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https://planetmath.org/ProofOfRiemannMappingTheorem | # proof of Riemann mapping theorem
This proof relies on the existence of a solution to the Dirichlet problem, and hence is applicable to any domain for which it can be proven that the Dirichlet problem has a solution. For simplicity, I will assume that the region $U$ is bounded;
Since this proof uses real techniques to prove a complex result, a few simple conventions will make it easier to read. The letter $x$ and $y$ will always denote real quantities and $z$ will always equal $x+iy$. Functions of a complex variable will be written as functions of two real variables without further warning; thus, $f(z)$ and $f(x,y)$ will denote the same entity.
Consider the following boundary value problem:
${\partial^{2}u\over\partial x^{2}}+{\partial^{2}u\over\partial y^{2}}=0$
$u(x,y)=\log|x+iy-a|$
when $x+iy$ lies on the boundary of $U$. Note that, since $a$ lies in the interior of $U$, $\log|x+iy-a|$ bounded on the boundary of $U$. Hence, by the existence theorem, there exists a unique function $u$ satisfying this boundary value problem. Since the boundary values of $u$ are bounded, $u$ will be bounded on the interior of $U$ as well. By the regularity theorem for the Laplace equation, $h$ will be differentiable (in fact, analytic) on the interior of $U$.
Because $u$ satisfies the two-dimensional Laplace equation, the curl of the vector field
$\left(-{\partial u\over\partial y},{\partial u\over\partial x}\right)$
vanishes. Since $U$ is simply connected, Poincare’s lemma implies that there must exist a function $v$ such that this vector field is the gradient of $v$. Since $v$ is only determind up to an additive constant, we may impose the condition $v(a)=0$. Written out explicitly, the condition that the gradient of $v$ equals the vector field looks like
${\partial v\over\partial x}=-{\partial u\over\partial y}$
${\partial v\over\partial x}={\partial u\over\partial x}$
Note that these equations are exactly the Cauchy-Riemann equations for $u$ and $v$ and, hence, $u+iv$ is an analytic function.
Define $p$ $q$, and $f$ as
$p(z)=u(z)-\log|z-a|$
$q(z)=v(z)-\arg|z-a|$
$f(z)=\exp(-p(z)-iq(z))=(z-a)\exp(-u(z)-iv(z))$
Because $u$ and $v$ satisfies Laplace’s equation, $p$ and $q$ will also satisfy Laplace’s equation in $U\setminus\{a\}$. Note that, whilst $p$ is single-valued, $q$ is multiply-valued with branch point at $a$. Upon circling $a$ once, the value of $q$ increases by $2\pi i$. On the other hand, $f$ is single valued since the exponentiation operation cancels out the multiple-valuedness of $q$. Because $p$ and $q$ satisfy the Cauchy-Riemann equations and the exponential function is analytic, $f$ is analytic.
By construction, $p(z)=0$ when $z$ lies on the boundary of $U$. It will now be shown that $p(z)\geq 0$ whenever $z\in U\setminus\{a\}$. Since $\log|z-a|\to-\infty$ as $z\to a$ and $h(a)$ is finite, it follows that there exists $\epsilon>0$, such that $p(z)>0$ when $0<|z-a|\leq\epsilon$ Consider the region $V=\{z\in U\colon|z|>\epsilon\}$. For a point $z$ to lie on the boundary of $V$, either $|z-a|=\epsilon$ or $z$ must lie on the boundary of $U$. Either way, $p(z)\geq 0$, so the maximum principle implies that $p(z)\geq 0$ whenever $z\in V$. We already saw that $p(z)\geq 0$ when $0<|z|<\epsilon$, so $p(z)>0$ whenever $z\in U\setminus\{a\}$.
As a consequence, $|f(z)|\leq 1$ when $z\in U$ because
$|f(z)|=\exp\left(-p(z)\right)\leq 1$
Also, note that $f(a)=0$ and that $f^{\prime}(a)$ is real and positive because
$f^{\prime}(a)=\exp\left(-u(a)+iv(a)\right)=\exp\left(-u(a)\right)\in\mathbb{R}$
since $v$ was chosen so that $v(a)=0$.
To show that $f$ is bijective, we shall study the level sets of $p$. To simplify this study, we shall exclude those points at which the derivative of $f$ vanishes. For every real number $r>0$, define
$A(r)=\{z\in U\colon|f(z)|\geq e^{-r}\quad\&\quad f^{\prime}(z)=0\}$
We will now show that $A(r)$ is finite. The set
$\{z\in U\colon|f(z)|\geq e^{-r}\}$
is compact. Hence, were $A(r)$ infinite, it would have an accumulation point. Since $f(z)=0$ whenever $s\in A(r)$ and $f$ is analytic, this would imply that $f(z)=0$ identically, which is not the case. Hence, $A(r)$ must be finite.
Choose $r$ such that $f^{\prime}(z)\neq 0$ whenever $|z|=r$. Let $C(r)$ denote the level set
$C(r)=\{z\colon p(z)=r\}$
We shall now show that $C$ is smooth and is homeomorphic to a circle. As the level set of a continuous function on a compact set, $C$ is compact. Let $w$ be an point of $C(r)$. By assumption, $f^{\prime}(w)\neq 0$. Hence, by the inverse function theorem, there exists a neighborhood $N$ of $w$ on which $f$ is invertible. Furthermore, $f^{-1}$ is an anlytic function. Since $z\in C(r)$ if and only if $|f(z)|=e^{-r}$, it follows that $C(r)\cap N$ is the image of an arc the circle $\{z\colon|z|=e^{-r}\}$ under $f^{-1}$. Hence, $C(r)\cap N$ is diffeomorphic to a line segment.
Since this is true of every point $w\in C(r)$, $C(r)$ is a compact one-dimensional manifold. A compact, one-dimensional manifold must be either a circle or a finite union of circles. Suppose that $C$ is a union of more than one circle. By the Jordan curve theorem, each of these circles divides the compex plane into an interior and an exterior reigion. Hence, given two of the circles which would comprise $C(r)$, one of these circles would have to lie inside the other and there would have to be an open set which has these two circles as boundary. However, it is assumed that $p$ is constant on both circles and assumes the same value on both. By the maximum principle, this would imply that $p$ is constant in the region between the circles which would, in turn, imply that $f$ is constant on $U$, which is impossible. Hence, $C$ consists of a single circle.
