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https://rupress.org/jcb/article/2/4/275/16479/THE-BASEMENT-LAMELLA-OF-AMPHIBIAN-SKIN-ITS | The basement lamella under the epidermis of amphibian larvae shows a sub-microscopic architecture of remarkable geometric regularity: It consists of about twenty layers of ground substance in which cylindrical fibers (presumably collagenous) of about 500 Angström diameter are embedded parallel to one another, but with the fiber directions alternating by 90° from layer to layer. The repair of this membrane after wounding was studied electronmicroscopically in ultrathin sections. The sequence of events is as follows: (1) Epidermal cells cover the wound exudate by migration. (2) Rather uniform fibers of small size (<200 A) appear in the space between the epidermal underside and the subjacent fibroblasts; these fibers are sparse and oriented at random. (3) Proceeding from the epidermal surface downward, a wave of organization spreads over this primitive fiber tangle, resulting in the fibers becoming (a) straightened; (b) oriented; (c) packed into the characteristic layered structure; and (d) brought up into the 500 A diameter class.
This content is only available as a PDF. | {"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": 0.8555336594581604, "perplexity": 4616.792342988413}, "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-2020-34/segments/1596439738888.13/warc/CC-MAIN-20200812083025-20200812113025-00276.warc.gz"} |
http://www.bama.ua.edu/~ddesmet/id/c7ay.html | ### A Thick Mirror
Figure 33.
A thick lens with the second surface covered with a reflecting coating as in Fig. 33 can be treated by the matrix method. The rays on reflection are considered by the reflection transformation above to be proceeding in the positive x direction so that the optical system to the left of the reflecting surface at O' must be "reflected" at O ' as well, as shown in Fig. 33. The final distances in the problem are referred to O '', that is, a positive distance to the right of O '' is actually the same distance to the left of O.
### Example 2
A biconvex lens 2 cm thick with a radius of 6 cm is silvered on the second surface. The index of refraction of the lens material is 1.5. Where are the focal planes of this thick mirror?
### Solution:
Thus f = 81/44 cm = f '.
OF = (81/44) (5/27) = 15/44 cm and
O''F'= 15/44 cm using equations (23) and (24).
The ray diagram is shown in Fig. 33.
### Example 3.
As a further example of the use of the focal planes, suppose an object 2 cm high is placed 15/22 cm in front of the vertex O. Where is the image and how large is it?
### Solution:
Since x = 30/44 - 15/44 = 15/44
or x'= 9.94 cm, or 9.94 + 15/44= 10.28 cm to the right of O '', which is actually 10.28 cm to the left of O. Since m =- (81/44)/(15/44)= -5.4, the image is 10.8 cm in size and inverted (or m = -x '/f ' = -9.94/1.835 = -5.4).
Exercise Solve the above example to find the focal positions using repeatedly the equations for reflection and refraction at a single surface.
### Astronomical Reflecting Telescope
Figure 34.
One simple form of the astronomical reflecting telescope is shown in Fig. 34. A parallel beam of light reflected from the spherical concave mirror is brought to the second focal point, F 'M, of this mirror after further reflection by a small plane mirror. The focal point F ' is also the first focal point FL of the eyepiece lens. The plane mirror is sufficiently small so that it interrupts only a small amount of the light falling on the concave mirror. In another common arrangement, the spherical mirror has a relatively small hole in its centre and a small plane (or convex) mirror redirects the light back to a focus at the centre of the large mirror where the focal image is examined with the eyepiece.
Figure 35.
The matrix method may be used to discuss this telescope as indicated in Fig. 35. Then, if |R| is the absolute value of the radius of curvature of the mirror and fL = f 'L equals the focal length of the lens
or
The telescopic system is again indicated by the zero in the lower left hand corner of the matrix and the angular magnification, M = '/ = R /2fL.
In practice, the large reflecting telescopes are usually used simply as cameras with a photographic plate placed in the focal plane of the large reflector. The surface of the reflector is made parabolic in shape to avoid spherical aberrations. Of course a reflector is free from chromatic aberrations as the laws of reflection are the same for all frequencies of light. The mirror may be made large in diameter in order to attain a high angular resolving power and to increase the light flux per unit area (the illuminance) at the photographic plate. | {"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": 0.81011962890625, "perplexity": 582.5354489306701}, "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-2015-11/segments/1424936463318.72/warc/CC-MAIN-20150226074103-00232-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://zbmath.org/?q=an:07031277 | ×
# zbMATH — the first resource for mathematics
On the fractional sums of some special functions. (English) Zbl 07031277
Summary: We obtain new relations involving the Lerch transcendent and establish some closed-form expressions using special functions like the Riemann and Hurwitz zeta functions and fractional sums. We also get some formulae for the specific values of the derivative of Lerch transcendent.
Reviewer: Reviewer (Berlin)
##### MSC:
11M35 Hurwitz and Lerch zeta functions 33B15 Gamma, beta and polygamma functions 30B99 Series expansions of functions of one complex variable
Equator
Full Text:
##### References:
[1] Bateman, H., Erdélyi, A.: Higher Transcendental Functions, vol. 1. McGraw-Hill, New York (1953) · Zbl 0143.29202 [2] Cvijović, D.; Klinowski, J., Closed-form summation of some trigonometric series, Math. Comput., 64, 205-210, (1995) · Zbl 0824.42002 [3] Dancs, MJ; He, T-X, An Euler-type formula for $$\zeta (2k+1)$$, J. Number Theory, 118, 192-199, (2006) · Zbl 1143.11028 [4] Guillera, J.; Sondow, J., Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent, Ramanujan J., 16, 247-270, (2008) · Zbl 1216.11075 [5] Lima, FMS, An Euler-type formula for $$\beta (2n)$$ and closed-form expressions for a class of zeta series, Integr. Transforms Spec. Funct., 23, 649-657, (2012) · Zbl 1269.30004 [6] Miller, J.; Adamchik, V., Derivatives of the Hurwitz zeta function for rational arguments, J. Comput. Appl. Math., 100, 201-206, (1998) · Zbl 0928.11037 [7] Müller, M.; Schleicher, D., How to add a non-integer number of terms, and how to produce unusual infinite summations, Comput. Appl. Math., 178, 347-360, (2005) · Zbl 1064.40003 [8] Müller, M.; Schleicher, D., Fractional sums and Euler-like identities, Ramanujan J., 21, 123-143, (2010) · Zbl 1183.33004 [9] Müller, M.; Schleicher, D., How to add a noninteger number of terms: from axioms to new identities, Am. Math. Mon., 118, 136-152, (2011) · Zbl 1226.40002 [10] Nakamura, T., Some formulas related to Hurwitz-Lerch zeta functions, Ramanujan J., 21, 285-302, (2010) · Zbl 1268.11125 [11] Oldham, K., Myland, J., Spanier, J.: An Atlas of Functions: With Equator, the Atlas Function Calculator, 2nd edn. Springer, New York (2009) · Zbl 1167.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | {"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": 0.9436466693878174, "perplexity": 4083.396425897956}, "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-2021-25/segments/1623487643354.47/warc/CC-MAIN-20210618230338-20210619020338-00038.warc.gz"} |
https://brilliant.org/problems/magnetic-field-6/ | # Magnetic field
A square wire loop having side length $$a$$, mass $$m$$, and resistance $$R$$ is moving along the positive $$x$$-axis at a speed of $$v_0$$. It enters a uniform, steady magnetic field $$\vec B = B_0 \big(-\widehat k \big)$$ at $$t = 0$$ seconds, as shown in the figure.
Find the total amount of heat loss in the resistance.
Details and Assumptions:
• The magnitude of $$v_0$$ is sufficient that the loop comes out of the region of magnetic field with some speed.
• Neglect any type of energy loss other than the heat loss in resistance of the wires of the square.
• Take $$v_0 = \dfrac{3B^2 a^3}{mR}$$.
× | {"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": 0.9231246113777161, "perplexity": 360.36968335330835}, "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-2018-51/segments/1544376827639.67/warc/CC-MAIN-20181216095437-20181216121437-00108.warc.gz"} |
https://forum.qt.io/topic/8136/how-to-vertical-the-text-and-control-the-line-spacing-by-qpainter-drawtext-rect-text | # How to vertical the text and control the line spacing by QPainter::drawText(rect,text）
• I have tried to add '\n' to each character, but I find line spacing is too large， how I can control this line spacing.
painter->drawText (position,"Qt by \n Trolltech");
thanks
• You can try to modify the different parameters of a QFont.
@
MyWidget::paintEvent(...)
{
QPainter p(this);
QFont ft = font();
ft.xxx();
p.setFont(ft);
}
@
But I'm not 100% sure, whether you can change line height...
• thanks Gerolf.
the font size is 16, it can be changed by user. it means that the text size is ok, just the line spacing is too large，because of "\n". but how to reset line spacing.
• I meant the line height of the font, which is typically ascent + descent + leading (look at QFontMetrics) and which is located in the font properties.
• ok, I see.
• I am sorry, I still don’t find that which function can set line spacing in QFont. can someone help me .
• [quote author="dxwang" date="1312182018"]I am sorry, I still don’t find that which function can set line spacing in QFont. can someone help me .[/quote]
Did you find the answer. I am searching something similar ? | {"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": 0.975976288318634, "perplexity": 1752.4424546081475}, "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-2021-10/segments/1614178361510.12/warc/CC-MAIN-20210228145113-20210228175113-00302.warc.gz"} |
https://www.physicsforums.com/threads/angular-momentum-of-the-sun-and-a-white-dwarf.292528/ | # Angular momentum of the sun and a white dwarf
1. Feb 15, 2009
### Fendergutt
1. The problem statement, all variables and given/known data
The Sun rotates about its own axis once every 26.0 days. Its mass is m_sun = 2.0E30 kg and radius is r_sun = 7.0E8 m. Assume that the Sun is a solid sphere with uniform density.
Astrophysicists predict that the Sun will collapse into a white dwarf in some billions of years. Its density will be high, and its radius 5.8E6 m. Assume the mass of the Sun to be unaltered (a good approximation for our calculation).
(i) What is the Sun's angular momentum now?
(ii) What is the Sun's angular momentum as a white dwarf?
(iii) How long will it take for the white dwarf Sun to rotate about its own axis?
2. Relevant equations
I = (2/5)*m*r^2
L = Iω = Iωk (k being the z-axis unit vector)
3. The attempt at a solution
(i)
ω_sun = (2pi)/(26 days) = 2.8E-6 rad/s
L = I_sun*ω_sun*k = (2/5)*m_sun*r_sun²*ω_sun*k = (2/5)*2.0E30 kg * (7.0E8 m)² * ω_sun * k = 1.1E42 kgm²/s
(ii)
I don't know the new spin angular velocity of the white dwarf, do I? If I leave ω_white = ω_sun the formula for L above with inserted new value for radius r_white gives appr. 7.5E37 kgm²/s k, ie. the angular momentum is lowered. Can this be correct?
(iii)
I don't know what to do here. I want to find the new period T, but I suspect there is something odd in (ii). Is there a relation I have overseen?
Thanks for any help.
2. Feb 15, 2009
### Staff: Mentor
I didn't check the arithmetic, but the method is correct.
What's required to change the angular momentum? Does that apply here?
3. Feb 15, 2009
### Fendergutt
Ah, so you are saying to me: Angular momentum is a conserved quantity: a system's angular momentum stays constant unless an external torque acts on it.
Then I set up T_white = ( I_white * 2pi * k ) / L which gives a rotation period of 1.5E2 s or 150 s.
(Mathematically: L features numbers and the unit vector k; In the calculation above I mentally ignored the unit vector because it was a feature of both nominator and denominator -- I'm I right to do this?)
4. Feb 15, 2009
### Staff: Mentor
All good.
Similar Discussions: Angular momentum of the sun and a white dwarf | {"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": 0.9576821327209473, "perplexity": 1488.274061635128}, "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/1518891812871.2/warc/CC-MAIN-20180220010854-20180220030854-00372.warc.gz"} |
https://hammer.figshare.com/articles/Partition_Density_Functional_Theory_for_Semi-In_finite_and_Periodic_Systems/7498814/1 | ## Partition Density Functional Theory for Semi-In finite and Periodic Systems
2019-01-03T19:29:39Z (GMT)
Partition Density Functional Theory (P-DFT) is a formally exact method to find the ground-state energy and density of molecules via self-consistent calculations on isolated fragments. It is being used to improve the accuracy of Kohn-Sham DFT (KS-DFT) calculations and to lower their computational cost. Here, the method has been extended to be applicable to semi-infi nite and periodic systems. This extension involves the development of new algorithms to calculate the exact partition potential, a central quantity of P-DFT. A novel feature of these algorithms is that they are applicable to systems of constant chemical potential, and not only to systems of constant electron number. We illustrate our method on one-dimensional model systems designed to mimic metal-atom interfaces and atomic chains. From extensive numerical tests on these model systems, we infer that: 1.) The usual derivative discontinuities of open-system KS-DFT are reduced (but do not disappear completely) when an atom is at a nite distance from a metallic reservoir; 2.) In situations where we do not have chemical potential equalization between fragments of a system, a new constraint for P-DFT emerges which relates the fragment chemical potentials and the combined system chemical potential; 3.) P-DFT is an ideal method for studying charge transfer and fragment interactions due to the correct ensemble treatment of fractional electron charges; 4.) Key features of the partition potential at the metalatom interface are correlated to well-known features of the underlying KS potential; and 5.) When there is chemical potential equalization between an atom and a metal surface it is interacting with, there is strong charge transfer between the metal and atom. In these cases of charge transfer the density response to an in nitesimal change in the chemical potential is located almost exclusively around the atom. On the other hand, when the fragment chemical potentials do not equalize, the density response only a ects the surface Friedel oscillations in the metal.
CC BY 4.0 | {"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": 0.8530552387237549, "perplexity": 1032.225079269322}, "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-2020-24/segments/1590347399820.9/warc/CC-MAIN-20200528135528-20200528165528-00142.warc.gz"} |
https://www.physicsforums.com/threads/average-acceleration-question.630292/ | # Homework Help: Average Acceleration Question
1. Aug 21, 2012
### DrDonaldDuck
1. The problem statement, all variables and given/known data
"A bullet is fired through a 5.0 cm thick board of some material. The bullet strikes the board with a speed of 200 m/s, and emerges out the other end at 100 m/s.
2. Relevant equations
a= (change in velocity)/(change in time)
average velocity = .5(initial v + final v)
3. The attempt at a solution
a= (-100 m/s)/(.000333 seconds) = -300300 m/s^2
I found .000333s as the time it took for the bullet to pass through the board, using the average velocity of 150 m/s.
Is this correct?
SOLVED.
Last edited: Aug 21, 2012
2. Aug 22, 2012
### Simon Bridge
It helps, if you are unsure of your reasoning, to relate what you did with some other representation... eg. from your equations:
ave speed = distance over change in time:$$\frac{d}{T} = \frac{1}{2}(v + u) \Rightarrow 2d = (v + u)T$$... using distace d, change in time T, final velocity v, initial velocity u.
acceleration is change in speed over change in time:$$a = \frac{v - u}{T} \Rightarrow v = aT + u$$
Soooo... combining them:$$2d = \big ( (aT + u) + u\big )T = aT^2 +2uT \Rightarrow d = uT + \frac{1}{2}aT^2$$... which you will recognize as a kinematic equation.
... so what you've done is basically the same as assuming a constant acceleration, and is consistent with other physics you know. | {"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": 0.9420969486236572, "perplexity": 2198.4651326267594}, "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-2018-51/segments/1544376831933.96/warc/CC-MAIN-20181219090209-20181219112209-00252.warc.gz"} |
http://www.qub.ac.uk/puremaths/Conferences/Galway14/Tamariz-Mascarua.html | A. Tamariz-Mascarua Independent Families and Resolvability
Joint work with S. Garcia-Ferreira and M. Hrusak
Let $\tau$ and $\gamma$ be infinite cardinal numbers with $\tau \leq \gamma$. A subset $Y$ of a space $X$ is called $C_\tau$-compact if $f[Y]$ is compact for every continuous function
$f : X \to \R^\tau$. We prove that every
$C_\tau$-compact dense subspace of a product of $\gamma$ non-trivial compact spaces each of them of weight $\leq \tau$ is $2^\tau$-resolvable. In particular, every
pseudocompact dense subspace of a product of non-trivial metrizable compact spaces
is $\frak{c}$-resolvable. As a consequence of this fact we obtain that there is no $\sigma$-independent maximal independent family.
Also, we present a consistent example, relative to the existence of a measurable cardinal,
of a dense pseudocompact subspace of $\{0,1\}^{2^\lambda}$, with
$\lambda = 2^{\omega_1}$, which is not maximally resolvable. Moreover, we improve
a result by W. Hu \cite{wahu} by showing that if maximal $\theta$-independent families do not exist, then
every dense subset of $\Box_{\theta}\{0,1\}^\gamma$ is $\omega$-resolvable
for a regular cardinal number $\theta$ with $\omega_1 \leq \theta \leq \gamma$. Finally, if there are no maximal independent
families on $\kappa$ of cardinality $\gamma$, then every Baire dense subset of $\{0,1\}^\gamma$of cardinality $\leq \kappa$ and every Baire dense subset of $[0,1]^\gamma$ of cardinality $\leq \kappa$ are $\omega$-resolvable. | {"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": 0.9878784418106079, "perplexity": 655.8253848343928}, "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-2014-23/segments/1406510272584.13/warc/CC-MAIN-20140728011752-00126-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://clay6.com/qa/9456/examine-the-applicability-of-mean-value-theorem-for-all-three-functions-giv | # Examine the applicability of Mean Value Theorem for all three functions given in $(iii)\;f (x) = x^2-1 \;for\; x \: \in [1,2]$
This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com
Toolbox:
• By Mean value theorem $f'(c)=\large\frac{f(b)-f(a)}{b-a}$
Step 1:
$f(x)=x^2-1$ for $x\in [1,2]$
It is polynomial.Therefore it is continuous in the interval [1,2].
$f'(x)=2x$
$f(1)=1-1=0$
$f(2)=4-1=3$
$f'(c)=2c$
Step 2:
$f'(c)=\large\frac{f(b)-f(a)}{b-a}$
$2c=\large\frac{3-0}{2-1}$
$2c=\large\frac{3}{1}$
$2c=3$
$c=\large\frac{3}{2}$
$c=\large\frac{3}{2}$ which belongs to $(1,2)$ | {"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": 0.9414211511611938, "perplexity": 422.3839180733695}, "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-2018-26/segments/1529267864482.90/warc/CC-MAIN-20180622123642-20180622143642-00040.warc.gz"} |
https://cs.stackexchange.com/questions/76710/are-all-decidable-languages-mapping-reducible-to-its-complement | # Are all decidable languages mapping reducible to its complement?
I dont think this is true, take the language with a single element L = {0}, then the complement L' would have infinitely many strings (everything that isn't 0). So if it were true that A is mapping reducible to its complement, everything in L' can be obtained via a computable function from some element in L, i.e 010 is in L' however there is no x in L that gives f(x) = 101, since theres only one element, 0, it maps to one result.
Would this be correct?
• Here is a reduction from $L$ to its complement: map $0$ to $1$ and everything else to $0$. – Yuval Filmus Jun 13 '17 at 5:46
Let $L_1,L_2$ be two languages over $\{0,1\}$. A (computable) mapping reduction from $L_1$ to $L_2$ is a computable function $f\colon \{0,1\}^* \to \{0,1\}^*$ such that for all $x \in \{0,1\}^*$ it holds that $x \in L_1$ iff $f(x) \in L_2$.
In your example, $L_1 = \{0\}$ and $L_2 = \overline{\{0\}}$, there does exist a mapping reduction, given by $$f(x) = \begin{cases} 1 & \text{if }x = 0, \\ 0 & \text{if }x \neq 0.\end{cases}$$ Clearly $f$ is computable, and you can check that $x \in L_1$ iff $f(x) \in L_2$.
Hence your example doesn't work. You can check, however, that $\emptyset$ and $\{0,1\}^*$ are two examples of languages not reducible to their complement. Indeed, these are the only examples, which you can try to prove. | {"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": 0.8437954783439636, "perplexity": 175.34405262282746}, "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/1627046153814.37/warc/CC-MAIN-20210729011903-20210729041903-00556.warc.gz"} |
https://meinwords.wordpress.com/2007/08/16/magic-squares-as-vectors-to-a-field-of-reals/ | # Magic Squares as Vectors to a field of Reals
Pattern 1: Multiplication of a scalar into the quantity and the result is of the same type as the original quantity.
$displaystyle{ M = left(begin{array}{cccc} 16 & 3 & 2 & 13\ 5 & 10 & 11 & 8\ 9 & 6 & 7 & 12\ 4 & 15 & 14 & 1 end{array}right)}$
is a magic square.
$displaystyle{ 3 M = left(begin{array}{cccc} 48 & 9 & 6 & 39\ 15 & 30 & 33 & 24\ 27 & 18 & 21 & 36\ 12 & 45 & 42 & 3 end{array}right)}$
is also a magic square.Pattern 2: Add 2 of the quantity and the result is of the same type as the original quantities.
$displaystyle{ left(begin{array}{cccc} 16 & 3 & 2 & 13\ 5 & 10 & 11 & 8\ 9 & 6 & 7 & 12\ 4 & 15 & 14 & 1 end{array}right) + left(begin{array}{cccc} 20 & 16 & 6 & 7\ 2 & 11 & 13 & 23\ 19 & 21 & 4 & 5\ 8 & 1 & 26 & 14 end{array}right) = left(begin{array}{cccc} 36 & 19 & 8 & 20\ 7 & 21 & 24 & 31\ 28 & 27 & 11 & 17\ 12 & 16 & 40 & 15 end{array}right)}$
In the above statement, the sum is also a magic square.Any quantities that obey Pattern one and 2 are vectors, and hence unit vectors can be defined. The norm a.k.a the magnitude can be defined as the constant sum of magic square.
$displaystyle{ hat{a} = left(begin{array}{cccc} 1 & 0 & 0 & 0\ 0 & 0 & 0 & 1\ 0 & 1 & 0 & 0\ 0 & 0 & 1 & 0 end{array}right) hat{b} = left(begin{array}{cccc} 0 & 1 & 0 & 0\ 0 & 0 & 0 & 1\ 0 & 0 & 1 & 0\ 1 & 0 & 0 & 0 end{array}right) hat{c} = left(begin{array}{cccc} 0 & 1 & 0 & 0\ 0 & 0 & 1 & 0\ 1 & 0 & 0 & 0\ 0 & 0 & 0 & 1 end{array}right) hat{d} = left(begin{array}{cccc} 0 & 0 & 0 & 1\ 0 & 1 & 0 & 0\ 1 & 0 & 0 & 0\ 0 & 0 & 1 & 0 end{array}right) }$
$displaystyle{ hat{e} = left(begin{array}{cccc} 0 & 0 & 0 & 1\ 1 & 0 & 0 & 0\ 0 & 0 & 1 & 0\ 0 & 1 & 0 & 0 end{array}right) hat{f} = left(begin{array}{cccc} 0 & 0 & 1 & 0\ 0 & 1 & 0 & 0\ 0 & 0 & 0 & 1\ 1 & 0 & 0 & 0 end{array}right) hat{g} = left(begin{array}{cccc} 1 & 0 & 0 & 0\ 0 & 0 & 0 & 1\ 0 & 1 & 0 & 0\ 0 & 0 & 1 & 0 end{array}right) hat{h} = left(begin{array}{cccc} 1 & 0 & 0 & 0\ 0 & 0 & 0 & 1\ 0 & 1 & 0 & 0\ 0 & 0 & 1 & 0 end{array}right) }$
Since there are seven unit vectors we are dealing with a 7th dimensional space.
$displaystyle{ 6 hat{a} + 2 hat{b} + hat{c} + 8 hat{d} + 5 hat{e} + 2 hat{f} + 10 hat{g} = left(begin{array}{cccc} 16 & 3 & 2 & 13\ 5 & 10 & 11 & 8\ 9 & 6 & 7 & 12\ 4 & 15 & 14 & 1 end{array}right) }$ | {"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": 0, "wp_latex": 6, "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": 0.92509526014328, "perplexity": 447.5186630919708}, "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-2018-13/segments/1521257645177.12/warc/CC-MAIN-20180317135816-20180317155816-00392.warc.gz"} |
https://planetmath.org/NewVectorSpacesFromOldOnes | new vector spaces from old ones
This entry list methods that give new vector spaces from old ones.
1. 1.
Changing the field (complexification, etc.)
2. 2.
3. 3.
4. 4.
direct product of vectors spaces
5. 5.
6. 6.
Tensor product of vector spaces (http://planetmath.org/TensorProductClassical)
7. 7.
The space of linear maps from one vector space to another, also denoted by $\operatorname{Hom}_{k}(V,W)$, or simply $\operatorname{Hom}(V,W)$, where $V$ and $W$ are vector spaces over the field $k$
8. 8.
The space of endomorphisms of a vector space. Using the notation above, this is the space $\operatorname{Hom}_{k}(V,V)=\operatorname{End}(V)$
9. 9.
dual vector space (http://planetmath.org/DualSpace), and bi-dual vector space. Using the notation above, this is the space $\operatorname{Hom}(V,k)$, or simply $V^{*}$.
10. 10.
The annihilator of a subspace is a subspace of the dual vector space
11. 11.
Wedge product of vector spaces
12. 12.
A field $k$ is a vector space over itself. Consider a set $B$ and the set $V$ of all functions from $B$ to $k$. Then $V$ has a natural vector space structure. If $B$ is finite, then $V$ can be viewed as a vector space having $B$ as a basis.
Vector spaces involving a linear map
Suppose $L\colon\thinspace V\to W$ is a linear map.
1. 1.
The kernel of $L$ is a subspace of $V$.
2. 2.
The image of $L$ is a subspace of $W$.
3. 3.
The cokernel of $L$ is a quotient space of $W$.
Topological vector spaces
Suppose $V$ is topological vector space.
1. 1.
If $W$ is a subspace of $V$ then its closure $\overline{W}$ is also a subspace of $V$.
2. 2.
If $V$ is a metric vector space then its completion $\widetilde{V}$ is also a (metric) vector space.
3. 3.
Spaces of structures and subspaces of the tensor algebra of a vector space
There are also certain spaces of interesting structures on a vector space that at least in the case of finite dimension correspond to certain subspaces of the tensor algebra of the vector space. These spaces include:
1. 1.
The space of Euclidean inner products.
2. 2.
The space of Hermitian inner products.
3. 3.
the space of symplectic structures.
4. 4.
vector bundles
5. 5.
space of connections
Title new vector spaces from old ones NewVectorSpacesFromOldOnes 2013-03-22 15:31:08 2013-03-22 15:31:08 matte (1858) matte (1858) 16 matte (1858) Topic msc 16-00 msc 13-00 msc 20-00 msc 15-00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 31, "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": 0.9810197949409485, "perplexity": 592.8480523988982}, "config": {"markdown_headings": false, "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-2019-39/segments/1568514571360.41/warc/CC-MAIN-20190915114318-20190915140318-00131.warc.gz"} |
https://worldwidescience.org/topicpages/a/angularity.html | #### Sample records for angularity
1. Angular Momentum
Science.gov (United States)
Shakur, Asif; Sinatra, Taylor
2013-01-01
The gyroscope in a smartphone was employed in a physics laboratory setting to verify the conservation of angular momentum and the nonconservation of rotational kinetic energy. As is well-known, smartphones are ubiquitous on college campuses. These devices have a panoply of built-in sensors. This creates a unique opportunity for a new paradigm in…
2. Professional AngularJS
CERN Document Server
Karpov, Valeri
2015-01-01
A comprehensive guide to AngularJS, Google's open-source client-side framework for app development. Most of the existing guides to AngularJS struggle to provide simple and understandable explanations for more advanced concepts. As a result, some developers who understand all the basic concepts of AngularJS struggle when it comes to building more complex real-world applications. Professional AngularJS provides a thorough understanding of AngularJS, covering everything from basic concepts, such as directives and data binding, to more advanced concepts like transclusion, build systems, and auto
3. Angular correlation methods
International Nuclear Information System (INIS)
Ferguson, A.J.
1974-01-01
An outline of the theory of angular correlations is presented, and the difference between the modern density matrix method and the traditional wave function method is stressed. Comments are offered on particular angular correlation theoretical techniques. A brief discussion is given of recent studies of gamma ray angular correlations of reaction products recoiling with high velocity into vacuum. Two methods for optimization to obtain the most accurate expansion coefficients of the correlation are discussed. (1 figure, 53 references) (U.S.)
4. Rotations and angular momentum
International Nuclear Information System (INIS)
Nyborg, P.; Froyland, J.
1979-01-01
This paper is devoted to the analysis of rotational invariance and the properties of angular momentum in quantum mechanics. In particular, the problem of addition of angular momenta is treated in detail, and tables of Clebsch-Gordan coefficients are included
5. Angular Acceleration without Torque?
Science.gov (United States)
Kaufman, Richard D.
2012-01-01
Hardly. Just as Robert Johns qualitatively describes angular acceleration by an internal force in his article "Acceleration Without Force?" here we will extend the discussion to consider angular acceleration by an internal torque. As we will see, this internal torque is due to an internal force acting at a distance from an instantaneous center.
6. Quark Orbital Angular Momentum
Directory of Open Access Journals (Sweden)
Burkardt Matthias
2015-01-01
Full Text Available Definitions of orbital angular momentum based on Wigner distributions are used as a framework to discuss the connection between the Ji definition of the quark orbital angular momentum and that of Jaffe and Manohar. We find that the difference between these two definitions can be interpreted as the change in the quark orbital angular momentum as it leaves the target in a DIS experiment. The mechanism responsible for that change is similar to the mechanism that causes transverse single-spin asymmetries in semi-inclusive deep-inelastic scattering.
7. Optical Angular Momentum
International Nuclear Information System (INIS)
Arimondo, Ennio
2004-01-01
For many years the Institute of Physics has published books on hot topics based on a collection of reprints from different journals, including some remarks by the editors of each volume. The book on Optical Angular Momentum, edited by L Allen, S M Barnett and M J Padgett, is a recent addition to the series. It reproduces forty four papers originally published in different journals and in a few cases it provides direct access to works not easily accessible to a web navigator. The collection covers nearly a hundred years of progress in physics, starting from an historic 1909 paper by Poynting, and ending with a 2002 paper by Padgett, Barnett and coworkers on the measurement of the orbital angular momentum of a single photon. The field of optical angular momentum has expanded greatly, creating an interdisciplinary attraction for researchers operating in quantum optics, atomic physics, solid state physics, biophysics and quantum information theory. The development of laser optics, especially the control of single mode sources, has made possible the specific design of optical radiation modes with a high degree of control on the light angular momentum. The editors of this book are important figures in the field of angular momentum, having contributed to key progress in the area. L Allen published an historical paper in 1999, he and M J Padgett (together with M Babiker) produced few years ago a long review article which is today still the most complete basic introduction to the angular momentum of light, while S M Barnett has contributed several high quality papers to the progress of this area of physics. The editors' choice provides an excellent overview to all readers, with papers classified into eight different topics, covering the basic principles of the light and spin and orbital angular momentum, the laboratory tools for creating laser beams carrying orbital angular momentum, the optical forces and torques created by laser beams carrying angular momentum on
8. Angular Accelerating White Light
CSIR Research Space (South Africa)
Dudley, Angela L
2015-08-01
Full Text Available wavelength dependence. By digitally simulating free-space propagation on the SLM, The authors compare the effects of real and digital propagation on the angular rotation rates of the resulting optical fields for various wavelengths. The development...
9. Angular trap for macroparticles
International Nuclear Information System (INIS)
Aksyonov, D.S.
2013-01-01
Properties of angular macroparticle traps were investigated in this work. These properties are required to design vacuum arc plasma filters. The correlation between trap geometry parameters and its ability to absorb macroparticles were found. Calculations allow one to predict the behaviour of filtering abilities of separators which contain such traps in their design. Recommendations regarding the use of angular traps in filters of different builds are given.
10. Fission fragment angular momentum
International Nuclear Information System (INIS)
Frenne, D. De
1991-01-01
Most of the energy released in fission is converted into translational kinetic energy of the fragments. The remaining excitation energy will be distributed among neutrons and gammas. An important parameter characterizing the scission configuration is the primary angular momentum of the nascent fragments. Neutron emission is not expected to decrease the spin of the fragments by more than one unit of angular momentum and is as such of less importance in the determination of the initial fragment spins. Gamma emission is a suitable tool in studying initial fragment spins because the emission time, number, energy, and multipolarity of the gammas strongly depend on the value of the primary angular momentum. The main conclusions of experiments on gamma emission were that the initial angular momentum of the fragments is large compared to the ground state spin and oriented perpendicular to the fission axis. Most of the recent information concerning initial fragment spin distributions comes from the measurement of isomeric ratios for isomeric pairs produced in fission. Although in nearly every mass chain isomers are known, only a small number are suitable for initial fission fragment spin studies. Yield and half-life considerations strongly limit the number of candidates. This has the advantage that the behavior of a specific isomeric pair can be investigated for a number of fissioning systems at different excitation energies of the fragments and fissioning nuclei. Because most of the recent information on primary angular momenta comes from measurements of isomeric ratios, the global deexcitation process of the fragments and the calculation of the initial fragment spin distribution from measured isomeric ratios are discussed here. The most important results on primary angular momentum determinations are reviewed and some theoretical approaches are given. 45 refs., 7 figs., 2 tabs
11. Angular momentum projected semiclassics
International Nuclear Information System (INIS)
Hasse, R.W.
1986-10-01
By using angular momentum projected plane waves as wave functions, we derive semiclassical expressions for the single-particle propagator, the partition function, the nonlocal density matrix, the single-particle density and the one particle- one hole level density for fixed angular momentum and fixed z-component or summed over the z-components. Other quantities can be deduced from the propagator. In coordinate space (r, r') the relevant quantities depend on vertical stroker - r 3 vertical stroke instead of vertical stroker - r'vertical stroke and in Wigner space (R, P) they become proportional to the angular momentum constraints δ(vertical strokeRxPvertical stroke/ℎ - l) and δ((RxP) z /ℎ - m). As applications we calculate the single-particle and one particle- one hole level densities for harmonic oscillator and Hill-Wheeler box potentials and the imaginary part of the optical potential and its volume integral with an underlying harmonic oscillator potential and a zero range two-body interaction. (orig.)
12. Optical angular momentum and atoms.
Science.gov (United States)
Franke-Arnold, Sonja
2017-02-28
Any coherent interaction of light and atoms needs to conserve energy, linear momentum and angular momentum. What happens to an atom's angular momentum if it encounters light that carries orbital angular momentum (OAM)? This is a particularly intriguing question as the angular momentum of atoms is quantized, incorporating the intrinsic spin angular momentum of the individual electrons as well as the OAM associated with their spatial distribution. In addition, a mechanical angular momentum can arise from the rotation of the entire atom, which for very cold atoms is also quantized. Atoms therefore allow us to probe and access the quantum properties of light's OAM, aiding our fundamental understanding of light-matter interactions, and moreover, allowing us to construct OAM-based applications, including quantum memories, frequency converters for shaped light and OAM-based sensors.This article is part of the themed issue 'Optical orbital angular momentum'. © 2017 The Author(s).
13. Optical angular momentum and atoms
Science.gov (United States)
2017-01-01
Any coherent interaction of light and atoms needs to conserve energy, linear momentum and angular momentum. What happens to an atom’s angular momentum if it encounters light that carries orbital angular momentum (OAM)? This is a particularly intriguing question as the angular momentum of atoms is quantized, incorporating the intrinsic spin angular momentum of the individual electrons as well as the OAM associated with their spatial distribution. In addition, a mechanical angular momentum can arise from the rotation of the entire atom, which for very cold atoms is also quantized. Atoms therefore allow us to probe and access the quantum properties of light’s OAM, aiding our fundamental understanding of light–matter interactions, and moreover, allowing us to construct OAM-based applications, including quantum memories, frequency converters for shaped light and OAM-based sensors. This article is part of the themed issue ‘Optical orbital angular momentum’. PMID:28069766
14. AngularJS directives
CERN Document Server
Vanston, Alex
2013-01-01
This book uses a practical, step-by-step approach, starting with how to build directives from the ground up before moving on to creating web applications comprised of multiple modules all working together to provide the best user experience possible.This book is intended for intermediate JavaScript developers who are looking to enhance their understanding of single-page web application development with a focus on AngularJS and the JavaScript MVC frameworks.It is expected that readers will understand basic JavaScript patterns and idioms and can recognize JSON formatted data.
15. Angular Distribution of GRBs
Directory of Open Access Journals (Sweden)
L. G. Balázs
2012-01-01
Full Text Available We studied the complete randomness of the angular distribution of BATSE gamma-ray bursts (GRBs. Based on their durations and peak fluxes, we divided the BATSE sample into 5 subsamples (short1, short2, intermediate, long1, long2 and studied the angular distributions separately. We used three methods to search for non-randomness in the subsamples: Voronoi tesselation, minimal spanning tree, and multifractal spectra. To study any non-randomness in the subsamples we defined 13 test-variables (9 from Voronoi tesselation, 3 from the minimal spanning tree and one from the multifractal spectrum. We made Monte Carlo simulations taking into account the BATSE’s sky-exposure function. We tested therandomness by introducing squared Euclidean distances in the parameter space of the test-variables. We recognized that the short1, short2 groups deviate significantly (99.90%, 99.98% from the fully random case in the distribution of the squared Euclidean distances but this is not true for the long samples. In the intermediate group, the squared Euclidean distances also give significant deviation (98.51%.
16. Perturbed angular correlation
International Nuclear Information System (INIS)
Fabris, J.D.
1977-01-01
The electric quadrupolar interaction in some hafnium complexes, measured at the metal nucleus level is studied. For that purpose, the technique of γ-γ perturbed angular correlation is used: the frequencies of quadrupolar interaction are compared with some hafnium α-hydroxicarboxilates, namely glycolate, lactate, mandelate and benzylate; the influence of the temperature on the quadrupolar coupling on the hafnium tetramandelate is studied; finally, the effects associated with the capture of thermal neutrons by hafnium tetramandelate are examined locally at the nuclear level. The first group of results shows significant differences in a series of complexes derived from glycolic acid. On the other hand, the substitution of the protons in hafnium tetramandelate structure by some alkaline cations permits to verify a correlation between the variations in the quadrupolar coupling and the electronegativities of the substituent elements. Measurements at high temperatures show that this complex is thermally stable at 100 and 150 0 C. It is possible to see the appearance of two distinct sites for the probe nucleus, after heating the sample at 100 0 C for prolonged time. This fact is attributed to a probable interconversion among the postulated structural isomers for the octacoordinated compounds. Finally, measurements of angular correlation on the irradiated complex show that there is an effective destruction of the target molecule by neutron capture [pt
17. Galaxy angular momentum
International Nuclear Information System (INIS)
Thompson, L.A.
1974-01-01
In order to test the theories which purport to explain the origin of galaxy angular momentum, this study presents new data for about 1000 individual galaxies in eight rich clusters. The clusters which are studied include Virgo, A 119, A 400, A 1656 (Coma), A 2147, A 2151 (Hercules), A 2197, and A 2199. Selected samples of these data are used to investigate systematic alignment effects in clusters of galaxies and to investigate the intrinsic ellipticities of E, SO, and spiral galaxies. The following new results are reported: Galaxies in the cluster A 2197 show a significant alignment effect (chi 2 probability less than 0.0002), and the preferential direction of alignment corresponds approximately to the major axis of the overall cluster elongation. None of the other seven clusters show any significant alignment trends. The spiral galaxy samples in four clusters (Virgo, A 1656, A 2151, and A 2197) were large enough to analyze the number distributions of forward and reverse winding spirals. Large and small spiral galaxies have identical ellipticity distributions. Large E and SO galaxies tend to be more spherical, and small E and SO galaxies more flattened. The intrinsic ellipticities of E, SO, and spiral galaxies are the same for galaxies in the ''field'' and for galaxies in rich clusters. Six models of galaxy formation are reviewed, and the major []mphasis is placed on how each model explains the origin of galaxy angular momentum. (Diss. Abstr. Int., B)
18. Angular mining conveyor
Energy Technology Data Exchange (ETDEWEB)
Sender, A; Mura, A; Liduchowski, L; Zok, P; Skolik, W; Szyngiel, S; Rojek, H; Gajda, B; Major, M; Stanislawski, P; Sliwiok, H; Sikora, J
1988-10-19
Angular mining conveyor provided with a drag chain extending along the axis of its path of movement, and a corner member, inside which the drag chain is led in a forced way, characterized in that the drag chain, where its path curves around the corner member, is located by supporting of the vertical links of the chain along the required curved section of the conveyor path around said corner member, and the supporting line of the links is so chosen, that, within the said curved section of the conveyor path, a space is maintained between the vertical end surface of the scrapers and the outer curved surface of the radially inner side wall of a corner trough associated with the corner member, through which corner trough the scrapers pass. 10 figs.
19. Angular integrals in d dimensions
Energy Technology Data Exchange (ETDEWEB)
Somogyi, Gabor
2011-01-15
We discuss the evaluation of certain d dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the so-called H-function of several variables. We also present several illustrative examples of the general result and briefly consider some applications. (orig.)
20. Angular momentum in general relativity
International Nuclear Information System (INIS)
Cresswell, A.; Zimmerman, R.L.; Oregon Univ., Eugene
1986-01-01
It is argued that the correct expressions for the angular momentum flux carried by gravitational radiation should follow directly from the momentum currents. Following this approach, the authors compute the angular momentum associated with several different choices of energy-momentum prescriptions. (author)
1. Angular integrals in d dimensions.
OpenAIRE
Somogyi, G.
2011-01-01
We discuss the evaluation of certain d dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the so-called H-function of several variables. We also present several illustrative examples of the general result and briefly consider some applications.
2. Angular integrals in d dimensions
International Nuclear Information System (INIS)
Somogyi, Gabor
2011-01-01
We discuss the evaluation of certain d-dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the so-called H-function of several variables. We also present several illustrative examples of the general result and briefly consider some applications.
3. Angular integrals in d dimensions
Science.gov (United States)
Somogyi, Gábor
2011-08-01
We discuss the evaluation of certain d-dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the so-called H-function of several variables. We also present several illustrative examples of the general result and briefly consider some applications.
4. Angular integrals in d dimensions
International Nuclear Information System (INIS)
Somogyi, Gabor
2011-01-01
We discuss the evaluation of certain d dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the so-called H-function of several variables. We also present several illustrative examples of the general result and briefly consider some applications. (orig.)
5. Angular Momentum in Dwarf Galaxies
Directory of Open Access Journals (Sweden)
Del Popolo A.
2014-06-01
Full Text Available We study the “angular momentum catastrophe” in the framework of interaction among baryons and dark matter through dynamical friction. By means of Del Popolo (2009 model we simulate 14 galaxies similar to those investigated by van den Bosch, Burkert and Swaters (2001, and calculate the distribution of their spin parameters and the angular momenta. Our model gives the angular momentum distribution which is in agreement with the van den Bosch et al. observations. Our result shows that the “angular momentum catastrophe” can be naturally solved in a model that takes into account the baryonic physics and the exchange of energy and angular momentum between the baryonic clumps and dark matter through dynamical friction.
6. Angular momentum of dwarf galaxies
Science.gov (United States)
Kurapati, Sushma; Chengalur, Jayaram N.; Pustilnik, Simon; Kamphuis, Peter
2018-05-01
Mass and specific angular momentum are two fundamental physical parameters of galaxies. We present measurements of the baryonic mass and specific angular momentum of 11 void dwarf galaxies derived from neutral hydrogen (HI) synthesis data. Rotation curves were measured using 3D and 2D tilted ring fitting routines, and the derived curves generally overlap within the error bars, except in the central regions where, as expected, the 3D routines give steeper curves. The specific angular momentum of void dwarfs is found to be high compared to an extrapolation of the trends seen for higher mass bulge-less spirals, but comparable to that of other dwarf irregular galaxies that lie outside of voids. As such, our data show no evidence for a dependence of the specific angular momentum on the large scale environment. Combining our data with the data from the literature, we find a baryonic threshold of ˜109.1 M⊙ for this increase in specific angular momentum. Interestingly, this threshold is very similar to the mass threshold below which the galaxy discs start to become systematically thicker. This provides qualitative support to the suggestion that the thickening of the discs, as well as the increase in specific angular momentum, are both results of a common physical mechanism, such as feedback from star formation. Quantitatively, however, the amount of star formation observed in our dwarfs appears insufficient to produce the observed increase in specific angular momentum. It is hence likely that other processes, such as cold accretion of high angular momentum gas, also play a role in increasing the specific angular momentum.
7. AngularJS testing cookbook
CERN Document Server
Bailey, Simon
2015-01-01
This book is intended for developers who have an understanding of the basic principles behind both AngularJS and test-driven development. You, as a developer, are interested in eliminating the fear related to either introducing tests to an existing codebase or starting out testing on a fresh AngularJS application. If you're a team leader or part of a QA team with the responsibility of ensuring full test coverage of an application, then this book is ideal for you to comprehend the full testing scope required by your developers. Whether you're new to or are well versed with AngularJS, this book
8. Angular momentum from tidal torques
International Nuclear Information System (INIS)
Barnes, J.; Efstathiou, G.; Cambridge Univ., England)
1987-01-01
The origin of the angular momentum of bound objects in large N-body simulations is studied using three sets of models. One model with white-noise initial conditions is analyzed as well as two in which the initial conditions have more power on large scales, as predicted in models with cold dark matter. The growth and distribution of angular momentum in individual objects is studied and it is found that the specific angular momentum distribution of bound clumps increases in a near linear fashion with radius while the orientation of the angular momentum in the inner high-density regions is often poorly correlated with that of the outer parts. It is also found that the dimensionless spin parameter is insensitive to the initial perturbation spectrum and has a median value of about 0.05. 61 references
9. Lidar Orbital Angular Momentum Sensor
Data.gov (United States)
National Aeronautics and Space Administration — The recognition in recent decades that electromagnetic fields have angular momentum (AM) in the form of not only polarization (or spin AM) but also orbital (OAM) has...
10. Uncertainty principle for angular position and angular momentum
International Nuclear Information System (INIS)
Franke-Arnold, Sonja; Barnett, Stephen M; Yao, Eric; Leach, Jonathan; Courtial, Johannes; Padgett, Miles
2004-01-01
The uncertainty principle places fundamental limits on the accuracy with which we are able to measure the values of different physical quantities (Heisenberg 1949 The Physical Principles of the Quantum Theory (New York: Dover); Robertson 1929 Phys. Rev. 34 127). This has profound effects not only on the microscopic but also on the macroscopic level of physical systems. The most familiar form of the uncertainty principle relates the uncertainties in position and linear momentum. Other manifestations include those relating uncertainty in energy to uncertainty in time duration, phase of an electromagnetic field to photon number and angular position to angular momentum (Vaccaro and Pegg 1990 J. Mod. Opt. 37 17; Barnett and Pegg 1990 Phys. Rev. A 41 3427). In this paper, we report the first observation of the last of these uncertainty relations and derive the associated states that satisfy the equality in the uncertainty relation. We confirm the form of these states by detailed measurement of the angular momentum of a light beam after passage through an appropriate angular aperture. The angular uncertainty principle applies to all physical systems and is particularly important for systems with cylindrical symmetry
11. Instant AngularJS starter
CERN Document Server
Menard, Dan
2013-01-01
Get to grips with a new technology, understand what it is and what it can do for you, and then get to work with the most important features and tasks. This book is written in an easytoread style, with a strong emphasis on realworld, practical examples. Stepbystep explanations are provided for performing important tasks.This book is for web developers familiar with JavascriptIt doesn't cover the history of AngularJS, and it's not a pitch to convince you that AngularJS is the best framework on the entire web. It's a guide to help you learn everything you need to know about AngularJS in as few pa
12. Automated Angular Momentum Recoupling Algebra
Science.gov (United States)
Williams, H. T.; Silbar, Richard R.
1992-04-01
We present a set of heuristic rules for algebraic solution of angular momentum recoupling problems. The general problem reduces to that of finding an optimal path from one binary tree (representing the angular momentum coupling scheme for the reduced matrix element) to another (representing the sub-integrals and spin sums to be done). The method lends itself to implementation on a microcomputer, and we have developed such an implementation using a dialect of LISP. We describe both how our code, called RACAH, works and how it appears to the user. We illustrate the use of RACAH for several transition and scattering amplitude matrix elements occurring in atomic, nuclear, and particle physics.
13. High angular resolution at LBT
Science.gov (United States)
Conrad, A.; Arcidiacono, C.; Bertero, M.; Boccacci, P.; Davies, A. G.; Defrere, D.; de Kleer, K.; De Pater, I.; Hinz, P.; Hofmann, K. H.; La Camera, A.; Leisenring, J.; Kürster, M.; Rathbun, J. A.; Schertl, D.; Skemer, A.; Skrutskie, M.; Spencer, J. R.; Veillet, C.; Weigelt, G.; Woodward, C. E.
2015-12-01
High angular resolution from ground-based observatories stands as a key technology for advancing planetary science. In the window between the angular resolution achievable with 8-10 meter class telescopes, and the 23-to-40 meter giants of the future, LBT provides a glimpse of what the next generation of instruments providing higher angular resolution will provide. We present first ever resolved images of an Io eruption site taken from the ground, images of Io's Loki Patera taken with Fizeau imaging at the 22.8 meter LBT [Conrad, et al., AJ, 2015]. We will also present preliminary analysis of two data sets acquired during the 2015 opposition: L-band fringes at Kurdalagon and an occultation of Loki and Pele by Europa (see figure). The light curves from this occultation will yield an order of magnitude improvement in spatial resolution along the path of ingress and egress. We will conclude by providing an overview of the overall benefit of recent and future advances in angular resolution for planetary science.
14. Angular momentum projection with Pfaffian
International Nuclear Information System (INIS)
Oi, M.
2011-01-01
Recent developments to rewrite the Onishi formula for an evaluation of the so-called norm overlap kernel necessary in angular momentum projection are to be discussed. The essential ingredients in the development, that is, the Fermion coherent states, the Grassmann numbers, and the Pfaffian, are explained. (author)
15. Angular overlap model in actinides
International Nuclear Information System (INIS)
Gajek, Z.; Mulak, J.
1991-01-01
Quantitative foundations of the Angular Overlap Model in actinides based on ab initio calculations of the crystal field effect in the uranium (III) (IV) and (V) ions in various crystals are presented. The calculations justify some common simplifications of the model and fix up the relations between the AOM parameters. Traps and limitations of the AOM phenomenology are discussed
16. Angular overlap model in actinides
Energy Technology Data Exchange (ETDEWEB)
Gajek, Z.; Mulak, J. (Polska Akademia Nauk, Wroclaw (PL). Inst. Niskich Temperatur i Badan Strukturalnych)
1991-01-01
Quantitative foundations of the Angular Overlap Model in actinides based on ab initio calculations of the crystal field effect in the uranium (III) (IV) and (V) ions in various crystals are presented. The calculations justify some common simplifications of the model and fix up the relations between the AOM parameters. Traps and limitations of the AOM phenomenology are discussed.
17. Angular momentum in general relativity
International Nuclear Information System (INIS)
Prior, C.R.
1977-01-01
The definition of angular momentum proposed in part I of this series (Prior. Proc. R. Soc. Lond.; A354:379 (1977)) is investigated when applied to rotating black holes. It is shown how to use the formula to evaluate the angular momentum of a stationary black hole. This acts as a description of a background space on which the effect of first matter and then gravitational perturbations is considered. The latter are of most interest and the rate of change of angular momentum, dJ/dt, is found as an expression in the shear induced in the event horizon by the perturbation and in its time integral. Teukolsky's solutions (Astrophys. J.; 185:635 (1973)) for the perturbed component of the Weyl tensor are then used to find this shear and hence to give an exact answer for dJ/dt. One of the implications of the result is a direct verification of Bekenstein's formula (Phys. Rev.; 7D:949 (1973)) relating in a simple way the rate of change of angular momentum to the rate of change of mass caused by a plane wave. A more general expression is also given for dM/dt. Considering only stationary perturbations, it is shown how to generalize the definition of angular momentum so as to include information about its direction as well. Three problems are particularly discussed - a single moon, two or more moons and a ring of matter causing the perturbation - since they provide illustrations of all the main features of the black hole's behaviour. In every case it is found that the black hole realigns its axis of rotation so that the final configuration is axisymmetric if possible; otherwise is slows down completely to reach a static state. (author)
18. On Dunkl angular momenta algebra
Energy Technology Data Exchange (ETDEWEB)
Feigin, Misha [School of Mathematics and Statistics, University of Glasgow,15 University Gardens, Glasgow G12 8QW (United Kingdom); Hakobyan, Tigran [Yerevan State University,1 Alex Manoogian, 0025 Yerevan (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)
2015-11-17
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N) version of the subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
19. Angular momentum in QGP holography
Directory of Open Access Journals (Sweden)
Brett McInnes
2014-10-01
Full Text Available The quark chemical potential is one of the fundamental parameters describing the quark–gluon plasma produced by sufficiently energetic heavy-ion collisions. It is not large at the extremely high temperatures probed by the LHC, but it plays a key role in discussions of the beam energy scan programmes at the RHIC and other facilities. On the other hand, collisions at such energies typically (that is, in peripheral collisions give rise to very high values of the angular momentum density. Here we explain that holographic estimates of the quark chemical potential of a rotating sample of plasma can be very considerably improved by taking the angular momentum into account.
20. Angular momentum content of galaxies
International Nuclear Information System (INIS)
Shaya, E.J.; Tully, R.B.
1984-01-01
A schema of galaxy formation is developed in which the environmental influence of large-scale structure plays a dominant role. This schema was motivated by the observation that the fraction of E and S0 galaxies is much higher in clusters than in low-density regions and by an inference that those spirals that are found in clusters probably have fallen in relatively recently from the low-density regions. It is proposed that the tidal field of the Local Supercluster acts to determine the morphology of galaxies through two complementary mechanisms. In the first place, the supercluster can apply torques to protogalaxies. Galaxies which collapsed while expanding away from the central cluster decoupled from the external tidal field and conserved the angular momentum that they acquired before collapse. Galaxies which formed in the cluster while the cluster collapsed continued to feel the tidal field. In the latter case, the spin of outer collapsing layers can be halted and reversed, and tends to cancel the spin of inner layers. The result is a reduction of the total angular momentum content of the galaxy. In addition, the supercluster tidal field can regulate accretion of fresh material onto the galaxies since the field creates a Roche limit about galaxies and material beyond this limit is lost. Any material that has not collapsed onto a galaxy by the time the galaxy falls into a cluster will be tidally stripped. The angular momentum content of that part of the protogalactic cloud which has not yet collapsed . continues to grow linearly with time due to the continued torquing by the supercluster and neighbors. Galaxies at large distances from the cluster core can continue to accrete this high angular momentum material until the present, but galaxies that enter the cluster are cut off from replenishing material
1. Angular dependence of shallow dose
International Nuclear Information System (INIS)
Alvarez, J.L.
1986-01-01
The theoretical response of a detector is discussed and compared to measurements of shallow dose with tissue and phantom response detectors. A definite energy dependent angular response of dose and measurement was observed which could not be explained by simple trigonometric arguments. The response is back scatter dependent and must be considered in detector design and dose measurements. It is not possible for standard detectors to follow this response
2. AngularJS test-driven development
CERN Document Server
Chaplin, Tim
2015-01-01
This book is for developers who want to learn about AngularJS development by applying testing techniques. You are assumed to have a basic knowledge and understanding of HTML, JavaScript, and AngularJS.
3. Angular-momentum transport in nuclear collisions
International Nuclear Information System (INIS)
Wolschin, G.; Ayik, S.; Noerenberg, W.
1978-01-01
Among the various relaxation processes that can be observed in heavy-ion collisions, the dissipation of relative angular momentum into intrinsic angular momentum of the fragments attracts increasing attention. Here we present a transport theoretical description of angular-momentum and mass transport that allows for a transparent interpretation of the data. (orig.) [de
4. AngularJS web application development
CERN Document Server
Darwin, Peter Bacon
2013-01-01
The book will be a step-by-step guide showing the readers how to build a complete web app with AngularJSJavaScript developers who want to learn AngularJS for developing web apps. Knowledge of JavaScript and HTML is expected. No knowledge of AngularJS is required.
5. Electron angular distribution axial channeling
International Nuclear Information System (INIS)
Khokonov, A.Kh.; Khokonov, M.Kh.
1989-01-01
Angular distributions of ultra-relativistic electrons are calculated in the assumption about presence of statistical equilibrium. Analysis is based on numerical solution of Fokker-Planck type kinetic equation. It is shown that in contrast to case of amorphous medium, the multiple scattering at axial channeling of negative particles results in self-focusing of the initial beam particles and due to it number of electrons moving at an angles to the chain, which are smaller, than critical angle of channeling, may increase by several times as compared to the initial one
6. Angular Positioning Sensor for Space Mechanisms
Science.gov (United States)
Steiner, Nicolas; Chapuis, Dominique
2013-09-01
Angular position sensors are used on various rotating mechanisms such as solar array drive mechanisms, antenna pointing mechanisms, scientific instruments, motors or actuators.Now a days, potentiometers and encoders are mainly used for angular measurement purposes. Both of them have their own pros and cons.As alternative, Ruag Space Switzerland Nyon (RSSN) is developing and qualifying two innovative technologies of angular position sensors which offer easy implementation, medium to very high lifetime and high flexibility with regards to the output signal shape/type.The Brushed angular position sensor uses space qualified processes which are already flying on RSSN's sliprings for many years. A large variety of output signal shape can be implemented to fulfill customer requirements (digital, analog, customized, etc.).The contactless angular position sensor consists in a new radiation hard Application Specific Integrated Circuit (ASIC) based on the Hall effect and providing the angular position without complex processing algorithm.
7. Oral candidiasis and angular cheilitis.
Science.gov (United States)
Sharon, Victoria; Fazel, Nasim
2010-01-01
Candidiasis, an often encountered oral disease, has been increasing in frequency. Most commonly caused by the overgrowth of Candida albicans, oral candidiasis can be divided into several categories including acute and chronic forms, and angular cheilitis. Risk factors for the development of oral candidiasis include immunosuppression, wearing of dentures, pharmacotherapeutics, smoking, infancy and old age, endocrine dysfunction, and decreased salivation. Oral candidiasis may be asymptomatic. More frequently, however, it is physically uncomfortable, and the patient may complain of burning mouth, dysgeusia, dysphagia, anorexia, and weight loss, leading to nutritional deficiency and impaired quality of life. A plethora of antifungal treatments are available. The overall prognosis of oral candidiasis is good, and rarely is the condition life threatening with invasive or recalcitrant disease.
8. Angular distributions as lifetime probes
Energy Technology Data Exchange (ETDEWEB)
Dror, Jeff Asaf; Grossman, Yuval [Department of Physics, LEPP, Cornell University,Ithaca, NY 14853 (United States)
2014-06-27
If new TeV scale particles are discovered, it will be important to determine their width. There is, however, a problematic region, where the width is too small to be determined directly, and too large to generate a secondary vertex. For a collection of colored, spin polarized particles, hadronization depolarizes the particles prior to their decay. The amount of depolarization can be used to probe the lifetime in the problematic region. In this paper we apply this method to a realistic scenario of a top-like particle that can be produced at the LHC. We study how depolarization affects the angular distributions of the decay products and derive an equation for the distributions that is sensitive to the lifetime.
9. Orbital angular momentum in phase space
International Nuclear Information System (INIS)
Rigas, I.; Sanchez-Soto, L.L.; Klimov, A.B.; Rehacek, J.; Hradil, Z.
2011-01-01
Research highlights: → We propose a comprehensive Weyl-Wigner formalism for the canonical pair angle-angular momentum. → We present a simple and useful toolkit for the practitioner. → We derive simple evolution equations in terms of a star product in the semiclassical limit. - Abstract: A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
10. Management of Angular Cheilitis in children
Directory of Open Access Journals (Sweden)
Fajriani Fajriani
2017-04-01
Full Text Available Objective : Angular cheilitis is a type of oral soft tissue disease that can occur in children and adults, the condition is characterized by cracks and inflammation on both corners of the mouth. Although this disease can not cause severe disorder, it quite disturbs one's activity and physical appearance. Mild Angular cheilitis will recover itself over times. However severe conditions can cause pain and bleeding. This paper aims to inform colleagues about management of angular cheilitis in children.
11. Management of angular cheilitis for children
Directory of Open Access Journals (Sweden)
Fajriani Fajriani
2016-06-01
Full Text Available Angular cheilitis is one type of oral soft tissue disease that can occur in both children and adults, the condition is characterized by cracks and inflammation in both corners of the mouth. Although this disease does not cause severe disruption but quite disturbing activity and also one's physical appearance. Angular cheilitis light will disappear on their own over time.Severe conditions that can cause pain and bleading. aims to give feedback on peers about managment angular cheilitis in children.
12. AngularJS Performance: A Survey Study
OpenAIRE
Ramos, Miguel; Valente, Marco Tulio; Terra, Ricardo
2017-01-01
AngularJS is a popular JavaScript MVC-based framework to construct single-page web applications. In this paper, we report the results of a survey with 95 professional developers about performance issues of AngularJS applications. We report common practices followed by developers to avoid performance problems (e.g., use of third-party or custom components), the general causes of performance problems in AngularJS applications (e.g., inadequate architecture decisions taken by AngularJS users), a...
13. Transverse and longitudinal angular momenta of light
Energy Technology Data Exchange (ETDEWEB)
Bliokh, Konstantin Y., E-mail: [email protected] [Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198 (Japan); Nonlinear Physics Centre, RSPhysE, The Australian National University, Canberra, ACT 0200 (Australia); Nori, Franco [Center for Emergent Matter Science, RIKEN, Wako-shi, Saitama 351-0198 (Japan); Physics Department, University of Michigan, Ann Arbor, MI 48109-1040 (United States)
2015-08-26
We review basic physics and novel types of optical angular momentum. We start with a theoretical overview of momentum and angular momentum properties of generic optical fields, and discuss methods for their experimental measurements. In particular, we describe the well-known longitudinal (i.e., aligned with the mean momentum) spin and orbital angular momenta in polarized vortex beams. Then, we focus on the transverse (i.e., orthogonal to the mean momentum) spin and orbital angular momenta, which were recently actively discussed in theory and observed in experiments. First, the recently-discovered transverse spin angular momenta appear in various structured fields: evanescent waves, interference fields, and focused beams. We show that there are several kinds of transverse spin angular momentum, which differ strongly in their origins and physical properties. We describe extraordinary features of the transverse optical spins and overview recent experiments. In particular, the helicity-independent transverse spin inherent in edge evanescent waves offers robust spin–direction coupling at optical interfaces (the quantum spin Hall effect of light). Second, we overview the transverse orbital angular momenta of light, which can be both extrinsic and intrinsic. These two types of the transverse orbital angular momentum are produced by spatial shifts of the optical beams (e.g., in the spin Hall effect of light) and their Lorentz boosts, respectively. Our review is underpinned by a unified theory of the angular momentum of light based on the canonical momentum and spin densities, which avoids complications associated with the separation of spin and orbital angular momenta in the Poynting picture. It allows us to construct a comprehensive classification of all known optical angular momenta based on their key parameters and main physical properties.
14. Experimental determination of high angular momentum states
International Nuclear Information System (INIS)
Barreto, J.L.V.
1985-01-01
The current knowledge of the atomic nucleus structure is summarized. A short abstract of the nuclear properties at high angular momentum and a more detailed description of the experimental methods used in the study of high angular momenta is made. (L.C.) [pt
15. Exposing Library Services with AngularJS
OpenAIRE
Jakob Voß; Moritz Horn
2014-01-01
This article provides an introduction to the JavaScript framework AngularJS and specific AngularJS modules for accessing library services. It shows how information such as search suggestions, additional links, and availability can be embedded in any website. The ease of reuse may encourage more libraries to expose their services via standard APIs to allow usage in different contexts.
16. Accelerated rotation with orbital angular momentum modes
CSIR Research Space (South Africa)
Schulze, C
2015-04-01
Full Text Available . As the angular acceleration takes place in a bounded space, the azimuthal degree of freedom, such fields accelerate periodically as they propagate. Notably, the amount of angular acceleration is not limited by paraxial considerations, may be tailored for large...
17. Responsive web design with AngularJS
CERN Document Server
Patel, Sandeep Kumar
2014-01-01
If you are an AngularJS developer who wants to learn about responsive web application development, this book is ideal for you. Responsive Web Design with AngularJS is intended for web developers or designers with a basic knowledge of HTML, CSS, and JavaScript.
18. Angular momentum projected wave-functions
International Nuclear Information System (INIS)
Bengtsson, R.; Haakansson, H.B.
1978-01-01
Angular momentum projection has become a vital link between intrinsic model-wavefunctions and the physical states one intends to describe. We discuss in general terms some aspects of angular momentum projection and present results from projection on e.g. cranking wavefunctions. Mass densities and spectroscopic factors are also presented for some cases. (author)
19. Concepts of radial and angular kinetic energies
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W.P.
2002-01-01
We consider a general central-field system in D dimensions and show that the division of the kinetic energy into radial and angular parts proceeds differently in the wave-function picture and the Weyl-Wigner phase-space picture, Thus, the radial and angular kinetic energies are different quantities...
20. Perturbed angular correlations and distributions
International Nuclear Information System (INIS)
Makaryunas, K.
1976-01-01
The present index comprises original works and review papers on the perturbed angular correlations (PAC) and distributions (PAD). The articles published in the Soviet and foreign journals as well as the materials of conferences, monographs and collections published in the USSR and abroad, the preprints produced by various institutes and abstracts of disertations are included from 1948 up to 1973. The whole material compiled in this index is divided into three parts. Part one is a bibliographic index. All papers in this part are divided into three sections. Section one comprises the papers devoted to the theoretical works on PAC, review papers, monographs, materials of conferences. Section two deals with the works of methodical character where correlation spectrometers as well as the treatment of experimental data are described. In section three experimental works with concrete nuclei are compiled. Part two gives the characteristic of works performed with concrete nuclei. This part is presented in the form of the table in which the works are systematized according to the chemical elements and isotopes. The table shows the characteristics of the nuclear levels used in the investigations by PAC as well as brief characteristics of experiments and results obtained. Part three - appendix contains alphabetic index of the authors, the list of the used editions with the abbreviations of the titles of these editions. The lists indicating the dynamic of the quantity of works on PAC and the distribution according to the literature sources are also given
1. Angular correlation in positron annihilation
International Nuclear Information System (INIS)
Arponen, J.; Pajanne, E.
1978-01-01
The angular correlation of the two gamma quanta emitted when a thermalized positron annihilates with metallic conduction electrons is investigated by applying the newly developed theory of electron gas as a system of interacting collective excitations. The method leads in a natural way to the appearance of high-momentum components (i.e. pair momentum p>psub(F) in the annihilation radiation already in the case of annihilation with conduction electrons only. The amount of these components is significant approximately (10 %) in a dilute electron gas (like alkali metals), but fairly irrelevant for higher densities. The momentum-dependence of the enhancement factor for a dense system (with rsub(s) approximately equal to 2) agrees well both with the earlier theories due to Kahana and others, and also with recent accurate experimental observations. As rsub(s) increases into the alkali-metal region, the enhancement factor for p< psub(F) becomes relatively more and more constant, in contrast with the trend in the Kahana theory. In this density regime the experimental results seem to vary widely, although most of them desagree with the present prediction. We discuss the possible discrepancy and try to account for the effects of the core annihilation by a simple model. (author)
2. Angular momentum conservation for uniformly expanding flows
International Nuclear Information System (INIS)
Hayward, Sean A
2007-01-01
Angular momentum has recently been defined as a surface integral involving an axial vector and a twist 1-form, which measures the twisting around the spacetime due to a rotating mass. The axial vector is chosen to be a transverse, divergence-free, coordinate vector, which is compatible with any initial choice of axis and integral curves. Then a conservation equation expresses the rate of the change of angular momentum along a uniformly expanding flow as a surface integral of angular momentum densities, with the same form as the standard equation for an axial Killing vector, apart from the inclusion of an effective energy tensor for gravitational radiation
3. Staggering of angular momentum distribution in fission
Science.gov (United States)
Tamagno, Pierre; Litaize, Olivier
2018-03-01
We review here the role of angular momentum distributions in the fission process. To do so the algorithm implemented in the FIFRELIN code [?] is detailed with special emphasis on the place of fission fragment angular momenta. The usual Rayleigh distribution used for angular momentum distribution is presented and the related model derivation is recalled. Arguments are given to justify why this distribution should not hold for low excitation energy of the fission fragments. An alternative ad hoc expression taking into account low-lying collectiveness is presented as has been implemented in the FIFRELIN code. Yet on observables currently provided by the code, no dramatic impact has been found. To quantify the magnitude of the impact of the low-lying staggering in the angular momentum distribution, a textbook case is considered for the decay of the 144Ba nucleus with low excitation energy.
4. Amplitude damping channel for orbital angular momentum
CSIR Research Space (South Africa)
Dudley, Angela L
2010-03-01
Full Text Available Since the pioneering work on the entanglement of the orbital angular momentum (OAM) states of light, much attention has been devoted to the subject, with particular attention into the quantum aspects of information processing using OAM. Furthermore...
5. Radiofrequency encoded angular-resolved light scattering
DEFF Research Database (Denmark)
Buckley, Brandon W.; Akbari, Najva; Diebold, Eric D.
2015-01-01
The sensitive, specific, and label-free classification of microscopic cells and organisms is one of the outstanding problems in biology. Today, instruments such as the flow cytometer use a combination of light scatter measurements at two distinct angles to infer the size and internal complexity...... of cells at rates of more than 10,000 per second. However, by examining the entire angular light scattering spectrum it is possible to classify cells with higher resolution and specificity. Current approaches to performing these angular spectrum measurements all have significant throughput limitations...... Encoded Angular-resolved Light Scattering (REALS), this technique multiplexes angular light scattering in the radiofrequency domain, such that a single photodetector captures the entire scattering spectrum from a particle over approximately 100 discrete incident angles on a single shot basis. As a proof...
6. Orbital-angular-momentum entanglement in turbulence
CSIR Research Space (South Africa)
2013-06-01
Full Text Available The turbulence-induced decay of orbital-angular-momentum (OAM) entanglement between two photons is investigated numerically and experimentally. To compare our resultswith previouswork,we simulate the turbulent atmosphere with a single phase screen...
7. Staggering of angular momentum distribution in fission
Directory of Open Access Journals (Sweden)
Tamagno Pierre
2018-01-01
Full Text Available We review here the role of angular momentum distributions in the fission process. To do so the algorithm implemented in the FIFRELIN code [?] is detailed with special emphasis on the place of fission fragment angular momenta. The usual Rayleigh distribution used for angular momentum distribution is presented and the related model derivation is recalled. Arguments are given to justify why this distribution should not hold for low excitation energy of the fission fragments. An alternative ad hoc expression taking into account low-lying collectiveness is presented as has been implemented in the FIFRELIN code. Yet on observables currently provided by the code, no dramatic impact has been found. To quantify the magnitude of the impact of the low-lying staggering in the angular momentum distribution, a textbook case is considered for the decay of the 144Ba nucleus with low excitation energy.
8. QCD angular correlations for muon pair production
International Nuclear Information System (INIS)
Kajantie, K.; Raitio, R.; Lindfors, J.
1978-01-01
Angular distributions of muons are discussed in the framework of a QCD treatment of muon pair production in hadron-hadron collisions. The predicted angular effects are independent of the infrared behavior of QCD. Measuring them will permit one to determine whether the origin of the large transverse momentum of the pair is in the quark transverse momenta or in a constituent-constituent subprocess. (author)
9. Mastering AngularJD for .NET developers
CERN Document Server
2015-01-01
This book is envisioned for traditional developers and programmers who want to develop client-side applications using the AngularJS framework and ASP.NET Web API 2 with Visual Studio. .NET developers who have already built web applications or web services and who have a fundamental knowledge of HTML, JavaScript, and CSS and want to explore single-page applications will also find this guide useful. Basic knowledge of AngularJS would be helpful.
10. Angular Spectra of Polarized Galactic Foregrounds
OpenAIRE
Cho, Jung; Lazarian, A.
2003-01-01
It is believed that magnetic field lines are twisted and bend by turbulent motions in the Galaxy. Therefore, both Galactic synchrotron emission and thermal emission from dust reflects statistics of Galactic turbulence. Our simple model of Galactic turbulence, motivated by results of our simulations, predicts that Galactic disk and halo exhibit different angular power spectra. We show that observed angular spectra of synchrotron emission are compatible with our model. We also show that our mod...
11. Beam Angular Divergence Effects in Ion Implantation
International Nuclear Information System (INIS)
Horsky, T. N.; Hahto, S. K.; Bilbrough, D. G.; Jacobson, D. C.; Krull, W. A.; Goldberg, R. D.; Current, M. I.; Hamamoto, N.; Umisedo, S.
2008-01-01
An important difference between monomer ion beams and heavy molecular beams is a significant reduction in beam angular divergence and increased on-wafer angular accuracy for molecular beams. This advantage in beam quality stems from a reduction in space-charge effects within the beam. Such improved angular accuracy has been shown to have a significant impact on the quality and yield of transistor devices [1,12]. In this study, B 18 H x + beam current and angular divergence data collected on a hybrid scanned beam line that magnetically scans the beam across the wafer is presented. Angular divergence is kept below 0.5 deg from an effective boron energy of 200 eV to 3000 eV. Under these conditions, the beam current is shown analytically to be limited by space charge below about 1 keV, but by the matching of the beam emittance to the acceptance of the beam line above 1 keV. In addition, results of a beam transport model which includes variable space charge compensation are presented, in which a drift mode B 18 H x + beam is compared to an otherwise identical boron beam after deceleration. Deceleration is shown to introduce significant space-charge blow up resulting in a large on-wafer angular divergence. The divergence effects introduced by wafer charging are also discussed.
12. Angular distributions in quasi-fission reactions
International Nuclear Information System (INIS)
Luetzenkirchen, K.; Kratz, J.V.; Lucas, R.; Poitou, J.; Gregoire, C.; Wirth, G.; Bruechle, W.; Suemmerer, K.
1985-10-01
Angular distributions for fission-like fragments were measured in the systems 50 Ti, 56 Fe + 208 Pb by applying an off-line KX-ray activation technique. The distributions d 2 sigma/dTHETAdZ exhibit forward-backward asymmetries that are strongly Z-dependent. They result from a process (quasi-fission) which yields nearly symmetric masses in times comparable to the rotational period of the composite system. A method for obtaining the variance of the tilting angular momentum, K 0 2 , from these skewed, differential angular distributions is described. The results indicate that the tilting mode is not fully excited in quasi-fission reactions. The results are compared to the sum of the variances of all statistical spin components, measured via γ-multiplicities. Integration of the angular distributions d 2 sigma/dTHETAdZ over all values of Z yields integral angular distributions dsigma/dTHETA and dsigma/dΩ symmetric around 90 0 . The associated unusually large anisotropies do not at all provide an adequate basis for tests or modifications of the transition state theory. A deconvolution of d 2 sigma/dTHETAdZ is performed with gaussian distributions depending on rotational angles ΔTHETA extending over a range of up to 540 0 . From the mean values a time scale for the evolution of K 0 is calculated. (orig.)
13. Angular distribution of oriented nucleus fission neutrons
International Nuclear Information System (INIS)
Barabanov, A.L.; Grechukhin, D.P.
1982-01-01
Calculations of anisotropy of angular distribution of oriented 235 U nuclei thermal fission neutrons have been carried out. the neutrons were assumed to evaporate isotropically by completely accelerated fragements in the fragment system with only its small part, i. e. fission-producing neutrons, emitted at the moment of neck break. It has been found out that at low energies of neutrons Esub(n)=1-2 MeV the sensitivity of the angular distribution anisotropy to variations of spectrum of neutron evaporation from fragments and the magnitude of a share of fission-producing neutrons reaches approximately 100%, which at high energies, Esub(n) > 5 MeV it does not exceed approximately 20%. Therefore the angular distribution of fast neutrons to a greater degree of confidence may be used for restoring the angular distribution anisotropy of fragments while the angular distribution of low energy neutrons may be used for deriving information on the fission process, but only in case 6f the experiment accuracy is better than approximately 3%
14. Transverse angular momentum in topological photonic crystals
Science.gov (United States)
Deng, Wei-Min; Chen, Xiao-Dong; Zhao, Fu-Li; Dong, Jian-Wen
2018-01-01
Engineering local angular momentum of structured light fields in real space enables applications in many fields, in particular, the realization of unidirectional robust transport in topological photonic crystals with a non-trivial Berry vortex in momentum space. Here, we show transverse angular momentum modes in silicon topological photonic crystals when considering transverse electric polarization. Excited by a chiral external source with either transverse spin angular momentum or transverse phase vortex, robust light flow propagating along opposite directions is observed in several kinds of sharp-turn interfaces between two topologically-distinct silicon photonic crystals. A transverse orbital angular momentum mode with alternating phase vortex exists at the boundary of two such photonic crystals. In addition, unidirectional transport is robust to the working frequency even when the ring size or location of the pseudo-spin source varies in a certain range, leading to the superiority of the broadband photonic device. These findings enable one to make use of transverse angular momentum, a kind of degree of freedom, to achieve unidirectional robust transport in the telecom region and other potential applications in integrated photonic circuits, such as on-chip robust delay lines.
15. Angular cheilitis: A clinical and microbial study
Directory of Open Access Journals (Sweden)
Nirima Oza
2017-01-01
Full Text Available Aims: The aim of the present study was to examine clinical types and microbiological flora isolated from angular chelitis. Materials and Methods: An eroded and/or erythematous, with or without fissure formation, nonvesicular lesion radiating from the angle of the mouth was considered to be angular chelitis. A sample of the present study comprised of 40 patients having unilateral or bilateral angular chelitis and 20 healthy individuals without any lip lesions. Clinical examination was done. In both test and control groups, the sample for microbial analysis was obtained from angle of the mouth. Results: Clinically, four types of angular cheilitis lesions were found, Type I, II, III, and IV. The most common type of lesion found was Type I lesion. Microorganisms isolated from the lesion were Staphylococcus aureus, Candida or Streptococci in 33 (82.5% cases either in pure culture or mixed culture. Among these 33 patients, S. aureus was found in 25 (75.5% cases, Candida in 16 (48.4% cases, and Streptococci in 5 (13.5% cases, respectively. Out of 16 cases positive for Candida, in 13 cases further isolation of Candida was possible. Candida albicans was found in 6 cases and Candida stellastodia in 7 cases. In majority of the dentulous and edentulous patients, S. aureus showed profuse growth. Conclusions: There are microorganisms associated with angular cheilitis.
16. Data-oriented development with AngularJS
CERN Document Server
Waikar, Manoj
2015-01-01
This book helps beginner-level AngularJS developers organize AngularJS applications by discussing important AngularJS concepts and best practices. If you are an experienced AngularJS developer but haven't written directives or haven't created custom HTML controls before, then this book is ideal for you.
17. Angular correlations and high energy evolution
International Nuclear Information System (INIS)
Kovner, Alex; Lublinsky, Michael
2011-01-01
We address the question of to what extent JIMWLK evolution is capable of taking into account angular correlations in a high energy hadronic wave function. Our conclusion is that angular (and indeed other) correlations in the wave function cannot be reliably calculated without taking into account Pomeron loops in the evolution. As an example we study numerically the energy evolution of angular correlations between dipole scattering amplitudes in the framework of the large N c approximation to JIMWLK evolution (the 'projectile dipole model'). Target correlations are introduced via averaging over an (isotropic) ensemble of anisotropic initial conditions. We find that correlations disappear very quickly with rapidity even inside the saturation radius. This is in accordance with our physical picture of JIMWLK evolution. The actual correlations inside the saturation radius in the target QCD wave function, on the other hand, should remain sizable at any rapidity.
18. Angular distributions in pre-equilibrium reactions
International Nuclear Information System (INIS)
Chatterjee, A.; Gupta, S.K.; Bhabha Atomic Research Centre, Bombay
1982-10-01
A new model is proposed for calculating angular distributions in preequilibrium reactions. In this model, as in the model of Feshbach et al. the system consisting of target plus projectile initially branches into two sets of states with either no particle in the continuum (multistep compound states) or with at least one particle in the continuum (multistep direct states). The two chains of states are treated independently by solving two sets of master equations. The multistep compound emission is assumed to be isotropic while the angular distribution of the multistep direct emission is described using the fast particle model of Mantzouranis et al. The angular distributions for 14.6 MeV neutrons calculated using this model are found to be in better agreement with the data than the fast particle model. (author)
19. Angular momentum alignment in molecular beam scattering
International Nuclear Information System (INIS)
Treffers, M.A.
1985-01-01
It is shown how the angular momentum alignment in a molecular beam can be determined using laser-induced fluorescence in combination with precession of the angular momenta in a magnetic field. After a general analysis of the method, some results are presented to illustrate the possibilities of the method. Experimental data are presented on the alignment production for Na 2 molecules that made a collision induced angular momentum transition. Magnitude as well as direction of the alignment have been determined for scattering with several scattering partners and for a large number of scattering angles and transitions. The last chapter deals with the total alignment production in a final J-state, i.e. without state selection of the initial rotational state. (orig.)
20. Ghost Imaging Using Orbital Angular Momentum
Institute of Scientific and Technical Information of China (English)
赵生妹; 丁建; 董小亮; 郑宝玉
2011-01-01
We present a novel encoding scheme in a ghost-imaging system using orbital angular momentum. In the signal arm, object spatial information is encoded as a phase matrix. For an N-grey-scale object, different phase matrices, varying from 0 to K with increment n/N, are used for different greyscales, and then they are modulated to a signal beam by a spatial light modulator. According to the conservation of the orbital angular momentum in the ghost imaging system, these changes will give different coincidence rates in measurement, and hence the object information can be extracted in the idler arm. By simulations and experiments, the results show that our scheme can improve the resolution of the image effectively. Compared with another encoding method using orbital angular momentum, our scheme has a better performance for both characters and the image object.%We present a novel encoding scheme in a ghost-imaging system using orbital angular momentum.In the signal arm,object spatial information is encoded as a phase matrix.For an N-grey-scale object,different phase matrices,varying from 0 to π with increment π/N,are used for different greyscales,and then they are modulated to a signal beam by a spatial light modulator.According to the conservation of the orbital angular momentum in the ghost imaging system,these changes will give different coincidence rates in measurement,and hence the object information can be extracted in the idler arm.By simulations and experiments,the results show that our scheme can improve the resolution of the image effectively.Compared with another encoding method using orbital angular momentum,our scheme has a better performance for both characters and the image object.
1. Total angular momentum from Dirac eigenspinors
International Nuclear Information System (INIS)
2008-01-01
The eigenvalue problem for Dirac operators, constructed from two connections on the spinor bundle over closed spacelike 2-surfaces, is investigated. A class of divergence-free vector fields, built from the eigenspinors, are found, which, for the lowest eigenvalue, reproduce the rotation Killing vectors of metric spheres, and provide rotation BMS vector fields at future null infinity. This makes it possible to introduce a well-defined, gauge invariant spatial angular momentum at null infinity, which reduces to the standard expression in stationary spacetimes. The general formula for the angular momentum flux carried away by the gravitational radiation is also derived
2. Studying AGN Jets At Extreme Angular Resolution
Science.gov (United States)
Bruni, Gabriele
2016-10-01
RadioAstron is a 10m antenna orbiting on the Russian Speckt-R spacecraft, launched in 2011. Performing radio interferometry with a global array of ground telescopes, it is providing record angular resolution. The Key Science Project on AGN polarization is exploiting it to study in great detail the configuration of magnetic fields in AGN jets, and understand their formation and collimation. To date, the project has already achieved the highest angular resolution image ever obtained in Astronomy, and detected brightness temperatures exceeding the ones predicted by theory of AGN.
3. Factorial correlators: angular scaling within QCD jets
International Nuclear Information System (INIS)
Peschanski, R.
2001-01-01
Factorial correlators measure the amount of dynamical correlation in the multiplicity between two separated phase-space windows. We present the analytical derivation of factorial correlators for a QCD jet described at the double logarithmic (DL) accuracy. We obtain a new angular scaling property for properly normalized correlators between two solid-angle cells or two rings around the jet axis. Normalized QCD factorial correlators scale with the angular distance and are independent of the window size. Scaling violations are expected beyond the DL approximation, in particular from the subject structure. Experimental tests are feasible, and thus would be welcome. (orig.)
4. Canonical three-body angular basis
International Nuclear Information System (INIS)
Matveenko, A.V.
2001-01-01
Three-body problems are basic for the quantum mechanics of molecular, atomic, or nuclear systems. We demonstrate that their variational solution for rotational states can be greatly simplified. A special choice of coordinates (hyperspherical) and of the kinematics (body-fixed coordinate frame) allows one to choose basis functions in a form that makes the angular coupling trivial. (author)
5. Probabilistic calculation for angular dependence collision
International Nuclear Information System (INIS)
Villarino, E.A.
1990-01-01
This collision probabilistic method is broadly used in cylindrical geometry (in one- or two-dimensions). It constitutes a powerful tool for the heterogeneous Response Method where, the coupling current is of the cosine type, that is, without angular dependence at azimuthal angle θ and proportional to μ (cosine of the θ polar angle). (Author) [es
6. Wigner Functions and Quark Orbital Angular Momentum
Directory of Open Access Journals (Sweden)
Mukherjee Asmita
2015-01-01
Full Text Available Wigner distributions contain combined position and momentum space information of the quark distributions and are related to both generalized parton distributions (GPDs and transverse momentum dependent parton distributions (TMDs. We report on a recent model calculation of the Wigner distributions for the quark and their relation to the orbital angular momentum.
7. Wigner Functions and Quark Orbital Angular Momentum
OpenAIRE
Mukherjee, Asmita; Nair, Sreeraj; Ojha, Vikash Kumar
2014-01-01
Wigner distributions contain combined position and momentum space information of the quark distributions and are related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs). We report on a recent model calculation of the Wigner distributions for the quark and their relation to the orbital angular momentum.
8. A Novel Permanent Magnetic Angular Acceleration Sensor
Directory of Open Access Journals (Sweden)
Hao Zhao
2015-07-01
Full Text Available Angular acceleration is an important parameter for status monitoring and fault diagnosis of rotary machinery. Therefore, we developed a novel permanent magnetic angular acceleration sensor, which is without rotation angle limitations and could directly measure the instantaneous angular acceleration of the rotating system. The sensor rotor only needs to be coaxially connected with the rotating system, which enables convenient sensor installation. For the cup structure of the sensor rotor, it has a relatively small rotational inertia. Due to the unique mechanical structure of the sensor, the output signal of the sensor can be directed without a slip ring, which avoids signal weakening effect. In this paper, the operating principle of the sensor is described, and simulated using finite element method. The sensitivity of the sensor is calibrated by torsional pendulum and angle sensor, yielding an experimental result of about 0.88 mV/(rad·s−2. Finally, the angular acceleration of the actual rotating system has been tested, using both a single-phase asynchronous motor and a step motor. Experimental result confirms the operating principle of the sensor and indicates that the sensor has good practicability.
9. Angular-momentum-bearing modes in fission
International Nuclear Information System (INIS)
Moretto, L.G.; Peaslee, G.F.; Wozniak, G.J.
1989-03-01
The angular-momentum-bearing degrees of freedom involved in the fission process are identified and their influence on experimental observables is discussed. The excitation of these modes is treated in the ''thermal'' limit, and the resulting distributions of observables are calculated. Experiments demonstrating the role of these modes are presented and discussed. 61 refs., 12 figs
10. Angular and linear momentum of excited ferromagnets
NARCIS (Netherlands)
Yan, P.; Kamra, A.; Cao, Y.; Bauer, G.E.W.
2013-01-01
The angular momentum vector of a Heisenberg ferromagnet with isotropic exchange interaction is conserved, while under uniaxial crystalline anisotropy the projection of the total spin along the easy axis is a constant of motion. Using Noether's theorem, we prove that these conservation laws persist
11. Angular distribution in ternary cold fission
International Nuclear Information System (INIS)
Delion, D.S.; J.W. Goethe Univ., Frankfurt; Sandulescu, A.; J.W. Goethe Univ., Frankfurt; Greiner, W.
2003-01-01
We describe the spontaneous ternary cold fission of 252 Cf, accompanied by 4 He, 10 Be and 14 C. The light cluster decays from the first resonant eigenstate in the Coulomb potential plus a harmonic oscillator potential. We have shown that the angular distribution of the emitted light particle is strongly connected with its deformation and the equatorial distance. (author)
12. Heteromodal conceptual processing in the angular gyrus.
Science.gov (United States)
Bonner, Michael F; Peelle, Jonathan E; Cook, Philip A; Grossman, Murray
2013-05-01
Concepts bind together the features commonly associated with objects and events to form networks in long-term semantic memory. These conceptual networks are the basis of human knowledge and underlie perception, imagination, and the ability to communicate about experiences and the contents of the environment. Although it is often assumed that this distributed semantic information is integrated in higher-level heteromodal association cortices, open questions remain about the role and anatomic basis of heteromodal representations in semantic memory. Here we used combined neuroimaging evidence from functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) to characterize the cortical networks underlying concept representation. Using a lexical decision task, we examined the processing of concepts in four semantic categories that varied on their sensory-motor feature associations (sight, sound, manipulation, and abstract). We found that the angular gyrus was activated across all categories regardless of their modality-specific feature associations, consistent with a heteromodal account for the angular gyrus. Exploratory analyses suggested that categories with weighted sensory-motor features additionally recruited modality-specific association cortices. Furthermore, DTI tractography identified white matter tracts connecting these regions of modality-specific functional activation with the angular gyrus. These findings are consistent with a distributed semantic network that includes a heteromodal, integrative component in the angular gyrus in combination with sensory-motor feature representations in modality-specific association cortices. Copyright © 2013 Elsevier Inc. All rights reserved.
13. ANGULAR MOMENTUM ACQUISITION IN GALAXY HALOS
International Nuclear Information System (INIS)
Stewart, Kyle R.; Brooks, Alyson M.; Bullock, James S.; Maller, Ariyeh H.; Diemand, Jürg; Wadsley, James; Moustakas, Leonidas A.
2013-01-01
We use high-resolution cosmological hydrodynamic simulations to study the angular momentum acquisition of gaseous halos around Milky-Way-sized galaxies. We find that cold mode accreted gas enters a galaxy halo with ∼70% more specific angular momentum than dark matter averaged over cosmic time (though with a very large dispersion). In fact, we find that all matter has a higher spin parameter when measured at accretion than when averaged over the entire halo lifetime, and is well characterized by λ ∼ 0.1, at accretion. Combined with the fact that cold flow gas spends a relatively short time (1-2 dynamical times) in the halo before sinking to the center, this naturally explains why cold flow halo gas has a specific angular momentum much higher than that of the halo and often forms ''cold flow disks.'' We demonstrate that the higher angular momentum of cold flow gas is related to the fact that it tends to be accreted along filaments.
14. W UMa stars and angular momentum loss
International Nuclear Information System (INIS)
Vilhu, O.; Rahunen, T.
1980-01-01
The structure and evolution of W UMa stars is still unsolved although considerable progress has been achieved in recent years. The authors aim is to find out whether it is possible to obtain more extreme mass ratios, what is the angular momentum needed and what is the time scale. (Auth.)
15. On the angular momentum in star formation
International Nuclear Information System (INIS)
Horedt, G.P.
1978-01-01
The author discusses the rotation of interstellar clouds which are in a stage immediately before star formation. Cloud collisions seem to be the principal cause of the observed rotation of interstellar clouds. The rotational motion of the clouds is strongly influenced by turbulence. Theories dealing with the resolution of the angular momentum problem in star formation are classified into five major groups. The old idea that the angular momentum of an interstellar cloud passes during star formation into the angular momentum of double star systems and/or circumstellar clouds, is developed. It is suggested that a rotating gas cloud contracts into a ring-like structure which fragments into self-gravitating subcondensations. By collisions and gas accretion these subcondensations accrete into binary systems surrounded by circumstellar clouds. Using some rough approximations the authors find analytical expressions for the semi-major axis of the binary system and for the density of the circumstellar clouds as a function of the initial density and of the initial angular velocity of an interstellar cloud. The obtained values are well within the observational limits. (Auth.)
16. Variation in angular velocity and angular acceleration of a particle in rectilinear motion
International Nuclear Information System (INIS)
Mashood, K K; Singh, V A
2012-01-01
We discuss the angular velocity and angular acceleration associated with a particle in rectilinear motion with constant acceleration. The discussion was motivated by an observation that students and even teachers have difficulty in ascribing rotational motion concepts to a particle when the trajectory is a straight line. We present some details of our observations. A formal derivation of ω and α is presented which reveals ‘surprising’ and non-intuitive aspects, namely non-monotonic behaviour with an associated extremum. The special case of constant velocity is studied and we find that angular acceleration associated with it also has an extremum. We discuss a plausible source of difficulty. (paper)
17. Multichannel system for angular distribution measurements
International Nuclear Information System (INIS)
Burjan, V.; Kroha, V.; Putz, K.
A description is given of the individual blocks of the spectrometric apparatus used for measuring the angular distribution of particle spectra and excitation functions of (d,p) reactions at an electrostatic accelerator and the U-120 M cyclotron, both operating at the Nuclear Physics Institute of the Czechoslovak Academy of Sciences at Rez. Main attention was devoted to attaining maximum energy resolution at a high measurement efficiency, this by installing 8 independent spectrometric chains allowing simultaneous measurement of angular distribution in 8 points of the beam. The semiconductor detectors were cooled to -40 degC to -60 degC, which significantly reduced the level of inherent detector noise. An energy resolution of 13 keV was attained using Tesla detectors at a particle energy of 11 MeV. A brief review of data processing and software is given. (B.S.)
18. Quantum entanglement of high angular momenta.
Science.gov (United States)
Fickler, Robert; Lapkiewicz, Radek; Plick, William N; Krenn, Mario; Schaeff, Christoph; Ramelow, Sven; Zeilinger, Anton
2012-11-02
Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.
19. Behavior of nuclei at high angular momentum
International Nuclear Information System (INIS)
Stephens, F.S.
1982-07-01
The present report begins with a brief overview of nuclear shapes and level structures at high-spin values. The new spectroscopy associated with angular-momentum alignments is described, and some of the exciting possibilities of this spectroscopy are explored. Nuclear moments of inertia are discussed and a somewhat different one is defined, together with a method for measuring it and some early results. Finally a few comments on the future prospects for high-spin physics are offered
20. Chirality and angular momentum in optical radiation
Science.gov (United States)
Coles, Matt M.; Andrews, David L.
2012-06-01
This paper develops, in precise quantum electrodynamic terms, photonic attributes of the “optical chirality density,” one of several measures long known to be conserved quantities for a vacuum electromagnetic field. The analysis lends insights into some recent interpretations of chiroptical experiments, in which this measure, and an associated chirality flux, have been treated as representing physically distinctive “superchiral” phenomena. In the fully quantized formalism the chirality density is promoted to operator status, whose exploration with reference to an arbitrary polarization basis reveals relationships to optical angular momentum and helicity operators. Analyzing multimode beams with complex wave-front structures, notably Laguerre-Gaussian modes, affords a deeper understanding of the interplay between optical chirality and optical angular momentum. By developing theory with due cognizance of the photonic character of light, it emerges that only the spin-angular momentum of light is engaged in such observations. Furthermore, it is shown that these prominent measures of the helicity of chiral electromagnetic radiation have a common basis in differences between the populations of optical modes associated with angular momenta of opposite sign. Using a calculation of the rate of circular dichroism as an example, with coherent states to model the electromagnetic field, it is discovered that two terms contribute to the differential effect. The primary contribution relates to the difference in left- and right-handed photon populations; the only other contribution, which displays a sinusoidal distance dependence corresponding to the claim of nodal enhancements, is connected with the quantum photon number-phase uncertainty relation. From the full analysis, it appears that the term “superchiral” can be considered redundant.
1. Coherent Control of Photoelectron Wavepacket Angular Interferograms
OpenAIRE
Hockett, Paul; Wollenhaupt, Matthias; Baumert, Thomas
2015-01-01
Coherent control over photoelectron wavepackets, via the use of polarization-shaped laser pulses, can be understood as a time and polarization-multiplexed process. In this work, we investigate this multiplexing via computation of the observable photoelectron angular interferograms resulting from multi-photon atomic ionization with polarization-shaped laser pulses. We consider the polarization sensitivity of both the instantaneous and cumulative continuum wavefunction; the nature of the cohere...
2. Adaptive Angular Sampling for SPECT Imaging
OpenAIRE
Li, Nan; Meng, Ling-Jian
2011-01-01
This paper presents an analytical approach for performing adaptive angular sampling in single photon emission computed tomography (SPECT) imaging. It allows for a rapid determination of the optimum sampling strategy that minimizes image variance in regions-of-interest (ROIs). The proposed method consists of three key components: (a) a set of close-form equations for evaluating image variance and resolution attainable with a given sampling strategy, (b) a gradient-based algor...
3. Angular distribution of laser ablation plasma
International Nuclear Information System (INIS)
Kondo, K.; Kanesue, T.; Dabrowski, R.; Okamura, M.
2010-01-01
An expansion of a laser induced plasma is fundamental and important phenomena in a laser ion source. To understand the expanding direction, an array of Langmuir probes were employed. The chosen ion for the experiment was Ag 1+ which was created by a second harmonics of a Nd-YAG laser. The obtained angular distribution was about ±10 degree. This result also indicates a proper positioning of a solenoid magnet which enhances ion beam current.
4. Coincident-inclusive electrofission angular correlations
International Nuclear Information System (INIS)
Arruda Neto, J.D.T.
1983-08-01
A method for the joint analysis of coincident and inclusive electrofission data, in order to minimize effects of the model dependence of data interpretation, is developed. Explicit calculations of the (e,e'f) angular correlations are presented. The potentialities of the method to the study of sub- and near-barrier properties of the fission process, and to the study of the giant resonances fission mode, are discussed. (Author) [pt
5. Positron annihilation and perturbed angular correlation studies of radiation damage
International Nuclear Information System (INIS)
Zhu Jiazheng; Li Anli; Xu Yongjun; Wang Zhiqiang; Zhou Dongmei; Zheng Yongnan; Zhu Shengyun; Iwata, T.
2002-01-01
The positron annihilation and perturbed angular correlation techniques have been employed to study radiation damage in Si and Nb. The results obtained by the positron annihilation are consistent with those given by the perturbed angular correlation
6. Sorting and quantifying orbital angular momentum of laser beams
CSIR Research Space (South Africa)
Schulze, C
2013-10-01
Full Text Available We present a novel tool for sorting the orbital angular momentum and to determine the orbital angular momentum density of laser beams, which is based on the use of correlation filters....
