupling constant usingthe precise negatively charged pion-proton and pion-deuteron scattering lengthsdeduced recently from pionic atom experiments. This direct determination leadsto a pseudoscalar charged pion-nucleon coupling constant of 14.23 +- 0.09(statistic) +- 0.17 (systematic). We obtain also accurate values for thepion-nucleon scattering lengths.
18. The tensor rank of tensor product of two three-qubit W states is eight
OpenAIRE
Chen, Lin; Friedland, Shmuel
2017-01-01
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
19. [Determination of 24 minerals in human milk by inductively coupled plasma mass spectrometry with microwave digestion].
Science.gov (United States)
Sun, Zhongqing; Yue, Bing; Yang, Zhenyu; Li, Xiaowei; Wu, Yongning; Yin, Shian
2013-05-01
To determine the levels of 24 minerals in human milk by inductively coupled plasma mass spectrometry with microwave digestion. The samples were digested by microwave. The contents of minerals were determined by inductively coupled plasma mass spectrometry. The standard reference minerals of 1849a and 1568a from National Institute of Science and Technology were used for quality control. The accuracy and reproduability for this method were evaluated with mix standards and 1849a and 1568a standard reference materials. The ranges of the levels of sodium, magnesium, phosphorus, potassium, calcium, aluminum, chromium, arsenic, selenium, iron, zinc, manganese, copper, molybdenum, vanadium, cobalt, nickel, gallium, cadmium, silver, strontium, cesium, barium, lead in human milk was 34.97-415.83 mg/kg, 19.00-39.52 mg/kg, 102.13-274.53 mg/kg, 351.19-713.99 mg/kg, 180.08-349.64 mg/kg, 0.06-0.44 mg/kg, 0.9-7.37 microg/kg, 0.92-2.72 microg/kg, 0.20-21.15 microg/kg, 0.10-0.70 mg/kg, 0.56-3.25 mg/kg, 3.00-16.12 micro.g/kg, 62.16-591.69 microg/kg, 0.02-6.91 microg/kg, 5.99-13.70 microg/kg, 0.07-2.11 microg/kg, 0.77-209.26 microg/kg, 0.005-0.28 microg/kg, 0.02-0.23 microg/kg, 0.02-0.71 microg/kg, 36.89-132.26 microg/kg, 0.01-4.72 microg/kg, 0.83-28.16 microg/kg, 2.5-5.3 microg/kg, respectively. The levels of minerals in human milk in present study were consisted with other similar studies. The experiment examined the levels of minerals in human milk satisfactorily. The method has high accuracy and good reproducibility, which could be used for understanding the levels of minerals in human milk.
20. Top-down approach in protein RDC data analysis: de novo estimation of the alignment tensor
International Nuclear Information System (INIS)
Chen Kang; Tjandra, Nico
2007-01-01
In solution NMR spectroscopy the residual dipolar coupling (RDC) is invaluable in improving both the precision and accuracy of NMR structures during their structural refinement. The RDC also provides a potential to determine protein structure de novo. These procedures are only effective when an accurate estimate of the alignment tensor has already been made. Here we present a top-down approach, starting from the secondary structure elements and finishing at the residue level, for RDC data analysis in order to obtain a better estimate of the alignment tensor. Using only the RDCs from N-H bonds of residues in α-helices and CA-CO bonds in β-strands, we are able to determine the offset and the approximate amplitude of the RDC modulation-curve for each secondary structure element, which are subsequently used as targets for global minimization. The alignment order parameters and the orientation of the major principal axis of individual helix or strand, with respect to the alignment frame, can be determined in each of the eight quadrants of a sphere. The following minimization against RDC of all residues within the helix or strand segment can be carried out with fixed alignment order parameters to improve the accuracy of the orientation. For a helical protein Bax, the three components A xx , A yy and A zz , of the alignment order can be determined with this method in average to within 2.3% deviation from the values calculated with the available atomic coordinates. Similarly for β-sheet protein Ubiquitin they agree in average to within 8.5%. The larger discrepancy in β-strand parameters comes from both the diversity of the β-sheet structure and the lower precision of CA-CO RDCs. This top-down approach is a robust method for alignment tensor estimation and also holds a promise for providing a protein topological fold using limited sets of RDCs
1. Piezo-optic tensor of crystals from quantum-mechanical calculations.
Science.gov (United States)
Erba, A; Ruggiero, M T; Korter, T M; Dovesi, R
2015-10-14
An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric tensor components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of the full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO4, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π61 constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.
2. Stress tensor fluctuations in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Pérez-Nadal, Guillem; Verdaguer, Enric [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain); Roura, Albert, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm (Germany)
2010-05-01
The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m{sup 2}/H{sup 2}. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.
3. New Diazo Coupling Reactions for Visible Spectrophotometric Determination of Alfuzosin in Pharmaceutical Preparations
Directory of Open Access Journals (Sweden)
M. Vamsi Krishna
2007-01-01
Full Text Available Simple, rapid and sensitive spectrophotometric procedures were developed for the analysis of Alfuzosin hydrochloride (AFZ in pure form as well as in pharmaceutical formulations. The methods are based on the reaction of AFZ with nitrite in acid medium to form diazonium ion, which is coupled with ethoxyethylenemaleic ester (Method A or ethylcyanoacetate (Method B or acetyl acetone (method C in basic medium to form azo dyes, showing absorption maxima at 440, 465 and 490 nm respectively. Beer’s law is obeyed in the concentration of 4-20 μg/mL of AFZ for methods A, B and 3-15 μg/mL of AFZ for method C. The molar absorptivity and sandell’s sensitivity of AFZ- ethoxyethylenemaleic ester, AFZ- ethylcyanoacetate and AFZ-acetyl acetone are1.90 × 104, 0.022; 1.93 × 104, 0.021 and 2.67 × 104 L mole-1 cm-1, 0.015 μg cm-2 respectively. The optimum reaction conditions and other analytical parameters were evaluated. The methods were successfully applied to the determination of AFZ in pharmaceutical formulations.
4. [Determination of arsenic speciation in Scomberomorus niphonius by capillary electrophoresis-inductively coupled plasma mass spectrometry].
Science.gov (United States)
Chen, Fa-rong; Zheng, Li; Wang, Zhi-Guang; Sun, Jie; Han, Li-Hui; Wang, Xiao-ru
2014-06-01
A method for the detection of arsenocholine (AsC), arsenobetaine (AsB), As(III), dimethylarsinic (DMA), monomethylarsonic (MMA) and As (V) by capillary electrophoresis-inductively coupled plasma mass spectrometry (CE-ICP-MS) was established. The results showed that the six species of arsenic were separated within 20 min under the optimized conditions. Good linearities of 6 arsenic species were observed in the range from 2 to 50 μg x L(-1) with the linear correlation greater than 0.996, the detection limits were 0.10-1.08 μg x L(-1) and the RSDs (n = 5) of the peak areas were smaller than 7%. The method was successfully adopted to the determination of the species in Scomberomorus niphonius. The recoveries were between 93% and 98%, and we found the arsenobetaine (AsB) was the main species in the sample. The method was suitable for the analysis of other biological samples with the advantages of good stability, less sample consumption, short analysis time and convenience.
5. Determination of 238U in marine organisms by inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Ishii, Toshiaki; Nakahara, Motokazu; Matsuba, Mitsue; Ishikawa, Masafumi
1991-01-01
Determination of 238 U in fifty-five species of marine organisms was carried out by inductively coupled plasma mass spectrometry which showed some advantages such as high sensitivity, wide dynamic range and small interferences from matrices for the analysis of high mass elements. The concentrations of 238 U in soft tissues of marine animals ranged from 0.076 to 5000 ng/g wet wt. Especially, the branchial heart of cephalopod molluscs showed the specific accumulation of 238 U. The concentration factor of the branchial heart of Octopus vulgaris, which indicated the highest value, was calculated to be about 10 3 by comparing it with the concentration of 238 U (3.2±0.2 ng/ml) in coastal seawaters of Japan. The concentrations of 238 U in hard tissues of marine invertebrates were similar to those in soft tissues. In contrast, hard tissues like bone, scale, fin, etc. of fishes showed much higher concentrations of 238 U than soft tissues like muscle and liver. The concentrations of 238 U of twenty species of algae ranged from 10 to 3700 ng/g dry wt. (author)
6. Radiochemical determination of zirconium by inductively coupled plasma mass spectrometry (ICPMS)
International Nuclear Information System (INIS)
Oliveira, Thiago C.; Oliveira, Arno Heeren de
2013-01-01
The zirconium isotope 93 Zr is a long-lived pure β-particle-emitting radionuclide thus occurring as one of the radionuclides found in nuclear reactors. It's produced from 235 U fission and from 92 Zr neutron activation. Due to its long half-life, 93 Zr is one of the interest radionuclides for assessment studies performance of waste storage or disposal. Measurement of 93 Zr is difficult owing to its trace level concentration and its low activity in nuclear wastes and further because its certified standards are not frequently available. The aim of this work was to apply a selective radiochemical separation methodology for 93 Zr determination in nuclear waste and analyze it by Inductively Coupled Plasma Mass Spectrometry (ICPMS). To set up the zirconium radiochemical separation procedure, a zirconium tracer solution was used in order to follow the zirconium behavior during the radiochemical separation. A tracer solution containing the main interferences, Ba, Co, Eu, Fe, Mn, Nb, Ni, Sr, and Y was used in order to verify the decontamination factor during separation process. The limit of detection of 0,039 ppb was obtained for zirconium standard solutions by ICPMS. Then, the protocol will be applied to low level waste (LLW) and intermediate level waste (ILW) from nuclear power plants. (author)
7. Levels of Essential Elements in Different Medicinal Plants Determined by Using Inductively Coupled Plasma Mass Spectrometry
Directory of Open Access Journals (Sweden)
Eid I. Brima
2018-01-01
Full Text Available The objective of this study was to investigate the content of essential elements in medicinal plants in the Kingdom of Saudi Arabia (KSA. Five different medical plants (mahareeb (Cymbopogon schoenanthus, sheeh (Artemisia vulgaris, harjal (Cynanchum argel delile, nabipoot (Equisetum arvense, and cafmariam (Vitex agnus-castus were collected from Madina city in the KSA. Five elements Fe, Mn, Zn, Cu, and Se were determined by using inductively coupled plasma mass spectrometry (ICP-MS. Fe levels were the highest and Se levels were the lowest in all plants. The range levels of all elements in all plants were as follows: Fe 193.4–1757.9, Mn 23.6–143.7, Zn 15.4–32.7, Se 0.13–0.92, and Cu 11.3–21.8 µg/g. Intakes of essential elements from the medical plants in infusion were calculated: Fe 4.6–13.4, Mn 6.7–123.2, Zn 7.0–42.7, Se 0.14–1.5, and Cu 1.5–5.0 µg/dose. The calculated intakes of essential elements for all plants did not exceed the daily intake set by the World Health Organization (WHO and European Food Safety Authority (EFSA. These medicinal plants may be useful sources of essential elements, which are vital for health.
8. Fluorescent Biosensor for Phosphate Determination Based on Immobilized Polyfluorene-Liposomal Nanoparticles Coupled with Alkaline Phosphatase.
Science.gov (United States)
Kahveci, Zehra; Martínez-Tomé, Maria José; Mallavia, Ricardo; Mateo, C Reyes
2017-01-11
This work describes the development of a novel fluorescent biosensor based on the inhibition of alkaline phosphatase (ALP). The biosensor is composed of the enzyme ALP and the conjugated cationic polyfluorene HTMA-PFP. The working principle of the biosensor is based on the fluorescence quenching of this polyelectrolyte by p-nitrophenol (PNP), a product of the hydrolysis reaction of p-nitrophenyl phosphate (PNPP) catalyzed by ALP. Because HTMA-PFP forms unstable aggregates in buffer, with low fluorescence efficiency, previous stabilization of the polyelectrolyte was required before the development of the biosensor. HTMA-PFP was stabilized through its interaction with lipid vesicles to obtain stable blue-emitting nanoparticles (NPs). Fluorescent NPs were characterized, and the ability to be quenched by PNP was evaluated. These nanoparticles were coupled to ALP and entrapped in a sol-gel matrix to produce a biosensor that can serve as a screening platform to identify ALP inhibitors. The components of the biosensor were examined before and after sol-gel entrapment, and the biosensor was optimized to allow the determination of phosphate ion in aqueous medium.
9. Determination of stable cesium and strontium in rice samples by inductively coupled plasma mass spectrometry
Science.gov (United States)
Srinuttrakul, W.; Yoshida, S.
2017-06-01
For long-term radiation dose assessment models, food ingestion is one of the major exposure pathways to human. In general, the stable isotopes can serve as analogues of radioisotopes. In this study, rice samples were collected from 30 paddy fields in Si Sa Ket, Yasothon and Roi Et in the northeast of Thailand in November 2014. The concentrations of stable cesium (Cs-133) and strontium (Sr-88) in polished rice were determined by inductively coupled plasma mass spectrometry (ICP-MS). The standard reference material of rice flour (NIST 1568a) with spiked Cs and Sr was used to validate the analytical method. The concentration of Cs in polished rice from Si Sa Ket, Yasothon and Roi Et was 0.158 ± 0.167 mg kg-1, 0.090 ± 0.117 mg kg-1 and 0.054 ± 0.031 mg kg-1, respectively. The concentration of Sr in polished rice from Si Sa Ket, Yasothon and Roi Et was 0.351 ± 0.108 mg kg-1, 0.364 ± 0.215 mg kg-1 and 0.287 ± 0.102 mg kg-1, respectively. Comparison of the results with Japanese data before the Fukushima Di-ichi nuclear power plant accident showed that the concentrations of both Cs and Sr for Thai rice were higher than those for Japanese rice.
10. Determination of stable cesium and strontium in rice samples by inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Srinuttrakul, W; Yoshida, S
2017-01-01
For long-term radiation dose assessment models, food ingestion is one of the major exposure pathways to human. In general, the stable isotopes can serve as analogues of radioisotopes. In this study, rice samples were collected from 30 paddy fields in Si Sa Ket, Yasothon and Roi Et in the northeast of Thailand in November 2014. The concentrations of stable cesium (Cs-133) and strontium (Sr-88) in polished rice were determined by inductively coupled plasma mass spectrometry (ICP-MS). The standard reference material of rice flour (NIST 1568a) with spiked Cs and Sr was used to validate the analytical method. The concentration of Cs in polished rice from Si Sa Ket, Yasothon and Roi Et was 0.158 ± 0.167 mg kg -1 , 0.090 ± 0.117 mg kg -1 and 0.054 ± 0.031 mg kg -1 , respectively. The concentration of Sr in polished rice from Si Sa Ket, Yasothon and Roi Et was 0.351 ± 0.108 mg kg -1 , 0.364 ± 0.215 mg kg -1 and 0.287 ± 0.102 mg kg -1 , respectively. Comparison of the results with Japanese data before the Fukushima Di-ichi nuclear power plant accident showed that the concentrations of both Cs and Sr for Thai rice were higher than those for Japanese rice. (paper)
11. Determination of zinc stable isotopes in biological materials using isotope dilution inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Patterson, K.Y.; Veillon, Claude
1992-01-01
A method is described for using isotope dilution to determine both the amount of natural zinc and enriched isotopes of zinc in biological samples. Isotope dilution inductively coupled plasma mass spectrometry offers a way to quantify not only the natural zinc found in a sample but also the enriched isotope tracers of zinc. Accurate values for the enriched isotopes and natural zinc are obtained by adjusting the mass count rate data for measurable instrumental biases. Analytical interferences from the matrix are avoided by extracting the zinc from the sample matrix using diethylammonium diethyldithiocarbamate. The extraction technique separates the zinc from elements which form interfering molecular ions at the same nominal masses as the zinc isotopes. Accuracy of the method is verified using standard reference materials. The detection limit is 0.06 μg Zn per sample. Precision of the abundance ratios range from 0.3-0.8%. R.S.D. for natural zinc concentrations is about 200-600 μg g -1 . The accuracy and precision of the measurements make it possible to follow enriched isotopic tracers of zinc in biological samples in metabolic tracer studies. (author). 19 refs.; 1 fig., 4 tabs
12. Copper Determination in Gunshot Residue by Cyclic Voltammetric and Inductive Coupled Plasma-Optical Emission Spectroscopy
Directory of Open Access Journals (Sweden)
Mohd Hashim Nurul’Afiqah Hashimah
2016-01-01
Full Text Available Analysis of gunshot residue (GSR is a crucial evidences for a forensic analyst in the fastest way. GSR analysis insists a suitable method provides a relatively simple, rapid and precise information on the spot at the crime scene. Therefore, the analysis of Cu(II in GSR using cyclic voltammetry (CV on screen printed carbon electrode (SPCE is a better choice compared to previous alternative methods such as Inductive Coupled Plasma-Optical Emission Spectroscopy (ICP-OES those required a long time for analysis. SPCE is specially designed to handle with microvolumes of sample such as GSR sample. It gives advantages for identification of copper in GSR on-site preliminary test to prevent the sample loss on the process to be analyzed in the laboratory. SPCE was swabbed directly on the shooter’s arm immediately after firing and acetate buffer was dropped on SPCE before CV analysis. For ICP-OES analysis, cotton that had been soaked in 0.5 M nitric acid was swabbed on the shooter’s arm immediately after firing and kept in a tightly closed sampling tube. Gold coated SPCE that had been through nanoparticles modification exhibits excellent performance on voltammograms. The calibration was linear from 1 to 50 ppm of copper, the limit of detection for copper was 0.3 ppm and a relative standard deviation was 6.1 %. The method was successfully applied to the determination of copper in GSR. The Cu determination on SPCE was compared and validated by ICP-OES method with 94 % accuracy.
13. Determination of the quark coupling strength vertical bar V-ub vertical bar using baryonic decays
NARCIS (Netherlands)
Aaij, R.; Adeva, B.; Adinolfi, M.; Older, A. A.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Cartelle, P. Alvarez; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Gutierrez, O. Aquines; Archilli, F.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Battista, V.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Bel, L. J.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Onderwater, C. J. G.; Pellegrino, A.; Tolk, S.
In the Standard Model of particle physics, the strength of the couplings of the b quark to the u and c quarks, vertical bar V-ub vertical bar and vertical bar V-ub vertical bar, are governed by the coupling of the quarks to the Higgs boson. Using data from the LHCb experiment at the Large Hadron
14. Couples' Career Orientation, Gender Role Orientation, and Perceived Equity as Determinants of Marital Power.
Science.gov (United States)
Sexton, Christine S.; Perlman, Daniel S.
1989-01-01
Investigated influence of resource exchanges and gender role on marital power. Compared dual-career (N=50) and single-career (N=50) couples. Found two couple types did not differ in perceived power nor in self-reported strategies for influencing spouses. Found gender role orientation did not affect marital power. (Author/CM)
15. Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....
16. Analytical effective tensor for flow-through composites
Science.gov (United States)
Sviercoski, Rosangela De Fatima [Los Alamos, NM
2012-06-19
A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.
17. Electrical conductivity tensor of an irradiated metal
International Nuclear Information System (INIS)
Corciovei, A.; Dumitru, R.D.
1979-01-01
A method to calculate the electrical conductivity tensor of an irradiated metal is presented. The proposed method relies on the use of the Kubo formula, evaluated by a perturbation method. The one electron Hamiltonian is written as a sum of two terms: the Hamiltonian of the conduction electrons moving in a periodic lattice and the perturbation, namely, the scattering potential due to the irradiation defects of the ideal crystal. Then, the lowest order of the conductivity is determined by the lowest order of the Laplace transform of the current. An integral equation is written for this last quantity. (author)
18. Tensor ghosts in the inflationary cosmology
International Nuclear Information System (INIS)
Clunan, Tim; Sasaki, Misao
2010-01-01
Theories with curvature-squared terms in the action are known to contain ghost modes in general. However, if we regard curvature-squared terms as quantum corrections to the original theory, the emergence of ghosts may be simply due to the perturbative truncation of a full non-perturbative theory. If this is the case, there should be a way to live with ghosts. In this paper, we take the Euclidean path integral approach, in which ghost degrees of freedom can be, and are integrated out in the Euclideanized spacetime. We apply this procedure to Einstein gravity with a Weyl curvature-squared correction in the inflationary background. We find that the amplitude of tensor perturbations is modified by a term of O(α 2 H 2 ) where α 2 is a coupling constant in front of the Weyl-squared term and H is the Hubble parameter during inflation.
19. Diffusion tensor MR microscopy of tissues with low diffusional anisotropy.
Science.gov (United States)
Bajd, Franci; Mattea, Carlos; Stapf, Siegfried; Sersa, Igor
2016-06-01
Diffusion tensor imaging exploits preferential diffusional motion of water molecules residing within tissue compartments for assessment of tissue structural anisotropy. However, instrumentation and post-processing errors play an important role in determination of diffusion tensor elements. In the study, several experimental factors affecting accuracy of diffusion tensor determination were analyzed. Effects of signal-to-noise ratio and configuration of the applied diffusion-sensitizing gradients on fractional anisotropy bias were analyzed by means of numerical simulations. In addition, diffusion tensor magnetic resonance microscopy experiments were performed on a tap water phantom and bovine articular cartilage-on-bone samples to verify the simulation results. In both, the simulations and the experiments, the multivariate linear regression of the diffusion-tensor analysis yielded overestimated fractional anisotropy with low SNRs and with low numbers of applied diffusion-sensitizing gradients. An increase of the apparent fractional anisotropy due to unfavorable experimental conditions can be overcome by applying a larger number of diffusion sensitizing gradients with small values of the condition number of the transformation matrix. This is in particular relevant in magnetic resonance microscopy, where imaging gradients are high and the signal-to-noise ratio is low.