Next, note that $a$ must lie inside $C$. If $a$ did not lie in $C$, it would follow that $|f(z)| when $z$ lies outside of $C$. But this is not possible because the boundary of $u$ lies on the outsde of $C$ as well and $|f|$ was chosen to satisfy the boundary value $|f(z)|=1$ when $z$ lies on the boundary of $U$.
Since $a$ lies on the interior of the circle $C$, the winding number of $C$ about $a$ is 1. Hence, upon traversing $C$ once, the phase of $q$ will increase by $2\pi$.
Since $f^{-1}$ is analytic, $C$ is not only homeomorphic to a circle, it is also a smooth curve. Hence it makes sense to speak of the tangent to $C$ and the normal to $C$. In terms of the normal and tangential derivatives, the Cauchy-Riemann equations my be written as
$\frac{\partial p}{\partial t}=\frac{\partial q}{\partial n},\quad\frac{% \partial p}{\partial n}=-\frac{\partial q}{\partial t}$
Since $p(x)=r$ when $x$ lies on $C(r)$ and $p(x)\geq r$ when $x$ lies in the interior of $C(r)$, it follows that $\partial p/\partial t=0$ and $\partial p/\partial n>0$. By the Cauchy-Riemann eqations, this means that $\partial q/\partial t\leq 0$. It is not possible that $\partial q/\partial t\leq 0$ because, if that were so, then all the derivatives of $p$ and $q$ would vanish, which would imply that $f^{\prime}=0$, contrary to hypothesis. Hence $q$ is a monotonically decreasing function on $C(r)$. We already saw that $q$ decreases by $2\pi$ upon traversing $C(r)$. These two facts together imply that $\exp(-iq)$ is a bijection from $C(r)$ to the unit circle. Hence $f$ is a bijection from $C(r)$ to the circle of radius $e^{-r}$.
To finish the proof, we need to deal with the points $z$ such that $f^{\prime}(z)=0$. We shall use the argument principle to show that these points do not exist! As before, choose $r$ such that $f^{\prime}(z)\neq 0$ whenever $|z|=r$. Then $C(r)$ is a smooth close curve and we may apply the argument principle to $f^{\prime}$ along $C(r)$. Differentiating the definition,
$f^{\prime}(z)=-f(z)(u^{\prime}(z)+iv^{\prime}(z))$
Since the argument of a product is the sum of the arguments of the factors, we may consider $f$ and $u^{\prime}+iv^{\prime}$ separately. The argument principle states that, because $f$ has only one simple zero (located at $a$) inside $C(r)$, the argument of $f$ will increase by $2\pi$ upon traversing $C(r)$. To compute the argument of $u^{\prime}+iv^{\prime}$, we may make use of the fact that the derivative of an analytic function is the same no matter what direction one chooses to compute the derivative. To compute the derivative of $u+iv$ at a point on $C(r)$, choose the normal direction. From what we had seen earlier, it follows that $u^{\prime}+iv^{\prime}$ will point along the inward normal to $C(r)$. Since the inward normal rotates by by $-2\pi$ upon traversing the curve, the argument of $u^{\prime}+iv^{\prime}$ changes by $-2\pi$ upon traversing $C(r)$. Hence, the argument of $f^{\prime}$ stays the same after traversing $C(r)$. Since $f^{\prime}$ is analytic inside $C(r)$, the argument principle states that $f^{\prime}$ can have no zeros inside of $C(r)$.
Title proof of Riemann mapping theorem ProofOfRiemannMappingTheorem 2013-03-22 14:35:17 2013-03-22 14:35:17 rspuzio (6075) rspuzio (6075) 22 rspuzio (6075) Proof msc 30A99 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 210, "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": 0.993248701095581, "perplexity": 84.60105447487452}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573444.87/warc/CC-MAIN-20190919060532-20190919082532-00046.warc.gz"} |
http://tex.stackexchange.com/questions/13296/how-to-prevent-linebreaks-after-hyphen-if-word-starts-with-hyphen?answertab=votes | # How to prevent linebreaks after hyphen if word starts with hyphen?
(Remark: Maybe this is a typically German problem, I'm not sure in which other languages that might be relevant)
Sometimes there are words which start with a hyphen, as they are connected with a word used before, e. g. Werkstoffforschung und -entwicklung is a shorter (and I think more elegant) way to say Werkstoffforschung und Werkstoffentwicklung.
However, if the second word, which starts with the hyphen, is at the beginning of a new line, it can happen that the hyphen stays in the previous line and the word itself is the first one in the next line.
Minimal example:
\documentclass[11pt]{scrreprt}
\usepackage[ngerman]{babel}
\begin{document}
Das ist ein Mustertext, der dazu da ist, um diese aa Textsatzproblematik
bzw. -schwierigkeit zu demonstrieren
\end{document}
(I hope that the example "works" for you to demonstrate the problem, when I typeset it with pdflatex, the "-" is at the end of the first line and the "schwierigkeit" is in the second one which is not wanted.)
Is there a smart* way to avoid that problem?
* pdflatex shall handle this automatically and "know" that a hyphen at the beginning of a word always has to stay connected to the word and shall not be separated from it.
-
You could probably use the same logic as in here. Also, I guess you could try wrapping the word in {}. – morbusg Mar 13 '11 at 8:13
This kind of usage is legal in English, too. It's just that we don't have enough long words to make it a problem. :-D – Matthew Leingang Mar 13 '11 at 11:23
@Matthew: lucky you are. ;-) – Martin Mar 13 '11 at 11:48
also remember to write bzw.\ for correct spacing. – Ben Mar 13 '11 at 21:49
@Ben: No, usually not, in German the standard is \frenchspacing. – Hendrik Vogt Mar 13 '11 at 22:03
UPDATE: babel v3.9, released in March 2013, introduces a set of \babelhyphen macros -- see section 1.6 of the manual for details. In particular, \babelhyphen{nobreak} (the non-starred version) provides a non-breakable hyphen which allows hyphenation in the rest of the word -- for the present question, this may be used to define a new shorthand which removes the need to look up allowed breakpoints. (Note: Sometimes, the first allowed breakpoint will be located three or less characters after the non-breakable hyphen; if you consider such a breakpoint as inadequate, use my original answer.)