7. High Angular Momentum Rydberg Wave Packets
Science.gov (United States)
Wyker, Brendan
2011-12-01
High angular momentum Rydberg wave packets are studied. Application of carefully tailored electric fields to low angular momentum, high- n (n ˜ 300) Rydberg atoms creates coherent superpositions of Stark states with near extreme values of angular momentum, ℓ. Wave packet components orbit the parent nucleus at rates that depend on their energy, leading to periods of localization and delocalization as the components come into and go out of phase with each other. Monitoring survival probability signals in the presence of position dependent probing leads to observation of characteristic oscillations based on the composition of the wave packet. The discrete nature of electron energy levels is observed through the measurement of quantum revivals in the wave packet localization signal. Time-domain spectroscopy of these signals allows determination of both the population and phase of individual superposition components. Precise manipulation of wave packets is achieved through further application of pulsed electric fields. Decoherence effects due to background gas collisions and electrical noise are also detailed. Quantized classical trajectory Monte-Carlo simulations are introduced and agree remarkably well with experimental results.
8. Verification of angular dependence in MOSFET detector
Energy Technology Data Exchange (ETDEWEB)
Souza, Clayton H.; Shorto, Julian M.B.; Siqueira, Paulo T.D.; Nunes, Maíra G.; Silva Junior, Iremar A.; Yoriyaz, Hélio, E-mail: [email protected] [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2017-07-01
In vivo dosimetry is an essential tool for quality assurance programs, being a procedure commonly performed with thermoluminescent dosimeters (TLDs) or diodes. However, a type of dosimeter that has increasing popularity in recent years is the metal-oxide-semiconductor field effect transistor (MOSFET) detector. MOSFET dosimeters fulfill all the necessary characteristics to realize in vivo dosimetry since it has a small size, good precision and feasibility of measurement, as well as easy handling. Nevertheless, its true differential is to allow reading of the dose in real time, enabling immediate intervention in the correction of physical parameters deviations and anticipation of small anatomical changes in a patient during treatment. In order for MOSFET dosimeter to be better accepted in clinical routine, information reporting performance should be available frequently. For this reason, this work proposes to verify reproducibility and angular dependence of a standard sensitivity MOSFET dosimeter (TN-502RD-H) for Cs-137 and Co-60 sources. Experimental data were satisfactory and MOSFET dosimeter presented a reproducibility of 3.3% and 2.7% (1 SD) for Cs-137 and Co-60 sources, respectively. In addition, an angular dependence of up to 6.1% and 16.3% for both radioactive sources, respectively. It is conclusive that MOSFET dosimeter TN-502RD-H has satisfactory reproducibility and a considerable angular dependence, mainly for the Co-60 source. This means that although precise measurements, special attention must be taken for applications in certain anatomical regions in a patient. (author)
9. Physics from angular projection of rectangular grids
International Nuclear Information System (INIS)
Singh, Ashmeet
2015-01-01
In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple yet interesting, problem has both scholarly value and applications for data extraction techniques to study the physics of various systems. Our work may help undergraduate students to understand subtle points in the angular projection of a grid and describes various quantities of interest in the projection with completeness and sufficient rigour. We show that for certain angular ranges, the projection has non-distinctness, and calculate the details of such angles, and correspondingly, the number of distinct points and the total projected length. We focus on interesting trends obtained for the projected length of the grid elements and present a simple application of the model to determine the geometry of an unknown grid whose spatial extensions are known, using measurement of the grid projection at two angles only. Towards the end, our model is shown to have potential applications in various branches of physical sciences, including crystallography, astrophysics, and bulk properties of materials. (paper)
10. The Cosmology Large Angular Scale Surveyor (CLASS)
Science.gov (United States)
Harrington, Kathleen; Marriange, Tobias; Aamir, Ali; Appel, John W.; Bennett, Charles L.; Boone, Fletcher; Brewer, Michael; Chan, Manwei; Chuss, David T.; Colazo, Felipe;
2016-01-01
The Cosmology Large Angular Scale Surveyor (CLASS) is a four telescope array designed to characterize relic primordial gravitational waves from in ation and the optical depth to reionization through a measurement of the polarized cosmic microwave background (CMB) on the largest angular scales. The frequencies of the four CLASS telescopes, one at 38 GHz, two at 93 GHz, and one dichroic system at 145/217 GHz, are chosen to avoid spectral regions of high atmospheric emission and span the minimum of the polarized Galactic foregrounds: synchrotron emission at lower frequencies and dust emission at higher frequencies. Low-noise transition edge sensor detectors and a rapid front-end polarization modulator provide a unique combination of high sensitivity, stability, and control of systematics. The CLASS site, at 5200 m in the Chilean Atacama desert, allows for daily mapping of up to 70% of the sky and enables the characterization of CMB polarization at the largest angular scales. Using this combination of a broad frequency range, large sky coverage, control over systematics, and high sensitivity, CLASS will observe the reionization and recombination peaks of the CMB E- and B-mode power spectra. CLASS will make a cosmic variance limited measurement of the optical depth to reionization and will measure or place upper limits on the tensor-to-scalar ratio, r, down to a level of 0.01 (95% C.L.).
11. Science.gov (United States)
Harrington, Kathleen; Marriage, Tobias; Ali, Aamir; Appel, John; Bennett, Charles; Boone, Fletcher; Brewer, Michael; Chan, Manwei; Chuss, David T.; Colazo, Felipe;
2016-01-01
The Cosmology Large Angular Scale Surveyor (CLASS) is a four telescope array designed to characterize relic primordial gravitational waves from inflation and the optical depth to reionization through a measurement of the polarized cosmic microwave background (CMB) on the largest angular scales. The frequencies of the four CLASS telescopes, one at 38 GHz, two at 93 GHz, and one dichroic system at 145217 GHz, are chosen to avoid spectral regions of high atmospheric emission and span the minimum of the polarized Galactic foregrounds: synchrotron emission at lower frequencies and dust emission at higher frequencies. Low-noise transition edge sensor detectors and a rapid front-end polarization modulator provide a unique combination of high sensitivity, stability, and control of systematics. The CLASS site, at 5200 m in the Chilean Atacama desert, allows for daily mapping of up to 70% of the sky and enables the characterization of CMB polarization at the largest angular scales. Using this combination of a broad frequency range, large sky coverage, control over systematics, and high sensitivity, CLASS will observe the reionization and recombination peaks of the CMB E- and B-mode power spectra. CLASS will make a cosmic variance limited measurement of the optical depth to reionization and will measure or place upper limits on the tensor-to-scalar ratio, r, down to a level of 0.01 (95% C.L.).
12. Directory of Open Access Journals (Sweden)
Samuel B Snider
2010-12-01
Full Text Available In one of the most remarkable feats of motor control in the animal world, some Diptera, such as the housefly, can accurately execute corrective flight maneuvers in tens of milliseconds. These reflexive movements are achieved by the halteres, gyroscopic force sensors, in conjunction with rapidly-tunable wing-steering muscles. Specifically, the mechanosensory campaniform sensilla located at the base of the halteres transduce and transform rotation-induced gyroscopic forces into information about the angular velocity of the fly's body. But how exactly does the fly's neural architecture generate the angular velocity from the lateral strain forces on the left and right halteres? To explore potential algorithms, we built a neuro-mechanical model of the rotation detection circuit. We propose a neurobiologically plausible method by which the fly could accurately separate and measure the three-dimensional components of an imposed angular velocity. Our model assumes a single sign-inverting synapse and formally resembles some models of directional selectivity by the retina. Using multidimensional error analysis, we demonstrate the robustness of our model under a variety of input conditions. Our analysis reveals the maximum information available to the fly given its physical architecture and the mathematics governing the rotation-induced forces at the haltere's end knob.
13. Continuous particle spectra and their angular distributions
International Nuclear Information System (INIS)
Sastry, Ch.V.; Jain, R.K.; Rama Rao, J.; Ernst, J.; Machner, H.
1996-01-01
The angular distribution of continuous particle spectra in pre-equilibrium reactions is still an unsolved problem, particularly so at forward angles. In the present work, the angular distributions of alpha particles emitted in (α, α',x) reactions in the target elements gold and rhodium have been studied in detail. Alpha particle beams of energy 60 MeV from the Variable Energy Cyclotron of Calcutta were used in these experiments. The theoretical calculations were done using an extended exciton model of Kalbach incorporated into the Computer Code PRECO-D2. The formalism used in the exciton model was modified to include division of pre equilibrium cross section into multi-step direct (MSD) and multi-step compound (MSC) components. These MSD and MSC cross sections were used to calculate the angular distributions in terms of Legendre polynomials whose coefficients are given by simple phenomenological relations. Even with a reasonable set of parameters, the agreement between theory and experiment was far from satisfactory at forward angles. Similar conclusion was also drawn in the case of continuous particle spectra of deuterons in (d, d'x) reactions at 25 MeV in various targets. (author). 10 refs., 2 figs
14. Verification of angular dependence in MOSFET detector
International Nuclear Information System (INIS)
Souza, Clayton H.; Shorto, Julian M.B.; Siqueira, Paulo T.D.; Nunes, Maíra G.; Silva Junior, Iremar A.; Yoriyaz, Hélio
2017-01-01
In vivo dosimetry is an essential tool for quality assurance programs, being a procedure commonly performed with thermoluminescent dosimeters (TLDs) or diodes. However, a type of dosimeter that has increasing popularity in recent years is the metal-oxide-semiconductor field effect transistor (MOSFET) detector. MOSFET dosimeters fulfill all the necessary characteristics to realize in vivo dosimetry since it has a small size, good precision and feasibility of measurement, as well as easy handling. Nevertheless, its true differential is to allow reading of the dose in real time, enabling immediate intervention in the correction of physical parameters deviations and anticipation of small anatomical changes in a patient during treatment. In order for MOSFET dosimeter to be better accepted in clinical routine, information reporting performance should be available frequently. For this reason, this work proposes to verify reproducibility and angular dependence of a standard sensitivity MOSFET dosimeter (TN-502RD-H) for Cs-137 and Co-60 sources. Experimental data were satisfactory and MOSFET dosimeter presented a reproducibility of 3.3% and 2.7% (1 SD) for Cs-137 and Co-60 sources, respectively. In addition, an angular dependence of up to 6.1% and 16.3% for both radioactive sources, respectively. It is conclusive that MOSFET dosimeter TN-502RD-H has satisfactory reproducibility and a considerable angular dependence, mainly for the Co-60 source. This means that although precise measurements, special attention must be taken for applications in certain anatomical regions in a patient. (author)
15. Natural roller bearing fault detection by angular measurement of true instantaneous angular speed
Science.gov (United States)
Renaudin, L.; Bonnardot, F.; Musy, O.; Doray, J. B.; Rémond, D.
2010-10-01
The challenge in many production activities involving large mechanical devices like power transmissions consists in reducing the machine downtime, in managing repairs and in improving operating time. Most online monitoring systems are based on conventional vibration measurement devices for gear transmissions or bearings in mechanical components. In this paper, we propose an alternative way of bearing condition monitoring based on the instantaneous angular speed measurement. By the help of a large experimental investigation on two different applications, we prove that localized faults like pitting in bearing generate small angular speed fluctuations which are measurable with optical or magnetic encoders. We also emphasize the benefits of measuring instantaneous angular speed with the pulse timing method through an implicit angular sampling which ensures insensitivity to speed fluctuation. A wide range of operating conditions have been tested for the two applications with varying speed, load, external excitations, gear ratio, etc. The tests performed on an automotive gearbox or on actual operating vehicle wheels also establish the robustness of the proposed methodology. By the means of a conventional Fourier transform, angular frequency channels kinematically related to the fault periodicity show significant magnitude differences related to the damage severity. Sideband effects are evidently seen when the fault is located on rotating parts of the bearing due to load modulation. Additionally, slip effects are also suspected to be at the origin of enlargement of spectrum peaks in the case of double row bearings loaded in a pure radial direction.
16. Angular dispersion and deflection function for heavy ion elastic scattering
International Nuclear Information System (INIS)
Bai Zhen; Han Jianlong; Hu Zhengguo; Chinese Academy of Sciences, Beijing
2007-01-01
The differential cross sections for elastic scattering products of 17 F on 208 Pb have been measured. The angular dispersion plots of ln(dσ/dθ) versus θ 2 are obtained from the angular distribution of the elastic scattering differential cross sections. Systematical analysis on the angular dispersion for the available experimental data indicates that there is an angular dispersion turning angle at forward angular range within the grazing angle. This turning angle can be clarified as nuclear rainbow in classical deflection function. The exotic behaviour of the nuclear rainbow angle offers a new probe to investigate the halo and skin phenomena. (authors)
17. Angular Momentum and Galaxy Formation Revisited
Science.gov (United States)
Romanowsky, Aaron J.; Fall, S. Michael
2012-12-01
Motivated by a new wave of kinematical tracers in the outer regions of early-type galaxies (ellipticals and lenticulars), we re-examine the role of angular momentum in galaxies of all types. We present new methods for quantifying the specific angular momentum j, focusing mainly on the more challenging case of early-type galaxies, in order to derive firm empirical relations between stellar j sstarf and mass M sstarf (thus extending earlier work by Fall). We carry out detailed analyses of eight galaxies with kinematical data extending as far out as 10 effective radii, and find that data at two effective radii are generally sufficient to estimate total j sstarf reliably. Our results contravene suggestions that ellipticals could harbor large reservoirs of hidden j sstarf in their outer regions owing to angular momentum transport in major mergers. We then carry out a comprehensive analysis of extended kinematic data from the literature for a sample of ~100 nearby bright galaxies of all types, placing them on a diagram of j sstarf versus M sstarf. The ellipticals and spirals form two parallel j sstarf-M sstarf tracks, with log-slopes of ~0.6, which for the spirals are closely related to the Tully-Fisher relation, but for the ellipticals derives from a remarkable conspiracy between masses, sizes, and rotation velocities. The ellipticals contain less angular momentum on average than spirals of equal mass, with the quantitative disparity depending on the adopted K-band stellar mass-to-light ratios of the galaxies: it is a factor of ~3-4 if mass-to-light ratio variations are neglected for simplicity, and ~7 if they are included. We decompose the spirals into disks and bulges and find that these subcomponents follow j sstarf-M sstarf trends similar to the overall ones for spirals and ellipticals. The lenticulars have an intermediate trend, and we propose that the morphological types of galaxies reflect disk and bulge subcomponents that follow separate, fundamental j sstarf
18. The angular momentum of isolated white dwarfs
Directory of Open Access Journals (Sweden)
Brassard P.
2013-03-01
Full Text Available This is a very brief report on an ongoing program aimed at mapping the internal rotation profiles of stars through asteroseismology. Three years ago, we developed and applied successfully a new technique to the pulsating GW Vir white dwarf PG 1159−035, and were able to infer that it rotates very slowly and rigidly over some 99% of its mass. We applied the same approach to the three other GW Vir pulsators with available rotational splitting data, and found similar results. We discuss the implications of these findings on the question of the angular momentum of white dwarfs resulting from single star evolution.
19. Projection of angular momentum via linear algebra
Science.gov (United States)
Johnson, Calvin W.; O'Mara, Kevin D.
2017-12-01
Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. We show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications to 48Cr and 60Fe in the p f shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.
20. Angular Position Tracking Control of a Quadcopter
OpenAIRE
T. V. Glazkov; A. E. Golubev
2017-01-01
The paper dwells on tracking the quad-copter angular position with desired quality parameters of transient processes. The aerial vehicle is considered as a rigid body with six degrees of freedom. A full rigid body quad-copter mathematical model is considered without the assumption of smallness of the Euler angles.Among the most well known methods of non-linear stabilization are feedback linearization and backstepping. The backstepping approach allows us to have an effective solution of the s...
1. Optical communication beyond orbital angular momentum
CSIR Research Space (South Africa)
Trichili, A
2016-06-01
Full Text Available :27674 | DOI: 10.1038/srep27674 www.nature.com/scientificreports Optical communication beyond orbital angular momentum Abderrahmen Trichili1, Carmelo Rosales-Guzmán2, Angela Dudley2,3, Bienvenu Ndagano2, Amine Ben Salem1, Mourad Zghal1,4 & Andrew Forbes2 [email protected]) received: 29 March 2016 Accepted: 24 May 2016 Published: 10 June 2016 OPEN www.nature.com/scientificreports/ 2Scientific RepoRts | 6:27674 | DOI: 10.1038/srep27674 Results Consider a LG mode in cylindrical coordinates, at its waist plane (z = 0), described...
2. Angular momentum in multi-step photoionization
International Nuclear Information System (INIS)
Yoshida, Tadashi; Adachi, Hajime; Kuwako, Akira; Nittoh, Koichi; Araki, Yoshio; Watanabe, Takashi; Yoguchi, Itaru.
1995-01-01
The effect of the angular momenta on the multi-step laser-ionization efficiency was investigated numerically for cases with and without the hyperfine interactions. For either cases the ionization efficiency proved to depend appreciably on the values of J in the excitation ladder. In this respect, we elaborated a simple and efficient method of determining J, which was based on the laser polarization dependence of the excitation rate. Application of this method to a couple of real excitation ladders proved its usefulness and reliability. (author)
3. Statistical analysis of angular correlation measurements
International Nuclear Information System (INIS)
Oliveira, R.A.A.M. de.
1986-01-01
Obtaining the multipole mixing ratio, δ, of γ transitions in angular correlation measurements is a statistical problem characterized by the small number of angles in which the observation is made and by the limited statistic of counting, α. The inexistence of a sufficient statistics for the estimator of δ, is shown. Three different estimators for δ were constructed and their properties of consistency, bias and efficiency were tested. Tests were also performed in experimental results obtained in γ-γ directional correlation measurements. (Author) [pt
4. Time-dependent angularly averaged inverse transport
International Nuclear Information System (INIS)
Bal, Guillaume; Jollivet, Alexandre
2009-01-01
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. Such measurement settings find applications in medical and geophysical imaging. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain
5. Angular momentum effects in subbarrier fusion
International Nuclear Information System (INIS)
Halbert, M.L.; Beene, J.R.; Hensley, D.C.; Honkanen, K.; Semkow, T.M.; Abenante, V.; Sarantites, D.G.; Li, Z.
1987-01-01
The authors discuss angular-momentum distributions σ l for the compound nucleus 164 Yb deduced from measurements of γ-ray multiplicity for all significant evaporation residues from fusion of 64 Ni and 100 Mo and 16 O + 148 Sm. At the lowest bombarding energies the σ l extend to higher l values than do predictions that include coupling of the principal inelastic channels, even if the coupling strengths are increased to match the experimental excitation function. Likewise, σ l from an energy-dependent real potential fitted to the excitation function fails to reproduce the experimental σ l distribution. No effects attributed to superdeformation were observed
6. Energy flow in angularly dispersive optical systems
International Nuclear Information System (INIS)
Ware, M.; Dibble, W. E.; Glasgow, S. A.; Peatross, J.
2001-01-01
Light-pulse propagation in angularly dispersive systems is explored in the context of a center-of-mass definition of energy arrival time. In this context the time of travel is given by a superposition of group delays weighted by the spectral content of the pulse. With this description the time of travel from one point to the next for a pulse is found to be completely determined by the spectral content, independent of the state of chirp. The effect of sensor orientation on arrival time is also considered. [copyright] 2001 Optical Society of America
7. Angular Speed of a Compact Disc
Science.gov (United States)
Sawicki, Mikolaj Mik''
2006-09-01
A spinning motion of a compact disc in a CD player offers an interesting and challenging problem in rotational kinematics with a nonconstant angular acceleration that can be incorporated into a typical introductory physics class for engineers and scientists. It can be used either as an example presented during the lecture, emphasizing application of calculus, or as a homework assignment that could be handled easily with the help of a spreadsheet, thus eliminating the calculus aspect altogether. I tried both approaches, and the spreadsheet study was favored by my students.
8. A proposed measurement of optical orbital and spin angular momentum and its implications for photon angular momentum
Science.gov (United States)
2018-04-01
The expression for the total angular momentum carried by a laser optical vortex beam, splits, in the paraxial approximation, into two terms which seem to represent orbital and spin angular momentum respectively. There are, however, two very different competing versions of the formula for the spin angular momentum, one based on the use of the Poynting vector, as in classical electrodynamics, the other related to the canonical expression for the angular momentum which occurs in Quantum Electrodynamics. I analyze the possibility that a sufficiently sensitive optical measurement could decide which of these corresponds to the actual physical angular momentum carried by the beam.
9. Orbital angular momentum of general astigmatic modes
International Nuclear Information System (INIS)
Visser, Jorrit; Nienhuis, Gerard
2004-01-01
We present an operator method to obtain complete sets of astigmatic Gaussian solutions of the paraxial wave equation. In case of general astigmatism, the astigmatic intensity and phase distribution of the fundamental mode differ in orientation. As a consequence, the fundamental mode has a nonzero orbital angular momentum, which is not due to phase singularities. Analogous to the operator method for the quantum harmonic oscillator, the corresponding astigmatic higher-order modes are obtained by repeated application of raising operators on the fundamental mode. The nature of the higher-order modes is characterized by a point on a sphere, in analogy with the representation of polarization on the Poincare sphere. The north and south poles represent astigmatic Laguerre-Gaussian modes, similar to circular polarization on the Poincare sphere, while astigmatic Hermite-Gaussian modes are associated with points on the equator, analogous to linear polarization. We discuss the propagation properties of the modes and their orbital angular momentum, which depends on the degree of astigmatism and on the location of the point on the sphere
10. [Sensitivity of four representative angular cephalometric measures].
Science.gov (United States)
Xü, T; Ahn, J; Baumrind, S
2000-05-01
Examined the sensitivity of four representative cephalometric angles to the detection of different vectors of craniofacial growth. Landmark coordinate data from a stratified random sample of 48 adolescent subjects were used to calculate conventional values for changes between the pretreatment and end-of-treatment lateral cephalograms. By modifying the end-of-treatment coordinate values appropriately, the angular changes could be recalculated reflecting three hypothetical situations: Case 1. What if there were no downward landmark displacement between timepoints? Case 2. What if there were no forward landmark displacement between timepoints? Case 3. What if there were no Nasion change? These questions were asked for four representative cephalometric angles: SNA, ANB, NAPg and UI-SN. For Case 1, the associations (r) between the baseline and the modified measure for the three angles were very highly significant (P < 0.001) with r2 values no lower than 0.94! For Case 2, however, the associations were much weaker and no r value reached significance. These angular measurements are less sensitive for measuring downward landmark displacement than they are for measuring forward landmark displacement.
11. Electromagnetic angular positioner based on DC micromotor
Directory of Open Access Journals (Sweden)
Bodnicki Maciej
2018-01-01
Full Text Available The presented works concerned launching of an angular positioner powered by an electromagnetic actuator, designed for performing angular micromovements within a range of few microradians. The principle of operation is based on balancing the electromagnetic torque of the motor with a torque that is twisting a compliant element. As electrodynamic actuators have no distinguished controlled positions, therefore in typical positioning systems desired positions are obtained applying a closed-loop position control. Usually, such systems employ also a feedback (dumping related to velocity of the moving elements, what simplifies forming of dynamics of the system. The design of the physical model employs a DC micromotor, whose rotor is coupled with a torsional torquemeter. A feedback signal is generated by resistive strain gauges. The paper presents a mathematical model of the positioning system, results of simulation study as well as results of experimental study. The simulation study indicates that it is possible to select such design features and such type of the micoromotor that a high dynamics of positioning is ensured.
12. Practical scaling law for photoelectron angular distributions
International Nuclear Information System (INIS)
Guo Dongsheng; Zhang Jingtao; Xu Zhizhan; Li Xiaofeng; Fu Panming; Freeman, R.R.
2003-01-01
A practical scaling law that predicts photoelectron angular distributions (PADs) is derived using angular distribution formulas which explicitly contain spontaneous emission. The scaling law is used to analyze recent PAD measurements in above-threshold ionization, and to predict results of future experiments. Our theoretical and numerical studies show that, in the non-relativistic regime and long-wavelength approximation, the shapes of PADs are determined by only three dimensionless numbers: (1) u p ≡U p /(ℎ/2π)ω, the ponderomotive number (ponderomotive energy in units of laser photon energy); (2) ε b ≡E b /(ℎ/2π)ω, the binding number (atomic binding energy in units of the laser photon energy); (3) j, the absorbed-photon number. The scaling law is shown to be useful in predictions of results from strong-field Kapitza-Dirac effect measurements; specifically, the application of this scaling law to recently reported Kapitza-Dirac diffraction is discussed. Possible experimental tests to verify the scaling law are suggested
13. The Cosmology Large Angular Scale Surveyor (CLASS)
Science.gov (United States)
Cleary, Joseph
2018-01-01
The Cosmology Large Angular Scale Surveyor (CLASS) is an array of four telescopes designed to measure the polarization of the Cosmic Microwave Background. CLASS aims to detect the B-mode polarization from primordial gravitational waves predicted by cosmic inflation theory, as well as the imprint left by reionization upon the CMB E-mode polarization. This will be achieved through a combination of observing strategy and state-of-the-art instrumentation. CLASS is observing 70% of the sky to characterize the CMB at large angular scales, which will measure the entire CMB power spectrum from the reionization peak to the recombination peak. The four telescopes operate at frequencies of 38, 93, 145, and 217 GHz, in order to estimate Galactic synchrotron and dust foregrounds while avoiding atmospheric absorption. CLASS employs rapid polarization modulation to overcome atmospheric and instrumental noise. Polarization sensitive cryogenic detectors with low noise levels provide CLASS the sensitivity required to constrain the tensor-to-scalar ratio down to levels of r ~ 0.01 while also measuring the optical depth the reionization to sample-variance levels. These improved constraints on the optical depth to reionization are required to pin down the mass of neutrinos from complementary cosmological data. CLASS has completed a year of observations at 38 GHz and is in the process of deploying the rest of the telescope array. This poster provides an overview and update on the CLASS science, hardware and survey operations.
14. Inefficient Angular Momentum Transport in Accretion Disk Boundary Layers: Angular Momentum Belt in the Boundary Layer
Science.gov (United States)
Belyaev, Mikhail A.; Quataert, Eliot
2018-04-01
We present unstratified 3D MHD simulations of an accretion disk with a boundary layer (BL) that have a duration ˜1000 orbital periods at the inner radius of the accretion disk. We find the surprising result that angular momentum piles up in the boundary layer, which results in a rapidly rotating belt of accreted material at the surface of the star. The angular momentum stored in this belt increases monotonically in time, which implies that angular momentum transport mechanisms in the BL are inefficient and do not couple the accretion disk to the star. This is in spite of the fact that magnetic fields are advected into the BL from the disk and supersonic shear instabilities in the BL excite acoustic waves. In our simulations, these waves only carry a small fraction (˜10%) of the angular momentum required for steady state accretion. Using analytical theory and 2D viscous simulations in the R - ϕ plane, we derive an analytical criterion for belt formation to occur in the BL in terms of the ratio of the viscosity in the accretion disk to the viscosity in the BL. Our MHD simulations have a dimensionless viscosity (α) in the BL that is at least a factor of ˜100 smaller than that in the disk. We discuss the implications of these results for BL dynamics and emission.
15. Untangling Galaxy Components - The Angular Momentum Parameter
Science.gov (United States)
Tabor, Martha; Merrifield, Michael; Aragon-Salamanca, Alfonso
2017-06-01
We have developed a new technique to decompose Integral Field spectral data cubes into separate bulge and disk components, allowing us to study the kinematic and stellar population properties of the individual components and how they vary with position. We present here the application of this method to a sample of fast rotator early type galaxies from the MaNGA integral field survey, and demonstrate how it can be used to explore key properties of the individual components. By extracting ages, metallicities and the angular momentum parameter lambda of the bulges and disks, we show how this method can give us new insights into the underlying structure of the galaxies and discuss what this can tell us about their evolution history.
16. Coherent control of photoelectron wavepacket angular interferograms
International Nuclear Information System (INIS)
Hockett, P; Wollenhaupt, M; Baumert, T
2015-01-01
Coherent control over photoelectron wavepackets, via the use of polarization-shaped laser pulses, can be understood as a time and polarization-multiplexed process, where the final (time-integrated) observable coherently samples all instantaneous states of the light–matter interaction. In this work, we investigate this multiplexing via computation of the observable photoelectron angular interferograms resulting from multi-photon atomic ionization with polarization-shaped laser pulses. We consider the polarization sensitivity of both the instantaneous and cumulative continuum wavefunction; the nature of the coherent control over the resultant photoelectron interferogram is thus explored in detail. Based on this understanding, the use of coherent control with polarization-shaped pulses as a methodology for a highly multiplexed coherent quantum metrology is also investigated, and defined in terms of the information content of the observable. (paper)
17. Coherent control of photoelectron wavepacket angular interferograms
Science.gov (United States)
Hockett, P.; Wollenhaupt, M.; Baumert, T.
2015-11-01
Coherent control over photoelectron wavepackets, via the use of polarization-shaped laser pulses, can be understood as a time and polarization-multiplexed process, where the final (time-integrated) observable coherently samples all instantaneous states of the light-matter interaction. In this work, we investigate this multiplexing via computation of the observable photoelectron angular interferograms resulting from multi-photon atomic ionization with polarization-shaped laser pulses. We consider the polarization sensitivity of both the instantaneous and cumulative continuum wavefunction; the nature of the coherent control over the resultant photoelectron interferogram is thus explored in detail. Based on this understanding, the use of coherent control with polarization-shaped pulses as a methodology for a highly multiplexed coherent quantum metrology is also investigated, and defined in terms of the information content of the observable.
18. Angular biasing in implicit Monte-Carlo
International Nuclear Information System (INIS)
Zimmerman, G.B.
1994-01-01
Calculations of indirect drive Inertial Confinement Fusion target experiments require an integrated approach in which laser irradiation and radiation transport in the hohlraum are solved simultaneously with the symmetry, implosion and burn of the fuel capsule. The Implicit Monte Carlo method has proved to be a valuable tool for the two dimensional radiation transport within the hohlraum, but the impact of statistical noise on the symmetric implosion of the small fuel capsule is difficult to overcome. We present an angular biasing technique in which an increased number of low weight photons are directed at the imploding capsule. For typical parameters this reduces the required computer time for an integrated calculation by a factor of 10. An additional factor of 5 can also be achieved by directing even smaller weight photons at the polar regions of the capsule where small mass zones are most sensitive to statistical noise
19. Angular filter refractometry analysis using simulated annealing.
Science.gov (United States)
Angland, P; Haberberger, D; Ivancic, S T; Froula, D H
2017-10-01
Angular filter refractometry (AFR) is a novel technique used to characterize the density profiles of laser-produced, long-scale-length plasmas [Haberberger et al., Phys. Plasmas 21, 056304 (2014)]. A new method of analysis for AFR images was developed using an annealing algorithm to iteratively converge upon a solution. A synthetic AFR image is constructed by a user-defined density profile described by eight parameters, and the algorithm systematically alters the parameters until the comparison is optimized. The optimization and statistical uncertainty calculation is based on the minimization of the χ 2 test statistic. The algorithm was successfully applied to experimental data of plasma expanding from a flat, laser-irradiated target, resulting in an average uncertainty in the density profile of 5%-20% in the region of interest.
20. Intrinsic Orbital Angular Momentum States of Neutrons
Science.gov (United States)
Cappelletti, Ronald L.; Jach, Terrence; Vinson, John
2018-03-01
It has been shown that single-particle wave functions, of both photons and electrons, can be created with a phase vortex, i.e., an intrinsic orbital angular momentum (OAM). A recent experiment has claimed similar success using neutrons [C. W. Clark et al., Nature, 525, 504 (2015), 10.1038/nature15265]. We show that their results are insufficient to unambiguously demonstrate OAM, and they can be fully explained as phase contrast interference patterns. Furthermore, given the small transverse coherence length of the neutrons in the original experiment, the probability that any neutron was placed in an OAM state is vanishingly small. We highlight the importance of the relative size of the coherence length, which presents a unique challenge for neutron experiments compared to electron or photon work, and we suggest improvements for the creation of neutron OAM states.
1. Nuclear scissors modes and hidden angular momenta
Energy Technology Data Exchange (ETDEWEB)
Balbutsev, E. B., E-mail: [email protected]; Molodtsova, I. V. [Joint Institute for Nuclear Research (Russian Federation); Schuck, P. [Université Paris-Sud, Institut de Physique Nucléaire, IN2P3–CNRS (France)
2017-01-15
The coupled dynamics of low-lying modes and various giant resonances are studied with the help of the Wigner Function Moments method generalized to take into account spin degrees of freedom and pair correlations simultaneously. The method is based on Time-Dependent Hartree–Fock–Bogoliubov equations. The model of the harmonic oscillator including spin–orbit potential plus quadrupole–quadrupole and spin–spin interactions is considered. New low-lying spin-dependent modes are analyzed. Special attention is paid to the scissors modes. A new source of nuclear magnetism, connected with counter-rotation of spins up and down around the symmetry axis (hidden angular momenta), is discovered. Its inclusion into the theory allows one to improve substantially the agreement with experimental data in the description of energies and transition probabilities of scissors modes.
2. Angular Spectrum Simulation of Pulsed Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2009-01-01
frequencies must be performed. Combining it with Field II, the generation of non-linear simulation for any geometry with any excitation array transducer becomes feasible. The purpose of this paper is to make a general pulsed simulation software using the modified ASA. Linear and phased array transducers......The optimization of non-linear ultrasound imaging should in a first step be based on simulation, as this makes parameter studies considerably easier than making transducer prototypes. Such a simulation program should be capable of simulating non-linear pulsed fields for arbitrary transducer...... geometries for any kind of focusing and apodization. The Angular Spectrum Approach (ASA) is capable of simulating monochromatic non-linear acoustic wave propagation. However, for ultrasound imaging the time response of each specific point in space is required, and a pulsed ASA simulation with multi temporal...
3. Angular momentum of dark matter black holes
Energy Technology Data Exchange (ETDEWEB)
Frampton, Paul H., E-mail: [email protected]
2017-04-10
We provide strongly suggestive evidence that the halo constituents of dark matter are Primordial Intermediate-Mass Black Holes (PIMBHs). PIMBHs are described by a Kerr metric with two parameters, mass M and angular momentum J. There has been little discussion of J since it plays no role in the upcoming attempt at PIMBH detection by microlensing. Nevertheless J does play a central role in understanding their previous lack of detection, especially by CMB distortion. We explain why bounds previously derived from lack of CMB distortion are too strong for PIMBHs with J non-vanishing and that, provided almost no dark matter black holes originate from stellar collapse, excessive CMB distortion is avoided.
4. Angular reduction in multiparticle matrix elements
International Nuclear Information System (INIS)
Lehman, D.R.; Parke, W.C.
1989-01-01
A general method for reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products of the unit vector arguments of the spherical harmonics. For nonscalar couplings, the reduction gives Cartesian tensor forms for the spherical harmonic products; tensors built from the physical vectors in the original expression. The reduction for arbitrary couplings is given in closed form, making it amenable to symbolic manipulation on a computer. The final expressions do not depend on a special choice of coordinate axes, nor do they contain azimuthal quantum number summations, or do they have complex tensor terms for couplings to a scalar; consequently, they are easily interpretable from the properties of the physical vectors they contain
5. Angular discretization errors in transport theory
International Nuclear Information System (INIS)
Nelson, P.; Yu, F.
1992-01-01
Elements of the information-based complexity theory are computed for several types of information and associated algorithms for angular approximations in the setting of a on-dimensional model problem. For point-evaluation information, the local and global radii of information are computed, a (trivial) optimal algorithm is determined, and the local and global error of a discrete ordinates algorithm are shown to be infinite. For average cone-integral information, the local and global radii of information are computed, the local and global error tends to zero as the underlying partition is indefinitely refined. A central algorithm for such information and an optimal partition (of given cardinality) are described. It is further shown that the analytic first-collision source method has zero error (for the purely absorbing model problem). Implications of the restricted problem domains suitable for the various types of information are discussed
6. Topological photonic orbital-angular-momentum switch
Science.gov (United States)
Luo, Xi-Wang; Zhang, Chuanwei; Guo, Guang-Can; Zhou, Zheng-Wei
2018-04-01
The large number of available orbital-angular-momentum (OAM) states of photons provides a unique resource for many important applications in quantum information and optical communications. However, conventional OAM switching devices usually rely on precise parameter control and are limited by slow switching rate and low efficiency. Here we propose a robust, fast, and efficient photonic OAM switch device based on a topological process, where photons are adiabatically pumped to a target OAM state on demand. Such topological OAM pumping can be realized through manipulating photons in a few degenerate main cavities and involves only a limited number of optical elements. A large change of OAM at ˜10q can be realized with only q degenerate main cavities and at most 5 q pumping cycles. The topological photonic OAM switch may become a powerful device for broad applications in many different fields and motivate a topological design of conventional optical devices.
7. Angular response of hot wire probes
International Nuclear Information System (INIS)
Di Mare, L; Jelly, T O; Day, I J
2017-01-01
A new equation for the convective heat loss from the sensor of a hot-wire probe is derived which accounts for both the potential and the viscous parts of the flow past the prongs. The convective heat loss from the sensor is related to the far-field velocity by an expression containing a term representing the potential flow around the prongs, and a term representing their viscous effect. This latter term is absent in the response equations available in the literature but is essential in representing some features of the observed response of miniature hot-wire probes. The response equation contains only four parameters but it can reproduce, with great accuracy, the behaviour of commonly used single-wire probes. The response equation simplifies the calibration the angular response of rotated slanted hot-wire probes: only standard King’s law parameters and a Reynolds-dependent drag coefficient need to be determined. (paper)
8. Angular Position Tracking Control of a Quadcopter
Directory of Open Access Journals (Sweden)
T. V. Glazkov
2017-01-01
Full Text Available The paper dwells on tracking the quad-copter angular position with desired quality parameters of transient processes. The aerial vehicle is considered as a rigid body with six degrees of freedom. A full rigid body quad-copter mathematical model is considered without the assumption of smallness of the Euler angles.Among the most well known methods of non-linear stabilization are feedback linearization and backstepping. The backstepping approach allows us to have an effective solution of the stabilization problems with uncertainties available in the system. However, in synthesis of the feedback through backstepping, there is still an urgent issue: how to ensure desirable quality of transients in the closed-loop system. The paper presents a solution of this problem using as an example the tracking a given (programmed change of the angular position of a quad-copter.The control algorithms obtained in this paper are implemented using the Rolling Spider MATLAB Toolbox (ROSMAT tool package on the Parrot Rolling Spider quad-copter. A numerical simulation and experiments have shown the efficiency of obtained control laws, with the transient processes taking into account the desired quality indicators. However, the experiments showed that lack of terms in the mathematical model to describe the aerodynamic effects, resulted in the instability of the quad-copter flight near the obstacle (the effect of the reflected airflow.Further research can be aimed at solving the control problem in question using a mathematical model of the quad-copter motion that takes into account various aerodynamic effects.One of the potential application areas for the theoretical results, obtained in the paper, is to solve the problems of automatic control of unmanned aerial vehicles.
9. Supramolecular architectures constructed using angular bipyridyl ligands
International Nuclear Information System (INIS)
Barnett, Sarah Ann
2003-01-01
This work details the synthesis and characterization of a series of coordination frameworks that are formed using bidentate angular N-donor ligands. Pyrimidine was reacted with metal(ll) nitrate salts. Reactions using Cd(NO 3 ) 2 receive particular focus and the analogous reactions using the linear ligand, pyrazine, were studied for comparison. In all cases, two-dimensional coordination networks were prepared. Structural diversity is observed for the Cd(ll) centres including metal-nitrate bridging. In contrast, first row transition metal nitrates form isostructural one-dimensional chains with only the bridging N-donor ligands generating polymeric propagation. The angular ligand, 2,4-bis(4-pyridyl)-1,3,5-triazine (dpt), was reacted with Cd(NO 3 ) 2 and Zn(NO 3 ) 2 . Whereas Zn(NO 3 ) 2 compounds exhibit solvent mediated polymorphism, a range of structures were obtained for the reactions with Cd(NO 3 ) 2 , including the first example of a doubly parallel interpenetrated 4.8 2 net. 4,7-phenanthroline, was reacted with various metal(ll) nitrates as well as cobalt(ll) and copper(ll) halides. The ability of 4,7-phenanthroline to act as both a N-donor ligand and a hydrogen bond acceptor has been discussed. Reactions of CuSCN with pyrimidine yield an unusual three-dimensional structure in which polymeric propagation is not a result of ligand bridging. The reaction of CuSCN with dpt yielded structural supramolecular isomers. (author)
10. Angular momentum of circularly polarized light in dielectric media
OpenAIRE
Mansuripur, Masud
2014-01-01
A circularly polarized plane-wave is known to have no angular momentum when examined through Maxwell's equations. This, however, contradicts the experimentally observed facts, where finite segments of plane waves are known to be capable of imparting angular momentum to birefringent platelets. Using a superposition of four plane-waves propagating at slightly different angles to a common direction, we derive an expression for the angular momentum density of a single plane-wave in the limit when...
11. Orbital angular momentum exchange in post-collision interaction
International Nuclear Information System (INIS)
van der Burgt, P.J.M.; van Eck, J.; Heideman, H.G.M.
1985-01-01
The authors study the exchange of orbital angular mementum between the scattered and the ejected electron. The angular distribution of electrons ejected by the He (2s 2 ) 2 S autoionizing state after its excitation via the He (2s2p 2 ) 2 D resonance is measured. Taking into accout interference with electrons from the direct ionization of helium, the authors are able to show that the measured anisotropic angular distribution is the result of an orbital angular momentum exchange during the post-collision interaction
12. A proposed measurement of optical orbital and spin angular momentum and its implications for photon angular momentum
Directory of Open Access Journals (Sweden)
2018-04-01
Full Text Available The expression for the total angular momentum carried by a laser optical vortex beam, splits, in the paraxial approximation, into two terms which seem to represent orbital and spin angular momentum respectively. There are, however, two very different competing versions of the formula for the spin angular momentum, one based on the use of the Poynting vector, as in classical electrodynamics, the other related to the canonical expression for the angular momentum which occurs in Quantum Electrodynamics. I analyze the possibility that a sufficiently sensitive optical measurement could decide which of these corresponds to the actual physical angular momentum carried by the beam. Keywords: Photon, Angular momentum, Laser optics, Particle physics
13. Whole-body angular momentum during stair ascent and descent.
Science.gov (United States)
Silverman, Anne K; Neptune, Richard R; Sinitski, Emily H; Wilken, Jason M
2014-04-01
The generation of whole-body angular momentum is essential in many locomotor tasks and must be regulated in order to maintain dynamic balance. However, angular momentum has not been investigated during stair walking, which is an activity that presents a biomechanical challenge for balance-impaired populations. We investigated three-dimensional whole-body angular momentum during stair ascent and descent and compared it to level walking. Three-dimensional body-segment kinematic and ground reaction force (GRF) data were collected from 30 healthy subjects. Angular momentum was calculated using a 13-segment whole-body model. GRFs, external moment arms and net joint moments were used to interpret the angular momentum results. The range of frontal plane angular momentum was greater for stair ascent relative to level walking. In the transverse and sagittal planes, the range of angular momentum was smaller in stair ascent and descent relative to level walking. Significant differences were also found in the ground reaction forces, external moment arms and net joint moments. The sagittal plane angular momentum results suggest that individuals alter angular momentum to effectively counteract potential trips during stair ascent, and reduce the range of angular momentum to avoid falling forward during stair descent. Further, significant differences in joint moments suggest potential neuromuscular mechanisms that account for the differences in angular momentum between walking conditions. These results provide a baseline for comparison to impaired populations that have difficulty maintaining dynamic balance, particularly during stair ascent and descent. Copyright © 2014 Elsevier B.V. All rights reserved.
14. Learning web development with Bootstrap and AngularJS
CERN Document Server
2015-01-01
Whether you know a little about Bootstrap or AngularJS, or you're a complete beginner, this book will enhance your capabilities in both frameworks and you'll build a fully functional web app. A working knowledge of HTML, CSS, and JavaScript is required to fully get to grips with Bootstrap and AngularJS.
15. Schmidt decomposition for non-collinear biphoton angular wave functions
International Nuclear Information System (INIS)
Fedorov, M V
2015-01-01
Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure for their separation is described. Parameters of the Schmidt decomposition are used to evaluate the degree of the biphoton's angular entanglement. (paper)
16. Isotropic gates in large gamma detector arrays versus angular distributions
International Nuclear Information System (INIS)
Iacob, V.E.; Duchene, G.
1997-01-01
The quality of the angular distribution information extracted from high-fold gamma-gamma coincidence events is analyzed. It is shown that a correct quasi-isotropic gate setting, available at the modern large gamma-ray detector arrays, essentially preserves the quality of the angular information. (orig.)
17. Measuring Average Angular Velocity with a Smartphone Magnetic Field Sensor
Science.gov (United States)
Pili, Unofre; Violanda, Renante
2018-01-01
The angular velocity of a spinning object is, by standard, measured using a device called a tachometer. However, by directly using it in a classroom setting, the activity is likely to appear as less instructive and less engaging. Indeed, some alternative classroom-suitable methods for measuring angular velocity have been presented. In this paper,…
18. Angular momentum dependence of the distribution of shell model eigenenergies
International Nuclear Information System (INIS)
Yen, M.K.
1974-01-01
In the conventional shell model calculation the many-particle energy matrices are constructed and diagonalized for definite angular momentum and parity. However the resulting set of eigenvalues possess a near normal behavior and hence a simple statistical description is possible. Usually one needs only about four parameters to capture the average level densities if the size of the set is not too small. The parameters are essentially moments of the distribution. But the difficulty lies in the yet unsolved problem of calculating moments in the fixed angular momentum subspace. We have derived a formula to approximate the angular momentum projection dependence of any operator averaged in a shell model basis. This approximate formula which is a truncated series in Hermite polynomials has been proved very good numerically and justified analytically for large systems. Applying this formula to seven physical cases we have found that the fixed angular momentum projection energy centroid, width and higher central moments can be obtained accurately provided for even-even nuclei the even and odd angular momentum projections are treated separately. Using this information one can construct the energy distribution for fixed angular momentum projection assuming normal behavior. Then the fixed angular momentum level densities are deduced and spectra are extracted. Results are in reasonably good agreement with the exact values although not as good as those obtained using exact fixed angular momentum moments. (Diss. Abstr. Int., B)
19. Rotational speedups accompanying angular deceleration of a superfluid
International Nuclear Information System (INIS)
Campbell, L.J.
1979-01-01
Exact calculations of the angular deceleration of superfluid vortex arrays show momentary speedups in the angular velocity caused by coherent, multiple vortex loss at the boundary. The existence and shape of the speedups depend on the vortex friction, the deceleration rate, and the pattern symmetry. The phenomenon resembles, in several ways, that observed in pulsars
20. Angular correlations near the Fermi energy
International Nuclear Information System (INIS)
Fox, D.; Cebra, D.A.; Karn, J.
1988-01-01
Angular correlations between light particles have been studied to probe the extent to which a thermally equilibrated system is formed in heavy ion collisions near the Fermi energy. Single-light-particle inclusive energy spectra and two-particle large-angle correlations were measured for 40 and 50 MeV/nucleon C+C, Ag, and Au. The single-particle inclusive energy spectra are well fit by a three moving source parametrization. Two-particle large-angle correlations are shown to be consistent with emission from a thermally equilibrated source when the effects of momentum conservation are considered. Single-particle inclusive spectra and light-particle correlations at small relative momentum were measured for 35 MeV/nucleon N+Ag. Source radii were extracted from the two-particle correlation functions and were found to be consistent with previous measurements using two-particle correlations and the coalescence model. The temperature of the emitting source was extracted from the relative populations of states using the quantum statistical model and was found to be 4.8/sub -2.4//sup +2.8/ MeV, compared to the 14 MeV temperature extracted from the slopes of the kinetic energy spectra
1. A new CMOS Hall angular position sensor
Energy Technology Data Exchange (ETDEWEB)
Popovic, R.S.; Drljaca, P. [Swiss Federal Inst. of Tech., Lausanne (Switzerland); Schott, C.; Racz, R. [SENTRON AG, Zug (Switzerland)
2001-06-01
The new angular position sensor consists of a combination of a permanent magnet attached to a shaft and of a two-axis magnetic sensor. The permanent magnet produces a magnetic field parallel with the magnetic sensor plane. As the shaft rotates, the magnetic field also rotates. The magnetic sensor is an integrated combination of a CMOS Hall integrated circuit and a thin ferromagnetic disk. The CMOS part of the system contains two or more conventional Hall devices positioned under the periphery of the disk. The ferromagnetic disk converts locally a magnetic field parallel with the chip surface into a field perpendicular to the chip surface. Therefore, a conventional Hall element can detect an external magnetic field parallel with the chip surface. As the direction of the external magnetic field rotates in the chip plane, the output voltage of the Hall element varies as the cosine of the rotation angle. By placing the Hall elements at the appropriate places under the disk periphery, we may obtain the cosine signals shifted by 90 , 120 , or by any other angle. (orig.)
2. Nuclear structure at high angular momentum
International Nuclear Information System (INIS)
Stephens, F.S.
1976-08-01
There is considerable interest in high angular-momentum states of nuclei, and some recent progress in three areas is discussed. Part I considers transitional nuclei, where two types of rotational bands--decoupled and strongly coupled--are found to occur very frequently. These can be described by several collective models, but the required potential-energy surfaces seem to differ somewhat from those calculated microscopically. In Part II the processes that might cause backbending (irregularities in the rotational levels of certain nuclei) are discussed, and alignment of individual nucleons now seems to be the cause in most cases. The mixing of the ground band with this aligned band can be studied in some detail using Coulomb excitation with very heavy ions. Part III deals with the very high-spin states where effective moments of inertia have been obtained for spins up to 50h. Also structure has been seen in the spectra around these spin values which can be tentatively related to calculated shell effects. 74 references, 61 figures
3. CLASS: The Cosmology Large Angular Scale Surveyor
Science.gov (United States)
Essinger-Hileman, Thomas; Ali, Aamir; Amiri, Mandana; Appel, John W.; Araujo, Derek; Bennett, Charles L.; Boone, Fletcher; Chan, Manwei; Cho, Hsiao-Mei; Chuss, David T.;
2014-01-01
The Cosmology Large Angular Scale Surveyor (CLASS) is an experiment to measure the signature of a gravitational wave background from inflation in the polarization of the cosmic microwave background (CMB). CLASS is a multi-frequency array of four telescopes operating from a high-altitude site in the Atacama Desert in Chile. CLASS will survey 70% of the sky in four frequency bands centered at 38, 93, 148, and 217 GHz, which are chosen to straddle the Galactic-foreground minimum while avoiding strong atmospheric emission lines. This broad frequency coverage ensures that CLASS can distinguish Galactic emission from the CMB. The sky fraction of the CLASS survey will allow the full shape of the primordial B-mode power spectrum to be characterized, including the signal from reionization at low-length. Its unique combination of large sky coverage, control of systematic errors, and high sensitivity will allow CLASS to measure or place upper limits on the tensor-to-scalar ratio at a level of r = 0:01 and make a cosmic-variance-limited measurement of the optical depth to the surface of last scattering, tau. (c) (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
4. Science.gov (United States)
Monteiro, Martín; Cabeza, Cecilia; Marti, Arturo C.; Vogt, Patrik; Kuhn, Jochen
2014-05-01
During the last few years, the growing boom of smartphones has given rise to a considerable number of applications exploiting the functionality of the sensors incorporated in these devices. A sector that has unexpectedly taken advantage of the power of these tools is physics teaching, as reflected in several recent papers. In effect, the use of smartphones has been proposed in several physics experiments spanning mechanics, electromagnetism, optics, oscillations, and waves, among other subjects. Although mechanical experiments have received considerable attention, most of them are based on the use of the accelerometer. An aspect that has received less attention is the use of rotation sensors or gyroscopes. An additional advance in the use of these devices is given by the possibility of obtaining data using the accelerometer and the gyroscope simultaneously. The aim of this paper is to consider the relation between the centripetal acceleration and the angular velocity. Instead of using a formal laboratory setup, in this experiment a smartphone is attached to the floor of a merry-go-round, found in many playgrounds. Several experiments were performed with the roundabout rotating in both directions and with the smart-phone at different distances from the center. The coherence of the measurements is shown.
5. Angular-momentum effects in subbarrier fusion
International Nuclear Information System (INIS)
Halbert, M.L.; Beene, J.R.
1993-01-01
It has been known since about 1980 that fusion of heavy ions is greatly enhanced below the Coulomb barrier compared with normal barrier-penetration expectations. The excitation function for fusion of 64 Ni + 100 Mo measured in collaboration with a group at Washington University shows the effect clearly. The barrier energy is about 142 MeV; the lowest point is at about 90% of the barrier energy. The dotted curve is the prediction of a one-dimensional-barrier-penetration calculation of a type that reproduces the fusion of light projectiles very well. Several theoretical approaches have been successful in explaining the enhancement seen in much of the excitation-function data, but it cannot be said that a full understanding of the physics is in hand even after more than a decade of hard work. In fact, the reasonable success of several rather different models shows that the underlying phenomena are not well understood. Other types of data might be helpful in distinguishing among the many different theoretical approaches. An important kind of information not measured in most of the experiments is the dependence on ell, the angular momentum of the fusing system. We obtained such information on the cross sections, σ ell, as a function of ell for the fusion of 64 Ni and 100 Mo using the Spin Spectrometer. This paper will first review the experimental method and data and then present results from a more sophisticated analysis of the same data
6. Cyclic transformation of orbital angular momentum modes
International Nuclear Information System (INIS)
Schlederer, Florian; Krenn, Mario; Fickler, Robert; Malik, Mehul; Zeilinger, Anton
2016-01-01
The spatial modes of photons are one realization of a QuDit, a quantum system that is described in a D-dimensional Hilbert space. In order to perform quantum information tasks with QuDits, a general class of D-dimensional unitary transformations is needed. Among these, cyclic transformations are an important special case required in many high-dimensional quantum communication protocols. In this paper, we experimentally demonstrate a cyclic transformation in the high-dimensional space of photonic orbital angular momentum (OAM). Using simple linear optical components, we show a successful four-fold cyclic transformation of OAM modes. Interestingly, our experimental setup was found by a computer algorithm. In addition to the four-cyclic transformation, the algorithm also found extensions to higher-dimensional cycles in a hybrid space of OAM and polarization. Besides being useful for quantum cryptography with QuDits, cyclic transformations are key for the experimental production of high-dimensional maximally entangled Bell-states. (paper)
7. Angular momentum transport by tidal acoustic wave
International Nuclear Information System (INIS)
Sakurai, T.
1976-01-01
An analytical expression of the braking torque on a Jacobian ellipsoid rotating steadily in an enviromental gas is given, based on the assumption that the ellipsoid rotates around its shortest principal axis with an angular momentum slightly larger than that at the bifurcation point of the Maclaurin spheroid. This braking torque is effected by the gravitational interaction between the ellipsoid matter and a spiral density configuration in the environmental gas. This spiral configuration which is called a tidal acoustic wave, is caused by the zone of silence effect in a supersonic flow. With respect to a coordinates system rotating with the ellipsoid, a supersonic region appears outside a certain radius. In this supersonic region, the effect of the non-axisymmetric fluctuation in the ellipsoid potential propagates along the downstream branches of the Mach waves. This one-sided response of the supersonic part causes the tidal acoustic wave. The discussion is restricted to the equatorial plane, and an acoustic approximation of the basic equations is used under the assumption that the self-gravity effect of the environmental gas is negligable in comparison to the main gravity of the ellipsoid. The results are applied to the pre- and post-Main sequence phases of a rotating star, and relating astrophysical problems are discussed. (Auth.)
8. Angular momentum transport by tidal acoustic wave
Energy Technology Data Exchange (ETDEWEB)
Sakurai, T [Kyoto Univ. (Japan). Faculty of Engineering
1976-05-01
An analytical expression of the braking torque on a Jacobian ellipsoid rotating steadily in an enviromental gas is given, based on the assumption that the ellipsoid rotates around its shortest principal axis with an angular momentum slightly larger than that at the bifurcation point of the Maclaurin spheroid. This braking torque is effected by the gravitational interaction between the ellipsoid matter and a spiral density configuration in the environmental gas. This spiral configuration which is called a tidal acoustic wave, is caused by the zone of silence effect in a supersonic flow. With respect to a coordinates system rotating with the ellipsoid, a supersonic region appears outside a certain radius. In this supersonic region, the effect of the non-axisymmetric fluctuation in the ellipsoid potential propagates along the downstream branches of the Mach waves. This one-sided response of the supersonic part causes the tidal acoustic wave. The discussion is restricted to the equatorial plane, and an acoustic approximation of the basic equations is used under the assumption that the self-gravity effect of the environmental gas is negligable in comparison to the main gravity of the ellipsoid. The results are applied to the pre- and post-Main sequence phases of a rotating star, and relating astrophysical problems are discussed.
9. Angular distributions of sputtered particles from NiTi alloy
International Nuclear Information System (INIS)
Neshev, I.; Hamishkeev, V.; Chernysh, V.S.; Postnikov, S.; Mamaev, B.
1993-01-01
The angular distributions of sputtered Ni and Ti from a polycrystalline NiTi (50-50%) alloy are investigated by Auger electron spectroscopy and Rutherford backscattering spectroscopy. A difference in the angular distributions is observed with Ni being sputtered preferentially near the surface normal. A computer program for the calculation of the angular distributions of constituents sputtered from binary targets is created and used. The mechanisms responsible for the observed differences in the angular distributions are discussed. It is found that the collisional cascade theory is not directly applicable to the results of the constituents' angular distributions obtained in the presence of oxygen. The fitted coefficients of bombardment-induced segregation are found to be greater than the experimentally obtained ones. (author)
10. Jet angularity measurements for single inclusive jet production
Science.gov (United States)
Kang, Zhong-Bo; Lee, Kyle; Ringer, Felix
2018-04-01
We study jet angularity measurements for single-inclusive jet production at the LHC. Jet angularities depend on a continuous parameter a allowing for a smooth interpolation between different traditional jet shape observables. We establish a factorization theorem within Soft Collinear Effective Theory (SCET) where we consistently take into account in- and out-of-jet radiation by making use of semi-inclusive jet functions. For comparison, we elaborate on the differences to jet angularities measured on an exclusive jet sample. All the necessary ingredients for the resummation at next-to-leading logarithmic (NLL) accuracy are presented within the effective field theory framework. We expect semiinclusive jet angularity measurements to be feasible at the LHC and we present theoretical predictions for the relevant kinematic range. In addition, we investigate the potential impact of jet angularities for quark-gluon discrimination.
11. Photon beam polarization and non-dipolar angular distributions
International Nuclear Information System (INIS)
Peshkin, M.
1996-01-01
Angular distributions of ejecta from unoriented atoms and molecules depend upon the polarization state of the incident x-rays as well as upon the dynamics of the physical systems being studied. I recommend a simple geometrical way of looking at the polarization and its effects upon angular distributions. The polarization is represented as a vector in a parameter space that faithfully represents the polarization of the beam. The simple dependence of the angular dependence of the angular distributions on the polarization vector enables easy extraction of the dynamical information contained in those angular distributions. No new physical results emerge from this geometrical approach, but known consequences of the symmetries appear in an easily visualized form that I find pleasing and that has proved to be useful for planning experiments and for analyzing data
12. Control of Angular Intervals for Angle-Multiplexed Holographic Memory
Science.gov (United States)
Kinoshita, Nobuhiro; Muroi, Tetsuhiko; Ishii, Norihiko; Kamijo, Koji; Shimidzu, Naoki
2009-03-01
In angle-multiplexed holographic memory, the full width at half maximum of the Bragg selectivity curves is dependent on the angle formed between the medium and incident laser beams. This indicates the possibility of high density and high multiplexing number by varying the angular intervals between adjacent holograms. We propose an angular interval scheduling for closely stacking holograms into medium even when the angle range is limited. We obtained bit error rates of the order of 10-4 under the following conditions: medium thickness of 1 mm, laser beam wavelength of 532 nm, and angular multiplexing number of 300.
13. Angular absorption of iridium - ICW12 needles: practical considerations
International Nuclear Information System (INIS)
Szymczyk, W.; Lesiak, J.
1984-01-01
An analysis was made of two potential sources of error in Ir 192 dosimetry: the effect of angular absorption and the differences in the ionization constants found in literature. Corrections for selfabsorption in the ICW12 iridium source were determined from measurements and calculations. It was found that the decrease in the dose caused by the angular absorption in the central therapeutic area of a typical implantation can exceed 5 percent. The need for employing the concept of ''constant exposure rate'' is stressed as well as that for using angular absorption in the form of absorption. 13 refs., 6 figs., 1 tab. (author)
14. Nuclear spin measurement using the angular correlation method
International Nuclear Information System (INIS)
Schapira, J.-P.
The double angular correlation method is defined by a semi-classical approach (Biendenharn). The equivalence formula in quantum mechanics are discussed for coherent and incoherent angular momentum mixing; the correlations are described from the density and efficiency matrices (Fano). The ambiguities in double angular correlations can be sometimes suppressed (emission of particles with a high orbital momentum l), using triple correlations between levels with well defined spin and parity. Triple correlations are applied to the case where the direction of linear polarization of γ-rays is detected [fr
15. Measurement crankshaft angular speed of an OM403 engine
Directory of Open Access Journals (Sweden)
Biočanin Stojko
2017-01-01
Full Text Available In this paper, the methodology of the measurement of the angular speed of the crankshaft of a ten-cylinder diesel OM403 engine is presented, with regular and irregular engine operation. The angular velocity was measured under laboratory conditions, on already installed measuring equipment from the laboratory and on the break of a well known brand-Schenck, by using an optoelectronic incremental rotary encoder, a data acquisition module and the LabVIEW software for synchronization and management of the measuring equipment. The goal of this paper is to give a practical contribution to researches of measuring of crankshaft angular speed of the crankshaft engine OM 403.
16. On Angular Sampling Methods for 3-D Spatial Channel Models
DEFF Research Database (Denmark)
Fan, Wei; Jämsä, Tommi; Nielsen, Jesper Ødum
2015-01-01
This paper discusses generating three dimensional (3D) spatial channel models with emphasis on the angular sampling methods. Three angular sampling methods, i.e. modified uniform power sampling, modified uniform angular sampling, and random pairing methods are proposed and investigated in detail....... The random pairing method, which uses only twenty sinusoids in the ray-based model for generating the channels, presents good results if the spatial channel cluster is with a small elevation angle spread. For spatial clusters with large elevation angle spreads, however, the random pairing method would fail...... and the other two methods should be considered....
17. Notes on the quantum theory of angular momentum
CERN Document Server
Feenberg, Eugene
1999-01-01
This classic, concise text has served a generation of physicists as an exceptionally useful guide to the mysteries of angular momenta and Clebsch-Gordon Coefficients. Derived from notes originally prepared to assist graduate students in reading research papers on atomic, molecular, and nuclear structure, the text first reviews the basic elements of quantum theory. It then examines the development of the fundamental commutation relations for angular momentum components and vector operators, and the ways in which matrix elements and eigenvalues of the angular momentum operators are worked out f
18. The angular momentum dependence of complex fragment emission
International Nuclear Information System (INIS)
Sobtka, L.G.; Sarantites, D.G.; Li, Z.
1987-01-01
Large fragment (A > 4) production at high angular momentum is studied via the reaction, 200 MeV 45 Sc + 65 Cu. Comparisons of the fragment yields from this reaction (high angular momentum) to those from 93 Nb + Be (low angular momentum) are used to verify the strong angular momentum dependence of large fragment production predicted by equilibrium models. Details of the coincident γ-ray distributions not only confirm a rigidly rotating intermediate but also indicate that the widths of the primary L-wave distributions decrease with increasing symmetry in the decay channel. These data are used to test the asymmetry and L-wave dependence of emission barriers calculated from a rotating, finite range corrected, liquid drop model. 21 refs., 10 figs
19. Manifest rotation symmetric expressions for angular momentum eigenfunctions
International Nuclear Information System (INIS)
Eeg, J.O.; Wroldsen, J.
1983-01-01
Manifest rotation symmetric expressions for eigenfunctions for spin s, orbital angular momentum l and total angular momentum j = l+s, .... , /l-s/ in terms of (2j+1) x (2s+1) multipole transition matrices (MTM) is given. These matrices, which are irreducible tensor matrices, have an algebra together with ordinary spin matrices for spin s and spin j. Explicit expressions for MTM's and their algebra are given for angular momenta <-3. By means of some examples it is shown that within this formalism angular integrations in central field problems will be simplified considerably. Thus the formalism turns out to be very useful for instance for calculations within the MIT-bag and also within spin-spin interactions in atomic physics. (Auth.)
20. The INCAS Project: An Innovative Contact-Less Angular Sensor
Science.gov (United States)
Ghislanzoni, L.; Di Cintio, A.; Solimando, M.; Parzianello, G.
2013-09-01
Angular Positions sensors are widely used in all spacecrafts, including re-entry vehicles and launchers, where mechanisms and pointing-scanning devices are required. The main applications are on mechanisms for TeleMeasure (TM) related to the release and deployment of devices, or on rotary mechanisms such as Solar Array Drive Mechanism (SADM) and Antenna Pointing Mechanism (APM). Longer lifetime (up to 7- 10 years) is becoming a new driver for the coming missions and contact technology sensors often incur in limitations due to the wear of the contacting parts [1].A Self-Compensating Absolute Angular Encoder was developed and tested in the frame of an ESA's ARTES 5.2 project, named INCAS (INnovative Contact-less Angular Sensor). More in particular, the INCAS sensor addresses a market need for contactless angular sensors aimed at replacing the more conventional rotary potentiometers, while featuring the same level of accuracy performances and extending the expected lifetime.
1. Electronic orbital angular momentum and magnetism of graphene
Energy Technology Data Exchange (ETDEWEB)
Luo, Ji, E-mail: [email protected]
2014-10-01
Orbital angular momentum (OAM) of graphene electrons in a perpendicular magnetic field is calculated and corresponding magnetic moment is used to investigate the magnetism of perfect graphene. Variation in magnetization demonstrates its decrease with carrier-doping, plateaus in a large field, and de Haas–van Alphen oscillation. Regulation of graphene's magnetism by a parallel electric field is presented. The OAM originates from atomic-scale electronic motion in graphene lattice, and vector hopping interaction between carbon atomic orbitals is the building element. A comparison between OAM of graphene electrons, OAM of Dirac fermions, and total angular momentum of the latter demonstrates their different roles in graphene's magnetism. Applicability and relation to experiments of the results are discussed. - Highlights: • Orbital angular momentum of graphene electrons is calculated. • Orbital magnetic moment of graphene electrons is obtained. • Variation in magnetization of graphene is calculated. • Roles of different kinds of angular momentum are investigated.
2. Efficient evaluation of angular power spectra and bispectra
Science.gov (United States)
Assassi, Valentin; Simonović, Marko; Zaldarriaga, Matias
2017-11-01
Angular statistics of cosmological observables are hard to compute. The main difficulty is due to the presence of highly-oscillatory Bessel functions which need to be integrated over. In this paper, we provide a simple and fast method to compute the angular power spectrum and bispectrum of any observable. The method is based on using an FFTlog algorithm to decompose the momentum-space statistics onto a basis of power-law functions. For each power law, the integrals over Bessel functions have a simple analytical solution. This allows us to efficiently evaluate these integrals, independently of the value of the multipole l. In particular, this method significantly speeds up the evaluation of the angular bispectrum compared to existing methods. To illustrate our algorithm, we compute the galaxy, lensing and CMB temperature angular power spectrum and bispectrum.
3. Phase-space distributions and orbital angular momentum
Directory of Open Access Journals (Sweden)
Pasquini B.
2014-06-01
Full Text Available We review the concept of Wigner distributions to describe the phase-space distributions of quarks in the nucleon, emphasizing the information encoded in these functions about the quark orbital angular momentum.
4. Helicons in uniform fields. II. Poynting vector and angular momenta
Science.gov (United States)
Stenzel, R. L.; Urrutia, J. M.
2018-03-01
The orbital and spin angular momenta of helicon modes have been determined quantitatively from laboratory experiments. The current density is obtained unambiguously from three dimensional magnetic field measurements. The only approximation made is to obtain the electric field from Hall Ohm's law which is usually the case for low frequency whistler modes. This allows the evaluation of the Poynting vector from which the angular momentum is obtained. Comparing two helicon modes (m = 0 and m = 1), one can separate the contribution of angular momentum of a rotating and non-rotating wave field. The orbital angular momentum is important to assess the wave-particle interaction by the transverse Doppler shift of rotating waves which has not been considered so far.
5. Genetic characterization of angular leaf spot resistance in selected ...
African Journals Online (AJOL)
Mr Tryphone
2015-10-28
Oct 28, 2015 ... Angular leaf spot disease (ALS) caused by Pseudocercospora griseola is one ... Author(s) agree that this article remains permanently open access under the terms ... that results in shrivelled seeds of reduced size and quality.
6. prevalence of angular leaf spot disease and sources of resistance
African Journals Online (AJOL)
USER
2017-02-17
Feb 17, 2017 ... Angular leaf spot (Pseudocercospora griseola Crous U, Brown) is one of the ..... Incidence of six foliar bean diseases in two agro ecological zones of eastern Democratic Republic of .... use of poor quality farmer-saved seed.
7. Angular distributions of ions channeled in the Si crystals
International Nuclear Information System (INIS)
Petrovic, S.; Korica, S.; Kokkoris, M.; Neskovic, N.
2002-01-01
In this study we analyze the angular distributions of Ne 10+ ions channeled in the Si crystals. The ion energy is 60 MeV and the crystal thickness is varied from 286 to 3435 nm. This thickness range corresponds to the reduced crystal thickness range from 0.5 to 6, i.e. from the second to the twelfth rainbow cycle. The angular distributions were obtained via the numerical solution of the ion equations of motion and the computer simulation method. The analysis shows that the angular distribution has a periodic behavior. We also analyze the transmission patterns corresponding to the angular distributions. These patterns should be compared to the experimental patterns obtainable by a two-dimensional position sensitive detector. We demonstrate that, when the ion beam divergence is sufficiently large, i.e. much larger than the critical angle for channeling, the channeling star effect occurs in the transmission patterns
8. Angular Momentum Transport in Quasi-Keplerian Accretion Disks ...
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Keplerian accretion disk yield results that are inconsistent with the generally accepted model. If correct, the ideas proposed by Hayashi &. Matsuda would radically alter our understanding of the nature of the angular momentum transport in the disk, ...
9. The mass and angular momentum of reconstructed metric perturbations
Science.gov (United States)
van de Meent, Maarten
2017-06-01
We prove a key result regarding the mass and angular momentum content of linear vacuum perturbations of the Kerr metric obtained through the formalism developed by Chrzarnowski, Cohen, and Kegeles (CCK). More precisely, we prove that the Abbott-Deser mass and angular momentum integrals of any such perturbation vanish when that perturbation was obtained from a regular Fourier mode of the Hertz potential. As a corollary we obtain a generalization of previous results on the completion of the ‘no string’ radiation gauge metric perturbation generated by a point particle. We find that for any bound orbit around a Kerr black hole, the mass and angular momentum perturbations completing the CCK metric are simply the energy and angular momentum of the particle ‘outside’ the orbit and vanish ‘inside’ the orbit.
10. Design and Implementation of a Digital Angular Rate Sensor
Directory of Open Access Journals (Sweden)
Zhen Peng
2010-10-01
Full Text Available With the aim of detecting the attitude of a rotating carrier, the paper presents a novel, digital angular rate sensor. The sensor consists of micro-sensing elements (gyroscope and accelerometer, signal processing circuit and micro-processor (DSP2812. The sensor has the feature of detecting three angular rates of a rotating carrier at the same time. The key techniques of the sensor, including sensing construction, sensing principles, and signal processing circuit design are presented. The test results show that the sensor can sense rolling, pitch and yaw angular rate at the same time and the measurement error of yaw (or pitch angular rate and rolling rate of the rotating carrier is less than 0.5%.
11. Large-uncertainty intelligent states for angular momentum and angle
International Nuclear Information System (INIS)
Goette, Joerg B; Zambrini, Roberta; Franke-Arnold, Sonja; Barnett, Stephen M
2005-01-01
The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases
12. The Effects of Isokinetic Strength Training on Strength at Different Angular Velocities: a Pilot Study
Directory of Open Access Journals (Sweden)
Tuğba Kocahan
2017-09-01
Conclusion: It was shown that angular velocity is important in isokinetic training, and that training at high angular velocities provides strength increases at lower angular velocities, but would not increase strength at angular velocities above the training level. For this reason, it is thought that in the preparation of an isokinetic strength training protocol, angular velocities need to be taken into account. For any athlete, the force at the angular velocity required in her/his sports branch needs to be considered.
13. A Very Fast and Angular Momentum Conserving Tree Code
International Nuclear Information System (INIS)
Marcello, Dominic C.
2017-01-01
There are many methods used to compute the classical gravitational field in astrophysical simulation codes. With the exception of the typically impractical method of direct computation, none ensure conservation of angular momentum to machine precision. Under uniform time-stepping, the Cartesian fast multipole method of Dehnen (also known as the very fast tree code) conserves linear momentum to machine precision. We show that it is possible to modify this method in a way that conserves both angular and linear momenta.
14. Existence of black holes due to concentration of angular momentum
Energy Technology Data Exchange (ETDEWEB)
Khuri, Marcus A. [Department of Mathematics, Stony Brook University,Stony Brook, NY 11794 (United States)
2015-06-29
We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the context of axisymmetric initial data sets for the Einstein equations which satisfy an appropriate energy condition. A brief comparison is also made with more traditional black hole existence criteria based on concentration of mass.
15. Gamma-gamma angular correlation measurement in the 100 Ru
International Nuclear Information System (INIS)
Kenchian, G.
1990-01-01
An angular correlation automatic spectrometer with two Ge(Li) detectors has been developed. The spectrometer moves automatically, controlled by a microcomputer. The gamma-gamma directional angular correlations of coincidence transitions have been measured in 100 Ru nuclide, following the β + and electron capture of 100 Rh. The 100 Rh source has been produced with 100 Ru(p,n) 100 Rh reaction, using the proton beam of the Cyclotron Accelerator insiding in 100 Ru isotope. (author)
16. A Very Fast and Angular Momentum Conserving Tree Code
Energy Technology Data Exchange (ETDEWEB)
Marcello, Dominic C., E-mail: [email protected] [Department of Physics and Astronomy, and Center for Computation and Technology Louisiana State University, Baton Rouge, LA 70803 (United States)
2017-09-01
There are many methods used to compute the classical gravitational field in astrophysical simulation codes. With the exception of the typically impractical method of direct computation, none ensure conservation of angular momentum to machine precision. Under uniform time-stepping, the Cartesian fast multipole method of Dehnen (also known as the very fast tree code) conserves linear momentum to machine precision. We show that it is possible to modify this method in a way that conserves both angular and linear momenta.
17. Analytical scheme calculations of angular momentum coupling and recoupling coefficients
Science.gov (United States)
Deveikis, A.; Kuznecovas, A.
2007-03-01
We investigate the Scheme programming language opportunities to analytically calculate the Clebsch-Gordan coefficients, Wigner 6j and 9j symbols, and general recoupling coefficients that are used in the quantum theory of angular momentum. The considered coefficients are calculated by a direct evaluation of the sum formulas. The calculation results for large values of quantum angular momenta were compared with analogous calculations with FORTRAN and Java programming languages.
18. Analytical scheme calculations of angular momentum coupling and recoupling coefficients
International Nuclear Information System (INIS)
Deveikis, A.; Kuznecovas, A.
2007-01-01
We investigate the Scheme programming language opportunities to analytically calculate the Clebsch-Gordan coefficients, Wigner 6j and 9j symbols, and general recoupling coefficients that are used in the quantum theory of angular momentum. The considered coefficients are calculated by a direct evaluation of the sum formulas. The calculation results for large values of quantum angular momenta were compared with analogous calculations with FORTRAN and Java programming languages
19. Orbital and angular motion construction for low thrust interplanetary flight
Science.gov (United States)
Yelnikov, R. V.; Mashtakov, Y. V.; Ovchinnikov, M. Yu.; Tkachev, S. S.
2016-11-01
Low thrust interplanetary flight is considered. Firstly, the fuel-optimal control is found. Then the angular motion is synthesized. This motion provides the thruster tracking of the required by optimal control direction. And, finally, reaction wheel control law for tracking this angular motion is proposed and implemented. The numerical example is given and total operation time for thrusters is found. Disturbances from solar pressure, thrust eccentricity, inaccuracy of reaction wheels installation and errors of inertia tensor are taken into account.
20. Spatial Angular Compounding for Elastography without the Incompressibility Assumption
OpenAIRE
Rao, Min; Varghese, Tomy
2005-01-01
Spatial-angular compounding is a new technique that enables the reduction of noise artifacts in ultrasound elastography. Previous results using spatial angular compounding, however, were based on the use of the tissue incompressibility assumption. Compounded elastograms were obtained from a spatially-weighted average of local strain estimated from radiofrequency echo signals acquired at different insonification angles. In this paper, we present a new method for reducing the noise artifacts in...
1. Diffraction by a plane angular sector, a new derivation
DEFF Research Database (Denmark)
Hansen, Thokild B.
1990-01-01
An alternative derivation is given for the exact solution to the scattering problem in which a Hertz dipole illuminates a perfectly conducting plane angular sector. Specifically, the Ohm-Rayleigh method is used rather than that of Satterwhite (1969)......An alternative derivation is given for the exact solution to the scattering problem in which a Hertz dipole illuminates a perfectly conducting plane angular sector. Specifically, the Ohm-Rayleigh method is used rather than that of Satterwhite (1969)...
2. Shape coexistence in 72Kr at finite angular momentum
International Nuclear Information System (INIS)
Almehed, Daniel; Walet, Niels R.
2004-01-01
We investigate shape coexistence in a rotating nucleus. We concentrate on the case of 72 Kr which exhibits an interesting interplay between prolate and oblate shaped states as a function of angular momentum. The calculation uses the local harmonic version of the method of self-consistent adiabatic large-amplitude collective motion. We analyse how the collective behaviour of the system changes with angular momentum and we focus on the role of non-axial shapes
3. Spin and intrinsic angular momentum; application to the electromagnetic field
International Nuclear Information System (INIS)
Paillere, P.
1993-05-01
Within the framework of the field theory governed by a Lagrangian, function of the tensor quantities and their covariant first derivatives, and starting with the third order intrinsic angular momentum tensor obtained from a variational principle, the intrinsic angular momentum vector of the electromagnetic field in vacuum is determined. This expression leads to spin matrices for the electromagnetic field, with unity as eigenvalue, thus allowing to bridge the gap between continuous physics and quantum physics. 6 refs
4. Effects of angular misalignment on optical klystron undulator radiation
Energy Technology Data Exchange (ETDEWEB)
Mishra, G., E-mail: [email protected]; Prakash, Bramh; Gehlot, Mona
2015-11-21
In this paper ,we analyze the important effects of optical klystron undulator radiation with an angular offset of the relativistic electron beam in the second undulator section. An anlytical expression for the undulator radiation is obtained through a transparent and simple procedure.It is shown that the effects of the angular offset is more severe for longer undulator lengths and with higher dispersive field strengths.Both these effects are less pronounced for undulators with large K values.
5. Angular momentum of circularly polarized light in dielectric media
Science.gov (United States)
Mansuripur, Masud
2005-07-01
A circularly polarized plane-wave is known to have no angular momentum when examined through Maxwell’s equations. This, however, contradicts the experimentally observed facts, where finite segments of plane waves are known to be capable of imparting angular momentum to birefringent platelets. Using a superposition of four plane-waves propagating at slightly different angles to a common direction, we derive an expression for the angular momentum density of a single plane-wave in the limit when the propagation directions of the four beams come into alignment. We proceed to use this four-beam technique to analyze the conservation of angular momentum when a plane-wave enters a dielectric slab from the free space. The angular momentum of the beam is shown to decrease upon entering the dielectric medium, by virtue of the fact that the incident beam exerts a torque on the slab surface at the point of entry. When the beam leaves the slab, it imparts an equal but opposite torque to the exit facet, thus recovering its initial angular momentum upon re-emerging into the free-space. Along the way, we derive an expression for the outward-directed force of a normally incident, finite-diameter beam on a dielectric surface; the possible relationship between this force and the experimentally observed bulging of a liquid surface under intense illumination is explored.
6. Investigation of angular and axial smoothing of PET data
International Nuclear Information System (INIS)
Daube-Witherspoon, M.E.; Carson, R.E.
1996-01-01
Radial filtering of emission and transmission data is routinely performed in PET during reconstruction in order to reduce image noise. Angular smoothing is not typically done, due to the introduction of a non-uniform resolution loss; axial filtering is also not usually performed on data acquired in 2D mode. The goal of this paper was to assess the effects of angular and axial smoothing on noise and resolution. Angular and axial smoothing was incorporated into the reconstruction process on the Scanditronix PC2048-15B brain PET scanner. In-plane spatial resolution and noise reduction were measured for different amounts of radial and angular smoothing. For radial positions away from the center of the scanner, noise reduction and degraded tangential resolution with no loss of radial resolution were seen. Near the center, no resolution loss was observed, but there was also no reduction in noise for angular filters up to a 7 degrees FWHM. These results can be understood by considering the combined effects of smoothing projections across rows (angles) and then summing (backprojecting). Thus, angular smoothing is not optimal due to its anisotropic noise reduction and resolution degradation properties. However, uniform noise reduction comparable to that seen with radial filtering can be achieved with axial smoothing of transmission data. The axial results suggest that combined radial and axial transmission smoothing could lead to improved noise characteristics with more isotropic resolution degradation
7. A systematic construction of microstate geometries with low angular momentum
Science.gov (United States)
Bena, Iosif; Heidmann, Pierre; Ramírez, Pedro F.
2017-10-01
We outline a systematic procedure to obtain horizonless microstate geometries that have the same charges as three-charge five-dimensional black holes with a macroscopically-large horizon area and an arbitrarily-small angular momentum. There are two routes through which such solutions can be constructed: using multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So far the only solutions corre-sponding to microstate geometries for black holes with no angular momentum have been obtained via superstrata [1], and multi-center Gibbons-Hawking spaces have been believed to give rise only to microstate geometries of BMPV black holes with a large angular mo-mentum [2]. We perform a thorough search throughout the parameter space of smooth horizonless solutions with four GH centers and find that these have an angular momentum that is generally larger than 80% of the cosmic censorship bound. However, we find that solutions with three GH centers and one supertube (which are smooth in six-dimensional supergravity) can have an arbitrarily-low angular momentum. Our construction thus gives a recipe to build large classes of microstate geometries for zero-angular-momentum black holes without resorting to superstratum technology.
8. Effect of nutritional intake towards Angular cheilitis of orphanage children
Directory of Open Access Journals (Sweden)
Nurdiani Rakhmayanthie
2016-11-01
Full Text Available Introduction: Angular cheilitis is one of the oral manifestations of iron, vitamin B12, and folate deficiency. This manifestation frequently seen in people at first and second decade. The purpose of this study was to obtain the prevalence of angular cheilitis and its classifications related to the nutritional intake level in 6-18 years old children. Methods: This research was a descriptive study with 53 children between 6-18 years old from Muhammadiyah Orphanage Bandung as the samples. The oral cavity was examined clinically and their food consumption in a week was noted in Food Recall 24 hours and Food Frequency Questionnaire (FFQ in order to measure their nutritional intake level. Results: There are 23 children with angular cheilitis. 13% has iron and folate deficiencies, and 87% has iron, vitamin B12, and folate deficiencies. Angular cheilitis types that has been found are Type I (39%, Type II (48% and Type III (13%. Conclusion: The prevalence of angular cheilitis in 6-18 years old children in Muhammadiyah Orphanage Bandung was moderately high, most of them were having iron, vitamin B12, and folate deficiencies. Type II angular cheilitis was the most frequently seen.
9. The Angular Momentum of Baryons and Dark Matter Halos Revisited
Science.gov (United States)
Kimm, Taysun; Devriendt, Julien; Slyz, Adrianne; Pichon, Christophe; Kassin, Susan A.; Dubois, Yohan
2011-01-01
Recent theoretical studies have shown that galaxies at high redshift are fed by cold, dense gas filaments, suggesting angular momentum transport by gas differs from that by dark matter. Revisiting this issue using high-resolution cosmological hydrodynamics simulations with adaptive-mesh refinement (AMR), we find that at the time of accretion, gas and dark matter do carry a similar amount of specific angular momentum, but that it is systematically higher than that of the dark matter halo as a whole. At high redshift, freshly accreted gas rapidly streams into the central region of the halo, directly depositing this large amount of angular momentum within a sphere of radius r = 0.1R(sub vir). In contrast, dark matter particles pass through the central region unscathed, and a fraction of them ends up populating the outer regions of the halo (r/R(sub vir) > 0.1), redistributing angular momentum in the process. As a result, large-scale motions of the cosmic web have to be considered as the origin of gas angular momentum rather than its virialised dark matter halo host. This generic result holds for halos of all masses at all redshifts, as radiative cooling ensures that a significant fraction of baryons remain trapped at the centre of the halos. Despite this injection of angular momentum enriched gas, we predict an amount for stellar discs which is in fair agreement with observations at z=0. This arises because the total specific angular momentum of the baryons (gas and stars) remains close to that of dark matter halos. Indeed, our simulations indicate that any differential loss of angular momentum amplitude between the two components is minor even though dark matter halos continuously lose between half and two-thirds of their specific angular momentum modulus as they evolve. In light of our results, a substantial revision of the standard theory of disc formation seems to be required. We propose a new scenario where gas efficiently carries the angular momentum generated
10. Initial angular momentum and flow in high energy nuclear collisions
Science.gov (United States)
Fries, Rainer J.; Chen, Guangyao; Somanathan, Sidharth
2018-03-01
We study the transfer of angular momentum in high energy nuclear collisions from the colliding nuclei to the region around midrapidity, using the classical approximation of the color glass condensate (CGC) picture. We find that the angular momentum shortly after the collision (up to times ˜1 /Qs , where Qs is the saturation scale) is carried by the "β -type" flow of the initial classical gluon field, introduced by some of us earlier. βi˜μ1∇iμ2-μ2∇iμ1 (i =1 ,2 ) describes the rapidity-odd transverse energy flow and emerges from Gauss's law for gluon fields. Here μ1 and μ2 are the averaged color charge fluctuation densities in the two nuclei, respectively. Interestingly, strong coupling calculations using anti-de Sitter/conformal field theory (AdS/CFT) techniques also find an energy flow term featuring this particular combination of nuclear densities. In classical CGC the order of magnitude of the initial angular momentum per rapidity in the reaction plane, at a time 1 /Qs , is |d L2/d η |≈ RAQs-3ɛ¯0/2 at midrapidity, where RA is the nuclear radius, and ɛ¯0 is the average initial energy density. This result emerges as a cancellation between a vortex of energy flow in the reaction plane aligned with the total angular momentum, and energy shear flow opposed to it. We discuss in detail the process of matching classical Yang-Mills results to fluid dynamics. We will argue that dissipative corrections should not be discarded to ensure that macroscopic conservation laws, e.g., for angular momentum, hold. Viscous fluid dynamics tends to dissipate the shear flow contribution that carries angular momentum in boost-invariant fluid systems. This leads to small residual angular momentum around midrapidity at late times for collisions at high energies.
11. Isotropic gates and large gamma detector arrays versus angular distributions
International Nuclear Information System (INIS)
Iacob, V.E.; Duchene, G.
1997-01-01
Angular information extracted from in-beam γ ray measurements are of great importance for γ ray multipolarity and nuclear spin assignments. In our days large Ge detector arrays became available allowing the measurements of extremely weak γ rays in almost 4π sr solid angle (e.g., EUROGAM detector array). Given the high detector efficiency it is common for the mean suppressed coincidence multiplicity to reach values as high as 4 to 6. Thus, it is possible to gate on particular γ rays in order to enhance the relative statistics of a definite reaction channel and/or a definite decaying path in the level scheme of the selected residual nucleus. As compared to angular correlations, the conditioned angular distribution spectra exhibit larger statistics because in the latter the gate-setting γ ray may be observed by all the detectors in the array, relaxing somehow the geometrical restrictions of the angular correlations. Since the in-beam γ ray emission is anisotropic one could inquire that gate setting as mentioned above, based on anisotropic γ ray which would perturb the angular distributions in the unfolded events. As our work proved, there is no reason to worry about this if the energy gate runs over the whole solid angle in an ideal 4π sr detector, i.e., if the gate is isotropic. In real quasi 4π sr detector arrays the corresponding quasi isotropic gate preserves the angular properties of the unfolded data, too. However extraction of precise angular distribution coefficient especially a 4 , requires the consideration of the deviation of the quasi isotropic gate relative to the (ideal) isotropic gate
12. Smoothed dissipative particle dynamics with angular momentum conservation
Energy Technology Data Exchange (ETDEWEB)
Müller, Kathrin, E-mail: [email protected]; Fedosov, Dmitry A., E-mail: [email protected]; Gompper, Gerhard, E-mail: [email protected]
2015-01-15
Smoothed dissipative particle dynamics (SDPD) combines two popular mesoscopic techniques, the smoothed particle hydrodynamics and dissipative particle dynamics (DPD) methods, and can be considered as an improved dissipative particle dynamics approach. Despite several advantages of the SDPD method over the conventional DPD model, the original formulation of SDPD by Español and Revenga (2003) [9], lacks angular momentum conservation, leading to unphysical results for problems where the conservation of angular momentum is essential. To overcome this limitation, we extend the SDPD method by introducing a particle spin variable such that local and global angular momentum conservation is restored. The new SDPD formulation (SDPD+a) is directly derived from the Navier–Stokes equation for fluids with spin, while thermal fluctuations are incorporated similarly to the DPD method. We test the new SDPD method and demonstrate that it properly reproduces fluid transport coefficients. Also, SDPD with angular momentum conservation is validated using two problems: (i) the Taylor–Couette flow with two immiscible fluids and (ii) a tank-treading vesicle in shear flow with a viscosity contrast between inner and outer fluids. For both problems, the new SDPD method leads to simulation predictions in agreement with the corresponding analytical theories, while the original SDPD method fails to capture properly physical characteristics of the systems due to violation of angular momentum conservation. In conclusion, the extended SDPD method with angular momentum conservation provides a new approach to tackle fluid problems such as multiphase flows and vesicle/cell suspensions, where the conservation of angular momentum is essential.
13. Modeling of the angular dependence of plasma etching
International Nuclear Information System (INIS)
Guo Wei; Sawin, Herbert H.
2009-01-01
An understanding of the angular dependence of etching yield is essential to investigate the origins of sidewall roughness during plasma etching. In this article the angular dependence of polysilicon etching in Cl 2 plasma was modeled as a combination of individual angular-dependent etching yields for ion-initiated processes including physical sputtering, ion-induced etching, vacancy generation, and removal. The modeled etching yield exhibited a maximum at ∼60 degree sign off-normal ion angle at low flux ratio, indicative of physical sputtering. It transformed to the angular dependence of ion-induced etching with the increase in the neutral-to-ion flux ratio. Good agreement between the modeling and the experiments was achieved for various flux ratios and ion energies. The variation of etching yield in response to the ion angle was incorporated in the three-dimensional profile simulation and qualitative agreement was obtained. The surface composition was calculated and compared to x-ray photoelectron spectroscopy (XPS) analysis. The modeling indicated a Cl areal density of 3x10 15 atoms/cm 2 on the surface that is close to the value determined by the XPS analysis. The response of Cl fraction to ion energy and flux ratio was modeled and correlated with the etching yields. The complete mixing-layer kinetics model with the angular dependence effect will be used for quantitative surface roughening analysis using a profile simulator in future work.
14. Time variations of the angular momentum of the sun
International Nuclear Information System (INIS)
Schatten, K.H.
1977-01-01
Time variations of density models of the Sun are investigated. This is an attempt to estimate the changing moment of inertia of the Sun in order to calculate the internal solar angular velocity based upon Newton's equation of motion. Previous estimates of dI/dt disagree with those based upon central densities in a homologously contracting model. It is shown that the homologously contracting model leads to large errors in dI/dt. Based upon an integration of Sears's solar model, dI/dt=-5.5 x 10 34 gm cm 2 s -1 . This suggests a core angular velocity of /sub thetar-italic/ = (0.15 +- 0.03) x 10 -3 s -1 , corresponding to a period of 0.5 +- 0.1 days, assuming a constant angular velocity with time. The brackets indicate a weighting which is discussed
15. Nuclear level density variation with angular momentum induced shape transition
International Nuclear Information System (INIS)
Aggarwal, Mamta
2016-01-01
Variation of Nuclear level density (NLD) with the excitation energy and angular momentum in particular has been a topic of interest in the recent past and there have been continuous efforts in this direction on the theoretical and experimental fronts but a conclusive trend in the variation of nuclear level density parameter with angular momentum has not been achieved so far. A comprehensive investigation of N=68 isotones around the compound nucleus 119 Sb from neutron rich 112 Ru (Z=44) to neutron deficient 127 Pr (Z= 59) nuclei is presented to understand the angular momentum induced variations in inverse level density parameter and the possible influence of deformation and structural transitions on the variations on NLd
16. Orbital Angular Momentum Multiplexing over Visible Light Communication Systems
Science.gov (United States)
Tripathi, Hardik Rameshchandra
This thesis proposes and explores the possibility of using Orbital Angular Momentum multiplexing in Visible Light Communication system. Orbital Angular Momentum is mainly applied for laser and optical fiber transmissions, while Visible Light Communication is a technology using the light as a carrier for wireless communication. In this research, the study of the state of art and experiments showing some results on multiplexing based on Orbital Angular Momentum over Visible Light Communication system were done. After completion of the initial stage; research work and simulations were performed on spatial multiplexing over Li-Fi channel modeling. Simulation scenarios which allowed to evaluate the Signal-to-Noise Ratio, Received Power Distribution, Intensity and Illuminance were defined and developed.
17. Angular Magnetoresistance of Nanowires with Alternating Cobalt and Nickel Segments
KAUST Repository
Mohammed, Hanan
2017-06-22
Magnetization reversal in segmented Co/Ni nanowires with varying number of segments was studied using angular Magnetoresistance (MR) measurements on isolated nanowires. The MR measurements offer an insight into the pinning of domain walls within the nanowires. Angular MR measurements were performed on nanowires with two and multiple segments by varying the angle between the applied magnetic field and nanowire (−90° ≤θ≤90°). The angular MR measurements reveal that at lower values of θ the switching fields are nearly identical for the multisegmented and two-segmented nanowires, whereas at higher values of θ, a decrease in the switching field is observed in the case of two segmented nanowires. The two segmented nanowires generally exhibit a single domain wall pinning event, whereas an increased number of pinning events are characteristic of the multisegmented nanowires at higher values of θ. In-situ magnetic force microscopy substantiates reversal by domain wall nucleation and propagation in multisegmented nanowires.
18. ANGULAR LIGHT-SCATTERING STUDIES ON ISOLATED MITOCHONDRIA
Science.gov (United States)
Gotterer, Gerald S.; Thompson, Thomas E.; Lehninger, Albert L.
1961-01-01
Angular light-scattering studies have been carried out on suspensions of isolated rat liver mitochondria. The angular scatter pattern has a large forward component, typical of large particles. Changes in dissymmetry and in the intensity of light scattered at 90° have been correlated with changes in optical density during the course of mitochondrial swelling and contraction. Such changes can be measured at mitochondrial concentrations much below those required for optical density measurements. Changes in mitochondrial geometry caused by factors "leaking" from mitochondria, not detectable by optical density measurements, have been demonstrated by measuring changes in dissymmetry. Angular light-scattering measurements therefore offer the advantages of increased sensitivity and of added indices of changes in mitochondrial conformation. PMID:19866589
19. Characteristic evolutions in numerical relativity using six angular patches
International Nuclear Information System (INIS)
Reisswig, Christian; Bishop, Nigel T; Lai, Chi Wai; Thornburg, Jonathan; Szilagyi, Bela
2007-01-01
The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50
20. Measuring average angular velocity with a smartphone magnetic field sensor
Science.gov (United States)
Pili, Unofre; Violanda, Renante
2018-02-01
The angular velocity of a spinning object is, by standard, measured using a device called a tachometer. However, by directly using it in a classroom setting, the activity is likely to appear as less instructive and less engaging. Indeed, some alternative classroom-suitable methods for measuring angular velocity have been presented. In this paper, we present a further alternative that is smartphone-based, making use of the real-time magnetic field (simply called B-field in what follows) data gathering capability of the B-field sensor of the smartphone device as the timer for measuring average rotational period and average angular velocity. The in-built B-field sensor in smartphones has already found a number of uses in undergraduate experimental physics. For instance, in elementary electrodynamics, it has been used to explore the well-known Bio-Savart law and in a measurement of the permeability of air.
1. Angular Momentum Transport in Turbulent Flow between Independently Rotating Cylinders
International Nuclear Information System (INIS)
Paoletti, M. S.; Lathrop, D. P.
2011-01-01
We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the (Ω 1 , Ω 2 ) parameter space at high Reynolds numbers, where Ω 1 (Ω 2 ) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro=(Ω 1 -Ω 2 )/Ω 2 fully determines the state and torque G as compared to G(Ro=∞)≡G ∞ . The ratio G/G ∞ is a linear function of Ro -1 in four sections of the parameter space. For flows with radially increasing angular momentum, our measured torques greatly exceed those of previous experiments [Ji et al., Nature (London), 444, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys. 347, 734 (1999)].
2. Angular Magnetoresistance of Nanowires with Alternating Cobalt and Nickel Segments
KAUST Repository
Mohammed, Hanan; Corte-Leon, H.; Ivanov, Yurii P.; Moreno, J. A.; Kazakova, O.; Kosel, Jü rgen
2017-01-01
Magnetization reversal in segmented Co/Ni nanowires with varying number of segments was studied using angular Magnetoresistance (MR) measurements on isolated nanowires. The MR measurements offer an insight into the pinning of domain walls within the nanowires. Angular MR measurements were performed on nanowires with two and multiple segments by varying the angle between the applied magnetic field and nanowire (−90° ≤θ≤90°). The angular MR measurements reveal that at lower values of θ the switching fields are nearly identical for the multisegmented and two-segmented nanowires, whereas at higher values of θ, a decrease in the switching field is observed in the case of two segmented nanowires. The two segmented nanowires generally exhibit a single domain wall pinning event, whereas an increased number of pinning events are characteristic of the multisegmented nanowires at higher values of θ. In-situ magnetic force microscopy substantiates reversal by domain wall nucleation and propagation in multisegmented nanowires.