20. The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
1. Tensor calculus for physics a concise guide
CERN Document Server
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
2. Endomorphism Algebras of Tensor Powers of Modules for Quantum Groups
DEFF Research Database (Denmark)
Andersen, Therese Søby
We determine the ring structure of the endomorphism algebra of certain tensor powers of modules for the quantum group of sl2 in the case where the quantum parameter is allowed to be a root of unity. In this case there exists -- under a suitable localization of our ground ring -- a surjection from...... the group algebra of the braid group to the endomorphism algebra of any tensor power of the Weyl module with highest weight 2. We take a first step towards determining the kernel of this map by reformulating well-known results on the semisimplicity of the Birman-Murakami-Wenzl algebra in terms of the order...... of the quantum parameter. Before we arrive at these main results, we investigate the structure of the endomorphism algebra of the tensor square of any Weyl module....
3. Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry
International Nuclear Information System (INIS)
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.
4. Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry
International Nuclear Information System (INIS)
Krishnamoorthy, Sriram; Bernholdt, David E.; Pitzer, R.M.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.
5. Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
6. A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
7. Tensor-based spatiotemporal saliency detection
Science.gov (United States)
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
8. Anti-symmetric rank-two tensor matter field on superspace for NT=2
International Nuclear Information System (INIS)
Spalenza, Wesley; Ney, Wander G.; Helayel-Neto, J.A.
2004-01-01
In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N T =2 SUSY. We start off from the N T =2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables
9. Relativistic symmetries in the Hulthén scalar—vector—tensor interactions
International Nuclear Information System (INIS)
Hamzavi Majid; Rajabi Ali Akbar
2013-01-01
In the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation for scalar—vector—tensor Hulthén potentials are obtained with any arbitrary spin—orbit coupling number κ using the Pekeris approximation. The Hulthén tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov—Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given. (general)
10. Induced vacuum energy-momentum tensor in the background of a cosmic string
OpenAIRE
Sitenko, Yu. A.; Vlasii, N. D.
2011-01-01
A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional space-time. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the space-time curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decr...
11. The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging
NARCIS (Netherlands)
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
12. Determination of uranium from nuclear fuel in environmental samples using inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Boulyga, S.F.; Becker, J.S.
2000-01-01
As a result of the accident at the Chernobyl nuclear power plant (NPP) the environment was contaminated with spent nuclear fuel. The 236 U isotope was used in this study to monitor the spent uranium from nuclear fallout in soil samples collected in the vicinity of the Chernobyl NPP. A rapid and sensitive analytical procedure was developed for uranium isotopic ratio measurement in environmental samples based on inductively coupled plasma quadrupole mass spectrometry with a hexapole collision cell (HEX-ICP-QMS). The figures of merit of the HEX-ICP-QMS were studied with a plasma-shielded torch using different nebulizers (such as an ultrasonic nebulizer (USN) and Meinhard nebulizer) for solution introduction. A 238 U + ion intensity of up to 27000 MHz/ppm in HEX-ICP-QMS with USN was observed by introducing helium into the hexapole collision cell as the collision gas at a flow rate of 10 ml min -1 . The formation rate of uranium hydride ions UH + /U + of 2 x 10 -6 was obtained by using USN with a membrane desolvator. The limit of 236 U/ 238 U ratio determination in 10 μg 1 -1 uranium solution was 3 x 10 -7 corresponding to the detection limit for 236 U of 3 pg 1 -1 . The precision of uranium isotopic ratio measurements in 10 μg 1 -1 laboratory uranium isotopic standard solution was 0.13% ( 235 U/ 238 U) and 0.33% ( 236 U/ 238 U) using a Meinhard nebulizer and 0.45% ( 235 U/ 238 U) and 0.88% ( 236 U/ 238 U) using a USN. The isotopic composition of all investigated Chernobyl soil samples differed from those of natural uranium; i.e. in these samples the 236 U/ 238 U ratio ranged from 10 -5 to 10 -3 . (orig.)
13. Tucker Tensor analysis of Matern functions in spatial statistics
KAUST Repository
Litvinenko, Alexander
2018-03-09
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will allow us to consider much larger data sets or finer meshes. Covariance matrices are crucial in spatio-temporal statistical tasks, but are often very expensive to compute and store, especially in 3D. Therefore, we approximate covariance functions by cheap surrogates in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence. We prove the exponential convergence of the Tucker and canonical approximations in tensor rank parameters. Several statistical operations are performed in this low-rank tensor format, including evaluating the conditional covariance matrix, spatially averaged estimation variance, computing a quadratic form, determinant, trace, loglikelihood, inverse, and Cholesky decomposition of a large covariance matrix. Low-rank tensor approximations reduce the computing and storage costs essentially. For example, the storage cost is reduced from an exponential O(n^d) to a linear scaling O(drn), where d is the spatial dimension, n is the number of mesh points in one direction, and r is the tensor rank. Prerequisites for applicability of the proposed techniques are the assumptions that the data, locations, and measurements lie on a tensor (axes-parallel) grid and that the covariance function depends on a distance, ||x-y||.
14. Cosmological simulations using a static scalar-tensor theory
Energy Technology Data Exchange (ETDEWEB)
RodrIguez-Meza, M A [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Gonzalez-Morales, A X [Departamento Ingenierias, Universidad Iberoamericana, Prol. Paseo de la Reforma 880 Lomas de Santa Fe, Mexico D.F. Mexico (Mexico); Gabbasov, R F [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico); Cervantes-Cota, Jorge L [Depto. de Fisica, Instituto Nacional de Investigaciones Nucleares, Col. Escandon, Apdo. Postal 18-1027, 11801 Mexico D.F (Mexico)
2007-11-15
We present {lambda}CDM N-body cosmological simulations in the framework of of a static general scalar-tensor theory of gravity. Due to the influence of the non-minimally coupled scalar field, the gravitational potential is modified by a Yukawa type term, yielding a new structure formation dynamics. We present some preliminary results and, in particular, we compute the density and velocity profiles of the most massive group.
15. Compact stars in vector-tensor-Horndeski theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood; Myrzakulov, Kairat; Myrzakulov, Ratbay [Eurasian National University, Department of General and Theoretical Physics, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2017-01-15
In this paper, we will analyze a theory of modified gravity, in which the field content of general relativity will be increased to include a vector field. We will use the Horndeski formalism to non-minimally couple this vector field to the metric. As we will be using the Horndeski formalism, this theory will not contain Ostrogradsky ghost degree of freedom. We will analyze compact stars using this vector-tensor-Horndeski theory. (orig.)
16. Werner-Wheeler mass tensor for fusionlike configuration
International Nuclear Information System (INIS)
Gherghescu, R.A.; Poenaru, D.N.
2005-01-01
The Werner-Wheeler approach is used to calculate the components of the mass tensor for a binary configuration of two intersected spheroids. Four free coordinates form the deformation space: the small semiaxis of the projectile, the two semiaxis ratios of the spheroids, and the distance between centers. A correction term is also calculated, due to the center of mass motion. Final results are presented for the fusion channel 54 Cr+ 240 Pu, and all possible couplings are analyzed
17. Scalar-tensor theory of fourth-order gravity
International Nuclear Information System (INIS)
Accioly, A.J.; Goncalves, A.T.
1986-04-01
A scalar-tensor theory of fourth-order gravity is considered. Some cosmological consequences, due to the presence of the scalar field, as well as of metric derivatives higher than second order, are analysed. In particular, upperbpunds are obtained for the coupling constant α and for the scale factor of the universe, respectively. The discussion is restricted to Robertson-Walker universes. (Author) [pt
18. Efficient Tensor Strategy for Recommendation
Directory of Open Access Journals (Sweden)
Aboagye Emelia Opoku
2017-07-01
Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.
19. Spherical Tensor Calculus for Local Adaptive Filtering
Science.gov (United States)
Reisert, Marco; Burkhardt, Hans
In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.
20. Determination of nonlinear nanomechanical resonator-qubit coupling coefficient in a hybrid quantum system.
Science.gov (United States)
Geng, Qi; Zhu, Ka-Di
2016-07-10
We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.
1. Determination of the quark coupling strength $|V_{ub}|$ using baryonic decays
CERN Document Server
2015-01-01
In the Standard Model of particle physics, the strength of the couplings of the $b$ quark to the $u$ and $c$ quarks, $|V_{ub}|$ and $|V_{cb}|$, are governed by the coupling of the quarks to the Higgs boson. Using data from the LHCb experiment at the Large Hadron Collider, the probability for the $\\Lambda^0_b$ baryon to decay into the p \\mu^- \\overline{\ 2. Plexcitons: The Role of Oscillator Strengths and Spectral Widths in Determining Strong Coupling Energy Technology Data Exchange (ETDEWEB) Thomas, Reshmi [School; Thomas, Anoop [School; Pullanchery, Saranya [School; Joseph, Linta [School; Somasundaran, Sanoop Mambully [School; Swathi, Rotti Srinivasamurthy [School; Gray, Stephen K. [Center; Thomas, K. George [School 2018-01-05 Strong coupling interactions between plasmon and exciton-based excitations have been proposed to be useful in the design of optoelectronic systems. However, the role of various optical parameters dictating the plasmon-exciton (plexciton) interactions is less understood. Herein, we propose an inequality for achieving strong coupling between plasmons and excitons through appropriate variation of their oscillator strengths and spectral widths. These aspects are found to be consistent with experiments on two sets of free-standing plexcitonic systems obtained by (i) linking fluorescein isothiocyanate on Ag nanoparticles of varying sizes through silane coupling and (ii) electrostatic binding of cyanine dyes on polystyrenesulfonate-coated Au nanorods of varying aspect ratios. Being covalently linked on Ag nanoparticles, fluorescein isothiocyanate remains in monomeric state, and its high oscillator strength and narrow spectral width enable us to approach the strong coupling limit. In contrast, in the presence of polystyrenesulfonate, monomeric forms of cyanine dyes exist in equilibrium with their aggregates: Coupling is not observed for monomers and H-aggregates whose optical parameters are unfavorable. The large aggregation number, narrow spectral width, and extremely high oscillator strength of J-aggregates of cyanines permit effective delocalization of excitons along the linear assembly of chromophores, which in turn leads to efficient coupling with the plasmons. Further, the results obtained from experiments and theoretical models are jointly employed to describe the plexcitonic states, estimate the coupling strengths, and rationalize the dispersion curves. The experimental results and the theoretical analysis presented here portray a way forward to the rational design of plexcitonic systems attaining the strong coupling limits. 3. FI/SI on-line solvent extraction/back extraction preconcentration coupled to direct injection nebulization inductively coupled plasma mass spectrometry for determination of copper and lead DEFF Research Database (Denmark) Wang, Jianhua; Hansen, Elo Harald 2002-01-01 An automated sequential injection on-line preconcentration procedure for determination of trace levels of copper and lead via solvent extraction/back extraction coupled to ICP-MS is described. In citrate buffer of pH 3, neutral complexes between the analytes and the chelating reagent, ammonium...... loop, the content of which is subsequently introduced into the ICP-MS, via a direct injection high efficiency nebulizer (DIHEN), for quantification. Enrichment factors of 29.6 (Cu) and 23.3 (Pb), detection limits of 17 ng/l (Cu) and 11 ng/l (Pb), along with a sampling frequency of 13 s/h were obtained... 4. Determinations of the QCD strong coupling αsub(s) and the scale Λsub(QCD) International Nuclear Information System (INIS) Duke, D.W.; Roberts, R.G. 1984-08-01 The authors review determinations, via experiment of the strong coupling of QCD, αsub(s). In almost every case, the results are used of perturbative QCD to make the necessary extraction from data. These include scaling violations of deep inelastic scattering, e + e - annihilation experiments (including quarkonium decays) and lepton pair production. Finally estimates for Λ from lattice calculations are listed. (author) 5. Determination of uranium in urine - Measurement of isotope ratios and quantification by use of inductively coupled plasma mass spectrometry NARCIS (Netherlands) Krystek, Petra; Ritsema, R. 2002-01-01 For analysis of uranium in urine determination of the isotope ratio and quantification were investigated by high-resolution inductively coupled plasma mass spectrometry (HR ICP-MS). The instrument used (ThermoFinniganMAT ELEMENT2) is a single-collector MS and, therefore, a stable sample-introduction 6. Implementation of Fully Coupled Heat and Mass Transport Model to Determine Temperature and Moisture State at Elevated Temperatures DEFF Research Database (Denmark) Pecenko, R.; Hozjan, Tomaz; Svensson, Staffan 2014-01-01 The aim of this study is to present precise numerical formulation to determine temperature and moisture state of timber in the situation prior pyrolysis. The strong formulations needed for an accurate description of the physics are presented and discussed as well as their coupling terms. From... 7. Determination of the ratio of axial-vector-to-vector weak coupling constants for beta decay of triton CERN Document Server Akulov, Y A 2002-01-01 Data on the chemical shifts of half-lives for atomic and molecular tritium were used to determine the ratio of axial-vector-to-vector weak coupling constants for beta decay of triton (G sub A /G sub V) sub t = -1.2646 +- 0.0035 8. A new Weyl-like tensor of geometric origin Science.gov (United States) Vishwakarma, Ram Gopal 2018-04-01 A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor. 9. Conflicts Within the Family and Within the Couple as Contextual Factors in the Determinism of Male Sexual Dysfunction. Science.gov (United States) Boddi, Valentina; Fanni, Egidia; Castellini, Giovanni; Fisher, Alessandra Daphne; Corona, Giovanni; Maggi, Mario 2015-12-01 The deterioration of a couple's relationship has been previously associated with impairment in male sexual function. Besides a couple's dystonic relationship, other stressors can unfavorably influence dyadic intimacy. A largely neglected etiopathogenetic factor affecting couple sexuality is the frustration caused by conflicts within the family. To evaluate the possible associations between male sexual dysfunction (SD) and conflictual relationships within the couple or the family. A consecutive series of 3,975 men, attending the Outpatient Clinic for SD for the first time, was retrospectively studied. Conflicts within the family and within the couple were assessed using two standard questions: "Are there any conflicts at home," and "Do you have a difficult relationship with your partner?" respectively, rating 0 = normal relationships, 1 = occasional quarrels, and 2 = frequent quarrels or always. Several clinical, biochemical, and psychological (Middlesex Hospital Questionnaire) parameters were studied. Among the 3,975 patients studied, we observed a high prevalence of conflicts within the family and within the couple (32% vs. 21.2%). When compared with the rest of the sample, subjects reporting both type of conflicts showed a higher prevalence of psychiatric comorbidities. Hence, all data were adjusted for this parameter and for age. Family and couple conflicts were significantly associated with free floating anxiety, depression symptoms, and with a higher risk of subjective (self-reported) and objective (peak systolic velocity at the penile color Doppler ultrasound conflicts. This study indicates that the presence of often unexplored issues, like conflicts within the family or within the couple, can represent an important contextual factor in the determinism of male SD. © 2015 International Society for Sexual Medicine. 10. Renormalized energy-momentum tensor of λΦ4 theory in curved ... Indian Academy of Sciences (India) Divergenceless expression for the energy-momentum tensor of scalar field is obtained using the momentum cut-off regularization technique. We consider a scalar field with quartic self-coupling in a spatially flat (3+1)-dimensional Robertson–Walker space-time, having arbitrary mass and coupled to gravity. As special cases ... 11. Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain. Science.gov (United States) Li, Wei; Liu, Chunlei 2013-10-01 Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity. 12. Dilaton and second-rank tensor fields as supersymmetric compensators International Nuclear Information System (INIS) Nishino, Hitoshi; Rajpoot, Subhash 2007-01-01 We formulate a supersymmetric theory in which both a dilaton and a second-rank tensor play roles of compensators. The basic off-shell multiplets are a linear multiplet (B μν ,χ,φ) and a vector multiplet (A μ ,λ;C μνρ ), where φ and B μν are, respectively, a dilaton and a second-rank tensor. The third-rank tensor C μνρ in the vector multiplet is ''dual'' to the conventional D field with 0 on-shell or 1 off-shell degree of freedom. The dilaton φ is absorbed into one longitudinal component of A μ , making it massive. Initially, B μν has 1 on-shell or 3 off-shell degrees of freedom, but it is absorbed into the longitudinal components of C μνρ . Eventually, C μνρ with 0 on-shell or 1 off-shell degree of freedom acquires in total 1 on-shell or 4 off-shell degrees of freedom, turning into a propagating massive field. These basic multiplets are also coupled to chiral multiplets and a supersymmetric Dirac-Born-Infeld action. Some of these results are also reformulated in superspace. The proposed mechanism may well provide a solution to the long-standing puzzle of massless dilatons and second-rank tensors in supersymmetric models inspired by string theory 13. Tensor voting for robust color edge detection OpenAIRE Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec 2014-01-01 The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ... 14. The Physical Interpretation of the Lanczos Tensor OpenAIRE Roberts, Mark D. 1999-01-01 The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall... 15. Estimation of full moment tensors, including uncertainties, for earthquakes, volcanic events, and nuclear explosions Science.gov (United States) Alvizuri, Celso R. We present a catalog of full seismic moment tensors for 63 events from Uturuncu volcano in Bolivia. The events were recorded during 2011-2012 in the PLUTONS seismic array of 24 broadband stations. Most events had magnitudes between 0.5 and 2.0 and did not generate discernible surface waves; the largest event was Mw 2.8. For each event we computed the misfit between observed and synthetic waveforms, and we used first-motion polarity measurements to reduce the number of possible solutions. Each moment tensor solution was obtained using a grid search over the six-dimensional space of moment tensors. For each event we show the misfit function in eigenvalue space, represented by a lune. We identify three subsets of the catalog: (1) 6 isotropic events, (2) 5 tensional crack events, and (3) a swarm of 14 events southeast of the volcanic center that appear to be double couples. The occurrence of positively isotropic events is consistent with other published results from volcanic and geothermal regions. Several of these previous results, as well as our results, cannot be interpreted within the context of either an oblique opening crack or a crack-plus-double-couple model. Proper characterization of uncertainties for full moment tensors is critical for distinguishing among physical models of source processes. A seismic moment tensor is a 3x3 symmetric matrix that provides a compact representation of a seismic source. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six-dimensional space of moment tensors by generating synthetic waveforms for each moment tensor and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M0 for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M0, we first convert the misfit function to a probability function. The uncertainty, or 16. Determination of uranium from nuclear fuel in environmental samples using inductively coupled plasma mass spectrometry Energy Technology Data Exchange (ETDEWEB) Boulyga, S.F. [Forschungszentrum Juelich GmbH (Germany). Zentralabteilung fuer Chemische Analysen]|[Radiation Physics and Chemistry Problems Inst., Minsk (Belarus); Becker, J.S. [Forschungszentrum Juelich GmbH (Germany). Zentralabteilung fuer Chemische Analysen 2000-11-01 As a result of the accident at the Chernobyl nuclear power plant (NPP) the environment was contaminated with spent nuclear fuel. The {sup 236}U isotope was used in this study to monitor the spent uranium from nuclear fallout in soil samples collected in the vicinity of the Chernobyl NPP. A rapid and sensitive analytical procedure was developed for uranium isotopic ratio measurement in environmental samples based on inductively coupled plasma quadrupole mass spectrometry with a hexapole collision cell (HEX-ICP-QMS). The figures of merit of the HEX-ICP-QMS were studied with a plasma-shielded torch using different nebulizers (such as an ultrasonic nebulizer (USN) and Meinhard nebulizer) for solution introduction. A {sup 238}U{sup +} ion intensity of up to 27000 MHz/ppm in HEX-ICP-QMS with USN was observed by introducing helium into the hexapole collision cell as the collision gas at a flow rate of 10 ml min{sup -1}. The formation rate of uranium hydride ions UH{sup +}/U{sup +} of 2 x 10{sup -6} was obtained by using USN with a membrane desolvator. The limit of {sup 236}U/{sup 238}U ratio determination in 10 {mu}g 1{sup -1} uranium solution was 3 x 10{sup -7} corresponding to the detection limit for {sup 236}U of 3 pg 1{sup -1}. The precision of uranium isotopic ratio measurements in 10 {mu}g 1{sup -1} laboratory uranium isotopic standard solution was 0.13% ({sup 235}U/{sup 238}U) and 0.33% ({sup 236}U/{sup 238}U) using a Meinhard nebulizer and 0.45% ({sup 235}U/{sup 238}U) and 0.88% ({sup 236}U/{sup 238}U) using a USN. The isotopic composition of all investigated Chernobyl soil samples differed from those of natural uranium; i.e. in these samples the {sup 236}U/{sup 238}U ratio ranged from 10{sup -5} to 10{sup -3}. (orig.) 17. Torsion tensor and covector in a unified field theory International Nuclear Information System (INIS) Chernikov, N.A. 1976-01-01 The Einstein unified field theory is used to solve a tensor equation to provide the unambiguous definition of affine connectedness. In the process of solving the Einstein equation limitations imposed by symmetry on the tensor and the torsion covector as well as on affine connectedness are elucidated. It is demonstrated that in a symmetric case the connectedness is unambiguously determined by the Einstein equation. By means of the Riemann geometry a formula for the torsion covector is derived. The equivalence of Einstein equations to those of the nonlinear Born-Infeld electrodynamics is proved 18. The 1/ N Expansion of Tensor Models Beyond Perturbation Theory Science.gov (United States) Gurau, Razvan 2014-09-01 We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models. 