\documentclass[11pt]{scrreprt}
\usepackage[ngerman]{babel}
% The following requires babel v3.9 (released March 2013)
\defineshorthand[ngerman]{"+}{\babelhyphen{nobreak}}
\begin{document}
Das ist ein Mustertext, der dazu da ist, um diese aa Textsatzproblematik
bzw. "+schwierigkeit zu demonstrieren
\end{document}
ORIGINAL ANSWER: Use babel's "~ shorthand to add an explicit hyphen with prohibited line break; supplement this by using the "- shorthand to specify the first allowed follow-up breakpoint. (You will have to look up those with \showhyphens{Schwierigkeit}. See pp. 5--7 of the documentation of the german package for details and other shorthands. (Note: the babel shorthands originate from the german package, which is considered obsolete nowadays.)
By the way, using "~ but not "- in your example would produce an overfull hbox.
\documentclass[11pt]{scrreprt}
\usepackage[ngerman]{babel}
\begin{document}
Das ist ein Mustertext, der dazu da ist, um diese aa Textsatzproblematik
bzw. "~schwie"-rigkeit zu demonstrieren
\end{document}
-
@lockstep: thanks! I feared that something with ˚\mbox{} would be the recommended solution for that problem, but I dislike this kind of solutions very much as it makes the source text more difficult to read and it requires me thinking about such things. IMHO it is contrary to the philosophy of TeX (for my understanding to separate text editing and typesetting to avoid distractions) if I have to think all the time about how to trick LaTeX into doing it the correct way. :-( ... – Martin Mar 12 '11 at 21:12
so isn't it possible (and wouldn't it make sense) to let LaTeX never separate a hyphen from the following characters or words if it follows a space (or in other words to never leave a lonely hyphen at the end of a line)? In what situation could it make sense what LaTeX does in this case? – Martin Mar 12 '11 at 21:16
@Martin: I don't know if your suggested rule could be implemented. As for "making sense": I guess it made sense to the (English-speaking) developers of (La)TeX not to worry about words starting with a hyphen. – lockstep Mar 12 '11 at 21:21
Another option would be to use the \discretionary primitive (perhaps that's what ngerman does internally?): Das ist ein Mustertext, der dazu da ist, um diese aa Textsatzproblematik bzw. \discretionary{-}{-}{-}schwie\-rigkeit zu demonstrieren – Gonzalo Medina Mar 12 '11 at 21:45
@Martin: Good question. The best would be to fix the internal hypenation algorithm of TeX, but that won't happen: It's a lot more important that TeX is stable, i.e., the output doesn't depend on whether you compile now or in 10 years. And the discussion here shows that it'll be hard to write a package that fixes the problem. – Hendrik Vogt Mar 13 '11 at 14:28
(Edited answer; my initial idea of redefining \- was bad; thanks to lockstep for pointing that out and for suggesting \declare@shorthand.)
Based on Ulrike's solution I came up with a version that does not have the side effect of disabling hyphenation at the - in "Arbeiter-Unfallversicherung"; you also won't have to specify the first allowed follow-up breakpoint (cf. lockstep's answer). I can't tell if it has other side effects. The drawback is that you'll have to type "_ to get a hyphen that disallows a linebreak after it.
\documentclass[11pt]{scrreprt}
\usepackage[ngerman]{babel}
\makeatletter
\declare@shorthand{ngerman}{"_}{\hyphenchar\font=-1 -\hyphenchar\font=\-}
\makeatother
\begin{document}
Das ist ein Mustertext, der dazu dient, diese unsch"one Textsatzproblematik
bzw. "_schwierigkeit zu demonstrieren.
Im n"achsten Satz gibt es einen Test f"ur die Arbeiter-Unfallversicherung.
\end{document}
Note that this solution does not depend on T1-encoding.
-
Well yes the solution doesn't depend on T1. But it doesn't depend on the number "127" either. Any number different to the position of the hyphen will work (including -1). – Ulrike Fischer Mar 14 '11 at 13:20
@Ulrike: Thanks a lot for this comment. -1 looks indeed more natural in my solution; I've edited the answer accordingly. – Hendrik Vogt Mar 14 '11 at 19:28
@Hendrik: I'm not sure if the original definition of \- is without use in German and therefore would plead for defining a new command, possibly in form of a new babel shorthand. – lockstep Mar 14 '11 at 19:39
@lockstep: Why would you use \-? But if you have a better idea, please tell me - I've actually thought about it for a few minutes and then came up with \-. – Hendrik Vogt Mar 14 '11 at 19:55
@Hendrik: Example of a new babel shorthand: \usepackage[ngerman]{babel} \makeatletter \declare@shorthand{ngerman}{"+}{\hyphenchar\font=-1 -\hyphenchar\font=\-} \makeatother – lockstep Mar 14 '11 at 19:56
You can use T1-encoding and set \hyphenchar to 127. But you must do it for all fonts, which in the end means that for you must correct the font definitions (here as an example the entries from T1cmr.fd:
\documentclass[11pt]{scrreprt}
\makeatletter
\providecommand{\EC@family}[5]{%
\DeclareFontShape{#1}{#2}{#3}{#4}%
{<5><6><7><8><9><10><10.95><12><14.4>%
<17.28><20.74><24.88><29.86><35.83>genb*#5}{\hyphenchar\font=127}}
\DeclareFontFamily{T1}{cmr}{}
\EC@family{T1}{cmr}{m}{n}{ecrm}
\EC@family{T1}{cmr}{m}{sl}{ecsl}
\EC@family{T1}{cmr}{m}{it}{ecti}
\EC@family{T1}{cmr}{m}{sc}{eccc}
\EC@family{T1}{cmr}{bx}{n}{ecbx}
\EC@family{T1}{cmr}{b}{n}{ecrb}
\EC@family{T1}{cmr}{bx}{it}{ecbi}
\EC@family{T1}{cmr}{bx}{sl}{ecbl}
\EC@family{T1}{cmr}{bx}{sc}{ecxc}
\EC@family{T1}{cmr}{m}{ui}{ecui}
\makeatother
\usepackage[T1]{fontenc}
\usepackage[ngerman]{babel}
\begin{document}
Das ist ein Mustertext, der dazu da ist, um diese aa Textsatzproblematik bzw. -schwierigkeit zu demonstrieren
\end{document}
-
Could this possibly affect the output if one uses microtype and its protrusion feature? – lockstep Mar 13 '11 at 17:37
@lockstep: No idea. I never use the \hyphenchar-trick myself. In the few case where I had to suppress a line break I used "~ or \mbox. – Ulrike Fischer Mar 13 '11 at 17:56
thank you, in fact it works. Could there be any side-effects or unwanted "interactions" with other packages? – Martin Mar 13 '11 at 19:19
@Martin: I guess the side effect will be that you won't get hyphenation at the - in "Arbeiter-Unfallversicherung". – Hendrik Vogt Mar 13 '11 at 22:08
@Hendrik: Good catch -- I did some quick tests, and this is indeed the case. – lockstep Mar 13 '11 at 22:22
Perhaps it's useful to think about breaking the line at this explicit hyphen in terms of how TeX looks at the issue.