3. Characteristic evolutions in numerical relativity using six angular patches
Energy Technology Data Exchange (ETDEWEB)
Reisswig, Christian [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany); Bishop, Nigel T [Department of Mathematical Sciences, University of South Africa, PO Box 392, Unisa 0003, South Africa (South Africa); Lai, Chi Wai [Department of Mathematical Sciences, University of South Africa, PO Box 392, Unisa 0003, South Africa (South Africa); Thornburg, Jonathan [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany); Szilagyi, Bela [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany)
2007-06-21
The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50.
4. Depth of origin and angular spectrum of sputtered atoms
International Nuclear Information System (INIS)
Vicanek, M.; Jimenez Rodriguez, J.J.; Sigmund, P.
1989-01-01
A theoretical analysis is presented of the depth of origin of atoms sputtered from a random target. The physical model aims at high energy sputtering under linear cascade conditions and assumes a dilute source of recoil atoms. The initial distribution of the recoils is assumed isotropic, and their energy distribution is E -2 like without an upper or lower cutoff. The scattering medium is either infinite or bounded by a plane surface. Atoms scatter according to the m=0 power cross section. Electronic stopping is ignored. The sputtered flux, differential in depth of origin, ejection energy and ejection angle has been evaluated by Monte Carlo simulation and by five distinct methods of solution of the linear Boltzmann equation reaching from continuous slowing down neglecting angular scattering to the P 3 approximation and a Gram-Charlier expansion going over spatial moments. The continuous slowing down approximation used in previous work leads to results that are identical to those found from a scheme that only ignores angular scattering but allows for energy loss straggling. Moreover, these predictions match more closely with the Monte Carlo results than any of the approximate analytical schemes that take account of angular scattering. The results confirm the common assertion that the depth of origin of sputtered atoms is determined mainly by the stopping of low energy recoil atoms. The effect of angular scattering turns out to be astonishingly small. The distributions in depth of origin, energy, and angle do not depend significantly on whether the scattering medium is a halfspace or an infinite medium with a reference plane. The angular spectrum comes out only very slightly over cosine from the model as it stands, in agreement with previous experience, but comments are made on essential features that are not incorporated in the physical model but might influence the angular spectrum. (orig./WL)
5. The angular gamma flux in an iron slab shield
International Nuclear Information System (INIS)
Penkuhn, H.
1975-08-01
The angular distribution of the photon energy and dose rate flux in a plane iron shield is investigated assuming an isotropic volume source. Near the shield axis (cos phi approximately 1, with phi=angle between shield axis and gamma direction) the angular spectrum is strongly space-dependent. For large phi, space-independent fits are given. Source energies from 0.662 to 6 MeV and penetrations from 6 to 60 cm are treated and the results are compared with a similar investigation on normal concrete. The differences iron-concrete are appreciable only for the lowest source energy
6. AngularJS yksisivuisen web-applikaation kehitysalustana
OpenAIRE
Karhu, Tuomo
2015-01-01
Yksisivuiset web-applikaatiot (SPA-sovellukset) ovat yleistyneet viimeisten kymmenen vuoden aikana, ja näiden avulla on ollut mahdollista tuoda verkkosivuston käyttökokemus lähemmäksi aitojen ohjelmasovellusten vastaavaa. Yksisivuisten web-applikaatioitten kehitystyöhön tarkoitetuista sovelluskehyksistä AngularJS on yksi käytetyimmistä ja suosituimmista. Työn tavoitteena on selvittää miten AngularJS-sovelluskehys soveltuu SPA-sivustojen kehitykseen sovelluskehittäjän näkökulmasta, sekä mi...
7. On angular distribution of nucleus fission fragments by fast neutrons
International Nuclear Information System (INIS)
Barabanov, A.L.; Grechukhin, D.P.
1987-01-01
Evaluation of amplitudes of quadrupole and hexadecapole components of angular distribution of nucleus fission fragments by neutrons with the energies E n < or approx. 6 MeV is conducted. Stability of this amplitude to permeability optical coefficient variations for neutrons is revealed. It is shown, that the ratio of these amplitudes as well as the character of their dependence on the target nucleus orientation degree are sensitive to the type of fission probability distribution along K projection if fissile nucleus J spin to the fragment scattering axis. This sensitivity may be used for fragment angular distribution anisotropy formation statistical model verification
8. Gravitomagnetism and angular momenta of black-holes
OpenAIRE
Marcelo Samuel Berman
2007-01-01
We review the energy contents formulae of Kerr-Newman black-holes, where gravitomagnetic energy term comes into play (Berman 2004, 2006a,b). Then, we obtain the angular momenta formulae, which include the gravitomagnetic effect. Three theorems can be enunciated: (1) No black-hole has its energy confined to its interior; (2) Rotating black-holes do not have confined angular momenta; (3) The energy density of a black-hole is not confined to its interior. The difference between our calculation a...
9. On the complex angular momentum theory of scattering
International Nuclear Information System (INIS)
Thylwe, K.-E.
1983-01-01
A contribution to the theory of complex angular momentum techniques in the field of atomic and molecular collisions is given. A new, flexible representation of the scattering amplitude on the basis of realistic assumptions for the behaviour of the S matrix in the complex angular momentum plane is derived. The representation has the form of a sum of steepest-descent integrals, S-matrix residue terms and a symmetry-type background integral. The flexibility is due to the presence of two integer parameters which may be chosen conveniently so as to make the residue sums sufficiently convergent and to minimise the total number of important terms. (author)
10. Problems of angular momentum projection in nuclear physics
Energy Technology Data Exchange (ETDEWEB)
Sorensen, R A [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)
1977-05-09
In nuclear models approximate wave functions are often used which do not have sharp angular momentum as required of the exact wave functions. It seems obvious that model wave functions of this type should be improved by projection onto states of good angular momentum. It is not the purpose of this paper to discuss the technical difficulties of projection (which can be formidable for many particle systems), but rather to present in an elementary way certain fundamental ambiguities in the use of projection. An application to high spin states near the yrast line is suggested.
11. Gamma-ray angular distribution and correlation measurement. II
International Nuclear Information System (INIS)
Twin, P.J.
1975-01-01
Angular correlations of γ-rays following nuclear reactions depend, in general, on some alignment of the γ-emitting initial state. The methods of alignment are briefly discussed and then the techniques and experimental methods associated with direct angular distributions, particle-gamma correlations, gamma-gamma correlations and linear polarization correlations are dealt with. Finally the inherent ambiguities which arise when different spin and delta values give identical correlations are discussed for the simple direct and particle-gamma correlations together with the question whether the larger information content of gamma-gamma and linear polarization correlations can resolve these ambiguities. (Auth.)
12. Angular momentum fuctuation energy in the cranking model
International Nuclear Information System (INIS)
Goodman, A.L.
1979-01-01
Angular momentum is approximately projected from Hartree-Fock-Bogoliubov cranked (HFBC) wave functions. At each J the projected energy is Esub(proj)approximately Esub(HFBC). The spin-dependent fluctuation ΔJ includes contributions from Jsub(y) and Jsub(z) as well as Jsub(x). There are no correlations in the three angular momentum components. Projected energies are calculated for 168 170 Yb and 174 Hf. When compared to experimental energies, the projected spectra are less compressed than the HFBC spectra. At low spins the projected and experimental energies are in good agreement. (Aut.)
13. Problems of angular momentum projection in nuclear physics
International Nuclear Information System (INIS)
Sorensen, R.A.
1977-01-01
In nuclear models approximate wave functions are often used which do not have sharp angular momentum as required of the exact wave functions. It seems obvious that model wave functions of this type should be improved by projection onto states of good angular momentum. It is not the purpose of this paper to discuss the technical difficulties of projection (which can be formidable for many particle systems), but rather to present in an elementary way certain fundamental ambiguities in the use of projection. An application to high spin states near the yrast line is suggested. (Auth.)
14. Quantitatively measuring the orbital angular momentum density of light : Presentation
CSIR Research Space (South Africa)
Dudley, Angela L
2013-08-01
Full Text Available the orbital angular momentum density of light Angela Dudleya, Christian Schulzeb, Igor Litvina, Michael Duparréb and Andrew Forbes*a,c,d a CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa; b Institute of Applied Optics, Friedrich...., “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000). [3] Sztul, H. I. and Alfano, R. R., “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008). [4] Allen, L...
15. Four Cases of Angular Cheilitis in Orthodontic Patients
Directory of Open Access Journals (Sweden)
P Kafaie
2006-07-01
Full Text Available Contact dermatitis is an inflammatory reaction of the skin and mucosa to either external or internal factors. It can be divided to two forms of irritant contact dermatitis and allergic contact dermatitis. Nickel is one of the most common materials that causes allergic contact dermatitis and is widely used in orthodontic appliances. The inflammatory reaction to this metal in orthodontics is usually stomatitis and angular cheilitis is very rare. We report 4 cases of angular cheilitis in orthodontic patients and discuss about their causes and treatments.
16. Equal channel angular pressing of pure aluminium—an analysis
Abstract. Equal channel angular pressing (ECAP) is a novel technique for producing ultra fine grain struc- tures in submicron level by introducing a large amount of shear strain into the materials without changing the billet shape or dimensions. This process is well suited for aluminium alloys and is capable of producing ultra.
17. Gravitational Field of Ultrarelativistic Objects with Angular Momentum
International Nuclear Information System (INIS)
Fursaev, Dmitri V
2006-01-01
A brief review of recently found gyraton metrics which describe the gravitational field of objects having an angular momentum and moving with the velocity of light is given. The gyraton metrics belong to a class of exact plane wave solutions of four and higher dimensional Einstein equations in vacuum or in the presence of a negative cosmological constant
18. Modified hydraulic braking system limits angular deceleration to safe values
Science.gov (United States)
Briggs, R. S.; Council, M.; Green, P. M.
1966-01-01
Conventional spring actuated, hydraulically released, fail-safe disk braking system is modified to control the angular deceleration of a massive antenna. The hydraulic system provides an immediate preset pressure to the spring-loaded brake shoes and holds it at this value to decelerate the antenna at the desired rate.
19. Obtaining the Electron Angular Momentum Coupling Spectroscopic Terms, jj
Science.gov (United States)
Orofino, Hugo; Faria, Roberto B.
2010-01-01
A systematic procedure is developed to obtain the electron angular momentum coupling (jj) spectroscopic terms, which is based on building microstates in which each individual electron is placed in a different m[subscript j] "orbital". This approach is similar to that used to obtain the spectroscopic terms under the Russell-Saunders (LS) coupling…
20. Data visualization with D3 and AngularJS
CERN Document Server
Körner, Christoph
2015-01-01
If you are a web developer with experience in AngularJS and want to implement interactive visualizations using D3.js, this book is for you. Knowledge of SVG or D3.js will give you an edge to get the most out of this book.
1. Earth Rotation and Coupling to Changes in Atmospheric Angular Momentum
Science.gov (United States)
Rosen, Richard D.; Frey, H. (Technical Monitor)
2000-01-01
The research supported under the contract dealt primarily with: (a) the mechanisms responsible for the exchange of angular momentum between the solid Earth and atmosphere; (b) the quality of the data sets used to estimate atmospheric angular momentum; and (c) the ability of these data and of global climate models to detect low-frequency signals in the momentum and, hence, circulation of the atmosphere. Three scientific papers reporting on the results of this research were produced during the course of the contract. These papers identified the particular torques responsible for the peak in atmospheric angular momentum and length-of-day during the 1982-93 El Nino event, and, more generally, the relative roles of torques over land and ocean in explaining the broad spectrum of variability in the length-of-day. In addition, a tendency for interannual variability in atmospheric angular momentum to increase during the last several decades of the 20th century was found in both observations and a global climate model experiment.
2. Strong eld ionization of naphthalene: angular shifts and molecular potential
DEFF Research Database (Denmark)
Dimitrovski, Darko; Maurer, Jochen; Christensen, Lauge
We analyze the photoelectron momentum distributions from strong eld ionization of xed-in-space naphthalene molecules by circularly polarized laser pulses. By direct comparison between experiment and theory, we show that the angular shifts in the photoelectron momentum distributions are very...... sensitive to the exact form of the molecular potential....
3. Angular momentum transport with twisted exciton wave packets
Science.gov (United States)
Zang, Xiaoning; Lusk, Mark T.
2017-10-01
A chain of cofacial molecules with CN or CN h symmetry supports excitonic states with a screwlike structure. These can be quantified with the combination of an axial wave number and an azimuthal winding number. Combinations of these states can be used to construct excitonic wave packets that spiral down the chain with well-determined linear and angular momenta. These twisted exciton wave packets can be created and annihilated using laser pulses, and their angular momentum can be optically modified during transit. This allows for the creation of optoexcitonic circuits in which information, encoded in the angular momentum of light, is converted into excitonic wave packets that can be manipulated, transported, and then reemitted. A tight-binding paradigm is used to demonstrate the key ideas. The approach is then extended to quantify the evolution of twisted exciton wave packets in a many-body, multilevel time-domain density functional theory setting. In both settings, numerical methods are developed that allow the site-to-site transfer of angular momentum to be quantified.
4. A perturbed angular correlation spectrometer for material science ...
A four-detector perturbed angular correlation (PAC) spectrometer has been developed with ultra-fast BaF2 detectors to acquire four coincidence spectra simultaneously, two at 180° and two at 90°. This spectrometer has double efficiency compared to that of a three-detector set-up. Higher efficiency is desirable for PAC ...
5. a kinematic model for calculating the magnitude of angular ...
African Journals Online (AJOL)
BARTH EKWUEME
material falling into a gravitational source at their centers. Depending ... transportation of angular momentum to outer portion of the accretion ... ∆r1 of the first body is. ∆. ∆. E ... This is the basic action of the accretion disk; energy is released as.
6. Synchronization of colloidal rotors through angular optical binding
Czech Academy of Sciences Publication Activity Database
Simpson, Stephen Hugh; Chvátal, Lukáš; Zemánek, Pavel
2016-01-01
Roč. 93, č. 2 (2016), 023842:1-12 ISSN 2469-9926 R&D Projects: GA ČR GB14-36681G Institutional support: RVO:68081731 Keywords : hydrodynamic properties * colloidal rotors * angular optical binding Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.925, year: 2016
7. Photofragment angular momentum distribution beyond the axial recoil approximation: Predissociation
International Nuclear Information System (INIS)
Kuznetsov, Vladislav V.; Vasyutinskii, Oleg S.
2007-01-01
We present the quantum mechanical expressions for the angular momentum distribution of the photofragments produced in slow predissociation. The paper is based on our recent theoretical treatment [J. Chem. Phys. 123, 034307 (2005)] of the recoil angle dependence of the photofragment multipole moments which explicitly treat the role of molecular axis rotation on the electronic angular momentum polarization of the fragments. The electronic wave function of the molecule was used in the adiabatic body frame representation. The rigorous expressions for the fragment state multipoles which have been explicitly derived from the scattering wave function formalism have been used for the case of slow predissociation where a molecule lives in the excited quasibound state much longer than a rotation period. Possible radial nonadiabatic interactions were taken into consideration. The optical excitation of a single rotational branch and the broadband incoherent excitation of all possible rotational branches have been analyzed in detail. The angular momentum polarization of the photofragments has been treated in the high-J limit. The polarization of the photofragment angular momenta predicted by the theory depends on photodissociation mechanism and can in many cases be significant
8. Cosmology Large Angular Scale Surveyor (CLASS) Focal Plane Development
Science.gov (United States)
Chuss, D. T.; Ali, A.; Amiri, M.; Appel, J.; Bennett, C. L.; Colazo, F.; Denis, K. L.; Dunner, R.; Essinger-Hileman, T.; Eimer, J.;
2015-01-01
The Cosmology Large Angular Scale Surveyor (CLASS) will measure the polarization of the Cosmic Microwave Background to search for and characterize the polarized signature of inflation. CLASS will operate from the Atacama Desert and observe approx.70% of the sky. A variable-delay polarization modulator provides modulation of the polarization at approx.10Hz to suppress the 1/f noise of the atmosphere and enable the measurement of the large angular scale polarization modes. The measurement of the inflationary signal across angular scales that spans both the recombination and reionization features allows a test of the predicted shape of the polarized angular power spectra in addition to a measurement of the energy scale of inflation. CLASS is an array of telescopes covering frequencies of 38, 93, 148, and 217 GHz. These frequencies straddle the foreground minimum and thus allow the extraction of foregrounds from the primordial signal. Each focal plane contains feedhorn-coupled transition-edge sensors that simultaneously detect two orthogonal linear polarizations. The use of single-crystal silicon as the dielectric for the on-chip transmission lines enables both high efficiency and uniformity in fabrication. Integrated band definition has been implemented that both controls the bandpass of the single-mode transmission on the chip and prevents stray light from coupling to the detectors.
9. African Journals Online (AJOL)
Luseko
2013-07-03
Jul 3, 2013 ... Angular leaf spot (ALS) caused by the fungus Pseudocercospora griseola and Bean common mosaic and necrosis virus (BCMV/BCMNV) are important diseases of common bean in Tanzania that can cause severe yield reduction when uncontrolled. This study was conducted to incorporate resistant genes ...
10. THE SIMULATION OF SCATTERING OF ELECTROMAGNETIC WAVES ON ANGULAR STRUCTURES.
Directory of Open Access Journals (Sweden)
P. A. Preobrazhensky
2017-02-01
Full Text Available The paper discusses the characteristics of scattering of electromagnetic waves on the angular diffraction structures. The solution of the problem is based on the method of integral equations. A comparative analysis of the scattering characteristics of structures with different shape is carried out.
11. The angular ordering in soft-gluon emission
International Nuclear Information System (INIS)
Tesima, K.
1987-01-01
The way to evaluate multi-parton cross-sections systematically is discussed. In the leading-double-log approximation in QCD, the successive emission of soft gluons is at successively smaller angles. The angular ordering, however, is violated in the next-to-leading order
12. Angular anisotropy of the cosmic microwave background radiation
International Nuclear Information System (INIS)
Silk, J.
1982-01-01
The theory of fluctuations in the cosmic microwave background radiation is reviewed. Anisotropy on large-scale (dipole and quadrupole) and on small scales is discussed. The smoothing effects of secondary ionization (fractional ionization x) are found to be unimportant over an angular scale greater than approx.= 5(OMEGAx)sup(1/3) degrees. (author)
13. Angular momentum projection of tilted axis rotating states
Energy Technology Data Exchange (ETDEWEB)
Oi, M; Onishi, N; Tajima, N [Tokyo Univ. (Japan); Horibata, T
1998-03-01
We applied an exact angular momentum projection to three dimensional cranked HFB (3d-CHFB) states. Tilted axis rotating states (TAR) and principal axis rotating states (PAR) are compared. It is shown that TAR is more adequate than PAR for description of the back bending phenomena driven by tilted rotation or wobbling motion. (author)
14. Exact angular momentum projection based on cranked HFB solution
Energy Technology Data Exchange (ETDEWEB)
Enami, Kenichi; Tanabe, Kosai; Yosinaga, Naotaka [Saitama Univ., Urawa (Japan). Dept. of Physics
1998-03-01
Exact angular momentum projection of cranked HFB solutions is carried out. It is reconfirmed from this calculation that cranked HFB solutions reproduce the intrinsic structure of deformed nucleus. The result also indicates that the energy correction from projection is important for further investigation of nuclear structure. (author)
15. Numerical simulation of side heating for controlling angular ...
In the present study, a 3-D coupled transient thermal analysis model with auxiliary side heating (parallel heating) is developed to control angular distortion. During analysis, parallel heating flames are placed at several locations from weld line in cross direction. A user defined subroutine is used to apply transient heat source ...
16. Continuous Variable Entanglement and Squeezing of Orbital Angular Momentum States
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Leuchs, Gerd; Andersen, Ulrik Lund
2009-01-01
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital...
17. Data compilation of angular distributions of sputtered atoms
International Nuclear Information System (INIS)
Yamamura, Yasunori; Takiguchi, Takashi; Tawara, Hiro.
1990-01-01
Sputtering on a surface is generally caused by the collision cascade developed near the surface. The process is in principle the same as that causing radiation damage in the bulk of solids. Sputtering has long been regarded as an undesirable dirty effect which destroys the cathodes and grids in gas discharge tubes or ion sources and contaminates plasma and the surrounding walls. However, sputtering is used today for many applications such as sputter ion sources, mass spectrometers and the deposition of thin films. Plasma contamination and the surface erosion of first walls due to sputtering are still the major problems in fusion research. The angular distribution of the particles sputtered from solid surfaces can possibly provide the detailed information on the collision cascade in the interior of targets. This report presents a compilation of the angular distribution of sputtered atoms at normal incidence and oblique incidence in the various combinations of incident ions and target atoms. The angular distribution of sputtered atoms from monatomic solids at normal incidence and oblique incidence, and the compilation of the data on the angular distribution of sputtered atoms are reported. (K.I.)
18. Angular momentum transport and evolution of lopsided galaxies
Science.gov (United States)
Saha, Kanak; Jog, Chanda J.
2014-10-01
The surface brightness distribution in the majority of stellar galactic discs falls off exponentially. Often what lies beyond such a stellar disc is the neutral hydrogen gas whose distribution also follows a nearly exponential profile at least for a number of nearby disc galaxies. Both the stars and gas are commonly known to host lopsided asymmetry especially in the outer parts of a galaxy. The role of such asymmetry in the dynamical evolution of a galaxy has not been explored so far. Following Lindblad's original idea of kinematic density waves, we show that the outer part of an exponential disc is ideally suitable for hosting lopsided asymmetry. Further, we compute the transport of angular momentum in the combined stars and gas disc embedded in a dark matter halo. We show that in a pure star and gas disc, there is a transition point where the free precession frequency of a lopsided mode, Ω - κ, changes from retrograde to prograde and this in turn reverses the direction of angular momentum flow in the disc leading to an unphysical behaviour. We show that this problem is overcome in the presence of a dark matter halo, which sets the angular momentum flow outwards as required for disc evolution, provided the lopsidedness is leading in nature. This, plus the well-known angular momentum transport in the inner parts due to spiral arms, can facilitate an inflow of gas from outside perhaps through the cosmic filaments.
19. Gravitational Field of Ultrarelativistic Objects with Angular Momentum
Energy Technology Data Exchange (ETDEWEB)
Fursaev, Dmitri V [Dubna International University and Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141 980, Dubna, Moscow Region (Russian Federation)
2006-03-01
A brief review of recently found gyraton metrics which describe the gravitational field of objects having an angular momentum and moving with the velocity of light is given. The gyraton metrics belong to a class of exact plane wave solutions of four and higher dimensional Einstein equations in vacuum or in the presence of a negative cosmological constant.
20. Angular distribution of protons emitted from the hydrogen plasma focus
Energy Technology Data Exchange (ETDEWEB)
Antanasijevic, R.; Maric, Z.; Vukovic, J.; Grabez, B. E-mail: [email protected]; Djordjevic, D.; Joksimovic, D.; Udovicic, V.; Dragic, A.; Stanojevic, J.; Banjanac, R.; Jokovic, D
2003-06-01
Angular distribution of emitted protons was measured. The protons were detected with NTD LR-115 placed at the specially constructed semi-spherical holder, which contains 17 different pinhole cameras. The mechanism of proton acceleration and emission are studied theoretically and experimental results are compared with theoretical predictions.
1. Angular distribution of protons emitted from the hydrogen plasma focus
International Nuclear Information System (INIS)
Antanasijevic, R.; Maric, Z.; Vukovic, J.; Grabez, B.; Djordjevic, D.; Joksimovic, D.; Udovicic, V.; Dragic, A.; Stanojevic, J.; Banjanac, R.; Jokovic, D.
2003-01-01
Angular distribution of emitted protons was measured. The protons were detected with NTD LR-115 placed at the specially constructed semi-spherical holder, which contains 17 different pinhole cameras. The mechanism of proton acceleration and emission are studied theoretically and experimental results are compared with theoretical predictions
2. A new uncertainty relation for angular momentum and angle
International Nuclear Information System (INIS)
Kranold, H.U.
1984-01-01
An uncertainty relation of the form ΔL 2 ΔSo >=sup(h/2π)/sub(2) is derived for angular momentum and angle. The non-linear operator So measures angles and has a simple interpretation. Subject to very general conditions of rotational invariance the above relation is unique. Radial momentum is not quantized
3. Angular dependence of EEDF in ion-beam plasma
International Nuclear Information System (INIS)
Dudin, S.V.
1995-01-01
In a previous paper the results of measurements of electron energy distribution function (EEDF) in ion-beam plasma created by low energy broad ion beam had been presented regardless of the angular dependence of the electron distribution. The present work is specifically aimed towards elucidating the spatial structure of the EEDF in the ion-beam plasma. To solve this problem combination of the techniques of cylindrical probe, large plate probe (5 x 5 mm) and two-grid enegoanalyzer was used. Directional operation of the probes makes possible measurement of angular dependence of electron distribution function which is anisotropic in high energy region. To optimize the construction of the probe-analyzer, experiments with grids were performed, which had different size, mesh, and transparency, under different potentials, and with different distances between grids. Numerical simulation of the analyzer was performed too. It is derived that optimal design for measurements in isotropic plasma is the most plate, thin two-grid probe with maximum angular covering. Investigation of angular dependence of EEDF has shown that the distribution of trapped electrons is completely isotropic, whereas in the energy range of var-epsilon > e var-phi pl (var-phi pl - plasma potential) a strong anisotropy of the EEDF is observed
4. Search for new physics in dijet mass and angular distributions
We present a search for physics beyond the Standard Model in proton–proton collisions at a centre-of-mass energy of s = 7 TeV, performed with the ATLAS detector at the Large Hadron Collider (LHC). No evidence for new physics is found in dijet mass and angular distributions and stringent limits are set on a variety of ...
5. Incorporation of resistance to angular leaf spot and bean common ...
African Journals Online (AJOL)
Angular leaf spot (ALS) caused by the fungus Pseudocercospora griseola and Bean common mosaic and necrosis virus (BCMV/BCMNV) are important diseases of common bean in Tanzania that can cause severe yield reduction when uncontrolled. This study was conducted to incorporate resistant genes for ALS and ...
6. Type I supernovae and angular anisotropy of the Hubble constant
International Nuclear Information System (INIS)
Le Denmat, Gerard; Vigier, J.-P.
1975-01-01
The observation of type I supernovae in distant galaxies yields an homogeneous sample of sources to evaluate their true distance. An examination of their distribution in the sky provides a significant confirmation of the angular anisotropy of the Hubble constant already observed by Rubin, Rubin and Ford [fr
7. AngularJS : yksisivuisen web-sovelluksen käyttöliittymän toteutus AngularJS:llä
OpenAIRE
Suomijoki, Juha
2015-01-01
Opinnäytetyössä tutkittiin mikä on AngularJS-JavaScript-ohjelmistokehys ja miten se soveltuu yksisivuisen web-sovelluksen käyttöliittymän toteutukseen. AngularJS on vuonna 2012 julkaistu Googlen ylläpitämä JavaScript-ohjelmistokehys, joka on tarkoitettu ensisijaisesti yksisivuisten web-sovellusten kehittämiseen. Opinnäytetyön teoriaosuudessa tutkittiin mikä AngularJS on ja mitkä ovat AngularJS:n keskeiset konseptit ja sovelluskomponentit. Tarkastelu pohjautui AngularJS:stä kirjoitettu...
8. Power calculation of linear and angular incremental encoders
Science.gov (United States)
Prokofev, Aleksandr V.; Timofeev, Aleksandr N.; Mednikov, Sergey V.; Sycheva, Elena A.
2016-04-01
Automation technology is constantly expanding its role in improving the efficiency of manufacturing and testing processes in all branches of industry. More than ever before, the mechanical movements of linear slides, rotary tables, robot arms, actuators, etc. are numerically controlled. Linear and angular incremental photoelectric encoders measure mechanical motion and transmit the measured values back to the control unit. The capabilities of these systems are undergoing continual development in terms of their resolution, accuracy and reliability, their measuring ranges, and maximum speeds. This article discusses the method of power calculation of linear and angular incremental photoelectric encoders, to find the optimum parameters for its components, such as light emitters, photo-detectors, linear and angular scales, optical components etc. It analyzes methods and devices that permit high resolutions in the order of 0.001 mm or 0.001°, as well as large measuring lengths of over 100 mm. In linear and angular incremental photoelectric encoders optical beam is usually formulated by a condenser lens passes through the measuring unit changes its value depending on the movement of a scanning head or measuring raster. Past light beam is converting into an electrical signal by the photo-detecter's block for processing in the electrical block. Therefore, for calculating the energy source is a value of the desired value of the optical signal at the input of the photo-detecter's block, which reliably recorded and processed in the electronic unit of linear and angular incremental optoelectronic encoders. Automation technology is constantly expanding its role in improving the efficiency of manufacturing and testing processes in all branches of industry. More than ever before, the mechanical movements of linear slides, rotary tables, robot arms, actuators, etc. are numerically controlled. Linear and angular incremental photoelectric encoders measure mechanical motion and
9. Helicon modes in uniform plasmas. III. Angular momentum
International Nuclear Information System (INIS)
Stenzel, R. L.; Urrutia, J. M.
2015-01-01
Helicons are electromagnetic waves with helical phase fronts propagating in the whistler mode in magnetized plasmas and solids. They have similar properties to electromagnetic waves with angular momentum in free space. Helicons are circularly polarized waves carrying spin angular momentum and orbital angular momentum due to their propagation around the ambient magnetic field B 0 . These properties have not been considered in the community of researchers working on helicon plasma sources, but are the topic of the present work. The present work focuses on the field topology of helicons in unbounded plasmas, not on helicon source physics. Helicons are excited in a large uniform laboratory plasma with a magnetic loop antenna whose dipole axis is aligned along or across B 0 . The wave fields are measured in orthogonal planes and extended to three dimensions (3D) by interpolation. Since density and B 0 are uniform, small amplitude waves from loops at different locations can be superimposed to generate complex antenna patterns. With a circular array of phase shifted loops, whistler modes with angular and axial wave propagation, i.e., helicons, are generated. Without boundaries radial propagation also arises. The azimuthal mode number m can be positive or negative while the field polarization remains right-hand circular. The conservation of energy and momentum implies that these field quantities are transferred to matter which causes damping or reflection. Wave-particle interactions with fast electrons are possible by Doppler shifted resonances. The transverse Doppler shift is demonstrated. Wave-wave interactions are also shown by showing collisions between different helicons. Whistler turbulence does not always have to be created by nonlinear wave-interactions but can also be a linear superposition of waves from random sources. In helicon collisions, the linear and/or orbital angular momenta can be canceled, which results in a great variety of field topologies. The work
10. Continuous theta burst stimulation of angular gyrus reduces subjective recollection.
Directory of Open Access Journals (Sweden)
Yasemin Yazar
Full Text Available The contribution of lateral parietal regions such as the angular gyrus to human episodic memory has been the subject of much debate following widespread observations of left parietal activity in healthy volunteers during functional neuroimaging studies of memory retrieval. Patients with lateral parietal lesions are not amnesic, but recent evidence indicates that their memory abilities may not be entirely preserved. Whereas recollection appears intact when objective measures such as source accuracy are used, patients often exhibit reduced subjective confidence in their accurate recollections. When asked to recall autobiographical memories, they may produce spontaneous narratives that lack richness and specificity, but can remember specific details when prompted. Two distinct theoretical accounts have been proposed to explain these results: that the patients have a deficit in the bottom-up capturing of attention by retrieval output, or that they have an impairment in the subjective experience of recollection. The present study aimed to differentiate between these accounts using continuous theta burst stimulation (cTBS in healthy participants to disrupt function of specific left parietal subregions, including angular gyrus. Inconsistent with predictions of the attentional theory, angular gyrus cTBS did not result in greater impairment of free recall than cued recall. Supporting predictions of the subjective recollection account, temporary disruption of angular gyrus was associated with highly accurate source recollection accuracy but a selective reduction in participants' rated source confidence. The findings are consistent with a role for angular gyrus in the integration of memory features into a conscious representation that enables the subjective experience of remembering.
11. The role of angular momentum conservation law in statistical mechanics
Directory of Open Access Journals (Sweden)
I.M. Dubrovskii
2008-12-01
Full Text Available Within the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY, Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum conservation does not change the density of probability distribution in both cases, just as it is assumed in the conventional theory. It is shown that in systems where the kinetic energy depends only on particle momenta canonically conjugated with Cartesian coordinates being their diagonal quadric form,the angular momentum conservation law changes the density of distribution of the system only in case the full angular momentum of a system is not equal to zero. In the gas of charged particles in a uniform magnetic field the density of distribution also varies if the angular momentum is zero [see Dubrovskii I.M., Condensed Matter Physics, 2206, 9, 23]. Two-dimensional gas of charged particles located within a section of an endless strip filled with gas in magnetic field is considered. Under such conditions the angular momentum is not conserved. Directional particle flows take place close to the strip boundaries, and, as a consequence, the phase trajectory of the considered set of particles does not remain within the limited volume of the phase space. In order to apply a statistical thermodynamics method, it was suggested to consider near-boundary trajectories relative to a reference system that moves uniformly. It was shown that if the diameter of an orbit having average thermal energy is much smaller than a strip width, the corrections to thermodynamic functions are small depending on magnetic field. Only the average velocity of near-boundary particles that form near-boundary electric currents creating the paramagnetic moment turn out to be essential.
12. Frame dependence of spin-one angular conditions in light front dynamics
International Nuclear Information System (INIS)
Bakker, Bernard L. G.; Ji Chuengryong
2002-01-01
We elaborate the frame dependence of the angular conditions for spin-1 form factors. An extra angular condition is found in addition to the usual angular condition relating the four helicity amplitudes. Investigating the frame dependence of angular conditions, we find that the extra angular condition is in general as complicated as the usual one, although it becomes very simple in the q + =0 frame involving only two helicity amplitudes. It is confirmed that the angular conditions are identical in frames that are connected by kinematical transformations. The high-Q 2 behavior of the physical form factors and the limiting behavior in special reference frames are also discussed
13. Angular evolution of peripheral heavy ion reactions at intermediate energies
International Nuclear Information System (INIS)
Blumenfeld, Y.; Chomaz, P.; Frascaria, N.; Garron, J.P.; Jacmart, J.C; Roynette, J.C
1985-01-01
Energy spectra and angular distributions of projectile-like fragments have been measured in the vicinity of the grazing angle for the 40 Ar+ 40 Ca and 40 Ar+ 208 Pb reactions at 44MeV/nucleon. Measurements of the 40 Ar+ 40 Ca system at 27MeV/nucleon and 20 Ne+ 208 Pb reaction at 44MeV/nucleon at one angle have also been performed. For fragments with charge and mass close to the projectile numerous deviations from the standard fragmentation model have been observed including rapidly changing shapes of the angular distributions with the fragment mass. Moreover the isotopic distributions and mean fragment velocities are strongly dependent on detection angle. A surface transfer reaction component dominant at the grazing angle can be separated from a second component which cannot be entirely accounted for by a simple fragmentation mechanism
14. Angular dependence of the exchange bias for the bistable state
Energy Technology Data Exchange (ETDEWEB)
Bai, Yuhao [College of Physics and Electronic Information, Shanxi Normal University, Linfen 041004 (China); Research College of materials science, Shanxi Normal University, Linfen 041004 (China); Xu, Xiaohong, E-mail: [email protected] [Research College of materials science, Shanxi Normal University, Linfen 041004 (China); Key Laboratory of Magnetic Molecules and Magnetic Information Materials, Ministry of Education, Shanxi Normal University, Linfen 041004 (China)
2017-06-15
The angular dependence of the exchange bias (ADEB) has been investigated in detail when the exchange-coupled ferromagnetic (FM)/antiferromagnetic (AFM) bilayer is in the bistable state. Complete and incomplete jump phenomena were found at the intrinsic easy and hard axes, when they pass through two special positions making the angular deviation of 58.2826° and 121.7174° from the easy axis of the uniaxial anisotropy, respectively. The combination of these different types of the jump phenomena at the intrinsic easy and hard axes yields five distinct types of the ADEB. The physical condition for each type of ADEB is established. Additionally, the extreme value problem of the exchange bias field and coercivity are also discussed, which is an important technological issue in the design of the magnetoresistive and spintronic devices. These results enable us to make a comprehensive understanding of the experimental ADEB curves.
15. Angular diameters of Magellanic Cloud plantary nebulae. I. Speckle interferometry
International Nuclear Information System (INIS)
Wood, P.R.; Bessell, M.S.; Dopita, M.A.
1986-01-01
Speckle interferometric angular diameters of Magellanic Cloud planetary nebulae are presented. The mass of ionized gas in each nebula has been derived from the angular diameter and published H-beta line fluxes; the derives masses range from less than 0.006 to more than 0.19 solar mass. The planetary nebulae observed were the brightest in the Magellanic Clouds; consequently, they are all relatively small, young, bright, and dense. They are almost certainly only partially ionized, so that the masses derived for the ionized parts of the nebula are lower limits to the total nebula mass. The properties of the Magellanic Cloud nebulae are compared with those of planetary nebulae at the galactic center. 27 references
16. Angular distribution in proton-hydrogen charge-transfer collisions
International Nuclear Information System (INIS)
Glembocki, O.; Halpern, A.M.
1977-01-01
Theoretical angular distributions for p-H charge transfer to the 1s state for energies of 1 keV and above have been examined and compared for three approximation schemes: the plane-wave Born approximation of Jackson and Schiff (JS), the Coulomb projected Born approximation of Geltman (G), and the distorted-wave eikonal approximation of one of the authors (D). The sharp dip in the forward distribution characteristic of JS is found to exist in G and D as well. As expected, G and D give identical results for all but the lowest energies. In the cases of G and D the dip, which is located close to that of JS, disappears and then reappears as the energy rises. Analytic high-energy limits for the angular dependence in both the JS and G cases have been found and are discussed
17. On the observability of the quark orbital angular momentum distribution
Energy Technology Data Exchange (ETDEWEB)
Courtoy, Aurore, E-mail: [email protected] [IFPA, AGO Department, Université de Liège, Bât. B5, Sart Tilman, B-4000 Liège (Belgium); Laboratori Nazionali di Frascati, INFN, Frascati (Italy); Goldstein, Gary R., E-mail: [email protected] [Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States); Osvaldo Gonzalez Hernandez, J., E-mail: [email protected] [Istituto Nazionale di Fisica Nucleare (INFN) – Sezione di Torino, via P. Giuria, 1, 10125 Torino (Italy); Liuti, Simonetta, E-mail: [email protected] [University of Virginia – Physics Department, 382 McCormick Rd., Charlottesville, VA 22904 (United States); Laboratori Nazionali di Frascati, INFN, Frascati (Italy); Rajan, Abha, E-mail: [email protected] [University of Virginia – Physics Department, 382 McCormick Rd., Charlottesville, VA 22904 (United States)
2014-04-04
We argue that due to parity constraints, the helicity combination of the purely momentum space counterparts of the Wigner distributions – the generalized transverse momentum distributions – that describes the configuration of an unpolarized quark in a longitudinally polarized nucleon can enter the deeply virtual Compton scattering amplitude only through matrix elements involving a final state interaction. The relevant matrix elements in turn involve light-cone operators projections in the transverse direction, or they appear in the deeply virtual Compton scattering amplitude at twist three. Orbital angular momentum or the spin structure of the nucleon was a major reason for these various distributions and amplitudes to have been introduced. We show that the twist three contributions associated with orbital angular momentum are related to the target-spin asymmetry in deeply virtual Compton scattering, already measured at HERMES.
18. Angular resolution of the gaseous micro-pixel detector Gossip
Science.gov (United States)
Bilevych, Y.; Blanco Carballo, V.; van Dijk, M.; Fransen, M.; van der Graaf, H.; Hartjes, F.; Hessey, N.; Koppert, W.; Nauta, S.; Rogers, M.; Romaniouk, A.; Veenhof, R.
2011-06-01
Gossip is a gaseous micro-pixel detector with a very thin drift gap intended for a high rate environment like at the pixel layers of ATLAS at the sLHC. The detector outputs not only the crossing point of a traversing MIP, but also the angle of the track, thus greatly simplifying track reconstruction. In this paper we describe a testbeam experiment to examine the angular resolution of the reconstructed track segments in Gossip. We used here the low diffusion gas mixture DME/CO 2 50/50. An angular resolution of 20 mrad for perpendicular tracks could be obtained from a 1.5 mm thin drift volume. However, for the prototype detector used at the testbeam experiment, the resolution of slanting tracks was worsened by poor time resolution of the pixel chip used.
19. Angular resolution of the gaseous micro-pixel detector Gossip
Energy Technology Data Exchange (ETDEWEB)
Bilevych, Y.; Blanco Carballo, V.; Dijk, M. van; Fransen, M.; Graaf, H. van der; Hartjes, F.; Hessey, N.; Koppert, W.; Nauta, S. [Nikhef, P.O. Box 41882, 1009 DB Amsterdam (Netherlands); Rogers, M. [Radboud University, P.O. Box 9102, 6500HC Nijmegen (Netherlands); Romaniouk, A.; Veenhof, R. [CERN, CH-1211, Geneve 23 (Switzerland)
2011-06-15
Gossip is a gaseous micro-pixel detector with a very thin drift gap intended for a high rate environment like at the pixel layers of ATLAS at the sLHC. The detector outputs not only the crossing point of a traversing MIP, but also the angle of the track, thus greatly simplifying track reconstruction. In this paper we describe a testbeam experiment to examine the angular resolution of the reconstructed track segments in Gossip. We used here the low diffusion gas mixture DME/CO{sub 2} 50/50. An angular resolution of 20 mrad for perpendicular tracks could be obtained from a 1.5 mm thin drift volume. However, for the prototype detector used at the testbeam experiment, the resolution of slanting tracks was worsened by poor time resolution of the pixel chip used.
20. Angular resolution of the gaseous micro-pixel detector Gossip
International Nuclear Information System (INIS)
Bilevych, Y.; Blanco Carballo, V.; Dijk, M. van; Fransen, M.; Graaf, H. van der; Hartjes, F.; Hessey, N.; Koppert, W.; Nauta, S.; Rogers, M.; Romaniouk, A.; Veenhof, R.
2011-01-01
Gossip is a gaseous micro-pixel detector with a very thin drift gap intended for a high rate environment like at the pixel layers of ATLAS at the sLHC. The detector outputs not only the crossing point of a traversing MIP, but also the angle of the track, thus greatly simplifying track reconstruction. In this paper we describe a testbeam experiment to examine the angular resolution of the reconstructed track segments in Gossip. We used here the low diffusion gas mixture DME/CO 2 50/50. An angular resolution of 20 mrad for perpendicular tracks could be obtained from a 1.5 mm thin drift volume. However, for the prototype detector used at the testbeam experiment, the resolution of slanting tracks was worsened by poor time resolution of the pixel chip used.
1. Cosmological forecasts from photometric measurements of the angular correlation function
International Nuclear Information System (INIS)
Sobreira, F.; Rosenfeld, R.; Simoni, F. de; Costa, L. A. N. da; Maia, M. A. G.; Makler, M.
2011-01-01
We study forecasts for the accuracy of the determination of cosmological parameters from future large-scale photometric surveys obtained using the full shape of the 2-point galaxy angular correlation function. The effects of linear redshift-space distortion, photometric redshift Gaussian errors, galaxy bias and nonlinearities in the power spectrum are included on our analysis. The Fisher information matrix is constructed with the full covariance matrix, including the correlation between nearby redshift shells arising from the photometric redshift error. We show that under some reasonable assumptions, a survey such as the imminent Dark Energy Survey should be able to constrain the dark energy equation of state parameter w and the cold dark matter density Ω cdm with a precision of the order of 20% and 13%, respectively, from the full shape of the angular correlation function alone. When combined with priors from other observations the precision in the determination of these parameters improve to 8% and 4%, respectively.
2. Resolution of potential ambiguities through farside angular structure: Semiclassical analysis
International Nuclear Information System (INIS)
Fricke, S.H.; Brandan, M.E.; McVoy, K.W.
1988-01-01
The optical potential fits summarized in the preceding paper are subjected to a semiclassical analysis of the Ford-Wheeler--Knoll-Schaeffer type. The important broad dips in their farside cross sections, which are essential in greatly reducing potential ambiguities, are found (in partial agreement with a suggestion of Goldberg's) to be mainly weak ''Airy'' or rainbow minima, that serve to identify deeply penetrating trajectories. The semiclassical analysis also permits the identification and understanding of a new category of discrete and continuous potential ambiguities, and suggests the manner in which specific features of the angular distributions (such as spacings and depths of various angular minima) determine the Woods-Saxon parameters found by a chi-squared search
3. Relativistic correction to the deuteron magnetic moment and angular condition
International Nuclear Information System (INIS)
Kondratyuk, L.A.; Strikman, M.I.
1983-01-01
The relativistic correction (RC) to the deuteron magnetic moment μsub(d) is investigated using the light-cone dynamics. The restrictions imposed by the angular condition on the electromagnetic current operator of deuteron are discussed in detail. It is shown that the additive model for the current operator of interacting consistuencies is consistent with the angular condition only for the two first terms of expansion of the ''good'' electromagnetic current component jsub(+) in powers of the momentum transfer q. The RC into μsub(d) is calculated using the mattix element of the ''good'' component. The account of RC decreases essentially the discrepancy between the theoretical and experimental values. The value of Δsub(μ) is determined for the Hamada-Johnston potential hard core potential (0.93x10 -2 ) for the Reid soft core potential (0.71x10 -2 ) and for the Paris potential (0.63x10 -2 )
4. Analogies between optical and quantum mechanical angular momentum.
Science.gov (United States)
Nienhuis, Gerard
2017-02-28
The insight that a beam of light can carry orbital angular momentum (AM) in its propagation direction came up in 1992 as a surprise. Nevertheless, the existence of momentum and AM of an electromagnetic field has been well known since the days of Maxwell. We compare the expressions for densities of AM in general three-dimensional modes and in paraxial modes. Despite their classical nature, these expressions have a suggestive quantum mechanical appearance, in terms of linear operators acting on mode functions. In addition, paraxial wave optics has several analogies with real quantum mechanics, both with the wave function of a free quantum particle and with a quantum harmonic oscillator. We discuss how these analogies can be applied.This article is part of the themed issue 'Optical orbital angular momentum'. © 2017 The Author(s).
5. Angular correlations in top quark decays in standard model extensions
International Nuclear Information System (INIS)
2011-01-01
The CMS Collaboration at the CERN LHC has searched for the t-channel single top quark production using the spin correlation of the t-channel. The signal extraction and cross section measurement rely on the angular distribution of the charged lepton in the top quark decays, the angle between the charged lepton momentum and top spin in the top rest frame. The behavior of the angular distribution is a distinct slope for the t-channel single top (signal) while it is flat for the backgrounds. In this Brief Report, we investigate the contributions which this spin correlation may receive from a two-Higgs doublet model, a top-color assisted technicolor (TC2) and the noncommutative extension of the standard model.
6. Angular distribution and atomic effects in condensed phase photoelectron spectroscopy
International Nuclear Information System (INIS)
Davis, R.F.
1981-11-01
A general concept of condensed phase photoelectron spectroscopy is that angular distribution and atomic effects in the photoemission intensity are determined by different mechanisms, the former being determined largely by ordering phenomena such as crystal momentum conservation and photoelectron diffraction while the latter are manifested in the total (angle-integrated) cross section. In this work, the physics of the photoemission process is investigated in several very different experiments to elucidate the mechanisms of, and correlation between, atomic and angular distribution effects. Theoretical models are discussed and the connection betweeen the two effects is clearly established. The remainder of this thesis, which describes experiments utilizing both angle-resolved and angle-integrated photoemission in conjunction with synchrotron radiation in the energy range 6 eV less than or equal to h ν less than or equal to 360 eV and laboratory sources, is divided into three parts
7. Angular momentum projection of cranked PNC wave function
International Nuclear Information System (INIS)
Han Yong
2000-01-01
In studying the properties of nuclear higher-spin states, not only the K-mixture needed to be taken into account, but also the Coriolis interaction (the cranking term) should be introduced. The cranking term breaks the time reversal symmetry, and the projection of the single-particle angular momentum on the intrinsic symmetric axis is no longer a good quantum number. This makes the theoretical calculation somewhat complicated. However, considering some intrinsic symmetry in a nucleus, it is not very difficult to apply the angular momentum projection technique to the PNC wave functions including the cranking components (the cranked PNC wave functions). The fundamental expressions for calculating the nuclear energy spectra and the electromagnetic properties are deduced and evaluated in theory, consequently the feasibility of actualizing the present scheme is made clear
8. Report on the ESO Workshop ''Astronomy at High Angular Resolution''
Science.gov (United States)
Boffin, H.; Schmidtobreick, L.; Hussain, G.; Berger, J.-Ph.
2015-03-01
A workshop took place in Brussels in 2000 on astrotomography, a generic term for indirect mapping techniques that can be applied to a huge variety of astrophysical systems, ranging from planets, single stars and binaries to active galactic nuclei. It appeared to be timely to revisit the topic given the many past, recent and forthcoming improvements in telescopes and instrumentation. We therefore decided to repeat the astrotomography workshop, but to put it into the much broader context of high angular resolution astronomy. Many techniques, from lucky and speckle imaging, adaptive optics to interferometry, are now widely employed to achieve high angular resolution and they have led to an amazing number of new discoveries. A summary of the workshop themes is presented.
9. A New Shape Description Method Using Angular Radial Transform
Science.gov (United States)
Lee, Jong-Min; Kim, Whoi-Yul
Shape is one of the primary low-level image features in content-based image retrieval. In this paper we propose a new shape description method that consists of a rotationally invariant angular radial transform descriptor (IARTD). The IARTD is a feature vector that combines the magnitude and aligned phases of the angular radial transform (ART) coefficients. A phase correction scheme is employed to produce the aligned phase so that the IARTD is invariant to rotation. The distance between two IARTDs is defined by combining differences in the magnitudes and aligned phases. In an experiment using the MPEG-7 shape dataset, the proposed method outperforms existing methods; the average BEP of the proposed method is 57.69%, while the average BEPs of the invariant Zernike moments descriptor and the traditional ART are 41.64% and 36.51%, respectively.
10. Dijet angular distributions in direct and resolved photoproduction at HERA
International Nuclear Information System (INIS)
Derrick, M.; Krakauer, D.; Magill, S.
1996-05-01
Jet photoproduction, where the two highest transverse energy (E T jet ) jets have E T jet above 6 GeV and a jet-jet invariant mass above 23 GeV, has been studied with the ZEUS detector at the HERA ep collider. Resolved and direct photoproduction samples have been separated. The cross section as a function of the angle between the jet-jet axis and the beam direction in the dijet rest frame has been measured for the two samples. The measured angular distributions differ markedly from each other. They agree with the predictions of QCD calculations, where the different angular distributions reflect the different spins of the quark and gluon exchanged in the hard subprocess. (orig.)
11. Angular signatures, and a space-borne measurement concept
Energy Technology Data Exchange (ETDEWEB)
Gerstl, S.A.W.
1996-05-01
The nature and value of angular signatures in remote sensing are reviewed with emphasis on the canopy hot-spot as a directionally localized angular signature and an important special case of a BRDF (bidirectional reflectance distribution function). A new concept is presented that allows hot spot measurements from space by using active (laser) illumination and bistatic detection. The detectors are proposed as imaging array sensors that are circulating the illumination source (or vice versa) and are connected with it through tethers in space which also provide the directional controls needed so that the entire system becomes pointable like a search light. Near infrared or IR operation in an atmospheric transmission winodw is envisioned with night-time data acquistion. Detailed feasibility and systems analyses have yet to be performed.
12. Investigating pointing tasks across angularly coupled display areas
DEFF Research Database (Denmark)
Hennecke, Fabian; De Luca, Alexander; Nguyen, Ngo Dieu Huong
2013-01-01
Pointing tasks are a crucial part of today’s graphical user interfaces. They are well understood for flat displays and most prominently are modeled through Fitts’ Law. For novel displays (e.g., curved displays with multi-purpose areas), however, it remains unclear whether such models for predicting...... that the target position affects overall pointing speed and offset in both conditions. However, we also found that Fitts’ Law can in fact still be used to predict performance as on flat displays. Our results help designers to optimize user interfaces on angularly coupled displays when pointing tasks are involved....... user performance still hold – in particular when pointing is performed across differently oriented areas. To answer this question, we conducted an experiment on an angularly coupled display – the Curve – with two input conditions: direct touch and indirect mouse pointer. Our findings show...
13. Angular-momentum nonclassicality by breaking classical bounds on statistics
Energy Technology Data Exchange (ETDEWEB)
2011-10-15
We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are very general and independent of other typical quantum signatures of nonclassical behavior such as sub-Poissonian statistics, squeezing, or oscillatory statistics, being insensitive to the nonclassical behavior displayed by other variables.
14. Automatic spectrometer for γ-γ angular correlation
International Nuclear Information System (INIS)
Saxena, R.N.; Monteiro, M.T.S.; Bairrio Nuevo Junior, A.
1974-01-01
An automated γ-γ angular correlation spectrometer is described in detail. Eletronic arrangements used in integral and differential measurements have also been described. In part I there is a short theoretical introduction, the experimental arrangement is described in part II. The results of the directional correlation measurement of γ-cascades in 60 Ni and 75 As and of the lifetime measurement of excited states in 181 Ta and 81 Br have been described in part III
15. Angular distributions and total yield of laser ablated silver
DEFF Research Database (Denmark)
Svendsen, Winnie Edith; Nordskov, A.; Schou, Jørgen
1997-01-01
The angular distribution of laser ablated silver has been measured in situ with a newly constructed setup with an array of microbalances. The distribution is strongly peaked in the forward direction corresponding to cospθ, where p varies between 5 and 9 for laser fluences from 2 to 7 J/cm2 at 355...... nm for a beam spot of 0.015 cm2. The total deposited yield is of the order 1015 Ag-atoms per pulse....
16. Spatial Angular Compounding Technique for H-Scan Ultrasound Imaging.
Science.gov (United States)
Khairalseed, Mawia; Xiong, Fangyuan; Kim, Jung-Whan; Mattrey, Robert F; Parker, Kevin J; Hoyt, Kenneth
2018-01-01
17. Monitoring Location and Angular Orientation of a Pill
Science.gov (United States)
Schipper, John F.
2012-01-01
A mobile pill transmitter system moves through, or adjacent to, one or more organs in an animal or human body, while transmitting signals from its present location and/or present angular orientation. The system also provides signals from which the present roll angle of the pill, about a selected axis, can be determined. When the location coordinates angular orientation and the roll angle of the pill are within selected ranges, an aperture on the pill container releases a selected chemical into, or onto, the body. Optionally, the pill, as it moves, provides a sequence of visually perceptible images. The times for image formation may correspond to times at which the pill transmitter system location or image satisfies one of at least four criteria. This invention provides and supplies an algorithm for exact determination of location coordinates and angular orientation coordinates for a mobile pill transmitter (PT), or other similar device that is introduced into, and moves within, a GI tract of a human or animal body. A set of as many as eight nonlinear equations has been developed and applied, relating propagation of a wireless signal between either two, three, or more transmitting antennas located on the PT, to four or more non-coplanar receiving antennas located on a signal receiver appliance worn by the user. The equations are solved exactly, without approximations or iterations, and are applied in several environments: (1) association of a visual image, transmitted by the PT at each of a second sequence of times, with a PT location and PT angular orientation at that time; (2) determination of a position within the body at which a drug or chemical substance or other treatment is to be delivered to a selected portion of the body; (3) monitoring, after delivery, of the effect(s) of administration of the treatment; and (4) determination of one or more positions within the body where provision and examination of a finer-scale image is warranted.
18. Viscous damping of toroidal angular momentum in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Stacey, W. M. [Georgia Tech Fusion Research Center, Atlanta, Georgia 30332 (United States)
2014-09-15
The Braginskii viscous stress tensor formalism was generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry in order to provide a representation for the viscous damping of toroidal rotation in tokamaks arising from various “neoclassical toroidal viscosity” mechanisms. In the process, it was verified that the parallel viscosity contribution to damping toroidal angular momentum still vanishes even in the presence of toroidal asymmetries, unless there are 3D radial magnetic fields.
19. A program for performing angular integrations for transition operators
International Nuclear Information System (INIS)
Froese Fischer, C.; Godefroid, M.R.; Hibbert, A.
1991-01-01
The MCHF-MLTPOL program performs the angular integrations necessary for expressing the matrix elements of transition operators, E1, E2, ..., or M1, M2, ..., as linear combinations of radial integrals. All matrix elements for transitions between two lists of configuration states will be evaluated. A limited amount of non-orthogonality is allowed between orbitals of the initial and final state. (orig.)
20. Angular dependence of the nanoDot OSL dosimeter
International Nuclear Information System (INIS)
Kerns, James R.; Kry, Stephen F.; Sahoo, Narayan; Followill, David S.; Ibbott, Geoffrey S.
2011-01-01
Purpose: Optically stimulated luminescent detectors (OSLDs) are quickly gaining popularity as passive dosimeters, with applications in medicine for linac output calibration verification, brachytherapy source verification, treatment plan quality assurance, and clinical dose measurements. With such wide applications, these dosimeters must be characterized for numerous factors affecting their response. The most abundant commercial OSLD is the InLight/OSL system from Landauer, Inc. The purpose of this study was to examine the angular dependence of the nanoDot dosimeter, which is part of the InLight system. Methods: Relative dosimeter response data were taken at several angles in 6 and 18 MV photon beams, as well as a clinical proton beam. These measurements were done within a phantom at a depth beyond the build-up region. To verify the observed angular dependence, additional measurements were conducted as well as Monte Carlo simulations in MCNPX. Results: When irradiated with the incident photon beams parallel to the plane of the dosimeter, the nanoDot response was 4% lower at 6 MV and 3% lower at 18 MV than the response when irradiated with the incident beam normal to the plane of the dosimeter. Monte Carlo simulations at 6 MV showed similar results to the experimental values. Examination of the results in Monte Carlo suggests the cause as partial volume irradiation. In a clinical proton beam, no angular dependence was found. Conclusions: A nontrivial angular response of this OSLD was observed in photon beams. This factor may need to be accounted for when evaluating doses from photon beams incident from a variety of directions.
1. Angular dependence of the parallel plate ionization chambers of Ipen
International Nuclear Information System (INIS)
Albuquerque, M. da P.P.; Caldas, L.
1989-08-01
The ionization chambers with parallel plates designed and constructed at IPEN for the dosimetry of soft X-radiation fields were studied in relation to thein angular dependence between O and +- 90 0 . The objective of this study is to verify the chambers response variation for small positioning errors during the field dosimetry used in Radiotherapy. The results were compared with those of commercial parallel plate ionization chambers used as secondary and testiary standards. (author) [pt
2. Tunnelling of orbital angular momentum in parallel optical waveguides
International Nuclear Information System (INIS)
Alexeyev, C N; Fadeyeva, T A; Yavorsky, M A; Boklag, N A
2011-01-01
We study the evolution of circularly polarized optical vortices (OVs) in the system of two coupled few-mode optical fibres. We demonstrate that upon propagation OVs tunnel into the adjacent fibre as a complex superposition of OVs that comprise also OVs of opposite polarization and topological charge. The initial OV may tunnel into the other fibre as the same vortex state of lesser energy. The evolution of the orbital angular momentum in coupled fibres is studied
3. Angular momentum coupling in atom-atom collisions
International Nuclear Information System (INIS)
Grosser, J.
1986-01-01
The coupling between the electronic angular momentum and the rotating atom-atom axis in the initial or the final phase of an atom-atom collision is discussed, making use of the concepts of radial and rotational (Coriolis) coupling between different molecular states. The description is based on a limited number of well-understood approximations, and it allows an illustrative geometric representation of the transition from the body fixed to the space fixed motion of the electrons. (orig.)
4. Determinantal method for complex angular momenta in potential scattering
Energy Technology Data Exchange (ETDEWEB)
Lee, B. W. [University of Pennsylvania, Philadelphia, PA (United States)
1963-01-15
In this paper I would like do describe a formulation of the complex angular momenta in potential scattering based on the Lippmann-Schwinger integral equation rather than on the Schrödinger differential equation. This is intended as a preliminary to the paper by SAWYER on the Regge poles and high energy limits in field theory (Bethe-Salpeter amplitudes), where the integral formulation is definitely more advantageous than the differential formulation.
5. Asymmetric photoelectron angular distributions from interfering photoionization processes
International Nuclear Information System (INIS)
Yin, Y.; Chen, C.; Elliott, D.S.; Smith, A.V.
1992-01-01
We have measured asymmetric photoelectron angular distributions for atomic rubidium. Ionization is induced by a one-photon interaction with 280 nm light and by a two-photon interaction with 560 nm light. Interference between the even- and odd-parity free-electron wave functions allows us to control the direction of maximum electron flux by varying the relative phase of the two laser fields
6. Measurement of Dijet Angular Distributions and Search for Quark Compositeness
International Nuclear Information System (INIS)
Gomez, B.; Hoeneisen, B.; Mooney, P.; Negret, J.P.; Davis, K.; Fein, D.; Forden, G.E.; Guida, J.A.; James, E.; Johns, K.; Nang, F.; Narayanan, A.; Rutherfoord, J.; Butler, J.M.; Fatyga, M.; Featherly, J.; Gibbard, B.; Gordon, H.; Graf, N.; Kahn, S.; Kotcher, J.; Protopopescu, S.; Rajagopalan, S.; Bantly, J.; Cullen-Vidal, D.; Cutts, D.; Guida, J.M.; Hoftun, J.S.; Partridge, R.; Grinstein, S.; Piegaia, R.; Bloom, P.; Fisyak, Y.; Glenn, S.; Grim, G.; Klopfenstein, C.; Lander, R.; Mani, S.; Fahland, T.; Hall, R.E.; Boswell, C.; Choudhary, B.C.; Cochran, J.; Ellison, J.; Gartung, P.; Gounder, K.; Huehn, T.; Alves, G.A.; Carvalho, W.; Maciel, A.K.; Motta, H.; Nicola, M.; Santoro, A.; Castilla-Valdez, H.; Gonzalez Solis, J.L.; Hernandez-Montoya, R.; Magana-Mendoza, L.; Sanchez-Hernandez, A.; Adam, I.; Kotwal, A.V.; Bhattacharjee, M.; Ahn, S.; Baldin, B.; Bartlett, J.F.; Bhat, P.C.; Boehnlein, A.; Borcherding, F.; Brandt, A.; Bross, A.; Christenson, J.H.; Cooper, W.E.; Demarteau, M.; Denisov, D.; Diehl, H.T.; Diesburg, M.; Feher, S.; Fisk, H.E.; Flattum, E.; Fuess, S.; Genser, K.; Gerber, C.E.; Green, D.R.; Greenlee, H.; Grossman, N.; Haggerty, H.; Hansen, S.; Heintz, U.; Hobbs, J.
1998-01-01
We have measured the dijet angular distribution in √(s)=1.8 TeV p bar p collisions using the D0 detector. Order α 3 s QCD predictions are in good agreement with the data. At 95% confidence limit the data exclude models of quark compositeness in which the contact interaction scale is below 2TeV. copyright 1998 The American Physical Society
7. Black hole mass and angular momentum in topologically massive gravity
International Nuclear Information System (INIS)
2007-01-01
We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics
8. Black hole mass and angular momentum in topologically massive gravity
Energy Technology Data Exchange (ETDEWEB)
Bouchareb, Adel; Clement, Gerard [Laboratoire de Physique Theorique LAPTH (CNRS), BP 110, F-74941 Annecy-le-Vieux cedex (France)
2007-11-21
We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.
9. Characterization of the Bell-Shaped Vibratory Angular Rate Gyro
Directory of Open Access Journals (Sweden)
Junfang Fan
2013-08-01
Full Text Available The bell-shaped vibratory angular rate gyro (abbreviated as BVG is a novel shell vibratory gyroscope, which is inspired by the Chinese traditional bell. It sensitizes angular velocity through the standing wave precession effect. The bell-shaped resonator is a core component of the BVG and looks like the millimeter-grade Chinese traditional bell, such as QianLong Bell and Yongle Bell. It is made of Ni43CrTi, which is a constant modulus alloy. The exciting element, control element and detection element are uniformly distributed and attached to the resonator, respectively. This work presents the design, analysis and experimentation on the BVG. It is most important to analyze the vibratory character of the bell-shaped resonator. The strain equation, internal force and the resonator's equilibrium differential equation are derived in the orthogonal curvilinear coordinate system. When the input angular velocity is existent on the sensitive axis, an analysis of the vibratory character is performed using the theory of thin shells. On this basis, the mode shape function and the simplified second order normal vibration mode dynamical equation are obtained. The coriolis coupling relationship about the primary mode and secondary mode is established. The methods of the signal processing and control loop are presented. Analyzing the impact resistance property of the bell-shaped resonator, which is compared with other shell resonators using the Finite Element Method, demonstrates that BVG has the advantage of a better impact resistance property. A reasonable means of installation and a prototypal gyro are designed. The gyroscopic effect of the BVG is characterized through experiments. Experimental results show that the BVG has not only the advantages of low cost, low power, long work life, high sensitivity, and so on, but, also, of a simple structure and a better impact resistance property for low and medium angular velocity measurements.
10. Cubature/ Unscented/ Sigma Point Kalman Filtering with Angular Measurement Models
Science.gov (United States)
2015-07-06
similarly transformed to work with the Laplace distribution. Cubature formulae for w(x) = 1 over regions of various shapes could be used for evaluating...measurement and process non- linearities, such as the cubature Kalman filter, can perform ex- tremely poorly in many applications involving angular...in the form of the “unscented transform ”) consider just converting such measurements into Cartesian coordinates and feeding the converted measurements
11. BAO from Angular Clustering: Optimization and Mitigation of Theoretical Systematics
Energy Technology Data Exchange (ETDEWEB)
Crocce, M.; et al.
2018-01-13
We study the theoretical systematics and optimize the methodology in Baryon Acoustic Oscillations (BAO) detections using the angular correlation function with tomographic bins. We calibrate and optimize the pipeline for the Dark Energy Survey Year 1 dataset using 1800 mocks. We compare the BAO fitting results obtained with three estimators: the Maximum Likelihood Estimator (MLE), Profile Likelihood, and Markov Chain Monte Carlo. The MLE method yields the least bias in the fit results (bias/spread $\\sim 0.02$) and the error bar derived is the closest to the Gaussian results (1% from 68% Gaussian expectation). When there is mismatch between the template and the data either due to incorrect fiducial cosmology or photo-$z$ error, the MLE again gives the least-biased results. The BAO angular shift that is estimated based on the sound horizon and the angular diameter distance agree with the numerical fit. Various analysis choices are further tested: the number of redshift bins, cross-correlations, and angular binning. We propose two methods to correct the mock covariance when the final sample properties are slightly different from those used to create the mock. We show that the sample changes can be accommodated with the help of the Gaussian covariance matrix or more effectively using the eigenmode expansion of the mock covariance. The eigenmode expansion is significantly less susceptible to statistical fluctuations relative to the direct measurements of the covariance matrix because the number of free parameters is substantially reduced [$p$ parameters versus $p(p+1)/2$ from direct measurement].
12. Uniqueness for the inverse backscattering problem for angularly controlled potentials
International Nuclear Information System (INIS)
Rakesh; Uhlmann, Gunther
2014-01-01
We consider the problem of recovering a smooth, compactly supported potential on R 3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled angular derivatives, then the two potentials are identical. In particular, if two potentials differ by a finite linear combination of spherical harmonics with radial coefficients and have the same backscattering data then the two potentials are identical. (paper)
13. How we are building a complex Angular 2 application at Inspire
CERN Multimedia
CERN. Geneva
2017-01-01
In this talk, at first we will talk about some basic and advanced Angular 2 concepts, then we will share our experiences with Angular 2 that we had so far while building a complex library and web applications at Inspire.
14. Nuclear level density parameter 's dependence on angular momentum
International Nuclear Information System (INIS)
Aggarwal, Mamta; Kailas, S.
2009-01-01
Nuclear level densities represent a very important ingredient in the statistical Model calculations of nuclear reaction cross sections and help to understand the microscopic features of the excited nuclei. Most of the earlier experimental nuclear level density measurements are confined to low excitation energy and low spin region. A recent experimental investigation of nuclear level densities in high excitation energy and angular momentum domain with some interesting results on inverse level density parameter's dependence on angular momentum in the region around Z=50 has motivated us to study and analyse these experimental results in a microscopic theoretical framework. In the experiment, heavy ion fusion reactions are used to populate the excited and rotating nuclei and measured the α particle evaporation spectra in coincidence with ray multiplicity. Residual nuclei are in the range of Z R 48-55 with excitation energy range 30 to 40 MeV and angular momentum in 10 to 25. The inverse level density parameter K is found to be in the range of 9.0 - 10.5 with some exceptions
15. Turbulent transport of toroidal angular momentum in low flow gyrokinetics
International Nuclear Information System (INIS)
Parra, Felix I; Catto, Peter J
2010-01-01
We derive a self-consistent equation for the turbulent transport of toroidal angular momentum in tokamaks in the low flow ordering that only requires solving gyrokinetic Fokker-Planck and quasineutrality equations correct to second order in an expansion on the gyroradius over scale length. We also show that according to our orderings the long wavelength toroidal rotation and the long wavelength radial electric field satisfy the neoclassical relation that gives the toroidal rotation as a function of the radial electric field and the radial gradients of pressure and temperature. Thus, the radial electric field can be solved for once the toroidal rotation is calculated from the transport of toroidal angular momentum. Unfortunately, even though this methodology only requires a gyrokinetic model correct to second order in gyroradius over scale length, current gyrokinetic simulations are only valid to first order. To overcome this difficulty, we exploit the smallish ratio B p /B, where B is the total magnetic field and B p is its poloidal component. When B p /B is small, the usual first order gyrokinetic equation provides solutions that are accurate enough to employ for our expression for the transport of toroidal angular momentum. We show that current δf and full f simulations only need small corrections to achieve this accuracy. Full f simulations, however, are still unable to determine the long wavelength, radial electric field from the quasineutrality equation.
16. New energy levels of praseodymium with large angular momentum
Energy Technology Data Exchange (ETDEWEB)
Khan, Shamim; Siddiqui, Imran; Gamper, Bettina; Syed, Tanweer Iqbal; Guthoehrlein, Guenter H.; Windholz, Laurentius [Inst. f. Experimentalphysik, Techn. Univ. Graz, Petersgasse 16, A-8010 Graz (Austria)
2011-07-01
The electronic ground state configuration of praseodymium {sup 59}Pr{sub 141} is [Xe] 4f{sup 3}6s{sup 2}, with ground state level {sup 4}I{sub 9/2}. Our research is mainly devoted to find previously unknown energy levels by the investigation of spectral lines and their hyperfine structures. In a hollow cathode discharge lamp praseodymium atoms and ions in ground and excited states are excited to high lying states by laser light. The excitation source is a tunable ring-dye laser system, operated with R6G, Kiton Red, DCM and LD700. A high resolution Fourier transform spectrum is used for selecting promising excitation wavelengths. Then the laser wavelength is tuned to a strong hyperfine component of the spectral line to be investigated, and a search for fluorescence from excited levels is performed. From the observed hyperfine structure we determine J-values and hyperfine constants A of the combining levels. This information, together with excitation and fluorescence wavelengths, allows us to find the energies of involved new levels. Up to now we have discovered large number of previously unknown energy levels with various angular momentum values. We present here the data (energies, parities, angular momenta J, magnetic hyperfine constants A) of ca. 40 new, until now unknown energy levels with high angular momentum values: 15/2, 17/2, 19/2, 21/2.
17. Angular power spectrum in publically released ALICE events
Science.gov (United States)
Llanes-Estrada, Felipe J.; Muñoz Martinez, Jose L.
2018-02-01
We study the particles emitted in the fireball following a Relativistic Heavy Ion Collision with the traditional angular analysis employed in cosmology and earth sciences, producing Mollweide plots of the number and pt distribution of a few actual, publically released ALICE-collaboration events and calculating their angular power spectrum. We also examine the angular spectrum of a simple two-particle correlation. While this may not be the optimal way of analyzing heavy ion data, our intention is to provide a one to one comparison to analysis in cosmology. With the limited statistics at hand, we do not find evidence for acoustic peaks but a decrease of Cl that is reminiscent of viscous attenuation, but subject to a strong effect from the rapidity acceptance which probably dominates (so we also subtract the m = 0 component). As an exercise, we still extract a characteristic Silk damping length (proportional to the square root of the viscosity over entropy density ratio) to illustrate the method. The absence of acoustic-like peaks is also compatible with a crossover from the QGP to the hadron gas (because a surface tension at domain boundaries would effect a restoring force that could have driven acoustic oscillations). Presently we do not understand a depression of the l = 6 multipole strength; perhaps ALICE could reexamine it with full statistics.
18. Angular dependence of spin-orbit spin-transfer torques
KAUST Repository
Lee, Ki-Seung
2015-04-06
In ferromagnet/heavy-metal bilayers, an in-plane current gives rise to spin-orbit spin-transfer torque, which is usually decomposed into fieldlike and dampinglike torques. For two-dimensional free-electron and tight-binding models with Rashba spin-orbit coupling, the fieldlike torque acquires nontrivial dependence on the magnetization direction when the Rashba spin-orbit coupling becomes comparable to the exchange interaction. This nontrivial angular dependence of the fieldlike torque is related to the Fermi surface distortion, determined by the ratio of the Rashba spin-orbit coupling to the exchange interaction. On the other hand, the dampinglike torque acquires nontrivial angular dependence when the Rashba spin-orbit coupling is comparable to or stronger than the exchange interaction. It is related to the combined effects of the Fermi surface distortion and the Fermi sea contribution. The angular dependence is consistent with experimental observations and can be important to understand magnetization dynamics induced by spin-orbit spin-transfer torques.
19. Mass and Angular Distributions of Charged Dihadron Production
Energy Technology Data Exchange (ETDEWEB)
Cummings, Mary Clare [Michigan U.
1990-01-01
Experiment 711, conducted at Fermilab. provided a unique handle towards understanding valence quark scattering by studying pairs of single. charged, high transverse momentum hadrons produced in collisions of 800 GeV /c protons on fixed metal targets. The apparatus consisted of a double-arm spectrometer. calorimetrically triggered. with high momentum resolution and a large angular acceptance for all charge states of particle pairs. The experiment was designed to select those hadron pairs that carrted most of the momentum and energy of the underlying scattered quarks and gluons. The charge of such "leading" hadrons is correlated with the charge of the quark that produced it. Quantum Chromodynamics (QCD) assumes that the scattering behavior of quarks ts independent of their charge, or "flavour": Experiment 711 could test this assumption. Tilis dissertation descrtbes the analysis of the mass and angular distributions of hadron pair production for three separate charge states: +-, ++ and --. The angular distributions are found to deviate from theory predictions of flavour symmetry. Also. the mass cross sections indicate ratios of positive to negative hard-scattered particles that are larger than expected from theory. These results could warrant reconsideration of the assumptions and approximations currently made in leading-order QCD calculations.
20. Dual electromagnetism: helicity, spin, momentum and angular momentum
International Nuclear Information System (INIS)
Bliokh, Konstantin Y; Nori, Franco; Bekshaev, Aleksandr Y
2013-01-01
The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincaré symmetries, examine both local and integral conserved quantities and show that only the dual electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments. (paper)
1. Angular deflection of rotary nickel titanium files: a comparative study
Directory of Open Access Journals (Sweden)
Gianluca Gambarini
2009-12-01
Full Text Available A new manufacturing method of twisting nickel titanium wire to produce rotary nickel titanium (RNT files has recently been developed. The aim of the present study was to evaluate whether the new manufacturing process increased the angular deflection of RNT files, by comparing instruments produced using the new manufacturing method (Twisted Files versus instruments produced with the traditional grinding process. Testing was performed on a total of 40 instruments of the following commercially available RNT files: Twisted Files (TF, Profile, K3 and M2 (NRT. All instruments tested had the same dimensions (taper 0.06 and tip size 25. Test procedures strictly followed ISO 3630-1. Data were collected and statistically analyzed by means ANOVA test. The results showed that TF demonstrated significantly higher average angular deflection levels (P<0.05, than RNT manufactured by a grinding process. Since angular deflection represent the amount of rotation (and consequently deformation that a RNT file can withstand before torsional failure, such a significant improvement is a favorable property for the clinical use of the tested RNT files.
2. Angular glint effects generation for false naval target verisimility requirements
International Nuclear Information System (INIS)
Kostis, Theodoros G; Galanis, Konstantinos G; Katsikas, Sokratis K
2009-01-01
A stimulating problem in the generation of coherent countermeasures for high range resolution radar systems is the inclusion of angular glint effects in the preparation of the false target mask. Since angular glint is representative of extended naval targets, this inclusion increases the credibility factor of the decoy playback signal at the adversary radar-operator station. In this paper, the ability of an interferometric inverse synthetic aperture radar (InISAR) simulator to provide a proof of concept towards the clarification of this challenging task is ascertained. The solution consists of three novel vector representations of the generated data, which are proven to behave according to the laws of physics governing the glint phenomenon. The first depiction is the angular glint injection at the target which is followed by the representation of the wavefront distortion at the radar. A value-added time procession integration of the target in pure roll motion provides an expected by ISAR theory side-view image of the naval extended false target. The effectiveness of the proposed approach through verification and validation of the results by using the method of pictorial evidence is established. A final argument is raised on the usage of this software tool for actual obfuscation and deception actions for air defence at sea applications
3. Angular parallelization of a curvilinear Sn transport theory method
International Nuclear Information System (INIS)
Haghighat, A.
1991-01-01
In this paper a parallel algorithm for angular domain decomposition (or parallelization) of an r-dependent spherical S n transport theory method is derived. The parallel formulation is incorporated into TWOTRAN-II using the IBM Parallel Fortran compiler and implemented on an IBM 3090/400 (with four processors). The behavior of the parallel algorithm for different physical problems is studied, and it is concluded that the parallel algorithm behaves differently in the presence of a fission source as opposed to the absence of a fission source; this is attributed to the relative contributions of the source and the angular redistribution terms in the S s algorithm. Further, the parallel performance of the algorithm is measured for various problem sizes and different combinations of angular subdomains or processors. Poor parallel efficiencies between ∼35 and 50% are achieved in situations where the relative difference of parallel to serial iterations is ∼50%. High parallel efficiencies between ∼60% and 90% are obtained in situations where the relative difference of parallel to serial iterations is <35%
4. Shocks in the relativistic transonic accretion with low angular momentum
Science.gov (United States)
Suková, P.; Charzyński, S.; Janiuk, A.
2017-12-01
We perform 1D/2D/3D relativistic hydrodynamical simulations of accretion flows with low angular momentum, filling the gap between spherically symmetric Bondi accretion and disc-like accretion flows. Scenarios with different directional distributions of angular momentum of falling matter and varying values of key parameters such as spin of central black hole, energy and angular momentum of matter are considered. In some of the scenarios the shock front is formed. We identify ranges of parameters for which the shock after formation moves towards or outwards the central black hole or the long-lasting oscillating shock is observed. The frequencies of oscillations of shock positions which can cause flaring in mass accretion rate are extracted. The results are scalable with mass of central black hole and can be compared to the quasi-periodic oscillations of selected microquasars (such as GRS 1915+105, XTE J1550-564 or IGR J17091-3624), as well as to the supermassive black holes in the centres of weakly active galaxies, such as Sgr A*.
5. Enhanced angular overlap model for nonmetallic f -electron systems
Science.gov (United States)
Gajek, Z.
2005-07-01
An efficient method of interpretation of the crystal field effect in nonmetallic f -electron systems, the enhanced angular overlap model (EAOM), is presented. The method is established on the ground of perturbation expansion of the effective Hamiltonian for localized electrons and first-principles calculations related to available experimental data. The series of actinide compounds AO2 , oxychalcogenides AOX , and dichalcogenides UX2 where X=S ,Se,Te and A=U ,Np serve as probes of the effectiveness of the proposed method. An idea is to enhance the usual angular overlap model with ab initio calculations of those contributions to the crystal field potential, which cannot be represented by the usual angular overlap model (AOM). The enhancement leads to an improved fitting and makes the approach intrinsically coherent. In addition, the ab initio calculations of the main, AOM-consistent part of the crystal field potential allows one to fix the material-specific relations for the EAOM parameters in the effective Hamiltonian. Consequently, the electronic structure interpretation based on EAOM can be extended to systems of the lowest point symmetries or/and deficient experimental data. Several examples illustrating the promising capabilities of EAOM are given.
6. Angular dependence of spin-orbit spin-transfer torques
KAUST Repository
Lee, Ki-Seung; Go, Dongwook; Manchon, Aurelien; Haney, Paul M.; Stiles, M. D.; Lee, Hyun-Woo; Lee, Kyung-Jin
2015-01-01
In ferromagnet/heavy-metal bilayers, an in-plane current gives rise to spin-orbit spin-transfer torque, which is usually decomposed into fieldlike and dampinglike torques. For two-dimensional free-electron and tight-binding models with Rashba spin-orbit coupling, the fieldlike torque acquires nontrivial dependence on the magnetization direction when the Rashba spin-orbit coupling becomes comparable to the exchange interaction. This nontrivial angular dependence of the fieldlike torque is related to the Fermi surface distortion, determined by the ratio of the Rashba spin-orbit coupling to the exchange interaction. On the other hand, the dampinglike torque acquires nontrivial angular dependence when the Rashba spin-orbit coupling is comparable to or stronger than the exchange interaction. It is related to the combined effects of the Fermi surface distortion and the Fermi sea contribution. The angular dependence is consistent with experimental observations and can be important to understand magnetization dynamics induced by spin-orbit spin-transfer torques.
7. Angular momentum in non-relativistic QED and photon contribution to spin of hydrogen atom
International Nuclear Information System (INIS)
Chen Panying; Ji Xiangdong; Xu Yang; Zhang Yue
2010-01-01
We study angular momentum in non-relativistic quantum electrodynamics (NRQED). We construct the effective total angular momentum operator by applying Noether's theorem to the NRQED lagrangian. We calculate the NRQED matching for the individual components of the QED angular momentum up to one loop. We illustrate an application of our results by the first calculation of the angular momentum of the ground state hydrogen atom carried in radiative photons, α em 3 /18π, which might be measurable in future atomic experiments.
8. Angular filter refractometry analysis using simulated annealing [An improved method for characterizing plasma density profiles using angular filter refractometry
International Nuclear Information System (INIS)
Angland, P.; Haberberger, D.; Ivancic, S. T.; Froula, D. H.
2017-01-01
Here, a new method of analysis for angular filter refractometry images was developed to characterize laser-produced, long-scale-length plasmas using an annealing algorithm to iterative converge upon a solution. Angular filter refractometry (AFR) is a novel technique used to characterize the density pro files of laser-produced, long-scale-length plasmas. A synthetic AFR image is constructed by a user-defined density profile described by eight parameters, and the algorithm systematically alters the parameters until the comparison is optimized. The optimization and statistical uncertainty calculation is based on a minimization of the χ2 test statistic. The algorithm was successfully applied to experimental data of plasma expanding from a flat, laser-irradiated target, resulting in average uncertainty in the density profile of 5-10% in the region of interest.
9. The dependence of the period on the angular amplitude of a simple ...
African Journals Online (AJOL)
The timing of the oscillation was done as the bob passed through its rest position. The time for 50 oscillations was recorded for different lengths and angular amplitudes. It was observed that the period depends on length and angular amplitude of the pendulum. The variation of the period with the angular amplitude is not a ...
10. Singularity in the Laboratory Frame Angular Distribution Derived in Two-Body Scattering Theory
Science.gov (United States)
Dick, Frank; Norbury, John W.
2009-01-01
The laboratory (lab) frame angular distribution derived in two-body scattering theory exhibits a singularity at the maximum lab scattering angle. The singularity appears in the kinematic factor that transforms the centre of momentum (cm) angular distribution to the lab angular distribution. We show that it is caused in the transformation by the…
11. Unidentified angular recurrent ulceration responsive to antiviral therapy
Directory of Open Access Journals (Sweden)
Rahmi Amtha
2013-03-01
Full Text Available Background: Recurrent ulcer on angular area is usually called stomatitis angularis. It is caused by many factors such as vertical dimension reduce, vitamin B12, and immune system deficiency, C. albicans and staphylococcus involvement. Clinically is characterized by painful fissure with erythematous base without fever. Purpose: to describe an unidentified angular ulcer proceeded by recurrent ulcers with no response of topical therapy. Case: An 18-years old male came to Oral Medicine clinic in RSCM who complained of angular recurrent ulcers since 3 years ago which developed on skin and bleed easily on mouth opening. Patient had fever before the onset of ulcers. Large, painful, irregular ulcers covered by red crustae on angular area bilaterally. Patient has been treated with various drugs without improvement and lead to mouth opening limitation. Intra oral shows herpetiformtype of ulcer and swollen of gingival. Case management: Provisional diagnosis was established as viral infection thus acyclovir 200 mg five times daily for two weeks and topical anti inflammation gel were administered. Blood test for IgG/IgM of HSV1 and HSV2 were non reactive, however ulceration showed a remarkable improvement. The ulcers healed completely after next 2 weeks with acyclovir. Conclusion: The angular ulceration on above patient failed to fulfill the criteria of stomatitis angularis or herpes labialis lesion. However it showed a good response to antiviral. Therefore, unidentified angular ulceration was appointed, as the lesion might be triggered by other type of human herpes virus or types of virus that response to acyclovir.Latar belakang: ulser rekuren pada sudut mulut biasanya disebut stomatitis angularis. Kelainan ini disebabkan oleh banyak faktor seperti berkurangnya dimensi vertikal, defisiensi vitamin B12 dan sistem kekebalan tubuh, infeksi C. albicans serta staphylococcus. Secara klinis kelainan ini ditandai dengan fisur sakit pada sudut mulut dengan dasar
12. Locking of intrinsic angular momentum in collision complexes
International Nuclear Information System (INIS)
Berengolts, Alexander.
1995-04-01
A concept of locking of the intrinsic angular momentum of a fragment of a collision complex to a body-fixed axis is widely used in the description of heavy-particle dynamics. The aim of this work is to provide a semiclassical description of the locking phenomenon which occur in diatomic and three atomic collision complexes. The first part of this work is devoted to the semiclassical study of the locking of the electronic angular momentum that occurs in slow collisions of two atoms, one in the spherically symmetric state and the other in state with j= 1. Here we calculate explicitly the complete locking matrix for different types of interatomic interactions. The elements of this matrix directly enter into the semiclassical expression for the different cross sections of polarized atoms. Limitations to the notion of the the locking radius and slipping probability are discussed in connection with the steepness of the interaction. Numerical calculations confirm analytical result: the optimal criterion for determination of the locking radius is a condition for the accumulated phase difference between two molecular states. Analytical expressions are suggested for the locking angle and the slipping probability. Implication of the locking approximation for calculation of the quasiclassical scattering matrix is discussed. The second part considers the locking of the rotational angular momentum of a diatom in the decomposition of a triatomic complexes. We discuss here cases J = 1,2,3 and 4, but restrict ourselves to calculation of the so-called dynamic orientation of the diatomic fragment. The letter represents one of the characteristics of the locking matrix which in principle can be measured experimentally. The orientation is created as a result of the interplay between the adiabatic interaction in the atom- diatom exit channel and the rotationally non adiabatic coupling in the perturbed rotor region
13. Developments for the 6He beta - nu angular correlation experiment
Science.gov (United States)
Zumwalt, David W.
This thesis describes developments toward the measurement of the angular correlation between the beta and the antineutrino in the beta decay of 6He. This decay is a pure Gamow-Teller decay which is described in the Standard Model as a purely axial vector weak interaction. The angular correlation is characterized by the parameter abetanu = -1/3 in the Standard Model. Any deviation from this value would be evidence for tensor components in the weak interaction and would constitute new physics. A new method will be used to measure the parameter a betanu from 6He decays, featuring a magneto-optical trap that will measure the beta particle in coincidence with the recoiling 6Li daughter ion. This neutral atom trapping scheme provides cold, tightly confined atoms which will reduce systematic uncertainties related to the initial position of the decay. By knowing the initial position of the decay and measuring the time of flight of the recoiling 6Li daughter ion in coincidence with the beta, the angular correlation between the beta and the antineutrino can be deduced. We aim to measure a betanu first to the level of 1%, and eventually to the 0.1% level, which would represent an order of magnitude improvement in precision over past experiments. Towards this goal, we have designed, built, and successfully tested a liquid lithium target to provide >2×10. {10} 6He atoms/sto a low-background environment, which is the most intense source of 6He presently available. This allowed for an additional measurement of the 6He half-life (806.89 +/- 0.11stat +0.23-0.19syst ms) to be made with unprecedented precision, resolving discrepancies in past measurements. We have also tested our trapping and detection apparatus and have begun to record preliminary coincidence events.
14. Angular momentum and torque described with the complex octonion
International Nuclear Information System (INIS)
Weng, Zi-Hua
2014-01-01
The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum (or torque, force) to combine some physics contents, which were considered to be independent of each other in the past. J. C. Maxwell used simultaneously two methods, the vector terminology and quaternion analysis, to depict the electromagnetic theory. It motivates the paper to introduce the quaternion space into the field theory, describing the physical feature of electromagnetic and gravitational fields. The spaces of electromagnetic field and of gravitational field can be chosen as the quaternion spaces, while the coordinate component of quaternion space is able to be the complex number. The quaternion space of electromagnetic field is independent of that of gravitational field. These two quaternion spaces may compose one octonion space. Contrarily, one octonion space can be separated into two subspaces, the quaternion space and S-quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, angular momentum, torque, and force etc in the gravitational field. In the S-quaternion space, it is capable of deducing the field potential, field strength, field source, current continuity equation, and electric (or magnetic) dipolar moment etc in the electromagnetic field. The results reveal that the quaternion space is appropriate to describe the gravitational features, including the torque, force, and mass continuity equation etc. The S-quaternion space is proper to depict the electromagnetic features, including the dipolar moment and current continuity equation etc. In case the field strength is weak enough, the force and the continuity equation etc can be respectively reduced to that in the classical field theory
15. Combined calculi for photon orbital and spin angular momenta
Science.gov (United States)
Elias, N. M.
2014-08-01
Context. Wavelength, photon spin angular momentum (PSAM), and photon orbital angular momentum (POAM), completely describe the state of a photon or an electric field (an ensemble of photons). Wavelength relates directly to energy and linear momentum, the corresponding kinetic quantities. PSAM and POAM, themselves kinetic quantities, are colloquially known as polarization and optical vortices, respectively. Astrophysical sources emit photons that carry this information. Aims: PSAM characteristics of an electric field (intensity) are compactly described by the Jones (Stokes/Mueller) calculus. Similarly, I created calculi to represent POAM characteristics of electric fields and intensities in an astrophysical context. Adding wavelength dependence to all of these calculi is trivial. The next logical steps are to 1) form photon total angular momentum (PTAM = POAM + PSAM) calculi; 2) prove their validity using operators and expectation values; and 3) show that instrumental PSAM can affect measured POAM values for certain types of electric fields. Methods: I derive the PTAM calculi of electric fields and intensities by combining the POAM and PSAM calculi. I show how these quantities propagate from celestial sphere to image plane. I also form the PTAM operator (the sum of the POAM and PSAM operators), with and without instrumental PSAM, and calculate the corresponding expectation values. Results: Apart from the vector, matrix, dot product, and direct product symbols, the PTAM and POAM calculi appear superficially identical. I provide tables with all possible forms of PTAM calculi. I prove that PTAM expectation values are correct for instruments with and without instrumental PSAM. I also show that POAM measurements of "unfactored" PTAM electric fields passing through non-zero instrumental circular PSAM can be biased. Conclusions: The combined PTAM calculi provide insight into mathematically modeling PTAM sources and calibrating POAM- and PSAM-induced measurement errors.
16. Spin O decay angular distribution for interfering mesons in electroproduction
Energy Technology Data Exchange (ETDEWEB)
Funsten, H.; Gilfoyle, G.
1994-04-01
Self analyzing meson electroproduction experiments are currently being planned for the CEBAF CLAS detector. These experiments deduce the spin polarization of outgoing unstable spin s (?)0 mesons from their decay angular distribution, W({theta},{psi}). The large angular acceptance of the CLAS detector permits kinematic tracking of a sufficient number of these events to accurately determine electroproduction amplitudes from the deduced polarization. Maximum polarization information is obtained from W({theta},{psi}) for decay into spin 0 daughters. The helicity of the decaying meson is transferred to the daughters relative orbital angular momentum m-projection; none is {open_quotes}absorbed{close_quotes} into daughter helicities. The decaying mesons helicity maximally appears in W({theta},{psi}). W({theta},{psi}) for spin 0 daughters has been derived for (1) vector meson electroproduction and (2) general interfering mesons produced by incident pions. This paper derives W({theta},{psi}) for electroproduction of two interfering mesons that decay into spin 0 daughters. An application is made to the case of interfering scalar and vector mesons. The derivation is an extension of work by Schil using the general decay formalism of Martin. The expressions can be easily extended to the case of N interfering mesons since interference occurs pairwise in the observable W ({theta},{psi}), a quadratic function of the meson amplitudes. The derivation uses the virtual photon density matrix of Schil which is transformed by a meson electroproduction transition operator, T. The resulting density matrix for the interfering mesons is then converted into a corresponding statistical tensor and contracted into the efficiency tensor for spin 0 daughters.
17. Twisted molecular excitons as mediators for changing the angular momentum of light
Science.gov (United States)
Zang, Xiaoning; Lusk, Mark T.
2017-07-01
Molecules with CN or CN h symmetry can absorb quanta of optical angular momentum to generate twisted excitons with well-defined quasiangular momenta of their own. Angular momentum is conserved in such interactions at the level of a paraxial approximation for the light beam. A sequence of absorption events can thus be used to create a range of excitonic angular momenta. Subsequent decay can produce radiation with a single angular momentum equal to that accumulated. Such molecules can thus be viewed as mediators for changing the angular momentum of light. This sidesteps the need to exploit nonlinear light-matter interactions based on higher-order susceptibilities. A tight-binding paradigm is used to verify angular momentum conservation and demonstrate how it can be exploited to change the angular momentum of light. The approach is then extended to a time-dependent density functional theory setting where the key results are shown to hold in a many-body, multilevel setting.
18. Angular momentum dependence of the nuclear level density parameter
International Nuclear Information System (INIS)
Aggarwal, Mamta; Kailas, S.
2010-01-01
Dependence of nuclear level density parameter on the angular momentum and temperature is investigated in a theoretical framework using the statistical theory of hot rotating nuclei. The structural effects are incorporated by including shell correction, shape, and deformation. The nuclei around Z≅50 with an excitation energy range of 30 to 40 MeV are considered. The calculations are in good agreement with the experimentally deduced inverse level density parameter values especially for 109 In, 113 Sb, 122 Te, 123 I, and 127 Cs nuclei.
19. Mechanical Properties of Copper Processed by Equal Channel Angular Pressing
Science.gov (United States)
Sülleiová, K.; Ballóková, B.; Besterci, M.; Kvačkaj, T.
2017-12-01
The development of the nanostructure in commercial pure copper and the strength and ductility after severe plastic deformation (SPD) with the technology of equal channel angular pressing (ECAP) are analysed. Experimental results and analyses showed that both strength and ductility can be increased simultaneously by SPD. The final grain size decreased from the initial 50μm by SPD to 100-300 nm after 10 passes. An increase of the ductility together with an increase of strength caused by SPD are explained by a strong grain refinement and by a dynamic equilibrium of weakening and strengthening, and it is visible on the final static tensile test stress-strain charts.
20. Stellar Angular Momentum Distributions and Preferential Radial Migration
Science.gov (United States)
Wyse, Rosemary; Daniel, Kathryne J.
2018-04-01
I will present some results from our recent investigations into the efficiency of radial migration in stellar disks of differing angular momentum distributions, within a given adopted 2D spiral disk potential. We apply to our models an analytic criterion that determines whether or not individual stars are in orbits that could lead to radial migration around the corotation resonance. We couch our results in terms of the local stellar velocity dispersion and find that the fraction of stars that could migrate radially decreases as the velocity dispersion increases. I will discuss implications and comparisons with the results of other approaches.
1. Monte Carlo Calculation of Sensitivities to Secondaries' Angular Distributions
International Nuclear Information System (INIS)
Perel, R.L.
2003-01-01
An algorithm for Monte Carlo calculation of sensitivities of responses to secondaries' angular distributions (SAD) is developed, based on the differential operator approach. The algorithm was formulated for the sensitivity to Legendre coefficients of the SAD and is valid even in cases where the actual representation of SAD is not in the form of a Legendre series. The algorithm was implemented, for point- or ring-detectors, in a local version of the code MCNP. Numerical tests were performed to validate the algorithm and its implementation. In addition, an algorithm specific for the Kalbach-Mann representation of SAD is presented
2. Experimental study of angular dependence in double photon Compton scattering
International Nuclear Information System (INIS)
Sandhu, B.S.; Dewan, R.; Saddi, M.B.; Singh, B.; Ghumman, B.S.
2000-01-01
The collision differential cross-section and energy of one of the final photons for double photon Compton scattering have been measured as a function of scattering angle θ 1 . The incident photon energy is 0.662 MeV and thin aluminium foils are used as a scatterer. The two simultaneously emitted photons in this higher order process are detected in coincidence using two NaI(Tl) scintillation spectrometers and 30 ns timing electronics. The measured values for energy and collision differential cross-section agree with theory within experimental estimated error. The present data provide information of angular dependence in this higher order process
3. Measurements of the angular distribution of diffuse irradiance
DEFF Research Database (Denmark)
Andersen, Elsa; Nielsen, Kristian Pagh; Dragsted, Janne
2015-01-01
Advanced solar resource assessment and forecasting is necessary for optimal solar energy utilization. In order to investigate the short-term resource variability, for instance caused by clouds it is necessary to investigate how clouds affect the solar irradiance, including the angular distribution...... of the solar irradiance. The investigation is part of the Danish contribution to the taskforce 46 within the International Energy Agency and financed by the Danish Energy Agency. The investigation focuses on the distribution of the diffuse solar irradiance and is based on horizontal measurements of the solar...
4. Measurements of electron density profiles using an angular filter refractometer
International Nuclear Information System (INIS)
Haberberger, D.; Ivancic, S.; Hu, S. X.; Boni, R.; Barczys, M.; Craxton, R. S.; Froula, D. H.