19. Robust estimation of adaptive tensors of curvature by tensor voting. Science.gov (United States) Tong, Wai-Shun; Tang, Chi-Keung 2005-03-01 Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise. 20. Antisymmetric tensor generalizations of affine vector fields. Science.gov (United States) Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro 2016-02-01 Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes. 1. Scattering tensors and optical transitions in Si and Ge CSIR Research Space (South Africa) Kunert, HW 2012-08-01 Full Text Available and L high symmetry points and the highest maximum of the valence band (VB) in the Brillouin zone of Oh7 space group symmetry are determined. The elements of El-Ph scattering tensors are linear combinations of the Clebsch-Gordon coefficients (CGC... 2. ULTRASONIC NEBULIZATION AND ARSENIC VALENCE STATE CONSIDERATIONS PRIOR TO DETERMINATION VIA INDUCTIVELY COUPLED PLASMA MASS SPECTROMETRY Science.gov (United States) An ultrasonic nebulizer (USN) was utilized as a sample introduction device for an inductively coupled plasma mass spectrometer in an attempt to increase the sensitivity for As. The USN produced a valence state response difference for As. The As response was suppressed approximate... 3. Determination of Arsenic in Sinus Wash and Tap Water by Inductively Coupled Plasma-Mass Spectrometry Science.gov (United States) Donnell, Anna M.; Nahan, Keaton; Holloway, Dawone; Vonderheide, Anne P. 2016-01-01 Arsenic is a toxic element to which humans are primarily exposed through food and water; it occurs as a result of human activities and naturally from the earth's crust. An experiment was developed for a senior level analytical laboratory utilizing an Inductively Coupled Plasma-Mass Spectrometer (ICP-MS) for the analysis of arsenic in household… 4. Residual dipolar couplings : a new technique for structure determination of proteins in solution NARCIS (Netherlands) van Lune, Frouktje Sapke 2004-01-01 The aim of the work described in this thesis was to investigate how residual dipolar couplings can be used to resolve or refine the three-dimensional structure of one of the proteins of the phosphoenol-pyruvate phosphotransferase system (PTS), the main transport system for carbohydrates in 5. Determination of tetrabromobisphenol-A/S and their main derivatives in water samples by high performance liquid chromatography coupled with inductively coupled plasma tandem mass spectrometry. Science.gov (United States) Liu, Lihong; Liu, Aifeng; Zhang, Qinghua; Shi, Jianbo; He, Bin; Yun, Zhaojun; Jiang, Guibin 2017-05-12 As the most widely used brominated flame retardants (BFRs), Tetrabromobisphenol-A (TBBPA) as well as its alternative Tetrabromobisphenol-S (TBBPS) and their derivatives have raised wide concerns due to their adverse effects on human health and hence the sensitive detection of those BFRs was urgently needed. Herein, a novel analytical method based on high-performance liquid chromatography (HPLC) coupled with inductively coupled plasma tandem mass spectrometry (ICP-MS/MS) has been developed for the determination of TBBPA/S and their derivatives, including TBBPA-bis(2-hydroxyethyl ether) (TBBPA-BHEE), TBBPA-bis(allylether) (TBBPA-BAE), TBBPA-bis(glycidyl ether) (TBBPA-BGE), TBBPA-bis(2,3-dibromopropyl ether) (TBBPA-BDBPE) and TBBPS-bis(2,3-dibromopropyl ether) (TBBPS-BDBPE) in water samples. After optimization, the TBBPA/S and their derivatives, especially the TBBPA-BAE and TBBPA-BDBPE were simultaneously and sensitively quantified by determination of bromine (m/z=79) by using the ICP-MS. The instrument limits of detection (LODs) for the TBBPA, TBBPA-BHEE, TBBPA-BGE, TBBPA-BAE, TBBPA-BDBPE, TBBPS and TBBPS-BDBPE were determined to be 0.12, 0.14, 0.19, 0.14, 0.12, 0.17 and 0.13μgL -1 , respectively, which was close to or much better than the reported methods. The relative standard deviations (RSDs, n=5) of peak area and retention time were better than 2.2% and 0.2% for intra-day analysis, indicating good repeatability and high precision. The proposed method had been successfully applied for the analysis of TBBPA/S and their derivatives in water samples with satisfactory recoveries (67.7%-113%). Copyright © 2017 Elsevier B.V. All rights reserved. 6. Extended vector-tensor theories Energy Technology Data Exchange (ETDEWEB) Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan) 2017-01-01 Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations. 7. Correlating the P-31 NMR Chemical Shielding Tensor and the (2)J(P,C) Spin-Spin Coupling Constants with Torsion Angles zeta and alpha in the Backbone of Nucleic Acids Czech Academy of Sciences Publication Activity Database Benda, Ladislav; Sochorová Vokáčová, Zuzana; Straka, Michal; Sychrovský, Vladimír 2012-01-01 Roč. 116, č. 12 (2012), s. 3823-3833 ISSN 1520-6106 R&D Projects: GA ČR GAP205/10/0228; GA ČR GPP208/10/P398; GA ČR GA203/09/2037 Institutional research plan: CEZ:AV0Z40550506 Keywords : nucleic acids * phosphorus NMR * NMR calculations * cross-correlated relaxation * spin–spin coupling constants Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.607, year: 2012 8. On-line preconcentration and determination of chromium in parenteral solutions by inductively coupled plasma optical emission spectrometry International Nuclear Information System (INIS) Gil, R.A.; Cerutti, S.; Gasquez, J.A.; Olsina, R.A.; Martinez, L.D. 2005-01-01 A method for the preconcentration and speciation of chromium was developed. On-line preconcentration and determination were obtained using inductively coupled plasma optical emission spectrometry (ICP-OES) coupled with flow injection. To determinate the chromium (III) present in parenteral solutions, chromium was retained on activated carbon at pH 5.0. On the other hand, a step of reduction was necessary in order to determine total chromium content. The Cr(VI) concentration was then determined by difference between the total chromium concentration and that of Cr(III). A sensitivity enrichment factor of 70-fold was obtained with respect to the chromium determination by ICP-OES without preconcentration. The detection limit for the preconcentration of 25 ml of sample was 29 ng l -1 . The precision for the 10 replicate determinations at the 5 μg l -1 Cr level was 2.3% relative standard deviation, calculated with the peak heights. The calibration graph using the preconcentration method for chromium species was linear with a correlation coefficient of 0.9995 at levels near the detection limits up to at least 60 μg l -1 . The method can be applied to the determination and speciation of chromium in parenteral solutions 9. Extraction inductively coupled plasma-optical emission spectrometry (ICP-OES). Determination of traces of phosphorus in tungsten International Nuclear Information System (INIS) Bauer, G.; Wegscheider, W.; Mueller, K. 1989-01-01 A method for the separation and preconcentration of traces of phosphorus from tungsten was developed. Solid phase extraction of the phosphovanadomolybdate complex performed on a micro-column was applied. Phosphorus was determined by optical emission spectroscopy (OES) with inductively coupled plasma (ICP) excitation. A limit of detection of 0,4 μg/g P with respect to the solid phase is obtained. By directly coupling the extraction/elution step to the ICP instrument a detection limit of 0,06 μg/g P in W was achieved. Besides, the complexity of spectral evaluation in ICP-OES determinations of traces in spectralline-rich matrices is discussed. (Authors) 10. Ab initio determination of effective electron-phonon coupling factor in copper Science.gov (United States) Ji, Pengfei; Zhang, Yuwen 2016-04-01 The electron temperature Te dependent electron density of states g (ε), Fermi-Dirac distribution f (ε), and electron-phonon spectral function α2 F (Ω) are computed as prerequisites before achieving effective electron-phonon coupling factor Ge-ph. The obtained Ge-ph is implemented into a molecular dynamics (MD) and two-temperature model (TTM) coupled simulation of femtosecond laser heating. By monitoring temperature evolutions of electron and lattice subsystems, the result utilizing Ge-ph from ab initio calculation shows a faster decrease of Te and increase of Tl than those using Ge-ph from phenomenological treatment. The approach of calculating Ge-ph and its implementation into MD-TTM simulation is applicable to other metals. 11. Cα chemical shift tensors in helical peptides by dipolar-modulated chemical shift recoupling NMR International Nuclear Information System (INIS) Yao Xiaolan; Yamaguchi, Satoru; Hong Mei 2002-01-01 The Cα chemical shift tensors of proteins contain information on the backbone conformation. We have determined the magnitude and orientation of the Cα chemical shift tensors of two peptides with α-helical torsion angles: the Ala residue in G*AL (φ=-65.7 deg., ψ=-40 deg.), and the Val residue in GG*V (φ=-81.5 deg., ψ=-50.7 deg.). The magnitude of the tensors was determined from quasi-static powder patterns recoupled under magic-angle spinning, while the orientation of the tensors was extracted from Cα-Hα and Cα-N dipolar modulated powder patterns. The helical Ala Cα chemical shift tensor has a span of 36 ppm and an asymmetry parameter of 0.89. Its σ 11 axis is 116 deg. ± 5 deg. from the Cα-Hα bond while the σ 22 axis is 40 deg. ± 5 deg. from the Cα-N bond. The Val tensor has an anisotropic span of 25 ppm and an asymmetry parameter of 0.33, both much smaller than the values for β-sheet Val found recently (Yao and Hong, 2002). The Val σ 33 axis is tilted by 115 deg. ± 5 deg. from the Cα-Hα bond and 98 deg. ± 5 deg. from the Cα-N bond. These represent the first completely experimentally determined Cα chemical shift tensors of helical peptides. Using an icosahedral representation, we compared the experimental chemical shift tensors with quantum chemical calculations and found overall good agreement. These solid-state chemical shift tensors confirm the observation from cross-correlated relaxation experiments that the projection of the Cα chemical shift tensor onto the Cα-Hα bond is much smaller in α-helices than in β-sheets 12. Sparse alignment for robust tensor learning. Science.gov (United States) Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming 2014-10-01 Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods. 13. Shape anisotropy: tensor distance to anisotropy measure Science.gov (United States) Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S. 2011-03-01 Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy. 14. Transposes, L-Eigenvalues and Invariants of Third Order Tensors OpenAIRE Qi, Liqun 2017-01-01 Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t... 15. Determination of trace elements in petroleum products by inductively coupled plasma techniques: A critical review International Nuclear Information System (INIS) Sánchez, Raquel; Todolí, José Luis; Lienemann, Charles-Philippe; Mermet, Jean-Michel 2013-01-01 The fundamentals, applications and latter developments of petroleum products analysis through inductively coupled plasma optical emission spectrometry (ICP-OES) and mass spectrometry (ICP-MS) are revisited in the present bibliographic survey. Sample preparation procedures for the direct analysis of fuels by using liquid sample introduction systems are critically reviewed and compared. The most employed methods are sample dilution, emulsion or micro-emulsion preparation and sample decomposition. The first one is the most widely employed due to its simplicity. Once the sample has been prepared, an organic matrix is usually present. The performance of the sample introduction system (i.e., nebulizer and spray chamber) depends strongly upon the nature and properties of the solution finally obtained. Many different devices have been assayed and the obtained results are shown. Additionally, samples can be introduced into the plasma by using an electrothermal vaporization (ETV) device or a laser ablation system (LA). The recent results published in the literature showing the feasibility, advantages and drawbacks of latter alternatives are also described. Therefore, the main goal of the review is the discussion of the different approaches developed for the analysis of crude oil and its derivates by inductively coupled plasma (ICP) techniques. - Highlights: • Analysis of petroleum products by inductively coupled plasma techniques is revisited. • Fundamental studies are included together with reports dealing with applications. • Conventional and non-conventional sample introduction methods are considered. • Sample preparation methods are critically compared and described 16. Gradients estimation from random points with volumetric tensor in turbulence Science.gov (United States) Watanabe, Tomoaki; Nagata, Koji 2017-12-01 We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales. 17. Validation of diffusion tensor MRI measurements of cardiac microstructure with structure tensor synchrotron radiation imaging. Science.gov (United States) Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E 2017-03-10 Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical 18. Polarized Neutron Diffraction as a Tool for Mapping Molecular Magnetic Anisotropy: Local Susceptibility Tensors in Co(II) Complexes. Science.gov (United States) Ridier, Karl; Gillon, Béatrice; Gukasov, Arsen; Chaboussant, Grégory; Cousson, Alain; Luneau, Dominique; Borta, Ana; Jacquot, Jean-François; Checa, Ruben; Chiba, Yukako; Sakiyama, Hiroshi; Mikuriya, Masahiro 2016-01-11 Polarized neutron diffraction (PND) experiments were carried out at low temperature to characterize with high precision the local magnetic anisotropy in two paramagnetic high-spin cobalt(II) complexes, namely [Co(II) (dmf)6 ](BPh4 )2 (1) and [Co(II) 2 (sym-hmp)2 ](BPh4 )2 (2), in which dmf=N,N-dimethylformamide; sym-hmp=2,6-bis[(2-hydroxyethyl)methylaminomethyl]-4-methylphenolate, and BPh4 (-) =tetraphenylborate. This allowed a unique and direct determination of the local magnetic susceptibility tensor on each individual Co(II) site. In compound 1, this approach reveals the correlation between the single-ion easy magnetization direction and a trigonal elongation axis of the Co(II) coordination octahedron. In exchange-coupled dimer 2, the determination of the individual Co(II) magnetic susceptibility tensors provides a clear outlook of how the local magnetic properties on both Co(II) sites deviate from the single-ion behavior because of antiferromagnetic exchange coupling. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 19. Determination of low cadmium concentrations in wine by on-line preconcentration in a knotted reactor coupled to an inductively coupled plasma optical emission spectrometer with ultrasonic nebulization Energy Technology Data Exchange (ETDEWEB) Lara, R.F. [Inst. de Investigaciones Mineras, Universidad Nacional de San Juan (Argentina); Wuilloud, R.G.; Salonia, J.A. [Dept. of Analytical Chemistry, National University of San Luis (Argentina); Olsina, R.A.; Martinez, L.D. [Dept. of Analytical Chemistry, National University of San Luis (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET) (Argentina) 2001-12-01 An on-line cadmium preconcentration and determination system implemented with inductively coupled plasma optical emission spectrometry (ICP-OES) associated to flow injection (FI) with ultrasonic nebulization system (USN) was studied. The cadmium was retained as the cadmium-2-(5-bromo-2-pyridylazo)-5-diethylaminophenol, Cd-(5-Br-PADAP), complex, at pH 9.5. The cadmium complex was removed from the knotted reactor (KR) with 3.0 mol/L nitric acid. A total enhancement factor of 216 was obtained with respect to ICP-OES using pneumatic nebulization (12 for USN and 18 for KR) with a preconcentration time of 60 s. The value of the detection limit for the preconcentration of 5 mL of sample solution was 5 ng/L. The precision for 10 replicate determinations at the 5 {mu}g/L Cd level was 2.9% relative standard deviation (RSD), calculated from the peak heights obtained. The calibration graph using the preconcentration system for cadmium was linear with a correlation coefficient of 0.9998 at levels near the detection limits up to at least 1000 {mu}g/L. The method was successfully applied to the determination of cadmium in wine samples. (orig.) 20. Unified cosmology with scalar-tensor theory of gravity Energy Technology Data Exchange (ETDEWEB) Tajahmad, Behzad [Faculty of Physics, University of Tabriz, Tabriz (Iran, Islamic Republic of); Sanyal, Abhik Kumar [Jangipur College, Department of Physics, Murshidabad (India) 2017-04-15 Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.) 1. Unified cosmology with scalar-tensor theory of gravity International Nuclear Information System (INIS) Tajahmad, Behzad; Sanyal, Abhik Kumar 2017-01-01 Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energy-momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized. (orig.) 2. Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings. Science.gov (United States) Iwasaki, Tohru; Furukawa, Tetsuo 2016-05-01 In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved. 3. A brief summary on formalizing parallel tensor distributions redistributions and algorithm derivations. Energy Technology Data Exchange (ETDEWEB) Schatz, Martin D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kolda, Tamara G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); van de Geijn, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States) 2015-09-01 Large-scale datasets in computational chemistry typically require distributed-memory parallel methods to perform a special operation known as tensor contraction. Tensors are multidimensional arrays, and a tensor contraction is akin to matrix multiplication with special types of permutations. Creating an efficient algorithm and optimized im- plementation in this domain is complex, tedious, and error-prone. To address this, we develop a notation to express data distributions so that we can apply use automated methods to find optimized implementations for tensor contractions. We consider the spin-adapted coupled cluster singles and doubles method from computational chemistry and use our methodology to produce an efficient implementation. Experiments per- formed on the IBM Blue Gene/Q and Cray XC30 demonstrate impact both improved performance and reduced memory consumption. 4. Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids Science.gov (United States) Abdoli-Arani, A.; Ramezani-Arani, R. 2012-11-01 The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented. 5. Parameterized Post-Newtonian Expansion of Scalar-Vector-Tensor Theory of Gravity International Nuclear Information System (INIS) Arianto; Zen, Freddy P.; Gunara, Bobby E.; Hartanto, Andreas 2010-01-01 We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in scalar-vector-tensor theory of gravity. In the calculation we restrict ourselves to the first post Newtonian. The parameterized post Newtonian (PPN) parameters are determined by expanding the modified field equations in the metric perturbation. Then, we compare the solution to the PPN formalism in first PN approximation proposed by Will and Nordtvedt and read of the coefficients (the PPN parameters) of post Newtonian potentials of the theory. We find that the values of γ PPN and β PPN are the same as in General Relativity but the coupling functions β 1 , β 2 , and β 3 are the effect of the preferred frame. 6. New results for algebraic tensor reduction of Feynman integrals Energy Technology Data Exchange (ETDEWEB) Fleischer, Jochem [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center 2012-02-15 We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2{epsilon}. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.) 7. New results for algebraic tensor reduction of Feynman integrals International Nuclear Information System (INIS) Fleischer, Jochem; Yundin, Valery 2012-02-01 We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2ε. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.) 8. Seamless warping of diffusion tensor fields DEFF Research Database (Denmark) Xu, Dongrong; Hao, Xuejun; Bansal, Ravi 2008-01-01 To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT... 9. Trilinear self couplings of vector bosons and their determination in e+e-→W+W- International Nuclear Information System (INIS) Gounaris, G.; Kneur, J.L.; Schildknecht, D.; Layssac, J.; Moultaka, G.; Renard, F.M. 1992-01-01 The constraints on the γW + W - and Z 0 W + W - couplings are summarized. They essentially follow from various symmetry requirements which are weaker than the ones embodied in the SU(2) L *U(1) Y theory. The theoretical considerations lead to a well-defined systematic procedure for the analysis of future data. The helicity amplitudes for e + e - →W + W - are discussed and, in particular, the high-energy limit of s>>4M W 2 , relevant at an energy of 500 GeV, is analyzed. (K.A.) 18 refs., 4 figs., 4 tabs 10. SAID analysis of meson photoproduction: Determination of neutron and proton EM couplings Directory of Open Access Journals (Sweden) Strakovsky Igor 2014-06-01 Full Text Available We present an overview of the GW SAID group effort to analyze on new pion photoproduction on both proton- and neutron-targets. The main database contribution came from the recent CLAS and MAMI unpolarized and polarized measurements. The differential cross section for the processes γn → π−p was extracted from new measurements accounting for Fermi motion effects in the impulse approximation (IA as well as NN- and πN effects beyond the IA. The electromagnetic coupling results are compared to other recent studies. 11. The presentation of the nonabelian tensor square of a Bieberbach group of dimension five with dihedral point group Science.gov (United States) Fauzi, Wan Nor Farhana Wan Mohd; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Ting, Tan Yee; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat 2014-12-01 One of the homological functors of a group, is the nonabelian tensor square. It is important in the determination of the other homological functors of a group. In order to compute the nonabelian tensor square, we need to get its independent generators and its presentation. In this paper, we present the calculation of getting the presentation of the nonabelian tensor square of the group. The presentation is computed based on its independent generators by using the polycyclic method. 12. On improving the efficiency of tensor voting OpenAIRE Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim 2011-01-01 This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v... 13. Should I use TensorFlow OpenAIRE Schrimpf, Martin 2016-01-01 Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,... 14. Efficient Low Rank Tensor Ring Completion OpenAIRE Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin 2017-01-01 Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana... 15. Composite antisymmetric tensor bosons in a four-fermion interaction model International Nuclear Information System (INIS) Dmitrasinovic, V. 2000-01-01 We discuss the phenomenological consequences of the U A (1) symmetry-breaking two-flavour four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the 'duality' symmetry of this interaction. Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (a) Four antisymmetric tensor and four AS pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (b) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (c) The mixing of massive AS tensor fields with vector fields leads to two sets of spin-1 states. The second set of spin-1 mesons is heavy and has not been observed. Moreover, at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the AS tensor interaction. The tachyonic state also shows up as a pole in the space-like region of the electromagnetic form factors. (d) The mixing of axial-vector fields with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift is negligible. (e) The AS tensor version of the Veneziano-Witten U A (1) symmetry-breaking interaction does not lead to tachyons, or any AS tensor field propagation to leading order in N C . (author) 16. The 1/ N Expansion of Tensor Models with Two Symmetric Tensors Science.gov (United States) Gurau, Razvan 2018-06-01 It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs. 17. AGREEMENT BETWEEN THE WHITE MATTER CONNECTIVITY BASED ON THE TENSOR-BASED MORPHOMETRY AND THE VOLUMETRIC WHITE MATTER PARCELLATIONS BASED ON DIFFUSION TENSOR IMAGING OpenAIRE Kim, Seung-Goo; Lee, Hyekyoung; Chung, Moo K.; Hanson, Jamie L.; Avants, Brian B.; Gee, James C.; Davidson, Richard J.; Pollak, Seth D. 2012-01-01 We are interested in investigating white matter connectivity using a novel computational framework that does not use diffusion tensor imaging (DTI) but only uses T1-weighted magnetic resonance imaging. The proposed method relies on correlating Jacobian determinants across different voxels based on the tensor-based morphometry (TBM) framework. In this paper, we show agreement between the TBM-based white matter connectivity and the DTI-based white matter atlas. As an application, altered white ... 