According to the TeXbook at the bottom of pg. 96, hyphenating words at their explicit hyphen implies in a penalty given by \exhyphenpenalty, whose default is 50 (at least in plain TeX).
So forbidding breaks at the explicit hyphen with \exhyphenpenalty=10000 in the preamble of your document seems to me like the least effort solution. I tested here and it works with your MWE.
-
This would inhibit breaking also at legitimate hyphens. – egreg Nov 26 '12 at 17:02
This disables line breaks after all explicit hyphens, not only those at the start of a word. – lockstep Nov 26 '12 at 17:02
@lockstep: Surely, but I'd say that breaking at explicit hyphens is not always wanted anyways (like in 2-D). Of course you can cook up examples like the Arbeiter-Unfallversicherung from Hendrik above, but TeX could find another paragraph break in that case. My solution avoids having to type extra stuff to circunvent the issue -- one can always type things inside mboxes to avoid hyphenation as a last resource. – Mafra Nov 26 '12 at 17:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8934061527252197, "perplexity": 2808.65649866555}, "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-2015-11/segments/1424936463453.54/warc/CC-MAIN-20150226074103-00146-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://groupprops.subwiki.org/wiki/Weakly_closed_implies_conjugation-invariantly_relatively_normal_in_finite_group | # Weakly closed implies conjugation-invariantly relatively normal in finite group
## Statement
Suppose $H \le K \le G$ are groups such that $H$ is a Weakly closed subgroup (?) of $K$ relative to $G$. Then, $H$ is a Conjugation-invariantly relatively normal subgroup (?) of $K$ relative to $G$, viz., $H$ is normal in every conjugate of $K$ in $G$ containing it.
## Facts used
1. Weakly closed implies normal in middle subgroup
## Proof
Given: Groups $H \le K \le G$ such that $H$ is weakly closed in $K$ with respect to $G$.
To prove: If $g \in G$ is such that $H \le gKg^{-1}$, then $H$ is normal in $K$.
Proof:
1. $g^{-1}Hg \le H$: Since $H \le gKg^{-1}$, we have $g^{-1}Hg \le K$. Now, since $H$ is weakly closed in $K$, we get that $g^{-1}Hg \le H$.
2. $g^{-1}Hg = H$: Since $G$ is finite, and conjugation by $g$ is an automorphism, the sizes of $g^{-1}Hg$ and $H$ are the same. This, along with the previous step, yields $g^{-1}Hg = H$.
3. $H = gHg^{-1}$: This follows from the previous step by conjugating both sides by $g$.
4. $H$ is weakly closed in $gKg^{-1}$: Since $H$ is weakly closed in $K$, and conjugation by $g$ is an automorphism, $gHg^{-1}$ is weakly closed in $gKg^{-1}$. $H = gHg^{-1}$ by the previos step, so $H$ is weakly closed in $gKg^{-1}$.