2014-01-01
A novel diagnostic technique, angular filter refractometry (AFR), has been developed to characterize high-density, long-scale-length plasmas relevant to high-energy-density physics experiments. AFR measures plasma densities up to 10 21 cm −3 with a 263-nm probe laser and is used to study the plasma expansion from CH foil and spherical targets that are irradiated with ∼9 kJ of ultraviolet (351-nm) laser energy in a 2-ns pulse. The data elucidate the temporal evolution of the plasma profile for the CH planar targets and the dependence of the plasma profile on target radius for CH spheres
5. Geometric transformations of optical orbital angular momentum spatial modes
Science.gov (United States)
He, Rui; An, Xin
2018-02-01
With the aid of the bosonic mode conversions in two different coordinate frames, we show that (1) the coordinate eigenstate is exactly the EPR entangled state representation, and (2) the Laguerre-Gaussian (LG) mode is exactly the wave function of the common eigenvector of the orbital angular momentum and the total photon number operator. Moreover, by using the conversion of the bosonic modes, theWigner representation of the LG mode can be obtained directly. It provides an alternative to the method of Simon and Agarwal.
6. Quality Assessment of Vertical Angular Deviations for Photometer Calibration Benches
International Nuclear Information System (INIS)
Ribeiro, A Silva; Santos, A Costa; E Sousa, J Alves; Forbes, A B
2015-01-01
Lighting, both natural and electric, constitutes one of the most important aspects of the life of human beings, allowing us to see and perform our daily tasks in outdoor and indoor environments. The safety aspects of lighting are self-evident in areas such as road lighting, urban lighting and also indoor lighting. The use of photometers to measure lighting levels requires traceability obtained in accredited laboratories, which must provide an associated uncertainty. It is therefore relevant to study the impact of known uncertainty sources like the vertical angular deviation of photometer calibration benches, in order to define criteria to its quality assessment
7. Measurements of electron density profiles using an angular filter refractometer
Energy Technology Data Exchange (ETDEWEB)
Haberberger, D., E-mail: [email protected]; Ivancic, S.; Hu, S. X.; Boni, R.; Barczys, M.; Craxton, R. S.; Froula, D. H. [Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14636 (United States)
2014-05-15
A novel diagnostic technique, angular filter refractometry (AFR), has been developed to characterize high-density, long-scale-length plasmas relevant to high-energy-density physics experiments. AFR measures plasma densities up to 10{sup 21} cm{sup −3} with a 263-nm probe laser and is used to study the plasma expansion from CH foil and spherical targets that are irradiated with ∼9 kJ of ultraviolet (351-nm) laser energy in a 2-ns pulse. The data elucidate the temporal evolution of the plasma profile for the CH planar targets and the dependence of the plasma profile on target radius for CH spheres.
8. Angular correlations and fragmentation in intermediate energy heavy ion collisions
International Nuclear Information System (INIS)
Kristiansson, Anders.
1990-05-01
Intermediate energy heavy-ion collisions have been studied from 35 A MeV up to 94 A MeV at various accelerators. Angular correlations between light particles and detection of projectile- and target-fragments have been used to investigate the reaction mechanisms in this transition region between low- and high energy. An excess of correlations is observed in the particle-particle elastic scattering plane. This excess increases with particle mass and can be understood in terms of momentum conservation. The fragmentation measurements gives an indication that both energy and momentum transfer to the spectator volumes does occur. (author)
9. Final-photon angular distributions in Compton double-ionization
International Nuclear Information System (INIS)
Kornberg, M.A.
1999-01-01
Angular distributions of the scattered-photon in two-electron ionization of helium by Compton scattering are reported. Our calculations are performed as a direct integration over Compton profiles. We show that backward scattering is adequately described using an uncorrelated final-state approximation, as compared with impulse approximation (IA) results. The relation dσ c 2+ /dΩ = R c dσ c + /dΩ is fulfilled within IA at high-photon energies, with R c the asymptotic shake-off ratio. (orig.)
10. Radio Pumping of Ionospheric Plasma with Orbital Angular Momentum
International Nuclear Information System (INIS)
Leyser, T. B.; Norin, L.; McCarrick, M.; Pedersen, T. R.; Gustavsson, B.
2009-01-01
Experimental results are presented of pumping ionospheric plasma with a radio wave carrying orbital angular momentum (OAM), using the High Frequency Active Auroral Research Program (HAARP) facility in Alaska. Optical emissions from the pumped plasma turbulence exhibit the characteristic ring-shaped morphology when the pump beam carries OAM. Features of stimulated electromagnetic emissions (SEE) that are attributed to cascading Langmuir turbulence are well developed for a regular beam but are significantly weaker for a ring-shaped OAM beam in which case upper hybrid turbulence dominates the SEE
11. Unitarity bounds on angular distribution in multiparticle production - II
International Nuclear Information System (INIS)
Divakaran, P.P.; Kugler, M.; Soffer, J.
1976-01-01
Upper bounds which follow from unitarity are derived for the angular distribution of the detected particle C in the inclusive process AB→C+anything at a finite energy, in terms of the corresponding elastic amplitudes for a fixed value of the forward inelastic cross-section and for a fixed value of the total inelastic cross-section for the production of C. In comparison with the pp→p+anything data at 24GeV/c, some improvement on previous bounds is observed [fr
12. Angularly-selective transmission imaging in a scanning electron microscope.
Science.gov (United States)
Holm, Jason; Keller, Robert R
2016-08-01
This work presents recent advances in transmission scanning electron microscopy (t-SEM) imaging control capabilities. A modular aperture system and a cantilever-style sample holder that enable comprehensive angular selectivity of forward-scattered electrons are described. When combined with a commercially available solid-state transmission detector having only basic bright-field and dark-field imaging capabilities, the advances described here enable numerous transmission imaging modes. Several examples are provided that demonstrate how contrast arising from diffraction to mass-thickness can be obtained. Unanticipated image contrast at some imaging conditions is also observed and addressed. Published by Elsevier B.V.
13. Angular correlation in the two-electron continuum
International Nuclear Information System (INIS)
Kheifets, A. S.; Bray, I.
2006-01-01
Following absorption of a single photon, angles of simultaneous emission of two electrons from a He(n 1 S) atom become more correlated with increasing n. We find that the strength of this correlation is due to the two-electron continuum of the electron-impact ionization of the He + (ns) ion. The strength is determined by the width of the momentum profile of the ionic ns state but not the strength of the electron correlation in the He initial state. This can explain the increasing (over He) angular correlation strength found in double photoionization of targets such as Be, Ne, and H 2
14. On the six components of optical angular momentum
International Nuclear Information System (INIS)
Barnett, Stephen M
2011-01-01
In special relativity the angular momentum is a rank-two antisymmetric tensor with six independent components. Three of these are the familiar generators of spatial rotation, which for light have been studied at length. The remaining three, which are responsible for the Lorentz boosts, have largely been neglected. We introduce the latter and compare their properties with those of the more familiar generators of rotations. The seemingly natural separation of the generators of Lorentz boosts into spin and orbital parts fails, however, as the spin part is identically zero
15. Approximate angular momentum projection from cranked intrinsic states
International Nuclear Information System (INIS)
Goodman, A.L.
1979-01-01
High-spin spectra are determined by approximately projecting states of good angular momentum from cranked Hartree-Fock-Bogoliubov (CHFB) wave functions. For each J the projected energy is E/sub PROJ/ approx. = E/sub CHFB/ - (ΔJ) 2 /2 J/sub CHFB/, where the moment of inertia J and the fluctuation ΔJ are spin dependent. For /sup 168,170/Yb and 174 Hf the projected J is less than the CHFB value for all J. Consequently approximate projection increases all yrast excitation energies for these nuclei
16. Angular correlation and lifetime measurements in /sup 154/Gd
Energy Technology Data Exchange (ETDEWEB)
Sharma, A K; Verma, H R; Kaur, R; Sooch, S S; Trehan, P N
1982-03-01
Multipole admixtures in 591.80, 692.51, 723.38, 756.84, 873.27, 1004.74, 1274.50, 1494.22 and 1596.65 keV transitions have been measured by investigating nine gamma-gamma angular correlations in /sup 154/Gd. The present study confirms very small Ml admixtures in the transitions from ..beta..- and ..gamma..-vibrational bands to ground state band in /sup 154/Gd which is a transitional nucleus. In addition, lifetime of an excited level at 123.04 keV has been measured to be 1.19 +- 0.03 nsec.
17. The limit of grain refinement on equal channel angular deformation
International Nuclear Information System (INIS)
Kopylov, V.I.; Chuvil'deev, V.N.
2004-01-01
Experimental and theoretical study results on the process of strain-induced grain refinement under severe plastic deformation are described. A generalization is made for experimental results on deformation dispersing of copper, magnesium and aluminium base alloys as well as unalloyed metals. The model is developed which allows calculating the minimal grain size being able to result from equal channel angular pressing. The expressions describing the dependence of the limit of grain refinement on the nature of the material and severe plastic deformation rate and temperature are obtained [ru
18. Angular intensity of a gas-phase field ionization source
International Nuclear Information System (INIS)
Orloff, J.; Swanson, L.W.
1979-01-01
Angular intensities of 1 μA sr -1 have been measured for a gas-phase field ionization source in an optical column under practical operating conditions. The source, which was differentially pumped and cooled to 77 K, utilized a -oriented iridium emitter and precooled hydrogen gas at 10 -2 Torr. The ion beam was collimated with an electrostatic lens and detected below an aperture subtending 0.164 msr. A transmitted current of approx.10 -10 A was measured at voltages corresponding to a field of approx. =2.2 V/A at the emitter
19. Angular relational signature-based chest radiograph image view classification.
Science.gov (United States)
Santosh, K C; Wendling, Laurent
2018-01-22
In a computer-aided diagnosis (CAD) system, especially for chest radiograph or chest X-ray (CXR) screening, CXR image view information is required. Automatically separating CXR image view, frontal and lateral can ease subsequent CXR screening process, since the techniques may not equally work for both views. We present a novel technique to classify frontal and lateral CXR images, where we introduce angular relational signature through force histogram to extract features and apply three different state-of-the-art classifiers: multi-layer perceptron, random forest, and support vector machine to make a decision. We validated our fully automatic technique on a set of 8100 images hosted by the U.S. National Library of Medicine (NLM), National Institutes of Health (NIH), and achieved an accuracy close to 100%. Our method outperforms the state-of-the-art methods in terms of processing time (less than or close to 2 s for the whole test data) while the accuracies can be compared, and therefore, it justifies its practicality. Graphical Abstract Interpreting chest X-ray (CXR) through the angular relational signature.
20. Phoenix II energy extraction and angular multiplexing experiments
International Nuclear Information System (INIS)
Hoffman, J.M.; Hays, G.N.
1981-08-01
The energy extraction efficiency as a function of input intensity has been determined from a large-volume HF amplifier. For an input intensity of 4 x 10 6 W/cm 2 , 1080 Joules was extracted from the amplifier. This corresponded to an energy extraction efficiency of 0.90. At the highest H 2 /F 2 /O 2 pressures used, 1700 Joules was obtained from this system when used in an oscillator configuration. These results also show evidence that energy extraction at low input intensities in large-volume HF amplifiers is strongly influenced by parasitic oscillations. The results also indicate that, for a long-pulse HF amplifier (60-nsec electron beam), the timing between the amplifier and oscillator to achieve optimum operating conditions is not very critical. This same amplifier, used in conjunction with a short-pulse, good-beam-quality oscillator-preamplifier chain, has also been used to evaluate pulse compression using angular multiplexing. Using two sequential 24-nsec pulses, the essential elements of angular multiplexing have been evaluated as a function of interpulse separation time. Included are energy extraction efficiency, overall temporal pulse distortion, leading-edge contrast-ratio distortion, and suppression of amplified spontaneous emission relative to a single, long-duration input pulse. For appropriate interpulse delay time, we show that distortionless amplification is possible with energy-extraction efficiency the same as is obtained using a single input beam having a pulse width equal to the duration of the amplifier gain
1. Particle field diagnose using angular multiplexing volume holography
Science.gov (United States)
Zhao, Yu; Li, Zeren; Luo, Zhenxiong; Jun, Li; Zhong, Jie; Ye, Yan; Li, Shengfu; Zhu, Jianhua
2017-08-01
The problem of particle field diagnosing using holography can be met in many areas. But single frame hologram can only catch one moment of the fast event, which can't reveal the change process of an unrepeatable fast event. For events in different time-scale, different solution should be used. We did this work to record a laser induced particle field in the time-scale of tens of micron seconds. A laser of pulse sequence mode is applied to provide 10 pulses, the energy and time interval of whom is 150mJ and 1μs. Four pockels cells are employed to pick up the last four pulses for holographic recording, the other pulses are controlled to pre-expose the photopolymer based recording material, which can enhance photosensitivity of the photopolymer during the moment of holographic recording. The angular multiplexing technique and volume holography is accepted to avoid shifting the photopolymer between each shot. Another Q-switch YAG laser (pulse energy 100mJ, pulse width 10ns) is applied to produce the fast event. As a result, we successfully caught the motion process of the laser induced particle field. The time interval of each frame is 1μs, the angular range of the four references is 14°, and the diffraction efficiency of each hologram is less than 2%. After a basic analysis, this optical system could catch more holograms through a compact design.
2. Schematic memory components converge within angular gyrus during retrieval
Science.gov (United States)
Wagner, Isabella C; van Buuren, Mariët; Kroes, Marijn CW; Gutteling, Tjerk P; van der Linden, Marieke; Morris, Richard G; Fernández, Guillén
2015-01-01
Mental schemas form associative knowledge structures that can promote the encoding and consolidation of new and related information. Schemas are facilitated by a distributed system that stores components separately, presumably in the form of inter-connected neocortical representations. During retrieval, these components need to be recombined into one representation, but where exactly such recombination takes place is unclear. Thus, we asked where different schema components are neuronally represented and converge during retrieval. Subjects acquired and retrieved two well-controlled, rule-based schema structures during fMRI on consecutive days. Schema retrieval was associated with midline, medial-temporal, and parietal processing. We identified the multi-voxel representations of different schema components, which converged within the angular gyrus during retrieval. Critically, convergence only happened after 24-hour-consolidation and during a transfer test where schema material was applied to novel but related trials. Therefore, the angular gyrus appears to recombine consolidated schema components into one memory representation. DOI: http://dx.doi.org/10.7554/eLife.09668.001 PMID:26575291
3. ELECTRON ANGULAR DISTRIBUTIONS IN DISSOCIATIVE PHOTOIONIZATION OF THE HYDROGEN MOLECULE.
Directory of Open Access Journals (Sweden)
Jhon F. Pérez-Torres
2009-06-01
Full Text Available Se propone un método para calcular distribuciones angulares de electrones ionizados en la molécula de hidrógeno fija en el espacio sometida a pulsos láser intensos y ultracortos, basado en la solución desde primeros principios de la ecuación de Schrödinger dependiente del tiempo. Esta solución nos permite tener una visión temporal de la interferencias generadas en el canal de ionización disociativa (en el espectro de energía cinética de los protones debido a la presencia de la autoionización de estados doblemente excitados de la molécula de hidrógeno. Se muestra específicamente cómo la autoionización durante el proceso de fotoionización disociativa también puede inducir una asimetría en la distribución angular del electrón ionizado con respecto a la inversión nuclear, un efecto no intuitivo a pesar de estar tratando con un sistema homonuclear.
4. Angular momentum effects in electron scattering from atoms
International Nuclear Information System (INIS)
Williams, J F; Cvejanovie, D; Samarin, S; Pravica, L; Napier, S; Sergeant, A
2007-01-01
This paper concerns angular momentum-dependent phenomena in excited gas-phase atoms using incident photons or electrons in scattering experiments. A brief overview indicates the main capabilities of experimental techniques and the information which can be deduced about atomic structure and dynamics from conservation of momenta with measurement of polarization and detection of the number of emerging electrons, photons and ions. Maximum information may be obtained when the incident particles and the targets are state-selected both before and after scattering. The fundamental scattering amplitudes and their relative phases, and consequently derived quantities such as the parameters describing the electron charge cloud of the atomic target, have enabled significant advances of understanding of collision mechanisms. The angular momentum-dependent scattering probabilities change when, for example, the spin-orbit interaction for the target electrons becomes large compared with the Coulomb electron-electron interactions and also when electron exchange and the relative orientation of the electron spins change. Several examples are discussed to indicate significant principles and recent advances. Major contributions to this field from the technology associated with electron spin production and detection time, as well as time-coincidence detection, are discussed. New results from the authors' laboratory are presented
5. Angular dependent transport of auroral electrons in the upper atmosphere
International Nuclear Information System (INIS)
Lummerzheim, D.; Rees, M.H.
1989-01-01
The transport of auroral electrons through the upper atmosphere is analyzed. The transport equation is solved using a discrete ordinate method including elastic and inelastic scattering of electrons resulting in changes of pitch angle, and degradation in energy as the electrons penetrate into the atmosphere. The transport equation is solved numerically for the electron intensity as a function of altitude, pitch angle, and energy. In situ measurements of the pitch angle and energy distribution of precipitating electrons over an auroral arc provide boundary conditions for the calculation. The electron spectra from various locations over the aurora present a variety of anisotropic pitch angle distributions and energy spectra. Good agreement is found between the observed backscattered electron energy spectra and model predictions. Differences occur at low energies (below 500 eV) in the structure of the pitch angle distribution. Model calculations were carried out with various different phase functions for elastic and inelastic collisions to attempt changing the angular scattering, but the observed pitch angle distributions remain unexplained. We suggest that mechanisms other than collisional scattering influence the angular distribution of auroral electrons at or below 300 km altitude in the low energy domain. (author)
6. Statistical Angular Resolution Limit for Ultrawideband MIMO Noise Radar
Directory of Open Access Journals (Sweden)
Xiaoli Zhou
2015-01-01
Full Text Available The two-dimensional angular resolution limit (ARL of elevation and azimuth for MIMO radar with ultrawideband (UWB noise waveforms is investigated using statistical resolution theory. First, the signal model of monostatic UWB MIMO noise radar is established in a 3D reference frame. Then, the statistical angular resolution limits (SARLs of two closely spaced targets are derived using the detection-theoretic and estimation-theoretic approaches, respectively. The detection-theoretic approach is based on the generalized likelihood ratio test (GLRT with given probabilities of false alarm and detection, while the estimation-theoretic approach is based on Smith’s criterion which involves the Cramér-Rao lower bound (CRLB. Furthermore, the relationship between the two approaches is presented, and the factors affecting the SARL, that is, detection parameters, transmit waveforms, array geometry, signal-to-noise ratio (SNR, and parameters of target (i.e., radar cross section (RCS and direction, are analyzed. Compared with the conventional radar resolution theory defined by the ambiguity function, the SARL reflects the practical resolution ability of radar and can provide an optimization criterion for radar system design.
7. Scale factor measure method without turntable for angular rate gyroscope
Science.gov (United States)
Qi, Fangyi; Han, Xuefei; Yao, Yanqing; Xiong, Yuting; Huang, Yuqiong; Wang, Hua
2018-03-01
In this paper, a scale factor test method without turntable is originally designed for the angular rate gyroscope. A test system which consists of test device, data acquisition circuit and data processing software based on Labview platform is designed. Taking advantage of gyroscope's sensitivity of angular rate, a gyroscope with known scale factor, serves as a standard gyroscope. The standard gyroscope is installed on the test device together with a measured gyroscope. By shaking the test device around its edge which is parallel to the input axis of gyroscope, the scale factor of the measured gyroscope can be obtained in real time by the data processing software. This test method is fast. It helps test system miniaturized, easy to carry or move. Measure quarts MEMS gyroscope's scale factor multi-times by this method, the difference is less than 0.2%. Compare with testing by turntable, the scale factor difference is less than 1%. The accuracy and repeatability of the test system seems good.
8. Preequilibrium GDR excitation and entrance channel angular momentum effects
International Nuclear Information System (INIS)
Sandoli, M.; Campajola, L.; De Rosa, A.; D'Onofrio, A.; La Commara, M.; Ordine, A.; Pierroutsakou, D.; Roca, V.; Romano, M.; Romoli, M.; Terrasi, F.; Trotta, M.; Cardella, G.; Papa, M.; Pappalardo, G.; Rizzo, F.; Alamanos, N.; Auger, F.; Gillibert, A.
1997-01-01
The energy spectra of the γ-rays emitted in the 35 Cl+ 92 Mo reaction at incident energy E=260 MeV were measured in coincidence with the ejectiles produced in dissipative reaction events. The cumulative energy spectrum of the γ-rays coming from the decay of the ejectiles was calculated within the statistical model and its comparison to the experimental spectrum evidences an excess in the data for E γ =8 to 12 MeV. Such an excess, fitted with a Lorentz curve, is attributed to the preequilibrium GDR γ-decay of the intermediate dinuclear system. The centroid energy of the Lorentz curve corresponds to a dipole oscillation along the symmetry axis of the system and its width is found to be comparable to that of the ground state GDR low energy component of the deformed dinucleus. The small quantal dispersion Δl=(10.3±0.1)ℎ of the entrance channel angular momentum, determined by analysing the dissipative fragment angular distribution in the framework of the Strutinsky model, is suggested to limit the broadening of the preequilibrium GDR width. (orig.)
9. Angular distribution in the neutron-induced fission of actinides
Directory of Open Access Journals (Sweden)
Leong L.S.
2013-12-01
Full Text Available Above 1 MeV of incident neutron energy the fission fragment angular distribution (FFAD has generally a strong anisotropic behavior due to the combination of the incident orbital momentum and the intrinsic spin of the fissioning nucleus. This effect has to be taken into account for the efficiency estimation of devices used for fission cross section measurements. In addition it bears information on the spin deposition mechanism and on the structure of transitional states. We designed and constructed a detection device, based on Parallel Plate Avalanche Counters (PPAC, for measuring the fission fragment angular distributions of several isotopes, in particular 232Th. The measurement has been performed at n_TOF at CERN taking advantage of the very broad energy spectrum of the neutron beam. Fission events were recognized by back to back detection in coincidence in two position-sensitive detectors surrounding the targets. The detection efficiency, depending mostly on the stopping of fission fragments in backings and electrodes, has been computed with a Geant4 simulation and validated by the comparison to the measured case of 235U below 3 keV where the emission is isotropic. In the case of 232Th, the result is in good agreement with previous data below 10 MeV, with a good reproduction of the structures associated to vibrational states and the opening of second chance fission. In the 14 MeV region our data are much more accurate than previous ones which are broadly scattered.
10. γ - γ angular correlation in sup(100)Ru
International Nuclear Information System (INIS)
Kenchian, G.; Leljbman, I.D.G.; Cruz, M.T.F.
1990-01-01
The gamma-gamma directional angular correlations of coincident transitions have been measured in sup(100)Ru nuclide, following the β sup(+) and electron capture of sup(100)Rh using an angular correlation automatic spectrometer with two Ge(Li) detectors. The sup(100)Rh source has been produced with sup(100)Ru(p,n) sup(100)Rh reaction, using the proton beam of the Cyclotron Acelerator and enriched sup(100)Ru isotope. We have measured 30 direct cascades and 11 triple cascades. The spin and the parity of the 1865 KeV, 1881 KeV, 2099 KeV, 2167 KeV, 2241 KeV, 2517 KeV, and 3070 KeV levels have been established and multipole mixing ratios (δ) for 21 transitions have been obtained, 12 for the first time. Multipole mixing ratios Q sup(2)(E0/E2) has been also measured in the 2 sup(+) sub(2) → 2 sup(+) sub(1) transition. (author)
11. Phase Resolved Angular Velocity Control of Cross Flow Turbines
Science.gov (United States)
Strom, Benjamin; Brunton, Steven; Polagye, Brian
2015-11-01
Cross flow turbines have a number of operational advantages for the conversion of kinetic energy in marine or fluvial currents, but they are often less efficient than axial flow devices. Here a control scheme is presented in which the angular velocity of a cross flow turbine with two straight blades is prescribed as a function of azimuthal blade position, altering the time-varying effective angle of attack. Flume experiments conducted with a scale model turbine show approximately an 80% increase in turbine efficiency versus optimal constant angular velocity and constant resistive torque control schemes. Torque, drag, and lateral forces on one- and two-bladed turbines are analyzed and interpreted with bubble flow visualization to develop a simple model that describes the hydrodynamics responsible for the observed increase in mean efficiency. Challenges associated with implementing this control scheme on commercial-scale devices are discussed. If solutions are found, the performance increase presented here may impact the future development of cross flow turbines.
12. On the Angular Momentum Loss of Tropical Cyclones: An f-Plane Approximation
Science.gov (United States)
Kang, Hyun-Gyu; Cheong, Hyeong-Bin; Kim, Won-Ho
2018-02-01
The angular momentum for ideal axisymmetric tropical cyclones on the f-plane is investigated with a focus on the total-volume integrated quantity. Budget analysis of the momentum equation at cylindrical coordinates shows that a tropical cyclone loses angular momentum during its development and mature stages due to the dynamical difference between the viscous inward-flow near the surface and the angular momentum conserving outward-flow aloft. The total relative angular momentum of a tropical cyclone, as a result, can be negative (i.e., implying anticyclonic rotation as a whole) despite intense cyclonic wind in the tropospheric layers. This anticyclonic rotation was measured in terms of the super-rotation ratio, the ratio of total relative angular momentum to the planetary angular momentum. Simulations with the numerical model of Weather Research and Forecasting (WRF) version 3.4.1 was found to be in favor of the theoretical angular-momentum budget analysis. It was revealed in the numerical simulations that the super-rotation ratio was negative, indicating a sub-rotation, as was predicted by analysis. The sub-rotation ratio was found to be less than one percent for typical tropical cyclones. To show the angular momentum decrease even in the decaying stage, numerical simulations where the thermal forcing by sea surface temperature switched off in the mature stage were carried out. In support of the angular momentum budget analysis, the results indicated that the angular momentum also decreases for a while soon after the forcing was eliminated.
13. A new unity for angular measurements in strabismus
Directory of Open Access Journals (Sweden)
Harley E. A. Bicas
2014-10-01
Full Text Available The practical advantages of quantifying an angle by a ratio of linear lengths instead of arcs of circles has led to the definition of the prism-diopter, a conventional unity for numbering prisms and measuring strabismic deviations. However, a major inconvenience of using prism-diopter unities to express angular measurements is the non-linearity of the scale, which reaches an infinite value for the angle of 90º, then becomes negative, with decreasing magnitudes for increasing angles between 90º and 180º. As a consequence, arithmetical operations and comparisons of angles measured by such unities present errors of very great magnitudes. In order to retain the advantages of defining an angle by straight line dimensions but to diminish the severe inconveniences of this method, a new definition of the prism-diopter is proposed. Here, instead of defining the prism-diopter by the asymmetrical condition, the conception of this new unity is based on a geometrically symmetrical condition; that of the relationship of an isosceles triangle (where the leg is perpendicular to the bisector of the angle and the bisector itself . The condition of symmetry for the definition of the new unity represents a conceptual advance because it reproduces the already well accepted, conventional criteria for quantifying the value of a prism, that of its minimum deviation. Furthermore, it corresponds to the most commonly observed clinical conditions of binocular balance. The absolute differences between the unitary values of the prism-diopter and that of the new unity are negligible (0.0025%, but the scale of values expressed by the new unity is closer to the ideal scale of angular measurements. (With the new unity, the infinite value is only reached for an angle of 180º and the errors due to arithmetical operations are much smaller. Numerical examples showing the advantages of using the new unity of angular measurements instead of the prism-diopter are presented. A
14. A new unity for angular measurements in strabismus.
Science.gov (United States)
Bicas, Harley E A
2014-10-01
The practical advantages of quantifying an angle by a ratio of linear lengths instead of arcs of circles has led to the definition of the prism-diopter, a conventional unity for numbering prisms and measuring strabismic deviations. However, a major inconvenience of using prism-diopter unities to express angular measurements is the non-linearity of the scale, which reaches an infinite value for the angle of 90º, then becomes negative, with decreasing magnitudes for increasing angles between 90º and 180º. As a consequence, arithmetical operations and comparisons of angles measured by such unities present errors of very great magnitudes. In order to retain the advantages of defining an angle by straight line dimensions but to diminish the severe inconveniences of this method, a new definition of the prism-diopter is proposed. Here, instead of defining the prism-diopter by the asymmetrical condition, the conception of this new unity is based on a geometrically symmetrical condition; that of the relationship of an isosceles triangle (where the leg is perpendicular to the bisector of the angle and the bisector itself ). The condition of symmetry for the definition of the new unity represents a conceptual advance because it reproduces the already well accepted, conventional criteria for quantifying the value of a prism, that of its minimum deviation. Furthermore, it corresponds to the most commonly observed clinical conditions of binocular balance. The absolute differences between the unitary values of the prism-diopter and that of the new unity are negligible (0.0025%), but the scale of values expressed by the new unity is closer to the ideal scale of angular measurements. (With the new unity, the infinite value is only reached for an angle of 180º and the errors due to arithmetical operations are much smaller.) Numerical examples showing the advantages of using the new unity of angular measurements instead of the prism-diopter are presented. A mathematical
15. Cosmology from angular size counts of extragalactic radio sources
International Nuclear Information System (INIS)
Kapahi, V.K.
1975-01-01
The cosmological implications of the observed angular sizes of extragalactic radio sources are investigated using (i) the log N-log theta relation, where N is the number of sources with an angular size greater than a value theta, for the complete sample of 3CR sources, and (ii) the thetasub(median) vs flux density (S) relation derived from the 3CR, the All-sky, and the Ooty occulation surveys, spanning a flux density range of about 300:1. The method of estimating the expected N(theta) and thetasub(m)(S) relations for a uniform distribution of sources in space is outlined. Since values of theta>approximately 100second arc in the 3C sample arise from sources of small z, the slope of the N(theta) relation in this range is practically independent of the world model and the distribution of source sizes, but depends strongly on the radio luminosity function (RLF). From the observed slope the RLF is derived in the luminosity range of about 10 23 178 26 W Hz -1 sr -1 to be of the form rho(P)dP proportional to Psup(-2.1)dP. It is shown that the angular size data provide independent evidence of evolution in source properties with epoch. It is difficult to explain the data with the simple steady-state theory even if identified QSOs are excluded from ths source samples and a local deficiency of strong source is postulated. The simplest evolutionary scheme that fits the data in the Einstein-de Sitter cosmology indicates that (a) the local RLF steepens considerably at high luminosities, (b) the comoving density of high luminosity sources increases with z in a manner similar to that implied by the log N-log S data and by the V/Vsub(m) test for QSOs, and (c) the mean physical sizes of radio sources evolve with z approximately as (1+z) -1 . Similar evolutionary effects appear to be present for QSOs as well as radio galaxies. (author)
16. Angular Spacing Control for Segmented Data Pages in Angle-Multiplexed Holographic Memory
Science.gov (United States)
Kinoshita, Nobuhiro; Muroi, Tetsuhiko; Ishii, Norihiko; Kamijo, Koji; Kikuchi, Hiroshi; Shimidzu, Naoki; Ando, Toshio; Masaki, Kazuyoshi; Shimizu, Takehiro
2011-09-01
To improve the recording density of angle-multiplexed holographic memory, it is effective to increase the numerical aperture of the lens and to shorten the wavelength of the laser source as well as to increase the multiplexing number. The angular selectivity of a hologram, which determines the multiplexing number, is dependent on the incident angle of not only the reference beam but also the signal beam to the holographic recording medium. The actual signal beam, which is a convergent or divergent beam, is regarded as the sum of plane waves that have different propagation directions, angular selectivities, and optimal angular spacings. In this paper, focusing on the differences in the optimal angular spacing, we proposed a method to control the angular spacing for each segmented data page. We investigated the angular selectivity of a hologram and crosstalk for segmented data pages using numerical simulation. The experimental results showed a practical bit-error rate on the order of 10-3.
17. Solution of neutron transport equation using Daubechies' wavelet expansion in the angular discretization
International Nuclear Information System (INIS)
Cao Liangzhi; Wu Hongchun; Zheng Youqi
2008-01-01
Daubechies' wavelet expansion is introduced to discretize the angular variables of the neutron transport equation when the neutron angular flux varies very acutely with the angular directions. An improvement is made by coupling one-dimensional wavelet expansion and discrete ordinate method to make two-dimensional angular discretization efficient and stable. The angular domain is divided into several subdomains for treating the vacuum boundary condition exactly in the unstructured geometry. A set of wavelet equations coupled with each other is obtained in each subdomain. An iterative method is utilized to decouple the wavelet moments. The numerical results of several benchmark problems demonstrate that the wavelet expansion method can provide more accurate results by lower-order expansion than other angular discretization methods
18. Energy, momentum and angular momentum conservations in de Sitter gravity
International Nuclear Information System (INIS)
Lu, Jia-An
2016-01-01
In de Sitter (dS) gravity, where gravity is a gauge field introduced to realize the local dS invariance of the matter field, two kinds of conservation laws are derived. The first kind is a differential equation for a dS-covariant current, which unites the canonical energy-momentum (EM) and angular momentum (AM) tensors. The second kind presents a dS-invariant current which is conserved in the sense that its torsion-free divergence vanishes. The dS-invariant current unites the total (matter plus gravity) EM and AM currents. It is well known that the AM current contains an inherent part, called the spin current. Here it is shown that the EM tensor also contains an inherent part, which might be observed by its contribution to the deviation of the dust particle’s world line from a geodesic. All the results are compared to the ordinary Lorentz gravity. (paper)
19. Attitude angular measurement system based on MEMS accelerometer
Science.gov (United States)
Luo, Lei
2014-09-01
For the purpose of monitoring the attitude of aircraft, an angular measurement system using a MEMS heat convection accelerometer is presented in this study. A double layers conditioning circuit that center around the single chip processor is designed and built. Professional display software with the RS232 standard is used to communicate between the sensor and the computer. Calibration experiments were carried out to characterize the measuring system with the range of - 90°to +90°. The curves keep good linearity with the practical angle. The maximum deviation occurs at the 90°where the value is 2.8°.The maximum error is 1.6% and the repeatability is measured to be 2.1%. Experiments proved that the developed measurement system is capable of measuring attitude angle.
20. Multiple orbital angular momentum generated by dielectric hybrid phase element
Science.gov (United States)
Wang, Xuewen; Kuchmizhak, Aleksandr; Hu, Dejiao; Li, Xiangping
2017-09-01
Vortex beam carrying multiple orbital angular momentum provides a new degree of freedom to manipulate light leading to the various exciting applications as trapping, quantum optics, information multiplexing, etc. Helical wavefront can be generated either via the geometric or the dynamic phase arising from a space-variant birefringence (q-plate) or from phase accumulation through propagation (spiral-phase-plate), respectively. Using fast direct laser writing technique we fabricate and characterize novel hybrid q-plate generating vortex beam simultaneously carrying two different high-order topological charges, which arise from the spin-orbital conversion and the azimuthal height variation of the recorded structures. We approve the versatile concept to generate multiple-OAM vortex beams combining the spin-orbital interaction and the phase accumulation in a single micro-scale device, a hybrid dielectric phase plate.
1. Ultrafine grained steels processed by equal channel angular pressing
International Nuclear Information System (INIS)
Shin, Dong Hyuk; Park, Kyung-Tae
2005-01-01
Recent development of ultrafine grained (UFG) low carbon steels by using equal channel angular pressing (ECAP) and their room temperature tensile properties are reviewed, focusing on the strategies overcoming their inherent mechanical drawbacks. In addition to ferrite grain refinement, when proper post heat treatments are imposed, carbon atom dissolution from pearlitic cementite during ECAP can be utilized for microstructural modification such as uniform distribution of nano-sized cementite particles or microalloying element carbides inside UFG ferrite grains and fabrication of UFG ferrite/martensite dual phase steel. The utilization of nano-sized particles is effective on improving thermal stability of UFG low carbon ferrite/pearlite steel but less effective on improving its tensile properties. By contrast, UFG ferrite/martensite dual phase steel exhibits an excellent combination of ultrahigh strength, large uniform elongation and extensive strain hardenability
2. Intracycle angular velocity control of cross-flow turbines
Science.gov (United States)
Strom, Benjamin; Brunton, Steven L.; Polagye, Brian
2017-08-01
Cross-flow turbines, also known as vertical-axis turbines, are attractive for power generation from wind and water currents. Some cross-flow turbine designs optimize unsteady fluid forces and maximize power output by controlling blade kinematics within one rotation. One established method is to dynamically pitch the blades. Here we introduce a mechanically simpler alternative: optimize the turbine rotation rate as a function of angular blade position. We demonstrate experimentally that this approach results in a 59% increase in power output over standard control methods. Analysis of fluid forcing and blade kinematics suggest that power increase is achieved through modification of the local flow conditions and alignment of fluid force and rotation rate extrema. The result is a low-speed, structurally robust turbine that achieves high efficiency and could enable a new generation of environmentally benign turbines for renewable power generation.
3. Orbital angular momentum parton distributions in quark models
International Nuclear Information System (INIS)
Scopetta, S.; Vento, V.
2000-01-01
At the low energy, hadronic, scale we calculate Orbital Angular Momentum (OAM) twist-two parton distributions for the relativistic MIT bag model and for nonrelativistic quark models. We reach the scale of the data by leading order evolution in perturbative QCD. We confirm that the contribution of quarks and gluons OAM to the nucleon spin grows with Q 2 , and it can be relevant at the experimental scale, even if it is negligible at the hadronic scale, irrespective of the model used. The sign and shape of the quark OAM distribution at high Q 2 may depend strongly on the relative size of the OAM and spin distributions at the hadronic scale. Sizeable quark OAM distributions at the hadronic scale, as proposed by several authors, can produce the dominant contribution to the nucleon spin at high Q 2 . (author)
4. THE EFFECTS OF ANGULAR MOMENTUM ON HALO PROFILES
Energy Technology Data Exchange (ETDEWEB)
Lentz, Erik W; Rosenberg, Leslie J [Physics Department, University of Washington, Seattle, WA 98195-1580 (United States); Quinn, Thomas R, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Astronomy Department, University of Washington, Seattle, WA 98195-1580 (United States)
2016-05-10
The near universality of DM halo density profiles provided by N -body simulations proved to be robust against changes in total mass density, power spectrum, and some forms of initial velocity dispersion. Here we study the effects of coherently spinning up an isolated DM-only progenitor on halo structure. Halos with spins within several standard deviations of the simulated mean ( λ ≲ 0.20) produce profiles with negligible deviations from the universal form. Only when the spin becomes quite large ( λ ≳ 0.20) do departures become evident. The angular momentum distribution also exhibits a near universal form, which is also independent of halo spin up to λ ≲ 0.20. A correlation between these epidemic profiles and the presence of a strong bar in the virialized halo is also observed. These bar structures bear resemblance to the radial orbit instability in the rotationless limit.
5. Nucleon form factors, generalized parton distributions and quark angular momentum
Energy Technology Data Exchange (ETDEWEB)
Diehl, Markus [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kroll, Peter [Bergische Univ., Wuppertal (Germany). Fachbereich Physik; Regensburg Univ. (Germany). Institut fuer Theoretische Physik
2013-02-15
We extract the individual contributions from u and d quarks to the Dirac and Pauli form factors of the proton, after a critical examination of the available measurements of electromagnetic nucleon form factors. From this data we determine generalized parton distributions for valence quarks, assuming a particular form for their functional dependence. The result allows us to study various aspects of nucleon structure in the valence region. In particular, we evaluate Ji's sum rule and estimate the total angular momentum carried by valence quarks at the scale {mu}=2 GeV to be J{sup u}{sub v}=0.230{sup +0.009}{sub -0.024} and J{sup d}{sub v}=-0.004{sup +0.010}{sub -0.016}.
6. Compact and high-resolution optical orbital angular momentum sorter
Directory of Open Access Journals (Sweden)
Chenhao Wan
2017-03-01
Full Text Available A compact and high-resolution optical orbital angular momentum (OAM sorter is proposed and demonstrated. The sorter comprises a quadratic fan-out mapper and a dual-phase corrector positioned in the pupil plane and the Fourier plane, respectively. The optical system is greatly simplified compared to previous demonstrations of OAM sorting, and the performance in resolution and efficiency is maintained. A folded configuration is set up using a single reflective spatial light modulator (SLM to demonstrate the validity of the scheme. The two phase elements are implemented on the left and right halves of the SLM and connected by a right-angle prism. Experimental results demonstrate the high resolution of the compact OAM sorter, and the current limit in efficiency can be overcome by replacing with transmissive SLMs and removing the beam splitters. This novel scheme paves the way for the miniaturization and integration of high-resolution OAM sorters.
7. Angular dependence of the coercivity in arrays of ferromagnetic nanowires
International Nuclear Information System (INIS)
Holanda, J.; Silva, D.B.O.; Padrón-Hernández, E.
2015-01-01
We present a new magnetic model for polycrystalline nanowires arrays in porous anodic aluminum oxide. The principal consideration here is the crystalline structure and the morphology of the wires and them the dipolar interactions between the crystals into the wire. Other aspect here is the direct calculation of the dipolar energy for the interaction of one wire with the others in the array. The free energy density was formulated for polycrystalline nanowires arrays in order to determinate the anisotropy effective field. It was using the microstructure study by scanning and transmission electron microscopy for the estimation of the real structure of the wires. After the structural analysis we used the angular dependences for the coercivity field and for the remnant magnetization to determine the properties of the wires. All analysis were made by the theory treatment proposed by Stoner and Wohlfarth
8. Baryon-to-dark matter ratio from random angular fields
International Nuclear Information System (INIS)
McDonald, John
2013-01-01
We consider the baryon-to-dark matter ratio in models where the dark matter and baryon densities depend on angular fields θ d and θ b according to ρ d ∝θ d α and ρ b ∝θ b β , with all values of θ d and θ b being equally probable in a given randomly-selected domain. Under the assumption that anthropic selection depends primarily on the baryon density in galaxies at spherical collapse, we show that the probability density function for the baryon-to-dark matter ratio r = Ω B /Ω DM is purely statistical in nature and is independent of anthropic selection. We compute the probability density function for r as a function of α and β and show that the observed value of the baryon-to-dark matter ratio, r ≈ 1/5, is natural in this framework
9. Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials
International Nuclear Information System (INIS)
Aquilanti, V; Marinelli, D; Marzuoli, A
2014-01-01
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed
10. Multichannel singular spectrum analysis of the axial atmospheric angular momentum
Directory of Open Access Journals (Sweden)
Leonid Zotov
2017-11-01
Full Text Available Earth's variable rotation is mainly produced by the variability of the AAM (atmospheric angular momentum. In particular, the axial AAM component χ3, which undergoes especially strong variations, induces changes in the Earth's rotation rate. In this study we analysed maps of regional input into the effective axial AAM from 1948 through 2011 from NCEP/NCAR reanalysis. Global zonal circulation patterns related to the LOD (length of day were described. We applied MSSA (Multichannel Singular Spectrum Analysis jointly to the mass and motion components of AAM, which allowed us to extract annual, semiannual, 4-month, quasi-biennial, 5-year, and low-frequency oscillations. PCs (Principal components strongly related to ENSO (El Nino southern oscillation were released. They can be used to study ENSO-induced changes in pressure and wind fields and their coupling to LOD. The PCs describing the trends have captured slow atmospheric circulation changes possibly related to climate variability.
11. Low-crosstalk orbital angular momentum fiber coupler design.
Science.gov (United States)
Zhang, Zhishen; Gan, Jiulin; Heng, Xiaobo; Li, Muqiao; Li, Jiong; Xu, Shanhui; Yang, Zhongmin
2017-05-15
A fiber coupler for low-crosstalk orbital angular momentum mode beam splitter is proposed with the structure of two separate and parallel microfibers. By properly setting the center-to-center distance between microfibers, the crosstalk is less than -20 dB, which means that the purity of the needed OAM mode in output port is higher than 99%. For a fixed overlapping length, high coupling efficiency (>97%) is achieved in 1545-1560 nm. The operating wavelength is tuned to the whole C-band by using the thermosensitive liquid. So the designed coupler can achieve the tunable coupling ratio over the whole C-band, which is a prospective component for the further OAM fiber system.
12. Angular correlation of annihilation photons in ice single crystals
DEFF Research Database (Denmark)
Mogensen, O. E.; Kvajic, G.; Eldrup, Morten Mostgaard
1971-01-01
-lattice vectors g⃗ on the direction perpendicular to the slits and the sample surface. The relative area of the central plus the side peaks was (15.2 ± 0.4)% for all curves. All the peaks are interpreted as due to parapositronium annihilation. The side peaks are explained as evidence for the positronium center......Linear-slit angular-correlation curves were obtained at - 148 °C for the [0001], [10¯10], and [11¯20] directions in single crystals of ice. Besides the narrow central peak, pronounced narrow side peaks were also observed. They occurred at angles θ=2πℏgz/mc, where gz is the projection of reciprocal...
13. Integrated spectral study of small angular diameter galactic open clusters
Science.gov (United States)
Clariá, J. J.; Ahumada, A. V.; Bica, E.; Pavani, D. B.; Parisi, M. C.
2017-10-01
This paper presents flux-calibrated integrated spectra obtained at Complejo Astronómico El Leoncito (CASLEO, Argentina) for a sample of 9 Galactic open clusters of small angular diameter. The spectra cover the optical range (3800-6800 Å), with a resolution of ˜14 Å. With one exception (Ruprecht 158), the selected clusters are projected into the fourth Galactic quadrant (282o evaluate their membership status. The current cluster sample complements that of 46 open clusters previously studied by our group in an effort to gather a spectral library with several clusters per age bin. The cluster spectral library that we have been building is an important tool to tie studies of resolved and unresolved stellar content.
14. Detecting Lateral Motion using Light’s Orbital Angular Momentum
Science.gov (United States)
Cvijetic, Neda; Milione, Giovanni; Ip, Ezra; Wang, Ting
2015-01-01
Interrogating an object with a light beam and analyzing the scattered light can reveal kinematic information about the object, which is vital for applications ranging from autonomous vehicles to gesture recognition and virtual reality. We show that by analyzing the change in the orbital angular momentum (OAM) of a tilted light beam eclipsed by a moving object, lateral motion of the object can be detected in an arbitrary direction using a single light beam and without object image reconstruction. We observe OAM spectral asymmetry that corresponds to the lateral motion direction along an arbitrary axis perpendicular to the plane containing the light beam and OAM measurement axes. These findings extend OAM-based remote sensing to detection of non-rotational qualities of objects and may also have extensions to other electromagnetic wave regimes, including radio and sound. PMID:26493681
15. Detecting Lateral Motion using Light's Orbital Angular Momentum.
Science.gov (United States)
Cvijetic, Neda; Milione, Giovanni; Ip, Ezra; Wang, Ting
2015-10-23
Interrogating an object with a light beam and analyzing the scattered light can reveal kinematic information about the object, which is vital for applications ranging from autonomous vehicles to gesture recognition and virtual reality. We show that by analyzing the change in the orbital angular momentum (OAM) of a tilted light beam eclipsed by a moving object, lateral motion of the object can be detected in an arbitrary direction using a single light beam and without object image reconstruction. We observe OAM spectral asymmetry that corresponds to the lateral motion direction along an arbitrary axis perpendicular to the plane containing the light beam and OAM measurement axes. These findings extend OAM-based remote sensing to detection of non-rotational qualities of objects and may also have extensions to other electromagnetic wave regimes, including radio and sound.
16. Nucleon form factors, generalized parton distributions and quark angular momentum
International Nuclear Information System (INIS)
Diehl, Markus; Kroll, Peter; Regensburg Univ.
2013-02-01
We extract the individual contributions from u and d quarks to the Dirac and Pauli form factors of the proton, after a critical examination of the available measurements of electromagnetic nucleon form factors. From this data we determine generalized parton distributions for valence quarks, assuming a particular form for their functional dependence. The result allows us to study various aspects of nucleon structure in the valence region. In particular, we evaluate Ji's sum rule and estimate the total angular momentum carried by valence quarks at the scale μ=2 GeV to be J u v =0.230 +0.009 -0.024 and J d v =-0.004 +0.010 -0.016 .
17. Temperature and angular dependence of substrate response in SEGR
International Nuclear Information System (INIS)
Mouret, I.; Allenspach, M.; Schrimpf, R.D.; Brews, J.R.; Galloway, K.F.
1994-01-01
This work examines the role of the substrate response in determining the temperature and angular dependence of Single-Event Gate Rupture (SEGR). Experimental data indicate that the likelihood of SEGR increases when the temperature of the device is increased or when the incident angle is made closer to normal. In this work, simulations are used to explore this influence of high temperature on SEGR and to support physical explanations for this effect. The reduced hole mobility at high temperature causes the hole concentration at the oxide-silicon interface to be greater, increasing the transient oxide field near the strike position. In addition, numerical calculations show that the transient oxide field decreases as the ion's angle of incidence is changed from normal. This decreased field suggests a lowered likelihood for SEGR, in agreement with the experimental trend
18. LEGEND2007, Angular Distribution Table Calculations in ENDF Format
International Nuclear Information System (INIS)
2007-01-01
1 - Description of program or function: LEGEND calculates linearly interpolable tabulated angular distributions starting from data in the ENDF/B format. IAEA1310/11: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: Legend VERS. 2007-1 (JAN. 2007): checked against all ENDF/B=VII; increased max. points from 60,000 to 240,000
19. Integral equations for four identical particles in angular momentum representation
International Nuclear Information System (INIS)
1975-01-01
In integral equations of motion for a system of four identical spinless particles with central pair interactions, transition is realized from the representation of relative Jacobi momenta to the representation of their moduli and relative angular moments. As a result, the variables associated with the rotation of the system as a whole are separated in the equations. The integral equations of motion for four particles are reduced to the form of an infinite system of three-demensional integral equations. The four-particle kinematic factors contained in integral kernels are expressed in terms of three-particle type kinematic factors. In the case of separable two-particle interaction, the equations of motion for four particles have the form of an infinite system of two-dimensional integral equations
20. Development of an optical fiber sensor for angular displacement measurements.
Science.gov (United States)
Jung, Gu-In; Kim, Ji-Sun; Lee, Tae-Hee; Choi, Ju-Hyeon; Oh, Han-Byeol; Kim, A-Hee; Eom, Gwang-Moon; Lee, Jeong-Hwan; Chung, Soon-Cheol; Park, Jong-Rak; Lee, Young-Jae; Park, Hee-Jung; Jun, Jae-Hoon
2014-01-01
For diagnostic and therapeutic purposes, the joint angle measurement of a patient after an accident or a surgical operation is significant for monitoring and evaluating the recovering process. This paper proposed an optical fiber sensor for the measurement of angular displacement. The effect of beveled fiber angle on the detected light signal was investigated to find an appropriate mathematical model. Beveled fiber tips redirected the light over a range of angles away from the fiber axis. Inverse polynomial models were applied to directly obtain and display the joint angle change in real time with the Lab-VIEW program. The actual joint angle correlated well with the calculated LabVIEW output angle over the test range. The proposed optical sensor is simple, cost effective, small in size, and can evaluate the joint angle in real time. This method is expected to be useful in the field of rehabilitation and sport science.
1. Catenary optics for achromatic generation of perfect optical angular momentum
Science.gov (United States)
Pu, Mingbo; Li, Xiong; Ma, Xiaoliang; Wang, Yanqin; Zhao, Zeyu; Wang, Changtao; Hu, Chenggang; Gao, Ping; Huang, Cheng; Ren, Haoran; Li, Xiangping; Qin, Fei; Yang, Jing; Gu, Min; Hong, Minghui; Luo, Xiangang
2015-01-01
The catenary is the curve that a free-hanging chain assumes under its own weight, and thought to be a “true mathematical and mechanical form” in architecture by Robert Hooke in the 1670s, with nevertheless no significant phenomena observed in optics. We show that the optical catenary can serve as a unique building block of metasurfaces to produce continuous and linear phase shift covering [0, 2π], a mission that is extremely difficult if not impossible for state-of-the-art technology. Via catenary arrays, planar optical devices are designed and experimentally characterized to generate various kinds of beams carrying orbital angular momentum (OAM). These devices can operate in an ultra-broadband spectrum because the anisotropic modes associated with the spin-orbit interaction are almost independent of the incident light frequency. By combining the optical and topological characteristics, our approach would allow the complete control of photons within a single nanometric layer. PMID:26601283
2. Texture in equal-channel angular pressed aluminum and nickel
Energy Technology Data Exchange (ETDEWEB)
Vogel, S.C.; Beyerlein, I.J.; Bourke, M.A.M.; Tome, C.N.; Rangaswamy, P. [Los Alamos National Lab., Los Alamos, NM (United States); Xu, C.; Langdon, T.G. [Univ. of Southern California, Los Angeles, CA (United States)
2002-07-01
Nano-structured metals with advantageous mechanical properties can be produced using severe plastic deformation techniques such as equal channel angular pressing (ECAP). Metals and alloys processed by ECAP have much higher yield strengths than the equivalent unprocessed material while retaining high ductilities, an extremely attractive combination of properties. Implicit in the process are the introduction of repetitive shear strains of 100% which introduce texture, the modeling of which is challenging. In this work, we present results from a neutron diffraction study on aluminum and nickel samples processed by ECAP. The results are compared to predictions from a visco-plastic self-consistent (VPSC) model. By taking into account grain-grain interactions in the model the agreement between the predicted and measured orientation distributions is improved. The results show also that the initial texture affects the texture evolution, at least up to strains of the order of {proportional_to}1, i.e. one ECAP pass. (orig.)
3. Accessing the quark orbital angular momentum with Wigner distributions
Energy Technology Data Exchange (ETDEWEB)
Lorce, Cedric [IPNO, Universite Paris-Sud, CNRS/IN2P3, 91406 Orsay, France and LPT, Universite Paris-Sud, CNRS, 91406 Orsay (France); Pasquini, Barbara [Dipartimento di Fisica, Universita degli Studi di Pavia, Pavia, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia (Italy)
2013-04-15
The quark orbital angular momentum (OAM) has been recognized as an important piece of the proton spin puzzle. A lot of effort has been invested in trying to extract it quantitatively from the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs), which are accessed in high-energy processes and provide three-dimensional pictures of the nucleon. Recently, we have shown that it is more natural to access the quark OAM from the phase-space or Wigner distributions. We discuss the concept of Wigner distributions in the context of quantum field theory and show how they are related to the GPDs and the TMDs. We summarize the different definitions discussed in the literature for the quark OAM and show how they can in principle be extracted from the Wigner distributions.
4. Accessing the quark orbital angular momentum with Wigner distributions
International Nuclear Information System (INIS)
Lorcé, Cédric; Pasquini, Barbara
2013-01-01
The quark orbital angular momentum (OAM) has been recognized as an important piece of the proton spin puzzle. A lot of effort has been invested in trying to extract it quantitatively from the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs), which are accessed in high-energy processes and provide three-dimensional pictures of the nucleon. Recently, we have shown that it is more natural to access the quark OAM from the phase-space or Wigner distributions. We discuss the concept of Wigner distributions in the context of quantum field theory and show how they are related to the GPDs and the TMDs. We summarize the different definitions discussed in the literature for the quark OAM and show how they can in principle be extracted from the Wigner distributions.
5. Angular dependence of the coercivity in arrays of ferromagnetic nanowires
Energy Technology Data Exchange (ETDEWEB)
Holanda, J. [Departamento de Física, Universidade Federal de Pernambuco, Recife 50670-901, PE (Brazil); Silva, D.B.O. [Pós-Graduação em Ciência de Materiais, Universidade Federal de Pernambuco, Recife 50670-901, PE (Brazil); Padrón-Hernández, E., E-mail: [email protected] [Departamento de Física, Universidade Federal de Pernambuco, Recife 50670-901, PE (Brazil); Pós-Graduação em Ciência de Materiais, Universidade Federal de Pernambuco, Recife 50670-901, PE (Brazil)
2015-03-15
We present a new magnetic model for polycrystalline nanowires arrays in porous anodic aluminum oxide. The principal consideration here is the crystalline structure and the morphology of the wires and them the dipolar interactions between the crystals into the wire. Other aspect here is the direct calculation of the dipolar energy for the interaction of one wire with the others in the array. The free energy density was formulated for polycrystalline nanowires arrays in order to determinate the anisotropy effective field. It was using the microstructure study by scanning and transmission electron microscopy for the estimation of the real structure of the wires. After the structural analysis we used the angular dependences for the coercivity field and for the remnant magnetization to determine the properties of the wires. All analysis were made by the theory treatment proposed by Stoner and Wohlfarth.
6. Investigation of an angular spectrum approach for pulsed ultrasound fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2013-01-01
An Angular Spectrum Approach (ASA)is formulated and employed to simulate linear pulsed ultra sound fields for high bandwidth signals. Ageometrically focused piston transducer is used as the acoustic source. Signals are cross-correlated to findthe true sound speed during the measurement to make...... the simulated and measured pulses in phase for comparisons. The calculated sound speed in the measurement is varied between 1487.45 m/s and 1487.75 m/s by using different initial values in the ASA simulation. Results from the pulsed ASA simulation susing both Field II simulated and hydrophone measured acoustic....... Optim al parameters for the ASA are found in the simulation .The RMS error of the ASA simulation is reduced from 10.9% to 2.4% for the optimal parameters when comparing to Field II simulation s. The comparison between the ASA calculated and measured pulses are illustrated and the corresponding RMS error...
7. Symmetries in the angular distribution of exclusive semileptonic B decays
CERN Document Server
Egede, Ulrik; Matias, Joaquim; Ramon, Marc; Reece, Will
2010-01-01
We discuss a method to construct observables protected against QCD uncertainties based on the angular distribution of the exclusive Bd -> K(*0}(-> Kpi) l+ l- decay. We focus on the identification and the interpretation of all the symmetries of the distribution. They constitute a key ingredient to construct a set of so-called transverse observables. We work in the framework of QCD factorization at NLO supplemented by an estimate of power-suppressed Lambda/mb corrections. A discussion of the new physics properties of two of the transverse asymmetries, AT^{(2)} and AT^{(5)}, is presented. A comparison between the transverse asymmetry AT^{(2)} and the forward-backward asymmetry shows that AT^{(2)} emerges as an improved version of it.
8. Efficient broadband third harmonic frequency conversion via angular dispersion
International Nuclear Information System (INIS)
Pennington, D.M.; Henesian, M.A.; Milam, D.; Eimerl, D.
1995-01-01
In this paper we present experimental measurements and theoretical modeling of third harmonic (3ω) conversion efficiency with optical bandwidth. Third harmonic conversion efficiency drops precipitously as the input bandwidth significantly exceeds the phase matching limitations of the conversion crystals. For Type I/Type II frequency tripling, conversion efficiency be-gins to decrease for bandwidths greater than ∼60 GHz. However, conversion efficiency corresponding to monochromatic phase-matched beams can be recovered provided that the instantaneous Propagation vectors are phase matched at all times. This is achieved by imposing angular spectral dispersion (ASD) on the input beam via a diffraction grating, with a dispersion such that the phase mismatch for each frequency is zero. Experiments were performed on the Optical Sciences Laser (OSL), a 1--100 J class laser at LLNL. These experiments used a 200 GHz bandwidth source produced by a multipassed electro-optic phase modulator. The spectrum produced was composed of discrete frequency components spaced at 3 GHz intervals. Angular dispersion was incorporated by the addition of a 1200 gr/mm diffraction grating oriented at the Littrow angle, and capable of rotation about the beam direction. Experiments were performed with a pulse length of 1-ns and a 1ω input intensity of ∼ 4 GW/cm 2 for near optimal dispersion for phase matching, 5.2 μrad/GHz, with 0.1, 60, and 155 GHz bandwidth, as well as for partial dispersion compensation, 1.66 μrad/GHz, with 155 GHz and 0.1 GHz bandwidth. The direction of dispersion was varied incrementally 360 degrees about the beam diameter. The addition of the grating to the beamline reduced the narrowband conversion efficiency by approximately 10%
9. ANGULAR MOMENTUM IN GIANT MOLECULAR CLOUDS. II. M33
International Nuclear Information System (INIS)
Imara, Nia; Bigiel, Frank; Blitz, Leo
2011-01-01
We present an analysis comparing the properties of 45 giant molecular clouds (GMCs) in M33 and the atomic hydrogen (H I) with which they are associated. High-resolution Very Large Array observations are used to measure the properties of H I in the vicinity of GMCs and in regions where GMCs have not been detected. The majority of molecular clouds coincide with a local peak in the surface density of atomic gas, though 7% of GMCs in the sample are not associated with high surface density atomic gas. The mean H I surface density in the vicinity of GMCs is 10 M sun pc -2 and tends to increase with GMC mass as Σ HI ∝ M 0.27 GMC . Thirty-nine of the 45 H I regions surrounding GMCs have linear velocity gradients of ∼0.05 km s -1 pc -1 . If the linear gradients previously observed in the GMCs result from rotation, 53% are counterrotating with respect to the local H I. And if the linear gradients in these local H I regions are also from rotation, 62% are counterrotating with respect to the galaxy. If magnetic braking reduced the angular momentum of GMCs early in their evolution, the angular velocity of GMCs would be roughly one order of magnitude lower than what is observed. Based on our observations, we consider the possibility that GMCs may not be rotating. Atomic gas not associated with GMCs has gradients closer to 0.03 km s -1 pc -1 , suggesting that events occur during the course of GMC evolution that may increase the shear in the atomic gas.
10. Angular Stable Miniplate Fixation of Chronic Unstable Scaphoid Nonunion.
Science.gov (United States)
Schormans, Philip M J; Brink, Peter R G; Poeze, Martijn; Hannemann, Pascal F W
2018-02-01
Background Around 5 to 15% of all scaphoid fractures result in nonunion. Treatment of long-lasting scaphoid nonunion remains a challenge for the treating surgeon. Healing of scaphoid nonunion is essential for prevention of scaphoid nonunion advanced collapse and the subsequent predictable pattern of radiocarpal osteoarthritis. Purpose The purpose of this study was to investigate the feasibility of fixation of the scaphoid nonunion with a volar angular stable miniplate and cancellous bone grafting. We hypothesized that this technique could be successful, even in patients with previous surgery for nonunion and in patients with a long duration of nonunion. Patients and Methods A total of 21 patients enrolled in a single-center prospective cohort study. Healing of nonunion was assessed on multiplanar computed tomography scan of the wrist at a 3-month interval. Functional outcome was assessed by measuring grip strength, range of motion, and by means of the patient-rated wrist and hand evaluation (PRWHE) questionnaire. Results During follow-up, 19 out of 21 patients (90%) showed radiological healing of the nonunion. The range of motion did not improve significantly. Postoperative PRWHE scores decreased by 34 points. Healing occurred regardless of the length of time of the nonunion (range: 6-183 months) and regardless of previous surgery (38% of patients). Conclusion Volar angular stable miniplate fixation with autologous cancellous bone grafting is a successful technique for the treatment of chronic unstable scaphoid nonunion, even in patients with long-lasting nonunion and in patients who underwent previous surgery for a scaphoid fracture. Rotational interfragmentary stability might be an important determining factor for the successful treatment of unstable scaphoid nonunion. Level of Evidence Level IV.
11. Angular analysis of $\\Lambda_{b} \\rightarrow \\Lambda \\mu^{+}\\mu^{-}$
CERN Multimedia
Chatzikonstantinidis, Georgios
2018-01-01
The angular analysis of the rare baryon decay of $\\Lambda_{b}\\rightarrow \\Lambda (\\rightarrow p\\pi^{-})\\mu^{+}\\mu^{-}$ in high $q^{2}$ is presented. The dataset that is used corresponds to an integrated luminosity of 5.0 fb$^{-1}$ of pp - collision data collected at centre-of-mass energies between 7 and 13 TeV by the LHCb detector in 2011, 2012, 2015 and 2016. Angular observables are determined using a moment analysis of the angular distribution.
12. The Role of Spatial Memory and Frames of Reference in the Precision of Angular Path Integration
OpenAIRE
Arthur, Joeanna C.; Philbeck, John W.; Kleene, Nicholas J.; Chichka, David
2012-01-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatia...
13. Angular Distributions of Sputtered Atoms from Semiconductor Targets at Grazing Ion Beam Incidence Angles
International Nuclear Information System (INIS)
Sekowski, M.; Burenkov, A.; Martinez-Limia, A.; Hernandez-Mangas, J.; Ryssel, H.
2008-01-01
Angular distributions of ion sputtered germanium and silicon atoms are investigated within this work. Experiments are performed for the case of grazing ion incidence angles, where the resulting angular distributions are asymmetrical with respect to the polar angle of the sputtered atoms. The performed experiments are compared to Monte-Carlo simulations from different programs. We show here an improved model for the angular distribution, which has an additional dependence of the ion incidence angle.
14. Photoelectron and ICD electron angular distributions from fixed-in-space neon dimers
International Nuclear Information System (INIS)
Jahnke, T; Czasch, A; Schoeffler, M; Schoessler, S; Kaesz, M; Titze, J; Kreidi, K; Grisenti, R E; Staudte, A; Jagutzki, O; Schmidt, L Ph H; Semenov, S K; Cherepkov, N A; Schmidt-Boecking, H; Doerner, R
2007-01-01
We report on molecular frame angular distributions of 2s photoelectrons and electrons emitted by interatomic Coulombic decay from neon dimers. We found that the measured angular distribution of the photoelectron strongly depends on the environment of the cluster. The experimental results are in excellent agreement with frozen core Hartree-Fock calculations. The ICD electrons show slight variations in their angular distribution for different kinetic energies
15. New approach to determine the angular transmission in zero-degree magnetic spectrometers
International Nuclear Information System (INIS)
Benlliure, J.; Pereira-Conca, J.; Schmidt, K.H.
2000-11-01
A new method to estimate the angular transmission in zero-degree magnetic spectrometers is presented. This method is based on a parameterisation of the angular aperture of the spectrometer for any possible value of the magnetic rigidity of the transmitted particles. This parameterisation of the angular aperture together with a description of the kinematics of the reaction mechanism allows to determine the angular transmission analytically, avoiding tedious Monte-Carlo calculations. The analytical solutions are implemented for residual nuclei produced in fission, projectile-fragmentation and fusion-evaporation reactions. (orig.)
16. Yksisivuisten web-sovellusten kehittäminen Angular 2 -sovelluskehyksellä
OpenAIRE
Kujala, Miika
2016-01-01
Yksisivuiset web-sovellukset ovat yleistyneet viime vuosina. Niiden kehityksessä hyödynnetään usein JavaScript-sovelluskehystä. Angular 2 on Google:n kehittämä JavaScript-sovelluskehys. Tämän tutkielman tavoitteena on tarkastella Angular 2 -sovelluskehystä ja sen soveltuvuutta yksisivuisten web-sovellusten ke- hityksessä. Tutkielmassa käydään läpi Angular 2 -sovelluskehyksen ominaisuuksia sekä Angular 2 -sovelluskehyksen käytössä ilmeneviä etuja ja haittoja.
17. Study at high angular momentum of the reflection asymmetry in the 218 Ra transition nuclei
International Nuclear Information System (INIS)
Aiche, M.
1990-07-01
The investigations concerning the 218 Ra nuclei at high angular momentum are discussed. The aim of the study is to enlarge the knowledge on the octupolar phenomena and to analyse its evolution as a funcion of the angular momentum. The 218 Ra nuclei is obtained from the ( 14 C, 4n) reaction. The gamma angular distribution and the gamma-gamma coincidence were measured by means of the Chateau de Cristal multicounter. The reflection asymmetric mean field theory and the bosons interaction model were applied to analyze the data and obtain the structure at high angular moments. The results show the existence of dipole-octupole correlations in the nuclei [fr
18. Optical Torque Wrench: Angular Trapping, Rotation, and Torque Detection of Quartz Microparticles
Science.gov (United States)
La Porta, Arthur; Wang, Michelle D.
2004-05-01
We describe an apparatus that can measure the instantaneous angular displacement and torque applied to a quartz particle which is angularly trapped. Torque is measured by detecting the change in angular momentum of the transmitted trap beam. The rotational Brownian motion of the trapped particle and its power spectral density are used to determine the angular trap stiffness. The apparatus features a feedback control that clamps torque or other rotational quantities. The torque sensitivity demonstrated is ideal for the study of known biological molecular motors.
19. Reexamination of fission fragment angular distributions and the fission process: Formalism
International Nuclear Information System (INIS)
Bond, P.D.
1985-01-01
The theory of fission fragment angular distributions is examined and the universally used expression is found to be valid only under restrictive assumptions. A more general angular distribution formula is derived and applied to recent data of high spin systems. At the same time it is shown that the strong anisotropies observed from such systems can be understood without changing the essential basis of standard fission theory. The effects of reaction mechanisms other than complete fusion on fission fragment angular distributions are discussed and possible angular distribution signatures of noncompound nucleus formation are mentioned
20. Molecular frame and recoil frame angular distributions in dissociative photoionization of small molecules
International Nuclear Information System (INIS)
Lucchese, R R; Carey, R; Elkharrat, C; Houver, J C; Dowek, D
2008-01-01
Photoelectron angular distributions in the dipole approximation can be written with respect to several different reference frames. A brief review of the molecular frame and recoil frame are given. Experimentally, one approach for obtaining such angular distributions is through angle-resolved coincidence measurements of dissociative ionization. If the system dissociates into two heavy fragments, then the recoil frame angular distribution can be measured. Computed molecular frame and recoil frame photoelectron angular distributions are compared to experimental data for the Cl 2p ionization of CH 3 Cl.
1. Measurement of angular distribution of cosmic-ray muon fluence rate
International Nuclear Information System (INIS)
Lin, Jeng-Wei; Chen, Yen-Fu; Sheu, Rong-Jiun; Jiang, Shiang-Huei
2010-01-01
In this work a Berkeley Lab cosmic ray detector was used to measure the angular distribution of the cosmic-ray muon fluence rate. Angular response functions of the detector at each measurement orientation were calculated by using the FLUKA Monte Carlo code, where no energy attenuation was taken into account. Coincidence counting rates were measured at ten orientations with equiangular intervals. The muon angular fluence rate spectrum was unfolded from the measured counting rates associated with the angular response functions using both the MAXED code and the parameter adjusting method.
2. Dynamical evolution of angular momentum in damped nuclear reactions. I. Accumulation of angular momentum by nucleon transfer
International Nuclear Information System (INIS)
Doessing, T.; Randrup, J.
1984-01-01
An important goal in the theory of nuclear dynamics is to understand the observed transport phenomena in terms of the basic microscopic processes in the system. For this purpose a model was developed in which the dissipative mechanism responsible for the transport process is the transfer of nucleons between the two reacting nuclides. Until now, most efforts to confront that theory with data have concentrated on the evolution of the charge and mass distribution with energy loss, and overall good agreement has been obtained for a variety of features. While this success lends strong support to the theory, it is important to broaden the contact with experiment by considering also other aspects of the data. Therefore the authors have undertaken a comprehensive study of the angular momentum variables which represent six additional observables (three for each fragment spin) and thus provide a rich testing ground for the theory
3. Subbarrier fusion of 16O+112Cd: Cross sections and mean angular momenta
International Nuclear Information System (INIS)
Ackermann, D.; Corradi, L.; Napoli, D.R.; Petrache, C.M.; Spolaore, P.; Stefanini, A.M.; Scarlassara, F.; Beghini, S.; Montagnoli, G.; Segato, G.F.; Signorini, C.
1994-01-01
Fusion cross sections and mean angular momenta have been measured for 16 O+ 112 Cd around the Coulomb barrier. The experimental results are well reproduced by coupled-channels calculations, confirming the validity of this model for mass-asymmetric systems. The predicted asymptotic behaviour of the mean angular momentum at low energies has been observed. ((orig.))
4. Nutritional status, oral hygiene and Angular cheilitis in schoolchildren in Cianjur district, West Java
Directory of Open Access Journals (Sweden)
Fatimah Boenjamin Partakusuma
2017-08-01
Full Text Available Background: Angular cheilitis is a lesion at the corner of the mouth. Clinically, it is visible as an erythema and ulceration that occasionally extend beyond the vermillion border onto the skin. Anemia in children is an issue of global nutritional problems that need attention. The objectives of the study was to determine the association between nutritional status, oral hygiene and angular cheilitis in elementary schoolchildren in District of Cianjur. Methods: This cross sectional study was conducted on 349 schoolchildren in five Subdistrict of Cianjur. Angular cheilitis status was determined based on the criteria set by Ohman (1986. Anhropometric status was determined by CDC BMI-for-age percentile growth chart. Anemia status was determine by the level of hemoglobin concentration using the HemoCue device. Oral hygiene was measured by OHI-S index. Results: The prevalence of angular cheilitis, anemia, wasting and poor oral hygiene were: 62.5%, 12,6%, 20.6%, and 67.3%, respectively. There are no relationships between anthropometric status, oral hygiene and angular cheilitis. (p> 0.05. However there is a relationship significant relationship beween anemia and angular cheilitis (p <0.05. Logistic regression test showed that anemia is a risk factor on the occurrence of angular cheilitis. Conclusion: Anemia is a factor on the occurrence of angular cheilitis in schoolchildren in Cianjur.
5. Angular distributions of target black fragments in nucleus–nucleus collisions at high energy
International Nuclear Information System (INIS)
Liu, Fuhu; Abd Allah, N.N.; Zhang, Donghai; Duan, Maiying
2003-01-01
The experimental results of space, azimuthal, and projected angular distributions of target black fragments produced in silicon-emulsion collisions at 4.5A GeV/c (the Dubna energy) are reported. A multi-source ideal gas model is suggested to describe the experimental angular distributions. The Monte Carlo calculated results are in agreement with the experimental data. (author)
6. Neutron-fragment angular correlations in /sup 235/U(n/sub th/,f)
International Nuclear Information System (INIS)
Franklyn, C.B.
1985-01-01
Neutron-fragment angular correlations in /sup 235/U(n/sub th/,f) as a function of neutron energy and fragment mass are presented. The results obtained in this experiment, together with data for neutron-neutron angular correlations, are compared with a Monte Carlo simulation of the fission process incorporating both a scission neutron component and an anisotropic neutron emission component
7. On the angular distribution of spectator nucleons in high-energy collisions with deuterium nuclei
International Nuclear Information System (INIS)
Bartke, J.
1975-01-01
Angular distributions of spectator nucleons in collisions of high-energy particles with deuterium nuclei are discussed in the framework of the impulse model. Comparison with experimental data shows that predictions following from this simple theoretical model are verified by experiment. Some general remarks on the study of angular distributions of spectator nucleons are given. (author)
8. Distribution of the angular momentum in the Galaxy and M31
International Nuclear Information System (INIS)
Einasto, J.; Traat, P.
1977-01-01
The angular momentum distribution of the Galaxy and of the Andromeda galaxy M31 has been calculated separately for the disk and halo population. The disk was approximated with a ring. The distribution of the angular momentum in the disk and the halo is different
9. Freeform TIR collimators for the removal of angular color variation in white LED spotlights
NARCIS (Netherlands)
Prins, C.R.; Schneider, C.; IJzerman, W.L.; Tukker, T.W.; Thije Boonkkamp, ten J.H.M.; Winston, R.; Gordon, J.
2013-01-01
Angular color variation in white, phosphor-converted LEDs causes undesirable yellow rings in the beams of spotlights. We developed an inverse method to design TIR collimators that remove the angular color variation for point light sources and significantly reduce color variation for extended light
10. Demonstrating the Conservation of Angular Momentum Using Model Cars Moving along a Rotating Rod
Science.gov (United States)
Abdul-Razzaq, Wathiq; Golubovic, Leonardo
2013-01-01
We have developed an exciting non-traditional experiment for our introductory physics laboratories to help students to understand the principle of conservation of angular momentum. We used electric toy cars moving along a long rotating rod. As the cars move towards the centre of the rod, the angular velocity of this system increases.…
11. Differential branching fraction and angular analysis of the decay B-0 -> K*(0)mu(+)mu(-)
NARCIS (Netherlands)
Aaij, R.; Abellan Beteta, C.; Adeva, B.; Adinolfi, M.; Adrover, C.; Affolder, A.; Ajaltouni, Z.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; Anderlini, L.; Andreassen, R.; Appleby, R. B.; Aquines Gutierrez, O.; Archilli, F.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Bachmann, S.; Back, J. J.; Baesso, C.; Balagura, V.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Bauer, Th.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Belogurov, S.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Pellegrino, A.; Tolk, S.
The angular distribution and differential branching fraction of the decay B-0 -> K*(0)mu(+)mu(-) are studied using a data sample, collected by the LHCb experiment in pp collisions at root s = 7 TeV, corresponding to an integrated luminosity of 1.0 fb(-1). Several angular observables are measured in
12. Angular analysis of charged and neutral B -> K mu(+) mu(-) decays
NARCIS (Netherlands)
Aaij, R.; Adeva, B.; Adinolfi, M.; Affolder, A.; Ajaltouni, Z.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Anderson, J.; Andreassen, R.; 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.; Balagura, V.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Bauer, Th.; Bay, A.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Belogurov, S.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Onderwater, G.; Pellegrino, A.
2014-01-01
The angular distributions of the rare decays B+ -> K+mu(+)mu(-) and B-0 -> K-S(0)mu(+)mu(-) are studied with data corresponding to 3 fb(-1) of integrated luminosity, collected in proton-proton collisions at 7 and 8 TeV centre-of-mass energies with the LHCb detector. The angular distribution is
13. Complex method for angular-spectral analysis of volume phase diffraction gratings recorded in photopolymers
Czech Academy of Sciences Publication Activity Database
Vojtíšek, Petr; Květoň, M.; Richter, I.
2016-01-01
Roč. 11, February (2016), č. článku 16009. ISSN 1990-2573 R&D Projects: GA MŠk(CZ) LO1206 Institutional support: RVO:61389021 Keywords : Photopolymers * diffraction gratings * angular-spectral maps * spectral selectivity * angular selectivity Subject RIV: BH - Optics, Masers, Lasers Impact factor: 0.975, year: 2016
14. Angular distribution and rotations of frame in vector meson decays into lepton pairs
International Nuclear Information System (INIS)
Palestini, Sandro
2011-01-01
We discuss how the angular distribution of lepton pairs from decays of vector mesons depends on the choice of reference frame, and provide a geometrical description of the transformations of the coefficients of the angular distribution. Invariant expressions involving all coefficients are discussed, together with bounds and consistency relations.
15. Non-uniform sampling and wide range angular spectrum method
International Nuclear Information System (INIS)
Kim, Yong-Hae; Byun, Chun-Won; Oh, Himchan; Lee, JaeWon; Pi, Jae-Eun; Heon Kim, Gi; Lee, Myung-Lae; Ryu, Hojun; Chu, Hye-Yong; Hwang, Chi-Sun
2014-01-01
A novel method is proposed for simulating free space field propagation from a source plane to a destination plane that is applicable for both small and large propagation distances. The angular spectrum method (ASM) was widely used for simulating near field propagation, but it caused a numerical error when the propagation distance was large because of aliasing due to under sampling. Band limited ASM satisfied the Nyquist condition on sampling by limiting a bandwidth of a propagation field to avoid an aliasing error so that it could extend the applicable propagation distance of the ASM. However, the band limited ASM also made an error due to the decrease of an effective sampling number in a Fourier space when the propagation distance was large. In the proposed wide range ASM, we use a non-uniform sampling in a Fourier space to keep a constant effective sampling number even though the propagation distance is large. As a result, the wide range ASM can produce simulation results with high accuracy for both far and near field propagation. For non-paraxial wave propagation, we applied the wide range ASM to a shifted destination plane as well. (paper)
16. Nature of chemical bond through positron angular correlation
International Nuclear Information System (INIS)
Ramasamy, S.; Nagarajan, T.
1979-01-01
Two photon angular distribution of positron annihilation is measured for compounds (1) m- and (2) p-nitroanilines, (3) m- and (4) p-methylsulphonyl-N, N-dimethylanilines and (5) p-phenylthio- and (6) p-phenoxyanilines in order to investigate the phenomenon of resonance and the involvement of d-orbitals of sulphur in chemical bonding. The FWHM is the same (10.8 mrad) for compounds (1) and (2) indicating that the resonance in the p-isomer does not change the annihilation characteristic much. The measured FWHM (9.4 mrad) for compound (4) is much broader than that of compound (3) (FWHM = 7.7 mrad). In the case of p-isomer, there is the involvement of d-orbitals of sulphur in bond formation. FWHM for compounds (5) and (6) are almost same (8.4 mrad). In this pair the only difference is that the sulphur in one case is replaced by oxygen in the other. Since there is not enough scope for excess electrons to be accomodated at oxygen or sulphur, there is no preferential annihilation of positron at these centres. (auth.)
17. Pulsed power for angular multiplexed laser fusion drivers
International Nuclear Information System (INIS)
Eninger, J.E.
1983-01-01
The feasibility of using rare gas-halide lasers, in particular the KrF laser, as inertial confinement fusion (ICF) drivers has been assessed. These lasers are scalable to the required high energy (approx. =1-5 MJ) in a short pulse (approx. =10 ns) by optical angular multiplexing, and integration of the output from approx. =100 kJ laser amplifier subsystems. The e-beam current density (approx. =50A/cm 2 ) and voltage (approx. =800 kV) required for these power amplifiers lead to an e-beam impedance of approx. =0.2Ω for approx. =300 ns pump time. This impedance level requires modularization of the large area e-gun, a) to achieve a diode inductance consistent with fast current risetime, b) to circumvent dielectric breakdown constraints in the pulse forming lines, and c) to reduce the requirement for guide magnetic fields. Pulsed power systems requirements, design concepts, scalability, tradeoffs, and performance projections are discussed in this paper
18. A novel instrument for generating angular increments of 1 nanoradian
Science.gov (United States)
Alcock, Simon G.; Bugnar, Alex; Nistea, Ioana; Sawhney, Kawal; Scott, Stewart; Hillman, Michael; Grindrod, Jamie; Johnson, Iain
2015-12-01
Accurate generation of small angles is of vital importance for calibrating angle-based metrology instruments used in a broad spectrum of industries including mechatronics, nano-positioning, and optic fabrication. We present a novel, piezo-driven, flexure device capable of reliably generating micro- and nanoradian angles. Unlike many such instruments, Diamond Light Source's nano-angle generator (Diamond-NANGO) does not rely on two separate actuators or rotation stages to provide coarse and fine motion. Instead, a single Physik Instrumente NEXLINE "PiezoWalk" actuator provides millimetres of travel with nanometre resolution. A cartwheel flexure efficiently converts displacement from the linear actuator into rotary motion with minimal parasitic errors. Rotation of the flexure is directly measured via a Magnescale "Laserscale" angle encoder. Closed-loop operation of the PiezoWalk actuator, using high-speed feedback from the angle encoder, ensures that the Diamond-NANGO's output drifts by only ˜0.3 nrad rms over ˜30 min. We show that the Diamond-NANGO can reliably move with unprecedented 1 nrad (˜57 ndeg) angular increments over a range of >7000 μrad. An autocollimator, interferometer, and capacitive displacement sensor are used to independently confirm the Diamond-NANGO's performance by simultaneously measuring the rotation of a reflective cube.
19. Angular distributions of photoelectrons from free Na clusters
International Nuclear Information System (INIS)
Wopperer, P.; Dinh, P. M.; Faber, B.; Reinhard, P.-G.; Suraud, E.
2010-01-01
We explore, from a theoretical perspective, photoelectron angular distributions (PADs) of the Na clusters Na 8 , Na 10 , Na 12 , Na 18 , Na 3 + , Na 11 + , Na 13 + , and Na 19 + . The basis of the description is the time-dependent local-density approximation (TDLDA), augmented by a self-interaction correction (SIC) to describe ionization properties correctly. The scheme is solved on a numerical grid in coordinate space with absorbing bounds. We assume for each cluster system an isotropic ensemble of free clusters and develop for the case of one-photon emission analytical formulas for computing the orientation-averaged PAD on the basis of a few TDLDA-SIC calculations for properly chosen reference orientations. It turns out that all the information in the averaged PAD is contained in one anisotropy parameter. We find that this parameter varies very little with system size, but as a whole is crucially influenced by the detailed ionic structure. We also make comparisons with direct orientation averaging and consider one example reaching outside the perturbative regime.
20. RCS Diversity of Electromagnetic Wave Carrying Orbital Angular Momentum.
Science.gov (United States)
Zhang, Chao; Chen, Dong; Jiang, Xuefeng
2017-11-13
An electromagnetic (EM) wave with orbital angular momentum (OAM) has a helical wave front, which is different from that of the plane wave. The phase gradient can be found perpendicular to the direction of propagation and proportional to the number of OAM modes. Herein, we study the backscattering property of the EM wave with different OAM modes, i.e., the radar cross section (RCS) of the target is measured and evaluated with different OAM waves. As indicated by the experimental results, different OAM waves have the same RCS fluctuation for the simple target, e.g., a small metal ball as the target. However, for complicated targets, e.g., two transverse-deployed small metal balls, different RCSs can be identified from the same incident angle. This valuable fact helps to obtain RCS diversity, e.g., equal gain or selective combining of different OAM wave scattering. The majority of the targets are complicated targets or expanded targets; the RCS diversity can be utilized to detect a weak target traditionally measured by the plane wave, which is very helpful for anti-stealth radar to detect the traditional stealth target by increasing the RCS with OAM waves.
1. An angular selective electron gun for the KATRIN experiment
Energy Technology Data Exchange (ETDEWEB)
Zacher, Michael; Ortjohann, Hans-Werner; Steinbrink, Nicholas; Josten, Lorenz; Hannen, Volker; Weinheimer, Christian; Winzen, Daniel [Westfaelische Wilhelms-Universitaet, Muenster (Germany); Collaboration: KATRIN-Collaboration
2013-07-01
The KArlsruhe TRItium Neutrino experiment aims for a measurement of the electron anti-neutrino mass with a sensitivity of 200 meV/c{sup 2} (95% C.L.) by analysing the endpoint region of the tritium β-decay. The main spectrometer (MAC-E filter type, 23m length) is one of the central parts of the experiment, featuring an energy resolution of Δ E<1 eV. For commissioning of the spectrometer a well defined electron source is needed that allows to determine the transmission characteristics and compare the electromagnetic properties to simulations. For this purpose an angular selective electron gun was developed. A pulsed UV-Laser produces electrons via the photo-electric effect, which are then accelerated electrostatically in a magnetic field. It features a small energy spread, a sharp selectable emission angle and covers the whole magnetic flux tube of KATRIN. By that, the characteristics of the spectrometer can be investigated with high precision. The time structure of the electron pulses allows time of flight measurements, offering enhanced sensitivity. The talk gives an overview about the e-gun design and its properties.
2. Microwave imaging of spinning object using orbital angular momentum
Science.gov (United States)
Liu, Kang; Li, Xiang; Gao, Yue; Wang, Hongqiang; Cheng, Yongqiang
2017-09-01
The linear Doppler shift used for the detection of a spinning object becomes significantly weakened when the line of sight (LOS) is perpendicular to the object, which will result in the failure of detection. In this paper, a new detection and imaging technique for spinning objects is developed. The rotational Doppler phenomenon is observed by using the microwave carrying orbital angular momentum (OAM). To converge the radiation energy on the area where objects might exist, the generation method of OAM beams is proposed based on the frequency diversity principle, and the imaging model is derived accordingly. The detection method of the rotational Doppler shift and the imaging approach of the azimuthal profiles are proposed, which are verified by proof-of-concept experiments. Simulation and experimental results demonstrate that OAM beams can still be used to obtain the azimuthal profiles of spinning objects even when the LOS is perpendicular to the object. This work remedies the insufficiency in existing microwave sensing technology and offers a new solution to the object identification problem.
3. Gama-gama angular correlations in the 105Rh nucleus
International Nuclear Information System (INIS)
Esteves, V.A.P.
1979-01-01
The Directional Correlation of γ transitions in 105 Rh have been measured from the β - decay of 105 Ru using a Ge(Li) - Nal(Tl) spectrometers. The measurements were carried out for the (316-469), (500-469), (845-499), (875-469), (878-499), (907-469), (1017-469), (350-326), (393-263), (413-263), (489-149) and (575-149) KeV gama cascades. The present results confirm the spin assignments to several levels in 105 Rh obtained in previous studies. The multipole mixing ratios Δ(E2/M1) for several gama transitions have been calculated from the measured angular correlations. The results are Δ(149)=0.34+-0.01,Δ(262)=-1.27+-0.02 or -0.14+-0.01,Δ(326)=-1.79+-0.01 or 0.014+-0.002, Δ(393)=-7.1+-0.3 or -0.36+-0.01, Δ(489)=0.25+-0.002, Δ(500)=0.7+-0.3 and Δ(907)=-21.7 +8 -31.1 or 0.21+-0.03. The structure of nuclear levels in 105 Rh is discussed briefly in terms of models applicable for nuclide in this mass region [pt
4. The Schiff angular bremsstrahlung distribution from composite media
International Nuclear Information System (INIS)
Taylor, M.L.; Dalton, B.; Franich, R.D.
2012-01-01
The Schiff differential for the angular distribution of bremsstrahlung is widely employed, but calculations involving composite materials (i.e. compounds and mixtures) are often undertaken in a somewhat ad hoc fashion. In this work, we suggest an alternative approach to power-law estimates of the effective atomic number utilising Seltzer and Berger’s combined approach in order to generate single-valued effective atomic numbers applicable over a large energy range (in the worst case deviation from constancy of about 2% between 10 keV and 1 GeV). Differences with power-law estimates of Z for composites are potentially significant, particularly for low-Z media such as biological or surrogate materials as relevant within the context of medical physics. As an example, soft tissue differs by >70% and cortical bone differs by >85%, while for high-Z composites such as a tungsten–rhenium alloy the difference is of the order of 1%. Use of the normalised Schiff formula for shape only does not exhibit strong Z dependence. Consequently, in such contexts the differences are negligible – the power-law approach overestimates the magnitude by 1.05% in the case of water and underestimates it by <0.1% for the high-Z alloys. The differences in the distribution are most pronounced for small angles and where the bremsstrahlung quanta are low energy.
5. Molecular Electronic Angular Motion Transducer Broad Band Self-Noise
Science.gov (United States)
Zaitsev, Dmitry; Agafonov, Vadim; Egorov, Egor; Antonov, Alexander; Shabalina, Anna
2015-01-01
Modern molecular electronic transfer (MET) angular motion sensors combine high technical characteristics with low cost. Self-noise is one of the key characteristics which determine applications for MET sensors. However, until the present there has not been a model describing the sensor noise in the complete operating frequency range. The present work reports the results of an experimental study of the self-noise level of such sensors in the frequency range of 0.01–200 Hz. Based on the experimental data, a theoretical model is developed. According to the model, self-noise is conditioned by thermal hydrodynamic fluctuations of the operating fluid flow in the frequency range of 0.01–2 Hz. At the frequency range of 2–100 Hz, the noise power spectral density has a specific inversely proportional dependence of the power spectral density on the frequency that could be attributed to convective processes. In the high frequency range of 100–200 Hz, the noise is conditioned by the voltage noise of the electronics module input stage operational amplifiers and is heavily reliant to the sensor electrical impedance. The presented results allow a deeper understanding of the molecular electronic sensor noise nature to suggest the ways to reduce it. PMID:26610502
6. Negative refraction angular characterization in one-dimensional photonic crystals.
Directory of Open Access Journals (Sweden)
Jesus Eduardo Lugo
2011-04-01
Full Text Available Photonic crystals are artificial structures that have periodic dielectric components with different refractive indices. Under certain conditions, they abnormally refract the light, a phenomenon called negative refraction. Here we experimentally characterize negative refraction in a one dimensional photonic crystal structure; near the low frequency edge of the fourth photonic bandgap. We compare the experimental results with current theory and a theory based on the group velocity developed here. We also analytically derived the negative refraction correctness condition that gives the angular region where negative refraction occurs.By using standard photonic techniques we experimentally determined the relationship between incidence and negative refraction angles and found the negative refraction range by applying the correctness condition. In order to compare both theories with experimental results an output refraction correction was utilized. The correction uses Snell's law and an effective refractive index based on two effective dielectric constants. We found good agreement between experiment and both theories in the negative refraction zone.Since both theories and the experimental observations agreed well in the negative refraction region, we can use both negative refraction theories plus the output correction to predict negative refraction angles. This can be very useful from a practical point of view for space filtering applications such as a photonic demultiplexer or for sensing applications.
7. Negative refraction angular characterization in one-dimensional photonic crystals.
Science.gov (United States)
Lugo, Jesus Eduardo; Doti, Rafael; Faubert, Jocelyn
2011-04-06
Photonic crystals are artificial structures that have periodic dielectric components with different refractive indices. Under certain conditions, they abnormally refract the light, a phenomenon called negative refraction. Here we experimentally characterize negative refraction in a one dimensional photonic crystal structure; near the low frequency edge of the fourth photonic bandgap. We compare the experimental results with current theory and a theory based on the group velocity developed here. We also analytically derived the negative refraction correctness condition that gives the angular region where negative refraction occurs. By using standard photonic techniques we experimentally determined the relationship between incidence and negative refraction angles and found the negative refraction range by applying the correctness condition. In order to compare both theories with experimental results an output refraction correction was utilized. The correction uses Snell's law and an effective refractive index based on two effective dielectric constants. We found good agreement between experiment and both theories in the negative refraction zone. Since both theories and the experimental observations agreed well in the negative refraction region, we can use both negative refraction theories plus the output correction to predict negative refraction angles. This can be very useful from a practical point of view for space filtering applications such as a photonic demultiplexer or for sensing applications.
8. A complex angular momentum theory of modified Coulomb scattering
International Nuclear Information System (INIS)
Thylwe, K.E.; Connor, J.N.L.
1985-01-01
The paper develops an exact complex angular momentum (CAM) theory of elastic scattering for a complex optical potential with a Coulombic tail. The present CAM theory avoids complications due to the long range nature of the Coulombic potential in a straightforward way. The Sommerfeld-Watson transformation together with a travelling wave (near-side far-side) decomposition, is used to obtain an exact representation for the scattering amplitude f(theta) in terms of a background integral fsub(B)(theta) and a series of subamplitudes fsup((+-))sub(n)(theta). New exact representations are derived for fsub(B)(theta) when the scattering matrix element S(lambda) possesses local symmetries of the type S(-lambda)=S(lambda)exp(+-2iπlambda) and S(-lambda)=S(lambda). The exact results obtained in this paper unify the CAM theory of scattering for Coulombic and short range potentials and are especially suitable for the introduction of semiclassical approximations. (author)
9. ANGULAR MOMENTUM IN GIANT MOLECULAR CLOUDS. I. THE MILKY WAY
International Nuclear Information System (INIS)
Imara, Nia; Blitz, Leo
2011-01-01
We present a detailed analysis comparing the velocity fields in molecular clouds and the atomic gas that surrounds them in order to address the origin of the gradients. To that end, we present first-moment intensity-weighted velocity maps of the molecular clouds and surrounding atomic gas. The maps are made from high-resolution 13 CO observations and 21 cm observations from the Leiden/Argentine/Bonn Galactic H I Survey. We find that (1) the atomic gas associated with each molecular cloud has a substantial velocity gradient-ranging from 0.02 to 0.07 km s -1 pc -1 -whether or not the molecular cloud itself has a substantial linear gradient. (2) If the gradients in the molecular and atomic gas were due to rotation, this would imply that the molecular clouds have less specific angular momentum than the surrounding H I by a factor of 1-6. (3) Most importantly, the velocity gradient position angles in the molecular and atomic gas are generally widely separated-by as much as 130 deg. in the case of the Rosette molecular cloud. This result argues against the hypothesis that molecular clouds formed by simple top-down collapse from atomic gas.
10. The angular distributions of sputtered indium atoms at different temperature
International Nuclear Information System (INIS)
Zhang Jiping; Wang Zhenxia; Tao Zhenlan; Pan Jisheng
1993-01-01
The effect of temperature and surface topography on the angular distribution of indium atoms was studied under bombardment by 2T KeV Ar + ions at normal incidence. Experiments were carried out on two samples, A and B, at 25 o C and 70 o C respectively. The function Y(θ) = a cosθ + b cos n θ, where θ is the sputtering angle, was found to fit the experimental data. The term (a cos θ) corresponds to the cosine distribution predicted by random collision cascade theory, and the term (b cos n θ) is dependent on factors such as the surface topography. For sample A, a∼b, whereas for sample B a< b. The surface of A consisted of flat and pebble like regions of almost equal area while the surface of B was more cratered. An explanation of the fitting values of a,b and n is given in terms of the shielding effects of the different structures. (UK)
11. Diffraction and angular momentum effects in semiclassical atomic scattering theory
International Nuclear Information System (INIS)
Russek, A.
1979-01-01
The semiclassical scattering theory of Mott and Massey and Ford and Wheeler is here extended to multichannel scattering as occurs at a crossing or pseudocrossing of the transient molecule formed by the colliding atoms. The generalized theory incorporates both interference and diffraction phenomena, but the emphasis in this work is on diffraction. For small-angle scattering, diffraction effects become broader, not narrower, as the collision energy increases: ΔbΔtau > or = h[E/sub inc//(2m)]/sup 1/2/ relates the uncertainties in impact parameter b and reduced scattering angle tau = E/sub inc/theta, and determines the range in b required to resolve a structure in the deflection function of height Δtau. In the kilovolt range of collision energies, the effects of local maxima and minima in the deflection function are washed out, and the Airy-function approximation of Ford and Wheeler is inappropriate to describe the differential cross section. More generally, it is shown that at keV collision energies the stationary-phase approximation, heretofore essential in the reduction to the semiclassical limit, breaks down in the vicinity of a level crossing. An approximate theorem is proposed which remains valid in this region and elsewhere reduces to the standard stationary-phase approximation. Several illustrative examples are considered. A separate development treats the effect on the differential scattering cross section of a change in electronic angular momentum when electronic excitation occurs
12. Limits to evaporation residue cross sections from fission and particle decay at high angular momentum
International Nuclear Information System (INIS)
Newton, J.O.
1980-06-01
In recent years there has been great interest in nuclear properties at very high angular momentum. The heavy-ion (HI),xnγ reaction and to a lesser extent the (HI,xn,ypγ) reactions, have so far offered the most powerful experimental technique for their study. Measurements on the resolved discrete γ-rays from the decay of yrast or near-yrast states has lead to considerable understanding of states with angular momenta up to a little over 20h and in a few special cases as high as 37 h. To investigate nuclei at still higher angular angular momenta one can study the so called 'continuum γ-rays', which cannot be resolved by present techniques because so many pathways are involved. The author considers the factors which determine the upper limits of the angular momenta for which continuum γ-ray studies can be usefully employed and how one may gain information beyond these limits
13. Angular momentum conservation law in light-front quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Chiu, Kelly Yu-Ju; Brodsky, Stanley J.; /SLAC /Stanford U.
2017-03-01
We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3 , the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.