18. Determination of coupled-lattice properties using turn-by-turn data International Nuclear Information System (INIS) Bourianoff, G.; Hunt, S.; Mathieson, D.; Pilat, F.; Talman, R.; Morpurgo, G. 1992-01-01 A formalism for extracting coupled betatron parameters from multiturn, shock excited, beam position monitor data is described. The most important results are nonperturbative in that they do not rely on the underlying ideal lattice model. Except for damping, which is assumed to be exponential and small enough to be removed empirically, the description is symplectic. As well as simplifying the description, this leads to self-consistency checks that are applied to the data. The most important of these is a ''magic ratio'' of Fourier coefficients that is required to be a lattice invariant, the same at every beam position monitor. All formulas are applied to both real and simulated data. The real data were acquired June 1992 at LEP as part of decoupling studies, using the LEP beam orbit measurement system. Simulated data, obtained by numerical tracking (TEAPOT) in the same (except for unknown errors) lattice, agrees well with real data when subjected to identical analysis. For both datasets, deviations between extracted and design parameters and deviations from self-consistency can be accounted for by noise and signal-processing limitations. This investigation demonstrates that the LEP beam position system yields reliable local coupling measurements. It can be conservatively assumed that systems of similar design at the SSC and LHC will provide the measurements needed for local decoupling 19. Loss of incoherence and determination of coupling constants in quantum gravity International Nuclear Information System (INIS) Giddings, S.B.; Strominger, A. 1988-01-01 The wave function of an interacting 'family' of one large 'parent' and many Planck-sized 'baby' universes is computed in a semiclassical approximation using an adaptation of Hartle-Hawking initial conditions. A recently discovered gravitational instanton which exists for general relativity coupled to axions is employed. The outcome of a single experiment in the parent universe is in general described by a mixed state, even if the initial state is pure. However, a sequence of measurements rapidly collapses the wave function of the family of universes into one of an infinite number of 'coherent' states for which quantum incoherence is not observed in the parent universe. This provides a concrete illustration of an unexpected phenomena whose existence has been argued for on quite general grounds by Coleman: Quantum incoherence due to information loss to baby universes is not experimentally observable. We further argue that all coupling constants governing dynamics in the parent universe depend on the parameters describing the particular coherent state into which the family wave function collapses. In particular, generically terms that violate any global symmetries will be induced in the effective action for the parent universe. These last results have much broader applicability than our specific model. (orig.) 20. Determination of coupled-lattice properties using turn-by-turn data International Nuclear Information System (INIS) Bourianoff, G.; Hunt, S.; Mathieson, D. 1992-12-01 A formalism for extracting coupled betatron parameters from multiturn, shock excited, beam position monitor data is described. The most important results are nonperturbative in that they do not rely on the underlying ideal lattice model. Except for damping, which is assumed to be exponential and small enough to be removed empirically, the description is symplectic. As well as simplifying the description, this leads to self-consistency checks that are applied to the data. The most important of these is a open-quotes magic ratioclose quotes of Fourier coefficients that is required to be a lattice invariant, the same at every beam position monitor. All formulas are applied to both real and simulated data. The real data was acquired June, 1992 at LEP as part of decoupling studies, using the LEP beam orbit measurement system. Simulated data, obtained by numerical tracking (TEAPOT) in the same (except for unknown errors) lattice, agrees well with real data when subjected to identical analysis. For both datasets, deviations between extracted and design parameters and deviations from self-consistency can be accounted for by noise and signal processing limitations. This investigation demonstrates that the LEP beam position system yields reliable local coupling measurements. It can be conservatively assumed that systems of similar design at the SSC and LHC will provide the measurements needed for local decoupling 1. Study of the 23Na EFG (Electrostatic Field Gradient) tensor on single crystals of Na2S.9H2O by wideline NMR International Nuclear Information System (INIS) Miksche, G. 1982-01-01 The quadrupole coupling constant |e 2 qQ/n| if 23 Na has been determined by measuring single crystals of Na 2 S.9H 2 O at room temperature. A value of 687.5 +- 1.2 kHz was found. The asymmetry parameter eta = (qsub(x'x') - qsub(y'y')) / qsub(z'z') of the efg-tensor is zero, there is axial symmetry. The principle axis of the efg-tensor runs parallel to the main crystallographic axis c, the value of the main component of the efg-tensor in c-direction is 171.875 +- 0.6 kHz. The longitudinal relaxation time T 1 has been evaluated as 1.8 s. On this account, the mean distance between two Na-atoms has been determined by measuring the splitting of the central line due to dipole-dipole interaction. The Na-Na distance was found with 0.36 +- 0.007 nm. This value is in good agreement with results from neutron diffraction studies. It was not possible to determine direction and length of hydrogen bonds by NMR-results. A method of growing single crystals of Na 2 S.9H 2 O of demanded size and purity has been described. Constructional details and technical data of a self-made wideline-NMR-spectrometer are added in an appendix. (Author) 2. Dictionary-Based Tensor Canonical Polyadic Decomposition Science.gov (United States) Cohen, Jeremy Emile; Gillis, Nicolas 2018-04-01 To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images. 3. Bayesian regularization of diffusion tensor images DEFF Research Database (Denmark) Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif 2007-01-01 Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing... 4. A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY OpenAIRE SASAKURA, NAOKI 2010-01-01 Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config... 5. Full moment tensor retrieval and fluid dynamics in volcanic areas: The case of phlegraean field (south Italy) International Nuclear Information System (INIS) Campus, P.; Cespuglio, G. 1994-04-01 When studying seismicity in volcanic areas it is appropriate to treat the seismic source in a form a priori not restricted to a double couple, since its mechanism may reflect not only small scale tectonics but also fluid dynamics. The monitoring of fluid dynamics can be therefore attempted from the retrieval of the rupture processes. It is not possible to use standard methods, based on the distribution of polarities of first arrivals to determine the non double-couple components of the seismic source. The new method presented here is based on the wave form inversion of the dominant part of the seismograms, where the signal to noise ratio is very large and allows the inversion of the full seismic moment tensor. The results of a pilot study in the Phlegraean Fields (South Italy) are presented. 13 refs, 10 figs, 4 tabs 6. The tensor network theory library Science.gov (United States) Al-Assam, S.; Clark, S. R.; Jaksch, D. 2017-09-01 In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org. 7. Dirac tensor with heavy photon Energy Technology Data Exchange (ETDEWEB) Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik 2012-01-15 For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.) 8. Principles and determinants of G-protein coupling by the rhodopsin-like thyrotropin receptor. Directory of Open Access Journals (Sweden) Gunnar Kleinau Full Text Available In this study we wanted to gain insights into selectivity mechanisms between G-protein-coupled receptors (GPCR and different subtypes of G-proteins. The thyrotropin receptor (TSHR binds G-proteins promiscuously and activates both Gs (cAMP and Gq (IP. Our goal was to dissect selectivity patterns for both pathways in the intracellular region of this receptor. We were particularly interested in the participation of poorly investigated receptor parts.We systematically investigated the amino acids of intracellular loop (ICL 1 and helix 8 using site-directed mutagenesis alongside characterization of cAMP and IP accumulation. This approach was guided by a homology model of activated TSHR in complex with heterotrimeric Gq, using the X-ray structure of opsin with a bound G-protein peptide as a structural template.We provide evidence that ICL1 is significantly involved in G-protein activation and our model suggests potential interactions with subunits G alpha as well as G betagamma. Several amino acid substitutions impaired both IP and cAMP accumulation. Moreover, we found a few residues in ICL1 (L440, T441, H443 and helix 8 (R687 that are sensitive for Gq but not for Gs activation. Conversely, not even one residue was found that selectively affects cAMP accumulation only. Together with our previous mutagenesis data on ICL2 and ICL3 we provide here the first systematically completed map of potential interfaces between TSHR and heterotrimeric G-protein. The TSHR/Gq-heterotrimer complex is characterized by more selective interactions than the TSHR/Gs complex. In fact the receptor interface for binding Gs is a subset of that for Gq and we postulate that this may be true for other GPCRs coupling these G-proteins. Our findings support that G-protein coupling and preference is dominated by specific structural features at the intracellular region of the activated GPCR but is completed by additional complementary recognition patterns between receptor and G 9. Principles and determinants of G-protein coupling by the rhodopsin-like thyrotropin receptor. Science.gov (United States) Kleinau, Gunnar; Jaeschke, Holger; Worth, Catherine L; Mueller, Sandra; Gonzalez, Jorge; Paschke, Ralf; Krause, Gerd 2010-03-18 In this study we wanted to gain insights into selectivity mechanisms between G-protein-coupled receptors (GPCR) and different subtypes of G-proteins. The thyrotropin receptor (TSHR) binds G-proteins promiscuously and activates both Gs (cAMP) and Gq (IP). Our goal was to dissect selectivity patterns for both pathways in the intracellular region of this receptor. We were particularly interested in the participation of poorly investigated receptor parts.We systematically investigated the amino acids of intracellular loop (ICL) 1 and helix 8 using site-directed mutagenesis alongside characterization of cAMP and IP accumulation. This approach was guided by a homology model of activated TSHR in complex with heterotrimeric Gq, using the X-ray structure of opsin with a bound G-protein peptide as a structural template.We provide evidence that ICL1 is significantly involved in G-protein activation and our model suggests potential interactions with subunits G alpha as well as G betagamma. Several amino acid substitutions impaired both IP and cAMP accumulation. Moreover, we found a few residues in ICL1 (L440, T441, H443) and helix 8 (R687) that are sensitive for Gq but not for Gs activation. Conversely, not even one residue was found that selectively affects cAMP accumulation only. Together with our previous mutagenesis data on ICL2 and ICL3 we provide here the first systematically completed map of potential interfaces between TSHR and heterotrimeric G-protein. The TSHR/Gq-heterotrimer complex is characterized by more selective interactions than the TSHR/Gs complex. In fact the receptor interface for binding Gs is a subset of that for Gq and we postulate that this may be true for other GPCRs coupling these G-proteins. Our findings support that G-protein coupling and preference is dominated by specific structural features at the intracellular region of the activated GPCR but is completed by additional complementary recognition patterns between receptor and G-protein subtypes. 10. Determination of rare earth elements in uranium bearing samples using Inductively Coupled Plasma Mass Spectrometry (ICPMS) International Nuclear Information System (INIS) Mishra, S.; Chaudhury, P.; Pradeepkumar, K.S.; Sahoo, S.K. 2017-01-01 In the present study a methodology has been described for determination of REEs without involving separation and the method is successfully applied for determination of REE concentration in uranium ore as well as in soil samples from a uranium mining site 11. Determination of the quark coupling strength|V_{ub}|$using baryonic decays CERN Document Server AUTHOR|(INSPIRE)INSPIRE-00392760 This thesis presents the first determination of$|V_{ub}|$at a hadron collider and in a baryonic decay. The determination is made by measuring the ratio of branching fractions of the baryonic decays$\\Lambda^0_b \\to p \\mu^-\\overline{\
12. The determination of the weak neutral current coupling constants and limits on the electromagnetic properties of the muon neutrino
International Nuclear Information System (INIS)
Callas, J.L.
1987-05-01
The goal of this thesis is to determine experimentally the cross section for nu/sub μ/e → nu/sub μ/e scattering from a sample of over 100 expected nu/sub μ/e → nu/sub μ/e events collected by the E734 neutrino detector in BNL wide band neutrino beam. By combining these results with results from an anti-neutrino determination of the cross section for anti nu/sub μ/e → anti nu/sub μ/e scattering in the form of a ratio of cross sections, the weak coupling constants for the electron, g/sub V/ and g/sub A/ can be determined in a model independent way to within a four fold ambiguity where three of the ambiguities can be eliminated by results from e + e - experiments. The predictions of the Standard Model for the weak coupling constants can then be tested and a precise determination of the electroweak mixing parameter, sin 2 θ/sub W/ can be made
13. NK sensitivity of neuroblastoma cells determined by a highly sensitive coupled luminescent method
International Nuclear Information System (INIS)
Ogbomo, Henry; Hahn, Anke; Geiler, Janina; Michaelis, Martin; Doerr, Hans Wilhelm; Cinatl, Jindrich
2006-01-01
The measurement of natural killer (NK) cells toxicity against tumor or virus-infected cells especially in cases with small blood samples requires highly sensitive methods. Here, a coupled luminescent method (CLM) based on glyceraldehyde-3-phosphate dehydrogenase release from injured target cells was used to evaluate the cytotoxicity of interleukin-2 activated NK cells against neuroblastoma cell lines. In contrast to most other methods, CLM does not require the pretreatment of target cells with labeling substances which could be toxic or radioactive. The effective killing of tumor cells was achieved by low effector/target ratios ranging from 0.5:1 to 4:1. CLM provides highly sensitive, safe, and fast procedure for measurement of NK cell activity with small blood samples such as those obtained from pediatric patients
14. Precision determination of the $\\pi N$ scattering lengths and the charged $\\pi NN$ coupling constant
CERN Document Server
Ericson, Torleif Eric Oskar; Thomas, A W
2000-01-01
We critically evaluate the isovector GMO sumrule for the charged $\\pi N N$ coupling constant using recent precision data from $\\pi ^-$p and $\\pi^-$d atoms and with careful attention to systematic errors. From the $\\pi ^-$d scattering length we deduce the pion-proton scattering lengths ${1/2}(a_{\\pi ^-p}+a_{\\pi ^-n})=(-20\\pm 6$(statistic)$\\pm 10$ (systematic))~$\\cdot 10^{-4}m_{\\pi_c}^{-1}$ and ${1/2}(a_{\\pi ^-p}-a_{\\pi ^-n})=(903 \\pm 14)\\cdot 10^{-4}m_{\\pi_c}^{-1}$. From this a direct evaluation gives $g^2_c(GMO) =14.20\\pm 0.07$(statistic)$\\pm 0.13$(systematic) or $f^2_c= 0.0786\\pm 0.0008$.
15. Simultaneous determination of 2 aconitum alkaloids and 12 ginsenosides in Shenfu injection by ultraperformance liquid chromatography coupled with a photodiode array detector with few markers to determine multicomponents
Directory of Open Access Journals (Sweden)
Ai-Hua Ge
2015-06-01
Full Text Available A method with few markers to determine multicomponents was established and validated to evaluate the quality of Shenfu injection by ultraperformance liquid chromatography coupled with a photodiode array detector. The separations were performed on an ACQUITY UPLC BEH C18 (2.1 × 50 mm2, 1.7 μm column. Methanol and 0.1% formic acid aqueous solution were used as the mobile phase. The flow rate was 0.3 mL/min. 2 aconitum alkaloids and 12 ginsenosides could be perfectly separated within 15 minutes. Ginsenoside Rg1 and benzoylmesaconine, the easily available active components, were employed as the maker components to calculate the relative correction factors of other components in Shenfu injection, Panax ginseng and Aconitum carmichaeli. The external standard method was also established to validate the feasibility of the method with few markers to determine multicomponents. Parameter p and the principal component analysis method were employed to investigate the disparities among batches for the effective quality control of Shenfu injection. The results demonstrated that the ultraperformance liquid chromatography coupled with a photodiode array detector method with few markers to determine multicomponents could be used as a powerful tool for the quality evaluation of traditional Chinese medicines and their preparations.
16. Anomalous coupling of scalars to gauge fields
Energy Technology Data Exchange (ETDEWEB)
Brax, Philippe [CEA, IPhT, CNRS, URA 2306, Gif-sur-Yvette (France). Inst. de Physique Theorique; Burrage, Clare [Geneve Univ. (Switzerland). Dept. de Physique Theorique; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Davis, Anne-Christine [Centre for Mathematical Sciences, Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics; Seery, David [Sussex Univ., Brighton (United Kingdom). Dept. of Physics and Astronomy; Weltman, Amanda [Cape Town Univ., Rondebosch (South Africa). Astronomy, Cosmology and Gravity Centre
2010-10-15
We study the transformation properties of a scalar-tensor theory, coupled to fermions, under the Weyl rescaling associated with a transition from the Jordan to the Einstein frame. We give a simple derivation of the corresponding modification to the gauge couplings. After changing frames, this gives rise to a direct coupling between the scalar and the gauge fields. (orig.)
17. Anomalous coupling of scalars to gauge fields
International Nuclear Information System (INIS)
Brax, Philippe; Davis, Anne-Christine; Seery, David; Weltman, Amanda
2010-10-01
We study the transformation properties of a scalar-tensor theory, coupled to fermions, under the Weyl rescaling associated with a transition from the Jordan to the Einstein frame. We give a simple derivation of the corresponding modification to the gauge couplings. After changing frames, this gives rise to a direct coupling between the scalar and the gauge fields. (orig.)
18. Development of an analytical method for the determination of polybrominated diphenyl ethers in sewage sludge by the use of gas chromatography coupled to inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Novak, Petra; Zuliani, Tea; Milačič, Radmila; Ščančar, Janez
2016-01-01
Polybrominated diphenyl ethers (PBDEs) are flame retardants. As a consequence of their widespread use, they have been released into the environment. PBDEs are lipophilic organic contaminants that enter wastewater treatment plants (WWTPs) from urban, agricultural and industrial discharges. Because of their low aqueous solubility and resistance to biodegradation, up to 90% of the PBDEs are accumulated in the sewage sludge during the wastewater treatment. To assess the possibilities for sludge re-use, a reliable determination of the concentrations of these PBDEs is of crucial importance. Six PBDE congeners (BDE 28, BDE 47, BDE 99, BDE 100, BDE 153 and BDE 154) are listed as priority substances under the EU Water Framework Directive. In the present work a simple analytical method with minimal sample-preparation steps was developed for a sensitive and reliable determination of the six PBDEs in sewage sludge by the use of gas chromatography coupled to inductively coupled plasma mass spectrometry (GC-ICP-MS). For this purpose an extraction procedure was optimised. Different extracting agents (methanol (MeOH), acetic acid (AcOH)/MeOH mixture (3:1) and 0.1 mol L"−"1 hydrochloric acid (HCl) in MeOH) followed by the addition of a Tris-citrate buffer (co-extracting agent) and iso-octane were applied under different modes of extraction (mechanical shaking, microwave- and ultrasound-assisted extraction). Mechanical shaking or the microwave-assisted extraction of sewage sludge with 0.1 mol L"−"1 HCl in MeOH and the subsequent addition of the Tris-citrate buffer and the iso-octane extracted the PBDEs from the complex sludge matrix most effectively. However, due to easier sample manipulation during the extraction step, mechanical shaking was used. The PBDEs in the organic phase were quantified with GC-ICP-MS by applying a standard addition calibration method. The spike recovery test (recoveries between 95 and 104%) and comparative analyses with the species-specific isotope
19. Development of an analytical method for the determination of polybrominated diphenyl ethers in sewage sludge by the use of gas chromatography coupled to inductively coupled plasma mass spectrometry
Energy Technology Data Exchange (ETDEWEB)
Novak, Petra [Department of Environmental Sciences, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana (Slovenia); Jožef Stefan International Postgraduate School, Jamova 39, 1000, Ljubljana (Slovenia); Zuliani, Tea [Department of Environmental Sciences, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana (Slovenia); Milačič, Radmila [Department of Environmental Sciences, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana (Slovenia); Jožef Stefan International Postgraduate School, Jamova 39, 1000, Ljubljana (Slovenia); Ščančar, Janez, E-mail: [email protected] [Department of Environmental Sciences, Jožef Stefan Institute, Jamova 39, 1000, Ljubljana (Slovenia); Jožef Stefan International Postgraduate School, Jamova 39, 1000, Ljubljana (Slovenia)
2016-04-07
Polybrominated diphenyl ethers (PBDEs) are flame retardants. As a consequence of their widespread use, they have been released into the environment. PBDEs are lipophilic organic contaminants that enter wastewater treatment plants (WWTPs) from urban, agricultural and industrial discharges. Because of their low aqueous solubility and resistance to biodegradation, up to 90% of the PBDEs are accumulated in the sewage sludge during the wastewater treatment. To assess the possibilities for sludge re-use, a reliable determination of the concentrations of these PBDEs is of crucial importance. Six PBDE congeners (BDE 28, BDE 47, BDE 99, BDE 100, BDE 153 and BDE 154) are listed as priority substances under the EU Water Framework Directive. In the present work a simple analytical method with minimal sample-preparation steps was developed for a sensitive and reliable determination of the six PBDEs in sewage sludge by the use of gas chromatography coupled to inductively coupled plasma mass spectrometry (GC-ICP-MS). For this purpose an extraction procedure was optimised. Different extracting agents (methanol (MeOH), acetic acid (AcOH)/MeOH mixture (3:1) and 0.1 mol L{sup −1} hydrochloric acid (HCl) in MeOH) followed by the addition of a Tris-citrate buffer (co-extracting agent) and iso-octane were applied under different modes of extraction (mechanical shaking, microwave- and ultrasound-assisted extraction). Mechanical shaking or the microwave-assisted extraction of sewage sludge with 0.1 mol L{sup −1} HCl in MeOH and the subsequent addition of the Tris-citrate buffer and the iso-octane extracted the PBDEs from the complex sludge matrix most effectively. However, due to easier sample manipulation during the extraction step, mechanical shaking was used. The PBDEs in the organic phase were quantified with GC-ICP-MS by applying a standard addition calibration method. The spike recovery test (recoveries between 95 and 104%) and comparative analyses with the species
20. The influence of fragmentation models on the determination of the strong coupling constant in e+e- annihilation into hadrons
International Nuclear Information System (INIS)
Behrend, H.J.; Chen, C.; Fenner, H.; Schachter, M.J.; Schroeder, V.; Sindt, H.; D'Agostini, G.; Apel, W.D.; Banerjee, S.; Bodenkamp, J.; Chrobaczek, D.; Engler, J.; Fluegge, G.; Fries, D.C.; Fues, W.; Gamerdinger, K.; Hopp, G.; Kuester, H.; Mueller, H.; Randoll, H.; Schmidt, G.; Schneider, H.; Boer, W. de; Buschhorn, G.; Grindhammer, G.; Grosse-Wiesmann, P.; Gunderson, B.; Kiesling, C.; Kotthaus, R.; Kruse, U.; Lierl, H.; Lueers, D.; Oberlack, H.; Schacht, P.; Colas, P.; Cordier, A.; Davier, M.; Fournier, D.; Grivaz, J.F.; Haissinski, J.; Journe, V.; Klarsfeld, A.; Laplanche, F.; Le Diberder, F.; Mallik, U.; Veillet, J.J.; Field, J.H.; George, R.; Goldberg, M.; Grossetete, B.; Hamon, O.; Kapusta, F.; Kovacs, F.; London, G.; Poggioli, L.; Rivoal, M.; Aleksan, R.; Bouchez, J.; Carnesecchi, G.; Cozzika, G.; Ducros, Y.; Gaidot, A.; Jadach, S.; Lavagne, Y.; Pamela, J.; Pansart, J.P.; Pierre, F.