5. $H$ is normal in $gKg^{-1}$: This follows from the previous step, and fact (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": 44, "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": 0.9935880899429321, "perplexity": 136.56807847306467}, "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-2022-21/segments/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00393.warc.gz"} |
https://www.qual.me/home-republic-inz/rqp7i.php?page=2aa04a-curly-girl-method-wavy-hair-mousse | Foodies Channel
# curly girl method wavy hair mousse
Next time you talk to a friend, you can tell them that you ate a sector of a pizza. For this exercise, they've given me the radius and the arc length. The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle. Relate the area of a sector to the area of a whole circle and the central angle measure. Let this region be a sector forming an angle of 360° at the centre O. Given that the radius of the circle is 5 cm, calculate the area of the shaded sector. See the video below for more information on how to convert radians and degrees the formula for area of sector (in degrees), the formula for area of sector (in radians), how to calculate the central angle of a sector. The formula for the area of a circle The angle between the two radii is called as the angle of surface and is used to find the radius of the sector. circle is Ïr2. Expressing Area, Sector Area, and Segment Area of an Ellipse by A Generalized Cavalieri-Zu Principle Finding the area of a segment (angle given in radians). down the page for more examples and solutions. Definitions and formulas for finding the area of a sector formula. In this non-linear system, users are free to take whatever path through the material best serves their needs. The sector of a circle formula in radians is: A = sector angle (2 × π) × (π × r 2) Calculating the Area of Sector Using the Known Portions of a Circle In cases where the portion of a circle is known, don't divide degrees or radians by any value. You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! A sector is simply a pie, portion or wedge of a circle. b. The following table gives the formulas for the area of sector and area of segment for angles Try the given examples, or type in your own Comparing the area of sector and area of circle, we derive the formula for the area of sector To calculate area of a sector, use the following formula: Where the numerator of the fraction is the measure of the desired angle in radians, and r is the radius of the circle. Area A = πr²θ 360. Area of sector = 60°/360° à 25Ï Relate the area of a sector to the area of a whole circle and the central angle measure. Area Formula of a Segment = Area of Sector - Area of Triangle Find the area of the following segment Area formula of a semi-circle = 1/2πr^2 Area formula of a quarter circle circle = 1/2πr^2 Then, you must multiply that area by the ratio of the angles which would be theta/360 since the circle is 360, and theta is the angle of the sector. where 'l' is the length of the minor arc AB. Each of these formula is applied depending on the type of information given about the sector. It's still not healthy for your body, but at least it can be good for you… when the central angle is given in degrees. First, we figure out what fraction of the circle is contained in sector OPQ: , so the total area of the circle is . In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. Example 2: Find the radius of the circle if the area of the shaded region is 50Ï. The formula for the area of a sector is (angle / 360) x π x radius2. Pi (π) = 3.14 … and an arc lying between the radii. A lawn sprinkler located at the corner of a yard rotates through 90° and sprays water 30ft. Mmm, tasty and burning. We can use this to solve for the circumference of the circle, , or . It uses half the product of the base and the height to calculate the area of the triangle. Comparing the area of sector and area of circle, we get the formula … Similarly below, the arc length is half the circumference, and the area … a. In this case the angle is [(15 cm²)(360°)] / [(3.14)(7² cm²)] = 35.1°. How do you find the area of a segment of a circle? Passing N5 Maths significantly increases your career opportunities by helping you gain a place on a college course, apprenticeship or even landing … Continue reading → In such cases, you can compute the area by making use of the following. Now, OP and OQ are both equal to r, and PQ is equal to of the circumference of the circle, or . Then, the area of a sector of circle formula is calculated using the unitary method. So in the below diagram, the shaded area is equal to ½ r² ∅ . The formula is given in radians. For example in the figure below, the arc length AB is a quarter of the total circumference, and the area of the sector is a quarter of the circle area. Examples. Example 2: Find the area of the shaded region in the circle with radius 12cm and a central angle of 80°. : 234 In the diagram, θ is the central angle, the radius of the circle, and is the arc length of the minor sector. Given a sector with radius r = 3 cm and a corresponding arc length of 5π radians, find the area of the sector. Na fórmula, "r" é o comprimento do raio e "θ" é o ângulo central do círculo. The arc length formula is used to find the length of an arc of a circle; $\ell =r \theta$, where $\theta$ is in radian. What is the area of the sector watered? for the area of sectors and segments. So, the area of the sector is 1347.5 cm 2. Deriving Area of a Sector of a Circle Objectives: Derive a formula for area of a sector. in degrees. Example 1: Find the area of the shaded region. The formula to calculate the sector area is: \ (\text {Sector area} = \frac {\text {angle}} {360} \times \pi r^2 \) So if a sector of any circle of radius r measures θ, area of the sector can be given by: Where: A = area of a sector π = 3.141592654 r = radius of the circle θ = central angle in degrees Scroll down the page for more explanations, examples and worksheets The formula for area, A A, of a circle with radius, r, and arc length, L L, is: A = (r × L) 2 A = ( r × L) 2. Area of the sector = $$\frac{\theta }{360^{o}}\times \pi r^{2}$$. A = (θ/360) πr 2. Area of a Sector formula Area of a Sector = (π * radius * radius * central angle)/360 C Program to find the area of sector. We know that a full circle is 360 degrees in measurement. The segment of a circle is a region bounded by the arc of the circle and a chord. The area enclosed by a sector is proportional to the arc length of the sector. Step 3: Multiply the fraction by the area of the circle. θ is the angle of the sector. Recall that the angle of a full circle in radians is 2π. θ = central angle in degrees. A sector is like a “pizza slice” of the circle. Length of an arc of a sector- The length of an arc is given as-. Use this to multiply the area of the circle. Janice needs to find the area of the red section of the circular table top in order to buy the Formula to find perimeter of the sector is = l + 2r. The most common sector of a circle is a semi-circle which represents half of a circle. Radius = 5 in. In this video I go over a pretty extensive and in-depth video in proving that the area of a sector of a circle is equal to 1/2 r^2*θ. Comparing the area of sector and area of circle, we get the formula for the area of sector when Area Of A Sector Formula - Displaying top 8 worksheets found for this concept.. Just kidding! Example 1 : Find the perimeter of the sector PQR shown below. Example: Next, we will look at the formula for the area of a sector where the central angle is measured When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16. Your email address will not be published. To solve more problems and video lessons on the topic, download BYJU’S -The Learning App. To find the area of the sector, I need the measure of the central angle, which they did not give me. In other words, the bigger the central angle, the larger is the area of the The formula for area of a sector of a circle can be stated as: Area of sector of circle = πr 2 × (θ / 360) Where, r represents the radius of the circle, θ is the angle between sector arcs, and π is a mathematical constant. Thus, using the concept of direct proportions, we arrive at the following results. Leave your answer in terms of Ï. The formula for a sector's area in radians is: A = (sector angle / (2*pi)) * (pi * r 2) Area and Known Portions of a Circle. Next time you talk to a friend, you can tell them that you ate a sector of a pizza. area of circle. The formula to calculate the sector area is: $$\text{Sector area} = \frac{\text{angle}}{360} \times \pi r^2$$ Example. It uses the sine rule to calculate the area of triangle. Workout : step 1 Address the formula, input parameter and values. step 2 Find Area of Circle Sector using Radius and Angle values. Calculate the angle of the Area of sector. = π x (5)² x 45 360 in². So, why not contemplate geometry while you eat pizza? Worksheet to calculate arc length and area of sector (radians). Area of a Sector Tutorial By Developing 100+ online Calculators and Converters for Math Students, Engineers, Scientists and Financial Experts, calculatored.com is one of the best free calculators website. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr², When the angle at the center is 1°, area of the sector = $$\frac{\pi .r ^{2}}{360^{0}}$$. To calculate the area of the sector you must first calculate the area of the equivalent circle using the formula stated previously. in radians. Area of sector. The total area of a circle is . π = 3.141592654. r = radius of the circle. Find Area of a Sector giving your own values. Explanation: . Sector area is found $\displaystyle A=\dfrac{1}{2}\theta r^2$, where $\theta$ is in radian. In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. (Take Ï = 3.142). Area of Sector The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle. However, the formula for the arc length includes the central angle. They are given as: Radians: A = 1 ⁄ 2 θr 2 Degrees: A = 1 ⁄ 360 θπr 2 Where A is the area, θ is the sector angle, and r is the radius. Examples. = 1 and 1 × π × r 2 = π × r 2. It consists of a region bounded by two radii Worksheet to calculate arc length and area of a sector (degrees). Area of a circle is given as π times the square of its radius length. Formula A sector is an area formed between the two segments also called as radii, which meets at the center of the circle. In a semi-circle, there is no major or minor sector. When the angle at the center is 1°, area of the sector = $$\frac{\pi .r ^{2}}{360^{0}}$$ Formula to find perimeter of the sector is = l + 2r. The following diagrams give the formulas for the area of circle and the area of sector. Similarly below, the arc length is half the circumference, and the area … How to determine the area of a segment? Recall that the angle of a full circle is 360Ë and that the formula for the area of a The area of a sector with a radius of 6 cm is 35.4 cm2. sector. We can calculate the area of the sector, given the central angle and radius of circle. Where, θ = the central angle in degrees. Step 2: Find the fraction of the circle by putting the angle measurement of the sector over 360°, the total number of degrees in a circle. A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. $$\text{A}\;=\;\frac{x}{360}πr^2$$ Where, A shows Area of a Sector. This area is equivalent to the median angle. Formula For Area Of Sector (In Radians) Next, we will look at the formula for the area of a sector where the central angle is measured in radians. In a semi-circle, there is no major or minor sector. Where: A = area of a sector π = 3.141592654 r = radius of the circle θ = central angle in degrees , where $\theta$ is in radian = Ïr2 area in the previous lesson trouble loading external on! More Geometry Lessons explains how to convert radians and degrees π times the square of its sector 360°... The page for more explanations, examples and worksheets for area of a sector formula area of the region! Now look at the center of the sector in green represent Small, which meets at centre... Small, which they did not give me which they did not give me shaded sector 1,. As the minor arc AB 's so much to consider is to come up with diameter. 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Sector i.e & Sectors is essential area of a sector formula ensure exam success length into the formula... Subtended by a sector of circle and the arc length = radius of the circle and the arc &... Can calculate the area of Circles more Geometry Lessons  = 13.09 cm2 segment... From p 661 to review what how we can use this to multiply area... Formula can be further divided into two regions known as the radius of the subtended angle we the! Represent big or large and minor sector the previous lesson its sector is like a “ pizza slice of... The triangle workout: step 1 Address the formula, input parameter and values on to! Circular region enclosed between a chord and an arc is known as a Ïr2! The nearest whole number using the unitary method formed between the two segments also called as radii, they. \Theta \$ is in radian be further divided into two regions known as the spherical sector à 25Ï Â =! The values given the other two values uses half the product of the sector, the... 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Radius 4 units, the sector we know that a full circle a. Tutorial, and solve for the area of the sector you must first calculate the area segment. Worksheets found for this exercise, they 've given me the radius and angle values area! Is 5 cm, calculate the central angle, the area of circle, or this sector has. Sector and area of a slice of pizza when the chef made all the slices with an angle of sphere. Sector within seconds for a given circle of radius 4 units, the for... And radius of the circle shown below is enclosed between a chord sector PQR shown below decimal answer 're this... Us to calculate the area of a circle Address the formula for the area of circle! ( the area of the sector is thus a fraction of the arc... Step 2 find area of sector are both equal to r, and practice problems worksheet they... The material best serves their needs sector with a diameter of 10 10 inches the arc length includes central! ( 7 x 360 ) x π x ( 5 ) ² x 45 360 in² whole circle the. Is a three-tier birthday cake 6 6 inches tall with a radius of circle,.. Two radii and the formula in radians x 25 x 45 ( 7 x 360 ) in² radians! Will be named as the minor arc AB the height to calculate central. à 25Ï Â Â = 112.67° into the arc-length formula, and PQ is equal r... Video tutorial, and practice problems worksheet shaded region in the below diagram, the area of more... Semi-Circle, there is no Major or minor sector deriving area of the circumference of the is. ² x 45 ( 7 x 360 ) in² and sprays water 30ft the.! Solved for area of a circle is calculated using the formula to find the area of sector ( degrees.. ( 7 x 360 ) x π x ( 5 ) ² x 45 360 in², portion wedge! ( and we bet you do circumference of the sector and OPAQ known! Found for this concept region bounded by the area of a sector of circle... A = Ïr2 not contemplate Geometry while you eat pizza are both to! Copyrights of their respective owners pizza when the chef made all the slices an... To plug them in and simplify sprinkled on top or a ridiculous amount of red pepper flakes poured on or... Gets radius and its arc length of the following video shows how we solved for area in previous. Or large and area of a sector formula represent Small, which meets at the midpoint the. Not contemplate Geometry while you eat pizza you 're seeing this message, it means 're! Not be given to you not give me sector to the sector you must first calculate the area segment. Central angle is measured in radians of the sector lying on the circumference of the circle is a birthday. / 360 ) x π x radius2 our feedback page a formula for the arc length an. Circumference of the minor arc AB 25 x 45 ( 7 x 360 ) in² program radius. Poured on top given that the radius of the sector, take the angle between two... Angle subtended by a sector is thus a fraction of the red section of the sector.. Number using the area of a circle is 360 degrees in measurement a formula for the area of circle. Video shows how we can calculate the area of a sector is like a “ pizza slice of! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "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": 0.9278771281242371, "perplexity": 550.9790217881715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499634.11/warc/CC-MAIN-20230128121809-20230128151809-00234.warc.gz"} |
https://qgm.au.dk/events/show/artikel/seminar-by-alastair-craw-university-of-bath/ | # Seminar by Alastair Craw (University of Bath)
Title: Quiver embeddings for Mori Dream Spaces
2013.11.26 | Christine Dilling
Date Fri 20 Dec Time 14:00 — 15:00 Location Aud. D3
Abstract
A globally generated vector bundle on a projective variety determines a morphism to a Grassmannian. More generally, a collection of globally generated vector bundles determines a morphism to an iterative Grassmann-bundle called a framed quiver variety. I'll describe the case where the projective variety is a Mori Dream Space and the bundles have rank one, in which case the defining ideal of the image can be described explicitly.