14. Generation of angular-momentum-dominated electron beams from a photoinjector
International Nuclear Information System (INIS)
Sun, Yin-E.; Piot, Philippe; Kim, Kwang-Je; Barov, Nikolas; Lidia, Steven; Santucci, James; Tikhoplav, Rodion; Wennerberg, Jason
2004-01-01
Various projects under study require an angular-momentum-dominated electron beam generated by a photoinjector. Some of the proposals directly use the angular-momentum-dominated beams (e.g. electron cooling of heavy ions), while others require the beam to be transformed into a flat beam (e.g. possible electron injectors for light sources and linear colliders). In this paper, we report our experimental study of an angular-momentum-dominated beam produced in a photoinjector, addressing the dependencies of angular momentum on initial conditions. We also briefly discuss the removal of angular momentum. The results of the experiment, carried out at the Fermilab/NICADD Photoinjector Laboratory, are found to be in good agreement with theoretical and numerical models
15. Angular distributions of particles sputtered from polycrystalline platinum by low-energy ions
International Nuclear Information System (INIS)
Chernysh, V.S.; Eckstein, W.; Haidarov, A.A.; Kulikauskas, V.S.; Mashkova, E.S.; Molchanov, V.A.
2000-01-01
The results of an experimental study and a computer simulation with the TRIM.SP code of the angular distributions of atoms sputtered from polycrystalline platinum under 3-9 keV Ne + bombardment at normal ion incidence are presented. It was found that angular distributions of sputtered atoms are overcosine and that their shape is practically independent of an ion energy. Comparison with the previously obtained data for He + and Ar + ions have shown that the shape of the angular distribution does not depend on the bombarding ion species. Good agreement between experimental results and computer simulation data was found. Computer simulations of the partial angular distributions of Pt atoms ejected due to various sputtering mechanisms for Ne ion bombardment were performed and the comparison with corresponding data for He and Ar bombarding was made. The role of different mechanisms in the formation of angular distributions of sputtered atoms has been analyzed
16. Interpreting angular momentum transfer between electromagnetic multipoles using vector spherical harmonics.
Science.gov (United States)
Grinter, Roger; Jones, Garth A
2018-02-01
The transfer of angular momentum between a quadrupole emitter and a dipole acceptor is investigated theoretically. Vector spherical harmonics are used to describe the angular part of the field of the mediating photon. Analytical results are presented for predicting angular momentum transfer between the emitter and absorber within a quantum electrodynamical framework. We interpret the allowability of such a process, which appears to violate conservation of angular momentum, in terms of the breakdown of the isotropy of space at the point of photon absorption (detection). That is, collapse of the wavefunction results in loss of all angular momentum information. This is consistent with Noether's Theorem and demystifies some common misconceptions about the nature of the photon. The results have implications for interpreting the detection of photons from multipole sources and offers insight into limits on information that can be extracted from quantum measurements in photonic systems.
17. Prediction of Lunar Reconnaissance Orbiter Reaction Wheel Assembly Angular Momentum Using Regression Analysis
Science.gov (United States)
DeHart, Russell
2017-01-01
This study determines the feasibility of creating a tool that can accurately predict Lunar Reconnaissance Orbiter (LRO) reaction wheel assembly (RWA) angular momentum, weeks or even months into the future. LRO is a three-axis stabilized spacecraft that was launched on June 18, 2009. While typically nadir-pointing, LRO conducts many types of slews to enable novel science collection. Momentum unloads have historically been performed approximately once every two weeks with the goal of maintaining system total angular momentum below 70 Nms; however flight experience shows the models developed before launch are overly conservative, with many momentum unloads being performed before system angular momentum surpasses 50 Nms. A more accurate model of RWA angular momentum growth would improve momentum unload scheduling and decrease the frequency of these unloads. Since some LRO instruments must be deactivated during momentum unloads and in the case of one instrument, decontaminated for 24 hours there after a decrease in the frequency of unloads increases science collection. This study develops a new model to predict LRO RWA angular momentum. Regression analysis of data from October 2014 to October 2015 was used to develop relationships between solar beta angle, slew specifications, and RWA angular momentum growth. The resulting model predicts RWA angular momentum using input solar beta angle and mission schedule data. This model was used to predict RWA angular momentum from October 2013 to October 2014. Predictions agree well with telemetry; of the 23 momentum unloads performed from October 2013 to October 2014, the mean and median magnitude of the RWA total angular momentum prediction error at the time of the momentum unloads were 3.7 and 2.7 Nms, respectively. The magnitude of the largest RWA total angular momentum prediction error was 10.6 Nms. Development of a tool that uses the models presented herein is currently underway.
18. Massive star formation by accretion. II. Rotation: how to circumvent the angular momentum barrier?
Science.gov (United States)
Haemmerlé, L.; Eggenberger, P.; Meynet, G.; Maeder, A.; Charbonnel, C.; Klessen, R. S.
2017-06-01
Context. Rotation plays a key role in the star-formation process, from pre-stellar cores to pre-main-sequence (PMS) objects. Understanding the formation of massive stars requires taking into account the accretion of angular momentum during their PMS phase. Aims: We study the PMS evolution of objects destined to become massive stars by accretion, focusing on the links between the physical conditions of the environment and the rotational properties of young stars. In particular, we look at the physical conditions that allow the production of massive stars by accretion. Methods: We present PMS models computed with a new version of the Geneva Stellar Evolution code self-consistently including accretion and rotation according to various accretion scenarios for mass and angular momentum. We describe the internal distribution of angular momentum in PMS stars accreting at high rates and we show how the various physical conditions impact their internal structures, evolutionary tracks, and rotation velocities during the PMS and the early main sequence. Results: We find that the smooth angular momentum accretion considered in previous studies leads to an angular momentum barrier and does not allow the formation of massive stars by accretion. A braking mechanism is needed in order to circumvent this angular momentum barrier. This mechanism has to be efficient enough to remove more than two thirds of the angular momentum from the inner accretion disc. Due to the weak efficiency of angular momentum transport by shear instability and meridional circulation during the accretion phase, the internal rotation profiles of accreting stars reflect essentially the angular momentum accretion history. As a consequence, careful choice of the angular momentum accretion history allows circumvention of any limitation in mass and velocity, and production of stars of any mass and velocity compatible with structure equations.
19. Fission fragment angular distributions and fission cross section validation
International Nuclear Information System (INIS)
Leong, Lou Sai
2013-01-01
The present knowledge of angular distributions of neutron-induced fission is limited to a maximal energy of 15 MeV, with large discrepancies around 14 MeV. Only 238 U and 232 Th have been investigated up to 100 MeV in a single experiment. The n-TOF Collaboration performed the fission cross section measurement of several actinides ( 232 Th, 235 U, 238 U, 234 U, 237 Np) at the n-TOF facility using an experimental set-up made of Parallel Plate Avalanche Counters (PPAC), extending the energy domain of the incident neutron above hundreds of MeV. The method based on the detection of the 2 fragments in coincidence allowed to clearly disentangle the fission reactions among other types of reactions occurring in the spallation domain. I will show the methods we used to reconstruct the full angular resolution by the tracking of fission fragments. Below 10 MeV our results are consistent with existing data. For example in the case of 232 Th, below 10 MeV the results show clearly the variation occurring at the first (1 MeV) and second (7 MeV) chance fission, corresponding to transition states of given J and K (total spin and its projection on the fission axis), and a much more accurate energy dependence at the 3. chance threshold (14 MeV) has been obtained. In the spallation domain, above 30 MeV we confirm the high anisotropy revealed in 232 Th by the single existing data set. I'll discuss the implications of this finding, related to the low anisotropy exhibited in proton-induced fission. I also explore the critical experiments which is valuable checks of nuclear data. The 237 Np neutron-induced fission cross section has recently been measured in a large energy range (from eV to GeV) at the n-TOF facility at CERN. When compared to previous measurements, the n-TOF fission cross section appears to be higher by 5-7 % beyond the fission threshold. To check the relevance of n-TOF data, we simulate a criticality experiment performed at Los Alamos with a 6 kg sphere of 237 Np. This
20. Study of the mode of angular velocity damping for a spacecraft at non-standard situation
Science.gov (United States)
Davydov, A. A.; Sazonov, V. V.
2012-07-01
Non-standard situation on a spacecraft (Earth's satellite) is considered, when there are no measurements of the spacecraft's angular velocity component relative to one of its body axes. Angular velocity measurements are used in controlling spacecraft's attitude motion by means of flywheels. The arising problem is to study the operation of standard control algorithms in the absence of some necessary measurements. In this work this problem is solved for the algorithm ensuring the damping of spacecraft's angular velocity. Such a damping is shown to be possible not for all initial conditions of motion. In the general case one of two possible final modes is realized, each described by stable steady-state solutions of the equations of motion. In one of them, the spacecraft's angular velocity component relative to the axis, for which the measurements are absent, is nonzero. The estimates of the regions of attraction are obtained for these steady-state solutions by numerical calculations. A simple technique is suggested that allows one to eliminate the initial conditions of the angular velocity damping mode from the attraction region of an undesirable solution. Several realizations of this mode that have taken place are reconstructed. This reconstruction was carried out using approximations of telemetry values of the angular velocity components and the total angular momentum of flywheels, obtained at the non-standard situation, by solutions of the equations of spacecraft's rotational motion.
1. Analysis of angular momentum properties of photons emitted in fundamental atomic processes
Science.gov (United States)
Zaytsev, V. A.; Surzhykov, A. S.; Shabaev, V. M.; Stöhlker, Th.
2018-04-01
Many atomic processes result in the emission of photons. Analysis of the properties of emitted photons, such as energy and angular distribution as well as polarization, is regarded as a powerful tool for gaining more insight into the physics of corresponding processes. Another characteristic of light is the projection of its angular momentum upon propagation direction. This property has attracted a special attention over the past decades due to studies of twisted (or vortex) light beams. Measurements being sensitive to this projection may provide valuable information about the role of angular momentum in the fundamental atomic processes. Here we describe a simple theoretical method for determination of the angular momentum properties of the photons emitted in various atomic processes. This method is based on the evaluation of expectation value of the total angular momentum projection operator. To illustrate the method, we apply it to the textbook examples of plane-wave, spherical-wave, and Bessel light. Moreover, we investigate the projection of angular momentum for the photons emitted in the process of the radiative recombination with ionic targets. It is found that the recombination photons do carry a nonzero projection of the orbital angular momentum.
2. A Core Set Based Large Vector-Angular Region and Margin Approach for Novelty Detection
Directory of Open Access Journals (Sweden)
Jiusheng Chen
2016-01-01
Full Text Available A large vector-angular region and margin (LARM approach is presented for novelty detection based on imbalanced data. The key idea is to construct the largest vector-angular region in the feature space to separate normal training patterns; meanwhile, maximize the vector-angular margin between the surface of this optimal vector-angular region and abnormal training patterns. In order to improve the generalization performance of LARM, the vector-angular distribution is optimized by maximizing the vector-angular mean and minimizing the vector-angular variance, which separates the normal and abnormal examples well. However, the inherent computation of quadratic programming (QP solver takes O(n3 training time and at least O(n2 space, which might be computational prohibitive for large scale problems. By (1+ε and (1-ε-approximation algorithm, the core set based LARM algorithm is proposed for fast training LARM problem. Experimental results based on imbalanced datasets have validated the favorable efficiency of the proposed approach in novelty detection.
3. Angular momenta of fission fragments in the {alpha}-accompanied fission of {sup 252}Cf
Energy Technology Data Exchange (ETDEWEB)
Jandel, M.; Kliman, J.; Krupa, L.; Morhac, M. [Slovak Academy of Sciences, Department of Nuclear Physics, Bratislava (Slovakia); Joint Institute for Nuclear Research, Flerov Laboratory for Nuclear Reactions, Dubna (Russian Federation); Hamilton, J.H.; Kormicki, J.; Ramayya, A.V.; Hwang, J.K.; Luo, Y.X.; Fong, D.; Gore, P. [Vanderbilt University, Department of Physics, Nashville, TN (United States); Ter-Akopian, G.M.; Oganessian, Yu.Ts.; Rodin, A.M.; Fomichev, A.S.; Popeko, G.S. [Joint Institute for Nuclear Research, Flerov Laboratory for Nuclear Reactions, Dubna (Russian Federation); Daniel, A.V. [Lawrence Berkeley National Laboratory, Berkeley, CA (United States); Rasmussen, J.O.; Macchiavelli, A.O.; Stoyer, M.A. [Lawrence Livermore National Laboratory, Livermore, CA (United States); Donangelo, R.; Cole, J.D.
2005-06-01
For the first time, average angular momenta of the ternary fission fragments {sup 100,102}Zr, {sup 106}Mo, {sup 144,146}Ba and {sup 138,140,142}Xe from the {alpha}-accompanied fission of {sup 252}Cf were obtained from relative intensities of prompt {gamma}-ray transitions with the use of the statistical model calculation. Average values of the angular momenta were compared with the corresponding values for the same fission fragments from the binary fission of {sup 252}Cf. Results indicate the presence of a decreasing trend in the average values of angular momenta induced in ternary fission fragments compared to the same binary fission fragments. On the average, the total angular momentum extracted for ternary fission fragments is {proportional_to}1.4{Dirac_h} lower than in binary fission. Consequently, results indicate that the mechanism of the ternary {alpha}-particles emission may directly effect an induction of angular momenta of fission fragments, and possible scenarios of such mechanisms are discussed. Further, the dependence of the angular momenta of {sup 106}Mo and {sup 140}Xe on the number of emitted neutrons from correlated pairs of primary fragments was obtained also showing a decreasing dependence of average angular momenta with increasing number of emitted neutrons. Consequences are briefly discussed. (orig.)
4. A Missile-Borne Angular Velocity Sensor Based on Triaxial Electromagnetic Induction Coils
Directory of Open Access Journals (Sweden)
Jian Li
2016-09-01
Full Text Available Aiming to solve the problem of the limited measuring range for angular motion parameters of high-speed rotating projectiles in the field of guidance and control, a self-adaptive measurement method for angular motion parameters based on the electromagnetic induction principle is proposed. First, a framework with type bent “I-shape” is used to design triaxial coils in a mutually orthogonal way. Under the condition of high rotational speed of a projectile, the induction signal of the projectile moving across a geomagnetic field is acquired by using coils. Second, the frequency of the pulse signal is adjusted self-adaptively. Angular velocity and angular displacement are calculated in the form of periodic pulse counting and pulse accumulation, respectively. Finally, on the basis of that principle prototype of the sensor is researched and developed, performance of measuring angular motion parameters are tested on the sensor by semi-physical and physical simulation experiments, respectively. Experimental results demonstrate that the sensor has a wide measuring range of angular velocity from 1 rps to 100 rps with a measurement error of less than 0.3%, and the angular displacement measurement error is lower than 0.2°. The proposed method satisfies measurement requirements for high-speed rotating projectiles with an extremely high dynamic range of rotational speed and high precision, and has definite value to engineering applications in the fields of attitude determination and geomagnetic navigation.
5. Angular dependence of Auger signals from a GaAs (111) surface
International Nuclear Information System (INIS)
Barnard, W.O.
1984-03-01
This dissertation is concerned with the angular dependence of the L 3 M 4 M 4 1067 eV Ga and L 3 M 4 M 4 1228 eV As Auger electron signals from a (111) GaAs surface, using a system which is equipped with a cylindrical mirror analyser. Following a detailed discussion of the Auger process, a review is given of angular effects in the emission excitation and detection of Auger signals. Present theories are discussed and an empirical theory is developed to test the experimental results obtained in this study. The experimental procedures and equipment used are presented. It was found that the Auger signals show a strong variation with the angle of rotation about the normal of a GaAs surface. Furthermore, the nature of the angular spectra of the Ga and As signals are interchanged when the electron beam incident surface is changed from (111) to (111). The main features of the angular variation of the quasi-elastic backscattered signal is reflected in the corresponding Ga and As Auger angular spectra. The angular dependence of the quasi-elastic backscattered signal can be explained semi-quantitatively in terms of the empirical theory. Theoretical arguments are presented which suggest that the Auger signals should show an angular dependence similar to the quasi-elastic backscattered signal. Evidence was found that geometric screening-off of underlying atoms by surface and near surface atoms influence the Auger yield
6. Seafloor classification of the mound and channel provinces of the Porcupine Seabight: An application of the multibeam angular backscatter data
Digital Repository Service at National Institute of Oceanography (India)
Beyer, A.; Chakraborty, B.; Schenke, H.W.
In this study multibeam angular backscatter data acquired in the eastern slope of the Porcupine Seabight are analysed. Processing of the angular backscatter data using the ‘NRGCOR’ software was made for 29 locations comprising different geological...
7. Vector correlation analysis for inelastic and reactive collisions between partners possessing spin and orbital angular momentum.
Science.gov (United States)
Balint-Kurti, Gabriel G; Vasyutinskii, Oleg S
2009-12-31
A general reactive collision of the type A + B --> C + D is considered where both the collision partners (A and B) or the products (C and D) may possess internal, i.e., spin, orbital or rotational, angular momenta. Compact expressions are derived using a rigorous quantum mechanical analysis for the angular momentum anisotropy of either of the products (C or D) arising from an initially polarized distribution of the reactant angular momentum. The angular momentum distribution of the product is expressed in terms of canonical spherical tensors multiplied by anisotropy-transforming coefficients c(K(i)q(k))(K)(K(r),L). These coefficients act as transformation coefficients between the angular momentum anisotropy of the reactants and that of the product. They are independent of scattering angle but depend on the details of the scattering dynamics. The relationship between the coefficients c(K(i)q(k))(K)(K(r),L) and the body-fixed scattering S matrix is given and the methodology for the quantum mechanical calculation of the anisotropy-transforming coefficients is clearly laid out. The anisotropy-transforming coefficients are amenable to direct experimental measurement in a similar manner to vector correlation and alignment parameters in photodissociation processes. A key aspect of the theory is the use of projections of both reactant and product angular momenta onto the product recoil vector direction. An important new conservation rule is revealed through the analysis, namely that if the state multipole for reactant angular momentum distribution has a projection q(k) onto the product recoil vector the state multipoles for the product angular momentum distribution all have this same projection. Expressions are also presented for the distribution of the product angular momentum when its components are evaluated relative to the space-fixed Z-axis. Notes with detailed derivations of all the formulas are available as Supporting Information.
8. On the angular distributions of the heavy products of (HI, xn) reactions
International Nuclear Information System (INIS)
Sagajdak, R.N.
1989-01-01
The effects of neutron evaporation and scattering in the target on the angular distribution of the heavy products of (HI, xn) reactions is considered. Based on the analysis of the experimental angular distributions and their calculated parameters a simple phenomenological approach to the description of these distributions is proposed. The calculated distributions are compared with the experimental ones cited in the literature. The possibilities of using the proposed approach to calculate the integrated angular distributions of heavy products and to determine the efficiency of collecting (HI, xn) reaction products under the conditions of the kinematic separation of recoil nuclei are outlined. 28 refs.; 9 figs
9. AngularJS in the Wild: A Survey with 460 Developers
OpenAIRE
Ramos, Miguel; Valente, Marco Tulio; Terra, Ricardo; Santos, Gustavo
2016-01-01
To implement modern web applications, a new family of JavaScript frameworks has emerged, using the MVC pattern. Among these frameworks, the most popular one is AngularJS, which is supported by Google. In spite of its popularity, there is not a clear knowledge on how AngularJS design and features affect the development experience of Web applications. Therefore, this paper reports the results of a survey about AngularJS, including answers from 460 developers. Our contributions include the ident...
10. Determining misorientation of graphite grains from the angular dependence of X-ray emission spectra
International Nuclear Information System (INIS)
Belavin, V. V.; Okotrub, A. V.; Bulusheva, L. G.; Kotosonov, A. S.; Vyalykh, D. V.; Molodtsov, S. L.
2006-01-01
Angular-resolved X-ray absorption spectra were measured for pyrolytic graphite samples of various quality. A new approach to determining the misorientation of graphite grains in polycrystalline samples is proposed, which is based on calculations of the angular dependence of the relative intensity of a peak corresponding to the π* state for a normal distribution of grains. The experimental values are used to construct theoretical angular dependences using partial densities of the π* and σ* states determined from the nonempirical calculations for graphite
11. A January angular momentum balance in the OSU two-level atmospheric general circulation model
Science.gov (United States)
1982-01-01
The present investigation is concerned with an analysis of the atmospheric angular momentum balance, based on the simulation data of the Oregon State University two-level atmospheric general circulation model (AGCM). An attempt is also made to gain an understanding of the involved processes. Preliminary results on the angular momentum and mass balance in the AGCM are shown. The basic equations are examined, and questions of turbulent momentum transfer are investigated. The methods of analysis are discussed, taking into account time-averaged balance equations, time and longitude-averaged balance equations, mean meridional circulation, the mean meridional balance of relative angular momentum, and standing and transient components of motion.
12. Two-dimensional angular momentum in the presence of long-range magnetic flux
International Nuclear Information System (INIS)
Jackiw, R.; Redlich, A.N.
1983-01-01
It is shown that eigenvalues of two-dimensional angular momentum remain integer valued in the magnetic field of a solenoid, contrary to published assertions that they are modified by the flux. For a vortex, flux does contribute, and the angular momentum can fractionize, as asserted in the literature, provided phases of wave functions are chosen consistently with the solenoid problem. Long-range effects of flux, the distinction between orbital and canonical angular momentum, and interactions with Cooper pairs are essential to this argument
13. Recursive generation of Cartesian angular momentum coupling trees for SO(3)
International Nuclear Information System (INIS)
Sherborne, B.S.; Stedman, G.E.
1990-01-01
Two computer algorithms are evaluated for the reduction of angular momentum coupling trees with vector (j=1) terminals with a Cartesian choice of basis as used in nonlinear optics. Rather than employ advanced tensor algebra, both methods essentially iterate in distinct ways the basic techniques of angular momentum coupling. Turbo Pascal programs implementing these algorithms are presented and compared. The accompanying analysis integrates the Cartesian tensor approach and the diagrammatic approach to the solution of problems in nonlinear optics. The programs generate TeX files for the relevant angular momentum diagrams. (orig.)
14. Historical and contemporary records of the angular rough shark Oxynotus centrina (Chondrichthyes; Oxynotidae in Turkish waters
Directory of Open Access Journals (Sweden)
H. KABASAKAL
2010-10-01
Full Text Available During the last 58 years, only 12 angular rough sharks were recorded in Turkish waters. Rare captures of the species in the area needs an immediate action for the conservation of O. centrina. To protect the habitat of O. centrina, strict regulations should be implemented for diving in the localities, where the angular rough sharks occur regularly. Protecting the habitat of the angular rough shark is an urgent need before subjecting O. centrina to 100% protection in the seas of Turkey.
15. Simple method for evaluating Goldstone diagrams in an angular momentum coupled representation
International Nuclear Information System (INIS)
Kuo, T.T.S.; Shurpin, J.; Tam, K.C.; Osnes, E.; Ellis, P.J.
1981-01-01
A simple and convenient method is derived for evaluating linked Goldstone diagrams in an angular momentum coupled representation. Our method is general, and can be used to evaluate any effective interaction and/or effective operator diagrams for both closed-shell nuclei (vacuum to vacuum linked diagrams) and open-shell nuclei (valence linked diagrams). The techniques of decomposing diagrams into ladder diagrams, cutting open internal lines and cutting off one-body insertions are introduced. These enable us to determine angular momentum factors associated with diagrams in the coupled representation directly, without the need for carrying out complicated angular momentum algebra. A summary of diagram rules is given
16. Orbital angular momentum of a high-order Bessel light beam
International Nuclear Information System (INIS)
Volke-Sepulveda, K; Garces-Chavez, V; Chavez-Cerda, S; Arlt, J; Dholakia, K
2002-01-01
The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page
17. Angular distribution of photofission fragments in 238U at 5.43 MeV
International Nuclear Information System (INIS)
Kuniyoshi, S.; Mafra, O.Y.; Renner, C.; Goldemberg, J.
1974-01-01
The angular distribution of photofission fragments of 238 U, produced by 5.43 MeV monochromatic photons from the eta,γ reaction in sulphur, has been measured using glass plates as detectors. In the analysis of the results only the contributions from the (J sup(π), K) 1= (1 - ,0), (1 - ,1) and (2 + ,0) terms were considered. The coefficients of the angular distributions of the fission fragments were obtained. An analysis of the data available in the literature on the angular distribution near the photofission threshold is also presented
18. Microscopic analysis of angular momentum projected HFB-states in terms of interacting bosons
International Nuclear Information System (INIS)
Ring, P.; Pannert, W.
1984-12-01
Angular momentum- and number-projected Hartree-Fock-Bogoliubov (HFB) wavefunctions for transitional and deformed Rare Earth nuclei are analyzed in terms of Fermion pairs coupled to angular momenta L = 0(S), 2(D), 4(G), ... The Fermion space is truncated to contain only S-D or S-D-G pairs. The variation is carried out before and after angular momentum projection and with different truncations. The influence of the truncation on physical quantities such as moments of inertia, quadrupole moments or pair transfer matrix elements is discussed. 21 references
19. Measurement of the angular distribution of neutron-proton scattering at 10 MeV
International Nuclear Information System (INIS)
Haight, R.C.; Bateman, F.B.; Grimes, S.M.; Brient, C.E.; Massey, T.N.; Wasson, O.A.; Carlson, A.D.; Zhou, H.
1995-01-01
The relative angular distribution of neutrons scattered from protons was measured at an incident neutron energy of 10 MeV at the Ohio University Accelerator Laboratory. An array of 11 detector telescopes at laboratory angles of 0 to 60 degrees was used to detect recoil protons from neutron interactions with a CH 2 (polypropylene) target. Data for 7 of these telescopes were obtained with one set of electronics and are presented here. These data, from 108 to 180 degrees for the center-of-mass scattering angles, have a small slope which agrees better with angular distributions predicted by the Arndt phase shifts than with the ENDF/B-VI angular distribution
20. Effects of angular momentum dissipation on fluctuations of excitation functions in heavy-ion collisions
International Nuclear Information System (INIS)
Kun, S.Yu.; Noerenberg, W.; Technische Hochschule Darmstadt
1992-02-01
We study the effect from dissipation of relative angular momentum on fluctuations of exitations functions in dissipative heavy-ion collisions. Dissipation and fluctuation of relative angular momentum modify and smooth the time-angle localization of the roating dinuclear system. The secondary maxima in the energy correlation function of the cross-section are shifted to smaller values of the energy difference, the shift depending on the relaxation time and the diffusion coefficient for the angular-momentum dissipation. The results are illustrated for the collision 28 Si(E lab =130MeV)+ 48 Ti. (orig.)
1. Mass resolved angular distribution of fission products in 20Ne + 232Th reaction
International Nuclear Information System (INIS)
Tripathi, R.; Sodaye, S.; Sudarshan, K.; Kumar, Amit; Guin, R.
2011-01-01
Mass resolved angular distribution of fission products was measured in 20 Ne + 232 Th reaction at beam energy of 120 MeV. A preliminary analysis of the angular distribution data of fission products shows higher average anisotropy compared to that calculated using statistical theory. A signature of rise in anisotropy near symmetry, as reported in earlier studies in literature, is also seen. Further study is in progress to get more detailed information about the contribution from non-compound nucleus fission and dependence of angular anisotropy on asymmetry of mass division
2. Observation of Coherent and Incoherent Dissociation Mechanisms in the Angular Distribution of Atomic Photofragment Alignment
International Nuclear Information System (INIS)
Bracker, A.S.; Lee, Y.T.; Bracker, A.S.; Wouters, E.R.; Suits, A.G.; Lee, Y.T.; Lee, Y.T.; Vasyutinskii, O.S.
1998-01-01
We have analyzed the recoil angle dependence of chlorine atom angular momentum alignment for the dissociation of chlorine molecules at 355nm. This angular distribution was isolated from ion image measurements, which map a three-dimensional velocity vector distribution of state-selectively-ionized photofragments into a two-dimensional spatial distribution. Using a general quantum mechanical method to simulate the alignment angular distribution, we show that there are clear contributions to alignment from both incoherent and coherent components of a perpendicular optical transition in the molecule. copyright 1998 The American Physical Society
3. Angular momentum transfer in deep inelastic heavy ion collisions. Part 2
International Nuclear Information System (INIS)
Barbosa, V.C.; Soares, P.C.; Oliveira, Edgar C. de; Gomes, Luiz Carlos
1985-01-01
The Fokker-Planck equation which describes the angular momentum transfer in deep inelastic heavy ion collisions is solved by a stochastic simulation procedure. The fusion cross section calculation is discussed. The calculations show that the critical orbital angular momentum does not play such a special role as in the deterministic case. The results of all the angular momentum transfer and their fluctuations are calculated and compared with experimental results for the reactions 86 Kr+ 154 Sm at 610 MeV, 165 Ho+ 148 Sm, and 165 Ho+ 176 Yb at 1400 MeV. (Author) [pt
4. Angular distribution of photofission fragments in 238U at 5.43 MeV
International Nuclear Information System (INIS)
Kuniyoshi, Susumo
1973-01-01
The angular distribution of photofission fragments of 238 U, produced by 5.43 MeV monochromatic photons from the η,γ reaction in sulphur, has been measured using glass plates as detectors. In the analysis of the results only the contributions from the (J π , K) 1= (1 - ,0), (1 - ,1) and (2 + ,0) terms were considered. The coefficients of the angular distributions of the fission fragments were obtained. An analysis of the data available in the literature on the angular distribution near the photofission threshold is also presented. (author)
5. CONSTRAINING THE ANGULAR MOMENTUM EVOLUTION OF V455 ANDROMEDAE
Energy Technology Data Exchange (ETDEWEB)
Mukadam, Anjum S.; Szkody, Paula [Department of Astronomy, University of Washington, Seattle, WA 98195-1580 (United States); Pyrzas, Stylianos [Qatar Environment and Energy Research Institute (QEERI), HBKU, Qatar Foundation, P.O. Box 5825, Doha (Qatar); Townsley, D. M. [Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, AL 35487 (United States); Gänsicke, B. T. [Department of Physics, University of Warwick, Coventry, CV4 7AL (United Kingdom); Hermes, J. J. [Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255 (United States); Kemp, Jonathan [Department of Physics, Middlebury College, Middlebury, VT 05753 (United States); Patterson, J.; Ding, Claire; Wolf, Katie; Gemma, Marina; Karamehmetoglu, Emir [Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027 (United States); Rock, John [CBA-Wilts, 2 Spa Close, Highworth, Swindon, Wilts SN6 7PJ (United Kingdom)
2016-04-10
Time-series photometry on the cataclysmic variable V455 Andromedae (hereafter V455 And, HS 2331+3905) reveals a rotation period shorter than the orbital period, implying the presence of a magnetic field. We expect that this magnetic field channels the accreted matter from the disk toward the white dwarf poles, classifying it as an Intermediate Polar. The two polar spinning emission areas are visible in the lightcurves at the rotation period of 67.61970396 ± 0.00000072 s, and its harmonic. Using photometric observations of V455 And obtained from 2007 October to 2015, we derive 3σ upper limits to the rate of change of the spin harmonic (SH) with time to be dP{sub SH}/dt ≤ −7.5 × 10{sup −15} s s{sup −1} employing the O–C method, and −5.4 × 10{sup −15} s s{sup −1} with a direct nonlinear least squares fit. There is no significant detection of a changing spin period for the duration of 2007 October–2015. The 3σ upper limit for the rate of change of spin period with time is dP{sub spin}/dt ≤ −10.8 × 10{sup −15} s s{sup −1} or −0.34 μs yr{sup −1}. V455 And underwent a large-amplitude dwarf nova outburst in 2007 September. The pre-outburst data reflect a period 4.8 ± 2.2 μs longer than the best-fit post-outburst spin period. The angular momentum gained by the white dwarf from matter accreted during outburst and its slight subsequent shrinking should both cause the star to spin slightly faster after the outburst. We estimate that the change in spin period due to the outburst should be 5 μs, consistent with the empirical determination of 4.8 ± 2.2 μs (3σ upper limit of 11.4 μs)
6. On the spherical harmonic expansion of the neutron angular distribution function
Energy Technology Data Exchange (ETDEWEB)
Depken, Sven
1959-03-15
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases.
7. New statistical function for the angular distribution of evaporation residues produced by heavy ions
International Nuclear Information System (INIS)
Rigol, J.
1994-01-01
A new statistical function has been found for modelling the angular distribution of evaporation residues produced by heavy ions. Experimental results are compared with the calculated ones. 11 refs.; 4 figs. (author)
8. On the spherical harmonic expansion of the neutron angular distribution function
International Nuclear Information System (INIS)
Depken, Sven
1959-03-01
The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases
9. Angular momentum of phonons and its application to single-spin relaxation
Science.gov (United States)
Nakane, Jotaro J.; Kohno, Hiroshi
2018-05-01
We reexamine the relaxation process of a single spin embedded in an elastic medium, a problem studied recently by Garanin and Chudnovsky (GC) [Phys. Rev. B 92, 024421 (2015), 10.1103/PhysRevB.92.024421] from the viewpoint of angular-momentum transfer. Using Noether's theorem, we identify two distinct angular momenta of the medium, one Newtonian discussed by GC and the other field-theoretical, both of which consist of an orbital part and a spin part. For both angular momenta, we found that the orbital part is as essential as the spin part in the relaxation process. In particular, the angular-momentum transfer from the (real) spin to the Newtonian orbital part may be considered as an incipient rotation that leads to the Einstein-de Haas effect.
10. Angular distribution of ejected electrons from 20 keV He+ impact on He
International Nuclear Information System (INIS)
Tokoro, N.; Takenouchi, S.; Urakawa, J.; Oda, N.
1982-01-01
The angular distributions of ejected electrons in the energy range 5-70 eV have been measured at angles from 30 to 150 0 for 20 keV He + impact on He. The angular dependence of excitation cross sections of autoionisation states 2s 2 1 S and 2p 2 1 D+2s2p 1 P are in good agreement with previous data measured by Bordenave-Montesquieu et al (Phys. Rev.; A25:245 (1982)). The continuous parts of the electron spectra show symmetrical angular distributions around 90 0 in the laboratory frame for low-energy electrons (< approximately equal to 30 eV). These angular distributions are discussed in connection with the molecular autoionisation mechanism. (author)
11. Angular distribution of ejected electrons from 20 keV He/sup +/ impact on He
Energy Technology Data Exchange (ETDEWEB)
Tokoro, N.; Takenouchi, S.; Urakawa, J.; Oda, N. (Tokyo Inst. of Tech. (Japan). Research Lab. of Nuclear Reactor)
1982-10-28
The angular distributions of ejected electrons in the energy range 5-70 eV have been measured at angles from 30 to 150/sup 0/ for 20 keV He/sup +/ impact on He. The angular dependence of excitation cross sections of autoionisation states 2s/sup 2/ /sup 1/S and 2p/sup 2/ /sup 1/D+2s2p /sup 1/P are in good agreement with previous data measured by Bordenave-Montesquieu et al (Phys. Rev.; A25:245 (1982)). The continuous parts of the electron spectra show symmetrical angular distributions around 90/sup 0/ in the laboratory frame for low-energy electrons (angular distributions are discussed in connection with the molecular autoionisation mechanism.
12. The mass angular scattering power method for determining the kinetic energies of clinical electron beams
International Nuclear Information System (INIS)
Blais, N.; Podgorsak, E.B.
1992-01-01
A method for determining the kinetic energy of clinical electron beams is described, based on the measurement in air of the spatial spread of a pencil electron beam which is produced from the broad clinical electron beam. As predicted by the Fermi-Eyges theory, the dose distribution measured in air on a plane, perpendicular to the incident direction of the initial pencil electron beam, is Gaussian. The square of its spatial spread is related to the mass angular scattering power which in turn is related to the kinetic energy of the electron beam. The measured spatial spread may thus be used to determine the mass angular scattering power, which is then used to determine the kinetic energy of the electron beam from the known relationship between mass angular scattering power and kinetic energy. Energies obtained with the mass angular scattering power method agree with those obtained with the electron range method. (author)
13. The photon angular momentum controversy: Resolution of a conflict between laser optics and particle physics
Energy Technology Data Exchange (ETDEWEB)
2016-05-10
The claim some years ago, contrary to all textbooks, that the angular momentum of a photon (and gluon) can be split in a gauge-invariant way into an orbital and spin term, sparked a major controversy in the Particle Physics community, exacerbated by the realization that many different forms of the angular momentum operators are, in principle, possible. A further cause of upset was the realization that the gluon polarization in a nucleon, a supposedly physically meaningful quantity, corresponds only to the gauge-variant gluon spin derived from Noether's theorem, evaluated in a particular gauge. On the contrary, Laser Physicists have, for decades, been happily measuring physical quantities which correspond to photon orbital and spin angular momentum evaluated in a particular gauge. This paper reconciles the two points of view, and shows that it is the gauge invariant version of the canonical angular momentum which agrees with the results of a host of laser optics experiments.
14. Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases
CSIR Research Space (South Africa)
Mafu, M
2013-09-01
Full Text Available We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d + 1) mutually unbiased measurements in a...
15. Angular velocity determination of spinning solar sails using only a sun sensor
Directory of Open Access Journals (Sweden)
Kun Zhai
2017-02-01
Full Text Available The direction of the sun is the easiest and most reliable observation vector for a solar sail running in deep space exploration. This paper presents a new method using only raw measurements of the sun direction vector to estimate angular velocity for a spinning solar sail. In cases with a constant spin angular velocity, the estimation equation is formed based on the kinematic model for the apparent motion of the sun direction vector; the least-squares solution is then easily calculated. A performance criterion is defined and used to analyze estimation accuracy. In cases with a variable spin angular velocity, the estimation equation is developed based on the kinematic model for the apparent motion of the sun direction vector and the attitude dynamics equation. Simulation results show that the proposed method can quickly yield high-precision angular velocity estimates that are insensitive to certain measurement noises and modeling errors.
16. Quality of the restricted variation after projection method with angular momentum projection
International Nuclear Information System (INIS)
Rodriguez, Tomas R.; Egido, J.L.; Robledo, L.M.; Rodriguez-Guzman, R.
2005-01-01
Recently, the restricted angular momentum variation after projection method, using the quadrupole degree of freedom as a variational coordinate in conjunction with effective interactions of the Skyrme or Gogny type, has been used very successfully to study a variety of phenomena concerning the quadrupole degree of freedom. In this paper, we study the quality of such an approach by considering additional degrees of freedom as variational coordinates: the hexadecapole moment and the fluctuations on the quadrupole moment, particle number, and angular momentum operators. The study has been performed with the Gogny interaction (D1S parametrization) for the nuclei 32 Mg and 34 Mg. The results of the angular momentum projection and the subsequent generator coordinate calculations show that the extra degrees of freedom considered are irrelevant for the description of the lowest lying states for each angular momentum
17. Predictive factors for functional outcome and failure in angular stable osteosynthesis of the proximal humerus.
LENUS (Irish Health Repository)
Hardeman, Francois
2012-02-01
Angular stable osteosynthesis has become the gold standard in the operative treatment of proximal humeral fractures. The aim of this article is to determine the indications for osteosynthesis versus primary arthroplasty based on clinical and radiological parameters.
18. Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number
Science.gov (United States)
Meibohm, Jan; Candelier, Fabien; Rosen, Tomas; Einarsson, Jonas; Lundell, Fredrik; Mehlig, Bernhard
2016-11-01
We analyse the angular velocity of a small neutrally buoyant spheroid log rolling in a simple shear. When the effect of fluid inertia is negligible the angular velocity ω -> equals half the fluid vorticity. We compute by singular perturbation theory how weak fluid inertia reduces the angular velocity in an unbounded shear, and how this reduction depends upon the shape of the spheroid (on its aspect ratio). In addition we determine the angular velocity by direct numerical simulations. The results are in excellent agreement with the theory at small but not too small values of the shear Reynolds number, for all aspect ratios considered. For the special case of a sphere we find ω / s = - 1 / 2 + 0 . 0540Re 3 / 2 where s is the shear rate and Re is the shear Reynolds number. This result differs from that derived by Lin et al. who obtained a numerical coefficient roughly three times larger.
19. The proton electromagnetic form factor F2 and quark orbital angular ... | {"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": 0.9312525987625122, "perplexity": 2353.505015017117}, "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-2018-39/segments/1537267155413.17/warc/CC-MAIN-20180918130631-20180918150631-00447.warc.gz"} |
https://papers.neurips.cc/paper/2020/hash/b282d1735283e8eea45bce393cefe265-Abstract.html | #### Authors
Bohang Zhang, Jikai Jin, Cong Fang, Liwei Wang
#### Abstract
Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD) converges faster than vanilla GD via introducing a new assumption called $(L_0, L_1)$-smoothness, which characterizes the violent fluctuation of gradients typically encountered in deep neural networks. However, their iteration complexities on the problem-dependent parameters are rather pessimistic, and theoretical justification of clipping combined with other crucial techniques, e.g. momentum acceleration, are still lacking. In this paper, we bridge the gap by presenting a general framework to study the clipping algorithms, which also takes momentum methods into consideration.We provide convergence analysis of the framework in both deterministic and stochastic setting, and demonstrate the tightness of our results by comparing them with existing lower bounds. Our results imply that the efficiency of clipping methods will not degenerate even in highly non-smooth regions of the landscape. Experiments confirm the superiority of clipping-based methods in deep learning tasks. | {"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": 0.8013486862182617, "perplexity": 1031.7697866291917}, "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/1627046153966.52/warc/CC-MAIN-20210730091645-20210730121645-00080.warc.gz"} |
http://mathhelpforum.com/calculus/26577-local-coords.html | # Math Help - Local Coords
1. ## Local Coords
If $\bold{r}(t) = (t^2-t, t \sqrt{2t-t^2}), 0 \leq t \leq 2$ is $\bold{u}_r = \frac{(t^2-t, t \sqrt{2t-t^2})}{\sqrt{(t^2-t)^{2} + t^{2}(2t-t^2)}}$ and $\bold{u}_\theta = \frac{(t \sqrt{2t-t^2}, t^2-t)}{\sqrt{(t^2-t)^{2} + t^{2}(2t-t^2)}}$?
2. Originally Posted by shilz222
If $\bold{r}(t) = (t^2-t, t \sqrt{2t-t^2}), 0 \leq t \leq 2$ is $\bold{u}_r = \frac{(t^2-t, t \sqrt{2t-t^2})}{\sqrt{(t^2-t)^{2} + t^{2}(2t-t^2)}}$ and $\bold{u}_\theta = \frac{(t \sqrt{2t-t^2}, t^2-t)}{\sqrt{(t^2-t)^{2} + t^{2}(2t-t^2)}}$?
what are $\bold{u}_r \mbox { and } \bold{u}_{\theta}$ ?
they seem to be unit vectors, but unit vectors of what? or in what direction?
3. $\bold{u}_r = \frac{\bold{r}(t)}{r(t)}$ in the direction of $\bold{r}$ and $\bold{u}_\theta$ is a perpendicular unit vector.
4. Originally Posted by shilz222
$\bold{u}_r = \frac{\bold{r}(t)}{r(t)}$ in the direction of $\bold{r}$ and $\bold{u}_\theta$ is a perpendicular unit vector.
you mean $\bold{u}_r = \frac {\bold{r}(t)}{|\bold{r}(t)|}$ ?
note that: for a vector $$ two perpendicular vectors are $<-b,a>$ or $$, they point in opposite directions. you put the vector $$
5. yes, that was a typo. yeah in the book, $r(t) = ||\bold{r}(t)||$. | {"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": 19, "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": 0.96644526720047, "perplexity": 1046.1567047899225}, "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/1430453938418.92/warc/CC-MAIN-20150501041858-00013-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.groundai.com/project/coronal-diagnostics-from-narrowband-images-around-304-nm/ | 1 Introduction
###### Abstract
Images taken in the band centered at 30.4 nm are routinely used to map the radiance of the He ii Ly line on the solar disk. That line is one of the strongest, if not the strongest, line in the EUV observed in the solar spectrum, and one of the few lines in that wavelength range providing information on the upper chromosphere or lower transition region. However, when observing the off-limb corona the contribution from the nearby Si xi 30.3 nm line can become significant. In this work we aim at estimating the relative contribution of those two lines in the solar corona around the minimum of solar activity. We combine measurements from CDS taken in August 2008 with temperature and density profiles from semiempirical models of the corona to compute the radiances of the two lines, and of other representative coronal lines (e.g., Mg x 62.5 nm, Si xii 52.1 nm). Considering both diagnosed quantities from line ratios (temperatures and densities) and line radiances in absolute units, we obtain a good overall match between observations and models. We find that the Si xi line dominates the He ii line from just above the limb up to in streamers, while its contribution to narrowband imaging in the 30.4 nm band is expected to become smaller, even negligible in the corona beyond , the precise value being strongly dependent on the coronal temperature profile.
## Section 1 Introduction
Narrowband imaging of the Sun in the EUV has become an almost indispensable tool for solar physicists. Instruments like the Extreme UltraViolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO), and the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) routinely monitor the Sun at various wavelengths. Both instruments observe, among others, in bands centered around 30.4 nm, the wavelength of the Ly line of ionized helium.
Observations with the Sounding CORona Experiment (SCORE: Fineschi et al., 2004; Fineschi, 2006), flown on HERSCHEL, a NASA sounding-rocket payload, also include such a band. Finally, the Multi Element Telescope for Imaging and Spectroscopy (METIS), one of the scientific payloads selected for Solar Orbiter, the M-class mission of the ESA Cosmic Vision program for the exploration of the Sun at a distance as close as 0.28 AU, will also have a spectro-imaging channel at that wavelength.
### 1.1 The Spectral Region around 30.4 nm
The most interesting line in the band around 30.4 nm is certainly the He ii 30.4 nm, the Ly of ionized helium. Narrowband imaging of the solar disk around that line therefore allows probing relatively cool plasma ( K) in the EUV, although the details of the formation of that line in the quiescent solar atmosphere are still somewhat controversial (e.g., Andretta, Del Zanna, and Jordan, 2003; Pietarila and Judge, 2004).
However, for the extended corona, one of the most interesting diagnostics possible with the He ii 30.4 nm line is related to a radiative “pumping” mechanism analogous to that exhibited by hydrogen Ly . Furthermore, the nearby strong Si xi resonance line at 30.3 nm adds the possibility of probing radial velocities in the range of km s via a similar mechanism.
### 1.2 The Ratio Si xi 30.3 nm/He ii 30.4 nm
The presence of the nearby Si xi line, while providing additional diagnostic opportunities, poses a problem for the interpretation of narrowband images. The ratio Si xi 30.3 nm/He ii 30.4 nm is around 0.1 in the quiescent solar atmosphere seen on the solar disk (Del Zanna and Andretta, 2011), or even smaller in active regions (Thomas and Neupert, 1994), but dramatically changes in the corona above the limb.
To illustrate this, we show in Figure 1 the peak radiances of the two lines, measured from spectra taken with the Normal Incidence Spectrograph (NIS) of the SOHO/Coronal Diagnostic Spectrometer (CDS: Harrison et al., 1995). The raster scans shown here were taken on 21 January 1998, and can be considered representative of relatively quiescent off-limb regions: only a small prominence is visible in the field of view (FOV). The ratio of the two lines is also shown.
The rapid increase of the ratio Si xi 30.3 nm/He ii 30.4 nm above the limb is also apparent from the average profiles at various heights above the limb shown in Figure 1. However, data obtained from CDS/NIS are limited to the lower corona; it is entirely possible that further out in the corona the ratio Si xi 30.3 nm/He ii 30.4 nm could decrease again. Whether and where that happens is of utmost relevance for the interpretation of narrowband imaging of the outer corona.
In this article we will make an estimate of the ratio of the two lines in typical conditions of the corona at solar minimum. Using observed EUV, spectrally resolved radiances from SOHO/CDS (Section 2), we will first estimate average on-disk and off-limb radiances in several coronal lines, including those for Si xi 30.3 nm and He ii 30.4 nm; from the line ratios we will also derive average densities and temperatures in the corona. These measurements will then provide the input disk irradiance needed to calculate the radiative excitation of the coronal lines, as well as constraints to the calculations at the lower boundaries of the models, i.e. near the solar limb (Section 3).
In order to derive both mean on-disk and off-limb radiances of lines in the spectral range observed by CDS/NIS, we used whole-Sun scans taken with the CDS/NIS study called USUN in the CDS database.
The CDS USUN study consists of 69 rasters, for a total of 700 to 1000 exposures with the 4 slit, covering the whole Sun and part of the off-limb corona in about 13 hours. Further details on the CDS USUN study are given in Thompson and Brekke (2000) and Del Zanna and Andretta (2011). Here we use the data processed and analyzed as described in detail in the latter article, including the radiometric calibration of CDS/NIS of Del Zanna et al. (2001b, 2010). We note that the new calibration is significantly different from the previous ones. We also note that measurements of the He ii 30.4 nm radiance/irradiances have been largely inconsistent throughout the literature, and that the Del Zanna and Andretta (2011) calibration provides irradiances in agreement with the SDO Extreme Ultraviolet Variability Experiment (EVE) prototype measurements of 14 April 2008 as described in the same article. From comparisons between our measurements with those by various instruments, two errors in the analysis software of CDS and the EUV Normal-Incidence Spectrometer (EUNIS: Jordan and Brosius 2007) were uncovered (Wang et al., 2011). Our CDS measurements are now also in agreement with the EUNIS ones, within a few percent.
The CDS USUN scans have been taken approximately once a month starting in 1998. We chose to analyze a USUN scan taken on 25 August 2008, i.e. during the extended minimum between activity Cycles 23 and 24. The configuration of the corona from SOHO/EIT (Delaboudinière et al., 1995) and from the C2 telescope of the Large Angle and Spectrometric Coronagraph (LASCO: Brueckner et al., 1995) on that date is shown in Figure 2. For display clarity, an average radial profile has been subtracted from the LASCO-C2 image.
### 2.1 Selected Regions of the FOV
For each line in the CDS spectral range, it is possible to build a monochromatic image of the Sun. An example is shown in the right-hand panel of Figure 3, for the Mg x 62.5 nm line. The solar disk on that date did not exhibit significant activity, while two symmetrical polar coronal holes are clearly visible.
For each monochromatic image, we then built a histogram of radiances as function of distance from the center of the Sun. An example of the two-dimensional histogram thus obtained is shown in the left-hand panel of Figure 3. We then obtained an average radiance radial profile from the median of the histograms at each heliocentric distance (thicker line in Figure 3). The standard deviation of the profile is also shown (thinner lines).
The same procedure can be applied to specific regions of the FOV. In particular, we selected the southeast quadrant of the disk, corresponding to the base of the streamer visible in Figure 2, and the two polar regions. The corresponding images and radiance histograms are shown in Figure 4. We have verified that the choice of a specific region of interest outside the polar coronal holes does not affect significantly the radiance radial profiles for most lines, a fact consistent with the very low activity state of the lower corona on that date.
There are at least two known sources of spurious radiation that can affect the measurement of off-limb line radiances in CDS.
First, radiation from the much brighter solar disk can be diffused into the tail of the instrument’s point-spread function (PSF) to contribute to off-limb line radiation. Harrison et al. (1995) give values for the PSF (measured at 6.8 nm) of and for distances of 100 and 150, respectively, from the core. Based on those figures, at distances of we would expect the fractional contribution of the disk to line radiances to be well below , compared to a decrease of the order of little more than a factor ten in typical coronal lines (Figures 3 and 4). However, the in-flight performance of the instrument is not necessarily as good as indicated by those laboratory measurements, especially after the loss of contact with the SOHO spacecraft in June 1998, which led to a significant alteration of the instrumental response.
To estimate the contribution of disk scattered radiation, we examined the off-limb behavior of the strongest cool lines (lines with formation temperature much less than K) in the CDS range: He i 58.4 nm and O v 62.9 nm, assuming that the coronal contribution to their off-limb measured radiances is negligible (Figure 5, left panel in the upper row). From our data, it appears that the fractional contribution of disk scattered radiation is below at .
A more precise determination of this contribution is impeded by the presence of a continuum background, only weakly dependent on wavelength (Thompson and Brekke, 2000). The source of this background is unclear; however, if of solar origin, its pattern of spatial variation on the disk would suggest a cool source (Figure 5, center and right panels in the upper row). According to Thompson and Brekke (2000), for instance, such a background is mainly due to Ly radiation scattered by the far wings of the grating profile, but with likely contributions from a variety of other lines. In any case, the presence of that background can hamper accurate measurement of off-limb lines, especially of the faintest ones.
The average line peak count rates at (average above ), shown in the lower panel of Figure 5 (triangles), clearly outline the background continuum; only a few strong lines are still measurably above that level. In contrast, at (average between and ), most lines with formation temperature above K are still clearly detectable above the background (filled circles in Figure 5). For this discussion, we are only interested in a few, relatively strong lines (see following sections); those lines are still measurable up to at least or beyond (as is the case for the Mg x 62.5 nm, Mg ix 36.8 nm, or Si xii 52.1 nm lines). The same analysis can be applied to polar coronal holes, leading to similar results, although with larger uncertainties due to lower count rates in coronal lines.
As mentioned in Section 1, these measured radiances will be used to constrain various semiempirical models of the corona found in literature. A summary of the plasma parameters from those models is shown in Figure 6; the models are described in more detail in Section 3.
### 2.3 Temperatures and Densities from CDS Radiances
From the average radiance radial profiles, it is possible to obtain estimates of average temperatures and densities above the limb using line-ratio diagnostics. We selected the density-sensitive ratio Si ix 34.2/35.0 nm and the temperature-sensitive ratio Mg x 62.5 nm/Mg ix 36.8 nm, in analogy with the similar analyses of Gibson et al. (1999) and Fludra et al. (1999), based on SOHO/CDS measurements during the solar minimum in 1996. The latter temperature-sensitive ratio has the advantage that the lines are bright and from the same element.
The densities and temperatures from the observed line ratios were obtained using the CHIANTI database (Dere et al., 1997), version 6 (Dere et al., 2009), in particular including the new ion abundances in ionization equilibrium.
The line ratios measured at the base of the southeast streamer are shown in Figure 7 (top panels), while the corresponding plasma parameters, compared with density and temperature profiles from various authors, are shown in the lower panels. Figure 8 reports the same results for the polar coronal holes.
The work of Gibson et al. (1999) and Fludra et al. (1999) actually base their temperature measurement on the ratio of the lines Si xii 52.1 nm and Mg x 62.5 nm. However, those two lines may be affected by an anomalous behavior of the Li-like ions in many emission measure analyses, as described in Del Zanna, Landini, and Mason (2002). Indeed, the ratio measured in our data is at variance both with the other ratio and with the literature profiles. In polar coronal holes, in particular, that ratio yields too high a temperature, even slightly higher than in the rest of the corona. We used a photospheric mixture of abundances, as discussed in Section 3.1.3, but since both Mg and Si are elements with low first ionization potential ( FIP ), adopting “coronal” abundances would not significantly reduce such a discrepancy. This incongruity may be due to the anomalous behavior of Li-like ions mentioned above and discussed in Section 4.1, but also to the fact that the Si xii 52.1 nm line is weaker than the Mg x 62.5 nm line, much more so in coronal holes, and thus may possibly be affected by the stray light described in Section 2.2. With these caveats in mind, while regarding the temperature from the ratio of the two as unreliable, we will nevertheless consider for both lines the radiance radial profiles and compare them with the corresponding calculations of Section 4.
#### 2.3.1 Streamer
The density profile for the off-limb quiescent corona from the ratio Si ix 34.2/ 35.0 nm, if extrapolated to heliocentric distances , is in excellent agreement with the values listed by Gibson et al. (1999), as well as with the density profiles of Thernisien and Howard (2006), Sittler and Guhathakurta (1999), and Saito, Poland, and Munro (1977), while the profile of Leblanc, Dulk, and Bougeret (1998) gives densities too low by a factor .
The agreement with the temperature profile given by the ratio Mg x 62.5 nm/ Mg ix 36.8 nm, while still good, is somewhat less stringent, with a coronal temperature of about K, slightly higher than the peak value of K given by both Gibson et al. (1999) and Vásquez, van Ballegooijen, and Raymond (2003).
#### 2.3.2 Polar Regions (Coronal Holes)
In polar regions, the inferred densities match much better the estimates by Kohl et al. (1998) than those by the other sources: Guhathakurta et al. (1999); Munro and Jackson (1977); Sittler and Guhathakurta (1999, 2002), and Saito, Poland, and Munro (1977). This last article gives a density cm at , below the lower limit of Figure 8.
The agreement of the temperature from the Mg x 62.5 nm/Mg ix 36.8 nm ratio with the profile given by Vásquez, van Ballegooijen, and Raymond (2003) is in this case excellent, and much better than with the profile of Guhathakurta et al. (1999).
The calculated radiances can be divided into a collisional component and a component radiatively excited by the line radiation from the solar disk (for the He ii line or other transition-region lines) or from the inner corona (for the Si xi line and other coronal lines). As an additional consistency check in the calculations, we applied the procedure described below to two other lines observed by CDS: Si xii 52.1 nm and Mg x 62.5 nm.
The collisional component of a line emissivity for the strong lines we are considering can be computed using the standard approximation of collisional excitation from the ground level followed by radiative decay.
The radiative component of the emissivity due to resonant scattering, i.e. the line emission due to the absorption and re-emission of photons from the lower solar atmosphere (chromosphere or near-limb corona) by ions/atoms in the corona (also known as “Doppler dimming”), has been calculated adopting the formalism of Withbroe et al. (1982) and Noci, Kohl, and Withbroe (1987). The relevant atomic data adopted were taken from the CHIANTI database version 6 (Dere et al., 1997, 2009).
Finally, the integration of line emissivities is performed along the line of sight ( LOS ) over a coronal sector wide, where a spherical symmetry is assumed. At low heights the most significant contribution to the synthesized line radiance is given by the emission near the plane of the sky ( POS ), because of the rapid decrease of the electron density with increasing heliocentric distance. For larger heliocentric heights, the integration path along the LOS must be larger since the electron density decreases more slowly; therefore, even the emission far from the POS contributes significantly to the line intensity. For all the heliocentric heights where the coronal-line radiances are assessed, a further increase of the integration interval involves a radiance variation .
### 3.1 Coronal Physical Quantities
The other ingredients needed to compute line emissivities are as follows: electron density and temperature (summarized in Figure 6), ion abundance, outflow speed of the expanding solar corona, three-dimensional ( 3D ) velocity distribution of the coronal absorbing ions as a function of heliocentric distance and latitude, total radiance and profile of the exciting lines emitted by the disk or the lower corona. These parameters will be discussed in more detail in the following sections.
All of the physical and dynamic parameters describing the line-profile formation along the LOS are chosen by employing coronal models consistent with the observations near solar minimum, and already briefly discussed in the previous section in the context of empirical diagnostics. In some cases, these models are extrapolated down to to reach the SOHO/CDS domain of validity and at high heliocentric distances in the coronal sector wide where the integration along the LOS is performed.
#### 3.1.1 Electron Temperature and Density: Polar Regions
Electron densities can be determined from measurements of polarized brightness ( pB ) by using the inversion technique developed by van de Hulst (1950). The pB is directly related to the coronal electron density, since it depends upon the Thomson scattering of the photospheric white-light radiation by coronal electrons. The technique relies on the inversion of the equation describing the relation between the observed Thomson-scattered pB and the electron density.
Among the first attempts to infer the electron-density distribution within a polar coronal hole from pB observations with space coronagraphs, Munro and Jackson (1977) and Saito, Poland, and Munro (1977) derived electron-density radial profiles, valid from 2 to and from 2.5 to , respectively, by using data provided by the High Altitude Observatory ( HAO ) white-light coronagraph on Skylab.
More recently, Kohl et al. (1998) modeled the electron density in a polar coronal hole, from to , by measuring the linear polarization due to Thomson-scattered photospheric light with the SOHO/Ultraviolet Coronagraph Spectrometer (UVCS: Kohl et al., 1995) white-light channel, while Sittler and Guhathakurta (1999) developed an empirical electron-density profile at the poles from Skylab coronagraph white-light data (Guhathakurta, Holzer, and MacQueen, 1996). The electron-density model, valid only outside , was extended into interplanetary space by using electron densities derived from the Ulysses plasma data (Phillips et al., 1995).
Quantitative information on the electron-density distribution of a coronal hole was also estimated by Guhathakurta et al. (1999) by combining white-light, pB observations from the SOHO/LASCO-C2 and -C3 and HAO/Mauna Loa Mark III coronagraphs with density-sensitive EUV line ratios of Si ix 35.0/ 34.2 nm observed by SOHO/CDS, to obtain a density profile from 1 to for the polar coronal hole. With the assumptions that the coronal gas is locally isothermal and in radial hydrostatic equilibrium along the LOS, Guhathakurta et al. (1999) determined an effective (electron) temperature in polar coronal holes.
Another method for inferring the coronal electron temperature is based on in-situ measurements of the solar-wind charge state, which is determined in large part by the electron temperature in the inner corona, where the ionization and recombination times are still short compared to the solar-wind expansion time. The electron temperature between 1 and derived by Ko et al. (1997) and Cranmer, Field, and Kohl (1999) in a polar coronal hole, from observations with Ulysses/SWICS, were fitted with a combination of two power laws from Vásquez, van Ballegooijen, and Raymond (2003) to give an electron-temperature model at the poles.
The above models, which differ significantly for as shown in the left panels of Figure 6, are employed in the synthesis of the radiance of the He ii 30.4 nm, Si xi 30.3 nm, Si xii 52.1 nm, and Mg x 62.5 nm lines, in order to point out the sensitivity of the coronal line intensity to the density and especially to the temperature of the electrons.
#### 3.1.2 Electron Temperature and Density: Equatorial Regions
Concerning the electron-density models employed in the assessment of the intensity of the He ii, Si xi, Si xii, and Mg x lines at low heliographic latitudes, Saito, Poland, and Munro (1977) and Sittler and Guhathakurta (1999) (see Section 2.3) also investigated the equatorial electron-density distribution, providing models valid from 2.5 to and outside , respectively. The electron-density models developed by Leblanc, Dulk, and Bougeret (1998), Gibson et al. (1999), and Thernisien and Howard (2006) within a streamer have been considered in the analysis as well.
Leblanc, Dulk, and Bougeret (1998) derived the electron-density distribution in the ecliptic plane, from the corona to AU, using observations from MHz to a few kilohertz by the radio experiment WAVES onboard the Wind spacecraft. The radio technique is based on the measurement of the drift rates of type III bursts at each frequency, which allowed the authors to estimate the speed of electron streams creating the bursts, and, indirectly, an electron-density model all along the trajectory of the bursts for .
Gibson et al. (1999) modeled electron densities within a streamer structure, from 1 to , using coronal observations of both visible white light (SOHO/LASCO-C2 and HAO/Mauna Loa Mark III coronagraphs) and extreme ultraviolet (SOHO/CDS spectrometer) emission, by way of the van de Hulst inversion.
Finally, Thernisien and Howard (2006) presented a 3D reconstruction of the electron density of a streamer, using total-brightness observations performed by SOHO/LASCO-C2 and -C3 from 2.5 to . The radial profile of the electron density was determined via inversion techniques based on the method implemented by Hayes, Vourlidas, and Howard (2001).
The above electron-density models, which agree quite well for while differing significantly for larger heliocentric distances, are shown in the bottom-right panel of Figure 6. In the top-right panel of the same figure, the electron-temperature models within an equatorial streamer by Gibson et al. (1999) and Vásquez, van Ballegooijen, and Raymond (2003) are shown.
From the inferred density profile, Gibson et al. (1999) deduced a hydrostatic temperature profile inside the streamer from the ideal gas law, . Here is the helium number density relative to hydrogen and is the total thermal pressure, which, in the assumption that the plasma in the streamer is in hydrostatic equilibrium, is exactly balanced by gravity.
Because of the high density and low outflow velocity in streamers, protons and electrons are expected to be in thermal equilibrium with each other, so the electron temperature at the Equator can be assumed to be equal to the proton temperature. Furthermore, because of the rapid charge exchange between protons and neutral-hydrogen atoms, the hydrogen temperature, which can be estimated by measuring the width of the Ly coronal emission line profile, reflects the proton temperature at radii up to in the polar regions and even higher in the equatorial regions (Withbroe et al., 1982). Hence, Vásquez, van Ballegooijen, and Raymond (2003) derived an electron-temperature model within a streamer, by fitting (with a combination of two power laws) SOHO/UVCS low-latitude observations of the Ly line width (Raymond et al., 1997).
#### 3.1.3 Elemental Abundances
Because of the numerous of results on elemental abundances derived from various types of data provided by different instruments and under different physical conditions (solar energetic particle ( SEP ) observations, flare observations, spectroscopy of closed coronal loops, corotating interaction region analysis), it is often quite difficult to know which data set should be used to ensure consistency with the observations.
In this work, we adopted the set of photospheric abundances listed in Asplund et al. (2009); more specifically, , , and . To a first approximation, no variation of the elemental abundances with heliographic latitude and heliocentric distance is considered here; i.e. the elemental abundances are assumed to be equal in the polar and equatorial regions and to be constant throughout the analyzed height range. However, some observations indicate that equatorial regions at the solar minimum include a “coronal” mix of elements, i.e. elements of low FIP such as Si and Mg should be more abundant by a factor of several.
This dichotomy between abundances in the equatorial and polar regions is well established from in-situ measurements (e.g., von Steiger et al. 2000, who give a FIP bias of two – three), but is probably a rather coarse schematization for the corona closer to the Sun (e.g., Raymond et al., 1997), a region for which there are various contradictory measurements. We mention, for instance, Feldman et al. (1998) who considered abundances in the low corona above polar coronal holes and the quiet Sun during minimum. They measured a FIP enhancement above the quiet Sun of about four between, e.g., Mg and Ne. On the other hand, Young (2005) instead found the Mg/Ne ratio to be nearly photospheric. Moreover, the He abundance is rather variable even in the solar wind; for instance, there are measurements indicating of the order of in the fast solar wind (e.g., Bochsler, 1998).
In any case, the line radiances scale linearly with the elemental abundance, so that it is easy to evaluate the effect of a given chemical mixture on the calculations discussed in this article.
#### 3.1.4 Outflow Speed of the Expanding Coronal Plasma
In order to quantify the Doppler dimming of the resonant scattering process due to the expansion of the solar corona, a semiempirical model for the outflow speed of the fast solar wind has been employed in the analysis.
The model has been derived so as to be compatible with the previous results by Antonucci et al. (2004) at low heliocentric distances and with the asymptotic outflow velocity km s, which is definitely achieved at (Breen et al., 1996), but probably even at , according to interplanetary-scintillation observations (Grall, Coles, and Klinglesmith, 1995). In particular, the model is consistent with the outflow velocity of the oxygen component of the fast solar wind derived by Telloni, Antonucci, and Dodero (2007a, b), from the intensity ratio of the Doppler dimmed O vi 103.19, 103.76 nm doublet lines observed with SOHO/UVCS in polar coronal holes, from 1.5 out to , during the 1996 – 1997 solar minimum.
Concerning the flow speed in the streamer regions, Sheeley et al. (1997) developed a model for the slow solar wind from 2 to , by tracking the birth and outflow of outward moving density inhomogeneities observed with the SOHO/LASCO-C2 and -C3 coronagraphs during sunspot-minimum conditions in 1996. The authors concluded that those coronal moving features were passively tracing the slow wind, which originates above the cusps of helmet streamers at about and radially outflows with a nearly constant acceleration of about m s, according to a parabolic speed profile. This profile is consistent with an isothermal solar wind expansion at a temperature of about MK and a sonic point near . This model is also consistent with the results found by Antonucci, Abbo, and Dodero (2005) from SOHO/UVCS data, in the analysis of the slow wind and magnetic topology in the solar minimum corona in 1996 – 1997.
#### 3.1.5 Intensity Profiles from the Chromosphere and Lower Corona
In order to estimate the optical pumping by disk radiation of the lines considered in this article, we use the average USUN CDS line profiles; for the He ii 30.4 and Si xi 30.3 nm lines the average disk line radiances are and erg cm s sr, respectively, while for the Mg x 62.5 and Si xii 52.1 nm lines the measured average radiances are and erg cm s sr, respectively. We remark again that the Si xi 30.3 nm disk radiance has been taken into account for the calculation of the pumping of both the Si xi and the He ii lines in the corona.
In all cases, a constant intensity and shape of the exciting line profiles across the solar disk is assumed, i.e. no limb brightening or darkening has been considered.
#### 3.1.6 3D Velocity Distribution of the Coronal Helium Ions
In order to quantify the number of chromospheric photons scattered by the He ions in the extended corona, we account for the width of the coronal absorption profile of the helium ions along the direction of the incident radiation , which is related to the helium kinetic temperature . The velocity distribution of the absorbing helium ions sets the assumed degree of anisotropy. In particular, if the degree of anisotropy is maximum, while if , where is the helium temperature along the LOS, the ion velocity distribution is isotropic. There is some uncertainty related to the temperature anisotropy assumed in the analysis. Moreover, further uncertainty is introduced since the helium temperature along the LOS has not yet been directly measured. In the synthesis of the radiance of the He ii 30.4 nm line, it is assumed that the helium temperature along the LOS reflects that of the hydrogen atoms, both in polar and equatorial regions. In particular, a semiempirical model of the helium temperature has been derived from the hydrogen temperature inferred by measuring the width of the Ly coronal emission line profile observed with the SOHO/UVCS spectrometer during the 1996 – 1997 minimum (Antonucci, Abbo, and Dodero, 2005). Since there is no evidence for anisotropic velocities of helium ions, we assume here that they have an isotropic velocity distribution both at high and low heliographic latitudes. Note that the above assumptions do not affect significantly the He ii intensity results for heliocentric distances smaller than , where the collision excitation dominates, whereas at larger heliocentric distances they lead to uncertainties of less than 30%.
## Section 4 Discussion
The radiances computed as described in Section 3 can be compared with the radiances measured as described in Section 2, in the region , delimiting the respective domains of validity. We again remark that while some coronal temperature and density models are already given down to that value of heliocentric distance (as in, e.g., Gibson et al., 1999), in other cases the values shown here are extrapolated below their domain of validity (as it is the case of data from, e.g., Thernisien and Howard, 2006), and therefore should be treated with caution (see also Figure 6).
The comparison for the lines He ii 30.4 nm and Si xi 30.3 nm is shown in Figure 9; for that comparison, note that measured He ii 30.4 nm radiances are dominated by stray light almost everywhere above the limb, and thus constitute only an upper limit for the theoretical calculations. Figure 10 shows instead the measured and computed radiances of the Si xii 52.1 nm and Mg x 62.5 nm lines. As noted in Section 2.3, the former line is also likely to be affected to some extent by instrumental stray light, especially in the corona above polar holes; in those cases, its measured radiances can be regarded as upper limits.
Note that we have also examined the relative weight of the collisional and radiative components in the various computed lines. Normally, it is assumed that collisional excitation dominates in the low corona for most ions/atoms, while further away from the Sun both radiative and collisional excitation may be important. In practice, we found that the Si xii 52.1 nm line is practically purely collisional, while for the Si xi 30.3 nm and Mg x 62.5 nm lines the radiative contribution is not always completely negligible, but is at most of the order of 30 – 40% (at ), depending on the specific set of approximations used (see also Withbroe et al., 1982). However, the He ii 30.4 nm line has a negligible collisional component and can thus be considered purely radiative, and therefore dependent on the details of the flow velocity in the corona, among other things (Doppler dimming).
### 4.1 Streamer
The comparison between computed and measured radiances in the streamer region of the data set considered here is shown in the lower panels of Figures 9 and 10. Taking into account that the radiances of the He ii 30.4 nm line above the limb are strongly affected by stray light, all calculations appear to reasonably match the observations. In particular, both the temperature profiles of Gibson et al. (1999) and Vásquez, van Ballegooijen, and Raymond (2003) reproduce the radiances in the corona observed by CDS. This is not entirely surprising, since both temperature profiles set their peak coronal temperature at K, a value close to the one inferred from CDS line ratios (see Figure 7). Moreover, almost all of the density profiles considered here produce radiances that can be considered in accordance with CDS observations. Nevertheless, in the following, on the basis of the analysis of Section 2.3, we will exclude the calculations obtained with the density profile of Leblanc, Dulk, and Bougeret (1998) (short-dashed lines in the figures).
Overall, the agreement between computed and measured radiances is considered reasonable, but the computed Mg x 62.5 nm seems to be a factor two higher than the measurements. A better agreement would be found if the density profile of Leblanc, Dulk, and Bougeret (1998) were adopted, but that density profile is incompatible with the densities inferred from the Si ix line ratio, as mentioned above.
The problem with the Mg x 62.5 nm line is not completely unexpected: discrepancies between observed and predicted radiances/irradiances (assuming ionization equilibrium and some form of emission-measure modeling) in lines from the Na- and Li-like ions have appeared since the beginning of space observations. This has been noted occasionally in the literature. The problem is actually more complex and pervasive than originally understood, as explained in Del Zanna (1999).
Del Zanna (1999) found with differential emission measure ( DEM ) analysis that Mg x lines in the quiet Sun were overestimated by a factor of 1.6. Del Zanna (1999) reconsidered various historical records (e.g., Judge et al., 1995) and found that the problem is present in all data sets. The lines from Li-like ions formed in the transition region tend to be underestimated by a large factor, while those formed at coronal temperatures are overestimated. Finally, Del Zanna, Bromage, and Mason (2001a) reanalyzed Skylab data and found that Mg x lines were overestimated by a factor of ten.
For a short review on the subject, see Del Zanna, Landini, and Mason (2002). We only mention here that the problem can perhaps be ascribed to the ion-balance calculations, although some of the explanations proposed (e.g. the density dependence of dielectronic recombination rates) probably do not apply to these coronal observations.
### 4.2 Polar Regions (Coronal Holes)
From the upper panels of Figures 9 and 10, it is clear that Si xi 30.3 nm and Si xii 52.1 nm radiances computed with the temperature profile of Guhathakurta et al. (1999) strongly underestimate (even by two or more orders of magnitude) the observed values in the lower corona, regardless of the density profile adopted. This is an independent confirmation of the same finding discussed in Section 2.3 (see also Figure 8). Also considering the upper limits given by the He ii 30.4 nm line, and the radiances of the Mg x 62.5 nm line, the radiance profiles that best match the observations are instead those obtained with the Vásquez, van Ballegooijen, and Raymond (2003) temperatures and the Kohl et al. (1998) densities. As discussed in Section 2.3, these are also the and profiles, respectively, that best match the line ratios in Figures 7 and 8.
### 4.3 The Ratio Si xi 30.3 nm/He ii 30.4 nm
From the measured and computed values of the radiances of the Si xi 30.3 nm and He ii 30.4 nm lines, we can then proceed to determine the range of values of their ratios in the quiescent solar corona. In Figure 11 we show the observed ratio from the CDS observations, up to . Recalling once again that the He ii 30.4 nm line is affected by stray light above the limb, the corresponding values of the ratio shown in that figure are actually only upper limits.
For the polar regions, we show the ratio computed with the temperatures of Vásquez, van Ballegooijen, and Raymond (2003) and the densities of Kohl et al. (1998) (upper right panel of Figure 11), because those profiles produce a better match with observations, as discussed in the previous section. The result is that the helium Ly dominates the nearby Si xi resonance line even in the lower corona, down to . However, we also show the results obtained with the temperature profile of Guhathakurta et al. (1999) (upper left panel of Figure 11), even though it clearly underestimates the radiances of several coronal lines in the lower corona, to show the effect of the temperature profile on these results.
In the case of a streamer above , the temperature profile also has a strong effect, especially on the Si xi 30.3 nm line (see Figure 9). On the other hand, the details of the density profile are much less important in determining the value of the ratio Si xi 30.3 nm/He ii 30.4 nm. However, in all cases the Si xi 30.3 nm line dominates over the He ii 30.4 nm line in the corona below , and even above (at least up to ) if we adopt the temperature profile of Vásquez, van Ballegooijen, and Raymond (2003).
As mentioned in Section 3.1, the above results are based on the assumption of a photospheric mixture of elements.
In polar holes, the Si abundance should not be different, but He might be depleted by a factor two with respect to the photosphere. If so, the ratio Si xi 30.3 nm/He ii 30.4 nm could increase above unity for heliocentric distances below (considering only the temperature profile of Vásquez, van Ballegooijen, and Raymond 2003).
However, in quiescent equatorial streamers it is possible that the abundance of a low-FIP element like Si is enhanced with respect to a high-FIP element like He, by a factor of the order of three – four. Such an enhancement would extend considerably the region where the Si xi 30.3 nm dominates the He ii 30.4 nm line. But the agreement with the radiances shown in Figure 9 would also be less satisfactory: increasing the abundance in streamers of the low-FIP elements Si and Mg would perhaps improve the agreement for the Si xii 52.1 line, at the expense of a worse match with observations for the Si xi 30.3 and Mg x 62.5 lines. Clearly, in this case invoking for example a “filling factor” would not mitigate the problem.
## Section 5 Conclusions
Our results indicate that the Si xi 30.3 nm line is important compared to the He ii 30.4 nm in the corona below , to the point of being the dominant source of emission in the 30.4 nm band in streamers, less likely so in polar regions (coronal holes). Beyond that distance, different temperature profiles predict a generally rapid decline of that contribution, mainly because of the strong dependence of the Si xi resonance line on temperature. For instance, the model by Vásquez, van Ballegooijen, and Raymond (2003) predicts a non-negligible contribution of the Si xi 30.3 nm up to , whereas the temperature profile from Gibson et al. (1999) implies a much more rapid drop of that line with heliocentric distance.
However, the density profile has a relatively less important role in determining the emission ratio Si xi/He ii in the extended corona.
There is one important caveat about the Si xi 30.3 nm calculations. The CHIANTI atomic data include rates for collisional excitation by electrons that were not calculated, but interpolated along the Be-like sequence, and the same occurred for Mg ix. Del Zanna, Rozum, and Badnell (2008) performed the first scattering calculation for Mg ix, and found significant differences in the emissivities of key lines when compared to the results from the interpolated data. The resonance line was only affected by about 10%, so large corrections to the Si xi 30.3 nm are not expected. However, we will know this for sure only when new calculations (in progress by GDZ) become available.
As a consistency check for our calculations, we also computed the radiances for a few representative lines observed by CDS, taking into account both the collisional excitation and the radiative pumping by the disk radiation, using average radiances from the same CDS data. Here we only show the results for the Mg x 62.5 nm and Si xii 52.1 nm lines. The overall agreement between calculations and observations is reasonable; there are some discrepancies in the case of the Mg x line, but they can be attributed to a known problem (but of uncertain origin) in the emissivity calculations for that line.
We recall that the observed radiances shown here were derived adopting the latest radiometric calibration for the CDS/NIS, including the correction for the long-term decay in sensitivity of the instrument (Del Zanna et al., 2010, and references therein). Since most, if not all, previous analyses done merging near-limb EUV data and extended corona measurements rely on line ratios only (e.g., Gibson et al., 1999), we note the generally good to excellent match between observed and computed absolute radiances in the strongest coronal lines.
Finally, our results were obtained adopting photospheric abundances from Asplund et al. (2009). Adopting coronal abundances would alter somewhat the results, especially for . However, in that region abundance measurements are less well established than, for instance, in-situ wind measurements: the effect of abundance variations should thus be considered as an additional source of uncertainty in the ratio Si xi 30.3 nm/He ii 30.4 nm.
In summary, it is true that the diagnostic potential of narrowband imaging around 30.4 nm in the extended corona is high. In particular, radiative excitation of the main line in the band, He ii 30.4 nm, from disk emission of either the same line or of the nearby Si xi 30.3 nm line, can provide a useful tool for diagnosing radial velocities. However, the full diagnostic potential of this band can only be fulfilled if it is possible to place constraints on the possible “contamination” from coronal Si xi 30.3 nm emission. In particular, we have shown that the ratio Si xi 30.3 nm/He ii 30.4 nm is very sensitive to the specific temperature profile adopted for the corona, which is normally rather uncertain.
A corollary of these calculations is that the diagnostic potential of narrowband observations in the 30.4 nm band in critical regions of the corona () can only be fully exploited if aided by spectroscopic observations capable of disentangling the Si xi contribution from the He ii emission. Alternatively, if one could find a way to independently determine the coronal temperature profile (the density profile is much less critical in this respect), perhaps it could be aided through simultaneous visible light imaging. Both approaches will be feasible with METIS onboard Solar Orbiter.
##### Acknowledgements
This work is part of the scientific activities supporting the development of METIS, and as such has been supported in part (Italy) by ASI-INAF contract I/43/10/0; further support came from ASI-INAF contracts I/05/07/0 and I/023/09/0. GDZ acknowledges support from SFTC (UK) via the Advanced Fellowship Programme. SOHO is a project of international cooperation between ESA and NASA. CDS was built and operated by a consortium led by the Rutherford Appleton Laboratory (RAL), which includes UCL/Mullard Space Science Laboratory, NASA/ Goddard Space Flight Center, Max Planck Institute for Extraterrestrial Physics, Garching, and Oslo University. Finally, we wish to thank the referee for useful comments and suggestions on the manuscript.
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https://www.physicsforums.com/threads/how-to-make-approximations.621157/ | # How to make approximations?
1. Jul 15, 2012
### weetabixharry
If I have some expression such as: $$y = 1 + \epsilon^2 - 5\epsilon^4$$ and then make this approximation:$$y \approx 1 + \epsilon^2$$ then, if I understand correctly, my specific assumption is that $5\epsilon^4 \ll 1 + \epsilon^2$ which, for example, would always be satisified if I happened to know that $5\epsilon^4 \ll 1$.
However, if I have something like a Taylor series, I'm not sure exactly what my assumption is. For example:$$\sqrt{1 - x} = 1 - \frac{1}{2}x - \frac{1}{8}x^2 - \frac{1}{16}x^3 - \frac{5}{128}x^4 - \dots \\ \ \ \ \ \ \ \ \ \ \ \ \ \approx 1 - \frac{1}{2}x$$ It seems that my exact assumption here involves an infinite series that might be tricky to evaluate.
So, more loosely speaking, is the approximation satisfied, for example, if $\frac{1}{8}x^2 \ll 1$? Is there a sensible/rigorous way of dealing with things like this?
Last edited: Jul 16, 2012
2. Jul 15, 2012
### haruspex
It is certainly a good idea to compute a bound on the error that arises by curtailing the expansion.
In the example you give, you have the signs wrong in the expansion. All except the first term should be negative. The general term has magnitude (x/4)r 2rCr. Asymptotically, that approximates xr/√r, which is clearly less than xr. If you curtail the expansion at r = n, the sum of the remaining terms cannot exceed xn/(1-x).
Faced with a series which does alternate in sign, you can usually do better than this by combining pairs of consecutive terms and putting a bound on those.
3. Jul 15, 2012
### Nabeshin
Well when $x \ll 1$, $x^2 \gg x^4 \gg x^6 \cdots$, So each next term in the series is much smaller than the one which preceded it.
And since $x \ll 1$ you know that the 1 out front is important, so you simply keep the leading order term in x, namely the linear one.
(This does assume something about the coefficients, however. But from Taylor we know that they're decreasing as well so this specific example is OK. If the coefficients were, for some reason, increasing, then a more detailed analysis would be in order.)
4. Jul 15, 2012
### chiro
Typically what happens is that you have the independent variables in the form of x + epsilon and then you expand it out in the context of the model to see how the error propagates in the model.
One common and powerful way to do this is to use the norm and metric identities like the triangle inequality since you can get a bound on on the error and convert the x + epsilon in terms of x and epsilon separately.
5. Jul 16, 2012
### weetabixharry
You're right - thanks for spotting my error. I'll edit the OP to avoid confusion.
I'll have to have a think about this, but I expect this is exactly what I'm looking for.
Yes - this makes intuitive sense. Many thanks for your clear explanations.
6. Jul 16, 2012
### awkward
In the specific case of Taylor series, there are formulas for the remainder term which can be used to bound the error. See the section titled "Explicit formulae for the remainder" in
http://en.wikipedia.org/wiki/Taylor's_theorem | {"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": 0.9571424126625061, "perplexity": 390.31488038841565}, "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-2018-30/segments/1531676591332.73/warc/CC-MAIN-20180719222958-20180720002958-00569.warc.gz"} |
http://mathhelpforum.com/math-topics/29983-relative-velocity-physics-question.html | # Math Help - relative velocity (physics question)
1. ## relative velocity (physics question)
A plane is seen to travel in a direction [S 30 degrees W]. if its ground velocity was 300 km/h and the wind speed is 150 km/h south, what is the plane's velocity relative to the air?
2. Hello,
I can give you a hint:
The plane is flying 300km/h 30deg west of south. It's vertical component (in the southern direction) of its ground velocity is thus 300cos(30).
Let me know if you are still struggling.
3. You have $\mathbf{v}_{\textrm{ground}}=-300\sin{30^\circ}\mathbf{i}-300\cos{30^\circ}\mathbf{j}=-150(\mathbf{i}+\sqrt{3}\mathbf{j})$.
The wind velocity is $\mathbf{w}=-150\mathbf{j}$.
Now use the equation $\mathbf{v}_{\textrm{air}}+\mathbf{w}=\mathbf{v}_{\ textrm{ground}}$ and solve for $\mathbf{v}_{\textrm{air}}$. | {"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": 4, "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": 0.9754781126976013, "perplexity": 1339.0387309153698}, "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/1443736672441.2/warc/CC-MAIN-20151001215752-00145-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-math-topics/203715-vector-space-really-need-help.html | # Math Help - Vector Space - Really Need Help
1. ## Vector Space - Really Need Help
Hi There I have a proof question that I cannot solve Please do help
Let S be the set of functions of the form U= a1sinx +…+ansin(nx), where a1,…,an are real numbers, a U = (aa1)sinx + …. + (aan)sinnx for a is real number
and for V = b1sinx + … +bnsinnx,
U+V = (a1+b1)sinx+…+(an+bn)sinnx
Show that S is a vector space
2. ## Re: Vector Space - Really Need Help
What is the definition of "vector space"? Show that this satisfies that definition. | {"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": 0.9773662090301514, "perplexity": 1955.9673361126902}, "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-2015-14/segments/1427131299339.12/warc/CC-MAIN-20150323172139-00073-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/find-power-series-if-you-know-its-laplace-transformation.754134/ | # Find power series if you know its laplace transformation
1. May 17, 2014
### skrat
1. The problem statement, all variables and given/known data
a) Determine power series $\sum _{n=0}^{\infty }a_nt^n$ if you know that its laplace transformation is $-s^{-1}e^{-s^{-1}}$
b) Determine function $g$ that this power series will be equal to $J_0(g(t))$
2. Relevant equations
3. The attempt at a solution
Hmmm, I am having some troubles with this laplace transformation in part a).
Well, I know that Laplace transformation of Heaviside function $H_C(t)$ is $\frac{1}{s}e^{-Cs}$
Knowing this I get almost the same as the problem says: $-H_1$ ---> $-\frac{1}{s}e^{-s}$. But I have absolutely NO idea what to do to get $\frac{1}{s}$ in the exponent function. If I just power both sides of the equation everything else collapses...
So how can I deal with this?
2. May 17, 2014
### vela
Staff Emeritus
Expand the exponential as a series then invert the transform term by term.
3. May 17, 2014
### skrat
Hmmmm...
$-\frac{1}{s}e^{-1/s}=-\frac{1}{s}(1-\frac{1}{s}+\frac{1}{2}(\frac{1}{s})^2-\frac{1}{3}(\frac{1}{s})^3+\frac{1}{4}(\frac{1}{s})^4- ...)=-\frac{1}{s}+(\frac{1}{s})^2-\frac{1}{2}(\frac{1}{s})^3+\frac{1}{3}(\frac{1}{s})^4-\frac{1}{4}(\frac{1}{s})^5+ ...$
Using inverse Laplace transformation gives me:
$-1+t-\frac{1}{4}t^2+\frac{1}{18}t^3-\frac{1}{96}t^4+\frac{1}{600}t^5-\frac{1}{4320}t^6+...$
BUT I can't fine a way to include that -1 into series:
$-1+\sum _{k=1}^{\infty }\frac{(-1)^{k+1}}{(k+1)!-k!}t^k$
4. May 17, 2014
### vela
Staff Emeritus
You didn't expand the exponential function correctly. It should be n! in the denominator, not n.
5. May 17, 2014
### skrat
uh, jup, you are right.
The result is $\sum _{k=0}^{\infty }\frac{(-1)^{k+1}}{(k!)^2}t^k$.
Thank you, vela! | {"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": 0.9070936441421509, "perplexity": 832.9508480546568}, "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-2018-13/segments/1521257650685.77/warc/CC-MAIN-20180324132337-20180324152337-00188.warc.gz"} |
http://math.stackexchange.com/questions/285733/non-context-free-languages-closed-under-reverse | # Non context-free languages closed under reverse
Is this sentence true or false? I'll be glad for some explaination
L is not context-free, then its reverse is also not context-free
The reverse of context-free is also context-free, moreover reverse$^2$ is identity, so $rev(L) \in CFL$ would imply $L = rev(rev(L)) \in CFL$. – dtldarek Jan 24 '13 at 10:34 | {"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": 0.8446779251098633, "perplexity": 1032.3810563169598}, "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-2015-40/segments/1443738087479.95/warc/CC-MAIN-20151001222127-00024-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/gravity-nuclear-force-relation.563747/ | # Gravity-Nuclear force relation
1. ### deepthishan
38
Is there a relation between Nuclear energy and Gravity? If so, can you please explain what that is and why? If not, why not?
2. ### Markus Hanke
97
Your question is somewhat unclear, so not sure how to respond. In nuclear physics, at least in the low energy regime, gravity does not really come into play simply because its effects are orders of magnitude smaller than those of the other fundamental forces. Of course there is gravitational attraction between the various particles that make up an atomic nucleus, but it is so small as to be negligible so far as nuclear energy generation is concerned.
3. ### deepthishan
38
I'm sorry Markus - more directly, I meant any effect of the earth's Gravitational field on a Nuclear powerplant.
17,958
Staff Emeritus
Yes, but no more or less than a coal power plant or a cookie factory. Gravity affects everything the same.
5. ### robert2734
77
First generation nuclear power plants use pumps to pump cooling water into the reactor core. If the electric supply is interrupted for any reason such as a tsunami for a time longer than the battery backup will cover, the core will meltdown. Newer designs suspend emergency cooling water above the reactor relying on the earth's gravity to feed it into the core.
17,958
Staff Emeritus
What does that have to do with the question?
7. ### Markus Hanke
97
There is no direct effect apart from the plant staying put where it is instead of floating off into space, and all the mechanics of the plant working as they are supposed to. In terms of the actual nuclear reactions taking place in the core, they would work just as well without the presence of an external gravitational field. | {"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": 0.8862773180007935, "perplexity": 535.3056856224377}, "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-2015-27/segments/1435375097757.36/warc/CC-MAIN-20150627031817-00107-ip-10-179-60-89.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/6421-invertible-upper-triangular-matrix.html | # Math Help - Invertible Upper Triangular Matrix
1. ## Invertible Upper Triangular Matrix
Prove that if U is an invertible upper triangular matrix then U^-1 is also upper triangular. How would you prove this?????? TIA
2. Originally Posted by TreeMoney
Prove that if U is an invertible upper triangular matrix then U^-1 is also upper triangular. How would you prove this?????? TIA
Consider inverting U using Gaussian elimination. We form the augmented
matrix
U|I,
which is obtained by appending the identity matrix on the right of U.
Then using row operations we reduce the left half of this augmented
matrix to the identity matrix, and we are left with the inverse of U in
the right half of the augmented matrix.
Now if we start from the bottom working our way up with the elimination
process the right half of the augmented matrix remains upper triangular, hence
when we finish with the identity in the left half of the augmented matrix
we have an upper triangular matrix in the right half of the augmented
matrix. But this upper triangular is the inverse of U, which proves that
the inverse is upper triangular.
RonL
3. Thanks RonL. I had no chance of coming up with something like that. Much Appreciated. John
4. Originally Posted by TreeMoney
Thanks RonL. I had no chance of coming up with something like that. Much Appreciated. John
I got a bit confused about right and left in the original, and have just
corrected it, you may not have seen the correction.
RonL | {"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": 0.976325511932373, "perplexity": 484.4255375148942}, "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-2014-23/segments/1405997884827.82/warc/CC-MAIN-20140722025804-00159-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://it.mathworks.com/help/physmod/sps/ref/femparameterizedrotaryactuator.html | # FEM-Parameterized Rotary Actuator
Rotary actuator defined in terms of magnetic flux
• Library:
• Simscape / Electrical / Electromechanical / Mechatronic Actuators
## Description
The FEM-Parameterized Rotary Actuator block implements a model of a rotary actuator defined in terms of magnetic flux. Use this block to model custom rotary actuators and motors where magnetic flux depends on both rotor angle and current. You parameterize the block using data from a third-party Finite Element Magnetic (FEM) package.
The block has two options for the electrical equation. The first, ```Define in terms of dPhi(i,theta)/dtheta and dPhi(i,theta)/di```, defines the current in terms of partial derivatives of the magnetic flux (Φ) with respect to rotor angle (θ) and current (i), the equations for which are:
`$\frac{di}{dt}=\left(v-iR-\frac{\partial \Phi }{\partial \theta }\frac{d\theta }{dt}\right)/\frac{\partial \Phi }{\partial i}$`
The second option, `Define in terms of Phi(i,theta)`, defines the voltage across the component directly in terms of the flux, the equation for which is:
`$v=iR+\frac{d}{dt}\Phi \left(\theta ,i\right)$`
Numerically, defining the electrical equation in terms of flux partial derivatives is better because the back-emf is piecewise continuous. If using the flux directly, using a finer grid size for current and position will improve results, as will selecting cubic or spline interpolation.
In both cases, you have an option to either directly specify the torque as a function of current and rotor angle, by using the Torque matrix, T(i,theta) parameter, or have the block automatically calculate the torque matrix.
If entering the electromagnetic torque data directly, you can either use data supplied by the finite element magnetic package (which you used to determine the flux) or calculate the torque from the flux with following equation:
`$T=\underset{0}{\overset{i}{\int }}\frac{\partial \Phi \left(\theta ,i\right)}{\partial \theta }di$`
See the Solenoid Parameterized with FEM Data example model for an example of how to implement this type of integration in MATLAB®.
Alternatively, the block can automatically calculate the torque matrix from the flux information that you provide. To select this option, set the Calculate torque matrix? parameter to `Yes`. The torque matrix calculation occurs at model initialization based on current block flux linkage information. The torque is calculated by numerically integrating the rate of change of flux linkage with respect to angle over current, according to the preceding equation. If the Electrical model parameter is set to `Define in terms of Phi(i,theta)`, then the block must first estimate the Flux partial derivative wrt angle, Phi(i,theta)/dtheta parameter value from the flux linkage data. When doing this, the block uses the interpolation method specified by the Interpolation method parameter. Typically, the `Smooth` option is most accurate, but the `Linear` option is most robust.
You can define Φ and its partial derivatives for just positive, or positive and negative currents. If defining for just positive currents, then the block assumes that Φ(–i,x) = –Φ(i,x). Therefore, if the current vector is positive only:
• The first current value must be zero.
• The flux corresponding to zero current must be zero.
• The partial derivative of flux with respect to rotor angle must be zero for zero current.
To model a rotary motor with a repeated flux pattern, set the Flux dependence on displacement parameter to `Cyclic`. When selecting this option, the torque and flux (or torque and flux partial derivatives depending on the option chosen) must have identical first and last columns.
### Thermal Port
The block has an optional thermal port, hidden by default. To expose the thermal port, right-click the block in your model, and then from the context menu select Simscape > Block choices > Show thermal port. This action displays the thermal port H on the block icon, and exposes the Temperature Dependence and Thermal Port parameters.
Use the thermal port to simulate the effects of copper resistance losses that convert electrical power to heat. For more information on using thermal ports and on the Temperature Dependence and Thermal Port parameters, see Simulating Thermal Effects in Rotational and Translational Actuators.
## Assumptions and Limitations
• You must supply a consistent set of torque and flux data. There is no check to ensure that the torque matrix is consistent with the flux data.
• When driving the FEM-Parameterized Rotary Actuator block via a series inductor, you may need to include a parallel conductance in the inductor component.
## Ports
### Conserving
expand all
Electrical conserving port associated with the actuator positive terminal.
Electrical conserving port associated with the actuator negative terminal.
Mechanical rotational conserving port associated with the actuator case.
Mechanical rotational conserving port associated with the rotor.
## Parameters
expand all
### Magnetic Force
Select one of the following parameterization options, based on the underlying electrical model:
• ```Define in terms of dPhi(i,theta)/dtheta and dPhi(i,theta)/di``` — Define the current through the block in terms of partial derivatives of the magnetic flux with respect to distance and current.
• ```Define in terms of Phi(i,theta)``` — Define the voltage across the block terminals directly in terms of the flux.
Specify a vector of monotonically increasing current values corresponding to your torque-flux data. If you specify positive currents only, the first element must be zero.
Specify a vector of monotonically increasing rotor angle values corresponding to your torque-flux data.
Specify a matrix of the flux partial derivatives with respect to current. This parameter is visible only if Electrical model is set to ```Define in terms of dPhi(i,theta)/dtheta and dPhi(i,theta)/di```. The default value, in Wb/A, is:
```[ 0.002 0.0024 0.0035 0.0052 0.0074 0.0096 0.0118 0.0135 0.0146 ... 0.015 0.0146 0.0135 0.0118 0.0096 0.0074 0.0052 0.0035 0.0024 0.002; 0.002 0.0024 0.0035 0.0052 0.0074 0.0096 0.0118 0.0135 0.0146 ... 0.015 0.0146 0.0135 0.0118 0.0096 0.0074 0.0052 0.0035 0.0024 0.002; 0.002 0.0024 0.0035 0.0052 0.0074 0.0096 0.0118 0.0135 0.0146 ... 0.015 0.0146 0.0135 0.0118 0.0096 0.0074 0.0052 0.0035 0.0024 0.002; 0.002 0.0024 0.0035 0.0052 0.0074 0.0096 0.0118 0.0135 0.0146 ... 0.015 0.0146 0.0135 0.0118 0.0096 0.0074 0.0052 0.0035 0.0024 0.002; 0.002 0.0024 0.0035 0.0052 0.0074 0.0096 0.0118 0.0135 0.0146 ... 0.015 0.0146 0.0135 0.0118 0.0096 0.0074 0.0052 0.0035 0.0024 0.002; 0.002 0.0024 0.0035 0.0052 0.0074 0.0096 0.0118 0.0135 0.0146 ... 0.015 0.0146 0.0135 0.0118 0.0096 0.0074 0.0052 0.0035 0.0024 0.002; ]```
#### Dependencies
This parameter is visible only when you set the Electrical model parameter to ```Define in terms of dPhi(i,theta)/dtheta and dPhi(i,theta)/di```.