1983-01-01
Hadronic events obtained with the CELLO detector at PETRA were compared with first-order QCD predictions using two different models for the fragmentation of quarks and gluons, the Hoyer model and the Lund model. Both models are in reasonable agreement with the data, although they do not completely reproduce the details of many distributions. Several methods have been applied to determine the strong coupling constant αsub(s). Although within one model the value of αsub(s) varies by 20% among the different methods, the values determined using the Lund model are 30% or more larger (depending on the method used) than the values determined with the Hoyer model. Our results using the Hoyer model are in agreement with previous results based on this approach. (orig.)
1. Determination of strontium and lead isotope ratios of grains using high resolution inductively coupled plasma mass spectrometer with single collector
International Nuclear Information System (INIS)
Shinozaki, Miyuki; Ariyama, Kaoru; Kawasaki, Akira; Hirata, Takafumi
2010-01-01
A method for determining strontium and lead isotope ratios of grains was developed. The samples investigated in this study were rice, barley and wheat. The samples were digested with nitric acid and hydrogen peroxide, and heated in a heating block. Strontium and lead were separated from the matrix by adding an acid digested solution into a column packed with Sr resin, which has selectivity for the absorption of strontium and lead. Strontium and lead isotope ratios were determined using a high-resolution inductively coupled plasma mass spectrometer (HR-ICP-MS) with a single collector. The intraday relative standard deviations of 87 Sr/ 86 Sr and lead isotope ratios ( 204 Pb/ 206 Pb, 207 Pb/ 206 Pb, 208 Pb/ 206 Pb) by HR-ICP-MS measurements were < 0.06% and around 0.1%, respectively. This method enabled us to determine strontium and lead isotope ratios in two days. (author)
2. Standard test method for determining elements in waste streams by inductively coupled plasma-atomic emission spectroscopy
International Nuclear Information System (INIS)
Anon.
1989-01-01
This test method covers the determination of trace, minor, and major elements in waste streams by inductively coupled plasma-atomic emission spectroscopy (ICP-AES) following an acid digestion of the specimen. Waste streams from manufacturing processes of nuclear and nonnuclear materials can be analyzed. This test method is applicable to the determination of total metals. Results from this test method can be used to characterize waste received by treatment facilities and to formulate appropriate treatment recipes. The results are also usable to process control within waste treatment facilities. This test method is applicable only to waste streams that contain radioactivity levels which do not require special personnel or environmental protection. A list of the elements determined in waste streams and the corresponding lower reporting limit is included
3. The nonabelian tensor square of Bieberbach group of dimension five with dihedral point group of order eight
Science.gov (United States)
Fauzi, Wan Nor Farhana Wan Mohd; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Sarmin, Nor Haniza
2014-07-01
The nonabelian tensor product was originated in homotopy theory as well as in algebraic K-theory. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action are taken to be conjugation. In this paper, the computation of nonabelian tensor square of a Bieberbach group, which is a torsion free crystallographic group, of dimension five with dihedral point group of order eight is determined. Groups, Algorithms and Programming (GAP) software has been used to assist and verify the results.
4. Monitoring of the tensor polarization of high energy deuteron beams; Monitoring tenzornoj polyarizatsii dejtronnykh puchkov vysokoj ehnergii
Energy Technology Data Exchange (ETDEWEB)
Zolin, L S; Litvinenko, A G; Pilipenko, Yu K; Reznikov, S G; Rukoyatkin, P A; Fimushkin, V V
1998-12-01
The method of determining the tensor component of high energy polarized deuteron beams, based on measuring of the tensor analyzing power in the deuteron stripping reaction, is discussed. This method is convenient for monitoring during long time runs on the tensor polarized deuteron beams. The method was tested in the 5-days run at the LHE JINR accelerator with the 3 and 9 GeV/c tensor polarized deuterons. The results made it possible to estimate the beam polarization stability in time 5 refs., 4 figs., 1 tab.
5. A forgotten argument by Gordon uniquely selects Abraham's tensor as the energy-momentum tensor for the electromagnetic field in homogeneous, isotropic matter
International Nuclear Information System (INIS)
Antoci, S.; Mihich, L.
1997-01-01
Given the present status of the problem of the electromagnetic energy tensor in matter, there is perhaps use in recalling a forgotten argument given in 1923 by W. Gordon. Let us consider a material medium which is homogeneous and isotropic when observed in its rest frame. For such a medium, Gordon's argument allows to reduce the above-mentioned problem to an analogous one, defined in a general relativistic vacuum. For the latter problem the form of the Lagrangian is known already, hence the determination of the energy tensor is a straightforward matter. One just performs the Hamiltonian derivative of the Lagrangian chosen in this way with respect to the true metric g ik . Abraham's tensor is thus selected as the electromagnetic energy tensor for a medium which is homogeneous and isotropic in its rest frame
6. Simultaneous determination of macronutrients, micronutrients and trace elements in mineral fertilizers by inductively coupled plasma optical emission spectrometry
International Nuclear Information System (INIS)
Oliveira Souza, Sidnei de; Silvério Lopes da Costa, Silvânio; Santos, Dayane Melo; Santos Pinto, Jéssica dos; Garcia, Carlos Alexandre Borges
2014-01-01
An analytical method for simultaneous determination of macronutrients (Ca, Mg, Na and P), micronutrients (Cu, Fe, Mn and Zn) and trace elements (Al, As, Cd, Pb and V) in mineral fertilizers was optimized. Two-level full factorial design was applied to evaluate the optimal proportions of reagents used in the sample digestion on hot plate. A Doehlert design for two variables was used to evaluate the operating conditions of the inductively coupled plasma optical emission spectrometer in order to accomplish the simultaneous determination of the analyte concentrations. The limits of quantification (LOQs) ranged from 2.0 mg kg −1 for Mn to 77.3 mg kg −1 for P. The accuracy and precision of the proposed method were evaluated by analysis of standard reference materials (SRMs) of Western phosphate rock (NIST 694), Florida phosphate rock (NIST 120C) and Trace elements in multi-nutrient fertilizer (NIST 695), considered to be adequate for simultaneous determination. Twenty-one samples of mineral fertilizers collected in Sergipe State, Brazil, were analyzed. For all samples, the As, Ca, Cd and Pb concentrations were below the LOQ values of the analytical method. For As, Cd and Pb the obtained LOQ values were below the maximum limit allowed by the Brazilian Ministry of Agriculture, Livestock and Food Supply (Ministério da Agricultura, Pecuária e Abastecimento — MAPA). The optimized method presented good accuracy and was effectively applied to quantitative simultaneous determination of the analytes in mineral fertilizers by inductively coupled plasma optical emission spectrometry (ICP OES). - Highlights: • Determination of inorganic constituents in mineral fertilizers was proposed. • Experimental design methodology was used to optimize analytical method. • The sample preparation procedure using diluted reagents (HNO 3 and H 2 O 2 ) was employed. • The analytical method was satisfactorily to the determination of thirteen elements. • The ICP OES technique can be
7. Determination of Tributyltin in Seafood Based on Magnetic Molecularly Imprinted Polymers Coupled with High-Performance Liquid Chromatography-Inductively Coupled Plasma Mass Spectrometry
Directory of Open Access Journals (Sweden)
Hua Yang
2017-01-01
Full Text Available In this study, Fe3O4 was adopted as a carrier for surface molecular imprinting with two-stage polymerization. First, the functional monomer (methacrylic acid, MAA was modified on the surface of Fe3O4, which was then polymerized with the template molecule (tributyltin, TBT, cross linking agent (ethylene glycol dimethacrylate, EGDMA, and porogen (acetonitrile, hereby successfully preparing Fe3O4@MIPs prone to specifically identify TBT. The physical properties of Fe3O4@MIPs were then characterized, and adsorption and selection capacities were also assessed. Compared with conventional imprinting polymers, this magnetic molecular imprinting polymer (MIP displayed significantly increased and more specific adsorption. Meanwhile, its pretreatment was simpler and faster due to magnetic separation characteristics. Using magnetic MIPs as adsorbents for enrichment and separation, detection limit, recovery rate, and linear range were 1.0 ng g−1, 79.74–95.72%, and 5 ng g−1~1000 ng g−1, respectively, for a number of seafood samples. High-performance liquid chromatography-inductively coupled plasma mass spectrometry (HPLC-ICP-MS was used to analyze Tegillarca granosa, mussels, large yellow croaker, and other specimens, with recovery rates of 79.74–95.72% and RSD of 1.3%–4.7%. Overall, this method has a shorter total analysis time, lower detection limit, and wider linear range and can be more effectively applied to determine MAA in seawater and seafood.
8. In-coupled syringe assisted octanol-water partition microextraction coupled with high-performance liquid chromatography for simultaneous determination of neonicotinoid insecticide residues in honey.
Science.gov (United States)
Vichapong, Jitlada; Burakham, Rodjana; Srijaranai, Supalax
2015-07-01
A simple and fast method namely in-coupled syringe assisted octanol-water partition microextraction combined with high performance liquid chromatography (HPLC) has been developed for the extraction, preconcentration and determination of neonicotinoid insecticide residues (e.g. imidacloprid, acetamiprid, clothianidin, thiacloprid, thiamethoxam, dinotefuran, and nitenpyram) in honey. The experimental parameters affected the extraction efficiency, including kind and concentration of salt, kind of disperser solvent and its volume, kind of extraction solvent and its volume, shooting times and extraction time were investigated. The extraction process was carried out by rapid shooting of two syringes. Therefore, rapid dispersion and mass transfer processes was created between phases, and thus affects the extraction efficiency of the proposed method. The optimum extraction conditions were 10.00 mL of aqueous sample, 10% (w/v) Na2SO4, 1-octanol (100µL) as an extraction solvent, shooting 4 times and extraction time 2min. No disperser solvent and centrifugation step was necessary. Linearity was obtained within the range of 0.1-3000 ngmL(-1), with the correlation coefficients greater than 0.99. The high enrichment factor of the target analytes was 100 fold and low limit of detection (0.25-0.50 ngmL(-1)) could be obtained. This proposed method has been successfully applied in the analysis of neonicotinoid residues in honey, and good recoveries in the range of 96.93-107.70% were obtained. Copyright © 2015 Elsevier B.V. All rights reserved.
9. Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress
OpenAIRE
Monserrat, Bartomeu; Drummond, N. D.; Needs, R. J.
2013-01-01
A unified approach is used to study vibrational properties of periodic systems with first-principles methods and including anharmonic effects. Our approach provides a theoretical basis for the determination of phonon-dependent quantities at finite temperatures. The low-energy portion of the Born-Oppenheimer energy surface is mapped and used to calculate the total vibrational energy including anharmonic effects, electron-phonon coupling, and the vibrational contribution to the stress tensor. W...
10. Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)
11. Urinary elimination of molybdenum by healthy subjects as determined by inductively coupled plasma mass spectrometry.
Science.gov (United States)
Allain, P; Berre, S; Prémel-Cabic, A; Mauras, Y; Cledes, A; Cournot, A
The concentration of molybdenum was measured by inductively coupled plasma mass spectrometry (ICPMS) in the urines of two groups of healthy people living in two areas of France, Brest and Paris, about 500 km away. The concentration of Mo in the 24-hour urines of 10 healthy subjects from the Brest region was 25 +/- 10 micrograms/l, 38 +/- 20 micrograms/24 h and 21 +/- 9 micrograms/g creatinine. The concentration of Mo in the morning urines of 23 healthy men of the Paris region was 41 +/- 34 micrograms/l and 21 +/- 15 micrograms/g creatinine. Thus the mean elimination of Mo per gram of creatinine was the same in the two groups (21 +/- 9 and 21 +/- 15). Since the three main isotopes of Mo m/z = 95, 96 and 98, corresponding to an abundance percentage of 16, 17 and 24.5, respectively, were simultaneously analyzed in each sample and led to similar results, the ICPMS method seems reliable.
12. Determination of Oxidized Phosphatidylcholines by Hydrophilic Interaction Liquid Chromatography Coupled to Fourier Transform Mass Spectrometry
Directory of Open Access Journals (Sweden)
Pia Sala
2015-04-01
Full Text Available A novel liquid chromatography-mass spectrometry (LC-MS approach for analysis of oxidized phosphatidylcholines by an Orbitrap Fourier Transform mass spectrometer in positive electrospray ionization (ESI coupled to hydrophilic interaction liquid chromatography (HILIC was developed. This method depends on three selectivity criteria for separation and identification: retention time, exact mass at a resolution of 100,000 and collision induced dissociation (CID fragment spectra in a linear ion trap. The process of chromatography development showed the best separation properties with a silica-based Kinetex column. This type of chromatography was able to separate all major lipid classes expected in mammalian samples, yielding increased sensitivity of oxidized phosphatidylcholines over reversed phase chromatography. Identification of molecular species was achieved by exact mass on intact molecular ions and CID tandem mass spectra containing characteristic fragments. Due to a lack of commercially available standards, method development was performed with copper induced oxidation products of palmitoyl-arachidonoyl-phosphatidylcholine, which resulted in a plethora of lipid species oxidized at the arachidonoyl moiety. Validation of the method was done with copper oxidized human low-density lipoprotein (LDL prepared by ultracentrifugation. In these LDL samples we could identify 46 oxidized molecular phosphatidylcholine species out of 99 possible candidates.
13. Applications of inductively coupled plasma-mass spectrometry to radionuclide determinations: Second volume
International Nuclear Information System (INIS)
Morrow, R.W.; Crain, J.S.
1998-01-01
Even from its early conception, inductively coupled plasma-mass spectrometry (ICP-MS) was thought to be well-suited to the unique measurement problems facing the nuclear industry. These thoughts were well-founded; indeed, one might consider it unusual if a modern nuclear research center did not have access to one or more ICP mass spectrometers (quadrupole or otherwise). However, as ICP-MS has matured, improvements in sensitivity and precision have made possible measurements that were inconceivable to the founding fathers of the technology. Therefore, there is a periodic need to gather information and obtain a snapshot in time of the technology and its applications in nuclear energy. This second symposium was an international event in which speakers from the US, Europe, and the Middle East described new developments in ICP-MS relevant to the nuclear energy community. The papers presented at the 1998 symposium are published herein. Several papers have been processed separately for inclusion on the data base
14. How precisely can the difference method determine the $\\pi$NN coupling constant?
CERN Document Server
Loiseau, B
2000-01-01
The Coulomb-like backward peak of the neutron-proton scattering differentialcross section is due to one-pion exchange. Extrapolation to the pion pole ofprecise data should allow to obtain the value of the charged pion-nucleoncoupling constant. This was classically attempted by the use of a smoothphysical function, the Chew function, built from the cross section. To improveaccuracy of such an extrapolation one has introduced a difference method. Itconsists of extrapolating the difference between the Chew function based onexperimental data and that built from a model where the pion-nucleon couplingis exactly known. Here we cross-check to which precision can work this novelextrapolation method by applying it to differences between models and betweendata and models. With good reference models and for the 162 MeV neutron-protonUppsala single energy precise data with a normalisation error of 2.3 , thevalue of the charged pion-nucleon coupling constant is obtained with anaccuracy close to 1.8
15. Determination of diphenylether herbicides in water samples by solid-phase microextraction coupled to liquid chromatography.
Science.gov (United States)
Sheu, Hong-Li; Sung, Yu-Hsiang; Melwanki, Mahaveer B; Huang, Shang-Da
2006-11-01
Solid-phase microextraction (SPME) coupled to LC for the analysis of five diphenylether herbicides (aclonifen, bifenox, fluoroglycofen-ethyl, oxyfluorfen, and lactofen) is described. Various parameters of extraction of analytes onto the fiber (such as type of fiber, extraction time and temperature, pH, impact of salt and organic solute) and desorption from the fiber in the desorption chamber prior to separation (such as type and composition of desorption solvent, desorption mode, soaking time, and flush-out time) were studied and optimized. Four commercially available SPME fibers were studied. PDMS/divinylbenzene (PDMS/DVB, 60 microm) and carbowax/ templated resin (CW/TPR, 50 microm) fibers were selected due to better extraction efficiencies. Repeatability (RSD, 0.994), and detection limit (0.33-1.74 and 0.22-1.94 ng/mL, respectively, for PDMS/DVB and CW/TPR) were investigated. Relative recovery (81-104% for PDMS/DVB and 83-100% for CW/TPR fiber) values have also been calculated. The developed method was successfully applied to the analysis of river water and water collected from a vegetable garden.
16. Supersymmetry breaking and determination of the unification gauge coupling constant in string theories
International Nuclear Information System (INIS)
Carlos, B. de; Casas, J.A.; Munoz, C.
1993-01-01
We study in a systematic and modular invariant way gaugino condensation in the hidden sector as a potential source of hierarchical supersymmetry breaking and a non-trivial potential for the dilaton S whose real part corresponds to the tree-level gauge coupling constant (Re S∝g gut -2 ). For the case of pure Yang-Mills condensation, we show that no realistic results (in particular no reasonable values for Re S) can emerge, even if the hidden gauge group is not simple. However, in the presence of hidden matter (i.e. the most frequent case) there arises a very interesting class of scenarios with two or more hidden condensing groups for which the dilaton dynamically acquires a reasonable value (Re S∝2) and supersymmetry is broken at the correct scale (m 3/2 ∝10 3 GeV) with no need of fine-tuning. Actually, good values for Re S and m 3/2 are correlated. We make an exhaustive classification of the working possibilities. Remarkably, the results are basically independent from the value of δ GS (the contributions from the Green-Schwarz mechanism). The radius of the compactified space also acquires an expectation value, breaking duality spontaneously. (orig.)
17. 'Age' determination of irradiated materials utilizing inductively coupled plasma mass spectrometric (ICP-MS) detection
International Nuclear Information System (INIS)
Sommers, J.; Cummings, D.; Giglio, J.; Carney, K.
2009-01-01
A gas pressurized extraction chromatography (GPEC) system has been developed to perform elemental separations on radioactive samples to determine total and isotopic compositions of Cs and Ba from an irradiated salt sample, fuel sample and two sealed radiation sources. The GPEC system employs compressed nitrogen to move liquid through the system, compared to gravity or pumped liquids that are typically used for separations. A commercially available Sr-Resin TM was used to perform the separation for the above mentioned analytes. A 1% acetic acid solution was determined to be the best extractant for Ba. A flow rate of 0.1 mL/min was determined to be optimal for the separation of Ba. Complete recovery of the Cs and Ba was achieved, within the systematic uncertainties of the experiments. (author)
18. A separation method to overcome the interference of aluminium on zinc determination by inductively coupled plasma atomic emission spectroscopy
OpenAIRE
Jesus, Djane S. de; Korn, Maria das Graças Andrade; Ferreira, Sergio Luis Costa; Carvalho, Marcelo Souza de
2000-01-01
Texto completo: acesso restrito. p.389–394 The use of polyurethane foam (PUF) to separate zinc from large amounts of aluminium and its determination by inductively coupled plasma atomic emission spectroscopy technique (ICP-AES) in aluminium matrices is described. The proposed method is based on the solid-phase extraction of the zinc(II) cation as a thiocyanate complex. Parameters such as effect of pH on zinc sorption, zinc desorption from the foam and analytical features of the procedure w...
19. Determination of Cr(VI) and Cr(III) in urine and dextrose by inductively coupled plasma emission spectroscopy
Science.gov (United States)
Mianzhi, Zhuang; Barnes, Ramon M.
The determination of Cr(VI) and Cr(III) in human urine and in commercial dextrose solution is performed by induclively coupled plasma-atomic emission spectroscopy after selective preconcentration of the chromium species at different pH values by poly(dithiocarbamate) and poly(acrylamidoxime) chelating resins. The chelating properties of these resins with chromium, including the kinetics of uptake and removal of Cr(III), and the influence of matrix concentrations were evaluated. Chromium in human urine was found to exist exclusively as Cr(III).
20. Distinct Phosphorylation Clusters Determine the Signaling Outcome of Free Fatty Acid Receptor 4/G Protein-Coupled Receptor 120
DEFF Research Database (Denmark)
Prihandoko, Rudi; Alvarez-Curto, Elisa; Hudson, Brian D
2016-01-01
of these phosphoacceptor sites to alanine completely prevented phosphorylation of mFFA4 but did not limit receptor coupling to extracellular signal regulated protein kinase 1 and 2 (ERK1/2) activation. Rather, an inhibitor of Gq/11proteins completely prevented receptor signaling to ERK1/2. By contrast, the recruitment...... activation. These unique observations define differential effects on signaling mediated by phosphorylation at distinct locations. This hallmark feature supports the possibility that the signaling outcome of mFFA4 activation can be determined by the pattern of phosphorylation (phosphorylation barcode...