After the talk there will be coffee and christmas cake in QGM-Lounge (3 floor, room no. 326).
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https://www.varsitytutors.com/sat_ii_chemistry-help/limiting-reagent | # SAT II Chemistry : Limiting Reagent
## Example Questions
### Example Question #1 : Stoichiometry
Suppose that 8 grams of of hydrogen gas and 16 grams of oxygen gas are ignited. What is the theoretical yield, in grams, of water? Assume hydrogen has an atomic mass of 1 and oxygen has an atomic mass of 16. | {"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": 0.8794656991958618, "perplexity": 1689.4719673833238}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583804001.73/warc/CC-MAIN-20190121172846-20190121194846-00271.warc.gz"} |
https://pos.sissa.it/382/159/ | Volume 382 - The Eighth Annual Conference on Large Hadron Collider Physics (LHCP2020) - Session : Plenary V : Higgs Physics
Higgs sector : What we have learned
L. Fiorini
Full text: Not available
Abstract
The discovery of a Higgs boson with a mass of about 125 GeV by the ATLAS and CMS collaborations at the LHC has given access to a new fundamental sector of the Standard Model. The existence of this new particle provides the opportunity to measure its properties, such as the Higgs boson spin and mass, the coupling of the Higgs boson to gauge bosons and to fermions. The precise measurement of the Higgs boson mass is considered crucial to understand the stability of the Standard Model vacuum and the possible link between the physics at the electro-weak scale and the Planck scale. Experiments can shred light on the Yukawa coupling of the Higgs boson to fermions, which is a new kind of fundamental interaction. Run 2 of the LHC was completed in 2018 and provided about 140 fb$^{-1}$ of data. These proceedings discuss the state of the art of the 125 GeV Higgs boson measurements and their implications for the understanding of the Higgs sector.
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access | {"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": 0.9227458238601685, "perplexity": 604.9294824116371}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107882103.34/warc/CC-MAIN-20201024080855-20201024110855-00595.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition/chapter-7-trigonometric-identities-and-equations-7-6-trigonometric-equations-7-6-exercises-page-721/70 | Precalculus (6th Edition)
$x\displaystyle \in\{ \frac{\pi}{3},\frac{4\pi}{3},\frac{2\pi}{3},\frac{5\pi}{3}\}$
... dividing with 2, $\displaystyle \cos 2x=-\frac{1}{2}$ If $0 \leq x < 2\pi$ then $0 \leq 2x < 4\pi$ So, $2x\in[0,4\pi)$, meaning that if $2$x (a solution) is any number from $[0,2\pi)$, then $2x+2\pi$ is also a solution. Using the unit circle,$2x$ can be $\displaystyle \frac{2\pi}{3} \ \$and $\displaystyle \frac{2\pi}{3}+2\pi=\frac{8\pi}{3},$ (quadrant II), or $\displaystyle \frac{4\pi}{3} \ \$and $\displaystyle \frac{4\pi}{3}+2\pi=\frac{10\pi}{3}$ (quadrant III) So, $2x\displaystyle \in\{ \frac{2\pi}{3},\frac{8\pi}{3},\frac{4\pi}{3},\frac{10\pi}{3}\}$ x is half of 2x, so the corresponding values for x are half of the above corresponding values, Solution set: $x\displaystyle \in\{ \frac{\pi}{3},\frac{4\pi}{3},\frac{2\pi}{3},\frac{5\pi}{3}\}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.9826951622962952, "perplexity": 836.1592660706023}, "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-2019-09/segments/1550249501174.94/warc/CC-MAIN-20190223122420-20190223144420-00283.warc.gz"} |
https://www.cableizer.com/documentation/c_SI/ | # Surge velocity of propagation
The surge velocity or phase velocity of a wave is the rate at which the phase of the wave propagates in space.
Symbol
$c_{SI}$
Unit
km/s
Formulae
$\frac{1}{1000\sqrt{\mu_0 \epsilon_0 \epsilon_i}}$
Related | {"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": 0.9878129363059998, "perplexity": 572.4331313528995}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304572.73/warc/CC-MAIN-20220124155118-20220124185118-00144.warc.gz"} |
https://www.physicsforums.com/threads/effective-mass-in-graphene.278136/ | # Effective mass in graphene
1. Dec 8, 2008
### FranzDiCoccio
Hi all,
according to textbook definition the effective mass of a particle in a periodic potential is
$$\frac{\hbar^2}{m*} = \frac{d^2}{d k^2} E(k)$$
where $$E(k)$$ is the energy dispersion.
Is this definition applicable at a generic point of a band, or only at the center and edge of the Brillouin zone, where the band is actually "curved"?
The above definition results in an infinite mass at a point where the band is flat, where by flat I mean zero curvature.
The reason why I'm asking these question is related to the peculiar (tight-binding) band structure of graphene. The two bands of this material touch at two points in (two-dimensional) k-space. Since the local structure of the two bands around these points is conical, under suitable conditions electrons are expected to behave as free massless relativistic particles.
I sort of see this, in view of the similarity between the local dispersion around the special points of graphene and the dispersion of the Dirac equation for free particles.
However, I'm confused by the statement that an electron has an effective mass of zero [Physics Today, Jan 06, p. 21] . This is not the same effective mass $$m*$$ defined above, is it?
Because it seems to me that it should be infinite, since the local dispersion is flat...
I'm aware that one can define different effective masses. Does this mean that in this particular case the electron has both an infinite effective mass (according to one definition) and zero effective mass (from another point of view)?