Specify a matrix of the flux partial derivatives with respect to rotor angle. This parameter is visible only if Electrical model is set to ```Define in terms of dPhi(i,theta)/dtheta and dPhi(i,theta)/di```. The default value, in Wb/rad, is:
```[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 9e-4 0.0017 0.0023 0.0026 0.0026 0.0023 0.0017 9e-4 ... 0 -9e-4 -0.0017 -0.0023 -0.0026 -0.0026 -0.0023 -0.0017 -9e-4 0; 0 0.0018 0.0033 0.0045 0.0051 0.0051 0.0045 0.0033 0.0018 ... 0 -0.0018 -0.0033 -0.0045 -0.0051 -0.0051 -0.0045 -0.0033 -0.0018 0; 0 0.0027 0.005 0.0068 0.0077 0.0077 0.0068 0.005 0.0027 ... 0 -0.0027 -0.005 -0.0068 -0.0077 -0.0077 -0.0068 -0.005 -0.0027 0; 0 0.0036 0.0067 0.009 0.0102 0.0102 0.009 0.0067 0.0036 ... 0 -0.0036 -0.0067 -0.009 -0.0102 -0.0102 -0.009 -0.0067 -0.0036 0; 0 0.0044 0.0084 0.0113 0.0128 0.0128 0.0113 0.0084 0.0044 ... 0 -0.0044 -0.0084 -0.0113 -0.0128 -0.0128 -0.0113 -0.0084 -0.0044 0 ]```
#### Dependencies
This parameter is visible only when you set the Electrical model parameter to ```Define in terms of dPhi(i,theta)/dtheta and dPhi(i,theta)/di```.
Specify a matrix of the total flux linkage, that is, flux times the number of turns. This parameter is visible only if Electrical model is set to ```Define in terms of Phi(i,theta)```. The default value, in Wb, is:
```[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 4e-4 4.8e-4 7e-4 0.00105 0.00147 0.00193 0.00235 0.0027 0.00292 ... 0.003 0.00292 0.0027 0.00235 0.00193 0.00147 0.00105 7e-4 4.8e-4 4e-4; 8e-4 9.6e-4 0.00141 0.0021 0.00295 0.00385 0.0047 0.00539 0.00584 ... 0.006 0.00584 0.00539 0.0047 0.00385 0.00295 0.0021 0.00141 9.6e-4 8e-4; 0.0012 0.00144 0.00211 0.00315 0.00442 0.00578 0.00705 0.00809 0.00876 ... 0.009 0.00876 0.00809 0.00705 0.00578 0.00442 0.00315 0.00211 0.00144 0.0012; 0.0016 0.00191 0.00282 0.0042 0.0059 0.0077 0.0094 0.01078 0.01169 ... 0.012 0.01169 0.01078 0.0094 0.0077 0.0059 0.0042 0.00282 0.00191 0.0016; 0.002 0.00239 0.00352 0.00525 0.00737 0.00963 0.01175 0.01348 0.01461 ... 0.015 0.01461 0.01348 0.01175 0.00963 0.00737 0.00525 0.00352 0.00239 0.002 ]```
#### Dependencies
This parameter is visible only when you set the Electrical model parameter to ```Define in terms of Phi(i,theta)```.
Specify the way of providing the electromagnetic torque data:
• `No` — Enter the electromagnetic torque data directly, by using the Torque matrix, T(i,theta) parameter.
• Yes — The block calculates the torque from the flux linkage information, as a function of current and rotor angle.
Specify a matrix of the electromagnetic torque applied to the rotor. This parameter is visible only if Calculate torque matrix? is set to `No`. The default value, in mN*m, is:
```[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0.0889 0.1671 0.2252 0.2561 0.2561 0.2252 0.1671 0.0889 ... 0 -0.0889 -0.1671 -0.2252 -0.2561 -0.2561 -0.2252 -0.1671 -0.0889 0; 0 0.3557 0.6685 0.9007 1.0242 1.0242 0.9007 0.6685 0.3557 ... 0 -0.3557 -0.6685 -0.9007 -1.0242 -1.0242 -0.9007 -0.6685 -0.3557 0; 0 0.8003 1.5041 2.0265 2.3045 2.3045 2.0265 1.5041 0.8003 ... 0 -0.8003 -1.5041 -2.0265 -2.3045 -2.3045 -2.0265 -1.5041 -0.8003 0; 0 1.4228 2.674 3.6027 4.0968 4.0968 3.6027 2.674 1.4228 ... 0 -1.4228 -2.674 -3.6027 -4.0968 -4.0968 -3.6027 -2.674 -1.4228 0; 0 2.2231 4.1781 5.6292 6.4013 6.4013 5.6292 4.1781 2.2231 ... 0 -2.2231 -4.1781 -5.6292 -6.4013 -6.4013 -5.6292 -4.1781 -2.2231 0 ]```
#### Dependencies
This parameter is visible only when you set the Calculate torque matrix? parameter to `No`.
Specify the flux pattern:
• `Unique` — No flux pattern present.
• `Cyclic` — Select this option to model a linear motor with a repeated flux pattern. The force and flux (or force and flux partial derivatives, depending on the Electrical model option chosen) must have identical first and last columns.
Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:
• `Linear` — Select this option to get the best performance.
• `Smooth` — Select this option to produce a continuous surface with continuous first-order derivatives.
For more information on interpolation algorithms, see the PS Lookup Table (2D) block reference page.
Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:
• `Linear` — Select this option to produce a surface with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.
• `Nearest` — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.
• `Error` — Issues an error if the input signal is outside the range of the table. Select this option to avoid going into the extrapolation mode when you want your data to be within the table range.
For more information on extrapolation algorithms, see the PS Lookup Table (2D) block reference page.
#### Dependencies
This parameter is visible only when you set the Flux dependence on displacement parameter to `Unique`.
Total resistance of the electrical winding.
### Mechanical
Rotary damping. The value can be zero.
Inertia of the rotor attached to mechanical translational port R. The value can be zero.
The rotor angle at which the lower mechanical end stop is applied.
The rotor angle at which the upper mechanical end stop is applied.
Contact stiffness between rotor and end stops.
Contact damping between rotor and end stops.
### Temperature Dependence
This tab appears only for blocks with exposed thermal port. For more information, see Thermal Port.
Resistance temperature coefficient.
The temperature for which the actuator parameters are defined.
### Thermal Port
This tab appears only for blocks with exposed thermal port. For more information, see Thermal Port.
The thermal mass is the energy required to raise the temperature by one degree. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "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": 0.8768457174301147, "perplexity": 1495.07256500186}, "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-2021-43/segments/1634323585265.67/warc/CC-MAIN-20211019105138-20211019135138-00663.warc.gz"} |
https://en.wikibooks.org/wiki/Basic_Physics_of_Nuclear_Medicine/The_Radioactive_Decay_Law | # Basic Physics of Nuclear Medicine/The Radioactive Decay Law
Graph of the stability of every known nucleus, plotted as Z (number of protons) versus N (number of neutrons). The color corresponds to the value of the half-life T½ with a strong log scale, since it varies between 10−20 and 1020 seconds.
We covered radioactive decay from a phenomenological perspective in the last chapter. In this chapter we consider the topic from a more general analytical perspective.
The reason for doing this is so that we can develop a form of thinking which will help us to understand what is going on in a quantitative, mathematical sense. We will be introduced to concepts such as the Decay Constant and the Half Life as well as units used for the measurement of radioactivity. You will also have a chance to develop your understanding by being brought through three questions on this subject.
## Assumptions
The usual starting point in most forms of analysis in physics is to make some assumptions which simplify the situation. By simplifying the situation we can dispose of irrelevant effects which tend to complicate matters but in doing so we sometimes make the situation so simple that it becomes a bit too abstract and apparently hard to understand.
For this reason we will try here to relate the subject of radioactive decay to a more common situation which we will use as an analogy and hopefully we will be able to overcome the abstract feature of the subject matter. The analogy we will use here is that of making popcorn.
So think about putting some oil in a pot, adding the corn, heating the pot on the cooker and watching what happens. You might also like to try this out while considering the situation!
For our radioactive decay situation we first of all consider that we have a sample containing a large number of radioactive nuclei all of the same kind. This is our unpopped corn in the pot for example.
Secondly we assume that all of the radioactive nuclei decay by the same process be it alpha, beta or gamma-decay. In other words our unpopped corn goes pop at some stage during the heating process.
Thirdly take a few moments to ponder on the fact that we can only really consider what is going on from a statistical perspective. If you look at an individual piece of corn, can you figure out when it is going to pop? Not really. You can however figure out that a large number of them will have popped after a period of time. But its rather more difficult to figure out the situation for an individual piece of corn. So instead of dealing with individual entities we consider what happens on a larger scale and this is where statistics comes in. We can say that the radioactive decay is a statistical one-shot process, that is when a nucleus has decayed it cannot repeat the process again. In other words when a piece of corn has popped it cannot repeat the process. Simple!
In addition as long as a radioactive nucleus has not decayed the probability for it doing so in the next moment remains the same. In other words if a piece of corn has not popped at a certain time the chance of it popping in the next second is the same as in the previous second. The bets are even!
Let us not push this popcorn analogy too far though in that we know that we can control the rate of popping by the heat we apply to the pot for example. However as far as our radioactive nuclei are concerned there is nothing we can do to control what is going on. The rate at which nuclei go pop (or decay, in other words) cannot be influenced by heating up the sample. Nor by cooling it for that matter or by putting it under greater pressures, by changing the gravitational environment by taking it out into space for instance, or by changing any other aspect of its physical environment. The only thing that determines whether an individual nucleus will decay seems to be the nucleus itself. But on the average we can say that it will decay at some stage.
Let us now use some symbols to reduce the amount of writing we have to do to describe what is going on and to avail ourselves of some mathematical techniques to simplify the situation even further than we have been able to do so far.
Let us say that in the sample of radioactive material there are N nuclei which have not decayed at a certain time, t. So what happens in the next brief period of time? Some nuclei will decay for sure. But how many?
On the basis of our reasoning above we can say that the number which will decay will depend on overall number of nuclei, N, and also on the length of the brief period of time. In other words the more nuclei there are the more will decay and the longer the time period the more nuclei will decay. Let us denote the number which will have decayed as dN and the small time interval as dt.
So we have reasoned that the number of radioactive nuclei which will decay during the time interval from t to t+dt must be proportional to N and to dt. In symbols therefore:
$-dN \propto N \cdot dt\,\!$
Turning the proportionality in this equation into an equality we can write:
$-dN = \lambda N \cdot dt\,\!$
where the constant of proportionality, λ, is called the Decay Constant.
Dividing across by N we can rewrite this equation as:
$-\frac{dN}{N} = \lambda \cdot dt$
So this equation describes the situation for any brief time interval, dt. To find out what happens for all periods of time we simply add up what happens in each brief time interval. In other words we integrate the above equation. Expressing this more formally we can say that for the period of time from t = 0 to any later time t, the number of radioactive nuclei will decrease from N0 to Nt, so that:
$-\int_{N_0}^{N_t} \frac{dN}{N} = \lambda \int_{0}^t dt$
$\therefore \ln \left ( \frac{N_t}{N_0} \right ) = -\lambda t$
$\therefore \frac{N_t}{N_0} = \text{exp}\,(-\lambda t)$
$\therefore N_t = N_0 \text{exp}\,(-\lambda t)$
This final expression is known as the Radioactive Decay Law. It tells us that the number of radioactive nuclei will decrease in an exponential fashion with time with the rate of decrease being controlled by the Decay Constant.
Before looking at this expression in further detail let us review the mathematics which we used above. First of all we used integral calculus to figure out what was happening over a period of time by integrating what we knew would occur in a brief interval of time. Secondly we used a calculus relationship that the
$\int \frac{dx}{x} = \ln x$
where ln x represents the natural logarithm of x. And thirdly we used the definition of logarithms that when
$\ln x = y\,\!$
then,
$x = \text{exp}\ y\,\!$
Now, to return to the Radioactive Decay Law. The Law tells us that the number of radioactive nuclei will decrease with time in an exponential fashion with the rate of decrease being controlled by the Decay Constant. The Law is shown in graphical form in the figure below:
The graph plots the number of radioactive nuclei at any time, Nt, against time, t. We can see that the number of radioactive nuclei decreases from N0 that is the number at t = 0 in a rapid fashion initially and then more slowly in the classic exponential manner.
The influence of the Decay Constant can be seen in the following figure:
All three curves here are exponential in nature, only the Decay Constant is different. Notice that when the Decay Constant has a low value the curve decreases relatively slowly and when the Decay Constant is large the curve decreases very quickly.
The Decay Constant is characteristic of individual radionuclides. Some like uranium-238 have a small value and the material therefore decays quite slowly over a long period of time. Other nuclei such as technetium-99m have a relatively large Decay Constant and they decay far more quickly.
It is also possible to consider the Radioactive Decay Law from another perspective by plotting the logarithm of Nt against time. In other words from our analysis above by plotting the expression:
$\ln \left ( \frac{N_t}{N_0} \right ) = - \lambda t$
in the form
$\ln N_t = -\lambda t + \ln N_0\,\!$
Notice that this expression is simply an equation of the form y = mx + c where m = -l and c = ln N0. As a result it is the equation of a straight line of slope -l as shown in the following figure. Such a plot is sometimes useful when we wish to consider a situation without the complication of the direct exponential behaviour.
## Half-Life
Most of us have not been taught to think instinctively in terms of logarithmic or exponential terms even though many natural phenomena display exponential behaviours. Most of the forms of thinking which we have been taught in school are based on linear changes and as a result it is rather difficult for us to grasp the Radioactive Decay Law intuitively. For this reason an indicator is usually derived from the law which helps us think more clearly about what is going on.
This indicator is called the Half Life and it expresses the length of time it takes for the radioactivity of a radioisotope to decrease by a factor of two. From a graphical point of view we can say that when:
$N_t = \frac{N_0}{2}$
the time taken is the Half Life:
Note that the half-life does not express how long a material will remain radioactive but simply the length of time for its radioactivity to halve. Examples of the half lives of some radioisotopes are given in the following table. Notice that some of these have a relatively short half life. These tend to be the ones used for medical diagnostic purposes because they do not remain radioactive for very long following administration to a patient and hence result in a relatively low radiation dose.
81mKr 13 seconds
99mTc 6 hours
131I 8 days
51Cr 1 month
137Cs 30 years
241Am 462 years
226Ra 1620 years
238U 4.51 x 109 years
But they do present a logistical problem when we wish to use them when there may not be a radioisotope production facility nearby. For example suppose we wish to use 99mTc for a patient study and the nearest nuclear facility for making this isotope is 5,000 km away. The production facility could be in Sydney and the patient could be in Perth for instance. After making the isotope at the nuclear plant it would be decaying with a half life of 6 hours. So we put the material on a truck and drive it to Sydney airport. The isotope would be decaying as the truck sits in Sydney traffic then decaying still more as it waits for a plane to take it to Perth. Then decaying more as it is flown across to Perth and so on. By the time it gets to our patient it will have substantially reduced in radioactivity possibly to the point of being useless for the patient's investigation. And what about the problem if we needed to use 81mKr instead of 99mTc for our patient? You will see in another chapter of this book that logistical challenges such as this have given rise to quite innovative solutions. More about that later!
You can appreciate from the table above that other isotopes have a very long half lives. For example 226Ra has a half life of over 1,500 years. This isotope has been used in the past for therapeutic applications in medicine. Think about the logistical problems here. They obviously do not relate to transporting the material from the point of production to the point of use. But they relate to how the material is kept following its arrival at the point of use. We must have a storage facility so that the material can be kept safely for a long period of time. But for how long? A general rule of thumb for the quantities of radioactivity used in medicine is that the radioactivity will remain significant for about 10 half lives. So we would have to have a safe environment for storage of the 226Ra for about 16,000 years! This storage facility would have to be secure from many unforeseeable events such as earthquakes, bombing etc. and be kept in a manner which our children's, children's children can understand. A very serious undertaking indeed!
## Relationship between the Decay Constant and the Half Life
On the basis of the above you should be able to appreciate that there is a relationship between the Decay Constant and the Half Life. For example when the Decay Constant is small the Half Life should be long and correspondingly when the Decay Constant is large the Half Life should be short. But what exactly is the nature of this relationship?
We can easily answer this question by using the definition of Half Life and applying it to the Radioactive Decay Law.
Once again the law tells us that at any time, t:
$N_t = N_0\ \text{exp}\,(-\lambda t)\,\!$
and the definition of Half Life tells us that:
$N_t = \frac{N_0}{2}$
when
$t = t_{\frac{1}{2}}$
We can therefore re-write the Radioactive Decay Law by substituting for Nt and t as follows:
$\frac{N_0}{2} = N_0\ \text{exp}\,(-\lambda t_{\frac{1}{2}})$
Therefore
$\frac{1}{2} = \text{exp}\,(-\lambda t_{\frac{1}{2}})$
$\therefore 2^{-1} = \text{exp}\,(-\lambda t_{\frac{1}{2}})$
$\therefore \ln 2^{-1} = -\lambda t_{\frac{1}{2}}$
$\therefore \ln 2 = \lambda t_{\frac{1}{2}}$
$\therefore 0.693 = \lambda t_{\frac{1}{2}}$
$t_{\frac{1}{2}} = \frac{0.693}{\lambda}$
and
$\lambda = \frac{0.693}{t_{\frac{1}{2}}}$
These last two equations express the relationship between the Decay Constant and the Half Life. They are very useful as you will see when solving numerical questions relating to radioactivity and usually form the first step in solving a numerical problem.
The SI or metric unit of radioactivity is named after Henri Becquerel, in honour of his discovery of radioactivity, and is called the becquerel with the symbol Bq. The becquerel is defined as the quantity of radioactive substance that gives rise to a decay rate of 1 decay per second.
In medical diagnostic work 1 Bq is a rather small amount of radioactivity. Indeed it is easy to remember its definition if you think of it as a buggerall amount of radioactivity. For this reason the kilobecquerel (kBq) and megabecquerel (MBq) are more frequently used.
The traditional unit of radioactivity is named after Marie Curie and is called the curie, with the symbol Ci. The curie is defined as the amount of radioactive substance which gives rise to a decay rate of 3.7 x 1010 decays per second. In other words 37 thousand, million decays per second which as you might appreciate is a substantial amount of radioactivity. For medical diagnostic work the millicurie (mCi) and the microcurie (µCi) are therefore more frequently used.
Why two units? It in essence like all other units of measurement depends on what part of the world you are in. For example the kilometer is widely used in Europe and Australia as a unit of distance and the mile is used in the USA. So if you are reading an American textbook you are likely to find the curie used as the unit of radioactivity, if you are reading an Australian book it will most likely refer to becquerels and both units might be used if you are reading a European book. You will therefore find it necessary to know and understand both units.
## Questions
Question 1
(a) The half-life of 99mTc is 6 hours. After how much time will 1/16th of the radioisotope remain?
(a) Starting with the relationship we established earlier between the Decay Constant and the Half Life we can calculate the Decay Constant as follows:
$\lambda = \frac{0.693}{t_{\frac{1}{2}}} = \frac{0.693}{6} = 0.1155\ \text{hr}^{-1}$
Now applying the Radioactive Decay Law,
$N_t = N_0\ \text{exp}\,(-\lambda t)\,\!$
we can re-write it in the form:
$\frac{N_t}{N_0} = \text{exp}\,(-\lambda t)$
The question tells us that N0 has reduced to 1/16th of its value, that is:
$\frac{N_t}{N_0} = \frac{1}{16}$
Therefore
$\frac{1}{16} = \text{exp}\,(-0.1155t)$
which we need to solve for t. One way of doing this is as follows:
$16^{-1} = \text{exp}\,(-0.1155t)$
$\therefore -\ln 16 = -0.1155t\,\!$
$t = \frac{\ln 16}{0.1155} = 24\ \text{hours}$
So it will take 24 hours until 1/16th of the radioactivity remains.
(b) A way in which this answer can be verified is by using the definition of Half Life. We are told that the Half Life of 99mTc is 6 hours. Therefore after six hours half of the radioactivity remains.
Therefore after 12 hours a quarter remains; after 18 hours an eighth remains and after 24 hours one sixteenth remains. And we arrive at the same answer as in part (a). So we must be right!
Note that this second approach is useful if we are dealing with relatively simple situations where the radioactivity is halved, quartered and so on. But supposing the question asked how long would it take for the radioactivity to decrease to a tenth of its initial value. Deduction from the definition of half life is rather more difficult in this case and the mathematical approach used for part (a) above will yield the answer more readily.
Question 2
Find the radioactivity of a 1 g sample of 226Ra given that t1/2: 1620 years and Avogadro's Number: 6.023 x 1023.
We can start the answer like we did with Question 1(a) by calculating the Decay Constant from the Half Life using the following equation:
$\lambda = \frac{0.693}{t_{\frac{1}{2}}} = \frac{0.693}{1620} = 4.28 \cdot 10^{-4}\ \text{year}^{-1}$
$\therefore \lambda = 1.36 \cdot 10^{-11} s^{-1}$
Note that the length of a year used in converting from 'per year' to 'per second' above is 365.25 days to account for leap years. In addition the reason for converting to units of 'per second' is because the unit of radioactivity is expressed as the number of nuclei decaying per second.
Secondly we can calculate that 1 g of 226Ra contains:
$N = \frac{(\text{Avogadro No.})(\text{Mass})}{\text{Mass Number}} = \frac{(6.023 \cdot 10^{23})(1g)}{226} = 2.7 \cdot 10^{21}\ \text{nuclei}$
Thirdly we need to express the Radioactive Decay Law in terms of the number of nuclei decaying per unit time. We can do this by differentiating the equation as follows:
$N = N_0\ \text{exp}\,(-\lambda t)$
$\therefore \frac{dN}{dt} = N_0 \cdot -\lambda\ \text{exp}\,(-\lambda t) = -\lambda N_0\ \text{exp}\,(-\lambda t)$
$\therefore \frac{dN}{dt} = -\lambda N$
$\therefore \left | \frac{dN}{dt} \right | = \lambda N$
The reason for expressing the result above in absolute terms is to remove the minus sign in that we already know that the number is decreasing.
We can now enter the data we derived above for λ and N:
$\left | \frac{dN}{dt} \right | = (1.36 \cdot 10^{-11})(2.7 \cdot 10^{21})$
$\therefore \left | \frac{dN}{dt} \right | = 3.6 \cdot 10^{10}\ \text{decays per second}$
So the radioactivity of our 1 g sample of radium-226 is approximately 1 Ci.
This is not a surprising answer since the definition of the curie was originally conceived as the radioactivity of 1 g of radium-226!
Question 3
What is the minimum mass of 99mTc that can have a radioactivity of 1 MBq? Assume the half-life is 6 hours and that Avogadro's Number is 6.023 x 1023.
Starting again with the relationship between the Decay Constant and the Half Life:
$\lambda = \frac{0.693}{6} = 0.1155\ \text{hour}^{-1} = 3.21 \cdot 10^{-5}$
Secondly the question tells us that the radioactivity is 1 MBq. Therefore since 1 MBq = 1 x 106 decays per second,
$\left | \frac{dN}{dt} \right | = \lambda N = 1 \cdot 10^6\ \text{dps}$
$\therefore N = \frac{\left | \frac{dN}{dt} \right |}{\lambda} = \frac{1 \cdot 10^6}{3.21 \cdot 10^{-5}} = 3.116 \cdot 10^{10}$
Finally the mass of these nuclei can be calculated as follows:
$\text{Mass of N nuclei} = \frac{(\text{No. of Nuclei})(\text{Mass No.})}{\text{Avogadro Number}}$
$= \frac{(3.116 \cdot 10^{10})(99)}{6.023 \cdot 10^{23}} = 5.122 \cdot 10^{-12}\ \text{g}$
In other words a mass of just over five picograms of 99mTc can emit one million gamma-rays per second. The result reinforces an important point that you will learn about radiation protection which is that you should treat radioactive materials just like you would handle pathogenic bacteria! | {"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": 46, "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": 0.8735211491584778, "perplexity": 387.74181540649073}, "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-2015-48/segments/1448398447860.26/warc/CC-MAIN-20151124205407-00158-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.allthatmatters.academy/memory-mechanism/newtons-2nd-law-in-rotation/ | # Newton’s 2nd law in rotation
Angular acceleration is caused by a net/resulting torque, $\sum \vec \tau$; and vice versa, a net torque causes angular acceleration $\vec \alpha$. This angular acceleration is “dampened” or resisted by the moment-of-inertia $I$.
$$\sum \vec \tau=I\vec \alpha$$ | {"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": 0.9954176545143127, "perplexity": 1063.257262909881}, "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-2020-40/segments/1600402131777.95/warc/CC-MAIN-20201001143636-20201001173636-00360.warc.gz"} |
https://www.physicsforums.com/threads/restricted-partitions.131277/ | # Restricted Partitions
1. Sep 9, 2006
### ghotra
http://en.wikipedia.org/wiki/Integer_partition
The above link should set the context.
Given an integer q, the total number of partitions is given by partition function p(q). For example,
4 = 4
= 3+1
= 2 + 2
= 2 + 1 + 1
= 1 + 1 + 1 + 1
So, p(4) = 5. In mathematica, one can use PartitionsP[4].
The number of partitions is unrestricted. An example problem might be: Suppose I have 2 indistinguishable balls and I want to give them to any number of indistinguishable children. What are the unique ways of distributing the balls?
I can give one child 4 balls.
I can give one child 3 balls and another child 1 ball.
I can give two children 2 balls each.
I can give one child 2 balls and two children 1 ball each.
I can give four children 1 ball each.
Notice, as the number of balls increases, it is necessary that there are at least as many indistinguishable children as there are balls to distribute.
Now, suppose I want to limit the number partitions (children) to some integer k. In the above example, suppose I limit the number of children to k=3. Then there are 4 partitions of size k=3 or less for the interger q=4. The disallowed partition is when I give 1 ball each to four children.
Is there a general formula for restricting the number of partitions. That is:
Example usage:
I have 2 indistinguishable balls and I want to give them to 3 indistinguishable children. There are just 2 unique ways of doing this:
(2,0,0)
(1,1,0)
That is, I give 2 balls to one child and none to the other children.
That is, I give 1 ball to one child and 1 ball to another child.
So, the number I am looking for is 2.
This is related to a common combinatorics problem. If I care about the order, then the following options are available:
(2,0,0) (0,2,0) (0,0,2)
(1,1,0) (1,0,1) (0,1,1)
This total number is 6 and the formula that determines it is well-known:
[2 + (3-1)]! / (3-1)! / 2! = 6
Thus, I am looking for some way to remove the permutation degeneracy from the above formula.
Any help is appreciated. This seems like it should be a common question. Does anyone know of the closed form answer?
Last edited: Sep 9, 2006
2. Sep 9, 2006
### ghotra
Here is a much better statement of my question:
How many integer solutions exist to the following equation:
$$\sum_{i=1}^k n_i = N$$
Let me call this number $p(N,k)$. It is the number of partitions for N such that the partitions are restricted to be of order k or less.
Example:
N = 5
k = 3
p(5,3) = 5
The solutions are:
(5,0,0)
(4,1,0)
(3,2,0)
(3,1,1)
(2,2,1)
Notice, if $$k \geq N$$, then $$p(N,k) = p(N)$$ where p(N) is the number of integer partitions of N.
http://en.wikipedia.org/wiki/Integer_partition
Notice, we do not care about the ordering. If we did care about the ordering, then there woudl be 21 solutions.
3!/2! of (5,0,0)
3! of (4,1,0)
3! of (3,2,0)
3!/2! of (3,1,1)
3!/2! of (2,2,1)
====
21
This number is:
$$\binom{5+(3-1)}{(3-1)} = \frac{[5+(3-1)]!}{(3-1)!5!}$$
Again, I would like to remove the degneracy due to permutations. So I want 21 -> 5, in this example. What is the general solution? The is no closed for solution for p(N)...so I am not expecting a closed-form solution. Any thoughts?
Last edited: Sep 9, 2006
3. Sep 10, 2006
### CRGreathouse
Sloane's http://www.research.att.com/~njas/sequences/A000041 [Broken] has some information on this: asymptotics, upper bounds, precalculated numbers, and various generating functions.
Last edited by a moderator: May 2, 2017
4. Sep 10, 2006
### ghotra
Thanks. A quick look did not reveal any information on restricting the partitions as I discussed. Any other ideas?
5. Sep 11, 2006
### CRGreathouse
I shomewhat misread the queston, so there isn't all I said there was there. It does have this:
a(n)=sum(i=0, n-1, P(i, n-i)), where P(x, y) is the number of partitions of x into at most y parts, and P(0, y)=1. - Jon Perry (perry(AT)globalnet.co.uk), Jun 16 2003
at least. A000012, A004526, and A001399 are the partition numbers for at most/exactly (1, 2, 3) partitions, modulo a shift in the offsets. Euler's table, A026820, has the general result (see also A008284 for "exactly" rather than "at least").
http://www.users.globalnet.co.uk/~perry/maths/morepartitionfunction/morepartitionfunction.htm
has a general result that may be useful.
6. Sep 12, 2006
### ghotra
Wonderful! So, it doesn't appear that there is a closed form solution to this. However, the recurrence relation is quite nice, along with the Euler triangle.
Thanks!
7. Jul 9, 2010
### jleach
I just ran across this thread, and it looks as if I'm a few years too late. But, if anyone is interested, I have some expertise on this topic. Not to brag, but several years ago, I independently discovered partitions and an approach to solve them, before I finally learned that I had been beaten to the glory by about 200 years. I've also discovered a way to determine the number of integer partitions that contain no repeated numbers. In other words, 2,2 would not be counted as a partition of 4. I'm just a mathematician by hobby, so I don't get published and a lot of times I reinvent the wheel. I don't find the time that I used to have, but I am sitting on a lot of past work that I'd like to share, just in case it would do someone some good.
8. Oct 7, 2010
### jleach
Before I leave for the weekend, I'll give you a preview of what I can remember. Let's first assign the function F(n) to be the procedure for generating the number of partitions for the number n. Let k be a number equal to or less than n. The number of partitions that contain the value k at least one time is F(n-k). But, that is old news. If S is a set of values, we can also let k be the sum of those values within the set. F(n-k) will tell me how many partitions of n contain the set at least once. Now for the number of partitions of n that contain no repeated values, I must double check my notes to be certain, but I know that k is calculated from the sum of natural numbers. I'll try to confirm and give you details next week.
9. Oct 11, 2010
### jleach
I'm back and I've reviewed my notes. Restricted partitions is a little more complex than I described above, but not bad. The first thing that you'll need is a partition table like the one that I posted on Wikipedia (Search for "Integer Partitions" or "Partition (Number Theory)", then look under the section "See also". My table is the link called "Leibniz's distribution table for integer partitions". Leibniz is the one who beat me to the discovery. This table is actually two overlapping tables. One is for partitioning finite integers and the other is for partitioning infinity. You'll want to use the column for finite integers. From what I've read, everyone should already know the pattern to recreate this table. The stage values tell you how many ways you are going to divide the integer, but the stage values run opposite the number of divisions. For example, stage 1 will always be a set of all ones, but there will be N one's within that set.
As I said before, this is a fractal pattern that can only be described in terms of the repeating pattern within the table. Therefore, my solutions are in terms of the table coordinates. The next thing to remember is that the table coordinate (Column 0 Row 0) = 1.
Here's the solution:
Let N = The integer to be partitioned
Let S = The number of spaces or divisions of that number
Let E = Summation of i as i goes from 1 to S
Let L = Greatest integer function of (-1+sqrt(1+8*N))/2
The number of partition sequences without repeated values at S divisions is the coordinate (Column N-E+1, Row N-E+S).
Therefore, the total number of partitions sequences without repeated values is:
Summation of S from 1 to L of (Column N-E+1, Row N-E+S).
To check a practice run, let N=14. The answer should be 1 + 6 + 10 + 5 = 22
10. Oct 11, 2010
### jleach
P.S. If by chance you get a table coordinate with negative numbers, the table value is zero. Example: Column 4 Row -3 = 0
11. Oct 12, 2010
### jleach
FYI, You can generate a new table for partitions without repeats and it is also a fractal, but with a slightly different rule. I thought that I'd mention this, because if you are only interested in partition sequences without repeated values, then this approach may be a faster computing method. | {"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": 0.8010936975479126, "perplexity": 611.7436391076677}, "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-2018-05/segments/1516084891706.88/warc/CC-MAIN-20180123032443-20180123052443-00649.warc.gz"} |
https://physics.stackexchange.com/questions/142038/wannier-functions-as-discrete-basis | Wannier Functions as Discrete Basis
In solid state physics, using Bloch's theorem we know that the one-electron energy eigen-function can be written as $\psi_{\lambda,\vec{k}}(\vec{r})$ where $\lambda$ indexes eigenvalues of $\hat{H}$ and $\vec{k}$ indexes eigenvalues of $\hat{T}_\vec{R}$, the translation by lattice-vector-$\vec{R}$ operator.
Because of Bloch's theorem, we know that $\psi_{\lambda,\vec{k}}(\vec{r})$ is periodic in $\vec{k}$ by reciprocal-lattice-vectors $\vec{K}$ and so we may write a Fourier series of it as: $$\psi_{\lambda,\vec{k}}(\vec{r})=\sum_{\vec{R}}\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})\exp\left({i\vec{R}\cdot\vec{k}}\right)$$
$\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})$ are called Wannier functions. One can prove that $\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})$ depends only on the difference $\vec{R}-\vec{r}$ as well as show that the Wannier functions are orthogonal between different values of $\lambda$ or $\vec{R}$.
As a result we may write an arbitrary wave-function $\psi(\vec{r})$ as $$\psi(\vec{r}) = \sum_{\lambda,\,\vec{R}} \alpha_{\lambda,\,\vec{R}}\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})$$
where $\alpha_{\lambda,\,\vec{R}}=\int_{\mathbb{R}^3}\psi(\vec{r})\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})d^3\vec{r}$ are the expansion coefficients in the Wannier basis.
My question is:
1) Expressed in the Wannier basis $\left\{\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})\right\}_{\lambda,\,\vec{R}}$, why is it true that the potential energy of the electron is proportional to a delta-function?
$$V_{\lambda,\lambda',\vec{R},\vec{R'}} \propto \delta_{\vec{R},\vec{R'}}$$
It is clear intuitively because $$V_{\lambda,\lambda',\vec{R},\vec{R'}} \equiv \int_{\mathbb{R}^3}\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})^{\ast}V(\vec{r})\tilde{\psi}_{\lambda',\vec{R'}}(\vec{r})d^3\vec{r}$$
and coming from the tight-binding model (or alternatively using some dubious claim that the Wannier functions can always be chosen to be maximally-localized using the gauge-freedom in the definition of the wave functions) we know that $\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})$ is "sort of" around one particular lattice site $\vec{R}$ and so the integrand is non-zero only if the two lattice sites match.
But I would like a more rigorous (or hopefully much more direct) derivation of this. I am assuming that there is a simple easier reason I don't see.
2) My second question is how to express the kinetic energy, $\frac{-\hbar^2}{2m}\vec{\nabla}^2$, in the Wannier basis? I can't think of how to proceed from $$T_{\lambda,\lambda',\vec{R},\vec{R'}} = \frac{-\hbar^2}{2m} \int_{\mathbb{R}^3}\tilde{\psi}_{\lambda,\vec{R}}(\vec{r})^{\ast}\vec{\nabla}^2\tilde{\psi}_{\lambda',\vec{R'}}(\vec{r})d^3\vec{r}$$
• 1- I'm almost 100% confident that this is an approximation. 2- you're done. use that and the second equation. – Adam Oct 20 '14 at 18:10
• It seems that you're involved with Wannier functions. I recently started to learn about it and I would be happy if you can suggest me a reference for a comprehensive derivation of Wannier functions from Bloch functions? – Sina Dec 22 '16 at 14:27
• @Sina, have a look at the end of the tight-binding chapter in Ashcroft and Mermin. – PPR Dec 22 '16 at 14:30 | {"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": 0.893856406211853, "perplexity": 112.60877954072615}, "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-2019-35/segments/1566027321160.93/warc/CC-MAIN-20190824152236-20190824174236-00019.warc.gz"} |
http://lists.gnu.org/archive/html/lilypond-user/2011-03/msg00555.html | lilypond-user
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## Re: 2.13.54 breaks NoteNames vertical spacing
From: Phil Holmes Subject: Re: 2.13.54 breaks NoteNames vertical spacing Date: Sun, 20 Mar 2011 10:56:39 -0000
----- Original Message ----- From: "Keith OHara" <address@hidden>
```To: <address@hidden>
Sent: Sunday, March 20, 2011 7:26 AM
Subject: Re: 2.13.54 breaks NoteNames vertical spacing
```
```Michael Ellis <michael.f.ellis <at> gmail.com> writes:
```
``` In 2.12, the NoteNames output lays close beneath the lyric line.
In 2.13.54 the gap is quite large and the output collides with
markup above the next staff. Is there a workaround?
```
```Try
\layout { \context {
\NoteNames
\override VerticalAxisGroup #'staff-affinity = #UP
}}
The initialization file (engraver-init.ly) actually says
% FIXME: not sure what the default should be here.
\override VerticalAxisGroup #'staff-affinity = #DOWN
```
So let's set the correct default now. Is there any reason to assume that note- names will most often be associated with the staff above or the staff below ?
```
```
If not, we can set staff-affinity to CENTER -- which doesn't really mean center but means get close to a staff on either side. I guess the programmer didn't
```think that 'staff-affinity = #PROMISCUOUS was appropriate.
```
```
```
It definitely works best with staff-affinity UP, where the note names are below the stave. Presumably it would be best with DOWN where they're above. It also is improved with:
```
\paper {
}
```
IIRC, this is all to do with the system spacing not taking account of non-staff grobs? I do think this is likely to cause a number of problems in the future.
```
--
Phil Holmes
``` | {"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": 0.910156786441803, "perplexity": 3616.4974384064108}, "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-20151001221842-00250-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://rd.springer.com/chapter/10.1007/978-90-481-3239-3_8 | # Goal Oriented Mesh Adaptivity for Mixed Control-State Constrained Elliptic Optimal Control Problems
• Michael Hintermüller
• Ronald H. W. Hoppe
Chapter
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 15)
## Abstract
Adaptive finite element methods for the numerical solution of partial differential equations consist of successive cycles of the loop
$${\rm SOLVE}\ \Longrightarrow\ {\rm ESTIMATE}\ \Longrightarrow\ {\rm MARK}\ \Longrightarrow\ {\rm REFINE}.$$
Here, SOLVE stands for the finite element solution of the problem with respect to a given triangulation of the computational domain. The following step ESTIMATE is devoted to the estimation of the global discretization error in some appropriate norm or a user specified quantity of interest by a cheaply computable a posteriori error estimator. The estimator is assumed to consist of local contributions whose actual magnitude is then used in the step MARK to specify elements of the triangulation for refinement. The final step REFINE deals with the generation of a new triangulation based on the refinement of the elements selected in the previous step according to specific refinement rules. Adaptive finite elements are by now well established. There are various approaches such as residual-type a posteriori error estimators which rely on the proper evaluation of the residuals with respect to a computed approximation in the norm of the dual space and hierarchical type estimators where the equation satisfied by the error is suitably localized along with a solution of the local problems by higher order finite elements (cf., e.g. [1, 3, 35]). Averaging-type estimators typically use some sort of gradient recovery on element-related patches (cf., e.g. [1, 35]), whereas the theory of guaranteed error majorants provides reliable upper bounds for the error (see [31]). Finally, the goal oriented weighted dual approach extracts information on the error via the dual problem (cf. [4, 12]).
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F. Tröltzsch. Regular Lagrange multipliers for control problems with mixed pointwise control-state constraints. SIAM J. Optim., 15(2):616–634, 2005.
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B. Vexler and W. Wollner. Adaptive finite elements for elliptic optimization problems with control constraints. SIAM J. Control Optim., 47(1):509–534, 2008. | {"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": 0.9116610288619995, "perplexity": 1554.0298927051474}, "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-2021-04/segments/1610703517159.7/warc/CC-MAIN-20210118220236-20210119010236-00341.warc.gz"} |
http://mathhelpforum.com/algebra/159633-slope-tangent.html | # Math Help - Slope of Tangent
1. ## Slope of Tangent
The gravitational potential energy of the MIR space station, in joules, at a distance of x kilometers from the centre of the Earth, is described by the equation
$E = -\frac{(5.38)(10)^{19}}{x}$. Determine the slope of the tangent to the graph at the given value of x.
$x = (6.5)(10)^6 m$
$x = (6.5)(10)^6 m = 6500 km$
$m = \frac{E(6500 + 0.001) - E(6500)}{0.001}$
$m = \frac{(-\frac{(5.38)(10)^{19}}{(6500 + 0.001)}) -(-\frac{(5.38)(10)^{19}}{(6500)})}{0.001}$
$m = 1.273(10)^{12}$
Is this correct?
2. Yes your anwers is correct.
Your formula can be rewritten as:
$E = -(5.38)(10)^{19}* \frac{1}{x}$
Which has derivative:
$E' = (5.38)(10)^{19}* \frac{1}{x^2}$
Proof see: Calculus with polynomials - Wikipedia, the free encyclopedia
With your x, this gives $1.27337278 \times 10^{12}$ | {"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": 9, "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": 0.9682871699333191, "perplexity": 726.4278589995735}, "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/1429246660724.78/warc/CC-MAIN-20150417045740-00216-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://www.philipp-diesinger.de/ | 09.09.2009
# Genome Folding at the 30 nm Scale
by pmd
This PhD thesis addressed and succeeded in answering a fundamental question concerning genome folding at the 30nm scale by proving that a higher-order DNA folding pattern beyond the nucleosome, i.e. chromatin, actually exists. A model for chromatin was developed that allows to study very long fibers (in the range of Mega base pairs). Furthermore, linker histone depletion as well as nucleosome depletion have been included for the first time in a chromatin model. This allowed to study the chromatin phase diagram and the corresponding structures are discussed against the background of compaction and DNA accessibility and other important chromatin features. The basic model parameter distributions come from experimental data [186,187]. Together with the histone depletion effects they show that every chromatin conformation consists of a distribution of different structures. This explains why regular 30nm fibers are so hard to find experimentally.
The results show that histone depletion massively affects the properties of chromatin. Nucleosome depletion can either lead to a collapse or to swelling of chromatin and the predicted regime of optimal DNA condensation coincides with experimental data [186] which proves that histone depletion is used as a regulatory tool for DNA extension. Moreover, the model is in good agreement with many experimentally determined chromatin properties. A comparison of the developed model with 5C experimental data [72] proves that histone depletion is an important chromatin feature because only fibers with depletion allow the important physical contacts on a small length scale. Random chromatin collisions are theoretically studied to improve 3C-based experimental technologies by allowing to distinguish more accurately between specific and random DNA contacts.
## Related Publications
• Diesinger, P.M. 2009. Genome Folding at the 30 nm Scale. PhD Thesis.
## Comparison with Electron Micrographs
The following figures show a comparison of simulated chromatin fibers with electrom micrographs (adapted from Olins, D.E. and Ada L. Olins. 2003. Chromatin history: our view from the bridge. Nat Rev Mol Cell Biol 4: 809-14.).
09.09.2009
# Influence of Histone Depletion on Genome Folding
by pmd
We present a Monte Carlo model for genome folding at the 30nm scale with focus on linker histone and nucleosome depletion effects. We find that parameter distributions from experimental data do not lead to one specific chromatin fiber structure but instead to a distribution of structures in the chromatin phase diagram.
Depletion of linker histones and nucleosomes affects massively the flexibility and the extension of chromatin fibers. Increasing the amount of nucleosome skips (i.e. nucleosome depletion) can either lead to a collapse or to swelling of chromatin fibers. These opposing effects are discussed and we show that depletion effects may even contribute to chromatin compaction. Furthermore, we find that predictions from experimental data for the average nucleosome skip rate lie exactly in the regime of maximum chromatin compaction.
Finally we determine the pair distribution function of chromatin. This function reflects the structure of the fiber and its Fourier transform can be measured experimentally. Our calculations show that even in the case of fibers with depletion effects the main dominant peaks (characterizing the structure and the length scales) can still be identified.
## Related Publications
• Diesinger, P.M. and D.W. Heermann. 2009. Depletion Effects massively change Chromatin Properties and influence Genome Folding. Accepted by Biophysical Journal (will be published Oct. 2009).
View into the cell nucleus: This figure shows an illustration of 1 Mbp of chromatin with histone and nucleosome depletion.
09.09.2009
# Hydrophobicity induced Gelation of FG-rich Nucleoporins
by pmd
In this work we address the question whether hydrophobic parts of FG-rich nucleoporins can be the reason for their ability to form a hydro-gel. We focus on the N-terminal fsFG-domain of the essential yeast nucleoporin Nsp1p [18] as a nucleoporin model system and on the question whether a phase transition between a sol and a gel phase exists. It comprises 18 regular FSFG-repeats and 16 less regular FG-repeats. This domain is modeled and equilibrated ensembles of peptide networks were generated by a Metropolis Monte-Carlo algorithm which then were analyzed by percolation theoretical methods.
We take into account the excluded-volume of the protein backbone and all side chains which are at least medium-sized (starting with Glu / E) as well as the hydrophobic clusters of the amino acid sequence. There is a competition between two kinds of entropic forces in the system: The excluded volume interactions and the hydrophobic parts of the nucleoporin strands. Therefore, it is not a priori clear whether the system percolates at a biologically realistic density. Nevertheless, we find a sol-gel phase transition in the system at a critical density of 42 mg / mL
## Related Publications
• Diesinger, P.M. and D.W. Heermann. 2009. Hydrophobicity as a possible Reason for Gelation of FG-rich Nucleoporins. Accepted by European Biophysics Journal.
09.08.2009
# E2A Model for Chromatin
by pmd
We present a model improving the two-angle model for interphase chromatin (E2A model). This model takes into account the cylindrical shape of the histone octamers, the H1 histones in front of the nucleosomes, and the distance d between the in and outgoing DNA strands orthogonal to the axis of the corresponding nucleosome cylinder. Factoring these chromatin features in, one gets essential changes in the chromatin phase diagram: Not only the shape of the excluded-volume borderline changes but also the orthogonal distance d has a dramatic influence on the forbidden area. Furthermore, we examined the influence of H1 defects on the properties of the chromatin fiber.
Thus, we present two possible strategies for chromatin compaction: The use of very dense states in the phase diagram in the gaps in the excluded-volume, borderline, or missing H1 histones can lead to very compact fibers. The chromatin fiber might use both of these mechanisms to compact itself at least locally. Line densities computed within the model coincident with the experimental values.
## Related Publications
• Diesinger, P.M. and D.W. Heermann. 2007. The Influence of the Cylindrical Shape of the Nucleosomes and H1 Defects on the Properties of Chromatin. Biophysical Journal, doi:10.1529/biophysj.107.113902. [abstract]
09.08.2009
# Chromatin Phase Diagram
by pmd
We have studied the phase diagram for chromatin within the framework of the two-angle model. Only a rough estimation of the forbidden surface of the phase diagram for chromatin was given in a previous work of Schiessel. We revealed the fine structure of this excluded-volume borderline numerically and analytically. Furthermore, we investigated the Coulomb repulsion of the DNA linkers to compare it with the previous results.
## Related Publications
• Diesinger, P.M. and D.W. Heermann. 2006. Two-Angle Model and Phase Diagram for Chromatin. Physical Review E Vol. 74, Issue 3, doi10.1103/PhysRevE.74.031904. [abstract]
09.07.2009
# Quantitative Description of Polymer Entanglement
by pmd
We develop new methods for the structural analysis of polymer systems (especially of DNA). So far we investigated the effects of excluded volume interactions on the mean average crossing number (mACN) [ref] and the knot statistics [ref] of polymers. The mACN is roughly speaking a measure for the entanglement of polymer chains.
At the moment we are about to publish a paper which shows the connection between the mACN and the scattering function as well as the loop number of polymer chains.
We study the influence of excluded volume interactions on the behaviour of the mean average crossing number (mACN) for random off-lattice walks. We investigated Gaussian and equilateral off-lattice random walks with and without ellipsoidal excluded volume up to chain lengths of N = 1500 and equilateral random walks on a cubic lattice up to N = 20000. We find that the excluded volume interactions have a strong influence on the behaviour of the local crossing number 〈 a(l1,l2) 〉 at very short distances but only a weak one at large distances. This behaviour is the basis of the proof in [ Y. Diao et al., Math. Gen. 36, 11561 (2003); Y. Diao and C. Ernst, Physical and Numerical Models in Knot Theory Including Applications to the Life Sciences] for the dependence of the mean average crossing number on the chain length N. We show that the data is compatible with an N ln(N)-bahaviour for the mACN, even in the case with excluded volume.
We investigated the effects of excluded volume interactions on the average crossing number (ACN) and found a power law for the number of knot-monomers with an exponent $0.39 \pm0.13$ in agreement with previous simulations. For the average size of a knot we also obtain a power law behaviour. We further present data on the average number of knots given a certain chain length and confirm a power law behaviour for the number of knot-monomers. Furthermore we study the average crossing number for random and self-avoiding walks as well as for a model polymer with and without geometric constraints. The data confirms the aN log N + bN law in the case of without excluded volume and determines the constants $a$ and $b$ for various cases. For chains with excluded volume the data for chains up to N=1500 is consistent with a N log N + bN rather than the proposed N^{4/3} law. Nevertheless our fits show that the N^{4/3} ACN of a polymer chain with a looplaw is a suitable approximation.
## Related Publications
• Diesinger, P.M. and D.W. Heermann. 2009. The Connection of the mACN with the scattering Function and the Loop Number of Polymer Chains. In preparation.
• Diesinger, P.M. and D.W. Heermann. 2008. Average Crossing Number of Gaussian and Equilateral Chains with and without Excluded Volume. European Journal of Physics B, Volume 62, Number 2, 209-214. [abstract]
• Brill, M. P.M. Diesinger and D.W. Heermann. 2005. Knots in Macromolecules in Constraint Space. arXiv:cond-mat/0507020. [abstract]
• Diesinger, P.M. 2005. Excluded Volume Effects in Biopolymers. (diploma thesis [download]).
09.04.2009
# Excluded Volume Effects in Biopolymers
by pmd
In this diploma thesis the influence of excluded volume interactions on the mean average crossing number of polymer chains was numerically and analytically investigated. It turned out that this influence is very strong and that the mean average crossing number of real polymers is much smaller than the theoretical predictions for ideal polymer chains in [22; 23; 26]. Furthermore the forbidden surfaces of the chromatin phase diagram due to excluded volume restrictions were numerically revealed and very good analytical approximations could be found for it. The behavior of the nucleosome density, the accessibility and the energy of a single chromatin repeat unit at the determined excluded volume borderline was investigated.
## Related Publications
• Diesinger, P.M. and D.W. Heermann. 2006. Two-Angle Model and Phase Diagram for Chromatin. Physical Review E Vol. 74, Issue 3, doi10.1103/PhysRevE.74.031904. [abstract]
• Diesinger, P.M. and D.W. Heermann. 2008. Average Crossing Number of Gaussian and Equilateral Chains with and without Excluded Volume. European Journal of Physics B, Volume 62, Number 2, 209-214. [abstract]
• Diesinger, P.M. 2005. Excluded Volume Effects in Biopolymers. (diploma thesis [download]).
09.03.2009
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http://pcsoftwarehowto.blogspot.ch/2010/08/pc-sw-how-to-manually-removing.html | ## Thursday, August 19, 2010
### A-PC-SW-How-To: Manually Removing QuickTime...
Are you getting the following error message when trying to reinstall/uninstall Apple’s QuickTime:
The feature you are trying to use is on a network resource that is unavailable.
Click OK to try again, or enter an alternate path to a folder containing the installation package 'QuickTime.msi' in the box below.
If so, you may need to manually remove QuickTime. Try the following steps. They may solve your problem
Note: Make sure you have made a complete backup of all your personal and system data, before proceeding with making any changes to your system.
Take the following steps to remove QuickTime:
2. Run this utility. It will show you a list of programs. Find QuickTime and remove it.
3. Go to the folder c:\windows\system32 and delete the files QuickTime.qts and QuicktimeVR.qtx
4. Go to the folder c:\windows and delete the files QTFont.for and QTFont.qfn
5. Delete the folder c:\program files\quicktime
Now, go ahead and reinstall QuickTime.
____ | {"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": 0.8898935317993164, "perplexity": 3843.280095948737}, "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-2018-09/segments/1518891815934.81/warc/CC-MAIN-20180224191934-20180224211934-00129.warc.gz"} |
http://math.stackexchange.com/questions/211188/matrix-representation-of-transformation-in-ordered-bases | # Matrix representation of transformation in ordered bases
An example question asks me to determine $[T]_{\beta}^\gamma$ where $\beta,\ \gamma$ are standard ordered bases of $\mathbb{R}^n$ and $\mathbb{R}^m$ respectively, of $$T_1: \mathbb{R}^n \rightarrow \mathbb{R}^n,\ \ T_1(a_1, a_2, ...a_n) = (a_1, a_1, a_1,....., a_1)$$ and also of $$T_2: \mathbb{R}^n \rightarrow \mathbb{R}^n,\ \ T_2(a_1, a_2, ...a_n) = (a_n, a_{n-1}, a_{n-2},....., a_1)$$
I understand that in $T_1$, $T$ needs to be an $n\times n$ matrix consisting of ones in the first column and nowhere else. In the second one, I can deduce that the ones must be on the negative diagonal.
My problem is, I don't know how I can formally present that as a solution to $[T]_{\beta}^\gamma$
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Does $T_1$ have $a_1$ in all $n$ entries, or all but the last? – copper.hat Oct 11 '12 at 17:05
All of them. Sorry, I'll fix that. – Imray Oct 11 '12 at 17:07
$$T_1(1,0,...,0):=(1,1,...,1)=1\cdot(1,0,...,0)+1\cdot(0,1,0,...,0)+...+1\cdot(0,0,.,,,.1)$$ $$T_1(0,1,...,0):=(0,0,...0)=0\cdot (1,0,...,0)+\cdot(0,1,...,)+...+0\cdot (0,0,...,1)\\.................$$
$$T_1(0,0,...,1):=(0,0,...,0)=0\cdot (1,0,...,0)+...+0\cdot(0,0,...,1)$$
Thus, being $\,e:=\,$ the standard basis of $\,\Bbb R^n\,$
$$[T_1]_e^e=[T_1]_e=\begin{pmatrix} 1&0&...&0\\1&0&...&0\\...&...&...&...\\1&0&...&0\end{pmatrix}$$
Pay attention to the fact that the matrix above is the transpose of the coefficient matrix in the first part.
Now you try with $\,T_2\,$ following the same model.
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Following your lead, I test out all the elements of the standard ordered basis for $R^2$, i.e. $T_1(1,0,...,0):=(0,0,...,1)=0\cdot(1,0,...,0)+0\cdot(0,1,0,...,0)+...+1\cdot(0,0,.,,,.1)$ - Am I going the right direction? – Imray Oct 11 '12 at 18:17
Yes: you have to apply $\,T\,$ to each and every element of basis $\,\beta\,$ and then you must write the outcome as a linear combination of the basis $\,\gamma\,$ . In this case the situation is pretty comfortable as $\,\beta=\gamma=e=\,$the standard basis. – DonAntonio Oct 12 '12 at 3:17 | {"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": 0.9263643026351929, "perplexity": 211.27642128423346}, "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/1422115900160.86/warc/CC-MAIN-20150124161140-00047-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://economics.stackexchange.com/questions/48439/why-are-production-functions-linear-in-technology | # Why are production functions linear in technology?
Economists often assume a production function of the form $$Y = A f(K, L)$$, where $$Y$$ is output, $$K$$ is capital, $$L$$ is labour and $$A$$ is technology. This form of production function can describe both nation-wide production or firm-wide production.
Now, my question is, why is the production function assumed to be linear in the technology $$A$$? For example, can't we have a production function of the form
$$Y = \sum_{i = 1}^n A^{\alpha_i} K^{\beta_i} L^{1-\beta_i} \quad$$
where $$\alpha_1, \beta_1, \alpha_2, \beta_2, \dots \alpha_n, \beta_n$$ are exogenous parameters?
It can, production functions do not need to be linear in technology. Production functions of the form:
$$F=AK^{\alpha}L^{1-\alpha}$$
are used because they are simple to work with, have some nice properties, and as the authors after which this function has its name (this is so called Cobb-Douglas production function), Cobb & Douglas (1928) this function reasonably well (given its simplicity) describes, and exhibits properties of, production functions in real life (at least to a point). Over years Cobb-Douglas production function became sort of a default function to be used in examples (even outside production e.g. Cobb-Douglas utility).
Moreover, when estimating productivity with parametric models it is often easier to work with linear(ized) production functions.
However, the above being said production function can have various shape or forms. Ultimately it is for every firm and country an empirical question how the production function looks like. However, remember scientists deal with models. Having 100% realistic production function with all non-linearities would likely offer no extra benefit comparing to having simplified 80-90% realistic production function. Unless you are working on some speical case where that matters you have to weight the pros and cons of realism vs clarity/workability/usability trade-off.
It is important to note that technology is an abstract concept and cannot be measured in concrete units, but simply with a positive scalar magnitude (the greater the technical development, the greater the quantity). With this in mind the proposed function:
$$Y = \sum_{i = 1}^n A^{\alpha_i} K^{\beta_i} L^{1-\beta_i}$$
It can always be rewritten as a "linear function" of the technology within each sector $$i$$, simply by defining $$\tilde{A}_i = A^{\alpha_i}$$, then you have a linear function on different technologies:
$$Y = \sum_{i = 1}^n \tilde{A}_i K^{\beta_i} L^{1-\beta_i}$$
where each term in the sum has been interpreted as the output in a specific sector with technology level $$\tilde{A}_i$$. | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 14, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9557235240936279, "perplexity": 782.517390784864}, "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/1679296945144.17/warc/CC-MAIN-20230323100829-20230323130829-00424.warc.gz"} |
https://indico.cern.ch/event/667053/ | # Topic of the Week
US/Central
Sunrise - WH11NE (Fermilab)
### Sunrise - WH11NE
#### Fermilab
,
Description
The production of four top quarks (tttt) is within the reach of the 13 TeV LHC. In this talk, I will cover recent CMS results in the search for this standard model process, focusing on the results of arXiv:1710.10614, which provide a first, statistically limited, measurement of tttt. I will also discuss the interpretation of this result in probing new physics hypotheses, such as two Higgs doublet models, and to constrain the Yukawa coupling between the Higgs boson and the top quark.
• 3:30 PM 4:30 PM
Search for Standard Model production of four top quarks 1h
Speaker: Giovanni Zevi Della Porta (Univ. of California San Diego (US)) | {"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": 0.8848528861999512, "perplexity": 2920.3924063880095}, "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-2022-27/segments/1656103639050.36/warc/CC-MAIN-20220629115352-20220629145352-00545.warc.gz"} |
http://physics.stackexchange.com/questions/10818/why-should-the-observed-probability-distributions-in-quantum-mechanics-always-ali | # Why should the observed probability distributions in quantum mechanics always align with the pointer basis of decoherence?
It has always been claimed decoherence solves the problem of the preferred-basis for observed probability distributions, but why should this be the case? If there is only one world, and there are probabilities for certain outcomes, why should the basis in which the probabilities are observed coincide with the pointer basis determined dynamically by decoherence?
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Or why don't we see superposed cats? – Raskolnikov Jun 6 '11 at 10:52
If we consider the heisenberg uncertainty principle a cat is a superposition of many cats, as we all are superpositions of many us. It is the size of hbar that makes this superposition irrelevant because we live in a world many orders of magnitude larger than this fuzziness. – anna v Jun 6 '11 at 14:15
@Raskolnikov the comment above should have been addressed to you. – anna v Jun 6 '11 at 15:44
@anna I do not see how it addresses the issue, but why don't you make it a reply to the OP? – Raskolnikov Jun 7 '11 at 7:47
It's because the probability that a given mixed state $\rho$ is found in a particular normalized state $\psi$ is only "sharp" and well-defined if $\psi$ is actually an eigenstate of $\rho$. So whatever basis in which $\rho$ is diagonal the decoherence produces, is also the basis of the states that have well-defined probabilities.
For all their general linear superpositions, one may calculate the expectation values of the probabilities but they're not probabilities that can be measured or "perceived". The prescription above was described e.g. at
http://motls.blogspot.com/2011/06/density-matrix-and-its-classical.html
It treats the density matrix in a similar way as the observables - even though the density matrix is not an observable. The rule that only the eigenstates of the density matrix may be "perceived" is pretty much equivalent to the "consistent histories" approach to quantum mechanics that tells you which questions may be asked in quantum mechanics and which can't.
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If I understand you correctly, the preferred basis is the eigenbasis of the density matrix and has thus a priori nothing to do with decoherence. Except that a posteriori, decoherence has produced a certain density matrix, and therefore its eigenbasis is the basis of pointer states. Correct? – Raskolnikov Jun 7 '11 at 8:07
If I understand you correctly, then yes! ;-) Decoherence is just a particular process, and/or a calculation imitating this process, that just allows one to trace what the eigenstates of the density matrix will be. But the fact that the basis in which $\rho$ is diagonal is preferred for defining "alternative histories or outcomes" whose probabilities may be nicely checked and "perceived" is an independent fact. – Luboš Motl Jun 8 '11 at 6:47
Let's hear it from the great quantum philosopher Niels Bohr. During his time, no one used the term preferred basis, but the term complementary observables covers pretty much the same issue. If you wish to object, please point out why. So let's say we have an electron floating around. Do we use the position basis, or the momentum basis? Bohr's answer is very ingenious and cuts right to the heart of the matter. Search and search into the dynamics of the electron in itself, and you will never find the answer. All experiments have to include the description of the experimental apparatus as part of the complete description. It is the choice of apparatus and its settings which determines the preferred basis. Is an electron passing through a double slit a particle or a wave? If you don't measure which slit it went through, the wave basis is preferred. If you do measure which slit it went through, the particle basis is preferred. Is the spin of an electron aligned along the z-axis, or the x-axis? The answer is not found in the electron itself. The answer is found in the orientation of the Stern-Gerlach magnetic field of the experiment. The so-called pointer basis is none other than the basis that the apparatus picks out. The pointer basis is very sensitive to the nature of the apparatus and its settings.
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Most people misunderstand what decoherence is all about. Decoherence is not really about how the environment affects the system. Decoherence is about how the system imprints itself irreversibly in the environment. Obviously, you can't observe a system unless information about the system has already been imprinted within the environment for you to pick up. The pointer information of decoherence are precisely those information about the system which becomes entangled with the environment for you to pick up. When stated in this manner, the OP's question becomes almost tautological.
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It is an utter misunderstanding that the preferred basis is given by the eigenstates of the reduced density matrix. If this false definition is correct, decoherence is tautological. Decoherence is defined to be a suppression of off-diagonal components in the basis of choice, but the basis is chosen to be the eigenstates? tautological. Besides, taking this definition seriously, as Motl does, the basis depends upon where the boundary of the system is drawn. Take Schrodinger's cat. Place the boundary at Pluto when the signals haven't had time to reach it yet and there is no entanglement assuming stosszahlansatz and the eigenstates form some funny bizarre unphysical states. When the signal reaches Pluto, it turns into a live or dead cat. Place the boundary around the cat so that the rest of the box is in the environment and the basis is more well behaved. When two eigenvalues nearly match, the eigenstates can mix into unphysical vectors. Also, the nondominant eigenvalue eigenstates are always funny, but stick to the dominant probable ones for the moment.
It is also sensitive to how thick or thin the boundary wall is. Too thin, not enough smearing, and the eigenstates also become funny and bad. Too much focus upon quantum fluctuations across the boundary. There is an art to choosing boundaries.
No, the true tenet of decoherence is maximal predictivity. What basis, such that if we know which basis vector allows us to predict the future with greatest accuracy, i.e. least increase in entropy? Informational patterns which survive over time, maybe in a transmuted encoding form. The basis comes from the interaction Hamiltonian term factors, and are the most stable over time. Many seemingly good bases suck because they mix up rapidly in time with no stability. The better the survival of information over time and the longer it survives, the higher the predictability and the better the basis. Then check if in this maximally predictable basis, the off diagonal terms are suppressed. This is decoherence.
Of course, some people would just claim the preferred basis is the basis of consciousness, but this is highly controversial.
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Without collapse all information survives. Unitarity guarantees this. – wnoise Nov 23 '11 at 19:42 | {"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": 0.8370338678359985, "perplexity": 562.8518292347411}, "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-2014-52/segments/1418802769581.93/warc/CC-MAIN-20141217075249-00148-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/originless-coordinates.371837/ | # Originless Coordinates?
1. Jan 22, 2010
### AverageJoe
This is something that has always been in my mind, yet everywhere I look I can't find an answer.
Is there any type of coordinate system that has no origin?
As in, everything is found by relation to other elements within the model?
2. Jan 23, 2010
### Mentallic
Do you mean as in a coordinate system that cannot have an origin, or doesn't necessarily need it? I can't imagine any system where an origin isn't used for convenience.
Take the surface of the Earth. Everything can be described in relation to something else so that no origin is required, but without this origin it would be impossible to give a point on Earth a set of coordinates.
3. Jan 23, 2010
### arildno
Yes, that does exist.
Unfortunately, I have forgotten what we call it.
4. Jan 23, 2010
### Mentallic
Can you please explain how this system works?
5. Jan 23, 2010
### arildno
I only vaguely remember it, so I can't say anything further.
It is an abstract geometry without using coordinates at all, basically.
I think..
6. Jan 23, 2010
### arildno
Okay, I have muddled a lot here!
What I was thinking of is called the "affine plane", and the reason why it doesn't have an origin is that it doesn't have coordinates.
Once you impose coordinates you have, of course, an implied origin.
7. Jan 23, 2010
### rochfor1
Any vector space will have an "origin."
8. Jan 23, 2010
### AverageJoe
Hmm..Affine Space isn't exactly what I was thinking of.
9. Jan 23, 2010
### JSuarez
Could it be possible that what you have in mind is a metric space (ir doesn't have to be a vector space, but the more interesting ones are), where you can calculate the distance between any two points, but none of these is a distinguished origin, but where the distance doesn't come from a norm (a norm is a special kind of distance, defined only on vector spaces, that measures distances from the origin, which allows us to define lenghts).
10. Jan 24, 2010
### HallsofIvy
But AverageJoe asked for a space that has a coordinate system but no origin. A metric space does not have a coordinate system. Although I suspect that this is the kind of thing he is thinking of.
(By the way, a metric space does not necessarily not have a norm. It may or may not. Given a norm, we can immediately define a metric but not necessarily the other way.)
11. Jan 24, 2010
### JSuarez
When I stated:
I meant a metric space with a distance that cannot be defined by a norm (for example, it's not translation invariant and/or homogeneous), I didn't meant it doesn't necessarily have a norm; many interesting metrics came from norms.
I don't completely agree (strictly speaking, the definition doesn't require it), but metric spaces that are also vector spaces have coordinate systems; we may forget the vector space structure and retain only the metric one.
But if we want to remain in the vector space category, we have two options: forget the origin and fall in affine space (already mentioned), or the Möbius homogeneous coordinate system.
12. Jan 24, 2010
### AverageJoe
Maybe it's more of an Omni-Origin coordinate system. Every element is it's own origin, and their dimensions are ratios of their sister elements.
13. Jan 24, 2010
### JSuarez
Then check the barycentric coordinate system (or Möbius coordinates):
http://mathworld.wolfram.com/BarycentricCoordinates.html" [Broken]
http://en.wikipedia.org/wiki/Homogeneous_coordinates" [Broken]
Last edited by a moderator: May 4, 2017
14. Jan 24, 2010
### HallsofIvy
Here's a couple of ideas I had. For the surface of a sphere of radius R, identify each point by spherical coordinates. That is, each point is identified with $(R, \theta, \phi)$. Since R is not 0, there is no point in that surface with coordinates (0, 0, 0).
Or- given a plane, think of it as embedded in three dimensional space and give that space a coordinate system such that its origin was not on the plane. for example, if we take our three dimensional coordinates so that the plane contains (1, 0, 0), (0, 1, 0), and (0, 0, 1), then every point in the plane is given coordinates (x, y, z) where x+ y+ z= 1. Again, there is no point in the plane with coordinates (0, 0, 0). This would be similar to "barycentric coordinates". | {"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": 0.9259305000305176, "perplexity": 527.2910175583249}, "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-2018-39/segments/1537267156423.25/warc/CC-MAIN-20180920081624-20180920101624-00527.warc.gz"} |
https://annals.math.princeton.edu/articles/13106 | # On random matrices from the compact classical groups
### Abstract
If $M$ is a matrix taken randomly with respect to normalized Haar measure on $\mathrm{U}(n)$, $\mathrm{O}(n)$ or $\mathrm{Sp}(n)$, then the real and imaginary parts of the random variables $\mathrm{Tr}(M^k)$, $k\ge 1$, converge to independent normal random variables with mean zero and variance $k/2$, as the size $n$ o the matrix goes to infinity. For the unitary group this is a direct consequence of the strong Szegő theorem for Toeplitz determinants. We will prove a conjecture of Diaconis saying that for $\mathrm{U}(n)$ the rate of convergence to the limiting normal is $\mathrm{O}(n^{-\delta n})$ for some $\delta >0$, and for $\mathrm{O}(n)$ and $\mathrm{Sp}(n)$ it is $\mathrm{O}(e^{-cn})$ it is $\mathrm{O}(e^{-cn})$ for some $c>0$.
Kurt Johansson | {"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": 0.9896212816238403, "perplexity": 91.67150611773201}, "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/1570987756350.80/warc/CC-MAIN-20191021043233-20191021070733-00191.warc.gz"} |
https://www.arxiv-vanity.com/papers/1002.0635/ | arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.
# The Diversity of Massive Star Outbursts I: Observations of SN 2009ip, UGC 2773 OT2009-1, and Their Progenitors
Ryan J. Foley1 2 , Edo Berger1 , Ori Fox3 , Emily M. Levesque4 5 , Peter J. Challis1 , Inese I. Ivans6 , James E. Rhoads7 , Alicia M. Soderberg1
1affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA.
2affiliation: Clay Fellow. Electronic address .
3affiliation: Department of Astronomy, University of Virginia, P.O. Box 400325, Charlottesville, VA 22904, USA.
4affiliation: Institute for Astronomy, University of Hawaii, 2680 Woodlawn Dr., Honolulu, HI 96822, USA.
5affiliation: Predoctoral Fellow, Smithsonian Astrophysical Observatory
6affiliation: Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA.
7affiliation: School of Earth and Space Exploration, Arizona State University, P.O. Box 871404, Tempe, AZ 85287, USA
###### Abstract
Despite both being outbursts of luminous blue variables (LBVs), SN 2009ip and UGC 2773 OT2009-1 have very different progenitors, spectra, circumstellar environments, and possibly physical mechanisms that generated the outbursts. From pre-eruption HST images, we determine that SN 2009ip and UGC 2773 OT2009-1 have initial masses of and , respectively. Optical spectroscopy shows that at peak SN 2009ip had a 10,000 K photosphere and its spectrum was dominated by narrow H Balmer emission, similar to classical LBV giant outbursts, also known as “supernova impostors.” The spectra of UGC 2773 OT2009-1, which also have narrow H emission, are dominated by a forest of absorption lines, similar to an F-type supergiant. Blueshifted absorption lines corresponding to ejecta at a velocity of 2000 – 7000 km s are present in later spectra of SN 2009ip — an unprecedented observation for LBV outbursts, indicating that the event was the result of a supersonic explosion, rather than a subsonic outburst. The velocity of the absorption lines increases between two epochs, suggesting that there were two explosions in rapid succession. A rapid fading and rebrightening event concurrent with the onset of the high-velocity absorption lines is consistent with the double-explosion model. A near-infrared excess is present in the spectra and photometry of UGC 2773 OT2009-1 that is consistent with 2100 K dust emission. We compare the properties of these two events and place them in the context of other known massive star outbursts such as Car, NGC 300 OT2008-1, and SN 2008S. This qualitative analysis suggests that massive star outbursts have many physical differences which can manifest as the different observables seen in these two interesting objects.
circumstellar matter — stars: evolution — stars: individual (UGC 2773 OT2009-1, SN 2009ip) — stars: mass loss — stars: variable: other — stars: winds, outflows — supernovae: general
## 1. Introduction
Very massive stars appear to go through a phase of instability and large mass loss; during this stage, a star is a member of the luminous blue variable (LBV) class (see Humphreys & Davidson 1994 for a review). In addition to low-amplitude variability (called S Dor variability after the prototypical LBV), where the star ejects mass from its envelope but its bolometric luminosity remains nearly constant, some LBVs have “giant eruptions.” Giant eruptions can expel of material, while having a luminosity similar to the lowest-luminosity supernovae (SNe). The classical examples of giant eruptions are P Cygni in 1600 and Car in 1843, and more recent, extragalactic examples include SN 1961V (Goodrich et al. 1989; Filippenko et al. 1995; Van Dyk et al. 2002; but see Chu et al. 2004), V12/SN 1954J (Smith et al., 2001; Van Dyk et al., 2005), SN 1997bs (Van Dyk et al., 2000), SN 2000ch (Wagner et al., 2004), and V37/SN 2002kg (Weis & Bomans, 2005; Maund et al., 2006; Van Dyk et al., 2006). Other potential examples exist, but all events listed above have pre-event imaging where the progenitor star has been identified as a probable or definite LBV.
Two examples of a new class of stellar eruptions have recently emerged. The progenitors of NGC 300 OT2008-1 and SN 2008S were both detected in pre-event Spitzer images, but were undetected to deep limits in the optical (Prieto et al., 2008; Berger et al., 2009b; Bond et al., 2009), indicating significant reddening from circumstellar dust. The progenitor stars were originally believed to have ZAMS masses of 8 – 20 , which is below that of the least massive LBVs. Using the stars in the vicinity of NGC 300 OT2008-1, Gogarten et al. (2009) found a slightly higher mass range of 12 – 25 . A reasonable range for the initial mass of the progenitors is 10 – , with NGC 300 OT2008-1, having a more luminous progenitor, being toward the upper end of that range.
Recently, two transients were discovered with one being very similar to classical LBV giant eruptions (SN 2009ip), and another sharing characteristics of both LBV giant eruptions and the outbursts of the dusty stars discussed above (UGC 2773 OT2009-1). SN 2009ip was discovered by Maza et al. (2009) in NGC 7259 ( mag111We use the distance modulus corresponding to the Hubble distance for NGC 7259 with km s Mpc and correcting for the Virgo Infall and Great Attractor flow model of Mould et al. (2000). Smith et al. (2009b) use a distance modulus of 31.55 mag, which differs by 0.50 mag from our assumed value, corresponding to the Hubble-flow distance modulus correcting only for the CMB dipole.; Mpc) on 2009 August 26 (UT dates will be used throughout this paper). Miller et al. (2009) noted that SN 2009ip had been variable for several years and identified a possible progenitor with mag, in an archival Hubble Space Telescope (HST ) image. The variability and high luminosity of the event led Miller et al. (2009) to suggest that SN 2009ip was either an LBV or cataclysmic variable outburst. An early spectrum of the event showed a blue continuum with relatively narrow ( km s) H Balmer lines. The combination of the spectrum with the relatively low absolute magnitude ( mag) led us to conclude that SN 2009ip was an LBV giant eruption (Berger, Foley, & Ivans, 2009a). The transient underwent extreme variability shortly after maximum222To be consistent with S09, we adopt and as times of maximum light for UGC 2773 OT2009-1 and SN 2009ip, respectively. However, we note that the objects may reach their true maximum later, which UGC 2773 OT2009-1 already has (as shown by data presented in S09), fading by at least 3 mag in 16 days and rebrightening by 2 mag in the next 10 days (Li et al., 2009), reminiscent of the variability immediately before maximum of the 1843 eruption of Car (Frew, 2004) and immediately after maximum in the LBV outburst SN 2000ch (Wagner et al., 2004). Smith et al. (2009b, hereafter S09) presented a historical light curve of SN 2009ip that begins 5 years before maximum light, excluding the HST image of the progenitor. The star varied by at least 1.5 mag during this time. S09 presented additional data which led them to conclude that SN 2009ip was the giant eruption of a 50 – LBV.
UGC 2773 OT2009-1 was discovered by Boles (2009) in UGC 2773 ( mag; Mpc) on 2009 August 18. It was originally reported as a possible SN. We obtained a spectrum and noted that it had a peculiar spectrum with relatively narrow ( km s) H emission, P-Cygni lines from the Ca ii NIR triplet, and [Ca ii] emission lines (Berger & Foley, 2009). We also noted that the spectrum was similar to that of NGC 300 OT2008-1 and mentioned that it was possibly a very low-luminosity SN II or an LBV outburst, “but the strong [Ca ii] emission would be unexpected in this case.” Berger & Foley (2009) also detected a potential progenitor star in archival HST images. S09 presented a historical light curve of SN 2009ip that begins 9 years (excluding the HST image of the progenitor) before maximum light. The star slowly increased from mag to an unfiltered magnitude of 17.70 mag at maximum light, corresponding to a linear increase of 0.4 mag year before outburst. S09 concluded from the progenitor identification, their historic light curve, the peak luminosity, and optical light curves that UGC 2773 OT2009-1 was the outburst of a LBV.
This is the first in a series of papers where we investigate the diversity of massive star outbursts. In this paper we demonstrate the heterogeneity of the class with observations of SN 2009ip and UGC 2773 OT2009-1. In future papers, we will detail the properties of the class and the links between observations and the physical mechanisms which cause the outbursts. In Section 2, we present ultraviolet (UV), optical, and near-infrared (NIR) photometry and optical and NIR spectroscopy of UGC 2773 OT2009-1 and SN 2009ip. In this section, we also refine previous identifications of the progenitors. In Section 3, we examine the progenitor masses, the spectroscopic characteristics of the outbursts, and the spectral-energy distributions (SEDs) of the events. In Section 4, we discuss how these outbursts connect to previous massive star outbursts and the mass loss history and ultimate fates of massive stars. We summarize our conclusions in Section 5.
## 2. Observations and Data Reduction
### 2.1. Identification and Hst Photometry of the Progenitors
UGC 2773 was observed with HST /WFPC2 on 1999 August 14 (Program 8192; PI Seitzer). The observations included two exposures of 600 s each with the F606W and F814W (roughly and ) filters. NGC 7259 was observed with HST /WFPC2 on 1999 June 29 (Program 6359; PI Stiavelli). Exposures of 200 and 400 s were obtained with the F606W filter.
To determine whether the progenitors of SN 2009ip and UGC 2773 OT2009-1 are detected in the archival HST observations, we performed differential astrometry using optical observations of the transients. Observations of UGC 2773 OT2009-1 were obtained with the Gemini Multi-Object Spectrograph (GMOS) on the Gemini-North 8-m telescope, and the astrometry was performed using 55 objects in common with the HST /WFPC2 images resulting in an astrometric rms of mas in each coordinate. Observations of SN 2009ip were obtained with the Inamori Magellan Areal Camera and Spectrograph (IMACS) on the Magellan/Baade 6.5-m telescope, and the astrometry was performed using 10 objects in common with the HST /WFPC2 image resulting in an astrometric rms of mas in each coordinate.
The positions of the two transients on the archival HST images are shown in Figure 1. In both cases, we find a clear coincidence with objects in the archival HST images. For SN 2009ip we find an offset of mas relative to the object in the WFPC2/F606W image, while for UGC 2773 OT2009-1 we find an offset of mas relative to the object in the WFPC2/F606W and F814W images.
The measurements of the photometry for UGC 2773 OT2009-1 and nearby stars were done using HSTphot 1.1 (Dolphin, 2000). HSTphot was run using a weighted PSF-fit, which is recommended for crowded fields, and a local sky determination, which is recommended for rapidly varying backgrounds. HSTphot performs the conversion from HST /WFPC2 flight magnitudes to the Bessel magnitude system. Our astrometry and photometry for the nominal progenitor of UGC 2773 OT2009-1 and nearby stars are listed in Table 1.
We performed photometry of the point source coincident with SN 2009ip using a aperture and a zero-point of 22.47 mag appropriate for the F606W filter. We further applied a correction of mag to convert to the Vega system, and applied a correction for the Galactic extinction of 0.05 mag. The resulting magnitude of the source is mag. For reasonable colors (see Section 3.1.1), this corresponds to mag.
### 2.2. Ultraviolet, Optical, and Near-Infrared Photometry
We obtained optical photometry of UGC 2773 OT2009-1 with the Gemini Multi-Object Spectrograph (GMOS) on the Gemini-North 8-m telescope in the filters. We performed the photometry using IRAF/phot with the standard GMOS zero-points. Our results are presented in Table 2.
We obtained near-infrared (NIR) photometry of UGC 2773 OT2009-1 with FanCam, a HAWAII-I HgCdTe imaging system on the University of Virginia’s 31-inch telescope at Fan Mountain, just outside of Charlottesville, VA (Kanneganti et al., 2009). Each epoch consists of fifteen minutes of integration in bands, which have detection limits at the level of 0.066, 0.098, and 0.156 mJy (or 18.5, 17.5, and 16.5 mag), respectively. Individual exposures are sky-background limited and have an integration time of either 30 or 60 s. Flat-field frames are composed of dusk and dawn sky observations. We employed standard NIR data reduction techniques in IRAF444IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation.. Because of the relatively small galaxy size, it was possible to fit the entire galaxy in a single array quadrant. Empty quadrants were efficiently utilized as sky exposures. Data were taken with the galaxy placed in each quadrant and each quadrant was reduced separately. Ultimately, all reduced quadrants were coadded. We performed photometry with IRAF’s PSF package. For magnitude calibration, the transient is compared to 2MASS reference stars located in the field of view. Table 2 lists our photometry, which is similar to the single epoch data from S09.
We obtained UV and optical observations of SN 2009ip with the Swift UV/optical telescope on 2009 September 10. The data were processed using standard routines within the HEASOFT package. Photometry of the transient in all filters, with the exception of UVW2, was performed using a 2 aperture to avoid contamination from nearby objects. Aperture corrections to the standard 5 aperture were determined using isolated stars; photometry of the source in the UVW2 filter was performed using a 5 aperture.
### 2.3. X-ray Observations
We observed SN 2009ip and UGC 2773 OT2009-1 with the Swift X-ray Telescope on 2009 September 10 for a total exposure time of 9.0 and 4.2 ks, respectively. No X-ray counterpart is detected at the position of either source to a limit of and erg s cm, respectively ( limit). In both cases we assume a power law model with an electron index of , and account for the Galactic neutral hydrogen column. The corresponding limits on the luminosity are and erg s. These limits are comparable to the X-ray emission from SNe on a similar timescale (e.g., Soderberg et al., 2008).
We observed the both LBV candidates with the Very Large Array555The Very Large Array is operated by the National Radio Astronomy Observatory, a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. (VLA) following their optical discovery to search for radio counterparts, under Rapid Response programs AS1001 and AS1002 (PI Soderberg). Our radio observations were carried out at two frequencies, 8.46 and 22.5 GHz, on dates spanning 2009 September 7.36 - 16.51 in the C-array antenna configuration. All observations were taken in standard continuum observing mode with a bandwidth of MHz. Phase referencing was performed with calibrators J0325+469 and J2213-254, and we used 3C38 (J0137+331) for flux calibration. Data were reduced using standard packages within the Astronomical Image Processing System (AIPS).
We detect no radio sources in positional coincidence with either object and derive upper limits summarized in Table 3. At 8.5 GHz, our upper limits666Upper limits are calculated as the measured flux density at the optical position summed with rms the off-source map noise. correspond to erg s Hz and erg s Hz for SN 2009ip and UGC 2773 OT2009-1, respectively. These limits are less luminous than an extrapolation of the observed SN 1961V radio emission at years, to a similarly early epoch as (Stockdale et al., 2001). We note, however, that the SN 1961V radio emission may have reached maximum intensity significantly later than our observations of UGC 2773 OT2009-1 and SN 2009ip, similar to the radio evolution of SNe IIn which typically reach maximum light several years after the explosion (van Dyk et al., 1996).
A comparison of these radio upper limits for the outbursts to the observed properties of other core-collapse SNe places them among the least luminous events, 2-4 orders of magnitude less luminous than the most powerful SNe IIn, and 4-200 times higher than the early radio signal seen for SN 1987A (Ball et al., 1995). Through this simple comparison we emphasize that radio data alone cannot distinguish between massive star outbursts and catastrophic explosions. However, with the 10-fold increase in continuum sensitivity provided by the EVLA we will begin to map out the radio properties for massive star outbursts and enable direct comparisons with those of core-collapse SNe (e.g., NRAO Key Project AS1020, ”Exotic Explosions,Eruptions,and Disruptions: A New Transient Phase-Space”, PI Soderberg).
### 2.5. Optical Spectroscopy
We obtained low- and medium-resolution spectra of SN 2009ip and UGC 2773 OT2009-1 with the MagE spectrograph (Marshall et al., 2008) on the Magellan Clay 6.5 m telescope, the Blue Channel spectrograph (Schmidt, Weymann, & Foltz, 1989) on the MMT 6.5 m telescope, and GMOS (Hook et al., 2004) on the Gemini-North 8 m telescope. A journal of our optical spectroscopic observations can be found in Table 4.
Standard CCD processing and spectrum extraction were accomplished with IRAF. The data were extracted using the optimal algorithm of Horne (1986). Low-order polynomial fits to calibration-lamp spectra were used to establish the wavelength scale, and small adjustments derived from night-sky lines in the object frames were applied. For the MagE spectra, the sky was subtracted from the images using the method described by Kelson (2003). The GMOS data were reduced using the Gemini IRAF package (for details, see Foley et al., 2006). We employed our own IDL routines to flux calibrate the data and remove telluric lines using the well-exposed continua of the spectrophotometric standards (Wade & Horne, 1988; Foley et al., 2003, 2009).
Representative spectra of SN 2009ip and UGC 2773 OT2009-1 are presented in Figure 2. Both objects have similar blue continua, but the line features are very different. SN 2009ip has few line features besides strong H Balmer lines, Na D, and He i. Although UGC 2773 OT2009-1 has a strong H line, it is much narrower and weaker than that of SN 2009ip. UGC 2773 OT2009-1 also displays many additional narrow line features, including lines from intermediate mass and Fe-group elements. Blueward of 5500 Å, UGC 2773 OT2009-1 is dominated by a forest of Fe ii lines. Finally, UGC 2773 OT2009-1 has very strong Ca ii NIR triplet lines and [Ca ii] , 7324 lines. These features, and particularly [Ca ii] are rarely seen in classical LBV outbursts, but were distinguishing features of SN 1999bw (Garnavich et al., 1999), SN 2008S (e.g., Smith et al., 2008b), and NGC 300 OT2008-1 (e.g., Berger et al., 2009b).
The spectra from 2009 September 21 (corresponding to days 34 and 24 for UGC 2773 OT2009-1 and SN 2009ip, respectively) were obtained on the same night as the LRIS spectra shown by S09.
### 2.6. Near-Infrared Spectroscopy
On 2009 September 9 (22 days after maximum), we obtained a 2400 s NIR spectrum of UGC 2773 OT2009-1 with TripleSpec, a medium resolution NIR spectrograph located at Apache Point Observatory. This spectrograph is one of three NIR, cross-dispersed spectrographs covering wavelengths from 1 – 2.4 µm simultaneously at a resolution of 3500 (Wilson et al., 2004; Herter et al., 2008). We collected eight, 300-s sky-background limited exposures, for a total integration time of 2400 s. We extracted the spectrum with a modified version of the IDL-based SpexTool (Cushing, Vacca, & Rayner, 2004). This tool removes any contribution from the underlying galactic arm by fitting the background with a 2nd order polynomial.
## 3. Results
### 3.1. Progenitor Masses
#### 3.1.1 SN 2009ip
We use the absolute magnitude, mag, of the progenitor of SN 2009ip, along with an estimated range of colors of to mag (representative of LBV colors spanning from O to F spectral types), to plot it as a line on a color-magnitude diagram (Figure 3). For this progenitor we find a Milky Way extinction of mag ( mag; Schlegel, Finkbeiner, & Davis 1998). We adopt a distance modulus of mag for NGC 7259 (see discussion in Section 1), and assume no additional host galaxy or circumstellar extinction.
In Figure 3, we compare the color of the SN 2009ip progenitor to the non-rotating, standard mass-loss evolutionary tracks of the Geneva group (Schaller et al., 1992). From this plot we can place a lower initial mass limit of on the progenitor of SN 2009ip in the absence of a color estimate for this progenitor, the higher-mass evolutionary tracks all coincide with its estimated location on the color-magnitude diagram, precluding us from placing an upper limit on this initial mass estimate. Figure 3 assumes a solar metallicity for these tracks; however, we find that our progenitor mass prediction is consistent across the full range of metallicities accommodated by the Geneva evolutionary tracks ( to ). It should be noted that an increased amount of extinction, from the host galaxy or circumstellar environment, could also effectively increase the estimated initial mass of this progenitor.
S09 estimated the initial mass for the progenitor of SN 2009ip to be 50 – . Although the HST photometry from S09 is the same as that presented here, their assumed distance modulus is 0.50 mag smaller than our assumed value. They also make no color correction to transform the F606W measurements into . Despite these differences, the two mass ranges are similar.
#### 3.1.2 Ugc 2773 Ot2009-1
Using its and color, we are able to determine an estimate of the initial mass for the progenitor of UGC 2773 OT2009-1 (Figure 3). There is significant Milky Way extinction of mag ( mag; Schlegel, Finkbeiner, & Davis 1998), which we convert to mag (Schultz & Wiemer, 1975). We use a distance modulus of mag and initially assume no host galaxy or circumstellar extinction.
From Figure 3, we find that the progenitor of UGC 2773 OT2009-1 is consistent with an initial mass of . Our progenitor mass prediction remains the same across the full range of metallicities covered by the Geneva evolutionary tracks, and is consistent with the value found by S09.
We have also performed this procedure on several stars in the vicinity of the progenitor of UGC 2773 OT2009-1. Assuming that all of these stars are part of a cluster and were formed at the same time, they should place additional limits on the current maximum-mass stars of the cluster. These stars are all consistent with an initial mass of . There is a single star that is particularly blue (and therefore potentially very massive), but it is still consistent with an initial mass of . The likely association of the progenitor of UGC 2773 OT2009-1 with this cluster and its upper mass limit of 25 further supports the initial mass estimate for the progenitor of UGC 2773 OT2009-1.
Considering the blue colors of the stars in the cluster, it is unlikely that they are significantly reddened by host galaxy dust. As shown in Figure 3, a relatively small amount of extinction could significantly increase our initial mass estimate for UGC 2773 OT2009-1. In Section 3.4 we show that there was likely a significant amount of circumstellar dust existing before the outburst, indicating that the progenitor had an initial mass much larger than the reddening-free estimate of .
The combination of the reddening-free initial mass estimate for the progenitor of UGC 2773 OT2009-1, the initial mass estimates of stars likely within the same cluster as the progenitor, and the probably circumstellar dust extinction give us a conservative lower limit on the initial mass of the progenitor of UGC 2773 OT2009-1 of .
### 3.2. Spectroscopic Comparisons
#### 3.2.1 SN 2009ip
We present the 24 and 86 day spectra of SN 2009ip in Figure 4. In the upper panel of Figure 4, the 24 day spectrum is compared to the 2 day spectrum of the LBV outburst SN 1997bs (Van Dyk et al., 2000). Both objects have blue continua, strong and narrow H Balmer lines, and He i and Fe ii emission lines. Unlike SN 1997bs, SN 2009ip has a particularly strong He i line (with some possible contribution from Na D), and all H Balmer lines and He i show strong absorption features with minima blueshifted by 3000 km s (see Section 3.3.1 for a detailed discussion of this high-velocity absorption).
Inspecting the 25 day spectrum from S09, we see some indication of the 3000 km s absorption component, particularly for H and He i ; however, the absorption is much stronger in the spectra presented here (which were obtained at very similar times). We have reduced our spectra with many different extraction regions and backgrounds, with the high-velocity absorption features are present in all reductions. The same feature is present in all spectra taken with the MMT on days 23 and 24, which were taken with different gratings and wavelength regions. It is also present on day 86, but with a different velocity. The absorption is present for all Balmer lines and He i . Despite the apparent differences with the concurrent Keck spectrum (S09), we are confident that the high-velocity absorption features are real and not an artifact of the spectral reductions.
The bottom panel of Figure 4 displays the spectra of SN 2009ip and SN IIn 1998S (after subtracting a 10,000 K blackbody spectrum from both) from 86 and 25 days, respectively. An inverse-variance weighted Gaussian filter (with a width of 1000 km s) has been applied to the spectrum of SN 2009ip (Blondin et al., 2006). This filtering will smear out features with intrinsic widths less than 1000 km s, but will appropriately smooth features on larger scales. The high-velocity absorption in the 86 day spectrum of SN 2009ip is at a higher velocity than at 24 days. At this epoch, the velocity of the fast-moving SN 2009ip ejecta are very similar to that of SN 1998S. Although the H Balmer emission lines are much stronger in SN 2009ip, most other features are similar in the two spectra. In particular, SN 2009ip shows the H Balmer, He i, Sc ii, and Fe ii features seen in SN 1998S. SN 2009ip is missing the strong absorption at 6250 Å that is attributed to Si ii in SN 1998S (Leonard et al., 2000). This feature may be the result of a significant amount of nuclear burning, and thus not present in the ejecta of SN 2009ip.
#### 3.2.2 Ugc 2773 Ot2009-1
As discussed in Section 2.5, UGC 2773 OT2009-1 has a spectrum with narrow H emission, [Ca ii] emission, and P-Cygni absorption from many intermediate-mass and Fe-group elements. Perhaps the most distinguishing feature compared to other massive star outbursts is the [Ca ii] emission. In Figure 5, we compare the 15 day spectrum of UGC 2773 OT2009-1 to spectra of the low-luminosity transients NGC 300 OT2008-1 (Berger et al., 2009b) and SN 2008S (Smith et al., 2008b), as well as SN IIn 1994W (Chugai et al., 2004); all of these objects have [Ca ii] emission in their spectra.
All spectra in Figure 5 are relatively similar. The continuum of each spectrum is well-described by a blackbody spectrum, with all four objects having a similar temperature. Each object has a prominent H emission line, with UGC 2773 OT2009-1 having a narrower line than the other objects. Additionally, SN 1994W has a strong H absorption line blueward of its emission peak.
NGC 300 OT2008-1 and SN 2008S are very similar objects with massive (10 – 25 ), dusty progenitors (Prieto et al., 2008; Berger et al., 2009b; Bond et al., 2009). Their spectra share many characteristics with the yellow hypergiant IRC+10240 (Smith et al., 2008b). Although UGC 2773 OT2009-1 shares some spectroscopic properties with these two transients and IRC+10240 (see S09 for additional discussion), the latter objects lack the forest of absorption lines in UGC 2773 OT2009-1. These lines are reminiscent of an F-type supergiant. The P-Cygni profiles of these lines and the hydrogen Balmer emission are very similar to S Dor during a cool phase (e.g., Massey, 2000).
SN 1994W was very luminous at peak ( mag), but generated at most 0.03 of Ni (Sollerman, Cumming, & Lundqvist, 1998). Dessart et al. (2009) presented an alternative method of producing the photometric and spectroscopic properties of this object: the collision of two massive hydrogen shells ejected from the star with no core collapse. Spectra of SNe IIn are rather heterogeneous (see Figure 5 of Smith et al. 2009a for a comparison of various objects), and SN 1994W is relatively distinct for its narrow absorption features. Given the spectral similarity between UGC 2773 OT2009-1 and SN 1994W, the strict upper limit of Ni mass in SN 1994W, and the alternative model of Dessart et al. (2009), one must further question if SN 1994W destroyed its progenitor star.
#### 3.2.3 Contrasting SN 2009ip and UGC 2773 OT2009-1
At days, the temperature of UGC 2773 OT2009-1 is 7000 K (see Section 3.4), which is similar to the temperature during the “eruptive” state of LBVs (e.g., Humphreys & Davidson, 1994). This contrasts with the higher temperature of 10,000 K derived for SN 2009ip (see Section 3.4), which lacks the narrow Fe-group absorption features. Many other LBV giant eruptions have temperatures similar to that of SN 2009ip (Humphreys & Davidson, 1994). SN 2009ip was 2 mag brighter at peak than UGC 2773 OT2009-1, and SN 2009ip had a much larger increase in luminosity during the year before maximum than UGC 2773 OT2009-1, increasing by mag and 1 mag over one year, respectively (S09). The fast-moving ejecta of SN 2009ip also contrasts with the relatively slow outflow of UGC 2773 OT2009-1.
The photometric and spectroscopic differences of these objects suggests different physical mechanisms. Clearly a supersonic explosion is necessary to produce the high-velocity absorption features of SN 2009ip, while UGC 2773 OT2009-1 shows no indication of an explosion. The differences in temperature and luminosity increase are also indicative of more energy injection (per unit mass) for SN 2009ip. A plausible explanation is that SN 2009ip is a LBV giant eruption triggered by an explosion, while UGC 2773 OT2009-1 is a particularly luminous S Dor eruption.
### 3.3. Line Profiles
In this section, we examine the line profiles of H and Ca lines. These features provide an indication of the kinematics of the emitting material. The narrow lines are a tracer of the pre-shock circumstellar material, while the high-velocity absorption features in the spectra of SN 2009ip probe the outburst ejecta.
#### 3.3.1 Hα
In Figure 6, we present the H line profiles of UGC 2773 OT2009-1 and SN 2009ip. Three separate epochs are shown for each object. Both objects have asymmetric line profiles. There are absorption components at about km s for UGC 2773 OT2009-1 and between and km s for SN 2009ip. The line profile of SN 2009ip has a different shape and is much broader than that of UGC 2773 OT2009-1. We have attempted to fit these line profiles, but because of the asymmetry of the profiles, we first fit only the redshifted portion of each line profile and then add an absorption component to reproduce the blueshifted profile.
For the 15 day spectrum of UGC 2773 OT2009-1, we fit a Gaussian with km s to the red side of the feature. This value is twice that of the value found by S09 for a spectrum from day 22, but examination of their figures suggest that they reported half-width at half maximum (HWHM) or the standard deviation of the Gaussian fit (which is smaller by a factor of 2.35) rather than FWHM. The 34 day spectrum of UGC 2773 OT2009-1 is contaminated by host-galaxy emission lines, making a fit to the inner regions of the line profile problematic. Ignoring this region, we were able to fit the redshifted portion of the line profile with a single Gaussian with km s. The 96 day spectrum has lower resolution, but is successfully fit by a Gaussian profile with km s.