1. Determination of sulfonamides in meat by liquid chromatography coupled with atmospheric pressure chemical ionization mass spectrometry
International Nuclear Information System (INIS)
Kim, Dal Ho; Choi, Jong Oh; Kim, Jin Seog; Lee, Dai Woon
2002-01-01
Liquid chromatography/atmospheric pressure chemical ionization-mass spectrometry (LC-APCI-MS) has been used for the determination of sulfonamides in meat. Five typical sulfonamides were selected as target compounds, and beef meat was selected as a matrix sample. As internal standards, sulfapyridine and isotope labeled sulfamethazine ( 13 C 6 -SMZ) were used. Compared to the results of recent reports, our results have shown improved precision to a RSD of 1.8% for the determination of sulfamethazine spiked with 75 ng/g level in meat
2. Studies in the determination of lead isotope ratios by inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Date, A.R.; Yuk Ying Cheung
1987-01-01
The application of ICP-MS to the determination of lead isotope ratios in geological materials is described. Data presented for a series of lead mineral concentrates are compared with reference values obtained by conventional solid source thermal ionisation mass spectrometry. The simultaneous determination of lead isotope ratios and trace elements is carried out in a rapid analysis mode. The application of an electrothermal vaporisation technique for small solution aliquots is described. Lead isotope ratio data for the United States Geological Survey standard reference silicate rock BCR-1, obtained without separation of lead from the matrix, are compared with previously published values obtained after separation. (author)
3. Mixed symmetry tensors in the worldline formalism
Energy Technology Data Exchange (ETDEWEB)
Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, I-41125 Modena (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Edwards, James P. [Department of Mathematical Sciences, University of Bath,Claverton Down, Bath BA2 7AY (United Kingdom)
2016-05-10
We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) “flavour” symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.
4. Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
5. Tensor Network Quantum Virtual Machine (TNQVM)
Energy Technology Data Exchange (ETDEWEB)
2016-11-18
There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.
6. Tensor product varieties and crystals. GL case
OpenAIRE
Malkin, Anton
2001-01-01
The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.
7. Energy momentum tensor in theories with scalar field
International Nuclear Information System (INIS)
Joglekar, S.D.
1992-01-01
The renormalization of energy momentum tensor in theories with scalar fields and two coupling constants is considered. The need for addition of an improvement term is shown. Two possible forms for the improvement term are: (i) One in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be derived from an action that is a finite function of bare quantities), (ii) One in which the improvement coefficient is a finite quantity, i.e. finite function of the renormalized quantities are considered. Four possible model of such theories are (i) Scalar Q.E.D. (ii) Non-Abelian theory with scalars, (iii) Yukawa theory, (iv) A model with two scalars. In all these theories a negative conclusion is established: neither forms for the improvement terms lead to a finite energy momentum tensor. Physically this means that when interaction with external gravity is incorporated in such a model, additional experimental input in the form of root mean square mass radius must be given to specify the theory completely, and the flat space parameters are insufficient. (author). 12 refs
8. Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
9. Unique characterization of the Bel-Robinson tensor
International Nuclear Information System (INIS)
Bergqvist, G; Lankinen, P
2004-01-01
We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors
10. Gas-diffusion microextraction coupled with spectrophotometry for the determination of formaldehyde in cork agglomerates.
Science.gov (United States)
Brandão, Pedro F; Ramos, Rui M; Valente, Inês M; Almeida, Paulo J; Carro, Antonia M; Lorenzo, Rosa A; Rodrigues, José A
2017-04-01
In this work, a simple methodology was developed for the extraction and determination of free formaldehyde content in cork agglomerate samples. For the first time, gas-diffusion microextraction was used for the extraction of volatile formaldehyde directly from samples, with simultaneous derivatization with acetylacetone (Hantzsch reaction). The absorbance of the coloured solution was read in a spectrophotometer at 412 nm. Different extraction parameters were studied and optimized (extraction temperature, sample mass, volume of acceptor solution, extraction time and concentration of derivatization reagent) by means of an asymmetric screening. The developed methodology proved to be a reliable tool for the determination of formaldehyde in cork agglomerates with the following suitable method features: low LOD (0.14 mg kg -1 ) and LOQ (0.47 mg kg -1 ), r 2 = 0.9994, and intraday and interday precision of 3.5 and 4.9%, respectively. The developed methodology was applied to the determination of formaldehyde in different cork agglomerate samples, and contents between 1.9 and 9.4 mg kg -1 were found. Furthermore, formaldehyde was also determined by the standard method EN 717-3 for comparison purposes; no significant differences between the results of both methods were observed. Graphical abstract Representation of the GDME system and its main components.
11. 'Age' Determination of Irradiated Materials Utilizing Inductively Coupled Plasma Mass Spectrometric (ICP-MS) Detection
International Nuclear Information System (INIS)
Sommers, James; Giglio, Jeffrey J.; Cummings, Daniel; Carney, Kevin P.
2009-01-01
A gas pressurized extraction chromatography (GPEC) system has been developed to perform elemental separations on radioactive samples to determine total and isotopic compositions of Cs and Ba from an irradiated salt sample, fuel sample and two sealed radiation sources. The separation is necessary to remove isobaric interferences in the determination of 137Cs, 135Cs, 137Ba, 135Ba, which are used to determine the age of a sample from radioactive decay or purification. The micro-column extraction chromatography system employs compressed nitrogen to move liquid through the system, compared to gravity or pumped liquids that are typically used for separations. The use of compressed gas allows for accurate and precise recovery of all liquids put into the chromatography system, enabling very accurate dilutions. The use of a small analytical column permits the use of very small amounts of liquids to be used. As a benefit, the amount of radiological waste that is generated in the separation process is minimized. For this work, a commercially available Sr-Resin(trademark) was used to perform the separation for the above mentioned analytes. The column consists of a 7 inch piece of 1/16 in. O.D. x 0.030 in I.D. Teflon(trademark) tubing having an internal volume of 81 (micro)L. To this column, 49 mg of resin was added. The columns are re-usable after regeneration with 3 M HNO3. All samples were separated using batch collection, although real time analysis is possible with the current experimental design. A 1 % acetic acid solution was determined to be the best extractant for Ba. A flow rate of 0.1 mL/min was determined to be optimal for the separation of Ba. Complete recovery of the Cs and Ba was achieved, within the systematic error of the experiments.
12. Tensor completion and low-n-rank tensor recovery via convex optimization
International Nuclear Information System (INIS)
Gandy, Silvia; Yamada, Isao; Recht, Benjamin
2011-01-01
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers
13. Determination of total tin in canned food using inductively coupled plasma atomic emission spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Perring, Loic; Basic-Dvorzak, Marija [Department of Quality and Safety Assurance, Nestle Research Centre, P.O. Box 44, Vers chez-les-Blanc, 1000, Lausanne (Switzerland)
2002-09-01
Tin is considered to be a priority contaminant by the Codex Alimentarius Commission. Tin can enter foods either from natural sources, environmental pollution, packaging material or pesticides. Higher concentrations are found in processed food and canned foods. Dissolution of the tinplate depends on the of food matrix, acidity, presence of oxidising reagents (anthocyanin, nitrate, iron and copper) presence of air (oxygen) in the headspace, time and storage temperature. To reduce corrosion and dissolution of tin, nowadays cans are usually lacquered, which gives a marked reduction of tin migration into the food product. Due to the lack of modern validated published methods for food products, an ICP-AES (Inductively coupled plasma-atomic emission spectroscopy) method has been developed and evaluated. This technique is available in many laboratories in the food industry and is more sensitive than atomic absorption. Conditions of sample preparation and spectroscopic parameters for tin measurement by axial ICP-AES were investigated for their ruggedness. Two methods of preparation involving high-pressure ashing or microwave digestion in volumetric flasks were evaluated. They gave complete recovery of tin with similar accuracy and precision. Recoveries of tin from spiked products with two levels of tin were in the range 99{+-}5%. Robust relative repeatabilities and intermediate reproducibilities were <5% for different food matrices containing >30 mg/kg of tin. Internal standard correction (indium or strontium) did not improve the method performance. Three emission lines for tin were tested (189.927, 283.998 and 235.485 nm) but only 189.927 nm was found to be robust enough with respect to interferences, especially at low tin concentrations. The LOQ (limit of quantification) was around 0.8 mg/kg at 189.927 nm. A survey of tin content in a range of canned foods is given. (orig.)
14. Accurate determination and certification of bromine in plastic by isotope dilution inductively coupled plasma mass spectrometry
Energy Technology Data Exchange (ETDEWEB)
Ohata, Masaki, E-mail: [email protected]; Miura, Tsutomu
2014-07-21
Highlights: • Accurate analytical method of Br in plastic was studied by isotope dilution ICPMS. • A microwave acid digestion using quartz vessel was suitable for Br analysis. • Sample dilution by NH{sub 3} solution could remove memory effect for ICPMS measurement. • The analytical result of the ID-ICPMS showed consistency with that of INAA. • The ID-ICPMS developed could apply to certification of Br in candidate plastic CRM. - Abstract: The accurate analytical method of bromine (Br) in plastic was developed by an isotope dilution inductively coupled plasma mass spectrometry (ID-ICPMS). The figures of merit of microwave acid digestion procedures using polytetrafluoroethylene (PTFE) or quartz vessels were studied and the latter one was suitable for Br analysis since its material was free from Br contamination. The sample dilution procedures using Milli-Q water or ammonium (NH{sub 3}) solution were also studied to remove memory effect for ICPMS measurement. Although severe memory effect was observed on Milli-Q water dilution, NH{sub 3} solution could remove it successfully. The accuracy of the ID-ICPMS was validated by a certified reference material (CRM) as well as the comparison with the analytical result obtained by an instrumental neutron activation analysis (INAA) as different analytical method. From these results, the ID-ICPMS developed in the present study could be evaluated as accurate analytical method of Br in plastic materials and it could apply to certification of Br in candidate plastic CRM with respect to such regulations related to RoHS (restriction of the use of hazardous substances in electrical and electronics equipment) directive.
15. Sulfonated polystyrene magnetic nanobeads coupled with immunochromatographic strip for clenbuterol determination in pork muscle.
Science.gov (United States)
Wu, Kesheng; Guo, Liang; Xu, Wei; Xu, Hengyi; Aguilar, Zoraida P; Xu, Guomao; Lai, Weihua; Xiong, Yonghua; Wan, Yiqun
2014-11-01
16. Accurate determination and certification of bromine in plastic by isotope dilution inductively coupled plasma mass spectrometry
International Nuclear Information System (INIS)
Ohata, Masaki; Miura, Tsutomu
2014-01-01
Highlights: • Accurate analytical method of Br in plastic was studied by isotope dilution ICPMS. • A microwave acid digestion using quartz vessel was suitable for Br analysis. • Sample dilution by NH 3 solution could remove memory effect for ICPMS measurement. • The analytical result of the ID-ICPMS showed consistency with that of INAA. • The ID-ICPMS developed could apply to certification of Br in candidate plastic CRM. - Abstract: The accurate analytical method of bromine (Br) in plastic was developed by an isotope dilution inductively coupled plasma mass spectrometry (ID-ICPMS). The figures of merit of microwave acid digestion procedures using polytetrafluoroethylene (PTFE) or quartz vessels were studied and the latter one was suitable for Br analysis since its material was free from Br contamination. The sample dilution procedures using Milli-Q water or ammonium (NH 3 ) solution were also studied to remove memory effect for ICPMS measurement. Although severe memory effect was observed on Milli-Q water dilution, NH 3 solution could remove it successfully. The accuracy of the ID-ICPMS was validated by a certified reference material (CRM) as well as the comparison with the analytical result obtained by an instrumental neutron activation analysis (INAA) as different analytical method. From these results, the ID-ICPMS developed in the present study could be evaluated as accurate analytical method of Br in plastic materials and it could apply to certification of Br in candidate plastic CRM with respect to such regulations related to RoHS (restriction of the use of hazardous substances in electrical and electronics equipment) directive
17. Determination of serum calcium levels by 42Ca isotope dilution inductively coupled plasma mass spectrometry.
Science.gov (United States)
Han, Bingqing; Ge, Menglei; Zhao, Haijian; Yan, Ying; Zeng, Jie; Zhang, Tianjiao; Zhou, Weiyan; Zhang, Jiangtao; Wang, Jing; Zhang, Chuanbao
2017-11-27
Serum calcium level is an important clinical index that reflects pathophysiological states. However, detection accuracy in laboratory tests is not ideal; as such, a high accuracy method is needed. We developed a reference method for measuring serum calcium levels by isotope dilution inductively coupled plasma mass spectrometry (ID ICP-MS), using 42Ca as the enriched isotope. Serum was digested with 69% ultrapure nitric acid and diluted to a suitable concentration. The 44Ca/42Ca ratio was detected in H2 mode; spike concentration was calibrated by reverse IDMS using standard reference material (SRM) 3109a, and sample concentration was measured by a bracketing procedure. We compared the performance of ID ICP-MS with those of three other reference methods in China using the same serum and aqueous samples. The relative expanded uncertainty of the sample concentration was 0.414% (k=2). The range of repeatability (within-run imprecision), intermediate imprecision (between-run imprecision), and intra-laboratory imprecision were 0.12%-0.19%, 0.07%-0.09%, and 0.16%-0.17%, respectively, for two of the serum samples. SRM909bI, SRM909bII, SRM909c, and GBW09152 were found to be within the certified value interval, with mean relative bias values of 0.29%, -0.02%, 0.10%, and -0.19%, respectively. The range of recovery was 99.87%-100.37%. Results obtained by ID ICP-MS showed a better accuracy than and were highly correlated with those of other reference methods. ID ICP-MS is a simple and accurate candidate reference method for serum calcium measurement and can be used to establish and improve serum calcium reference system in China.
18. Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
19. A recursive reduction of tensor Feynman integrals
International Nuclear Information System (INIS)
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
20. On Lovelock analogs of the Riemann tensor
Science.gov (United States)
2016-03-01
It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.
1. Effective gravitational wave stress-energy tensor in alternative theories of gravity
International Nuclear Information System (INIS)
Stein, Leo C.; Yunes, Nicolas
2011-01-01
The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants and show that the gravitational wave stress-energy tensor still reduces to Isaacson's. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.
2. Filtering overpopulated isoscalar tensor states with mass relations
International Nuclear Information System (INIS)
Burakovsky, Leonid; Page, Philip R.
2000-01-01
Schwinger-type mass formulas are used to analyze glueball-meson mixing for isoscalar tensor mesons. In one solution, the f J (2220) is the physical glueball, and in the other the glueball is distributed over various states, with f 2 (1810) having the largest glueball component. Neither the f 2 (1565) nor the f J (1710) are among the physical states without assuming significant coupling to decay channels. The decay f 2 (1525)→ππ is consistent with experiment, and f J (2220) is neither narrow nor decays flavor democratically. (c) 2000 The American Physical Society
3. Cosmology and a general scalar-tensor theory of gravity
International Nuclear Information System (INIS)
Bishop, N.T.
1976-01-01
The cosmological models resulting from a general scalar-tensor theory of gravity are discussed. Those models for which the scalar field varies as a power of the cosmological expansion factor (i.e. phi varies as Rsup(n)) are considered in detail, leading to a set of such models compatible with observation. This set includes models in which the scalar coupling parameter ω is negative. The models described here are similar to those of Newtonian cosmology obtained from an impotence principle. (author)
4. Nonuniversal scalar-tensor theories and big bang nucleosynthesis
International Nuclear Information System (INIS)
Coc, Alain; Olive, Keith A.; Uzan, Jean-Philippe; Vangioni, Elisabeth
2009-01-01
We investigate the constraints that can be set from big bang nucleosynthesis on two classes of models: extended quintessence and scalar-tensor theories of gravity in which the equivalence principle between standard matter and dark matter is violated. In the latter case, and for a massless dilaton with quadratic couplings, the phase space of theories is investigated. We delineate those theories where attraction toward general relativity occurs. It is shown that big bang nucleosynthesis sets more stringent constraints than those obtained from Solar System tests.
5. Nonuniversal scalar-tensor theories and big bang nucleosynthesis
Science.gov (United States)
Coc, Alain; Olive, Keith A.; Uzan, Jean-Philippe; Vangioni, Elisabeth
2009-05-01
We investigate the constraints that can be set from big bang nucleosynthesis on two classes of models: extended quintessence and scalar-tensor theories of gravity in which the equivalence principle between standard matter and dark matter is violated. In the latter case, and for a massless dilaton with quadratic couplings, the phase space of theories is investigated. We delineate those theories where attraction toward general relativity occurs. It is shown that big bang nucleosynthesis sets more stringent constraints than those obtained from Solar System tests.
6. Headspace single-drop microextraction coupled to microvolume UV-vis spectrophotometry for iodine determination
International Nuclear Information System (INIS)
Pena-Pereira, Francisco; Lavilla, Isela; Bendicho, Carlos
2009-01-01
Headspace single-drop microextraction has been combined with microvolume UV-vis spectrophotometry for iodine determination. Matrix separation and preconcentration of iodide following in situ volatile iodine generation and extraction into a microdrop of N,N'-dimethylformamide is performed. An exhaustive characterization of the microextraction system and the experimental variables affecting iodine generation from iodide was carried out. The procedure employed consisted of exposing 2.5 μL of N,N'-dimethylformamide to the headspace of a 10 mL acidic (H 2 SO 4 2 mol L -1 ) aqueous solution containing 1.7 mol L -1 Na 2 SO 4 for 7 min. Addition of 1 mL of H 2 O 2 1 mol L -1 for in situ iodine generation was performed. The limit of detection was determined as 0.69 μg L -1 . The repeatability, expressed as relative standard deviation, was 4.7% (n = 6). The calibration working range was from 5 to 200 μg L -1 (r 2 = 0.9991). The large preconcentration factor obtained, ca. 623 in only 7 min, compensate for the 10-fold loss in sensitivity caused by the decreased optical path, which results in improved detection limits as compared to spectrophotometric measurements carried out with conventional sample cells. The method was successfully applied to the determination of iodine in water, pharmaceutical and food samples
7. Anti-symmetric rank-two tensor matter field on superspace for N{sub T}=2
Energy Technology Data Exchange (ETDEWEB)
Spalenza, Wesley; Ney, Wander G; Helayel-Neto, J A
2004-05-06
In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N{sub T}=2 SUSY. We start off from the N{sub T}=2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables.
8. Coupled nutrient cycling determines tropical forest trajectory under elevated CO2.
Science.gov (United States)
Bouskill, N.; Zhu, Q.; Riley, W. J.
2017-12-01
Tropical forests have a disproportionate capacity to affect Earth's climate relative to their areal extent. Despite covering just 12 % of land surface, tropical forests account for 35 % of global net primary productivity and are among the most significant of terrestrial carbon stores. As atmospheric CO2 concentrations increase over the next century, the capacity of tropical forests to assimilate and sequester anthropogenic CO2 depends on limitation by multiple factors, including the availability of soil nutrients. Phosphorus availability has been considered to be the primary factor limiting metabolic processes within tropical forests. However, recent evidence points towards strong spatial and temporal co-limitation of tropical forests by both nitrogen and phosphorus. Here, we use the Accelerated Climate Modeling for Energy (ACME) Land Model (ALMv1-ECA-CNP) to examine how nutrient cycles interact and affect the trajectory of the tropical forest carbon sink under, (i) external nutrient input, (ii) climate (iii) elevated CO2, and (iv) a combination of 1-3. ALMv1 includes recent theoretical advances in representing belowground competition between roots, microbes and minerals for N and P uptake, explicit interactions between the nitrogen and phosphorus cycles (e.g., phosphatase production and nitrogen fixation), the dynamic internal allocation of plant N and P resources, and the integration of global datasets of plant physiological traits. We report nutrient fertilization (N, P, N+P) predictions for four sites in the tropics (El Verde, Puerto Rico, Barro Colorado Island, Panama, Manaus, Brazil and the Osa Peninsula, Coast Rica) to short-term nutrient fertilization (N, P, N+P), and benchmarking of the model against a meta-analysis of forest fertilization experiments. Subsequent simulations focus on the interaction of the carbon, nitrogen, and phosphorus cycles across the tropics with a focus on the implications of coupled nutrient cycling and the fate of the tropical
9. Avoiding bias effects in NMR experiments for heteronuclear dipole-dipole coupling determinations: principles and application to organic semiconductor materials.
Science.gov (United States)
Kurz, Ricardo; Cobo, Marcio Fernando; de Azevedo, Eduardo Ribeiro; Sommer, Michael; Wicklein, André; Thelakkat, Mukundan; Hempel, Günter; Saalwächter, Kay
2013-09-16
Carbon-proton dipole-dipole couplings between bonded atoms represent a popular probe of molecular dynamics in soft materials or biomolecules. Their site-resolved determination, for example, by using the popular DIPSHIFT experiment, can be challenged by spectral overlap with nonbonded carbon atoms. The problem can be solved by using very short cross-polarization (CP) contact times, however, the measured modulation curves then deviate strongly from the theoretically predicted shape, which is caused by the dependence of the CP efficiency on the orientation of the CH vector, leading to an anisotropic magnetization distribution even for isotropic samples. Herein, we present a detailed demonstration and explanation of this problem, as well as providing a solution. We combine DIPSHIFT experiments with the rotor-directed exchange of orientations (RODEO) method, and modifications of it, to redistribute the magnetization and obtain undistorted modulation curves. Our strategy is general in that it can also be applied to other types of experiments for heteronuclear dipole-dipole coupling determinations that rely on dipolar polarization transfer. It is demonstrated with perylene-bisimide-based organic semiconductor materials, as an example, in which measurements of dynamic order parameters reveal correlations of the molecular dynamics with the phase structure and functional properties. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
10. Determination of ammonium in wastewaters by capillary electrophoresis on a column-coupling chip with conductivity detection.