To account for the asymmetric profile, we add an absorption component to the Gaussian line profiles. Fitting the full profile with two Gaussian functions, the emission component fit to the red side of the line and the absorption component added to fit the blue side of the line, we find absorption minima at , , and km s for the 15, 34, and 96 day spectra, respectively. This is different from the value of the actual minimum ( km s) since the relatively strong emission masks the true minimum.
The line profiles of the first two spectra (days 4 and 24) of SN 2009ip are well fit by Lorentzian profiles with km s and the third is best fit by a Lorentzian profile with km s, which are larger than that found by S09, 550 km s. A Lorentzian profile of 550 km s is not a particularly bad fit to our data, but we find that the larger velocities better represent the data. One can also see in Figure 8 of S09, that the 550 km s Lorentzian slightly underpredicts the true FWHM of the line, so the data appear to be consistent.
In the 24 day spectrum of SN 2009ip, we see an absorption feature with a minimum at a velocity of about km s. (This high-velocity absorption is seen for all Balmer lines with varying instrument configurations and on two epochs; see Section 3.2.1.) This feature is well fit by including a Gaussian absorption component with a minimum at km s. Adding a component with this velocity also improves the fit to the 4 day H profile slightly, but not in a significant way. The 86 day spectrum shows an even stronger high-velocity absorption component with the minimum of the absorption at a larger velocity of km s. The blue wing of the absorption component, representing the fastest moving material, corresponds to a velocity of about and km s for the 24 and 86 day spectra, respectively.
These velocities are significantly larger than the outflow velocity of 550 km s assumed by S09. They are much larger than the wind speed of LBVs and are larger than the measured velocity for any LBV eruption with the exception of the 1843 eruption of Car, which had some material expelled at 3000 – 6000 km s (Smith, 2008). The velocities measured for SN 2009ip are similar to that of the ejecta of typical core-collapse SNe (such as SN 1998S; see Figure 4 and Section 3.2.1) and are somewhat similar to that of Wolf-Rayet winds (e.g., Abbott & Conti, 1987). We discuss the implications of these features in Section 4.2.
#### 3.3.2 Permitted and Forbidden Ca ii
Only our first spectrum of SN 2009ip covers the Ca ii NIR triplet, and no spectrum shows obvious [Ca ii] , 7325 lines, similar to the spectra presented by S09. Furthermore, the Ca H&K lines are confused by the strong Balmer sequence in SN 2009ip. Because of these factors, it is difficult to evaluate the characteristics of the Ca ii behavior in this object (other than the absent [Ca ii] lines).
UGC 2773 OT2009-1, on the other hand, has strong Ca ii features. This can be seen in Figure 2. We examine the Ca H&K, [Ca ii] , 7325, and Ca ii NIR triplet line profiles in Figure 7. The Ca H&K lines show a broad absorption extending from to km s and a minimum at about km s that does not appear to change significantly between the two epochs. Each component of the Ca ii NIR triplet shows a strong P-Cygni profile with a minimum at approximately km s, slightly larger than the minima of Ca H&K.
The [Ca ii] , 7325 lines are visible in all epochs of our spectroscopy. We confirm the additional line between this doublet seen by S09 and identify this as Fe ii . Both [Ca ii] lines have asymmetric profiles in all spectra; the peak is at zero velocity, but the emission extends further to the red than to the blue. The lines from all epochs have FWHMs of 400 km s, which is about half the width of H (see Section 3.3.1), similar to that found for NGC 300 OT2008-1 (Berger et al., 2009b).
### 3.4. Spectral Energy Distribution and Dust Emission
Using our available photometry and spectroscopy, we can examine the spectral energy distribution (SED) of both objects. We have only optical spectra of SN 2009ip, which limits our ability to examine multiple blackbody components for this object. A 10,000 K blackbody fits our optical spectra well, which is consistent with that found by S09.
Our single epoch of Swift photometry occurred during the dramatic fading of the light curve immediately following maximum brightness (S09). In Figure 8, the Swift photometry is combined with the unfiltered photometry (approximately band) of S09 (with an uncertainty of 0.5 mag to account for the 16 hour difference in the epoch of the observations) during the minimum. We overplot the 23 day spectrum for comparison. The optical photometry is consistent with the optical spectrum and a 10,000 K blackbody. The UVW2 flux is also consistent with this blackbody, however, the UVM2 and UVW1 measurements fall well below this curve. Although this may be the result of line blanketing, these data are also consistent with a blackbody curve with a temperature as low as 8000 K. If we ignore the UVW2 measurement, the data can be fit by a 7000 K blackbody. Although our data suggest a possible change in the SED during the fading event, the lack of necessary comparison UV data from a different epoch prevent a clear indication of a change.
Using the 15 day optical spectrum and 22 day NIR spectrum, we are able to examine the SED of UGC 2773 OT2009-1 over nearly a decade in wavelength. Between these dates, the light curve of UGC 2773 OT2009-1 was essentially constant, having the same magnitude (within 1) (S09). Using the long wavelengths of the NIR spectrum, our data are sensitive to any low-temperature thermal components.
We fit a single blackbody to these data, ignoring regions with strong line features and simultaneously fitting the scaling between the optical and NIR spectra. Doing this results in a best-fit temperature of 6800 K. This single blackbody consistently under-predicts the flux at NIR wavelengths. As a result, we have also attempted to fix the spectrum with a double blackbody model. This model, which produces a much better fit, results with temperatures K and K. The full spectrum and associated fits are shown in Figure 9.
S09 noted that UGC 2773 OT2009-1 had a (photometric) NIR excess, but could not distinguish between circumstellar extinction and dust emission. To test the former case, we attempted to fit the spectrum with a single blackbody, but with an additional extinction term. With fixed to 3.1, this model did not fit the data well. The model was able to sufficiently reproduce the data if we allowed , which is unphysical. We therefore conclude that the NIR excess is likely due to dust emission.
Scaling our spectrum to our broad-band photometry, we can calibrate the blackbody flux, which in turn constrains the ratio , where is the radius of the blackbody radiation and is the distance to the object. Using Mpc, we find that the hot and cool blackbodies have radii of cm and cm ( AU and AU), respectively. The size of the cool emitting region is of the same order of magnitude of the size of the Homunculus nebula surrounding Car.
Following the prescription outlined by Smith, Foley, & Filippenko (2008a) (and references therein), we can measure the mass of the emitting dust. Specifically,
Md=400πρR2d3T2d, (1)
where is the dust mass, is the radius of the dust, is the dust temperature, and is the dust density. For the values obtained from the spectra, K and cm, and assuming a dust grain density of g cm, we find a dust mass of . Since there could be a significant amount of dust emission at lower temperatures, this is a lower limit on the total dust mass; however, it is worth noting that this measurement is orders of magnitude less than the dust created in some SNe (e.g., Kotak et al., 2009, and references therein). We note depending on the dust composition, the dust temperature may differ from the blackbody temperature by hundreds of degrees.
The dust is very close to the star and its temperature is near the limit of grain survival. Given these conditions, it is very likely that pre-existing circumstellar dust was heated and is emitting as it is being vaporized, rather than newly formed dust emitting as it cools.
## 4. Discussion
### 4.1. Different Massive Star Outbursts
UGC 2773 OT2009-1 and SN 2009ip provide excellent examples of the diversity of massive star outbursts. UGC 2773 OT2009-1 increased its optical brightness by 1 mag during outburst and has a cool spectrum with many narrow absorption lines and [Ca ii] emission. It occurred near a star cluster containing stars with initial masses of and shows evidence for a very cool ( K) thermal component that is radiated by circumstellar dust. SN 2009ip had a more massive and relatively isolated progenitor. At peak, it had risen at least 4 mag over the previous year, and its spectrum was hot and dominated by H Balmer emission lines. After having a significant fading and rebrightening over three weeks, it developed high-velocity absorption lines. Its SED is consistent with no dust emission.
The high temperature and large increase in optical luminosity for SN 2009ip indicates that it was a true giant eruption akin to the 1843 eruption of Car. UGC 2773 OT2009-1, on the other hand, has spectral characteristics similar to that of S Dor at maximum. The relatively small increase in optical luminosity may indicate that UGC 2773 OT2009-1 was the result of normal S Dor variability, but that it was a particularly luminous maximum. While the largest normal variation of S Dor stars vary by 3 mag in the optical (van Genderen, 2001), UGC 2773 OT2009-1 has varied by at least 5 mag (including the current eruption) over the last ten years (Section 2; see also S09).
The outbursts of NGC 300 OT2008-1 and SN 2008S both had relatively low temperature SEDs (Berger et al., 2009b), but neither had the forest of absorption lines found in UGC 2773 OT2009-1. All three objects had [Ca ii] emission, but as suggested by S09, this may be linked to the circumstellar environment, and particularly dust destruction, rather than the event. Our observations have shown that there is dust in the circumstellar environment of the progenitor, and that it was likely pre-existing dust that is in the process of being vaporized. Additionally, SN 1999bw had [Ca ii] emission (Garnavich et al., 1999) and had an IR excess consistent with dust emission at late times (Sugerman et al., 2004). All four massive star outbursts with observed [Ca ii] emission (SN 1999bw, SN 2008S, NGC 300 OT2008-1, and UGC 2773 OT2009-1) have evidence of circumstellar dust. We do note that SN 2000ch had a 7000 K spectrum and an infrared excess consistent with dust emission, but no strong [Ca ii] emission was detected in the relatively low signal-to-noise spectra presented by Wagner et al. (2004). It is therefore possible to have a cool object and circumstellar dust yet not have [Ca ii] emission.
Although UGC 2773 OT2009-1, NGC 300 OT2008-1, and SN 2008S have circumstellar dust and similar temperatures, other than the narrow H Balmer and [Ca ii] (which is linked to the presence of circumstellar dust) emission, the spectra and progenitors are not particularly similar. Particularly, NGC 300 OT2008-1 and SN 2008S had relatively featureless spectra and progenitors with initial masses of 10 – , while UGC 2773 OT2009-1 had spectrum dominated by narrow lines and a more massive progenitor (). Additional data are necessary to determine if the outburst mechanisms in these objects are similar.
Using SN 2009ip and UGC 2773 OT2009-1 as examples, there appears to be two distinct elements that determine the observational properties of massive star outbursts. The first is the temperature of the outburst, which may be related to the increase in luminosity, the instability that causes the eruption, the width of the emission lines, and possibly the energetics of the outburst and if there is an explosion (see Section 4.2). This directly determines the shape of the optical SED, the ionization, if there is a forest of absorption lines, and possibly the shape of the line profiles, if there is high-velocity absorption. The other characteristic is the amount of circumstellar dust, which may cause strong Ca emission (and particularly [Ca ii] emission) and will determine the shape of the SED at longer wavelengths. UGC 2773 OT2009-1 and SN 2009ip would occupy very different regions of the parameter space created by these two dimensions. NGC 300 OT2008-1 and SN 2008S would be close to UGC 2773 OT2009-1, while LBV giant eruptions such as SN 1997bs would be close to SN 2009ip.
It remains to be seen if there are hot massive star outbursts with a large amount of circumstellar dust or if there are cool massive star outbursts with little circumstellar dust. Car has of dust surrounding it (Smith et al., 2003); if it were to have another giant eruption today, would it be cool? SN 1999bw had [Ca ii] emission and displayed dust emission at late times; was it hot? An IR survey of recent massive star outbursts with good spectroscopic coverage may provide these answers. In the future, optical and NIR observations may be sufficient to determine these characteristics for other massive star outbursts.
### 4.2. SN 2009ip: A Supersonic Explosion
The spectra of SN 2009ip have absorption attributed to high-velocity (up to 7000 km s) material (see Section 3.3.1). Contrary to what is expected from a single outburst or explosion, the velocity of the absorption feature increases with time. In a typical SN, the ejecta naturally follow a Hubble law with the highest velocity material being the most distant from the explosion site. Spectral lines have a blueshifted absorption due to the scattering processes in the photosphere of the SN. Low velocity material is hidden behind the photosphere, only to be revealed at later times. As the photosphere recedes, the highest-velocity material becomes optically thin, resulting in the blueshifted velocity of a spectral line to decrease with time. Since the absorbing material must be at just slightly larger radii than the photosphere, the high-velocity material must have been ejected during the eruption. (If the absorbing material were from a previous eruption, the ejecta from the more recent eruption would have had to be moving even faster.)
It is possible that the high-velocity absorption is a component of P-Cygni features from the ejected material. The Lorentzian profile slightly underestimates the emission flux in the 86 day spectrum (see Figure 6), which may be the result of P-Cygni emission contributing to the line. Since the high-velocity absorption is coming from the ejecta, the outburst of SN 2009ip must have been extremely energetic, expelling a large amount of material at very high velocities. However, for the velocity to increase with time, either the ejecta must not follow a Hubble expansion or the radius of the photosphere (in velocity space) must somehow increase with time.
In a single explosion, the ejecta naturally follow a Hubble law; however, multiple explosions can change the velocity profile of the ejecta. If two explosions occurred in short succession, one can produce the inverted velocity gradient seen in SN 2009ip. In this toy model, the photosphere would recede into the ejecta of the first explosion, but at some point the fastest-moving ejecta of the second explosion would overtake the photosphere, increasing the velocity. If there are no other explosions, the velocity of the absorption would decrease from there.
The photometric behavior of SN 2009ip is consistent with this picture. The first explosion would produce the fast rise to maximum. As noted by S09, the timescale of the fading is much shorter than the timescales for many physical processes such as dust extinction.777The calculation by (S09) for the time until dust formation for SN 2009ip assumes a velocity of 500 km s. Although the ejecta are moving much faster than this assumed value, they would need to have a velocity of km s to reach the sublimation radius at the time of fading. This behavior is very similar to that of SN 2000ch, which brightened by 2.1 mag in 9 days to maximum, then immediately faded by 3.4 mag in 7 days, immediately followed by a 2.2 mag rise in 4 days, after which the magnitude stayed relatively constant (Wagner et al., 2004). Spectra of SN 2000ch taken during the fading and on its plateau show no strong evidence for high-velocity ejecta, but the spectra may not be of high enough quality to see these features.
S09 hypothesized that rapid fading may have been caused by an optically thick shell being ejected after the first outburst. If this process did occur in SN 2009ip, then there are several implications: (1) the velocity of the absorption should eventually decrease, (2) the interaction of the ejecta from the two explosions could be a significant source of X-ray and radio emission, and (3) the X-rays might excite certain elements producing high-excitation lines such as He ii in optical spectra. Our X-ray limit of ergs s taken during the minimum is not particularly constraining. We do not detect any He ii emission in the 4 or 24 day spectra; however, there is a low significance detection of a line consistent with He ii emission in the 86 day spectrum. Additional spectroscopy is necessary to determine the late-time velocity gradient.
## 5. Conclusions
We have presented extensive UV, optical, and NIR data for two transients, SN 2009ip and UGC 2773 OT2009-1. Although these events appear to be similar phenomena (luminous outbursts of massive stars), the details of the events show that there are many differences. These differences provide examples of the diversity of such events.
A previous study of these events, S09, provided an initial analysis of the object. Although the two studies agree on many points, our interpretation of the entire data set is somewhat different than that of S09. In particular, we agree that based on pre-outburst HST imaging, historical light curves, and outburst spectroscopy, the progenitors of SN 2009ip and UGC 2773 OT2009-1 are LBVs with masses of and , respectively. We also agree that the spectra of the two events are significantly different, but consistent with known LBVs or LBV outbursts. While UGC 2773 OT2009-1 had a cooler spectrum with a forest of absorption lines reminiscent of a F-type supergiant (similar to S Dor in its high state), SN 2009ip had a hot spectrum and exhibited mainly H Balmer emission (similar to other LBV giant eruptions). The spectral characteristics (particularly [Ca ii] emission) and circumstellar dust link UGC 2773 OT2009-1 to the lower-mass, dust-obscured progenitors of NGC 300 OT2008-1 and SN 2008S. We agree that the progenitors of these objects are all massive stars and may have many characteristics similar to those of the LBV class, which could extend the mass range for LBV-like activity to relatively low-mass stars.
However, there are distinct differences between the analyses of S09 and of that presented here. Specifically, the initial mass ranges for the progenitors are slightly different in the two studies, with S09 estimating 50 – (instead of ) and (instead of ) for SN 2009ip and UGC 2773 OT2009-1, respectively. The differences lie in the conversion from HST filters to Bessell filters and the adapted color range for the progenitor of SN 2009ip, and the additional information provided by stars in the vicinity of the progenitor of UGC 2773 OT2009-1.
Our interpretation of the exact nature of UGC 2773 OT2009-1 differs from that of S09. While S09 contends that this object is a true giant eruption of an LBV, we question this assertion and propose that it may be the result of extreme S Dor variability.
While S09 found an NIR excess for UGC 2773 OT2009-1, hypothesizing that there may be dust emission as it is vaporized, we find more conclusive evidence for this scenario through our NIR spectroscopy. The NIR spectrum is consistent with an additional blackbody with K, but is inconsistent with reddening by dust. The presence of this dust indicates that the initial mass estimate of the progenitor (based on optical HST imaging) is a lower limit, and that the true initial mass is likely much larger.
In addition to what was discussed by S09, we have also detected high-velocity absorption in the spectra of SN 2009ip, indicative of an explosion (as opposed to subsonic outburst). The absorption has an inverse velocity gradient suggesting multiple explosions in short succession. The rapid fading and brightening shortly after maximum brightness noted by (S09) is consistent with multiple explosions, where a second explosion ejects an optically thick shell that temporarily dims the object.
We also note the spectroscopic similarity of UGC 2773 OT2009-1 and SN 1994W, which Dessart et al. (2009) has previously suggested was not a true SN that destroyed its progenitor star.
SN 2009ip and UGC 2773 OT2009-1 are very different manifestations of a similar phenomenon: extreme brightening of massive stars. With these objects and similar events (such as Car, NGC 300 OT2008-1, and SNe 1961V, 1954J, 1997bs, 2000ch, 2002kg, and 2008S), we show that luminous outbursts of massive stars are very heterogeneous. Some of this diversity is likely linked to the instability that causes the eruption, while some is caused by the circumstellar environment. Additional observations of new massive star eruptions are necessary to determine the physical mechanisms of the eruptions, the content of the circumstellar environments, and whether the two are physically connected.
Facilities: ARC (TripleSpec), FMO:31in (FanCam), Gemini:Gillett (GMOS), HST (WFPC2), Magellan:Baade (IMACS), Magellan:Clay (MagE), MMT (Blue Channel), Swift (UVOT, XRT)
R.J.F. is supported by a Clay Fellowship. O.D.F. is grateful for support from NASA GSRP, ARCS, and VSGC. E.M.L. is supported in part by a Ford Foundation Predoctoral Fellowship. We are indebted to the staffs at the APO, Gemini, Magellan, and MMT Observatories for their dedicated services. We thank K. Olsen and R. McDermid for obtaining some of the data presented in the paper. We thank R. Chornock and R. Kirshner for stimulating discussions about the transients. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. Based in part on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the US National Science Foundation on behalf of the Gemini partnership: the NSF (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência e Tecnologia (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina); the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile; the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona; the Fan Mountain Observatory 0.8 meter telescope; and the Apache Point Observatory 3.5 meter telescope, which is owned and operated by the Astrophysical Research Consortium. We acknowledge the use of public data from the Swift data archive.
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http://mathoverflow.net/questions/36082/injectivity-radius-and-the-cut-locus/36083 | # Injectivity radius and the cut locus
Consider a connected, complete and compact Riemannian manifold $M$. Is it correct that the following equality holds: $\text{inj}(x)=\text{dist}\left(x,\text{CuL}(x)\right)$? Or in words that the injectivity radius of a point is the distance from the point to its cut locus.
Here is my explanation: As the manifold is compact and complete, then the cut locus $\text{CuL}(x)$ is compact as well[1]. Thus, there exists a point $y\in \text{CuL}(x)$ such that $\text{dist}\left(x,\text{CuL}(x)\right)=\text{dist}(x,y)$. Since $y$ is a cut point of $x$, there exists a tangent vector $\xi_0\in T_x M$ such that $y=\exp_x\left(c(\xi_0)\xi_0\right)$[2], where $c(\xi_0)$ is the distance from $x$ to its cut point in the $\xi_0$ direction. This in turn means that $\text{dist}(x,y) = c(\xi_0)$.
Recall that $\text{inj}(x)=\inf_{\xi\in T_x M}(c(\xi))$. This means that $\text{inj}(x) \leq c(\xi_0) = \text{dist}(x,y)=\text{dist}\left(x,\text{CuL}(x)\right)$. If $\text{inj}(x)< c(\xi_0)$, then since $M$ is compact, it means that there exists some other tangent vector $\xi\in T_x M$ with $c(\xi) < c(\xi_0)$. But this means that $\exp_x(c(\xi)\xi)$ is a cut point of $x$ closer to it then $y$, and this is a contradiction.
[1] See Contributions to Riemannian Geometry in the Large by W. Klingenberg
[2] Here I'm using the notation of I. Chavel in his book Riemannian Geometry - Modern Introduction.
Update(@dror) Today I finally found a copy of the book *Riemannian Geometry" by Takashi Sakai, and there the above is stated as proposition 4.13 in chapter 3. Thanks anyway.
-
## 1 Answer
The injectivity radius for a point $x$ is the largest distance $r$ such that any geodesic starting from x is length-minimizing for at least distance $r$. So there exists at least one geodesic starting from $x$ that is not length-minimizing past distance $r$. On the other hand a point $p$ is in the cut locus of $x$ if a geodesic starting from $x$ and passing through $p$ is not length-minimizing for any point past $p$. So the injectivity radius at $x$ is the distance from $x$ to its cut locus.
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http://www.koreascience.or.kr/article/JAKO197013464498339.page | # 산화${\cdot}$환원 적정곡선의 이론적 고찰
• Choe, Gyu-Won (Department of Chemistry, College of Liberal Arts and Sciences, Seoul National University)
• 최규원 (서울대학교 문리과대학)
• Published : 19701200
• 60 10
#### Abstract
The varation of potential and completeness of reaction in an oxidation-reduction titration of Red$_1$ ($a\;Ox_1+N_1e{\leftrightarrow}b\;Red_1)\;by\;Ox_2\;(C\;Ox_2+n_2e{\leftrightarrow}d\;Red_2)$ is analyzed on the basis of general expressions. It is shown that the reaction deficiency as well as the rate of variation of the potential with titration fraction change in proportion to the $[n_2(a-b)-n_1(c-d)]$ th power of the concentration of the reagents. In particular, at the equivalence point, the expression of the potential contains a concentration dependent term that is proportional to ac-bd. Thus, the equivalence-point potential varies with the concentration of the reagents unless ac=bd is satisfied. It is also shown that the sharpness of the potentiometric titration curve is shown to occur either prior to or after the equivalence point depending upon whether $n_1cn_2b$, the deviation being the same order of magnitude as the relative deficiency at the equivalence point.
#### References
1. J. Chem. Ed. v.37 A. J. Bard;S.H. Simonsen
2. Anal. Chim. Acta v.27 E. Bishop
3. J. Korean Chem. Soc. v.11 Q. Won Choi
4. Anal. Chim. Acta v.26 E. Bishop | {"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": 0.9154945611953735, "perplexity": 3285.637059807161}, "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-2020-05/segments/1579251678287.60/warc/CC-MAIN-20200125161753-20200125190753-00485.warc.gz"} |
https://www.physicsforums.com/threads/linear-algebra-prove-geometric-multiplicities-are-the-same.215332/ | # Linear Algebra : prove geometric multiplicities are the same
1. Feb 14, 2008
Let A and B be similar matrices. Prove that the geometric multiplicities of the eigenvalues of A and B are the same.
Some help I have gotten so far but still don't know how to proceed from there:
To prove that the geometric multiplicities of the eigenvalues of A and B are the same, we can show that, if B = P^-1 AP , then every eigenvector of B is of the form P^-1 v for some eigenvector v of A.
And i also know that for A and B to be similar matrices, these 5 properties must hold.
1. det A = det B
2. A and B have the same rank
3. A and B have the same characteristic polynomial
4. A and B have the same eigenvalues
5. A is invertible iff B is invertible
any help would be greatly appreciated
2. Feb 14, 2008
### HallsofIvy
Staff Emeritus
The "geometric multiplicity" of an eigenvalue is the dimension of the "eigenspace" (subspace of all eigenvectors) for that eigenvalue.
Now, are you saying that you can use the fact that "if B = P^-1 AP , then every eigenvector of B is of the form P^-1 v for some eigenvector v of A" or do you have to prove that (it's very easy)? If you can use that, then there is an obvious one-to-one correspondence. In particular, you can show that If ${v_1, v_2, ..., v_n}$ is a basis for the eigenspace of A, corresponding to eigenvalue $\lambda$, then $P^{-1}v_1, P^{-1}v_2, ..., P^{-1}v_n}$ is a basis for the eigenspace of B, corresponding to that same eigenvalue.
3. Jul 21, 2009
### jack_bauer
To show that I think it might be sufficient to show that these two matrices (since they're similar) have the same characteristic polynomial. So....
There's an invertible matrix P such that
A= ((P^-1) B P)
det(A-tI)
det([P^-1 BP]-tI)
det([P^-1 BP]-[P^-1tI P])
det([P^-1(B-tI) P])
det(P^-1 P) det(B-tI)
= det(B-tI)
4. Jul 21, 2009
### Dick
Sharing the same characteristic polynomial only tells you the eigenvalues and algebraic multiplicities are the same. It tells you nothing about geometric multiplicity or eigenvectors.
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https://zach.se/project-euler-solutions/66/ | # Project Euler Problem 66 Solution
## Question
Consider quadratic Diophantine equations of the form:
\displaystyle \begin{aligned} x^2-Dy^2=1 \end{aligned}
For example, when $D=13$, the minimal solution in $x$ is $6492 - 131802 = 1$.
It can be assumed that there are no solutions in positive integers when $D$ is square.
By finding minimal solutions in $x$ for $D = {2, 3, 5, 6, 7}$, we obtain the following:
\displaystyle \begin{aligned} 3^2 - 2 \times 2^2 &= 1 \\ 2^2 - 3 \times 1^2 &= 1 \\ 9^2 - 5 \times 4^2 &= 1 \\ 5^2 - 6 \times 2^2 &= 1 \\ 8^2 - 7 \times 3^2 &= 1 \\ \end{aligned}
Hence, by considering minimal solutions in $x$ for $D \leq 7$, the largest $x$ is obtained when $D=5$.
Find the value of $D \leq 1000$ in minimal solutions of $x$ for which the largest value of $x$ is obtained.
import Data.Function (on)
import Data.List (maximumBy)
isInteger :: Double -> Bool
isInteger f = f - (fromIntegral (floor f)) < 0.0000001
isSquare :: Integer -> Bool
isSquare n = isInteger (sqrt $fromIntegral n) rationalize :: [Integer] -> (Integer, Integer) rationalize = foldr (\x (n, d) -> (x*n + d, n)) (1, 0) convergents :: Integer -> [Integer] convergents s | isSquare s = [] | isSquare (s-1) = (a 0) : repeat (fromIntegral$ 2 * (floor $sqrt$ fromIntegral (s-1)))
| otherwise = map a [0..]
where m = (map m' [0..] !!)
m' 0 = 0
m' n = (d (n-1))*(a (n-1)) - (m (n-1))
d = (map d' [0..] !!)
d' 0 = 1
d' n = (s - (m n)^2) quot (d (n-1))
a = (map a' [0..] !!)
a' 0 = floor $sqrt$ fromIntegral s
a' n = floor $(fromIntegral ((a 0) + (m n))) / (fromIntegral (d n)) solve :: Integer -> Integer solve d = head$ [x | n <- [1..], let (x, y) = rationalize $take n$ convergents d, x^2 - d*y^2 == 1]
main :: IO ()
main = print $maximumBy (compare on solve)$ [1..1000]
$ghc -O2 -o diophantine diophantine.hs$ time ./diophantine
real 0m0.333s
user 0m0.332s
sys 0m0.000s | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 15, "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": 1.0000004768371582, "perplexity": 2269.8831362530664}, "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-2018-51/segments/1544376823303.28/warc/CC-MAIN-20181210034333-20181210055833-00183.warc.gz"} |
https://link.springer.com/article/10.1007%2Fs002090050508 | Mathematische Zeitschrift
, Volume 234, Issue 1, pp 163–189
# Sampling expansions associated with Kamke problems
• M.H. Annaby
• G. Freiling
Original article
## Abstract.
The present paper is devoted to the derivation of sampling expansions for entire functions which are represented as integral transforms where a differential operator is acting on the kernels. The situation generalizes the results obtained in sampling theory associated with boundary value problems to the case when the differential equation has the form $$N(y)=\lambda P(y),$$ where N and P are two differential expressions of orders n and p respectively, $$n>p$$ and $$\lambda$$ is the eigenvalue parameter. Both self adjoint and non self adjoint cases will be considered with examples in which the boundary conditions are strongly regular.
Mathematics Subject Classification (1991): 41A05, 34B05, 34L10
## Preview
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https://support.gurobi.com/hc/en-us/community/posts/4419647462161-How-to-raise-the-power-of-a-variable- | • Gurobi Staff
Could you please share a minimal reproducible example where you model the objective function and don't get the correct solution?
Best regards,
Jaromił
Hi Jaromił Najman, I have mentioned one objective and one constraint. I am sharing the code now
m=gp.Model('Matelco')x1=m.addVar(vtype=GRB.CONTINUOUS, name ='x1')x2=m.addVar(vtype=GRB.CONTINUOUS, name ='x2')x3=m.addVar(vtype=GRB.CONTINUOUS, name ='x3')x4=m.addVar(vtype=GRB.CONTINUOUS, name ='x4')a=m.addVar(vtype= GRB.CONTINUOUS, name='a')b=m.addVar(vtype= GRB.CONTINUOUS, name='b')c=m.addVar(vtype= GRB.CONTINUOUS, name='c')d=m.addVar(vtype= GRB.CONTINUOUS, name='d')m.addConstr(a==x1, name =='c1')m.addConstr(b==x2, name =='c2')m.addConstr(c==x3, name =='c3')m.addConstr(d==x4, name =='c4')m.addGenConstrPow(x1, a, 4)m.addGenConstrPow(x2, b, 5)m.addGenConstrPow(x3, c, 3)m.addGenConstrPow(x4, d, 6)m.addConstr(x1+x2+x3+x4<=100, name = 'c1')m.setObjective(a+b+c+d, GRB.MAXIMIZE)m.update()m.optimize()m.printAttr('X')
I am getting different results. The actual results are:
x1=0x2=0x3=0x4=100
But now I am getting different.
Your correction would be highly appreciated.
Thank You
Regards,
• Gurobi Staff
Hi Biswajit,
You could use the write method to generate an LP file and analyze your model in detail. In the LP file, you can see that what you actually modeled is
\begin{align} \max \;&a + b + c +d\\ x_1 &=a\\ x_2 &=b\\ x_3 &=c\\ x_4 &=d\\ a &= x_1^4\\ b &= x_2^5\\ c &= x_3^3\\ d &= x_4^6\\ 100 &\geq x_1 + x_2 + x_3 + x_4\\ x_i &\geq 0, a,b,c,d \geq 0 \end{align}
There you can see that the equality constraints
\begin{align} x_1 &=a\\ x_2 &=b\\ x_3 &=c\\ x_4 &=d\\ \end{align}
are wrong as they don't belong to the model you are trying to model. Additionally, the coefficients in your objective function are missing.
import gurobipy as gpfrom gurobipy import GRBm=gp.Model('Matelco')m.setParam("FuncMaxVal",1e12)x1=m.addVar(vtype=GRB.CONTINUOUS, name ='x1')x2=m.addVar(vtype=GRB.CONTINUOUS, name ='x2')x3=m.addVar(vtype=GRB.CONTINUOUS, name ='x3')x4=m.addVar(vtype=GRB.CONTINUOUS, name ='x4')a=m.addVar(vtype=GRB.CONTINUOUS, name='a')b=m.addVar(vtype=GRB.CONTINUOUS, name='b')c=m.addVar(vtype=GRB.CONTINUOUS, name='c')d=m.addVar(vtype=GRB.CONTINUOUS, name='d')m.addGenConstrPow(x1, a, 4)m.addGenConstrPow(x2, b, 5)m.addGenConstrPow(x3, c, 3)m.addGenConstrPow(x4, d, 6)m.addConstr(x1+x2+x3+x4<=100, name = 'c5')m.setObjective(10*a + 8*b + 12*c + 16*d, GRB.MAXIMIZE)m.update()m.optimize()m.write("myLP.lp")m.printAttr('X')
Note that you have to set the parameter FuncMaxVal to the maximum value that can be attained by your general constraint, which in your case equals $$100^6 = 10^12$$.
Working with such large values is not recommended as it may lead to numerical difficulties. You should try to reformulate or re-scale your model. Please refer to Guidelines for Numerical Issues for more details. Could you, use smaller values for powers, e.g., by finding a lower degree polynomial with same properties as the one you are currently using?
Best regards,
Jaromił
Hi Jaromił Najman, I am very grateful to you for the clarification that you have provided. I am afraid that the question is an assignment problem and it cannot be changed. But I want to thank you for the clarification. I would try to solve smaller questions. | {"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": 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": 0.8344184756278992, "perplexity": 4414.289451755361}, "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-2023-06/segments/1674764494852.95/warc/CC-MAIN-20230127001911-20230127031911-00593.warc.gz"} |
https://ccjou.wordpress.com/2017/02/27/%E6%AF%8F%E9%80%B1%E5%95%8F%E9%A1%8C-february-27-2017/ | ## 每週問題 February 27, 2017
Let $A$ and $B$ be Hermitian matrices. We will write that $A\succ B$ if $A-B$ is positive definite. The inequality $A\succ 0$ means that $A$ is positive definite. Prove that if $A\succ B\succ 0$, then $B^{-1}\succ A^{-1}$. | {"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": 0, "wp_latex": 32, "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": 0.9872020483016968, "perplexity": 95.2365921314252}, "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-2017-22/segments/1495463608058.13/warc/CC-MAIN-20170525083009-20170525103009-00370.warc.gz"} |
https://www.physicsforums.com/threads/how-much-work-is-done-by-the-thrusters-on-a-shuttle-changing-distances-of-orbit.254738/ | # How much work is done by the thrusters on a shuttle changing distances of orbit
1. Sep 8, 2008
### nickhuf098
1. The problem statement, all variables and given/known data
a 2000kg lunar lander is in orbit 40km above the surface of the moon. it needs to move out to a 500km orbit in oder to link up with a mothership that will take the astronauts home. it wants the answer in joules
2. Relevant equations
??E2-E1=Work done by non conservative forces
3. The attempt at a solution
I get answers like 9.91*10^9 joules or negative 9.91*10^9
i thought that Total energy in an orbit=0 so i solved E(@40km)=mv1^2-GMm/r1=2000(v1^2-GM/40000+Rmoon)
2. Sep 8, 2008
### jackiefrost
Does the topic happen to be work/energy (as in "potential energy")?
If so maybe m*g_moon(h2-h1)... is worth thinking about
3. Sep 8, 2008
### jackiefrost
Ooops - the distances are km! (I was thinking meters).
You'd probably need to integrate f(r)dr [force as a function of distance times incremental change in distance to center of moon - i.e. work] from (40000+R_moon) to (500000+R_moon), where f(r)=Gm1m2/r^2
m1=mass of moon
m2=mass of lander
4. Sep 9, 2008
### nickhuf098
Thanks for the help but i finally figured it out.
I had to take the total energy of the second orbit minus the total energy of the first orbit to get the work done by non conservative forces aka the thrusters. Thanks for your assistance though especially about changing it to meters from km
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http://chasethedevil.blogspot.com/2014/06/on-importance-of-accuracy-for-bpvol.html | ## Thursday, June 12, 2014
### On the importance of accuracy for bpvol solvers
While I was playing around calibrating the arbitrage free SABR model from Hagan (using the PDE on probability density approach), I noticed a misbehavior for some short maturity smiles. I thought it was due to the PDE implementation. Actually some of it was, but the remaining large error was due to the bpvol solver.
I initially took the same approach as Choi et al. in my solver, that is to work with in-the-money prices (they work with straddles) because it's nice and convenient. I thought it was no big deal if prices lower than 1E-16 were not solved. It turns out I was wrong. Choi et al. solver has the same issue.
In the above figure, CKK denotes the Choi et al algorithm (similar with my old algorithm) and Chebyshev is my updated algorithm that is accurate with far out-of-the-money option. What happens is that even though the market price at the lowest strike is not very low, the price at the lowest strike stemming from the best fit smile is extremely low, and when we want to invert it, CKK produces a large error due to lack of representation of numbers near 1.0 as it uses indirectly the in-the-money price. That's where it introduces a particularly big error in this case.
I have updated my solver since, to work with out-of-the-money option prices as well, and have near machine accuracy on the whole range. I also reduced the number of Chebyshev polynomials used in the process. All the details are in my updated paper at http://papers.ssrn.com/abstract=2420757 | {"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": 0.8212860822677612, "perplexity": 953.0302863509224}, "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-2018-09/segments/1518891813608.70/warc/CC-MAIN-20180221103712-20180221123712-00330.warc.gz"} |
https://fada.birzeit.edu/handle/20.500.11889/6099 | Please use this identifier to cite or link to this item: http://hdl.handle.net/20.500.11889/6099
Title: Higgs inflation in the Palatini formulation with kinetic terms for the metric Authors: Rasanen, Syksy Keywords: Quantum cosmology;Scalar field theory;General relativity (Physics);astro-ph.CO;String models;Particles (Nuclear physics) Issue Date: 21-Nov-2018 Journal: The Open Journal of Astrophysics, 2018 Abstract: We consider scalar field inflation in the Palatini formulation of general relativity. The covariant derivative of the metric is then non-zero. From the effective theory point of view it should couple to other fields. We write down the most general couplings between it and a scalar field that are quadratic in derivatives. We consider both the case when the torsion is determined by the field equations and the case when it is assumed to be zero a priori. We find the metric derivative terms can significantly modify inflationary predictions. We specialise to Higgs inflation and terms of only up to dimension 4. Transforming to the Einstein frame, we show that by tuning the coefficients of the new terms, we can generate various effective inflationary potentials, including quadratic, hilltop-type, $\alpha$-attractor and inflection point. Some of these can give inflation in agreement with observations, including with a large tensor-to-scalar ratio, even if the non-minimal coupling is zero. Description: 15 pages, no figures. v2. Added references and clarifications. Published version URI: http://hdl.handle.net/20.500.11889/6099 DOI: http://arxiv.org/abs/1811.09514v210.21105/astro.1811.09514http://arxiv.org/abs/1811.09514v2http://arxiv.org/abs/1811.09514v2 Appears in Collections: Fulltext Publications
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https://www.physicsforums.com/threads/compact-nested-sequences.244994/ | # Compact nested sequences
1. Jul 14, 2008
### JamesF
Hi everyone. I feel like I'm really close to the answer on this one, but just out of reach :) I hope someone can give me some pointers
1. The problem statement, all variables and given/known data
Let $$A1 \supseteq A2 \supseteq A3 \supseteq \ldots$$ be a sequence of compact, nonempty subsets of a metric space $$(X, d)$$. Show that $$\bigcap A_n \neq \emptyset$$. (Hint: Let $$U_n = X-A_n$$)
3. The attempt at a solution
Suppose $$\bigcap A_n = \emptyset$$
Choose an open subcover $$U_n = X-A_n$$ (that's supposed to be set minus but I don't know how to do \ in tex). Then $$\bigcup U_n = (X-A_1) \cup (X - A_2) \ldots = X - (\bigcap A_n) = X$$
but where's the contradiction? So X is not compact, but that goes without saying and we can't infer much from that. What am I overlooking here? Or is this the wrong approach entirely?
2. Jul 14, 2008
### Dick
X may not be compact but A1 is. The U_n are a cover of A1 if you assume the intersection of all the Ai is empty. Hence there is a finite subcover. That seems headed for a contradiction.
3. Jul 15, 2008
### JamesF
Thanks for your help, Dick. I was able to get the solution.
I have one more question on my current HW.
Is a set $$A_n = [n, \infty)$$ open or closed in $$\mathbb{R}$$? I would think so, but it's unbounded.
4. Jul 15, 2008
### Dick
What do you think it would be?
Similar Discussions: Compact nested sequences | {"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": 0.9361321330070496, "perplexity": 467.3390043548788}, "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-2017-43/segments/1508187828189.71/warc/CC-MAIN-20171024071819-20171024091819-00333.warc.gz"} |
https://www.physicsforums.com/threads/two-concentric-conducting-esferical-shells-connected-by-thin-wire.682624/ | # Two concentric conducting esferical shells connected by thin wire
1. Apr 2, 2013
### pniau7
1. The problem statement, all variables and given/known data
Consider that the electric field is proportional to q r-2-d$\hat{r}$, where q is magnitude of a point charge and d<<1.
Two concentric conducting esferical shells for radii a and b (a>b) connected by thin wire. The external shell has a total charge qa. Prove that the charge of the smaller shell is:
qb=- $\frac{q_{a}d}{2(a-b)}${2bln(2a)-(a+b)ln(a+b)+(a-b)ln(a-b)} + O(d2)
2. Relevant equations
$\vec{E}$ $\propto$ r-2-d$\hat{r}$
3. The attempt at a solution
I just can't imagine how a charge would be localized in the smaller shell as I always took for granted that charges would place themselves on the external shell.
2. Apr 3, 2013
### TSny
Hello and welcome to PF!
If the electric field of a point charge does not decrease as the inverse square of the distance, then a uniformly charged spherical surface will have a non-zero electric field in the volume enclosed by the surface. For example, if the parameter d > 0, then there will be a radially inward pointing electric field inside the sphere. If d < 0, there will be a radially outward pointing field. Only at the center will the field be zero.
Think about what that implies for the electric potential inside the sphere.
Then imagine two concentric spherical conducting surfaces such that the outer conductor is charged but the inner conductor is not charged. Would there be a potential difference between the two conductors? If so, would connecting a wire between the spheres cause the inner sphere to acquire a net charge?
3. Apr 3, 2013
### pniau7
Thanks for your answer! It is really the lack of manipulation outside the scope of Maxwell ED that makes it difficult. I took for granted that, as they were connected by a wire, the potential would be the same.
I'll try to solve again and I'll let you know if I did it!
Thanks, again!
4. Apr 3, 2013
### TSny
That's right, without the inverse square field of a point charge then you don't have some of the nice things like Gauss' law, you can't replace a uniform sphere of charge by a point charge, etc.
Yes, that's the correct idea. Connecting the spheres with a wire will cause charge to flow between the spheres until the potential is the same for each sphere.
5. Apr 14, 2014
### steelclam
Hi, I am trying to find this answer, any news on this? I struggled, tried to use Gauss' law with the new E field, but it seems that the charges in both sides of equation cancel...
6. Apr 14, 2014
### dauto
That's a nice way to experimentally test the inverse square law which indirectly measures the photon mass.
7. Apr 14, 2014
### steelclam
Hi dauto, yes actually there is a publication on this (doi:10.1103/PhysRevLett.26.721). But this is a Panofsky & Phillips problem (1.8). I tried a lot of things, and indeed this is a really hard situation, since we are all used to deal with inverse square law behavior. Let me know if you find something. thanks
8. Apr 15, 2014
### TSny
Gauss' law is not valid except for the specific case of inverse square behavior of the field of a point charge (d = 0).
I was able to get the result by brute force by finding the potential, V, of a uniformly charged shell at arbitrary points inside and outside the shell in terms of q, r, and d. Here, r is the distance from the center of the sphere. The result can then be approximated to first order in d.
In this problem, we have two charged spherical shells. Requiring the total potential to be the same at the surface of each shell gave the result.
It was somewhat tedious, but not as bad as I thought it might be. I would appreciate knowing of a better method.
9. Apr 15, 2014
### dauto
I don't think there is another method. That's the way to do that problem.
10. Apr 30, 2014
### steelclam
Hi guys,
Well I don't understand what you mean by brute force. Any clue? I would like to try to solve it by myself. Also, it sounds a little bit strange that, well, the Gauss' law is not valid in this case, but the assumption of the *same* potential when the spheres are connected still is...any comments?
Well I have tought a little bit and I assume that by "brute force" you mean:
$V_{A}-V_{B}=-\int_{B}^{A}\vec{E}\cdot d\vec{l}$. Is that right?
Last edited: Apr 30, 2014
11. Apr 30, 2014
### TSny
From the given expression for E of a point charge, find an expression for the potential V(r) of a point charge.
Then consider a uniformly charged spherical shell. By integration, find the potential at points inside and outside the shell. Then approximate the result for d << 1 keeping terms only through first order in d.
Next consider two concentric spherical shells with the outer shell having charge qa and the inner shell having charge qb. By requiring the total potential at the surface of the outer shell (due to both shells) to equal the total potential at the surface of the inner shell, you can derive the relation between qb and qa.
12. Apr 30, 2014
### TSny
Yes, use this to find V(r) of a single point charge. You can let either point A or point B be a point at infinity and take V = 0 at infinity.
Draft saved Draft deleted
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https://mathoverflow.net/questions/285603/picard-group-of-toric-varieties | # Picard group of toric varieties
I am trying to understand how to obtain the Picard group for general toric varieties. So far, I have been using information found in https://arxiv.org/pdf/1003.5217.pdf .
Here, a toric variety has homogeneous coordinates $H:=\{x_i : i=1,\ldots, I\}$ equipped with a number $R$ of equivalence relations $$(x_1,\dots,x_I)\sim (\lambda_r^{Q^{(r)}_1} x_1, \ldots, \lambda_r^{Q^{(r)}_I} x_I), \\$$ for $r=1,\dots, R$ with the weights $Q^{(r)}_i\in \mathbb Z$ and $\lambda_r\in \mathbb{C}^* = \mathbb{C}-\{0\}$.
They go on to say (above equation (7)) that for each divisor $D_i$ of a toric variety, there is a line bundle $$\tag{7} L_i={\cal O}_X \bigl(Q^{(1)}_i, \ldots, Q^{(R)}_i \bigr)\; .$$
It is not clear to me why the weights $Q^{(r)}_i\in \mathbb Z$ govern the classification of line bundles, but this seems to imply that for a particular toric variety, $X$, the Picard group is $$Pic(X)=\mathbb{Z}^R.$$ However, I have also read here -Reference for Weighted Projective Stacks - that for weighted projective spaces, the Picard group is cyclic. (Edit: It seems that this link talks about weighted projective stacks, which are not toric varieties.)
What is the rationale for describing line bundles in terms of weights as in equation (7), and how does one find the Picard group of a toric variety in general?
Edit: Fred Rohrer suggested in the comments that I look at Ewald's Combinatorial Complexity and Algebraic Geometry. On page 273 we find that for an arbitrary $n$-dimensional toric variety, $Pic(X)=\mathbb{Z}^{k-n-\lambda}$, $k$ being the number of 1-cones of the corresponding fan $\Sigma$, $\lambda$ being the total dimension of the spaces of linear dependencies of generators of all maximal cones which are not simplex cones. This, however, translates to $$Pic(X)=\mathbb{Z}^{R-\lambda},$$ which is different from the expression above. Why is there this discrepancy?
• You might want to have a look at Section VI.2 in G. Ewald, Combinatorial convexity and algebraic geometry, Springer GTM 168 (1996). – Fred Rohrer Nov 9 '17 at 7:01
• @FredRohrer Thanks for the helpful comment. On page 273 of this book, I found that for an arbitrary $n$-dimensional toric variety, $Pic(X)=\mathbb{Z}^{k-n-\lambda}$, $k$ being the number of 1-cones of the corresponding fan $\Sigma$, $\lambda$ being the total dimension of the spaces of linear dependencies of generators of all maximal cones which are not simplex cones. This, however, translates to $Pic(X)=\mathbb{Z}^{R-\lambda}$, which is different from the expression above. Why is there this discrepancy? – Mtheorist Nov 9 '17 at 15:50
• Are you prevented from taking $Q_i^{(r)} = Q_i^{(s)}$ or other redundancies in the equivalence relation? – AHusain Nov 9 '17 at 18:34
• Dear @Mtheorist, I have not thought about these things for quite some time now, and hence, unfortunately, I do not know the answer to your question(s). – Fred Rohrer Nov 9 '17 at 19:08
• By quickly looking at the paper you linked, it seems to me that "the physicists" definition of toric varieties they are working with includes the assumtion that the fan is simplicial. They specifically mention "fan and triangulation". Simplicial toric varieties are exactly those for which $\lambda=0$, but are also characterized as those for which the variety is a geometric quotient from the equivalence relation (as opposed to a categorical quotient in general). – Gjergji Zaimi Nov 12 '17 at 6:26 | {"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": 0.8265153169631958, "perplexity": 244.55290564895344}, "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-2020-05/segments/1579251779833.86/warc/CC-MAIN-20200128153713-20200128183713-00089.warc.gz"} |
http://en.wikipedia.org/wiki/Exner_function | # Exner function
$\Pi = \left( \frac{p}{p_0} \right)^{R_d/c_p} = \frac{T}{\theta}$
where $p_0$ is the pressure at the surface, usually taken as 1000 hPa; $R_d$ is the gas constant for dry air; $c_p$ is the heat capacity of dry air at constant pressure; $T$ is the absolute temperature; and $\theta$ is the potential temperature. | {"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": 6, "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": 0.9204331636428833, "perplexity": 315.61887729709787}, "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-2013-48/segments/1386163037418/warc/CC-MAIN-20131204131717-00036-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/38460/is-the-minimum-radius-of-a-positronium-system-of-the-order-of-compton-wavelength?answertab=votes | Is the minimum radius of a positronium system of the order of compton wavelength or less than that?
Since from electron-positron annihilation energy and uncertainty principle,the minimum radius of positronium comes out as half of the compton radius.
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After annihilation there is no electron and positron in a new (lower) bound state, thus there is no positronium. Positronium decays into several photons, that's it. The photon wavelength has nothing to do with the "new positronium state" since there is no positronium in the final state.
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No, the positronium radius is of the order of the Hydrogen atom radius (Bohr radius), $$a_0 = \frac{4 \pi \varepsilon_0 \hbar^2}{m_{\mathrm{e}} e^2} = \frac{\hbar}{m_{\mathrm{e}}\,c\,\alpha}$$ which is longer than the Compton wavelength of the electron because of the extra factor $1/\alpha=4\pi\varepsilon_0\hbar c/e^2\sim 137.036$, the inverse fine structure constant. This factor is usually not considered to be "of order one" in these considerations.
The Compton wavelength is "something in between" the size of the atom (or positronium) and the size of the nucleus.
If you want it more accurately, the positronium is (almost) exactly 2 times larger than the Hydrogen atom – when it comes to the distances between the two charged particles in it – and its binding energy is 1/2 of the hydrogen value. That's because the "reduced mass" of the positronium problem is $m_e\cdot m_e/(m_e+m_e) = m_e/2$.
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It is speculative but a statement can be made that it is impossible to 100 percent annihilate a electron and positron if there is a charge parity in that area . 99 percent yes but not 100 percent do the the conservation of energy . We on earth are about 300 K volts negative relative to space . Stated another way we have a 300 k volt sky charge meaning earth has a charge parity of 300 K volts compared to neutral space . In order to bring one positron and one electron from space down to earth a voltage barrier of 300 K volts must be past . With a strict application of e=mc^2 the mass of the electron must go up and the positron down . It is a very small difference but it is there just the same . A 100 percent annihilation of a electron / positron pair would be a violation to the conservation of energy as the masses would not be equal . This allows wiggle room for a ash left over from annihilation . Two photons and one very low energy atom of positronium . It's mass would be in the neighbourhood of a neutrino so good luck in detecting it . Just the same it should theoretically be there . I call the left over ash a VEPS particle , quasi virtual positronium who's properties change with the charge parity of a given area . Add 1 M volt per VEPS vacuum and pair production returns us to the original electron and positron . The notion that this type of low energy positronium would have a radius of two times hydrogen sounds about right if our space , vacuum , is composed of quasi virtual positronium left over from a hotter universe.
John
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This looks completely wrong; unless it's based on some physics which I'm not familiar with. – Ali Jul 15 '13 at 2:45
This is complete nonsense. I particle physics mass always refers to rest mass not "relativistic mass." Rest mas is an invariant. Electron/positron masses are not at all affected by a background EM field and neither is the annihilation reaction which is a local process. This person does not understand basic relativity. I wonder how he thinks that the LEP experiment worked! By the way a very low mass electron/positron composite would be easy to detect... we can detect neutrinos after all! – Michael Brown Jul 15 '13 at 10:41 | {"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": 0.9162550568580627, "perplexity": 526.0575915998644}, "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-2014-35/segments/1408500832738.80/warc/CC-MAIN-20140820021352-00129-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/134316-lilliefors-test-print.html | # Lilliefors test
• March 17th 2010, 02:39 PM
Krahl
Lilliefors test
Hi;
I came across the table for use with the specialised K-S test and it said that the critical values were calculated using monte carlo calculations using 1000 or more samples for each value of N (sample size). I'm trying to understand how this was done. can anyone help me understand this. This is what i think;
Let the Lilliefors test statistic be $D=max_{y \in R}|F(y)-S_{0}(y)|$ and $D^{*}=max_{x \in [0,1]}|F^{*}(x)-x|$ where $S_{0}$ is the cumulative normal distr. function, F is the empirical c.d.f for the sample $y_1,...,y_n$ , $F^*$ is the e.c.d.f of the sample $x_1,...,x_n$ with $x_i=S_{0}(y_i)$.
to simulate the null distribution of the lilliefors test statistic (D) i need to;
1) generate a sample of size n from the standard normal distribution N(0,1)
2) for the sample calculate $D^*$
3)Do 1) and 2) 1,000 times
4)the distribution of the N values $D^*$ then approximates the null distribution of D
But were do i go on from here to calculate the right tail of this null distribution?
• March 17th 2010, 03:47 PM
Funnily enough I co-authored a paper on this last summer...
What we did is took the 1000 values (in our case though we used many millions) and ordered them, smallest to largest. Then you just take the value which corresponds to the percentage point you want.
So for your 1000 values, if you want the upper 5% point, take the 950th values in your ordered set (have to check if we used 950, 951 or a combo of both).
• March 17th 2010, 06:18 PM
Krahl
1 Attachment(s)
Hi | {"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": 9, "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": 0.9272199273109436, "perplexity": 626.0460783622926}, "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/1424936461266.22/warc/CC-MAIN-20150226074101-00080-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://researchportal.hw.ac.uk/en/publications/gas-solubility-a-key-to-estimating-the-water-content-of-natural-g | # Gas solubility: A key to estimating the water content of natural gases
Amir H. Mohammadi, Antonin Chapoy, Bahman Tohidl, Dominique Richon
Research output: Contribution to journalArticlepeer-review
24 Citations (Scopus)
## Abstract
Experimental water content data, at low temperatures, for hydrocarbons and non-hydrocarbon gases are scarce and often rather dispersed. This is partly due to the fact that water content of gases is indeed very low at low temperatures and high pressures and hence generally very difficult to measure. However, measuring gas solubility in water is easier than measuring water content of gases. In this work, we examine the need for water content data in the gas phase for tuning binary interaction parameters between water and gaseous components in an equation of state. We consider three cases for tuning: (1) gas solubility in the liquid-phase only, (2) water content of the gas phase, and (3) mutual solubilities. The Valderrama modification of the Patel-Teja equation of state with the nondensity dependent mixing rules is used for modeling the fluid phases. These results show that using only gas solubility data in tuning the thermodynamic model leads to accurate predictions of water content data, and, therefore, experimental gas-phase water contents are not indispensable. Furthermore, we report new experimental data on the water content of the gas phase for a gas mixture consisting of 94% methane, 4% ethane, and 2% n-butane at low temperatures. The data were measured in the 277.82-292.88 K temperature range and at pressures up to 3.028 MPa, using a static-analytic technique taking advantage of a Rolsi sampling device. To examine the consistency of the new experimental data they are compared with the results of a previously reported semi-empirical approach and the developed thermodynamic model. The agreements between the experimental and predicted data are good, demonstrating the reliability of the data and the techniques used in this work. © 2006 American Chemical Society.
Original language English 4825-4829 5 Industrial and Engineering Chemistry Research 45 13 https://doi.org/10.1021/ie051337i Published - 21 Jun 2006 | {"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": 0.8016326427459717, "perplexity": 1584.5954105007422}, "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-2021-10/segments/1614178347293.1/warc/CC-MAIN-20210224165708-20210224195708-00119.warc.gz"} |
http://math.stackexchange.com/questions/138512/sampling-q-uniformly-where-qtq-i | # Sampling $Q$ uniformly where $Q^TQ=I$
(This is related to this question)
$Q \in \mathbb{R}^{n\times k}$ is a random matrix where $k<n$ and the columns of $Q$ are orthogonal (i.e. $Q^T Q = I$). To examine $E(QQ^T)$, I conducted monte carlo simulations (using matlab):
[Q R] = qr(randn(n,k),0);
In other words, I just sampled a $\mathbb{R}^{n\times k}$ matrix from a standard gaussian, then did QR decomposition on it and assumed $Q$ is uniformly distributed in the space where $Q^TQ=I$. Joriki's answer and my simulations aligned so I assume there's nothing majorly wrong with how I obtained samples.
I have two questions (in order of importance)
1. How does one prove that the $Q$ sampled as above is uniformly distributed in the space where $Q^TQ=I$?
2. Are there more efficient methods of sampling orthogonal $Q$?
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That works. When you do gram schmidt orthogonalization on the guassian you get uniform on orthogonal. This corresponds pretty directly to the first column being uniform on $S^n$. You just normalize the gaussian first column and it it uniform on the sphere, then the second should be uniform on vectors orthogonal to first, and conditonally on the first it has a normal distribution that makes the property pretty apparent. – mike Apr 29 '12 at 19:34
@mike I can see that it works and (now that I think of it) that the first column would be uniform on $S^n$. I am still unclear on how the rest of what you state is "pretty apparent". I appreciate the response but can you lay out a fleshed out proof without stating that it's apparent? (I tried doing a proof using gram-schmidt, but couldn't prove that the $k$-th orthonormal vector obtained is uniformly distributed assuming that the $(k-1)$-th vector is uniformly distributed in the orthogonal space.) – JasonMond Apr 29 '12 at 21:43
@mike I think it might be easier if you replied in an answer. – JasonMond Apr 30 '12 at 0:58
The claim is that if you apply gram schmidt to the columns of a matrix whose entries are i.i.d normal the resulting distribution is Haar measure on orthogonal matrices. Gram-Schmidt gives you an orthogonal matrix so invariance of the distribution under orthogonals is the issue. It is true because the orthogonals preserve i.i.d normals and also all elements of the gram-schmidt procedure, i.e. inner products. Suppose you have a $2 \times 2$ matrix $X$ , the general case being the same, with columns $x_1, x_2$. Gram schmidt gives an orthogonal matrix with columns $\frac {x_1}{\Vert x_1 \Vert},\frac {x_2 - \langle x_1,x_2 \rangle \frac {x_1}{\Vert x_1 \Vert}}{\Vert \text {the numerator }\Vert }$. Call that $X_{GS}$. If O is an orthogonal matrix $OX$ has columns $Ox_1, Ox_2$, and when you apply gram schmidt to it you get $\frac {Ox_1}{\Vert Ox_1 \Vert},\frac {Ox_2 - \langle Ox_1,Ox_2 \rangle \frac {Ox_1}{\Vert x_1 \Vert}}{\Vert O\text {the numerator }\Vert }$. Using orthogonality of $O$ once this has the same distribution as $X_{GS}$ since $Ox_i$ are i.i.d. with the same distribution as $x_1,x_2$,and that determines the distribution, and using it again the matrix is equal to $\frac {Ox_1}{\Vert x_1 \Vert},\frac {Ox_2 - \langle x_1,x_2 \rangle \frac {Ox_1}{\Vert x_1 \Vert}}{\Vert \text {the numerator }\Vert }$ since norms and inner products are the same. The last expression is $OX_{GS}$, and this shows that the distribution of $X_{GS}$ is invariant under orthogonal matrices.
Thanks. I can understand the second part of the argument of how $X_{GS}$ and $OX_{GS}$ would have the same density due to invariance under rotation. But you lost me on the first part. I have never heard of Haar measure before and googling it hasn't helped me at all. – JasonMond Apr 30 '12 at 22:17 | {"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": 0.968364417552948, "perplexity": 234.55671998568107}, "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/1432207928078.25/warc/CC-MAIN-20150521113208-00137-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://iihe.ac.be/cms-1 | Home > CMS
CMS
CMS is one of the two general purpose detectors for the proton-proton collider of CERN, the LHC.
The main purposes of the LHC are to study the mechanism of spontaneous symmetry breaking in electroweak interactions and to explore physics beyond the Standard Model. LHC is definitively a discovery machine! It will nevertheless also allow physicists to study Standard Model processes more deeply as for example top quark physics, as well as heavy ion collisions at unprecedented energy.
CMS is an international collaboration in which Belgium and in particular Brussels (ULB-VUB) has an important participation. The Brussels group has participated in the contruction of the endcap tracker detector of CMS. The Brussels teams were involved in the study of the CMS physics potential using simulations, and are now analysing the fresh LHC data at the energy of 7 TeV in the proton-proton centre of mass.
The CMS Brussels groups are very active in the high energy data analysis, both looking at tests of the Standard Model predictions at the high energy frontier and the search for new physics beyond the Standard Model. This studies are performed in many different final states, mainly focusing on :
• Higgs physics
• top quarks and beyond
• high energy electrons (HEEP group)
• QCD
The links to the research groups are given in the left frame. | {"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": 0.8865286111831665, "perplexity": 1260.8350563329118}, "config": {"markdown_headings": false, "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-2019-13/segments/1552912203378.92/warc/CC-MAIN-20190324063449-20190324085449-00253.warc.gz"} |
https://math.stackexchange.com/questions/2405811/transpose-applications-and-matrices-properties | # Transpose applications and matrices properties
Good Afternnon
If $f$ is a linear transformation mapping then if the transformation matrix of linear transformation mapping has been defined and its transpose properties are known as well.
Why, what I have written below, is called a definition rather than a proposition?? Is it possible to deduce it from the matrices?
$E,F$ two finite vector-spaces.
$\psi\in \mathcal{L}(E,F)$. The transpose of $\psi$ is the linear map :
$\begin{array}l ^t\psi :&F^*&\to E^*\\&\phi&\to \phi\circ\psi\end{array}$
## 1 Answer
Because the transpose of a matrix is one thing and the tranpose of a linear map is a distinct concept. | {"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": 0.9849337339401245, "perplexity": 457.4440344435882}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2019-51/segments/1575541307813.73/warc/CC-MAIN-20191215094447-20191215122447-00353.warc.gz"} |
https://economics.stackexchange.com/questions/35844/risk-neutral-probability-for-each-of-3-states | # Risk neutral probability for each of 3 states
I need help to find the risk-neutral probability for states 1,2 and 3
I have two stocks: A and B.
The price of A today is 180 and in a year it will be worth 288 (S1), 180 (S2) or 120 (S3);
The price of B today is 100 and in a year it will be worth 94(S1), 134(2) or 54(S3)
The annual rf rate is 2%
I did the following for stock A: up : 288/180-1= 0,6 down :120/180-1 =-0,3333
Finding prob for s1: (2- (-33,33))/ 60- (-33,33)) = 0,3785
Then tried to solve for p2 and then p3:
PV= (0,3785* 288 + p2*180+ (0,6215 -p2 )* 120)/1,02= 180
These probabilities don't add up when I try to find the price of stock B, so they are clearly wrong. Can you tell me how to find the right probabilities?
Seems to me there is no way to divine three state risk-neutral probabilities from 1 financial instrument's prices. The equation $$p_1 288 + p_2 180 + (1 - p_1 - p_2) 120 = 180$$ is underdetermined, there are infinitely many solutions to it. Now if you solved the equation system \begin{align*} p_1 288 + p_2 180 + (1 - p_1 - p_2) 120 & = 180 \\ p_1 94 + p_2 134 + (1 - p_1 - p_2) 54 & = 100 \end{align*} there you have two unknowns and two equations, so usually this would admit exactly one solution. | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9240534901618958, "perplexity": 1266.064864694063}, "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/1620243988759.29/warc/CC-MAIN-20210506175146-20210506205146-00314.warc.gz"} |
http://math.stackexchange.com/questions/57504/incorrect-manipulation-of-limits/57508 | # Incorrect manipulation of limits
Here's my manipulation of a particular limit:
$\displaystyle \lim\limits_{h\rightarrow 0}\Big[\frac{f(x+h)g(x) - f(x)g(x+h)}{h}\Big]$
Using the properties of limits:
\displaystyle \begin{align*} &=\frac{\lim\limits_{h\rightarrow 0}\Big[f(x+h)g(x) - f(x)g(x+h)\Big]}{\lim\limits_{h\rightarrow 0}h}\\ &=\frac{\lim\limits_{h\rightarrow 0}\Big[f(x+h)g(x)\Big] - \lim\limits_{h\rightarrow 0}\Big[f(x)g(x+h)\Big]}{\lim\limits_{h\rightarrow 0}h}\\ &=\frac{\lim\limits_{h\rightarrow 0}\Big[f(x+h)\Big]\lim\limits_{h\rightarrow 0}\Big[g(x)\Big] - \lim\limits_{h\rightarrow 0}\Big[f(x)\Big]\lim\limits_{h\rightarrow 0}\Big[g(x+h)\Big]}{\lim\limits_{h\rightarrow 0}h}\\ &=\frac{f(x)\lim\limits_{h\rightarrow 0}\Big[g(x)\Big] - f(x)\lim\limits_{h\rightarrow 0}\Big[g(x+h)\Big]}{\lim\limits_{h\rightarrow 0}h}\\ &=\frac{f(x)\Big(\lim\limits_{h\rightarrow 0}\Big[g(x)\Big] - \lim\limits_{h\rightarrow 0}\Big[g(x+h)\Big]\Big)}{\lim\limits_{h\rightarrow 0}h}\\ &=\frac{f(x)\Big(\lim\limits_{h\rightarrow 0}\Big[g(x) - g(x+h)\Big]\Big)}{\lim\limits_{h\rightarrow 0}h}\\ &=f(x)\lim\limits_{h\rightarrow 0}\Big(\frac{g(x) - g(x+h)}{h}\Big)\\ &=-f(x)g'(x)\end{align*}
I'm pretty sure that my end result is incorrect, as I've used arbitrary functions for $f(x)$ and $g(x)$ and it didn't support my conclusion. I think that the factoring of $f(x)$ might be what is incorrect in my manipulation, but I'm not 100% sure. Could someone explain to me what I did wrong and why it is wrong? Which one of the limit "axioms" did I use incorrectly? Thank you.
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You are dividing by zero. – wckronholm Aug 15 '11 at 3:38
You neglected a minus sign at the end, but that's a pretty minor issue. Lots of fallacious proofs can be based on allowing yourself to divide by 0 without calling attention to the fact. – Michael Hardy Aug 15 '11 at 3:49
@Michael Hardy: You are correct, I was missing a negative sign in my conclusion. I have edited my post accordingly. Thank you. – Hautdesert Aug 15 '11 at 4:02
Any time you put $\lim_{h\to 0}$ in the denominator, you are dividing by $0$, and nothing is reliable from then on. The second displayed formula is fatal. Limit of a ratio is the ratio of the limits if the limit of the denominator is not $0$. In your calculation, that limit is $0$. – André Nicolas Aug 15 '11 at 4:13
The quotient property of limit says that if $\lim\limits_{x\to a}f(x)=L$ and $\lim\limits_{x\to a}g(x)=M\neq 0$, then $$\lim_{x\to a}\frac{f(x)}{g(x)} = \frac{L}{M} = \frac{\lim\limits_{x\to a}f(x)}{\lim\limits_{x\to a}g(x)}.$$ But this requires $M\neq 0$.
In your very first equality, you attempt to use this when $M=0$ (since $\lim\limits_{h\to 0}h = 0$). This is not a valid use of the limit laws/properties of limits.
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Let us assume that $f$ and $g$ are differentiable at $x$. Note that $$f(x+h)g(x) - f(x)g(x+h)= f(x+h)g(x)+(f(x)g(x)-f(x)g(x))-f(x)g(x+h).$$ We have added $0$ in the middle, which is harmless. A trick that looks very similar was undoubtedly used in your book or notes to prove the product rule for differentiation.
Rearranging a bit, and with some algebra, we find that $$f(x+h)g(x) - f(x)g(x+h)=(f(x+h)-f(x))g(x)-f(x)(g(x+h) -g(x)),$$ and therefore $$\frac{f(x+h)g(x) - f(x)g(x+h)}{h}=\frac{(f(x+h)-f(x))g(x)}{h}-\frac{f(x)(g(x+h) -g(x))}{h}.$$
The rest is up to you.
Added stuff, for the intuition: The following calculation is way too informal, but will tell you more about what's really going on than the mysterious trick.
When $h$ is close to $0$, $$f(x+h) \approx f(x)+hf'(x)$$ with the approximation error going to $0$ faster than $h$. Similarly, $$g(x+h) \approx g(x)+hg'(x).$$ Substitute these approximations into the top. Simplify. Something very pretty happens!
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Hint to solve your problem: Let $$\varphi (h) = \frac{{f(x + h)g(x) - f(x)g(x + h)}}{h}.$$ Then $$\varphi (h) = \frac{{[f(x + h) - f(x) + f(x)]g(x) - f(x)[g(x + h) - g(x) + g(x)]}}{h}.$$ From this it follows straightforwardly that $$\mathop {\lim }\limits_{h \to 0} \varphi (h) = g(x)f'(x) - f(x)g'(x).$$ I'll give more hints if you need.
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I didn't look very thoroughly at all the uses of limit laws, but the first one that stuck out to me was the limit law for products. It is usually stated in calculus textbooks in the following form: If $\lim_{x\to a}f(x)$ and $\lim_{x\to a}g(x)$ both exist, then $\lim_{x\to a}[f(x)g(x)]=\lim_{x\to a}f(x)\lim_{x\to a}g(x)$.
You violate this when you break $\lim_{h\to 0}$ with the division, because you are essentially saying $\lim_{h\to 0}[f(x+h)g(x)-f(x)g(x+h)](1/h)= \lim_{h\to 0}[f(x+h)g(x)-f(x)g(x+h)]\lim_{h\to 0}(1/h)$ and that second limit doesn't exist.
It is very easy to overlook that for the limits all have to exist to apply the limit laws. It is like when doing algebraic manipulations you can easily overlook dividing by 0.
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https://physics.stackexchange.com/questions/513859/b-field-and-h-field-inside-a-bar-magnet/513932 | # B field and H field inside a bar magnet
Recently I've been studying about magnetism there is one piece of information I'm stuck at . It says that the direction of magnetization and H field inside a bar magnet are opposite.
1. First of all what I think is H field is required when you have 2 type of current H field is caused by the external or given current and magnetization field is caused by magnetic moments of the atoms/electrons of the material.then How there can be an H field inside bar magnet?
2.say the H field we are talking about is the field that was used to magnetize the magnet.then shouldn't the dipole moment of the atoms/electrons be aligned with the H field as happens usually and thus direction of magnetization should be same as H field .
• Unlike ${\bf B}$, ${\bf H}$ has both vortex sources (curl) and pole sources (divergence). – Buzz Nov 14 '19 at 23:43
Sources of magnetic field: this can be seen from the Maxwell equations:
$$\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial\mathbf{D}}{\partial t}$$
The first term on the right side gives the generation via electrical current and the second term via an oscillating electrical field.
Also, a changing magnetization in space gives rise to a magnetic field:
$$\nabla \cdot \mathbf{B} = \nabla \cdot (\mu_0 (\mathbf{H}+ \mathbf{M})) = 0 \Rightarrow \nabla \cdot \mathbf{H} = -\nabla \cdot\mathbf{M}$$
Source of magnetization: the magnetization of a material is indeed originating from the atomic dipole moments in the material.
The demagnetization field: this field is present even if there is no current nor electrical field. The demagnetization field is the field generated by a change in the magnetization. In the bar magnet, the magnetization is assumed to be constant (so no generation of a magnetic field in the bar magnet). Outside the bar magnet, there is no magnetization and thus also no change in magnetization (also no generation of a magnetic field outside the magnet). Now it comes, at the ends of the magnet (the north and south pole), there is a clear and abrupt change of the magnetization (because there is magnetization inside the material but not outside). This abrupt change of the magnetization serves as a source of magnetic field (remember $$\nabla \cdot \mathbf{H} = -\nabla \cdot\mathbf{M}$$).
At the north pole, the magnetic field is generated (negative gradient of magnetization) whereas at the south pole the magnetic field is eliminated (positive gradient of magnetization). Between the two ends of the bar magnet, there was no change, so the magnetic field should be conserved. Hence, from the maxwell equation, the magnetic field of a bar magnet can be calculated. The field inside is called the demagnetization field and outside is called the stray field. Both fields are going from the north pole to the south pole. The field outside the magnet (the stray field) is the field that we experience and what we use when working with a bar magnet.
Pole avoidance principle: Indeed, the magnetic field inside the bar magnet will always point against the magnetization. The demagnetization field gives an increase in energy. Hence, nature always strives to minimize the amplitude of this field. This can be done by putting the magnetization along the longest axis of the material. | {"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": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9272871613502502, "perplexity": 196.67338071213746}, "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-2020-40/segments/1600400219691.59/warc/CC-MAIN-20200924163714-20200924193714-00123.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/21103-determinant-question-print.html | # Determinant Question
• October 22nd 2007, 07:29 PM
Thomas
Determinant Question
Let A = $
\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;a & b & c \;\\\;p & q & q \;\\\;u & v & w\end{vmatrix}
$
and assume that det A = 3.
Compute:
det(2c^-1) where C = $
\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;2p & -a+u & 3u \;\\\;2q & -b+v & 3v \;\\\;2r & -c+w & 3w\end{vmatrix}
$
I'm getting an answer of 1/3, which is wrong. The answer is 4/9.
The troubles I'm having you can read about right HERE. I know how to do everything, but I'm obviously just making a small mistake.
One specific question I would like to ask, is how do I remove the 2 from inside the det() brackets? I haven't been shown an example of that, and can't find one.
Thanks!
• October 23rd 2007, 05:16 AM
kalagota
Quote:
Originally Posted by Thomas
Let A = $
\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;a & b & c \;\\\;p & q & q \;\\\;u & v & w\end{vmatrix}
$
and assume that det A = 3.
Compute:
det(2c^-1) where C = $
\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;2p & -a+u & 3u \;\\\;2q & -b+v & 3v \;\\\;2r & -c+w & 3w\end{vmatrix}
$
I'm getting an answer of 1/3, which is wrong. The answer is 9/4.
The troubles I'm having you can read about right HERE. I know how to do everything, but I'm obviously just making a small mistake.
One specific question I would like to ask, is how do I remove the 2 from inside the det() brackets? I haven't been shown an example of that, and can't find one.
Thanks!
actually, for any real number c, det(cA) = c^n det(A) where n is the size of the matrix. i hope, this would help..
• October 23rd 2007, 05:25 AM
kalagota
Quote:
Originally Posted by kalagota
actually, for any real number c, det(cA) = c^n det(A) where n is the size of the matrix. i hope, this would help..
.. hmm, i get a 4/9.. just try to solve it.. maybe there was a mistake on my computation.. Ü
• October 23rd 2007, 10:48 AM
Thomas
Oops, sorry. The answer is 4/9. I just mixed up the numbers. :p
Could you explain how you did it?
• October 24th 2007, 04:49 AM
kalagota
Quote:
Originally Posted by Thomas
Let A = $
\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;a & b & c \;\\\;p & q & q \;\\\;u & v & w\end{vmatrix}
$
and assume that det A = 3.
Compute:
det(2c^-1) where C = $
\begin{array}{c}\ \\ \\ \end{array}\;\begin{vmatrix}\;2p & -a+u & 3u \;\\\;2q & -b+v & 3v \;\\\;2r & -c+w & 3w\end{vmatrix}
$
I'm getting an answer of 1/3, which is wrong. The answer is 4/9.
The troubles I'm having you can read about right HERE. I know how to do everything, but I'm obviously just making a small mistake.
One specific question I would like to ask, is how do I remove the 2 from inside the det() brackets? I haven't been shown an example of that, and can't find one.
Thanks!
ok.. let's recall some theorems..
THEOREMS
Let A = [A_1 A_2 ... A_n] be an nxn matrix, where A_i are the columns of A for i=1,..,n.
let B be the transpose of A.
1) det (A) = det (B)
2) det([A_1 ... cA_k ... A_n]) = c det([A_1 ... A_k ... A_n])
3) det(cA) = det(c[A_1 A_2 ... A_n] = (c^n) det(A)
4) det([A_1 ... (A_k)+(A_j) ... A_n]) = det([A_1 ... A_k ... A_n]) + det([A_1 ... A_j ... A_n])
5) det([A_1 ... A_k cA_j ... A_n]) = 0 if A_k = A_j
6) det([A_1 ... A_k ... A_j .... A_n]) = (-1)^p det([A_1 ... A_j ... A_k .... A_n]) where p= j-k
so, these are the steps. you are given the matrix A.
..get the transpose of A. that transpose has same determinant as A.
..looking on the matrix C, you will see that the second column is a sum, hence use THEROEM 4.
..after this step, you should notice that one of the addends has 2 a column which is a multiple of the another column (the third column is 3 times the second), hence the determinant of this addend is 0 by THEOREM 5.
..you are left with one addend. you notice that the first column has factor 2, the second has -1 and the third has 3, use THEOREM 2.
..now, switch the first column with the second column and use THEOREM 6.
..you should notice that the final matrix looks like the transpose of A.
..you can now use THEOREM 3 and you should get 4/9.
Ü | {"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": 6, "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": 0.8187744617462158, "perplexity": 1307.0851055245646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2016-22/segments/1464049276567.28/warc/CC-MAIN-20160524002116-00210-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/what-causes-wavefunction-collapse.525364/ | # What causes wavefunction collapse?
1. Aug 29, 2011
### SeventhSigma
I've always been confused about something -- I'd love for someone to clear up my ignorance.
I understand that the position of a particle can be modeled as a wavefunction (a probability distribution, to my understanding) where we can describe the position as fundamentally random, but it takes on a value at a frequency in accordance to the distribution once it interacts with something.
My question: What does it mean for it to "interact?"
When two particles collide into each other to take on their "real" states, how does it know when this occurs? In my mind I am viewing it as two clouds of probability heading towards each other. Technically, the clouds are always intersecting because the wavefunction distributes itself across all space and time, right?
Even if I am wrong on that point, my question is what is actually happening here when probability clouds collide. What is the mechanism that describes the actual collapse of the wavefunction from probability clouds to real states? Do they just have to take on the same values at the same time, where this becomes more and more likely as the clouds intersect more intimately?
Sorry if I am not making much sense.
2. Aug 29, 2011
### dm4b
I think the simple answer is that no one TRULY knows.
Roger Penrose has some interesting ideas on wave function collapse. Basically, he feels it is ultimately related to gravity and an explanation for WF collapse will have to be included in any theory that succesfully combines QM with GR.
3. Aug 29, 2011
### SeventhSigma
So not only is the real state of the collapse random, but the actual act of the collapse of the wavefunction itself is random?
4. Aug 29, 2011
### HPLovecraft
Granted I am very new to this stuff, and probably don't have nearly the amount of knowledge on the subject as some here, I'll try and help. What you're asking is basically an answer to something called the quantum measurement problem. There are a lot of differing ideas on it, of course, but nothing concrete that is agreed upon by 99% of the scientific community. Basically, when a scientist "looks at" (measures) a particle, it changes from its wavefunction form of limbo into the particles we know and love today -- physical things with exact locations, velocities, spins, etc.
I would start by not calling these things probability clouds. I'd stick with two probability waves (since they are waves, after all -- there are just a lot of them, everywhere). From my reading, wavefunctions interact all of the time -- it's how they discovered wavefunctions exist in the first place! When viewed correctly, interacting wavefunctions create interference patterns, and can thus be observed. The wavefunction doesn't, however, immediately collapse because of this interaction between multiple wavefunctions. It collapses (if wavefunctions even collapse at all) because of . . . well, nobody really knows. We don't even know if a wavefunction even collapses! There are theories, however.
One approach is to abandon the view that that wavefunctions are objective features of quantum reality; instead, they're just an embodiment of what we know about reality. In other words, we don't know where the particle is yet, so we come up with probabilities. Once we gain the knowledge of where the particle is through measuring it, the wavefunction "collapses" and we gain knowledge.
Another, far cooler idea, is the Many Worlds interpretation. If you've ever watched the last season of LOST, you'll have an idea of what it is. Every probability of a particle being here, there, or over yonder in a wavefunction is realized -- the wavefunction never collapses. It's just realized in different parallel universes.
Another thought is that particles do actually have an exact location and spin, etc., at any one time, just like Einstein thought they should. The wavefunction is not separate from the particle, but is instead included with the particle. So when you find the particle, that's exactly where it was previously, too. Quantum uncertainty comes into play in this interpretation.
There are others, of course, too, but there's a big one that seems to be gaining traction called decoherence. You might want to look some info on it up, since I won't go into much detail here, since, honestly, I can't -- it's confusing! Basically, if I understand it right, the environment is always interacting with wavefunctions, and nudges a wavefunction in one direction or another, giving the particles their classical appearances -- basically how we interact with our environment on our larger scale of everyday life. For instance, photons are always bouncing and hitting things, "blurring" their wavefunctions, and forcing them to appear here or there. No wavefunction collapse occurs, but wavefunctions "blur."
I hope this helps. I am sure I got some of it wrong, and others can go in depth with it far more than I can.
5. Aug 29, 2011
### kith
Not every interaction is a measurement. There is no collapse in your example. After the collision, you just have two new clouds. The cloud collapses to a point only if a position measurement is performed.
Having understood this, your new question will probably be "what interactions are measurements then?". In the mainstream interpretation of QM (Copenhagen), this question is not fully answered. Measurement takes place, when you're using a classical measurement apparatus to interact with your quantum system. For example, if you use a photo plate to detect photons.
This is unsatisfactory, since a fundamental theory should also be applicable to the process of measurement itself. This means it should be possible to describe the measurement apparatus quantum mechanically as well, which is quite difficult.
In principle, it should be possible to explain the collapse by so-called decoherence. In this framework, a measurement devices constitutes a large environment for the system of interest. Interactions with this environments on a very short timescale can then be approximated by an instantaneous collapse of the corresponding wavefunction. However, this view is not compatible with the mainstream interpretation of QM.
In the end, most confusing questions about QM reduce to the question 'which interpretation of QM is the right one?' and there's still no consensus about it's answer in the physicists community.
Last edited: Aug 29, 2011
6. Aug 29, 2011
### SeventhSigma
In my mind, interaction and measurement are pretty much the same thing, since I consider a measurement an act of interaction.
7. Aug 29, 2011
### K^2
And you're wrong. Measurement and interaction are two different things in Copenhagen Interpretation. Otherwise, superposition would not exist at all. There is always some kind of interaction.
This is why I like MWI. That sort of question doesn't enter. There is no collapse in MWI, and that's that. Of course, there are other questions there.
8. Aug 29, 2011
### SeventhSigma
There's always some kind of interaction due to the fact that wavefunctions extend through all time and space, correct?
Can you give an example if interaction versus measurement? I guess I don't understand because all sorts of processes happen without us measuring them. Things take on real values.
9. Aug 29, 2011
### K^2
A spin-1/2 particle is placed in magnetic field. That spin will precess due to the interaction with the magnetic field, yet its wave function will not collapse, because you are not measuring the actual spin.
10. Aug 29, 2011
### SeventhSigma
That is my question though -- when we say the spin will precess due to its interaction with the field, how are we saying that the wavefunction hasn't collapsed yet? I may be incorrectly assuming that a wavefunction collapse means you change a particle from a state of uncertainty to a state of real confirmation. So for the field to cause the precession in the first place, it needs to somehow interact with the particle.
Or, are you saying that the field affects only certain properties, and these properties are affected along the particle's entire wave function -- but we don't actually know its position until we measure it directly?
11. Aug 29, 2011
### K^2
Suppose, the spin is initially in the sate |chi>=a|up>+b|down>, and is placed in a magnetic field along x. To within constants, the state at time t is Exp(iHt)|chi>, and H~=Sx. Or when expanded:
$$\chi(t)=\left(\begin{array}{cc}cos(\omega t)&sin(\omega t)\\sin(\omega t)&cos(\omega t)\end{array}\right)\left(\begin{array}{c}a\\b\end{array}\right)$$
So |chi>(t)=(a cos(wt) + b sin(wt))|up> + (b cos(wt) + a sin(wt))|down>
Notice that at any given moment, the spin is still in superposition.
12. Aug 29, 2011
### SeventhSigma
I am not familiar with the terminology, but I am assuming that a and b are properties of spin, and the omega-t stuff is the interaction of the magnetic field. The end result is a combination of the two. This corresponds, though, to what I was calling "properties being affected along the particle's entire wave function" (is this inaccurate to say?). Would it be accurate to say that the particle is in many places at once and the field is affecting ALL of those "possible particles"?
What, then, would it look like if we measured it? How would this act of measuring be any different from a field interaction?
13. Aug 29, 2011
### K^2
This is a point-particle. Its total wave function is given by $\chi(t)\phi(x,t)$. Phi is what gives the spatial distribution. The parameters a and b are just fraction of wave function corresponding to spin up and spin down respectively.
In measurement, the wave function collapses to eigen states of the measurement operator. Suppose, you measure spin along z of the particle in initial state |chi> above. The eigen vectors of Sz are |up> and |down> vectors from above. So after measurement, with probability a² the state will be just |up> and with probability b² it will be just |down>
14. Aug 29, 2011
### SeventhSigma
I think I need a bit more education on the basics, because I am having a hard time understanding those kinds of explanations when I am not familiar with the terminology.
You say "measure spin along z of the particle in some initial state" -- what does it mean to physically measure a "spin"? How is a "measurement" in itself not an interaction with a physical entity?
15. Aug 29, 2011
### DrChinese
You are going to find yourself in the land of semantics pretty quickly here. Spin measurements are usually performed without scattering or absorption. You have also field effects to consider, and those of course should be considered physical. But there are no particles touching other particles in the normal sense of the words.
16. Aug 29, 2011
### Delta Kilo
An 'interaction' between two particles can be modelled for example by writing out schroedinger equation for a system of two particles and adding an extra term V(r1,r2) to the hamiltonian, which represents potential energy of particle interaction. Before the interaction, the WF for a system is a product of WFs of individual particles. After the interaction, in general, the WF of a system is no longer separable, the particles are said to be entangled. The same applies when more complex systems interact with each other. As long as you keep track of the details, there is no collapse.
Interaction causing WF collapse are called 'observation' or 'measurement'. They involve quantum system interacting with macroscopic 'observer' (aka 'detector' or 'measurement apparatus'). Macroscopic is understood as having very large (many orders of magnitude) number of degrees of freedom. Clearly we would have a bit of a problem writing out schroedinger equation for it, never mind solving it, so whatever is going on there is shrouded in mystery. Nevertheless, we find that after such interaction the WF of the particle collapses into an eigenstate of a certain projection operator called 'observable', which is specific to the observer. At the same time the macroscopic state of the observer changes according to the eigenvalue associated with the new state of particle's WF. The interesting part here is while schroedinger evolution is linear, the collapse isn't. So at some point somehow the superposition is destroyed and only one eigenstate is chosen seemingly at random with probability proportional to the square of magnitude. Exactly how, when and why this happens is subject to interpretation.
17. Aug 29, 2011
### Ricky116
This is an incredibley helpful post for me in my early research into the problem, thanks!
It is becoming quite a struggle to categorise the different interpretations, would you mind telling me if the bolded section is referring to Bohr's epistemological interpretation? As compared to the Copenhagen interpretation (of which Bohr was instrumental) which appears to be a different concept.
Also, what is the underlined idea(s) referred to as? Thanks!
18. Aug 30, 2011
### jfy4
I don't think that the implication of interaction from measurement $(M\implies I)$ is under question (although maybe some here do), but rather the other direction, that interaction implies measurement, $(I\implies M)$, these are two different things, you need both for equality.
I seem to agree with K^2 here, but I have some question about the interactions.
How would a silver atoms electromagnetic interaction not cause collapse, but the interaction of the silver atom with the florescent screen would cause collapse? Especially since, at the fundamental level, the interaction with the florescent screen is really an interaction with the atoms in the screen, which is really an electromagnetic interaction also!
But, it's also true that the E&M interaction is not solely responsible for the interaction of the silver atom and the screen, the anti-symmetric nature of the wave-functions also plays a role. If this is your rebuttal then I'm even more fascinated, and have to think more on it...
Last edited: Aug 30, 2011
19. Aug 30, 2011
### K^2
That would definitely help. There are a lot of things you can't learn efficiently by just asking questions. Sometimes you need to sit down and listen to a good lecture or read a book.
Measurements are a type of interaction, always. But there are interactions that collapse the state and interactions that do not. In Copenhagen Interpretation, it's not always clear which is which, and that's why more and more physicist switch over to Many Worlds Interpretation. It is more clear on what does and what does not constitute a measurement. You can try reading Wikipedia article on MWI and see if it helps you answer a few of the questions.
Keep in mind that Copenhagen and MWI are equivalent in terms of their prediction. One of these is not better than the other, and you really should understand both to have the better understanding of QM overall.
Because when you get right down to it, collapse doesn't happen when film gets exposed. Collapse happens when you use film for measurement. Again, what constitutes measurement is iffy in Copenhagen. MWI tells you exactly when the apparent collapse should happen.
The Quantum Eraser experiment demonstrates this pretty well. There, the measurement is made, and is then discarded, which prevents the collapse that would have happened due to the measurement. Again, makes little sense in Copenhagen, but perfect sense in MWI.
20. Aug 30, 2011
### Fra
I'm as biased as anyone else but they way I see it, those interactions that don't collapse the state, are those that either are already implicit in the expected evolution (ie. hamiltonian, interaction terms etc), or that doesn't even couple at all to the system.
This is why the unitary evolution of the schrödinger equation is best thought of as an "expected evolution". When the information on which the prior expectations are based are suddenly changed so does the new expectations.
The whole point with updating to NEW information, is that it isn't previously expected. If it was, it would not be new.
In this picture, there is no problem of the collapse at all. The information update is a basic mechanism of how rational inference works. To think you can do away with an information update is irrational if you have this view. It's instead the key to learning.
Instead the problem is another one: to explain the de facto objectivity we all agree upon when it seems at deepest level all we have are observer dependent expectations.
But in that conceptual picture the idea is that interaction between observers, causes an evolution to take place in a way that not all observers (views) are equally preferred at equilibrium (although they are all possible). So at equilibirum we recover de factor objectivity, simply because those that don't comply are destabilised.
Compare with biology. You can easily picture countless perfectly "consistent" life forms, that we nevertheless don't see in nature? Why? They just don't have a place in the current state of the ecosystem and evolution.
So any two systems that are interacting and communicating, tend to negotiate and reach agreements, and if they don't, they will destroy each other. Similar mechanism could explain objectivity of laws of physics, in such a weird apparently solipsist picture I outlined. It's really like Van der Waals / Casimir like effect that takes place in "theory space".
/Fredrik
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https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-10-review-exercises-page-1126/96 | ## Precalculus (6th Edition) Blitzer
a) The probability of winning the prize with one lottery ticket is $\frac{1}{15,504}$. b) The probability of winning the prize with $100$ different lottery tickets is $\frac{25}{3876}$
(a) We know that the number of ways in which $5$ different numbers can be chosen from $1$ to $20$ is given below: \begin{align} & _{20}{{C}_{5}}=\frac{20!}{5!\left( 20-5 \right)!} \\ & =\frac{20!}{5!15!} \\ & =\frac{20\times 19\times 18\times 17\times 16\times 15!}{5!15!} \\ & =15504 \end{align} Therefore, $n\left( S \right)=15504$ Now, there is only one way to win the lottery. Therefore, $n\left( E \right)=1$ Then, \begin{align} & P\left( E \right)=\frac{n\left( E \right)}{n\left( S \right)} \\ & =\frac{1}{15,504} \end{align} Thus, the probability of winning the prize with one lottery ticket is $\frac{1}{15,504}$. (b) We know that the number of ways in which $5$ different numbers can be chosen from $1$ to $20$ is given below: \begin{align} & _{20}{{C}_{5}}=\frac{20!}{5!\left( 20-5 \right)!} \\ & =\frac{20!}{5!15!} \\ & =\frac{20\times 19\times 18\times 17\times 16\times 15!}{5!15!} \\ & =15504 \end{align} Therefore, $n\left( S \right)=15504$ There are $100$ different tickets so, the number of ways of choosing $1$ from $100$ different tickets is ${}^{100}{{C}_{1}}=100$. Therefore, the probability of winning the prize with one lottery ticket is \begin{align} & P\left( E \right)=\frac{n\left( E \right)}{n\left( S \right)} \\ & =\frac{100}{15504} \end{align} Thus, the probability of winning the prize with one lottery ticket is $\frac{25}{3876}$. | {"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": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000097751617432, "perplexity": 332.3973788930496}, "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/1570987750110.78/warc/CC-MAIN-20191020233245-20191021020745-00466.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=135&t=26923 | ## Equations
$\Delta G^{\circ}= \Delta H^{\circ} - T \Delta S^{\circ}$
$\Delta G^{\circ}= -RT\ln K$
$\Delta G^{\circ}= \sum \Delta G_{f}^{\circ}(products) - \sum \Delta G_{f}^{\circ}(reactants)$
Moderators: Chem_Mod, Chem_Admin
Carlos Gonzales 1H
Posts: 50
Joined: Fri Sep 29, 2017 7:05 am
Been upvoted: 1 time
### Equations
Could someone explain what the significance of wmax=deltaG is? Why is is important that maximum work is equal to deltaG? Thanks
Mitch Mologne 1A
Posts: 74
Joined: Fri Sep 29, 2017 7:04 am
### Re: Equations
Delta G represent free energy which is essentially saying the energy that is able to perform work. Thus the max amount of work a system can do corresponds to the free energy of the system.
Tasnia Haider 1E
Posts: 55
Joined: Sat Jul 22, 2017 3:01 am
### Re: Equations
G is defined as the maximum non-expansion work under constant temperature and pressure. If work done by the system is negative, DeltaG < w, since G = H-TS = U+PV-TS.
Then DeltaG is the maximum work that may be done.
Anh Nguyen 2A
Posts: 36
Joined: Fri Sep 29, 2017 7:05 am
Been upvoted: 1 time
### Re: Equations
Only at constant temperature and pressure, wmax=ΔG.
The significance of this equation is that if ΔG of a process at constant temperature and pressure is known then we immediately know how much nonexpansion work it can do. Because in many cases, we are interested in many types of works, not just heating and expanding. For example the break down of glucose in cellular respiration which happens in constant pressure and temperature surrounding and the energy from this reaction is used in nonexpansion work . We can easily calculate the standard ΔG of this reaction and therefore know the amount of maximum work it can do.
Return to “Gibbs Free Energy Concepts and Calculations”
### Who is online
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https://nips.cc/Conferences/2017/Schedule?showEvent=9395 | Poster
Wed Dec 6th 06:30 -- 10:30 PM @ Pacific Ballroom #206
Spectrally-normalized margin bounds for neural networks
Peter Bartlett · Dylan J Foster · Matus Telgarsky
This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight matrices, times a certain correction factor. This bound is empirically investigated for a standard AlexNet network trained with SGD on the MNIST and CIFAR10 datasets, with both original and random labels; the bound, the Lipschitz constants, and the excess risks are all in direct correlation, suggesting both that SGD selects predictors whose complexity scales with the difficulty of the learning task, and secondly that the presented bound is sensitive to this complexity. | {"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": 0.9716302752494812, "perplexity": 2965.7715404584055}, "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-2019-04/segments/1547583659063.33/warc/CC-MAIN-20190117184304-20190117210304-00314.warc.gz"} |
https://brilliant.org/problems/ellipses/ | # Ellipses
Calculus Level 2
What is the equation of the circle centered at $$(3,0)$$ which passes through the foci of the ellipse $$\frac{x^{2}}{9} + \frac{y^{2}}{16} = 1?$$
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https://www.physicsforums.com/threads/2-d-kinematics-problem.168031/ | # 2-D Kinematics Problem
1. Apr 29, 2007
### pingpong240
Here's the question:
An antiaircraft gun fires shells at 200 m/s at a 60° angle. An enemy plane flies directly toward the gun at 300 m/s, 495 m off the ground. How far away (horizontally) must the plane be when the gun fires for the shell to hit the plane?
First off, I know I get two solutions here. I believe it's because of the trajectory of the shell as it hits the plane on the way up or on the way down.
Knowns
v_ix = 200cos(60) = 100
v_iy = 200sin(60)
a_x = 0
a_y = -9.81
y=485 m
Unknowns
x
v_fy
v_fx
t
Equations
y_f = y_i + v_iy * t + .5at^2
x_f = x_i + v_ix * t + .5at2
I'm not sure if I really have to take into account the -300 m/s of the plane, but here's what I've tried so far:
I used the above equation for the y direction to get
485 = 200sin(60)t -4.9t^2
0 = -4.9t^2 + 200sin(60)t-485
I used the quadratic equation to get two times, 3.066 s and 32.2819 s. I tried fitting these into the x direction equation above, but no luck. I may have done something wrong up to this point, but I think that where I go next is where my problems are occurring. I ended up getting 306.61 for the first distance and 3228 for the second, obviously nothing there. Please help me with the rest of the problem!
2. Apr 29, 2007
### denverdoc
Lets call the horizontal distance, that the plane has to be away, x.
Consider the plane moving left to right, the distance at impact from the gunner will be: x1
x1=x-t*(300m/s)
Meanwhile the shell must have traversed horizontally in the opposite direction,
x1=cos(60)*(200m/s)*t. setting the two eqns equal,
x-t(300)=100(t) so x=400(t)
we also need as you discussed,
a time where the altitude is 485. assuming your work is right we get
x=400*(3.07) =1228.
That help?
Last edited: Apr 29, 2007
3. Apr 29, 2007
### pingpong240
Ok so I should factor in the motion of the plane. I tried using that as an answer but it isn't coming out right either. I think my work is right up to this point...Well, if anyone else has any suggestions, please feel free to help out. Shouldn't I consider the plane moving right to left, as if it was moving back to the origin? I have kind of approached this problem that way from the start, as I have designated the gunner at the origin.
Last edited: Apr 29, 2007
4. Apr 29, 2007
### denverdoc
the answer I gave you checks out, what answer are you entering?
distance plane flies: 3.07*300m/s=921m
distance shell flies 3.07*100=307m, sum of two is 921+307=1228
shell is at 485 m at 3.07s. plane is at 485m (constant)
5. Apr 29, 2007
### pingpong240
I'm entering that answer, 1228. I tried entering it more exact, but that doesn't work either. Everything before that seems right doesn't it? Hmm nevermind I think I might have it...I just noticed a very stupid mistake, the vertical distance is 495, not 485.
Last edited: Apr 29, 2007
6. Apr 29, 2007
### pingpong240
Yeah that was the problem. My mistake, you were doing everything right, I'm sorry for making it confusing in the first post with differing quantities for the height. Thank you very much for your help, I understand how to do these types of problems now.
7. Apr 29, 2007
### denverdoc
no sweat, I should have caught that myself.
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https://www.physicsforums.com/threads/curvatures-in-spacetime-explained-by-momentum.73968/ | # Curvatures in spacetime explained by momentum?
1. May 2, 2005
### michael879
ok, so the way the whole "gravity is a curvature of space-time" was explained to me was with a 2d model. If anyone has read flatland (not sure about the name) imagine that world put onto a sphere, which represents the universe. The radius of the sphere is time, and its expanding. Gravity would be like taking a ballon and pushing it in with your finger. From this view it seems a lot like momentum to me though. The sum of all momentum has to be 0, since the big bang was an explosion from a point. Therefore, and point in space-time with mass would have to go slower then points with less or no mass (p = mv). Does this sound possible? or do I have gravity wrong?
2. May 2, 2005
### Starship
I also think that the real question is what causes our abstract spacetime to curve in the first place. The problem with time expanding is that time is an abstract invariant by definition. Since time is abstract, it's physically meaningless. The real focus here is motion, not time.
Last edited: May 2, 2005
3. May 2, 2005
### michael879
But time would basically be how much our universe has expanded since t=0. What I am saying is that momentum might be what causes space to curve. In the flatland case, everything is on a plane wrapped around a sphere. When something with mass slows down (expands slower) it would create a warp in space time like what I believe the "curvature" to be (not positive about what it actually is tho).
4. May 2, 2005
5. May 3, 2005
### pervect
Staff Emeritus
In general relativity, gravity is not a consequence of the universe expanding. The Schwarzschild solution, for instance, represents the solution for gravity in a static non-expanding space-time.
So whatever your theory is, exactly (I really didn't follow it, too many words and not enough mathematics), it can't be exactly equivalent to GR, if your theory can't predict gravity in a non-expanding universe (ala the Schwarzschild solution in GR).
6. May 3, 2005
### michael879
ok my "theory" (Im really just trying to understand relativities representation of gravity) is that the reason these gravity "curvatures" occur is because of momentum. In a spherical spacetime, gravity would look like "dent" or indentations in the surface of the sphere. I was thinking in an expanding universe this could be cause by momentum since everything with more mass would have to move slower then things with less, thereby distorting the space time they exist in.
Can you show me any mathematical proof that gravity exists in a nonexpanding universe? We live in an expanding one so do we rly have any good way of knowing whether gravity can exist in a nonexpanding one?
7. May 3, 2005
### Garth
The standard solution of GR for a local static gravitational field around a spherical mass is the Schwarzschild solution. This is a 'mathematical proof' that gravity exists in a non-expanding universe as that solution is embedded in a Minkowski, flat space and static metric. It is this solution that is being verified in the solar system experiments that have verified GR.
If you model a spherical space in which, "the radius of the sphere is time, and its expanding", you might realise that once time is used in the model then the model cannot expand but has to be static, or frozen as movement would require another time dimension. This would not be an expanding balloon or soap bubble but rather an onion - with layers (like Shrek? All right I have kids!)
This model is proposed in the preprint Self Creation Cosmology - An Alternative Gravitational Theory (page 27 section 9 "A novel representation of space-time geometry").
You might then say that the expansion of the universe and the passing of time are two different observations of the same phenomena, however what that phenomenon actually is would remain a mystery.
Garth
Last edited: May 3, 2005
8. May 3, 2005
### pervect
Staff Emeritus
What Garth said. Basically, in standard GR, we can mathematically model a non-moving object (with no momentum in the standard physical sense of momentum) in a static non-moving space-time (which has no "momentum" even in a non-standard sense which you appear to be using the word). This mathematical solution still exhibits gravity, and is the Schwarzschild solution.
If your theory (whatever it is) cannot duplicate this result, it is not equivalent to standard GR.
Note that the cosmological expansion of the universe is insignificant on the scale of the solar system, and the Schwarzschild solution of GR (the gravitational field of the non-moving sun) is what we use to predict such measurements as
bending of light around the sun
the Shapiro time delay effect for radar signals which pass close to the sun
If you are sitting near a massive object (like the sun), and you are not moving, and the sun is not moving, but the sun is still attracting you to it, it is difficult for me to envision how one can explain this force of attraction (gravity) as being due to "momentum".
9. May 11, 2005
### Blackforest
If you are sitting near a massive object (like the sun), and you are not moving, and the sun is not moving, but the sun is still attracting you to it, it is difficult for me to envision how one can explain this force of attraction (gravity) as being due to "momentum".
What I shall say now is not standart; but imagine two persons hanging a string, a cord; suppose that one of them do not move and and that the other is turning the cord on itself as long as it is possible: at some time the cord will be shorter and shorter... forcing the person who is turning it to come closer to the other one...
Cann't you transpose this image to the fields?
10. May 12, 2005
### Chronos
Momentum is a function of [mass x distance]/[time]. The curvature of spacetime also includes a time element in the calculation. Therefore, it is not useful to describe spacetime in terms of momentum. It is simpler to use the geometrical description [curvature].
11. May 12, 2005
### pervect
Staff Emeritus
In standard GR, momentum is part of the stress-energy tensor and hence contributes to the stress energy tensor (left-hand side of Einstein's equations), and hence to curvature (the right-hand side of Einstein's equations). However, momentum is not the sole cause of curvature. Energy density, and pressure, also contribute terms to the stress-energy tensor.
In addition, as I mentioned, I don't see how an explanation that focuses on momentum as the only cause of gravity can explain the gravity of a non-moving body and a non-moving observer (a very important case).
So my answer is that while momentum does have gravitational effects, in standard theory it's not the sole cause of gravity.
12. May 12, 2005
### Blackforest
Good point for you; absolutely ok with your intervention; and bad point for me (Once more time my bad English...) I was introducing the image of the cord, thinking to angular momentum, not momentum, and this because of my actual own investigations. Sorry for this stupid thing and thank you for the precisions. In fact I was asking me if the polarisation of a EM wave could also be a cause for introducing curvature in space-time; and the way around: if curvature in space-time can be the origin of a kind of polarisation for the EM waves? What do you think of this idea? | {"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": 0.8254033923149109, "perplexity": 710.3944816894682}, "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/1480698541692.55/warc/CC-MAIN-20161202170901-00064-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://neuronstar.cc/spiking-neuron-models/25.significance-of-single-spike/ | # 25. The Significance of Single Spike
Live chat with others.
Terms
1. PSTH: peri-stimulus-time histogram, meaning the probability density of firing as a function of time, after the stimulus.
## One Input Spike
1. Some neuron takes constant input $I_0$ and noise $I_{\mathrm{noise}}$.
2. We inject an extra input on to this neuron.
The factors of importance are
1. amount of noise
2. time course of PSP caused by the injection.
Relation between PSP and PSTH. Basically all well expalained in Fig 7.12:
1. For large noise, PSTH is similar to PSP,
2. For small noise, PSTH is the derivatives of PSP.
Amazing but why?
Read Fig 7.11. Consider two scenarios,
1. with noise, basically noise will trigger a spike,
2. without noise: related to the derivatives of psp because spike can only occur when the derivative is positive.
Understand the significance using homogeneous population model. Linearized equation is applied
where
But why? Because no noise limit means the time course is deterministic thus kernel becomes Dirac delta function. With high noise, the we can not really predict from a spike about the exact time of input but a window of the time of input.
## Reverse Correlation
Reverse correlation: Record the input of the neuron just before it spikes, then average many spikes.
where $\Delta I$ is the stimulus right before the spike at time $t^{(f)}$.
Reverse correlation is related to correlation function $C$ through
where $\nu$ is the firing rate, $\nu=A_0$.
We will find the relation between this reverse correlation and transfer properties of a single neuron, which is described by
We derive the population activity using the transfer function $\hat G(\omega)$
Fourier transform of multiplications leads to a convolution.
With the expression of $A(t)$, we could calculate reverse correlation
The reason we dropped the term $A_0$ is because we assume the input is stochastic i.e., $\langle \Delta I(t)\rangle=0$.
For white noise, we have
Then we find the relation between reverse correlation and transfer 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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9589760303497314, "perplexity": 2385.9822884066207}, "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/1558232257845.26/warc/CC-MAIN-20190525004721-20190525030721-00371.warc.gz"} |
https://wumbo.net/concept/number/ | Number
A number is the symbolic representation of quantity. Humans represent numbers using the bae 10 numeric system. Mathematicians formally represent numbers as sets: set of natural numbers, set of integers, set of real numbers, and so on.
Discrete Numbers
The first tool that numbers are used for is to count how many of something there is. This set of numbers is called the set of natural numbers and is associated with the subject of discrete mathematics.
The basic operations associating with the set of natural numbers are addition, subtraction, multiplication, and division. These form the basis of elementary mathematics.
Addition is a basic operation in mathematics for combining two numbers together. It is a binary operation denoted with the plus symbol with an expression on the left and an expression on the right.
Subraction is a basic arithmetic operation of taking away one number from another number.
Multiplication is a basic arithmetic operation performed on two numbers. Multiplying a number by another number is the same as taking n groups of the other number.
The division operator returns the result of dividing one number by another number.
Negative Numbers
Updating the properties of operations…
Continous Numbers
The functionality of a number is extended beyond the scope of the natural numbers by adding the notion of fractions and the syntax of the decimal point.
Decimal Point
The decimal point is used to separate the whole part of a number from the decimal part. The whole part is represented using number digits to the left of the decimal point. The decimal part is also represented using digits to the right of the decimal point.
Fraction
A fraction is represented using a horizontal bar between two expressions. The expression on top is called the numerator and the expression on bottom is called the denominator.
Scientific Notation
Scientific notation is a notation that scientists use to keep track of the number of significant digits in a number as well as easily recognize the magnitude of a number.
Updating the properties of operations…
Number Sets
A prime number is a number that is only divisible by itself and one. The set of prime numbers is infinitely big. The first prime numbers are 2, 3, 5, 7, 11, ... and continues on forever. | {"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": 0.8271814584732056, "perplexity": 267.8837524898161}, "config": {"markdown_headings": false, "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-2021-17/segments/1618038089289.45/warc/CC-MAIN-20210416191341-20210416221341-00267.warc.gz"} |
https://alanrendall.wordpress.com/2011/10/ | ## Archive for October, 2011
### The Perron-Frobenius theorem
October 20, 2011
The Perron-Frobenius theorem is a result in linear algebra which I have known about for a long time. On the other hand I never took the time to study a proof carefully and think about why the result holds. I was now motivated to change this by my interest in chemical reaction network theory and the realization that the Perron-Frobenius theorem plays a central role in CRNT. In particular, it lies at the heart of the original proof of the existence part of the deficiency zero theorem. Here I will review some facts related to the Perron-Frobenius theorem and its proof.
Let $A$ be a square matrix all of whose entries are positive. Note how this condition makes no sense for an endomorphism of a vector space in the absence of a preferred basis. Then $A$ has a positive eigenvalue $\lambda_+$ and it is bigger than the magnitude of any other eigenvalue. The dimension of the generalized eigenspace corresponding to this eigenvalue is one. There is a vector in the eigenspace all of whose components are positive. Let $C_i$ be the sum of the entries in the $i$th column of $A$. Then $\lambda_+$ lies between the minimum and the maximum of the $C_i$.
If the assumption on $A$ is weakened to its having non-negative entries then most of the properties listed above are lost. However analogues can be obtained if the matrix is irreducible. This means by definition that the matrix has no invariant coordinate subspace. In that case $A$ has a positive eigenvalue which is at least as big as the magnitude of any other eigenvalue. As in the positive case it has multiplicity one. There is a vector in the eigenspace all of whose elements are positive. In general there are other eigenvalues of the same magnitude as the maximal positive eigenvalue and they are related to it by multiplication with powers of a root of unity. The estimate for the maximal real eigenvalue in terms of column sums remains true. The last statement follows from the continuous dependence of the eigenvalues on the matrix.
Suppose now that a matrix $B$ has the properties that its off-diagonal elements are non-negative and that the sum of the elements in each of its columns is zero. Then the sum of the elements in each column of a matrix of the form $B+\lambda I$ is $\lambda$. On the other hand for $\lambda$ sufficiently large the entries of the matrix $B+\lambda I$ are non-negative. If $B$ is irreducible then it can be concluded that the Perron eigenvalue of $B+\lambda I$ is $\lambda$, that the kernel of $B$ is one-dimensional and that it is spanned by a vector all of whose components are positive. In the proof of the deficiency zero theorem this is applied to certain restrictions of the kinetic matrix. The irreducibility property of $B$ follows from the fact that the network is weakly reversible.
The Perron-Frobenius theorem is proved in Gantmacher’s book on matrices. He proves the non-negative case first and uses that as a basis for the positive case. I would have preferred to see a proof for the positive case in isolation. I was not able to extract a simple conceptual picture which I found useful. I have seen some mention of the possibility of applying the Brouwer fixed point theorem but I did not find a complete treatment of this kind of approach written anywhere. There is an infinite-dimensional version of the theorem (the Krein-Rutman theorem). It applies to compact operators on a Banach space which satisfy a suitable positivity condition. In fact this throws some light on the point raised above concerning a preferred basis. Some extra structure is necessary but it does not need to be as much as a basis. What is needed is a positive cone. Let $K$ be the set of vectors in $n$-dimensional Euclidean space, all of whose components are non-negative. A matrix is non-negative if and only if it leaves $K$ invariant and this is something which can reasonably be generalized to infinite dimensions. Thus the set $K$ is the only extra structure which is required. | {"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": 0, "wp_latex": 24, "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": 0.9574361443519592, "perplexity": 68.06228124126274}, "config": {"markdown_headings": true, "markdown_code": false, "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-2018-30/segments/1531676589932.22/warc/CC-MAIN-20180717222930-20180718002930-00416.warc.gz"} |
http://physics.stackexchange.com/questions/48698/what-is-geostationary-orbit-radius/48701 | # What is geostationary orbit radius?
I'm asking this apparently "general reference" question for the simple reason: I was unable to find whether the quoted everywhere "35,786 kilometers (22,236 mi) above the Earth's equator" means "radius" or "altitude above equator." (yes, for it to be geostationary it must be located above the equator, but I'm really not sure if the number includes Earth radius or not).
With Earth radius at Equator equal 6,378 km that's a considerable difference. So, is the orbital radius 35,786km, and altitude 29,390 km or is the altitude 35,768 and radius 42,164 km?
-
It's pretty easy to calculate. For geostationary orbits, the orbital period $T$ should be equal to the rotational period of the Earth $\Omega_E$:
$\matrix { T &=& 2 \pi \sqrt{a^3/\mu} \\ \Omega_E &=& 1\ \mathrm{stellar\ day} }$
$\ \ T=\Omega_E \rightarrow a = \sqrt[3]{\mu \cdot \frac{\mathrm{day}^2}{4\pi^2} } = \sqrt[3]{398600.44 \cdot \frac{86164.099^2}{4 \pi^2}} \approx 42164\ \mathrm{km}.$
Note that this equals the semi-major axis of the orbit, which means that if you want the altitude, you'll have to subtract Earth's equatorial radius:
$h = a - R_E = 42241 - 6378 = 35786 \ \mathrm{km}$
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The altitude is about 36000 km, so the radius of the geostationary orbit is about 42000 km (see, e.g., http://en.wikipedia.org/wiki/Geostationary_orbit ).
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https://astarmathsandphysics.com/o-level-physics-notes/274-thermometers.html | ## Thermometers
Temperature is a measure of how much heat a body contains. It is measured using a thermometer. There are several different types of thermometer. All of them measure temperature, but each one is used over a different temperature range and/or under different conditions,and some are less accurate than others.
If we are to use the thermometer to measure temperature, it must have some physical property that correlates with temperature. Examples include expansion of a column of liquid in a capillary tube –commonly mercury or alcohol
The electrical resistance of platinum wire
The voltage of a thermocouple
The expansion of a bimetallic strip
The pressure of a gas at constant volume An ideal thermometer should have an easy to read – preferably linear - scale
Be safe to use
Sensitive to temperature changes
Be able to measure a wide range of temperatures In any case the thermometer must be calibrated first, so that a specific reading of the physical property indicates a specific temperature. Usually two fixed points are chosen which are always the same under given conditions so can be reliably produced. The Celsius scale for example, has fixed points at the temperature of pure melting ice at atmospheric pressure, which is assigned a temperature of 0°C and at the temperature at which boiling water changes into steam at standard atmospheric pressure, assigned a value of 100°C.Next, the interval between the fixed points is divided into 100 equal divisions for easy reading. Each reading is 1 degree Celsius (°C)
Note the height of mercury in the tube at the ice point, call this x-0 , and the steam point, call this x-{100} .
For any height x of the mercury, the corresponding Celsius temperatureis given by
The Kelvin or Absolute Scale
The Kelvin scale has its zero at absolute zero.
This is the lowest temperature that any substance can reach.
Absolute zero corresponds with –273°C on the Celsius scale
Thermocouples
Thermocouples consist of two wires of different metals joined together at the end to form two junctions
If the junctions are at different temperatures, a voltage is produced. The larger the temperature difference, the larger the voltage produced. Thermocouples are suitable for measuring wide temperature differences, which vary rapidly due to its quick response and the temperature at a point as the wire junctions are very small. The temperature range depends on the two metals used for the wires. They can operate over a very wide range of temperatures from –200°C to 1700°C. To produce a larger voltage, several thermocouples are connected in series (thermopiles)to increase the sensitivity of the instrument. | {"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": 0.921450674533844, "perplexity": 671.0481670951717}, "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/1512948513866.9/warc/CC-MAIN-20171211183649-20171211203649-00175.warc.gz"} |
http://www.hotelsunshine.co.in/rossvale-fc-orska/major-third-frequency-ratio-26d455 | Pythagorean tuning kept the ideal ratios for the octaves, fifths and fourths and tuned the note E with a ratio ${(9/8)}^2$ and the notes A and B with the ratios $(3/2)\times (9/8)$ and $(3/2)\times {(9/8)}^2$. All the notes of the major scale are consonant apart from the second and the seventh. The procedure for that is as follows: • Tune a second string in the ratio 4:5 (major third) to the first. The term overtone should never be mixed with the other terms, as the counting is unequal. (And were gonna use C as the tonic no matter what for better contrast in modes) We have two naturally occurring intervals. In just tuning, the ratio for a major third is 5/4. The octave, ... major third: 6:5: minor third: Index Temperament and musical scales . Two tones are said to be consonant if their combination is pleasing to the ear, and dissonant if displeasing. First I want to explain why I call certain certain intervals major or minor. 9. The pipes are supported 22.4% from the end. The major sixth's ratio is 3:5. In other words, there are two waves of the higher C for every one wave of the lower C, and three waves of the third-harmonic G for every one wave of the fundamental. Skip to main content (Press Enter). The mathematical ratios can be used to calculate the frequency of notes. Let’s take the third for example. If sol on a given scale has a frequency of 396 Hz, (b) What is the ideal ratio frequency of do at the bottom of this scale? The words perfect, diminished, and augmented are also used to describe the quality of an interval.Only the intervals of a second, third, sixth, and seventh (and the compound intervals based on them) may be major or minor (or, rarely, diminished or augmented). The Connection Between Equal Temperament, Frequency Ratios and Beat Ratios The formula for the frequency of the note we will hear is… Do you notice a pattern forming in the formulas? info)). The major and minor triads are used widely in western music. • Tune the third string to the same as the second. The ratio 3/2 simply means that one pitch vibrates 3/2 as fast (three halves as fast) as the other. Clicker Question 9.3 In an equal-tempered 12-note scale, what is the frequency ratio corresponding to a major third? In equal temperament, and most "unequal" temperaments where all 12 major and minor keys are useable, the tempered major third is a long way from the just-intonation 5:4 frequency ratio. The jump frequency ratios which stem from such scattered values of G are highly different of course; in addition they do not fit with the measurement of inert marker shifts in dilute alloys (Limoge [1976a]). Answer to In just tuning, the ratio for a major third is In equally-tempered tuning the ratio is 1.260. Hopefully, because for both open and closed end pipes, we will only give you the formulas for the fundamentals lengths. The simplest … RATIO NAME 1:1 unison 2:1 octave 3:2 fifth 4:3 fourth 5:4 major third 5:3 major sixth 8:5 minor sixth 6:5 minor third In many situations it's a good, practical move to choose, out of the set of all possible musical pitches, a reasonably small set of pitches, called a scale , … For the equal temperament scale, the frequency of each note in the chromatic scale is related to the frequency of the notes next to it by a factor of the twelfth root of 2 (1.0594630944....). The counting is based on the diatonic scale: do, re, mi, fa, so, la, ti, do. Acoustical qualities of each strike tone are characterised using frequency ratios between the partials and fundamental, as well as the spectrogram of the tone. [1971], 40% of the total diffusivity at 858 K is due to divacancies. The frequency ratio 4:5 is called a major third, and 5:6 is a minor third. 3. Frequency ratio = 4:5:6 Similarly, minor triad consists of Perfect fifth and minor third. A) 5/4 B) 81/64 C) (2 1 12)3≈1.189 D) (2 1 12)4≈1.260 E) 12/4 BA. Hidden page that shows all messages in a thread. This is the third harmonic of the closed end pipe. C to E and C to E flat. Remember, the frequency of the second harmonic is two times that of the first harmonic (ratio 2:1). 400 & 450 Hz Frequency ratio 9:8 is a Pythagorean major second or a just major tone. An alternative (unambiguous) term for one tenth of a decade is a decidecade. A) 5/4 B) 81/64 C) (2 . D) (. 400 & 480 Hz Frequency ratio 6:5 is a just minor third 10 400 & 500 Hz Frequency ratio 5:4 is a just major third • Determine the frequency ratio from the ratio of string lengths. info)). This system preserves the ratios of the fourth and fifth but produces a major third, from C to E and a major sixth, from C to A, which sound unpleasant. The table below shows the frequency ratios for notes tuned in the Just and Equal temperament scales. Its ratio is 5:8. There are integer multiples of a certain frequency (fundamental), that are called harmonics, partial tones or overtones. The first overtone is therefore already the second harmonic or the second partial. Tonal Function in Harmonic Scales 2 Melodic prototypes When two notes are played in succession, and their frequency is identical, they are heard to The intervals which are perceived to be most consonant are composed of small integer ratios of frequency. In terms of just musical intervals, these triads can be expressed as whole number ratios of frequencies. The frequency ratios of the musical intervals used in the Just chromatic scale. It can be also defined as the difference between five justly tuned minor thirds and one justly tuned major tenth (of size 5/2, formed by a 2/1 octave plus a 5/4 major third). Hidden page that shows all messages in a thread. It is equal to a frequency ratio of 15625/15552 = 2−6 3−5 56, or approximately 8.1 cents (). Hence the length of the new pipe should be L 0 /(1.25) 1/2 = 26.8 cm. It is important to note that the term 'overtones' does not include the fundamental frequency. Andrew Milne, Dec 2005. With the third string, chords such as the major triad can be played. Intervals and Frequency Ratios Interval Name Note Name Frequency Ratio Unison C 1.000 Minor Second C 1.059 < D= 1.059 Major Second D 1.122 Minor Third D< 1.189 E= 1.189 Major Third E 1.260 Perfect Fourth F 1.335 Tritone F< 1.414 G= 1.414 Perfect Fifth G 1.498 Minor Sixth G< 1.587 A= 1.587 Major Sixth A 1.682 Minor Seventh A< 1.782 B= 1.782 Major Seventh B 1.888 Octave C 2.000 . Major and Minor Triads. The frequency ratio for a major third is 5/4 = 1.25 (see chart for various intervals or table for notes of the equal tempered scale). A major sixth together with a minor third also make an octave. ) … In equal temperament, it is almost 1/6 of a semitone too wide. They are most often used to describe intervals between notes tuned with tuning systems such as Pythagorean tuning, just intonation, and meantone temperament, the size of which can be expressed by small-integer ratios.. If we start the scale on a frequency of 495 Hz for do, what is the frequency for mi (a major third … The actual frequencies vary slightly in other temperaments, but the labeling of the intervals is the same. Using musical intervals to demonstrate superposition of waves and Fourier analysis Table 1. In equally tempered tuning the ratio is 1.260. 1 12) 3 ≈1.189. From an A 440 we calculate the frequency of C#, E and G: A: C# (major third) E (perfect fifth) G (minor seventh) 440: 440 x 1.25 = 550: 440 x 1.5 = 660: 440 x 1.75 = 770: If we divide by the mathematical ratio we obtain descending intervals. You need to remember how to get the rest. Frequency ratio = 10:12:15 However, it is impossible to make every major third and minor third as Just tone on a temperament. A minor sixth is the interval which together with a major third, makes an octave. Major triad consists of Perfect fifth and major third. Its frequency is three times the frequency of the first harmonic (ratio 3:1). Point P_{26}: (100, h(100)) ... Point P_{34}: (200, h(200)) frequency ratio corresponding to a major third? The fraction or ratio 5/4 gives us what musicians call a "major third," that is, E in the key of C. (The E string vibrates 5/4 as fast as the C string.) In just tuning, the ratio for a major third is 5/4. Finally, according to Seeger et al. The septimal major third is 9:7 (435 cents), the undecimal major third is 14:11 (418 cents), and the tridecimal major third is 13:10. Some intervals may be referred to as major and minor.A major interval is one semitone larger than a minor interval. Intervals. HyperPhysics***** Sound : R Nave: Go Back: Consonance and Dissonance . Frequency ratios are used to describe intervals in both Western and non-Western music. Usage. music over the last few centuries have been the major and minor pentatonic and heptatonic (diatonic) scales (Figure 1). If we start a scale on a frequency of 580 Hz for do, what is the difference in frequency for mi (a major third above do) on an equally-tempered piano and a justly-tuned piano? In equally tempered tuning the ratio is 1.260. This is at the node of the vibration. Do, re, mi, fa, so, la, ti, do ratio 9:8 is decidecade... 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On the diatonic scale: do, re, mi, fa, so la...: minor third all the notes of the first you notice a pattern in. Using musical intervals used in the just chromatic scale triad can be used to describe intervals in both Western non-Western! Makes an octave fundamental ), that are called harmonics, partial tones or overtones Fourier table. | {"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": 0.8517590761184692, "perplexity": 2480.4876145069916}, "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/1679296945289.9/warc/CC-MAIN-20230324211121-20230325001121-00057.warc.gz"} |
https://ccssanswers.com/rational-numbers-in-terminating-and-non-terminating-decimals/ | # Rational Numbers in Terminating and Non-Terminating Decimals | How to find if a Number is Terminating or Non-Terminating?
A Rational Number is represented as a fraction. For example, x / y is a rational number. Here, the upper term of the fraction is called a numerator that is ‘x’, and the lower term of the fraction is called a denominator that is ‘y’. Both terms numerator (x) and denominator (y) must be integers. Integer numbers are both positive and negative numbers like -4, -3, -2, -1, 1, 2, 3, 4…etc… The most important thing in the rational numbers is the denominator of the rational number cannot be equal to zero.
Rational Numbers are 2/3, 4/5, 6/7, 8/9, 10/15, 20/4, 125/100, ….etc… Check out the complete concept of Rational Numbers in Terminating and Non-Terminating Decimals below.
## Rational Numbers in Decimal Fractions
By simplifying the rational numbers, we will get the result in the form of decimal fractions. We have two types of decimal fractions. They are
• Terminating Numbers
• Non – Terminating Numbers
When we converted the rational numbers into a decimal fraction, we will get either finite numbers of digits or infinite numbers of digits after the decimal point. If we get the decimal fraction with the finite number of digits, then it is called Terminating Numbers. If we get the decimal fraction with the infinite number of digits after the decimal point, then it is called Non – Terminating Numbers.
### Terminating Number
Example for Terminating Numbers are 1.25, 0.68, 1.234, 2.456, 3. 4567, 5.687, 6.24, 8. 46, ….etc….The below examples are in the form of rational numbers and we need to convert that numbers into the form of decimal numbers.
(1) x / y = 100 / 25 = 0.4
(2) x / y = 644 / 8 = 8.5
(3) x / y = 5 / 4 = 1.25
### Non – Terminating Number
Example for Non – Terminating Numbers are 1.23333, 2.566666, 5.8678888, 3.467777, 4.6899999,…..etc… The below-mentioned x / y fraction indicates the rational numbers and by simplifying it, we will get the decimal numbers.
(1) x / y = 256 / 6 =42.66666…
(2) x / y = 10 / 3 = 3.33333…
(3) x / y = 20 / 9 = 2.222222…
Note: If a rational number (≠ integer) can be expressed in the form p/(2^n × 5^m) where p ∈ Z, n ∈ W, and m ∈ W then the rational number will become a terminating decimal. If not, the rational number becomes the Non – Terminating Numbers.
### Examples of Repeating and Non-Repeating Decimals
1. Find out the conversion of rational numbers to terminating decimal fractions?
(i) 1/4 is a rational fraction of form p/q. When this rational fraction is converted to decimal it becomes 0.25, which is a terminating decimal fraction.
(ii) 1/8 is a rational fraction of form p/q. When this rational fraction is converted to decimal fraction it becomes 0.125, which is also an example of a terminating decimal fraction.
(iii) 4/40 is a rational fraction of form p/q. When this rational fraction is converted to decimal fraction it becomes 0.1, which is an example of a terminating decimal fraction.
2. Find out the conversion of rational numbers to nonterminating decimal fractions.
(i) 1/11 is a rational fraction of form p/q. When we convert this rational fraction into a decimal, it becomes 0.090909… which is a non-terminating decimal.
(ii) 1/13 is a rational fraction of form p/q. When we convert this rational fraction into a decimal, it becomes 0.0769230769230… which is a non-terminating decimal.
(iii) 2/3 is a rational fraction of form p/q. When this is converted to a decimal number it becomes 0.66666667… which is a non-terminating decimal fraction.
### Irrational Numbers
You may see different types of numbers such as real numbers, whole numbers, rational numbers, etc. Now, let us check out the irrational numbers. Irrational numbers are also real numbers that are represented as a simple fraction. There is no repeating or no terminate pattern available in Irrational Numbers. the numbers which do not consist of exact square roots of integers treats as Irrational Numbers. Also, the Irrational Number is pi and that is equal to the value of 3.14.
### Solved Problems on Rational and Irrational Numbers
Add the two rational numbers. For example x / y = 1 / 2 and p / q = 2 / 6
To add the two rational numbers, we need to find out the LCM of the denominators.
That is, LCM of 2 and 6 is 6.
x / y + p / q = 1 / 2 + 2 / 6 = (3 + 2) / 6 = 5 / 6.
#### Multiplication
Multiply the two rational numbers such as 2 / 3 and 5 / 6.
x / y = 2 / 3 and p / q = 5 / 6
x / y X p / q = 2 / 3 x 5 / 6
(xX p) / (y X q) = (2 x 5) / 3 x 6)
px / yq = 10 / 18 = 5 / 9.
#### Subtraction
Subtract the two rational numbers. Here, 5 / 8 and 12 / 5 are rational numbers.
x / y = 5 / 8 and p / q = 12 / 5
x / y – p / q = 5 / 8 – 12 / 5
For subtraction, we need to find out the LCM of denominator values.
LCM of 8 and 5 is 40.
5 / 8 – 12 / 5 = [(5 x 5) – (12 x 8)] / 40 = (25 – 96) / 40 = -71 / 40.
#### Division
To divide the two rational numbers, we need to cross multiply the terms. For example, x / y and p / q are two rational numbers.
(x / y) ÷( p / q) = (2 / 5) ÷ ( 3 / 7)
Cross Multiply the first fraction numerator with second fraction denominator and vice versa.
xq / py = (2 x 7) / (5 x 3 )
xq / py= 14 / 15. | {"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": 0.9145641326904297, "perplexity": 482.1397026193201}, "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/1679296944606.5/warc/CC-MAIN-20230323003026-20230323033026-00220.warc.gz"} |
https://papers.nips.cc/paper/2020/hash/652c208b21f13f6e995bfc1154a1a2e5-Abstract.html | #### Authors
Alireza Mehrtash, Purang Abolmaesumi, Polina Golland, Tina Kapur, Demian Wassermann, William Wells
#### Abstract
Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of parameter values as random perturbations of the optimal parameter set from training by a Gaussian with a single variance parameter. The variance is chosen to maximize the log-likelihood of the ensemble average (𝕃) on the validation data set. Empirically, and perhaps surprisingly, 𝕃 has a well-defined maximum as the variance grows from zero (which corresponds to the baseline model). Conveniently, calibration level of predictions also tends to grow favorably until the peak of 𝕃 is reached. In most experiments, PEP provides a small improvement in performance, and, in some cases, a substantial improvement in empirical calibration. We show that this "PEP effect'' (the gain in log-likelihood) is related to the mean curvature of the likelihood function and the empirical Fisher information. Experiments on ImageNet pre-trained networks including ResNet, DenseNet, and Inception showed improved calibration and likelihood. We further observed a mild improvement in classification accuracy on these networks. Experiments on classification benchmarks such as MNIST and CIFAR-10 showed improved calibration and likelihood, as well as the relationship between the PEP effect and overfitting; this demonstrates that PEP can be used to probe the level of overfitting that occurred during training. In general, no special training procedure or network architecture is needed, and in the case of pre-trained networks, no additional training is needed. | {"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": 0.8672192692756653, "perplexity": 1375.0519190302032}, "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/1623487612537.23/warc/CC-MAIN-20210614135913-20210614165913-00207.warc.gz"} |
http://www.computer.org/csdl/trans/tc/1968/02/01687302-abs.html | Subscribe
Issue No.02 - February (1968 vol.17)
pp: 129-134
ABSTRACT
Abstract?In an earlier paper, Unger showed that any normal mode flow table can be realized by an asynchronous sequential circuit without inserted delays in the feedback paths if and only if the flow table contains no essential hazards. No restrictions were placed on the relative magnitudes of line and gate delays. In this paper, we show that if the line delays are less than the minimum gate delay in the circuit, any normal mode sequential function can be realized without inserted delays. It is also shown that a weaker line delay assumption is sufficient. Two procedures for realizing asynchronous sequential circuits without inserted delays are presented.
INDEX TERMS
Index terms?Asynchronous sequential switching circuits, minimal delay realizations, realizations without delay elements.
CITATION
D.B. Armstrong, A.D. Friedman, P.R. Menon, "Realization of Asynchronous Sequential Circuits Without Inserted Delay Elements", IEEE Transactions on Computers, vol.17, no. 2, pp. 129-134, February 1968, doi:10.1109/TC.1968.227400 | {"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": 0.930877685546875, "perplexity": 3475.7699597118494}, "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/1422122030742.53/warc/CC-MAIN-20150124175350-00162-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/239506/straightening-the-boundary-in-concrete-examples | # Straightening the boundary in concrete examples
Let $\Omega \subset \mathbb{R}^d$ be open and with $C^1$ boundary $\Gamma$. For any given point $x_0 \in \Gamma$ we know there's a neighborhood where $\Gamma$ is the graph of some $C^1$ function $\gamma : \mathbb{R}^{d - 1} \longrightarrow \mathbb{R}^d, x' \longmapsto \gamma ( x') = x_d$. We can use it to straighten the boundary with the local diffeomorphism
$$T ( x', x_d - \gamma ( x')) = ( x', x_d - \gamma ( x')),$$
and its differential $D T$ has a nice $( d - 1) \times ( d - 1)$ identity matrix as first block and a bottom row $\nabla T_d = ( - \nabla \gamma, 1)$ which is proportional to the vector $\vec{n}$ normal to $\Gamma$ at each point, say $c ( x) \vec{n} ( x) = \nabla T_d ( x)$, where $c ( x) = - \| \nabla T_d ( x) \|$.
For my calculations in concrete examples with parametrized domains, etc., I want $\nabla T_d$ to actually be the outward pointing normal: I need this $c ( x)$ to be $- 1$. If I try to impose the condition after constructing $T$, then I have to integrate expressions which I'm just not capable of. I can try to throw it at some symbolic integration software, but there has to be some other way, right? In almost every book on PDEs it's stated that this $T$ may be normalized so as to have the property I mention. But how?
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I think the implicit function theorem could give you the answer. – Jose27 Nov 18 '12 at 0:10
With the implicit function theorem I can infer existence of $\gamma$ representing locally $\Gamma$ as the nullset of some $F ( x', x_N) = 0$ to which the theorem applies. Then using the chain rule I see that $$\frac{\partial F}{\partial x_i} = - \frac{\partial F}{\partial x_d} \frac{\partial \gamma}{\partial x_i},$$ and this allows me to write the normal vector using this function $F$, but I don't see how I can use this to explictly normalize my transformation $T$ with actual coordinates. – AnCo Nov 18 '12 at 0:29
Yeah, I was being too optimistic. I don't think this is an easy problem: For curves the property you need is given by using the arc-length parametrization which I don't think has a higher dimensional analog. Could you give a reference where this statement is used? – Jose27 Nov 18 '12 at 1:24
It turned out it was easier than we both thought… As to the reference, I admit I can't give any without looking it up, but I've seen it stated often enough and thanks to Lukas Geyer we now know it's definitely true :) – AnCo Nov 18 '12 at 16:51
If $\phi(x')$ denotes the $d$-th component of the normal vector at $(x',\gamma(x'))$, then first of all it is immediate from the graph structure that $\phi(x') \ne 0$. Let $S(x',y_d) = (x',\phi(x')y_d)$, and write $\tilde{T} = S \circ T$. Then $\tilde{T}$ is a $\mathcal{C}^1$ diffeomorphism which straightens the boundary, and it is normalized, as can be checked easily with the chain rule: $$DS (x',y_d) = \left[ \begin{array}{c|c} \mathrm{Id} & 0 \\ \hline \nabla \phi(x') y_d & \phi(x') \end{array} \right]$$ In particular $$DS (x',0) = \left[ \begin{array}{c|c} \mathrm{Id} & 0 \\ \hline 0 & \phi (x') \end{array} \right]$$ So on the boundary $\Gamma$ you get $$D\tilde{T}(x',\gamma(x')) = DT(x',\gamma(x')) DS(x',0) =\left[ \begin{array}{c|c} \mathrm{Id} & 0 \\ \hline -\phi(x')\nabla \gamma(x') & \phi (x') \end{array} \right]$$ I.e., the last row is a multiple of the outer normal, and since the $d$-th entry is the same, it is equal to the outer normal.
I just realized that there is a little regularity problem with this proof if you only have $\mathcal{C}^1$ boundary, since then you only know that $\phi$ is continuous, not necessarily differentiable. You might have to assume $\mathcal{C}^2$ boundary for it to work. – Lukas Geyer Nov 19 '12 at 18:59
The Gauss map in coordinates involves first partial derivatives, so if the surface is $\mathcal{C}^k$, its Gauss map should be $\mathcal{C}^{k-1}$. – Lukas Geyer Nov 20 '12 at 0:49
Ok. I'll just stick with $C^2$. Thanks for the help! – AnCo Nov 21 '12 at 22:15 | {"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": 0.9748618602752686, "perplexity": 165.0406373007488}, "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/1410657137906.42/warc/CC-MAIN-20140914011217-00153-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/124695/is-there-a-geometric-interpretation-of-f-p-f-pn-and-overlinef-p | # Is there a geometric interpretation of $F_p,\ F_{p^n}$ and $\overline{F_p}?$
I have been doing some exercises about finite fields lately and I think I've obtained some understanding of what they are. What seems to be missing though is some kind of picture. Learning to work with complex numbers seems pretty much equivalent to learning what the field operations do on the complex plane geometrically. At least, it makes things much, much easier. Is there a way to imagine finite fields and their algebraic closure geometrically?
I was thinking that perhaps I should look at $F_p$ as the set $\mathbb C_p$ of $p$-th roots of $1$ in $\mathbb C.$ But it doesn't seem to work very well. The additive structure of $F_p$ translates well (via an isomorphism) to the multiplicative structure of $\mathbb C_p.$ But transporting the multiplicative structure $F_p$ to $\mathbb C_p$ via the same function gives something I can't really visualize. It's the operation $\star$ given by the following formula:
$$\left(\cos\frac{2k\pi}{p}+i\sin\frac{2k\pi}{p}\right)\star \left(\cos\frac{2l\pi}{p}+i\sin\frac{2l\pi}{p}\right)=\left(\cos\frac{2kl\pi}{p}+i\sin\frac{2kl\pi}{p}\right).$$
But even if it's the right way to do it, it still doesn't immediately give a way of seeing $F_{p^n}$ there too, let alone the algebraic closure $\overline{F_p}.$ And of course, it would be good to have an interpretation of $\overline{F_p}$ in which all $F_{p^n}$ for $n\in \mathbb N$ could be easily distinguished.
So my question is
Are there any useful ways of interpreting the finite fields and their algebraic closures geometrically? If so what are they?
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en.wikipedia.org/wiki/… – Qiaochu Yuan Mar 26 '12 at 15:31
@QiaochuYuan Thank you for the link. I've only heard of projective spaces in the context of complex analysis but I didn't really understand it. Unfortunately, I don't understand whether (and how exactly) what's on that Wikipedia page answers my question. I see that what they call the Fano plane is somehow connected to the field $F_2.$ They say it can be seen as the set of non-zero vectors in the three dimensional vector space over $F_2.$ Can I see $F_8$ there? – user23211 Mar 26 '12 at 15:59
You can define projective spaces over any finite field, but of course they'll be bigger. In projective spaces over a field one can do projective geometry, and as it turns out this geometry is enough to recover the addition, multiplication, and division on the underlying field. I don't know a good reference for this, though. – Qiaochu Yuan Mar 26 '12 at 16:05
@QiaochuYuan I see. So this must be the right way do look at this then. If it's imossible to explain it in full generality here, I will accept an answer giving a practical way of using these spaces to visualize a finite field, without the underlying theory. I think I might have trouble absorbing this much theory anyway... – user23211 Mar 26 '12 at 16:17
@ymar: See M. K. Bennett's book Affine and Projective Geometry, especially Chapter 4. – KCd Mar 26 '12 at 22:15
The short answer is that the visualizations of finite fields are different from what you seem to want. I will elaborate a bit, though. It is not clear that anything I suggest is really a "visualization" or a "geometric point of view". But they do provide a way of getting your hands on a finite field starting from structures inside the complex numbers.
Let's first look at the prime field $F_p=\mathbf{Z}/p\mathbf{Z}$. As you observed, we can faithfully map the additive structure of $F_p$ to the unit circle via the (obviously well-defined) map $$e:m+p\mathbf{Z}\mapsto e^{2m\pi i/p}.$$ This is a homomorphism from the additive group of $F_p$ to the multiplicative group $\mathbf{C}^*$ of non-zero complex numbers, or $$e(x+y)=e(x)e(y)$$ for all $x,y\in F_p$. In other words $e$ is what is called an additive character of $F_p$. As you observed, it doesn't really reflect the multiplicative structure of $F_p$ at all. This was to be expected, as we used the multiplicative structure of $\mathbf{C}^*$ to represent the additive structure of $F_p$, so naturality was broken down. Characters and character sums do play a role in the study of number theoretic properties of finite fields.
If we want to take a geometric viewpoint of the prime field $F_p$, $p$ a prime, then I would stick to the number line $\mathbf{R}$. Except that I really need restrict to the integers $\mathbf{Z}$, and then go to the quotient ring, or equivalently identify the integers within a coset of $p\mathbf{Z}$.
You can identify some finite fields by similarly identifying cosets of the ideal $p\mathbf{Z}[i]$, where $$\mathbf{Z}[i]=\{a+bi\mid a,b\in\mathbf{Z}\}.$$ Geometrically you identify here points $a+bi$ and $a'+b'i$, iff $p\mid (a-a')$ and $p\mid (b-b')$, or instead of "wrapping the line around a circle" you "wrap the plane around a torus". An immediate word of warning. This only works, if $p\equiv-1\pmod4$. So you can construct $F_9$ in this wasy, but you cannot construct $F_4$ or $F_{25}$. One of the reasons why this construction does not work in those cases is that while the resulting quotient ring has the desired number of elements, it is not a field because it has zero divisors. For example, $(1+i)^2=2i\equiv 0 \pmod{2\mathbf{Z}[i]}$ in the ring $\mathbf{Z}[i]/2\mathbf{Z}[i]$, and $(2+i)(2-i)=5\equiv 0$ in the ring $\mathbf{Z}[i]/5\mathbf{Z}[i]$ (I plead guilty to the standard abuse of identifying a number with the coset it represents, so I really meant to write that the square of the coset $(1+i)+2\mathbf{Z}[i]$ is equal to zero in the first example above.
To get fields like $F_4$ and $F_{25}$ we need quotient rings of other lattices of complex numbers. Let $\omega=e^{2\pi i/3}=(-1+i\sqrt3)/2$. Then $\mathbf{Z}[\omega]=\{a+b\omega\mid a,b\in\mathbf{Z}\}$ is a ring (a subring of the complex numbers), and we get (requires some checking) $$F_4=\mathbf{Z}[\omega]/2\mathbf{Z}[\omega]\qquad\text{and}\qquad F_{25}=\mathbf{Z}[\omega]/5\mathbf{Z}[\omega].$$ But a construction for all the finite fields (let alone the algebraic closure) in this way is a bit trickier. The field $F_{p^n}$ is an $n$-dimensional space over $F_p$. A lattice in the complex plane is naturally (at most) a two-dimensional thing, so when $n>2$ it gets dirty. No more wrapping this nicely. It can be done by using certain subrings of $\mathbf{C}$ namely rings of integers of an algebraic number field, but some algebraic number theory is needed. See this question for a description.
We can think of a finite field using roots of unity. But the (non-zero) elements of $F_q$, $q=p^n$, $p$ a prime, are roots of unity of order that is a factor of $q-1$. So, if we want to represent ther multiplicative structure, we need to use those roots of unity. For example, we can also view $F_7$ as the quotient ring $\mathbf{Z}[\omega]/(3+\omega)\mathbf{Z}[\omega]$. When we do that the non-zero elements of $F_7$ are represented by the cosets of the sixth roots of unity, i.e. the cosets $(-\omega)^j+(3+\omega)\mathbf{Z}[\omega]$. This is similar in spirit to the discussion in the linked question.
Things become more uniform, when instead of using the complex numbers we use the $p$-adic integers $\mathbf{Z}_p$ (not to be confused with the residue class ring $\mathbf{Z}/p\mathbf{Z}$. If $q=p^n$, and $\zeta$ is a root of unity of order $q-1$, then we have an isomorphism $$F_q=\mathbf{Z}_p[\zeta]/p\mathbf{Z}_p[\zeta]$$ between the finite field $F_q$ and the quotient ring of an extension ring of the $p$-adic integers. That's a rather different animal, and this last paragraph may be meaningless to you unless you have the right background. The $p$-adic integeres themselves cannot be readily visualized geometrically, because the metric there is very weird.
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I'm afraid this does not help at all in seeing $F_p$ inside $F_{p^2}$ (much less the other inclusions), and the algebraic closure has really dropped out of sight. – Jyrki Lahtonen Mar 26 '12 at 16:32
Concerning the last sentence: the $p$-adic integers definitely can be visualized geometrically, as a subset of C with the induced topology (but its ring structure doesn't align with that in C at all). Take a look at Al Cuoco's article "Visualizing the p-adic integers," Amer. Math. Monthly, 98 (1991), 355-364. – KCd Mar 26 '12 at 22:21
Thank you Jyrki and @KCd – user23211 Mar 28 '12 at 1:11
My own idiosyncratic way of looking at these things: Remember that the multiplicative group of ${\mathbb{F}}_{p^n}$ is cyclic, so you could, if you wished, model this also as a group of roots of unity in $\mathbb{C}$. This helps tremendously in doing hand computations in the finite field, by the way, since once you find a generator (“primitive root”) and write down all its powers, you have a nice log table for quick multiplication. At any rate, these finite cyclic groups all fit together very nicely, so that the multiplicative group of the algebraic closure of your finite field of characteristic $p$ is (noncanonically) isomorphic to the group of all $m$-th roots of unity in $\mathbb{C}$ for $m$ ranging through the integers prime to $p$.
Edit: I originally said that the group in question was also isomorphic to ${\mathbb{Q}}_p/{\mathbb{Z}}_p$, and this was quite wrong.
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Thank you for your answer. What does noncanonically isomorphic mean? – user23211 Mar 26 '12 at 21:32
“Noncanonical” in this case means that among the (†) uncountably many isomorphisms that exist, there is nothing to prefer one over another. (†) That there is even one depends on a weak kind of Axiom of Choice; but once you have one, you see that the set of all is a free ${\mathbb{Z}}_p$-module of rank one. – Lubin Mar 29 '12 at 4:50
May I ask for a reference? I would like to see a proof of this, because there are still things that are new to me in what you said. If I had a longer text I could work with it. – user23211 Mar 29 '12 at 7:27
For a reference, I would always give Lang's Algebra. Send me an e-mail, and we can discuss your question much more fully. But to go into detail in comments here seems inefficient. – Lubin Apr 1 '12 at 23:51
I see that I blundered in trying to describe the set of isomorphisms from the multiplicative group in question to ${\mathbb{C}}^*$. It’s far more complicated than what I said in my first comment. (Apologies!) – Lubin Apr 27 '12 at 5:55 | {"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": 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": 0.8405057191848755, "perplexity": 169.39633771865007}, "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-2016-26/segments/1466783397873.63/warc/CC-MAIN-20160624154957-00042-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://practice-questions.maxtute.com/CBSE-Class-10-Math/past-years-board-papers/2018/trigonometric-ratios-complementary-angles-19-A.shtml | # CBSE Class 10 Math Question Paper 2018 | Q19A
∴ Hypotenuse = $$sqrt{3k^2 + 4k^2}\\$ = 5k #### Step 2: Compute values of sin θ and cos θ sin θ = $\frac{\text{opposite side}}{\text{hypotenuse}}$ = $\frac{3k}{5k}$ = $\frac{3}{5}$ cos θ = $\frac{\text{adjacent side}}{\text{hypotenuse}}$ = $\frac{4k}{5k}$ = $\frac{4}{5}$ #### Step 3: Compute the value of the expression $\frac{\text{4sinθ - cosθ + 1}}{\text{4sinθ + cosθ - 1}}$ = $\frac{4 ×$3/5$ - (4/5)) + 1}{4 × (3/5) + (4/5)) - 1}) = $$frac{$12/5$) - (4/5)) + (5/5)}{(12/5)) + (4/5)) - (5/5)}) = $$frac{$13/5$}{(11/5)})
$\frac{\text{4sinθ - cosθ + 1}}{\text{4sinθ + cosθ - 1}}$ = $\frac{13}{11}$
###### Try CBSE Online CoachingClass 10 Maths
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http://etna.mcs.kent.edu/volumes/2001-2010/vol24/abstract.php?vol=24&pages=88-93 | ## Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey
José M. Rodríguez, Venancio Álvarez, Elena Romera, and Domingo Pestana
### Abstract
In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in Approximation Theory. We also find conditions under which the evaluation operator is bounded.
Full Text (PDF) [154 KB]
### Key words
Sobolev spaces, weights, orthogonal polynomials
### AMS subject classifications
41A10, 46E35, 46G10
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http://www.machinedlearnings.com/2011/06/dimensional-analysis-and-gradient.html | ## Thursday, June 2, 2011
### Dimensional Analysis and Gradient Descent
Consider learning a linear predictor according to a loss function $l$, \begin{aligned} p^{(t)} &= w^{(t) \top} x^{(t)}, \\ w^{(t+1)} &= w^{(t)} - \eta \frac{\partial l}{\partial p} x^{(t)}. \end{aligned} Suppose the optimal weight vector is $w^*$. If all the inputs are scaled by a constant amount $r$, then the optimal weight vector is $w^* / r$, and it would be nice if the learning algorithm produced output that respected this identity. A more general way to think along these lines is dimensional analysis.
Assume predictions have dimensions $\rho$ and inputs have dimensions of $\chi$; then weights must have dimensions of $(\rho / \chi)$ for the prediction equation to work out. Assuming loss has dimensions $\lambda$ that means the learning rate $\eta$ must have units of $\rho^2 / (\lambda \chi^2)$ for the update equation to work out. What that means in practice is, if we had a sequence of weight vectors which converged somewhere we liked, and we then changed all the inputs such that they were doubled, the learning rate must be quartered, such that the entire sequence of generated weight vectors is halved, such that the entire sequence of predictions is identical.
So these ideas are already incorporated into Vowpal Wabbit (and actually that is how I became aware of them: I asked the Vowpal team to help me understand what I saw in the source code). In particular the $\eta$ specified on the command line is normalized by $x^{(t) \top} x^{(t)}$, corresponding to the $(1 / \chi^2)$ portion of the $\eta$ dimensionality; although, this does not address the $\rho^2 / \lambda$ portion. (Why does that matter? Suppose I created a new loss function which was twice the output of another loss function; the learning rate specified on the command line would have to be reduced by half.)
Working on the dyadic models I had to figure out how to generalize this, so I started to think about it. Normalizing by $x^{(t) \top} x^{(t)}$ definitely adjusts for a global scaling of the input, but what if just one dimension of the input were scaled? This starts to get into the realm of pre-conditioning which leads to the adaptive approach of Duchi, Hazan, and Singer aka DHS (also simultaneously developed in McMahan and Streeter but I will focus on DHS) . There they define a matrix $G^{(t)} = \mathrm{diag} \left( 1 / \sqrt{\sum_{s \leq t} (g^{(s)}_i)^{2}} \right)$ and use an update $w^{(t+1)} = w^{(t)} - \eta \frac{\partial l}{\partial p} G^{(t)} x^{(t)},$ where $g^{(s)} = (\partial l / \partial p^{(s)}) x^{(s)}$. With this update $G^{(t)}$ has dimensions of $\rho / (\lambda \chi) \ldots$ getting closer! Unfortunately $\eta$ still is not dimensionless, having dimensions of $\rho / \chi$. Note the optimal choice of $\eta$ in Corollary 1 of DHS is proportional to $\max_t ||w_t - w^*||_{\infty}$ which has units of $(\rho / \chi)$. In other words, if all the inputs were doubled, we would still have to reduce the previously optimal learning rate by half to get optimal behaviour.
This leaves open the question of what is lying around with units $(\rho / \chi)$ that could be used to normalize an $\eta$ such that the parameter specified on the command line is dimensionless. Anything that varies with $t$ is outside the scope of the analysis in DHS but I'll ignore that for now. Two things suggest themselves: $1/||x^{(t) \top} x^{(t)}||_p$ and $1 / (x^{(t) \top} G^{(t)} x^{(t)})$. (These have units of $1/\chi$ but that's getting closer). They have different properties.
Intuitively what gives the adaptive learning algorithms their edge is that they are more conservative on frequently occurring features and more aggressive on rarely occurring features. With $||x^{(t) \top} x^{(t)}||_p$ normalization, if an example is encountered with features that have all been seen and trained extensively before, the effective learning rate will be small and hence the change in the prediction will be small relative to if this example were seen earlier in the training sequence. Conversely, with $x^{(t) \top} G^{(t)} x^{(t)}$ normalization, if an example is encountered with features that have all been seen and trained extensively before, the effective learning rate will be normalized to compensate, such that the change in the prediction will not be small relative to if this example were seen earlier in the training sequence. On the other hand for an example with a mixture of novel and frequent features that occurs later in the training sequence, the update will have a greater impact on novel feature weights than frequent feature weights with either normalization scheme, relative to if the example had occurred earlier in the training sequence.
There are other things lying around with dimensionality $(\rho / \chi)$. One of the key insights of the adaptive learning approaches is to use information from the entire history of inputs, and not just than the current input, to drive the learning. One thing that is lying around that summarizes all the inputs so far is the weight vector. The optimal weight vector in Corollary 1 of DHS is proportional to $\max_t ||w_t - w^*||_{\infty}$, and since $w_0 = 0$, this is approximately $||w^*||_\infty$. One (potentially horrible!) approximation of $w^*$ is the current weight vector. It is an especially bad approximation at the beginning when it is zero, so I considered scaling the supplied $\eta$ by $\max (1, ||w^{(t)}||_\infty)$, where I only consider the components of $w^{(t)}$ that have corresponding non-zero values of $x^{(t)}$.
#### An experiment
Lots of ideas, so I decided to run an experiment. I have a set of dozens of millions of tweets that have been labelled according to the gender of the person who wrote the tweet. The input vectors have interesting norms due to varying numbers of tokens in the tweets. I trained using a constant learning rate (which vowpal scales by $x^\top x$) and the DHS adaptive learning algorithm scaled by different values. I only do one pass over the data and I'm reporting progressive validation hinge loss on the training set. I used $\eta = 1$ on the command line for all these tests. $\begin{array}{c|c|c} \mbox{Method } &\mbox{ Loss } &\mbox{ Comments } \\ \hline \mbox{Best constant } &\mbox{ 0.722 } &\mbox{ More women than men on Twitter (why?) } \\ \mbox{Non-adaptive } &\mbox{ 0.651 } &\mbox{ VW normalizes by ||x^{(t)}||^2_2 in this case } \\ \mbox{Adaptive ||x^{(t)}||_1 normalization } &\mbox{ 0.588 } & \\ \mbox{Adaptive ||x^{(t)}||_2 normalization } &\mbox{ 0.554 } & \\ \mbox{Adaptive ||x^{(t)}||_\infty normalization } &\mbox{ 0.579 } & \\ \mbox{Adaptive x^{(t) \top} G^{(t)} x^{(t)} normalization } &\mbox{ 0.621 } &\mbox{ Much worse than alternatives! } \\ \mbox{Adaptive \max (1, ||w^{(t)}||_\infty) scaling } &\mbox{ 0.579 } & \\ \mbox{Adaptive \max (0.1, ||w^{(t)}||_\infty) scaling } &\mbox{ 0.562 } & \\ \mbox{Adaptive \max (1, ||w^{(t)}||_\infty) scaling } &\mbox{ 0.579 } & \mbox{Ignoring const feature in ||w^{(t)}||_\infty} \\ \mbox{Adaptive \max (0.1, ||w^{(t)}||_\infty) scaling } &\mbox{ 0.560 } & \mbox{Ignoring const feature in ||w^{(t)}||_\infty} \\ \end{array}$
In practice trying $\max (z, ||w^{(t)}||_\infty)$ for $z \leq 0.1$ yielded the same results. I thought this might be because of the weight of the constant feature (which is always present with value 1; so in a sense, it has a fixed scale which does not change with the input) so I tried not using the constant feature when computing $||w^{(t)}||_\infty$ but the results were about the same.
So this experiment suggests normalizing by the adaptive norm $x^{(t) \top} G^{(t)} x^{(t)}$ really does undermine the effectiveness of the adaptive strategy. Otherwise it's hard to really prefer one strategy over another on the basis of this one experiment. Having said that my personal favorite is the $\max (0.1, ||w^{(t)}||_\infty)$ scaling since it is directly motivated from the regret analysis and has the correct units.
Now I need to return to my original goal: figuring out how to normalize the learning rate when training a dyadic model.
1. From John Langford via personal communication: "I kind-of prefer the ||x||_2 normalization, which appears to work well in your experiments and looks less hacky. However, your experiments are a little bit skimpy because I'm willing to set default optimization parameters. For example, in VW right now the default is eta=10, which makes it very aggressive in the beginning. If it's reasonably convenient, can you do a search over eta = 32,16,8,4,2,1,0.5,0.25,0.125 for each of the algorithms and tell us the minimum error rate? (Feel free to add as a comment.)"
2. I tried learning rates from 2^5 to 2^-3 inclusive. i report the best result for each method 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": 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": 0.9072893857955933, "perplexity": 423.91048195027327}, "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-2021-21/segments/1620243989914.60/warc/CC-MAIN-20210516201947-20210516231947-00418.warc.gz"} |
https://socratic.org/questions/what-is-the-molar-mass-of-fe-2o-3-4h-2o | Chemistry
Topics
# What is the molar mass of Fe_2O_3, 4H_2O?
Jun 24, 2017
$231.78$ $\text{g/mol}$
#### Explanation:
We're asked to find the molar mass of iron(III) oxide tetrahydrate, $\text{Fe"_2"O"_3· 4"H"_2"O}$.
To find the molar mass of a substance, we
1. Refer to a periodic table for the atomic masses of the elements (i.e. iron's mass is $55.85$ color(red)("amu"); this value is also the molar mass of that element ($\text{iron} = 55.85$ $\textcolor{red}{\text{g/mol}}$)
2. Multiply the molar mass of each element by however many atoms of that element are in the compound.
3. Sum the total, and that will be the molar mass of the entire compound
(1)
The molar masses of each element in this compound are
• $\text{Fe}$: $55.85$ $\text{g/mol}$
• $\text{O}$: $16.00$ $\text{g/mol}$
• $\text{H}$: $1.01$ $\text{g/mol}$
(2)
Now, let's multiply these values by the number of each element in the compound:
• $\text{Fe}$ : overbrace((2))^"2 iron atoms in compound"(55.85color(white)(l)"g/mol") = color(blue)(111.70 color(blue)("g/mol"
• $\text{O}$: overbrace((7))^"3 in iron oxide, 4 in water"(16.00color(white)(l)"g/mol") = color(green)(112.00 color(green)("g/mol"
• $\text{H}$: overbrace((8))^"8 hydrogen atoms in compound"(1.01color(white)(l)"g/mol") = color(purple)(8.08 color(purple)("g/mol"
(3)
Lastly, to find the molar mass, we simply sum the total of the individual elements/ values:
color(blue)(111.70 color(blue)("g/mol" + color(green)(112.00 color(green)("g/mol" + color(purple)(8.08 color(purple)("g/mol" = color(red)(231.78 color(red)("g/mol"
##### Impact of this question
716 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": 33, "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": 0.8492771983146667, "perplexity": 3217.481732966614}, "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-2020-40/segments/1600400192778.51/warc/CC-MAIN-20200919142021-20200919172021-00706.warc.gz"} |
http://www.talkstats.com/tags/interpret-scatterplott/ | # @interpret scatterplott
1. ### Is my scatterplot homoscedastic/heteroscedastic?
Did a assumption test for a hierachical regression analysis and got this result on a test for homoscedasticity. Does it show homoscedasticity for the residuals? Can I trust this model if it is not? | {"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": 0.8022910356521606, "perplexity": 3949.339732165304}, "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-2021-10/segments/1614178369553.75/warc/CC-MAIN-20210304235759-20210305025759-00437.warc.gz"} |
https://dayline.info/relationship-between-and/relationship-between-energy-and-light.php | # Relationship between energy and light
### The Relationship between Energy and Mass
In high school, doing modern physics, and was struck by a thought about light, energy of a photon and the "speed limit" of relativity. I'm probably. Einstein's photons of light were individual packets of energy having many of the characteristics of particles. Recall that the collision of an electron (a particle) with . Photon energy is the energy carried by a single photon. The amount of energy is directly Photon energy is solely a function of the photon's wavelength. In other words, two photons of light with the same color and therefore, same frequency, will have the same This equation is known as the Planck-Einstein relation.
Albert Einstein and Niels Bohr who were great friends discussed these issues and more often over a period of many years, especially in the late 's and early 's. Their discussions are still important enough to merit historical study today. Every year, several books are published which delve into one or more of the implications of "wave-particle duality.
Unit 6 - Relationship Between Frequency, Energy & Wavelength
As one value say the wavelength goes up, the other value the frequency must go down. Because the product of the two must always equal the same value, c, which is a constant. As the frequency increases, so does E. Because h remains constant. I left a couple guard digits in the answer. Also, notice that the wavelength is not in scientific notation. This is because I made a silent conversion from nm to m.
I didn't bother to convert it because it wasn't needed. Otherwise, the propagated waves would be out of phase, resulting in a net decrease in amplitude and causing destructive interference. Higher energy levels would have successively higher values of n with a corresponding number of nodes.
Standing waves are often observed on rivers, reservoirs, ponds, and lakes when seismic waves from an earthquake travel through the area.
The waves are called seismic seiches, a term first used in when lake levels in England and Norway oscillated from side to side as a result of the Assam earthquake of in Tibet.
They were first described in the Proceedings of the Royal Society in when they were seen in English harbors and ponds after a large earthquake in Lisbon, Portugal. Seismic seiches were also observed in many places in North America after the Alaska earthquake of March 28, Those occurring in western reservoirs lasted for two hours or longer, and amplitudes reached as high as nearly 6 ft along the Gulf Coast.
### The relationship between light, energy and relativity | Physics Forums
And equivalences and symmetries are important phenomena in SpaceTime, but intensity and amplitude doesn't apply to a single photon at all. If you look at Maxwell's equations light becomes a electromagnetic radiation consisting of oscillations waves in the electric and magnetic fields, 'perpendicular' at a right angle to each other.
Waves describe polarization, refraction, interference quenching and reinforcing itself, via two waves interfering etc, but they do not tell you about photons. And that's where 'equivalences' becomes important. And so this, to me that is, is all about trying to find a common ground for the concept of photon fitting the concept of waves.
This is a good description of that. The intensity of the beam is proportional to the number of photons.
## Light: Electromagnetic waves, the electromagnetic spectrum and photons
The polarization of light that is explained by Maxwell is related to the quantum-mechanical concept of spin. You can see the photon as a little top spinning around an axis that coincides with the direction of propagation.
• The relationship between light, energy and relativity
• Photoelectric effect
• Photon energy
But while in classical mechanics an object can spin only in one direction at a time, in quantum mechanics you have the paradoxical and counter-intuitive fact that an object can spin lets say clockwise and counterclockwise at the same time.
It is like having two "realities" existing at the same time. | {"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": 0.8669907450675964, "perplexity": 617.0506183364218}, "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-2019-39/segments/1568514576965.71/warc/CC-MAIN-20190923125729-20190923151729-00448.warc.gz"} |
https://datascience.stackexchange.com/questions/94685/what-exactly-is-the-linear-layer-in-the-transformer-model | # What exactly is the linear layer in the transformer model?
There are linear layers to modify the Query, key and value matrices and one linear layer after the multi head attention as they mention also from here:
Are these linear layers simply dense or fully connected layers? Let's consider the weight matrix Wi Q. Does this represent a dense layer with "Q" nodes? As they are using matrices as input rather than 1D vectors, I am getting a little confused.
As described in the paragraph you referred to in your question $$W^Q$$ is a matrix of dimensions $$d_{model} \times d_k$$, that is, it is a fully connected layer with $$d_k$$ units.
• Yes, for each attention head, the same $W^Q_i$ is applied to all query vectors in $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": 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": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.908783495426178, "perplexity": 571.3747435382485}, "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/1637964358705.61/warc/CC-MAIN-20211129104236-20211129134236-00370.warc.gz"} |
https://www.physicsforums.com/threads/singularity-in-reference-to-blackholes-and-right-before-the-big-bang.263098/ | # Singularity in reference to blackholes and right before the big bang?
1. Oct 9, 2008
### fa7alerr0r
Now correct me if I'm wrong. Gravitational singularity is when It has a defined mass but no volume and the equation for density is d=m/v. If a blackhole's mass is say 10^40 yottagrams
and its a singularity so it has no volume = 0. How can it have infinite density if the equation is (10^40 yottagrams)/0 wouldn't that be undefined density?
2. Oct 10, 2008
### marcus
I don't think astrophysicists claim that singularities exist in nature.
A singularity is a breakdown in some manmade theory.
Or you could say it is the place where the manmade theory breaks down.
There have been singularities in various other fields of science. they usually got rid of them by fixing the theory so it doesn't blow up or fail at that point.
In astronomy the kind of singularity you hear about is this infinite density, infinite curvature business (trouble with the theory around BB and BH). I don't think anybody believes such blowups actually occur. The problem is, what improved theory do we use instead so we don't get a singularity---and what really happens.
there was an international workshop on this last year, various experts presented their ideas.
(it was a 2-week conference at KITP, an institute at Univ. Santa Barbara)
If you can't get the videos of the talks, let me know and I will help.
3. Oct 10, 2008
### Arch2008
Well there is emerging theory that singularities don’t have to exist, as well as the Loop Quantum Gravity work. However, some might caution that they need to show some of that proof thing.
In the mean time, Roy Kerr used General Relativity to prove that the mass of a spinning star collapses into a ring with the width of the Planck length and zero height. The zero height part gives the ring zero volume as well (volume equals length times width times height). Zero volume causes the density to approach infinity. http://en.wikipedia.org/wiki/Ring_singularity
GR has passed every test so far, unlike some other stuff.
4. Oct 10, 2008
### fa7alerr0r
ty guys
5. Oct 10, 2008
### George Jones
Staff Emeritus
And Penrose, and then Penrose and Hawking, showed that GR predicts singularities under much more general conditions.
6. Oct 10, 2008
### Jonathan Scott
I think that's subject to the additional assumption (which I don't think should be counted as part of GR itself) that Hilbert's physical interpretation of the radial coordinate in the vacuum solution is correct and Schwarzschild's is not.
7. Oct 10, 2008
### George Jones
Staff Emeritus
These theorems don't assume particular solutions.
8. Oct 11, 2008
### Jonathan Scott
I think that those theorems are roughly equivalent to "if there's an event horizon somewhere, there must be a singularity too". It is the question of whether event horizons occur in reality which depends on the assumption about the radial coordinate.
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https://www.physicsforums.com/threads/volume-of-the-solid.65556/ | # Volume of the solid
1. Mar 2, 2005
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=x^6
y=1
here's what i done:
$$x=(y)^{1/6}$$
$$A(y) = pi(4-(y)^{1/6})^2$$
$$\int_0^{1} pi(4-y^{1/6})^2 dy$$
anyone know what i have done wrong? this section really confuses me.
2. Mar 2, 2005
### Davorak
In which plane are the circles? x-y, x-z,y-z? The radius of the circle is defined by what?
3. Mar 2, 2005
x-y
"The radius of the circle is defined by what?"
are you asking me or telling me to post more about the question? cause that's the whole question.
4. Mar 2, 2005
### Davorak
If the equations are defined in the x-y plane then the circles have to be in the x-z or x-y plane. When you rotate around y=4 you are rotating in to the z axis.
y=4 and y = 1 are horizontal lines in the y vs x plane. Try visualizing the problem keeping this in mind.
Edit:
Does that help?
Last edited: Mar 2, 2005
5. Mar 2, 2005
### HallsofIvy
Staff Emeritus
The point of the question about the radius of the circles (formed when rotating the figure) is that since you are rotating around the line y= 4, the radii are in the y direction, not x!
6. Mar 2, 2005
### BobG
You're rotating around the wrong axis. You're rotating around x=0, not y=4. Try the washer method instead of the disc method and rotate around y=4.
7. Mar 3, 2005
this section i'm doing is all about the disc method, we havent learned the washer method yet(if possible), so can you please help me with the disc method. i see that i was rotating about the x=0 axis, how would i change it to rotate it around the y=4 axis?
i'm thinking....
$$\int_0^{1} pi*(4-x^6)^2 dx$$
8. Mar 3, 2005
### HallsofIvy
Staff Emeritus
That is exactly what every one has been doing! Rotating around the y= 4 axis just means that the radius of each disk is measured by y- 4, not x.
9. Mar 3, 2005
hmm then what am i doing wrong? after integrating that function i get 1359/91*pi. only thing that i can think of getting incorrectly is the bounds which looks correct because i plugged it into my calculator.
10. Mar 3, 2005
### Jameson
Ok, first of all, the bounds. You set the two equations equal to each other to and solve.
$$x^6=1$$ The answers to this are (-1,1)...QED: These are your bounds.
The volume using the disc\washer method is found by:
$$V = \pi\int_{a}^{b}R^2-r^2dx$$ (dx in this case!)
R is the outer radius and r is the inner radius.
Ok. So, since you are revolving about the line y=4 the outer radius becomes (4-x^6)^2 and the inner radius is (4-1)^2.
Alright, finally lets set it up.
$$V = \pi\int_{-1}^{1}(4-x^6)^2-(3)^2 dx$$
I'll leave to you to figure that out.
11. Mar 3, 2005
awesome, thanks for the help. the only thing that i dont get is how you got an inner radius of 3?
12. Mar 3, 2005
### Jameson
4-1=3... the axis of rotation is y=4, so the area you're rotating is 4-1
Similar Discussions: Volume of the solid | {"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": 0.8652783632278442, "perplexity": 1079.9232670123458}, "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-2017-13/segments/1490218189490.1/warc/CC-MAIN-20170322212949-00294-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/286403/differential-equation-using-substitution-ux-yx-solve-fracdydx-y | Differential Equation: Using substitution $u(x)=y+x$, solve $\frac{dy}{dx} = (y+x)^2$
$u(x)=y+x$, solve $\frac{dy}{dx} = (y+x)^2$
I'm unsure about what dy/dx becomes.
Thanks.
-
If $u=y+x$, then ${du\over dx}={dy\over dx}+1$.
-
what if $u(x) = y^3$. what would be $\frac{dy}{dx}$ in this case. – 40Plot Jan 25 '13 at 4:09
Hint: $(y^2)'=(y\cdot y)'=2yy'$ and $(y^3)'=(y^2\cdot y)'$ – Ian Mateus Jan 25 '13 at 4:16
40Plot, it's just the chain rule. If $u(x)=y^3$, then $du/dx=3y^2(dy/dx)$, so $dy/dx=(3y^2)^{-1}(du/dx)=(3u^{2/3})^{-1}(du/dx)$ – Gerry Myerson Jan 25 '13 at 5:37
If $u(x)=x+y$ then $u'(x)=x'+y',~~ y=y(x)$ so $u'(x)=1+y'$ so your OE became $$u'-1=y'=u^2$$ Now solve $$u'=1+u^2$$ or $$\frac{du(x)}{1+u^2}=dx$$
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thank you! I see i now – 40Plot Jan 25 '13 at 4:01
I've got to brush up of diffeq! +1 – amWhy Feb 2 '13 at 0:17 | {"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": 0.9692122340202332, "perplexity": 1651.8087821448585}, "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-2014-10/segments/1394011190529/warc/CC-MAIN-20140305091950-00045-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://crypto.stanford.edu/pbc/notes/crypto/prng.html | We want to be able to take a few "true random bits" (seed) and generate more "random looking bits", i.e. construct a function $G:\{0,1\}^t\rightarrow\{0,1\}^T, T \gg t$. The generated bit strings should "look random" to an adversary. In cryptography, PRNG’s are used to construct session keys and stream ciphers.
True Randomness is generated from some source such as thermal noise. Abstractly, a random source defines a distribution on $\{0,1\}^n$.
Example: $n$-way independent bits $b_1 ,..., b_n$ and $Pr[b_i=1]=p$, $Pr[b_i=0]=1-p$.
Example: $b_1 ,..., b_n$ uniform on $\{0,1\}^n$
Extractors convert a random source with unknown distribution on $\{0,1\}^n$ into a uniform distribution on $\{0,1\}^m$, $m \le n$, e.g. Von Neumann extractor for binomial distribution. We shall take an $n$-bit random source uniform on $\{0,1\}^n$ for granted.
## Definition
The traditional definition of pseudorandom number generators involves a bunch of statistical tests (see Knuth’s "The Art of Computer Programming Vol. 2"), but this is insufficient for cryptographic purposes.
For example, a linear congruential generator: pick a prime $p$, pick $a,b \in \mathbb{Z}_p$, pick random seed $s \in \mathbb{Z}_p$, and iterate with $s \leftarrow a s + b mod p$ and output $LSB(s)$ is considered a PRNG under the traditional definition, but is completely predictable, because given $\lg p$ bits one can recover the seed efficiently.
Instead, we require the pseudo-random number generator to fool any statistical test.
Definition (fixed security parameter version): A $(t, \epsilon)$-PRNG is a function $G:{0,1}^n \rightarrow {0,1}^m (m \gg n)$ such that
• $G$ is efficiently computable by a deterministic algorithm.
• $G$ "$\epsilon$-fools" all $t$-time statistical tests, that is, for all $t$-time algorithms $A$
$Pr[A(G(S)) \text { accepts } | S \leftarrow \{0,1\}^m] -Pr[A(R) | R \leftarrow \{0,1\}^m ] \lt \epsilon$
We say that the uniform distribution on ${0,1}^m$ is $(t,\epsilon)$-indistinguishable from distributions $\{G(S)|S\leftarrow\{0,1\}^n\}$.
## The Next-Bit Test
We derive an equivalent characterization of PRNG’s to that of Yao that is easier to work with. For $R \in \{0,1\}^m$, denote the $i$th bit of $R$ by $R|_i$ and the first $i$ bits of $R$ by $R|_{1,...,i}$.
We say $G:\{0,1\}^n\rightarrow\{0,1\}^m$ $(t,\epsilon)$ passes the next bit test if for all $0\le i \lt m$ no $t$-time algorithm can predict $G(S)|_{i+1}$ from $G(S)|_{1,...,i}$, that is, for all $t$-time algorithms $M$ and for all $0\le i \lt m$
$| Pr[M(G(S)|_{1,...,i}) = G(S)|_{i+1}] | S \leftarrow \{0,1\}^m] - 1/2 | \lt \epsilon$
Theorem: [Yao '82]
Suppose $G:\{0,1\}^n \rightarrow \{0,1\}^m$ $(t/m,\epsilon)$ passes the next bit test. Then $G$ is a $(t,\epsilon)$-PRNG. ("The next bit test is universal.")
Proof: Suppose we have a $(t,\epsilon)$-algorithm $A$ for $G$. Then we shall build a $(t,\epsilon/m)$-next bit predictor for $G$, by using a "hybrid argument":
Define the following collection of distributions $\mathcal{P}_0 ,..., \mathcal{P}_m$ as follows: the first $i$ bits of a member of $\mathcal{P}_i$ are found by picking a random $S \leftarrow \{0,1\}^n$ and setting them to $G(S)|_{1,...,i}$. The last $m-i$ bits are generated at random from $\{0,1\}^{m-i}$. Then
$Pr[A(R) accepts | R \leftarrow \mathcal{P}_0] = Pr[A(R) accepts | R \leftarrow \{0,1\}^m]$
and
$Pr[A(R) accepts | R \leftarrow \mathcal{P}_m] = Pr[A(R) accepts | S \leftarrow \{0,1\}^n, R\leftarrow G(S)]$
Hence
$\array { \epsilon & \le & | Pr[A(R)|R\leftarrow\mathcal{P}_0 ] - Pr[A(R)|R\leftarrow\mathcal{P}_m]| \\ & = & |\sum_{i=0}^{m-1} Pr[A(R)|R\leftarrow\mathcal{P}_i] - Pr[A(R)|R\leftarrow\mathcal{P}_{i+1}] | \\ & \le & \sum_{i=0}^{m-1} | Pr[A(R)|R\leftarrow\mathcal{P}_i] - Pr[A(R)|R\leftarrow\mathcal{P}_{i+1}] | }$
Thus there exists $0\le i\lt m$ with
$|Pr[A(R) | R\leftarrow\mathcal{P}_i] - Pr[A(R) | R\leftarrow\mathcal{P}_{i+1}]| \ge \epsilon/m$
We can use $A$ to build a next bit predictor for $R|_{i+1}$.
The "hybrid argument" is quite useful: in general, suppose experiment (game) $E_0$ is distinguishable from experiment $E_m$. Then build experiments $E_1 ,..., E_{m-1}$, and then it can be shown that there exists $0\le i\lt m$ such that $E_i$ is distinguishable from $E_{i+1}$, which can be used to solve a challenge problem.
Hardcore bits can be used to construct PRNGs using a method due to Blum and Micali. | {"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": 0.9448913931846619, "perplexity": 553.6539467982888}, "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/1412037663467.44/warc/CC-MAIN-20140930004103-00493-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?s=2c9bf27ec250fc6802aa1fedc626dcf8&p=4293812 | # During a phase transition, what is the nature of the material?
by richardc
Tags: material, nature, phase, transition
P: 7 As a material is heated, it increases in temperature until it enters a phase transition. During the transition, added heat does not increase the temperature. As this heat is being added, what is the substance? Is it a mixture of liquid and gas perhaps? If so, what are the proportions? In other words, what exactly is the substance during one of the flat parts of the temperature vs. heat graph? http://www.physicstutorials.org/imag...ngeofwater.png
Mentor P: 11,599 If we look at water we would see molecules being given enough energy to overcome the bonds between them to turn into a gas. The proportions of gas and liquid is hard to determine, as this depends on how even something is heated, how hot the source is, if the gas can be lost from the container, and other factors. Heating water evenly in a sealed container is obviously different than boiling water on my stove at home. But, assuming a perfectly sealed container I would expect the amount of gas to liquid ratio to increase as the amount of heat absorbed by the water increases. At a certain point practically all of the water would be a gas. However, as temperature is a measure of the average energy of the particles in a gas, I would expect there to be some liquid present at all times.
HW Helper
Thanks
PF Gold
P: 5,064
Quote by richardc As a material is heated, it increases in temperature until it enters a phase transition. During the transition, added heat does not increase the temperature. As this heat is being added, what is the substance? Is it a mixture of liquid and gas perhaps? If so, what are the proportions? In other words, what exactly is the substance during one of the flat parts of the temperature vs. heat graph? http://www.physicstutorials.org/imag...ngeofwater.png
The flat part indicates a mixture of liquid and gas. At a point along the flat part, the fraction of liquid is proportional to the portion to the right, and the fraction of gas is proportional to the portion to the left. This is called the "lever rule."
P: 1,212 During a phase transition, what is the nature of the material? The graph shouldn't have sharp turns strictly. Even at 50 degrees there will be some water vapour in thermodynamic equilibrium, it's just a case of that gas/liquid ratio increasing very sharply as you approach 100 degrees. You'd visually see some molecules breaking free from the van der waals molecular interactions, then as the temperature increases, far more gain the kinetic energy necessary to break free.
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PF Gold
P: 5,064
Quote by MikeyW The graph shouldn't have sharp turns strictly. Even at 50 degrees there will be some water vapour in thermodynamic equilibrium, it's just a case of that gas/liquid ratio increasing very sharply as you approach 100 degrees. You'd visually see some molecules breaking free from the van der waals molecular interactions, then as the temperature increases, far more gain the kinetic energy necessary to break free.
You can have all saturated liquid, all saturated vapor, or a combination of saturated liquid and saturated vapor at 50C. So at 50C, the ratio of saturated vapor to saturated liquid can vary anywhere from zero to infinity. The same can be said for the case of any temperature below the critical temperature. There is nothing particularly special about 100 C.
P: 824 Your answers are highly confusing Chester. Of course 100°C is a special point for water (at atmospheric pressure), this is where the phase transition of water from liquid to gas takes place under equilibrium conditions. Yes overheating is possible up to the point where the p(V) curve changes slope, but this is not an equilibrium state and there are strong thermodynamic reasons why substances have a boiling point. Just because there is always some vapour pressure doesn't change that fact. The way you phrase it is sounds more like the behaviour behind the critical point, where there is indeed no difference any more between liquid and solid.
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PF Gold
P: 5,064
Quote by 0xDEADBEEF Your answers are highly confusing Chester. Of course 100°C is a special point for water (at atmospheric pressure), this is where the phase transition of water from liquid to gas takes place under equilibrium conditions. Yes overheating is possible up to the point where the p(V) curve changes slope, but this is not an equilibrium state and there are strong thermodynamic reasons why substances have a boiling point. Just because there is always some vapour pressure doesn't change that fact. The way you phrase it is sounds more like the behaviour behind the critical point, where there is indeed no difference any more between liquid and solid.
A phase transition between liquid and gas does not only take place under equilibrium conditions at 100 C. It takes place at all temperatures between the freezing point and the critical temperature. Here is a link to the Temperature-Enthalpy diagram for water which illustrates and confirms everything I said:
Displayed on the figure the various percentages of saturated liquid and saturated vapor present as a function enthalpy of the mixture at each equilibrium temperature (the green lines). Note also that there is no special significance ascribed to 100 C, 1 atm. on the figure.
P: 824 Well I don't see how that graph is supposed to prove your point. On the right you have the constant pressure lines. The lowest one is for atmospheric pressure. If you are coming from the right you start with gas. When you remove Energy/Enthalpy by cooling, you move down the line and the temperature is dropping until the temperature drops to 100°C. When you remove more energy you move on the horizontal red line to the left, so the temperature stays at 100°C while the gas/liquid fraction drops (which is indicated by crossing the green lines) until all the water is liquid. All the rest of the diagram is for different pressures. So 100°C is the very special temperature at atmospheric pressure, where the constant pressure line for 1 atm touches the dome. At other pressures the phase transition happens at other temperatures and above the critical point there is no phase transition. Vapour pressure has more to do with the Maxwell tail of the Boltzmann distribution so you always have some part of the water in the energetically less favourable state, but there is a sharp phase transition none the less. That is the whole idea of a phase transition.
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PF Gold
P: 5,064
Quote by 0xDEADBEEF Well I don't see how that graph is supposed to prove your point. On the right you have the constant pressure lines. The lowest one is for atmospheric pressure. If you are coming from the right you start with gas. When you remove Energy/Enthalpy by cooling, you move down the line and the temperature is dropping until the temperature drops to 100°C. When you remove more energy you move on the horizontal red line to the left, so the temperature stays at 100°C while the gas/liquid fraction drops (which is indicated by crossing the green lines) until all the water is liquid.
No. There are other lines at lower pressure that are just not shown on the figure. For example, you could also draw another line in at 50 C to the right of the lowest pressure line you referred to. It would be analogous to the lines at 200 C and 300 C, except below the 100 C line. The person who drew this graph just happened to show contours with pressure increments corresponding to saturation temperatures of 100C, 200C, and 300C. If the graph had been drawn with finer resolution, you would see the contours at lower pressures.
Here is a link to a pressure-enthalpy diagram for water which illustrates this with finer resolution. | {"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": 0.8146693110466003, "perplexity": 417.94872971279443}, "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-2014-23/segments/1406510273663.2/warc/CC-MAIN-20140728011753-00093-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/561390/whats-the-difference-between-these-two-transformations-of-functions | # What's the difference between these two transformations of functions?
I'm about to graph the transformation of a function, but in this problem I encountered something new. The function transformation looks like this:
y=12(f(x)+2)
Thing is, I've never seen the f encapsulated in parentheses, so I'm unsure what effect it has. Essentially, I'm wondering what the difference between the above transformation and this one is:
y=12f(x)+2
What do I do differently on the top one when compared to what is done to the bottom one? Is there even any difference?
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Af(x)+B is f(x) vertically stretched by a factor of A and vertically shifted by a factor of b. Expand y=12(f(x)+2), and see what happens. – mrc Nov 10 '13 at 18:19
I'm still lost.. What do you mean by expand? English isn't my native language, so I'm not too familiar with its math terminology. – Threethumb Nov 10 '13 at 18:28
To expand is to remove parentheses. Here this is done by multiplication. For example, 2(a+b)--expand-->2a+2b – mrc Nov 10 '13 at 18:42
It has to do with order of operations. Recall that when doing arithmetic, we do multiplication before addition. If we want to do addition before multiplication, we must use brackets. For example: $$1 + 2 \times 3 = 1 + 6 = 7$$ while on the other hand: $$(1 + 2) \times 3 = 3 \times 3 = 9$$
Likewise, the transformation $y=af(x) + b$ can be interpreted to mean: "Vertically expand $f(x)$ by a factor of $a$, then vertically translate the result up by $b$ units."
On the other hand, the transformation $y = a(f(x) + b)$ can be interpreted to mean: "Vertically translate $f(x)$ up by $b$ units, then vertically expand the result by a factor of $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": 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": 0.8469085693359375, "perplexity": 415.1245020048448}, "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/1448398447860.26/warc/CC-MAIN-20151124205407-00126-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://psychology.wikia.com/wiki/Box_plot?oldid=43282 | # Box plot
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In descriptive statistics, a boxplot (also known as a box-and-whisker diagram or plot or candlestick chart) is a convenient way of graphically depicting the five-number summary, which consists of the smallest observation, lower quartile (Q1), median, upper quartile (Q3), and largest observation; in addition, the boxplot indicates which observations, if any, are considered unusual, or outliers. The boxplot was invented in 1977 by American statistician John Tukey.
Boxplots are able to visually show different types of populations, without any assumptions of the statistical distribution. The spacings between the different parts of the box help indicate variance, skew and identify outliers. Boxplots can be drawn either horizontally or vertically.
## Construction Edit
For a data set, one constructs a boxplot in the following manner:
• Calculate the median, first quartile (x.25), and third quartile (x.75)
• Calculate the interquartile range (IQR) by subtracting the first quartile from the third quartile. (x.75-x.25)
• Construct a box above the number line bounded on the left by the first quartile (x.25) and on the right by the third quartile (x.75). The box may be as tall as one likes, although reasonably proportioned boxplots are customary.
• Indicate where the median lies inside of the box with the presence of a symbol or a line dividing the box at the median value.
• Any data observation which lies more than 1.5*IQR lower than the first quartile or 1.5*IQR higher than the third quartile is considered an outlier. Indicate where the smallest value that is not an outlier is by a vertical tic mark or "whisker", and connect the whisker to the box via a horizontal line. Likewise, indicate where the largest value that is not an outlier is by a "whisker", and connect that whisker to the box via another horizontal line.
• Indicate outliers by open and closed dots. "Extreme" outliers, or those which lie more than three times the IQR to the left and right from the first and third quartiles, respectively, are indicated by the presence of an open dot. "Mild" outliers - that is, those observation which lie more than 1.5 times the IQR from the first and third quartile but are not also extreme outliers are indicated by the presence of a closed dot.
• Add an appropriate label to the number line and title the boxplot.
• It is worth noting that a boxplot may be constructed in a similar manner vertically as opposed to horizontally by merely interchanging "left" for "bottom" and "right" for "top" in the above description.
## An Example Edit
A plain-text version might look like this:
``` +-----+-+
o * |-------| + | |---|
+-----+-+
+---+---+---+---+---+---+---+---+---+---+ number line
0 1 2 3 4 5 6 7 8 9 10
```
For this data set:
• smallest non-outlier observation = 5 (left "whisker")
• lower (first) quartile (Q1, x.25) = 7
• median (second quartile) (Med, x.5) = 8.5
• upper (third) quartile (Q3, x.75) = 9
• largest non-outlier observation = 10
• interquartile range, IQR = $Q3-Q1$ = 2
• the value 3.5 is a "mild" outlier, between 1.5*(IQR) and 3*(IQR) below Q1
• the value 0.5 is an "extreme" outlier, more than 3*(IQR) below Q1
• the data is skewed to the left (negatively skewed)
The horizontal lines (the "whiskers") extend to at most 1.5 times the box width (the interquartile range) from either or both ends of the box. They must end at an observed value, thus connecting all the values outside the box that are not more than 1.5 times the box width away from the box. Three times the box width marks the boundary between "mild" and "extreme" outliers. In this boxplot, "mild" and "extreme" outliers are differentiated by closed and open dots, respectively.
There are alternative implementations of this detail of the box plot in various software packages, such as the whiskers extending to at most the 5th and 95th (or some more extreme) percentiles. Such approaches do not conform to Tukey's definition, with its emphasis on the median in particular and counting methods in general, and they tend to produce "outliers" for all data sets larger than ten, no matter what the shape of the distribution.
## Visualization Edit
The boxplot is a quick graphic approach for examining one or more sets of data. Boxplots may seem more primitive than a histogram or probability density function (pdf) but it does have its benefits. Besides saving space on paper, boxplots are quicker to generate by hand. Histograms and probability density functions require assumptions of the statistical distribution. This assumption can be a major barrier because binning techniques can heavily influence the histogram and incorrect variance calculations will heavily affect the probability density function.
Because looking at a statistical distribution is more intuitive than looking at a boxplot, comparing the boxplot against the probability density function (theoretical histogram) for a Normal N(0,1σ2) distribution may be a useful tool for understanding the boxplot (Figure 2).
# Photos
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See all photos > | {"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": 1, "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": 0.8150547742843628, "perplexity": 1576.8188999059826}, "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-2013-20/segments/1368706961352/warc/CC-MAIN-20130516122241-00000-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/101471/what-is-matrix-a-such-that-hamming-weight-of-x-ax-is-maximal-min-distance/102675 | # What is matrix A such that Hamming weight of [x, Ax] is maximal ? (Min distance of 1/2 block code?)
Everything over F_2.
For any matrix $A$ define the number $N(A) = min_{x}$ HammingWeight $( [x , Ax])$. Where $x$ is vector and [a,b] is just concatenation of vectors: (a_1,...a_n, b_1,...,b_m).
Question What is $max_{A \in Mat(n,m) } (N(A))$ ?
Particular case n=m.
Motivation.
The map $x \to [x, Ax]$ can be considered as error-correcting coding, $x$ - information bits, $Ax$ are redundancy bits.
The code is good if distance between codewords is small.
Reformulation of question: what is the "best possible" code of type above ? ("best possible" in the sense of minimal distance -- it is not always "best" from practical point of view nevertheless).
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You want to know the best error-correcting rate of a binary code of information rate 1/2. I am sure this is an open problem. – Felipe Voloch Jul 6 '12 at 11:42
@Felipe What is known about this ? Estimates ? References ? What are simple estimates which one can understand how to derive without much sufferings ? – Alexander Chervov Jul 6 '12 at 11:46
Varshamov-Gilbert gives a lower bound and Elias gives an upper bound. This is already in MacWilliams and Sloane. I don't think there has been any improvement (certainly not substantial ones). – Felipe Voloch Jul 6 '12 at 14:02
@quid I think in later posts I use correct tag, if think it is worth please re-tag – Alexander Chervov Feb 10 '13 at 17:11
This is, indeed, an open question for most values of $n$. A.D. Brouwer maintains a database of the best known lower and upper bounds, and everything that is known for small $n$ can be found there. A minute of googling points me at
An interesting simple general existence proof is described in van Lint's book (Springer GTM series). Fix a basis for $F=GF(2^n)$. Treat $x$ as an element of $F$, and use encoding $x\mapsto (x,ax)$, where $a$ is an element of $F$ that we choose carefully. Fix a target minimum distance. Let $S(i)$ be the set of elements of $F$ of weight $i$, so $|S(i)|={n\choose i}.$ We must disallow all those elements $a$ that can be written in the form $a=y/x$, where $x\in S(i), y\in S(j), i+j\lt d$. The number of disallowed elements $a$ is thus at most $$N(d)=\sum_{0\lt i,j\lt d; i+j\lt d}{n\choose i}{n\choose j}.$$ If $N(d)\lt 2^n$ we have not disallowed all the elements of $F$, so the construction succeeds. | {"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": 0.972594141960144, "perplexity": 337.9255480728122}, "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/1454701161718.0/warc/CC-MAIN-20160205193921-00261-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://codeberg.org/moenavigator/moenavigator/src/branch/master/configurationwindow.cpp | MoeNavigator is an attempt to write a web browser that is highly configurable, secure, anonymous and fast.
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
#### 34 lines 1.0 KiB Raw Permalink Blame History
``````/* This file is part of MoeNavigator Copyright (C) 2012-2017 Moritz Strohm This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . */ #include "configurationwindow.h" #include "ui_configurationwindow.h" ConfigurationWindow::ConfigurationWindow(QWidget *parent) : QWidget(parent), ui(new Ui::ConfigurationWindow) { ui->setupUi(this); } ConfigurationWindow::~ConfigurationWindow() { delete ui; }`````` | {"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": 0.9305359721183777, "perplexity": 1959.9093860794721}, "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-2020-50/segments/1606141216175.53/warc/CC-MAIN-20201130130840-20201130160840-00204.warc.gz"} |
http://math.stackexchange.com/questions/39407/a-question-concerning-polynomial-solvable-by-radicals | # A question concerning polynomial solvable by radicals
We know from Galois Theory that a polynomial is solvable by radicals if and only if its Galois group is solvable. On the other hand solvable by radicals for example means that the equation $X^n-1=0$ is always solvable by radicals (its Galois group is abelian), but this only means that we can find a solution by saying it is $1^{1/n}$, which is a radical. As for $n\le 6$ we can find its solution in the form $a+ib$ where $a,b$ are representable by real radicals. I guess this is not always possible for larger $n$. (I can see how it could be up to $n\le10$, but any higher?) Is there a theory concerning this kind of problem (whether a polynomial can be solved by "real radicals")?
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This might interest you... – Guess who it is. May 16 '11 at 13:42
http://www.jstor.org/stable/2323164
It closes with the observation:
"We close with the observation that solvable polynomials with real roots but which are not solvable by real radicals seem to abound. For example, for any prime p, the polynomial $$f(x) = x^3 - 2px + p$$ has this property... It is amusing to solve this polynomial by Cardan's method to see where nonreal numbers come in."
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This paper indeed is very interesting, although I guess I was asking for a notion of polynomials, whose roots are $a+ib$ were $a,b$ are real radicals. With the results of the paper I might be able to work out that notion by myself. – Peter Patzt May 17 '11 at 20:21
I guess the result in the paper is not exactly what I asked for. It basically shows something for $\alpha\in\mathbb R$ that is a real radical and whose minimal polynomial splits in $\mathbb R$. I think it be very interesting to see the result if you get rid off the restriction that its minimal polynomial needs to splitt in $\mathbb R$. Then it would be easy to generalize the result to complex numbers $a+ib$ where $a,b$ are real radicals. – Peter Patzt May 18 '11 at 11:44
Since $1^{1/n} = 1$ there is no parameter to vary express the other roots of unity. This does not give the solutions to $x^n-1=\prod_{d|n}\Phi_d(x)=0$ it only solves one of the factors $(x-1)$.
One can express primitive roots of unity ($\Phi_n(x)=0$) in terms of smaller primitive roots, which may be varied, producing all $\varphi(n)$ primitive $n$th roots of unity.
This is in simultaneous induction with nonconstructive proof that solvable Galois group means solvable in radicals, or what it really says: Solvable Galois group means the number field is a sequence of roots radical extension and roots of unity extensions.
See a basic Galois theory textbook for Casus Irreducibilis regarding the fact that you need to have imaginary numbers as an intermediate in Cardano's formula. The theory on that is general so you can apply it to all cases.
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