Science.gov (United States)
Luc, Milan; Kruk, Pavol; Masár, Marián
2011-07-01
Analytical potentialities of a chip-based CE in determination of ammonium in wastewaters were investigated. CZE with the electric field and/or ITP sample stacking was performed on a column-coupling (CC) chip with integrated conductivity detectors. Acetate background electrolytes (pH ∼3) including 18-crown-6-ether (18-crown-6) and tartaric acid were developed to reach rapid (in 7-8 min) CZE and ITP-CZE resolutions of ammonium from other cations (sodium, potassium, calcium and magnesium) present in wastewater samples. Under preferred working conditions (suppressed hydrodynamic flow (HDF) and EOF on the column-coupling chip), both the employed methods did provide very good repeatabilities of the migration (RSD of 0.2-0.8% for the migration time) and quantitative (RSD of 0.3-4.9% for the peak area) parameters in the model and wastewater samples. Using a 900-nL sample injection volume, LOD for ammonium were obtained at 20 and 40 μg/L concentrations in CZE and ITP-CZE separations, respectively. Very good agreements of the CZE and ITP-CZE determinations of ammonium in six untreated wastewater samples (only filtration and dilution) with the results obtained by a reference spectrometric method indicate a very good accuracy of both the CE methods presented. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
11. Classification of Antarctic algae by applying Kohonen neural network with 14 elements determined by inductively coupled plasma optical emission spectrometry
Energy Technology Data Exchange (ETDEWEB)
Balbinot, L. [Departamento de Quimica Analitica-Instituto de Quimica-Unicamp, PO Box 6154, CEP: 13083-971, Campinas, SP (Brazil); Smichowski, P. [Comision Nacional de Energia Atomica, Unidad de Actividad Quimica, Centro Atomico Constituyentes, Av. Gral Paz 1499, B1650KNA, San Martin, Provincia de Buenos Aires (Argentina); Farias, S. [Comision Nacional de Energia Atomica, Unidad de Actividad Quimica, Centro Atomico Constituyentes, Av. Gral Paz 1499, B1650KNA, San Martin, Provincia de Buenos Aires (Argentina); Arruda, M.A.Z. [Departamento de Quimica Analitica-Instituto de Quimica-Unicamp, PO Box 6154, CEP: 13083-971, Campinas, SP (Brazil); Vodopivez, C. [Instituto Antartico Argentino, Cerrito 1010, C1248AAZ, Buenos Aires (Argentina); Poppi, R.J. [Departamento de Quimica Analitica-Instituto de Quimica-Unicamp, PO Box 6154, CEP: 13083-971, Campinas, SP (Brazil)]. E-mail: [email protected]
2005-06-30
Optical emission spectrometers can generate results, which sometimes are not easy to interpret, mainly when the analyses involve classifications. To make simultaneous data interpretation possible, the Kohonen neural network is used to classify different Antarctic algae according to their taxonomic groups from the determination of 14 analytes. The Kohonen neural network architecture used was 5x5 neurons, thus reducing 14-dimension input data to two-dimensional space. The input data were 14 analytes (As, Co, Cu, Fe, Mn, Sr, Zn, Cd, Cr, Mo, Ni, Pb, Se, V) with their concentrations, determined by inductively coupled plasma optical emission spectrometry in 11 different species of algae. Three taxonomic groups (Rhodophyta, Phaeophyta and Cholorophyta) can be differentiated and classified through only their Cu content.
12. Major constituent quantitative determination in uranium alloys by coupled plasma atomic emission spectrometry and X ray fluorescence wavelength dispersive spectrometry
International Nuclear Information System (INIS)
Oliveira, Luis Claudio de; Silva, Adriana Mascarenhas Martins da; Gomide, Ricardo Goncalves; Silva, Ieda de Souza
2013-01-01
A wavelength-dispersive X-ray fluorescence (WD-XRF) spectrometric method for determination of major constituents elements (Zr, Nb, Mo) in Uranium/Zirconium/Niobium and Uranium/Molybdenum alloy samples were developed. The methods use samples taken in the form of chips that were dissolved in hot nitric acid and precipitate particles melted with lithium tetraborate and dissolved in hot nitric acid and finally analyzed as a solution. Studies on the determination by inductively coupled plasma optic emission spectrometry (ICP OES) using matched matrix in calibration curve were developed. The same samples solution were analyzed in both methods. The limits of detection (LOD), linearity of the calibrations curves, recovery study, accuracy and precision of the both techniques were carried out. The results were compared. (author)
13. Classification of Antarctic algae by applying Kohonen neural network with 14 elements determined by inductively coupled plasma optical emission spectrometry
International Nuclear Information System (INIS)
Balbinot, L.; Smichowski, P.; Farias, S.; Arruda, M.A.Z.; Vodopivez, C.; Poppi, R.J.
2005-01-01
Optical emission spectrometers can generate results, which sometimes are not easy to interpret, mainly when the analyses involve classifications. To make simultaneous data interpretation possible, the Kohonen neural network is used to classify different Antarctic algae according to their taxonomic groups from the determination of 14 analytes. The Kohonen neural network architecture used was 5x5 neurons, thus reducing 14-dimension input data to two-dimensional space. The input data were 14 analytes (As, Co, Cu, Fe, Mn, Sr, Zn, Cd, Cr, Mo, Ni, Pb, Se, V) with their concentrations, determined by inductively coupled plasma optical emission spectrometry in 11 different species of algae. Three taxonomic groups (Rhodophyta, Phaeophyta and Cholorophyta) can be differentiated and classified through only their Cu content
14. The determination of low level trace elements in coals by laser ablation-inductively coupled plasma-mass spectrometry
Energy Technology Data Exchange (ETDEWEB)
Booth, C.A.; Spears, D.A.; Krause, P.; Cox, A.G. [University of Sheffield, Sheffield (United Kingdom). Dept. of Earth Sciences
1999-11-01
The rapid determination of elements present in low level concentrations in bituminous coals is possible using laser abalation-inductively coupled plasma-mass spectrometry (l.a.-i.c.p.-m.s.). A wide range of trace elements can routinely be determined using this technique but it is for environmentally sensitive elements, such as As, Cd, Mo, Sb, Se and Hg, that it is of most use due to the low levels of detection. Calibration of the i.c.p.-m.s. was achieved using a series of uncertified coals and the method evaluated using the South African certified coals, Sarm 18, 19 and 20. A critical evaluation of the data obtained shows that for many of the elements studied the results obtained are both accurate and precise, even at very low concentrations, with the limits of detection for all of the elements being in the {mu}g/kg (parts per billion) range. 6 refs., 3 figs., 9 tabs.
15. One-loop tensor integrals in dimensional regularisation
International Nuclear Information System (INIS)
Campbell, J.M.; Glover, E.W.N.; Miller, D.J.
1997-01-01
We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of n- and (n-1)-point scalar integrals that are finite in the limit of vanishing Gram determinant. These non-trivial combinations of dilogarithms, logarithms and constants are systematically obtained by either differentiating with respect to the external parameters - essentially yielding scalar integrals with Feynman parameters in the numerator - or by developing the scalar integral in D=6-2ε or higher dimensions. An additional advantage is that other spurious kinematic singularities are also controlled. As an explicit example, we develop the tensor integrals and associated scalar integral combinations for processes where the internal particles are massless and where up to five (four massless and one massive) external particles are involved. For more general processes, we present the equations needed for deriving the relevant combinations of scalar integrals. (orig.)
16. Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description.
Science.gov (United States)
Shetty, Anil N; Chiang, Sharon; Maletic-Savatic, Mirjana; Kasprian, Gregor; Vannucci, Marina; Lee, Wesley
2014-01-01
In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal-Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.
17. Solitons in a six-dimensional super Yang-Mills-tensor system and non-critical strings
International Nuclear Information System (INIS)
Nair, V.P.; Randjbar-Daemi, S.
1997-11-01
In this letter we study a coupled system of six-dimensional N = 1 tensor and super Yang-Mills multiplets. We identify some of the solitonic states of this system which exhibit stringy behaviour in six dimensions. A discussion of the supercharges and energy for the tensor multiples as well as zero modes is also given. We speculate about the possible relationship between our solution and what is known as tensionless strings. (author)
18. Determination of zearalenone content in cereals and feedstuffs by immunoaffinity column coupled with liquid chromatography.
Science.gov (United States)
Fazekas, B; Tar, A
2001-01-01
The zearalenone content of maize, wheat, barley, swine feed, and poultry feed samples was determined by immunoaffinity column cleanup followed by liquid chromatography (IAC-LC). Samples were extracted in methanol-water (8 + 2, v/v) solution. The filtered extract was diluted with distilled water and applied to immunoaffinity columns. Zearalenone was eluted with methanol, dried by evaporation, and dissolved in acetonitrile-water (3 + 7, v/v). Zearalenone was separated by isocratic elution of acetonitrile-water (50 + 50, v/v) on reversed-phase C18 column. The quantitative analysis was performed by fluorescence detector and confirmation was based on the UV spectrum obtained by a diode array detector. The mean recovery rate of zearalenone was 82-97% (RSD, 1.4-4.1%) on the original (single-use) immunoaffinity columns. The limit of detection of zearalenone by fluorescence was 10 ng/g at a signal-to-noise ratio of 10:1 and 30 ng/g by spectral confirmation in UV. A good correlation was found (R2 = 0.89) between the results obtained by IAC-LC and by the official AOAC-LC method. The specificity of the method was increased by using fluorescence detection in parallel with UV detection. This method was applicable to the determination of zearalenone content in cereals and other kinds of feedstuffs. Reusability of immunoaffinity columns was examined by washing with water after sample elution and allowing columns to stand for 24 h at room temperature. The zearalenone recovery rate of the regenerated columns varied between 79 and 95% (RSD, 3.2-6.3%). Columns can be regenerated at least 3 times without altering their performance and without affecting the results of repeated determinations.
19. Simultaneous determination of macronutrients, micronutrients and trace elements in mineral fertilizers by inductively coupled plasma optical emission spectrometry
Science.gov (United States)
de Oliveira Souza, Sidnei; da Costa, Silvânio Silvério Lopes; Santos, Dayane Melo; dos Santos Pinto, Jéssica; Garcia, Carlos Alexandre Borges; Alves, José do Patrocínio Hora; Araujo, Rennan Geovanny Oliveira
2014-06-01
An analytical method for simultaneous determination of macronutrients (Ca, Mg, Na and P), micronutrients (Cu, Fe, Mn and Zn) and trace elements (Al, As, Cd, Pb and V) in mineral fertilizers was optimized. Two-level full factorial design was applied to evaluate the optimal proportions of reagents used in the sample digestion on hot plate. A Doehlert design for two variables was used to evaluate the operating conditions of the inductively coupled plasma optical emission spectrometer in order to accomplish the simultaneous determination of the analyte concentrations. The limits of quantification (LOQs) ranged from 2.0 mg kg- 1 for Mn to 77.3 mg kg- 1 for P. The accuracy and precision of the proposed method were evaluated by analysis of standard reference materials (SRMs) of Western phosphate rock (NIST 694), Florida phosphate rock (NIST 120C) and Trace elements in multi-nutrient fertilizer (NIST 695), considered to be adequate for simultaneous determination. Twenty-one samples of mineral fertilizers collected in Sergipe State, Brazil, were analyzed. For all samples, the As, Ca, Cd and Pb concentrations were below the LOQ values of the analytical method. For As, Cd and Pb the obtained LOQ values were below the maximum limit allowed by the Brazilian Ministry of Agriculture, Livestock and Food Supply (Ministério da Agricultura, Pecuária e Abastecimento - MAPA). The optimized method presented good accuracy and was effectively applied to quantitative simultaneous determination of the analytes in mineral fertilizers by inductively coupled plasma optical emission spectrometry (ICP OES).
20. A Coupled CFD/FEM Structural Analysis to Determine Deformed Shapes of the RSRM Inhibitors
Science.gov (United States)
Dill, Richard A.; Whitesides, R. Harold
1996-01-01
Recent trends towards an increase in the stiffness of the acrylonitrile butadiene rubber (NBR) insulation material used in the construction of the redesigned solid rocket motor (RSRM) propellant inhibitors prompted questions about possible effects on RSRM performance. The specific objectives of the computational fluid dynamics (CFD) task included: (1) the definition of pressure loads to calculate the deformed shape of stiffer inhibitors, (2) the calculation of higher port velocities over the inhibitors to determine shifts in the vortex shedding or edge tone frequencies, and (3) the quantification of higher slag impingement and collection rates on the inhibitors and in the submerged nose nozzle cavity. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8821082711219788, "perplexity": 2899.809245159416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027320156.86/warc/CC-MAIN-20190824084149-20190824110149-00469.warc.gz"} |
http://www.phy.duke.edu/~rgb/General/latex/ltx-223.html | ## eqnarray
\begin{eqnarray[*]}
var_1 & rel_1 & eq1 \\
var_2 & rel_2 & eq2 \\
....
\end{eqnarray[*]}
The eqnarray environment is typically used to display a sequence of equations or inequalities; it may also be used to manage spacing for long equations. The \lefteqn command is useful in this environment for splitting long equations over several lines.
It is very much like a three-column array environment, with position argument rcl, i.e., the columns are justified right, center, and left, respectively. (However, \multicolumn may not be used.)
Consecutive rows are separated by \\ commands and consecutive items within a row separated by an &. Any item may be empty, i.e., no text.
A separate equation number is placed on every line unless that line has a \nonumber command. The optional eqnarray* form does not generate any equation numbers.
A \label command anywhere within a row generates a reference to that row's number.
Related topics | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9888563752174377, "perplexity": 3511.1382479038275}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510276353.59/warc/CC-MAIN-20140728011756-00103-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://mathematica.stackexchange.com/questions/32555/reducing-quality-of-graphics3d-scene-to-improve-performance | # Reducing quality of Graphics3D scene to improve performance?
ProteinData["SERPINA1", "MoleculePlot"] gives the detailed Graphics3D plot below. I'd like to make many small copies of this object and place them in a single Graphics3D scene, but I'm running into performance problems because the molecule graphics-object is a pretty complicated mesh.
Are there general methods of reducing the quality/detail of graphics objects like the one below that would allow me to place many of these in a single scene?
-
This plot is very complex one, as each from ProteinData. If you want to loose some weight I can help with the following tricks.
But even with this I don't think you will be able to put large number of the elements with in one plot.
plot = ProteinData["SERPINA1", "MoleculePlot"];
In order to have an idea how the structure of this data looks you can use this:
(plot // First) /. List[(_?NumericQ) ..] :> Sequence[]
No we know what we can get rid of:
reduced = First @ plot /. {Specularity[___] :> Sequence[],
(VertexNormals -> _) :> Sequence[],
(VertexColors -> _) :> Sequence[],
EdgeForm[__] :> Sequence[],
RGBColor[_, _, _] :> Sequence[],
AbsoluteThickness[_] :> Sequence[]};
To improve performance with 3D plots which include duplicate objects the best way is to use GeometricTransoformation + TranslationTransform(for example). It is described well in this fenomenal training by Yu-Sung Chang around 28th minute mark.
Graphics3D[{GeometricTransformation[reduced,
Flatten[Table[TranslationTransform[10000. {i, j, k}],
{i, 2}, {j, 2}, {k, 2}]]]}
, Lighting -> None]
I was able to rotate this quite smoothly with an old pc with on board graphics card!
To go even further I tried to delete half of elements in the molecule, maybe it is not what you need but maybe you can use it:
i = 1;
new = reduced /. x : GraphicsComplex[___] :> (++i; If[OddQ@i, x, Sequence[]])
Graphics3D[{GeometricTransformation[new,
Flatten[Table[TranslationTransform[10000. {i, j, k}],
{i, 3}, {j, 3}, {k, 3}]]]
}, Lighting -> None]
27 elements and I'm able to rotate it easily while for this many copies it is not so obvious that they are reduced by half.
-
Never used ProteinData, but can you try this and see if it speeds thing a little?
g = ProteinData["SERPINA1", "MoleculePlot"];
Block[{$PerformanceGoal = "Speed"}, g] For me, it seems the plot was a little faster to move around with the mouse with this vs. "Quality" (but you can try it yourself and see). If this seems faster, then you can put all the graphics in that Block to that this option affects all rendering inside. - I'm still thinking if this works. If you try Block[{$PerformanceGoal = "Speed"}, g] === g it yellds True so it seem's not, but then I'm thinking, well, maybe it is about rendering so it will not be seen in the structure of the code. But when I try Block[{\$PerformanceGoal = "Speed"}, Plot3D[Sin[x y], {x, -1, 1}, {y, -1, 1}]] === Plot3D[Sin[10 x y], {x, -1, 1}, {y, -1, 1}] it yellds False so it seems SameQ is a good way to test this. And it means that this is not working :/ – Kuba Sep 18 '13 at 8:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.16363142430782318, "perplexity": 2217.3690615956134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701161775.86/warc/CC-MAIN-20160205193921-00288-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://ir.ymlib.yonsei.ac.kr/handle/22282913/92330 | ### BROWSE
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Tox-Info 시스템의 중독정보 데이터베이스와 응급실에 내원하는 중독 환자 분포의 비교
Title
Tox-Info 시스템의 중독정보 데이터베이스와 응급실에 내원하는 중독 환자 분포의 비교
Other Titles
Comparison between Emergency Patient Poisoning Cases and the Tox-Info System Database
Authors
김현종;김양원;정성필;조준호;조규종;이장영;이성우;이경원;이경우;이경룡;소병학;박창배;김현
Issue Date
2012
Journal Title
대한임상독성학회지
ISSN
1738-1320
Citation
대한임상독성학회지, Vol.10(1) : 8~14, 2012
Abstract
Purpose: The Tox-Info system is a poisonous substance information database developed by the Korean National Institute of Food and Drug Safety Evaluation. The aim of this study was to estimate the coverage effectiveness of the Tox-Info system by comparing the toxic substances included in the database with the distribution of the toxic substances implicated in the cases of intoxicated patients presenting to emergency departments. The secondary aim of the study was to propose any additional substances that should be added to the database. Methods: We retrospectively reviewed the medical records of patients suffering with toxic exposure who had visited any of 12 selected emergency departments in Korea from January 2010 to December 2011. The identified toxic substances were classified into groups including prescription drugs, agricultural chemicals, household products, animals or plants, herbal drugs, and others. We calculated the coverage rate of the Tox-Info database relative to the number of intoxication cases and the type of toxic substances involved. Results: A total of 5,840 intoxicated patient records were collected. Their mean age was $46.6{\pm}20.5$ years and 56.2% were female. Of the total intoxication cases, 87.8% of the identified toxic substances were included in the Tox-Info database, while only 41.6% of all of the types of identified toxic substances were included. Broken down by category, 122 prescription drugs, 15 agricultural chemicals, 12 household products, 14 animals or plants and 2 herbal drugs involved in poisoning cases were not included in the Tox-info database. Conclusion: This study demonstrated the clinical usefulness of the Tox-Info system. While 87.8% of the substances involved in the cases were included in the Tox-Info database, the database should be continuously updated in order to include even the most uncommon toxic substances.
URI
http://ir.ymlib.yonsei.ac.kr/handle/22282913/92330
Appears in Collections:
1. 연구논문 > 1. College of Medicine > Dept. of Emergency Medicine
Yonsei Authors
사서에게 알리기
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https://de.maplesoft.com/support/help/errors/view.aspx?path=PDEtools/ChangeSymmetry | ChangeSymmetry - Maple Help
PDEtools
ChangeSymmetry
perform a change of variables on the infinitesimals of a symmetry generator
Calling Sequence ChangeSymmetry(TR, S, ITR, DepVars, NewVars, 'options'='value')
Parameters
TR - a transformation equation or a set of them S - a list with the infinitesimals of a symmetry generator or the corresponding infinitesimal generator differential operator ITR - optional - the inverse transformation equation or a set of them DepVars - optional - may be required, a function or a list of them indicating the (old) dependent variables of the problem NewDepVars - optional - a function or a list of them representing the new dependent variables jetnotation = ... - (optional) can be true (default, the notation found in S), false, jetvariables, jetvariableswithbrackets, jetnumbers or jetODE; to respectively return or not using the different jet notations available output = ... - optional - can be list or operator, indicating the output to be a list of infinitesimal components or the corresponding infinitesimal generator differential operator simplifier = ... - optional - indicates the simplifier to be used instead of the default simplify/size
Description
• The ChangeSymmetry command performs changes of variables in a list of infinitesimals of a symmetry generator or its corresponding infinitesimal generator differential operator. This transformation takes into account that the infinitesimals are coefficients of differentiation operators which are also changed by the transformation, thus contributing to the resulting infinitesimals in the new variables.
• To avoid having to remember the optional keywords if you misspell the keyword, or just a portion of it, a matching against the correct keywords is performed, and when there is only one match, the input is automatically corrected.
Examples
> $\mathrm{with}\left(\mathrm{PDEtools},\mathrm{ChangeSymmetry},\mathrm{CanonicalCoordinates},\mathrm{InfinitesimalGenerator}\right)$
$\left[{\mathrm{ChangeSymmetry}}{,}{\mathrm{CanonicalCoordinates}}{,}{\mathrm{InfinitesimalGenerator}}\right]$ (1)
Consider a PDE problem with two independent variables and one dependent variable, u(x, t), and consider the list of infinitesimals of a symmetry group
> $S≔\left[\mathrm{_ξ}\left[x\right]=x,\mathrm{_ξ}\left[t\right]=1,\mathrm{_η}\left[u\right]=u\right]$
${S}{≔}\left[{{\mathrm{_ξ}}}_{{x}}{=}{x}{,}{{\mathrm{_ξ}}}_{{t}}{=}{1}{,}{{\mathrm{_η}}}_{{u}}{=}{u}\right]$ (2)
In the input above you can also pass the symmetry as without infinitesimals' labels, as in $\left[x,1,u\right]$. The corresponding infinitesimal generator is
> $G≔\mathrm{InfinitesimalGenerator}\left(S,u\left(x,t\right)\right)$
${G}{≔}{f}{→}{x}{}\left(\frac{{\partial }}{{\partial }{x}}{}{f}\right){+}\frac{{\partial }}{{\partial }{t}}{}{f}{+}{u}{}\left(\frac{{\partial }}{{\partial }{u}}{}{f}\right)$ (3)
Consider now the following transformation to be applied to the infinitesimals S
> $\mathrm{TR}≔\left\{t=r+v\left(r,s\right),x=\mathrm{exp}\left(v\left(r,s\right)\right),u\left(x,t\right)=s\mathrm{exp}\left(v\left(r,s\right)\right)\right\}$
${\mathrm{TR}}{≔}\left\{{t}{=}{r}{+}{v}{}\left({r}{,}{s}\right){,}{x}{=}{{ⅇ}}^{{v}{}\left({r}{,}{s}\right)}{,}{u}{}\left({x}{,}{t}\right){=}{s}{}{{ⅇ}}^{{v}{}\left({r}{,}{s}\right)}\right\}$ (4)
A direct application of this transformation to each component of $S$ is incorrect because these infinitesimals are coefficients of differentiation operators in the infinitesimal generator $G$ above. That fact is taken into account by ChangeSymmetry; the syntax it uses is the same as that of PDEtools[dchange] and DEtools[Xchange]
> $\mathrm{ChangeSymmetry}\left(\mathrm{TR},S\right)$
$\left[{{\mathrm{_ξ}}}_{{r}}{=}{0}{,}{{\mathrm{_ξ}}}_{{s}}{=}{0}{,}{{\mathrm{_η}}}_{{v}}{=}{1}\right]$ (5)
You can change variables directly in the infinitesimal generator differential operator, in which case the output has the same format, is also a differential operator
> $\mathrm{ChangeSymmetry}\left(\mathrm{TR},G\right)$
${f}{→}\frac{{\partial }}{{\partial }{v}}{}{f}$ (6)
You can also optionally request the output to be in list or operator format to override returning in the same format of the symmetry.
The transformation used in this example introduces the canonical coordinates of the symmetry group with infinitesimals S. That is why the result above is the normal form of the generator, all infinitesimals equal to 0 but for one equal to 1.
Consider now changing variables in a different symmetry, using the same transformation $\mathrm{TR}$
> $\mathrm{ChangeSymmetry}\left(\mathrm{TR},\left[\mathrm{_ξ}\left[x\right]=u,\mathrm{_ξ}\left[t\right]=x,\mathrm{_η}\left[u\right]=t\right]\right)$
$\left[{{\mathrm{_ξ}}}_{{r}}{=}{{ⅇ}}^{{v}}{-}{s}{,}{{\mathrm{_ξ}}}_{{s}}{=}\frac{{-}{{ⅇ}}^{{v}}{}{{s}}^{{2}}{+}{r}{+}{v}}{{{ⅇ}}^{{v}}}{,}{{\mathrm{_η}}}_{{v}}{=}{s}\right]$ (7)
Compare with the output in different jetnotation or in function notation (jetnotation = false); we also pass the symmetry without the infinitesimals' labels to save some keystrokes; correspondingly the output also comes without infinitesimals' labels
> $\mathrm{ChangeSymmetry}\left(\mathrm{TR},\left[u,x,t\right],\mathrm{jetnotation}=\mathrm{jetnumbers}\right)$
$\left[{{ⅇ}}^{{v}\left[\right]}{-}{s}{,}\frac{{-}{{ⅇ}}^{{v}\left[\right]}{}{{s}}^{{2}}{+}{r}{+}{v}\left[\right]}{{{ⅇ}}^{{v}\left[\right]}}{,}{s}\right]$ (8)
> $\mathrm{ChangeSymmetry}\left(\mathrm{TR},\left[u,x,t\right],\mathrm{jetnotation}=\mathrm{false}\right)$
$\left[{{ⅇ}}^{{v}{}\left({r}{,}{s}\right)}{-}{s}{,}\frac{{-}{{ⅇ}}^{{v}{}\left({r}{,}{s}\right)}{}{{s}}^{{2}}{+}{r}{+}{v}{}\left({r}{,}{s}\right)}{{{ⅇ}}^{{v}{}\left({r}{,}{s}\right)}}{,}{s}\right]$ (9) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 22, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8093209862709045, "perplexity": 882.9785986055333}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948765.13/warc/CC-MAIN-20230328042424-20230328072424-00261.warc.gz"} |
https://www.tutorialspoint.com/how-to-create-a-vector-of-matrices-in-r | # How to create a vector of matrices in R?
As of now it is not possible to create a vector of matrices in R. If we want to do it, we should prefer a list, hence we can create a list with matrices.
For Example, if we have matrices say M1, M2, and M3 and we want to create a list of these matrices then we can use the below given command −
list(M1,M2,M3)
## Example
To create a vector of matrices in R, use the following snippet −
List<-
list(M1=matrix(rpois(40,5),ncol=2),M2=matrix(rnorm(30),ncol=3),M3=matrix(sample(1:100,60),ncol=3))
List
The vector of matrices are as follows −
$M1 [,1] [,2] [1,] 5 6 [2,] 10 5 [3,] 3 5 [4,] 5 5 [5,] 7 4 [6,] 6 1 [7,] 5 3 [8,] 5 8 [9,] 9 7 [10,] 6 6 [11,] 3 5 [12,] 5 6 [13,] 3 1 [14,] 7 3 [15,] 5 6 [16,] 2 2 [17,] 2 3 [18,] 6 2 [19,] 2 6 [20,] 3 3$M2
[,1] [,2] [,3]
[1,] 1.9578909 0.45914071 -2.00944775
[2,] 0.1823403 1.05974964 0.42974335
[3,] 0.5921457 0.05078855 -0.03403513
[4,] -0.9808145 0.72762418 -1.09157212
[5,] -0.1980738 -2.32805205 0.68170467
[6,] 0.4682491 -0.48228947 -1.97650905
[7,] 0.2745822 -0.75218847 0.37580828
[8,] 1.5170457 0.02360123 0.33017557
[9,] -0.9706965 0.95314822 0.71276779
[10,] -0.9584967 0.09087230 0.52793781
\$M3
[,1] [,2] [,3]
[1,] 10 14 22
[2,] 99 46 83
[3,] 16 60 39
[4,] 28 3 72
[5,] 95 44 79
[6,] 96 29 42
[7,] 61 59 45
[8,] 55 47 67
[9,] 25 43 75
[10,] 70 18 89
[11,] 82 48 2
[12,] 86 54 57
[13,] 21 69 12
[14,] 19 100 85
[15,] 63 32 88
[16,] 56 62 91
[17,] 41 52 33
[18,] 24 40 7
[19,] 30 17 38
[20,] 98 93 97 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7398655414581299, "perplexity": 1673.1328684542536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949598.87/warc/CC-MAIN-20230331082653-20230331112653-00047.warc.gz"} |
http://math.stackexchange.com/questions/229184/what-is-the-effect-of-axis-rotation-on-functions-defined-on-mathbbr2 | # What is the effect of axis rotation on functions defined on $\mathbb{R}^{2}$
I haven't studied multivariable calculus yet but I have a question that bothers me. Let $F$ be a function $\mathbb{R}^2 \to \mathbb{R}$. Imagine that we rotate the co-ordinate axis by an angle $\theta$. I think the shape of the function should change. How should this function change if we make a rotation of the co-ordinate axis by some angle?
-
Do you mean to rotate in the plane of inputs $R^2$? If so this will only rotate the entire graph of $F$. If you want to rotate the entire $R^3$ in which the graph lies, the rotation may not even give the graph of a function. – coffeemath Nov 4 '12 at 23:04
Yes, I mean to rotate the domain . How can we express the new function in terms of the old function and the angle $\theta$? – Nabil Nov 5 '12 at 8:45
Let $F : \mathbb{R}^2 \to \mathbb{R}$ be the given function, and let $G_{\theta} : \mathbb{R}^2\to\mathbb{R}^2$ be rotation by $\theta$, then you want to consider the function $F\circ G_{\theta}$. Note that $G_{\theta}$ is a linear transformation and its standard matrix is a rotation matrix so we obtain
$$G_{\theta}\left(\left[\begin{array}\ x\\ y\end{array}\right]\right) = \left[\begin{array}\ \cos\theta & -\sin\theta\\ \sin\theta & \cos\theta\end{array}\right]\left[\begin{array}\ x\\ y\end{array}\right] = \left[\begin{array}\ x\cos\theta - y\sin\theta\\ x\sin\theta + y\cos\theta\end{array}\right].$$
$$(F\circ G_{\theta})(x, y) = F(G_{\theta}(x, y)) = F(x\cos\theta - y\sin\theta, x\sin\theta + y\cos\theta).$$
Note that the graph of $F\circ G_{\theta}$ is just the graph of $F$ rotated around the $z$-axis by $\theta$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8725774884223938, "perplexity": 128.34993006483535}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929956.54/warc/CC-MAIN-20150521113209-00144-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://en.wikipedia.org/wiki/Supermanifold | # Supermanifold
Jump to: navigation, search
In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below.
## Physics
In physics, a supermanifold is a manifold with both bosonic and fermionic coordinates. These coordinates are usually denoted by
$(x,\theta,\bar{\theta})$
where x is the usual spacetime vector, and $\theta\,$ and $\bar{\theta}$ are Grassmann-valued spinors.
Whether these extra coordinates have any physical meaning is debatable. However this formalism is very useful for writing down supersymmetric Lagrangians.
## Supermanifold: a definition
Although supermanifolds are special cases of noncommutative manifolds, the local structure of supermanifolds make them better suited to study with the tools of standard differential geometry and locally ringed spaces.
A supermanifold M of dimension (p,q) is a topological space M with a sheaf of superalgebras, usually denoted OM or C(M), that is locally isomorphic to $C^\infty(\mathbb{R}^p)\otimes\Lambda^\bullet(\xi_1,\dots\xi_q).$
Note that the definition of a supermanifold is similar to that of a differentiable manifold, except that the model space Rp has been replaced by the model superspace Rp|q.
### Side comment
This is different from the alternative definition where, using a fixed Grassmann algebra generated by a countable number of generators Λ, one defines a supermanifold as a point set space using charts with the "even coordinates" taking values in the linear combination of elements of Λ with even grading and the "odd coordinates" taking values which are linear combinations of elements of Λ with odd grading. This raises the question of the physical meaning of all these Grassmann-valued variables. Many physicists claim that they have none and that they are purely formal; if this is the case, this may make the definition in the main part of the article preferable.
## Properties
Unlike a regular manifold, a supermanifold is not entirely composed of a set of points. Instead, one takes the dual point of view that the structure of a supermanifold M is contained in its sheaf OM of "smooth functions". In the dual point of view, an injective map corresponds to a surjection of sheaves, and a surjective map corresponds to an injection of sheaves.
An alternative approach to the dual point of view is to use the functor of points.
If M is a supermanifold of dimension (p,q), then the underlying space M inherits the structure of a differentiable manifold whose sheaf of smooth functions is OM/I, where I is the ideal generated by all odd functions. Thus M is called the underlying space, or the body, of M. The quotient map OMOM/I corresponds to an injective map MM; thus M is a submanifold of M.
## Examples
• Let M be a manifold. The odd tangent bundle ΠTM is a supermanifold given by the sheaf Ω(M) of differential forms on M.
• More generally, let EM be a vector bundle. Then ΠE is a supermanifold given by the sheaf Γ(ΛE*). In fact, Π is a functor from the category of vector bundles to the category of supermanifolds.
## Batchelor's theorem
Batchelor's theorem states that every supermanifold is noncanonically isomorphic to a supermanifold of the form ΠE. The word "noncanonically" prevents one from concluding that supermanifolds are simply glorified vector bundles; although the functor Π maps surjectively onto the isomorphism classes of supermanifolds, it is not an equivalence of categories.
The proof of Batchelor's theorem relies in an essential way on the existence of a partition of unity, so it does not hold for complex or real-analytic supermanifolds.
## Odd symplectic structures
### Odd symplectic form
In many physical and geometric applications, a supermanifold comes equipped with an Grassmann-odd symplectic structure. All natural geometric objects on a supermanifold are graded. In particular, the bundle of two-forms is equipped with a grading. An odd symplectic form ω on a supermanifold is a closed, odd form, inducing a non-degenerate pairing on TM. Such a supermanifold is called a P-manifold. Its graded dimension is necessarily (n,n), because the odd symplectic form induces a pairing of odd and even variables. There is a version of the Darboux theorem for P-manifolds, which allows one to equip a P-manifold locally with a set of coordinates where the odd symplectic form ω is written as
$\omega = \sum_{i} d\xi_i \wedge dx_i ,$
where $x_i$ are even coordinates, and $\xi_i$ odd coordinates. (An odd symplectic form should not be confused with a Grassmann-even symplectic form on a supermanifold. In contrast, the Darboux version of an even symplectic form is
$\sum_i dp_i \wedge dq_i+\sum_j \frac{\varepsilon_j}{2}(d\xi_j)^2,$
where $p_i,q_i$ are even coordinates, $\xi_i$ odd coordinates and $\varepsilon_j$ are either +1 or -1.)
### Antibracket
Given an odd symplectic 2-form ω one may define a Poisson bracket known as the antibracket of any two functions F and G on a supermanifold by
$\{F,G\}=\frac{\partial_rF}{\partial z^i}\omega^{ij}(z)\frac{\partial_lG}{\partial z^j}.$
Here $\partial_r$ and $\partial_l$ are the right and left derivatives respectively and z are the coordinates of the supermanifold. Equipped with this bracket, the algebra of functions on a supermanifold becomes an antibracket algebra.
A coordinate transformation that preserves the antibracket is called a P-transformation. If the Berezinian of a P-transformation is equal to one then it is called an SP-transformation.
### P and SP-manifolds
Using the Darboux theorem for odd symplectic forms one can show that P-manifolds are constructed from open sets of superspaces ${\mathcal{R}}^{n|n}$ glued together by P-transformations. A manifold is said to be an SP-manifold if these transition functions can be chosen to be SP-transformations. Equivalently one may define an SP-manifold as a supermanifold with a nondegenerate odd 2-form ω and a density function ρ such that on each coordinate patch there exist Darboux coordinates in which ρ is identically equal to one.
### Laplacian
One may define a Laplacian operator Δ on an SP-manifold as the operator which takes a function H to one half of the divergence of the corresponding Hamiltonian vector field. Explicitly one defines
$\Delta H=\frac{1}{2\rho}\frac{\partial_r}{\partial z^a}\left(\rho\omega^{ij}(z)\frac{\partial_l H}{\partial z^j}\right)$.
In Darboux coordinates this definition reduces to
$\Delta=\frac{\partial_r}{\partial x^a}\frac{\partial_l}{\partial \theta_a}$
where xa and θa are even and odd coordinates such that
$\omega=dx^a\wedge d\theta_a$.
The Laplacian is odd and nilpotent
$\Delta^2=0$.
One may define the cohomology of functions H with respect to the Laplacian. In Geometry of Batalin-Vilkovisky quantization, Albert Schwarz has proven that the integral of a function H over a Lagrangian submanifold L depends only on the cohomology class of H and on the homology class of the body of L in the body of the ambient supermanifold.
## SUSY
A pre-SUSY-structure on a supermanifold of dimension (n,m) is an odd m-dimensional distribution $P\subset TM$. With such a distribution one associates its Frobenius tensor $S^2 P \mapsto TM/P$ (since P is odd, the skew-symmetric Frobenius tensor is a symmetric operation). If this tensor is non-degenerate, e.g. lies in an open orbit of $GL(P)\times GL(TM/P)$, M is called a SUSY-manifold. SUSY-structure in dimension (1, k) is the same as odd contact structure.
## References
[1] Joseph Bernstein, Lectures on Supersymmetry (notes by Dennis Gaitsgory) [1], "Quantum Field Theory program at IAS: Fall Term"
[2] A. Schwarz, Geometry of Batalin-Vilkovisky quantization, hep-th/9205088
[3] C. Bartocci, U. Bruzzo, D. Hernandez Ruiperez, The Geometry of Supermanifolds (Kluwer, 1991) ISBN 0-7923-1440-9
[4] A. Rogers, Supermanifolds: Theory and Applications (World Scientific, 2007) ISBN 981-02-1228-3
[5] L. Mangiarotti, G. Sardanashvily, Connections in Classical and Quantum Field Theory (World Scientific, 2000) ISBN 981-02-2013-8 (arXiv: 0910.0092) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 22, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9806106686592102, "perplexity": 672.8363656055512}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645167592.45/warc/CC-MAIN-20150827031247-00261-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://learnzillion.com/lesson_plans/7680-explore-the-results-of-bivariate-data | # Explore the results of bivariate data
teaches Common Core State Standards CCSS.Math.Content.HSS-ID.B.6b http://corestandards.org/Math/Content/HSS/ID/B/6/b
## You have saved this lesson!
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Card of | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9476495981216431, "perplexity": 17456.79399619084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542217.43/warc/CC-MAIN-20161202170902-00246-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://blog.plover.com/math/sqrt-2-addendum.html | # The Universe of Discourse
Thu, 26 Jan 2006
More irrational numbers
Gaal Yahas has written in with a delightfully simple proof that a particular number is irrational. Let x = log2 3; that is, such that 2x = 3. If x is rational, then we have 2a/b = 3 and 2a = 3b, where a and b are integers. But the left side is even and the right side is odd, so there are no such integers, and x must be irrational.
As long as I am on the subject, undergraduates are sometimes asked whether there are irrational numbers a and b such that ab is rational. It's easy to prove that there are. First, consider a = b = √2. If √2√2 is rational, then we are done. Otherwise, take a = √2√2 and b = √2. Both are irrational, but ab = 2.
This is also a standard example of a non-constructive proof: it demonstrates conclusively that the numbers in question exist, but it does not tell you which of the two constructed pairs is actually the one that is wanted. Pinning down the real answer is tricky. The Gelfond-Schneider theorem establishes that it is in fact the second pair, as one would expect. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.941335916519165, "perplexity": 263.3169071009548}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257831771.10/warc/CC-MAIN-20160723071031-00250-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1362282/sum-of-factors-of-multiplication-of-different-numbers/1370336 | # Sum of factors of multiplication of different numbers
Given $N$ numbers $n_i$ such that $\forall i \le N, n_i$ $\le10^9$, is there a method to calculate the sum of divisors of their product?
For example, given $\{11,15,17\}$ their product would is $2805$. The divisors of 2805 are $\{1,3,5,11,15,17,33,51,55,85,165,187,255,561,935,2805\}$, and the sum of those divisors (which is what I'm looking for) is $5184$.
I am a programmer and looking to implement this equation in my code. Tackling it with loops does work, but on large numbers it takes about 5 minutes to give a result!
If you have access to MatLab, you could use this divisor(n) function by Yash. From there, just call sum to get your total. For example:
>> sum(divisor(2805)) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4781184494495392, "perplexity": 169.5764975583176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145621.28/warc/CC-MAIN-20200221233354-20200222023354-00288.warc.gz"} |
https://www.physicsforums.com/threads/i-have-a-conservation-of-momentum-equation-q.25491/ | # I have a conservation of momentum equation Q
1. May 13, 2004
### Divergent13
I have a conservation of momentum equation Q!!
A 0.25kg skeet (clay target) is fired at an angle of 30 degrees to the horizon with a speed of 30 m/s. When it reaches its maximum height, it is hit from below by a 15g pellet traveling vertically upward at a speed 200m/s, the pellet is imbedded in the skeet.
So they want to know how much higher the skeet would go, and how much EXTRA horizontal distance the skeet would travel because of that collision...
I believe you can get the height from using conservation of energy. Then you can use what you know about projectiile motion to find all the different time intervals involved. From there, Distance in the x direction is simply Vx*t
I am just not sure if im getting the correct numbers? What would you guys do?
2. May 13, 2004
### arildno
Step 1.
Energy conservation up to maximal height h for the skeet:
$$\frac{1}{2}V_{0}^{2}=\frac{1}{2}V_{0,x}^{2}+gh$$
($$V_{0}$$ is initial velocity, with components $$V_{0,x},V_{0,y})$$
Step 2. Conservation of momentum in inelastic collision.
This will yield a non-zero upwards velocity component.
Step 3. Book-keeping:
Record horizontal distance already traveled, $$X_{1}$$, and vertical and horizontal velocities after collision.
Step 4.
Solve for landing position as a function of time, using parameters obtained in Step 3.
3. May 13, 2004
### Theelectricchild
But since Vo x is constant why would you use that equation to solve it?
4. May 13, 2004
### arildno
Because I forgot to eliminate it on both sides of the equation..
5. May 13, 2004
### Divergent13
I get an impact height of 11.43 m. Is this correct? (Using your equation.)
6. May 13, 2004
### arildno
If $$11.43=\frac{(30\sin30)^{2}}{2g}$$, then it is correct, as long as you with "impact height" means the height of the sleet when the proctile hits it.
7. May 13, 2004
### Divergent13
Cool then I just use conservation of momentum to find the new Vx and Vy and treat it like an ordinary 2D kinematics problem.
8. May 13, 2004
### arildno
Yes; that would be it.
Similar Discussions: I have a conservation of momentum equation Q | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8576478362083435, "perplexity": 1297.0360986762787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934807650.44/warc/CC-MAIN-20171124104142-20171124124142-00146.warc.gz"} |
http://math.stackexchange.com/questions/149361/is-every-semi-simple-ring-a-product-of-simple-rings | # Is every semi-simple ring a product of simple rings
I was wondering if the following statements were true;
1) Every semi-simple ring is a product of simple rings.
2) Every module over a division ring $R$ is free.
I think both of these statements are false but cannot come up with any counterexamples. Does anyone have any ideas?
-
Both statements are true. The first follows from Artin-Wedderburn and the proof of the second is the same as the corresponding proof for fields (Zorn's lemma). – Qiaochu Yuan May 24 '12 at 20:30
If you use "semisimple" as I do (to mean "$R$ is the direct sum of its simple right ideals" or "$R$ is Artinian with $rad(R)=0$") then the Artin-Wedderburn theorem proves the first statement true.
For the second question, I assume you are familiar with the proof that every vector space over a field $F$ has a basis. Once you know that is true, and $V$ has a basis $\{v_i\mid i\in I\}$, then you can map elements of $V$ to their coefficients in $\bigoplus_{i\in I} F$ to produce an isomorphism, showing that $V$ is free. If you review try this with division rings, you will find that commutativity was not necessary, and everything goes through here as well.
You also can try to work out the converse: if all right $R$ modules are free, then $R$ is a division ring. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8427186012268066, "perplexity": 104.0037981855936}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783392159.3/warc/CC-MAIN-20160624154952-00195-ip-10-164-35-72.ec2.internal.warc.gz"} |
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