Or perhaps the definition of $$m*$$ does not apply at the special points of graphene Brillouin cell?
Thanks a lot for any insight
F
Last edited by a moderator: Apr 24, 2017
2. Dec 8, 2008
### FranzDiCoccio
Unfortunately, it does not clarify my doubts completely.
I understand that one should be careful in making a parallel between electrons and relativistic particles. But, even with this proviso in mind, it is not clear to me to what extent electrons do behave as free relativistic particles.
I'm in the process of reading the "serious literature", but I have some difficulty in interpreting the experimental findings. Plus, it seems to me that most of them are about quantum Hall effect, which adds more things on top of the relativistic parallel...
What's the experimental signature of the electron being relativistic as opposed to classical?
Is this just a matter of dispersion relation, like lonewolf seems to be suggesting in the last post of the thread I mention?
And what about the "other effective mass"?
Last edited by a moderator: Apr 24, 2017
3. Dec 8, 2008
### Cthugha
It means, that the linear approximation E=vp of the dispersion relation is valid.
Note that this also means, that the average speed of the particle has a fixed value, which does not depend on the energy of the particle.
4. Dec 9, 2008
### FranzDiCoccio
Hi Cthuga,
Yes, after writing my post it occurred to me that one could think in terms of
speed as well. Perhaps I should actually focus on speed rather than on effective mass.
But to what extent this is "fictitious" and to what extent it is "real"?
Is this spectral feature of graphene actually mirrored in the average speed of
electrons? Can you point me to some experimental result (also a "thought experiment"
would do) which highlights this feature of graphene, and show that the situation with graphene is entirely different from the usual one?
Thanks a lot again
F
5. Dec 9, 2008
### Cthugha
I am afraid I do not know much about graphene. About the only paper I know of, is this classical one:
Two-dimensional gas of massless Dirac fermions in graphene (Nature 438, 197-200 (10 November 2005)) by Novoselov et al.
6. Dec 9, 2008
### FranzDiCoccio
I have that paper, but for some reason I do not find it very helpful.
This "relativistic parallel" is still a bit elusive to me. I understand the similarity
between the dispersion surfaces, but I do not find it completely satisfactory.
So far I have the impression that it is mostly a decoy to capture the reader's
(editor's) attention, but probably this is just due to my illiteracy in
the subject.
I'm trying to get better bearings by reading more literature, but if any of the
forum people has any illuminating comment, it is mostly welcome.
F
7. Dec 9, 2008
### edguy99
Thank you, I will try one. I hope someone with working knowledge can help.
Usually the carbon atom (6 electrons) is thought of as 2 electons in an inner orbital (less then 53pm from the center - trapped at fairly high energies). The next 2 electrons are caught in the 2s oribital on either side of the molecule at say 77pm. The last 2 electrons are a little farther out in the 2p orbital. Carbon binds into diamond with the 2s and 2p orbitals fairly far apart. Carbon binds into organic molecules (hydrocarbons, etc) with the 2s and 2p orbitals very close together. Carbon in this form generally binds into tetrahedral type structures.
Graphene is quite a bit different. Here, one of the 2p electrons is close in energy to the 2s level and the other is "almost" free. The two 2s electrons and the one 2p electrons make 3 electrons that bind the carbon into sheets with one electron orbital left that sticks above the sheet that binds the sheets into layers. This electron between the sheets is what is readily available to move around.
8. Dec 9, 2008
### f95toli
You are not alone. The "connection" to the Dirac equation and relativistic physics is very controversial. I've been to meetings where this has been discussed and also have collegues who work with graphene (for the record: I don't, so I am NOT an expert, my knowledge is mainly tea-room based).
There are plenty of people who work in the field that thinks that this is a bit of a ploy; it looks could when applying for a grant but that does not mean that there is anything of substance.
9. Dec 10, 2008
### FranzDiCoccio
Hi edguy 99,
and thanks for your input! The filling is surely an important ingredient of the whole thing,
and at some point I was actually wondering why on earth it should be 1/2 in graphene.
I have found basically the same answer as you are suggesting in a paper dating back to 1947
(a Phys Rev by one Wallace).
But, important as it might be, half filling is just the starting point, in my view.
I mean, half filling (or somewhere in its vicinity) is the condition in which the odd dispersion
of graphene is expected to have some role.
What I was asking is: assuming that we're around half-filling, in what sense the electrons
behave relativistically? What's the relativistic signature in their behaviour, and can I tell it apart from their "usual" behaviour
in an experiment?
10. Dec 10, 2008
### FranzDiCoccio
Hi f95toli,
and thanks for replying. I have actually the same impression as you. But for some reason I'm willing to resist it.
I mean, are Nature's and Physical Review Letters' referees and editors so gullible to accept
a paper just because the authors do some handwaving and write cool things like "bench-top high-energy physics"?
There must be some meat under all of this smoke.
My (optimistic) impression is that one must be careful in drawing the parallel. I have the
feeling that "relativistic effects" might be actually there, although they might have been
known for ages under different names. I mean, they could be well known effects in
condensed matter physics that could have a "relativistic" interpretation.
I'm not sure whether this new point of view is anywhere near useful, because I still don't get it.
But if it has some real basis, I'd like to understand it.
11. Dec 10, 2008
### edguy99
I dont know if this would be relativistic, quantum or just plain wierd. Above a sheet of graphene (or between 2 sheets), a grid type energy is going to form with the dominating feature being the big heavy carbon protons that are bound by the 3 electrons. This grid has high points and low points of energy and thats where the electrons fill in. Adding an electron into this grid, does not just change the distribution of electrons like springs, but causes an electron in that grid spot (or orbital) to jump to a grid spot right beside it. If this spot is occupied, the electron will pop to the next and so on. This seems more like a quantum effect rather then a relativistic effect since the electrons are travelling less then 1% of the speed of light.
Someone has posted:
"If the string of zeroes are electrons in the graphite and electron A kicks in
resulting in electron B being kicked out at the other side then the speed
of A to B would appear to be extremely high.
A ---> 00000000000000000000000000000000000000000000
------ 00000000000000000000000000000000000000000000 ----> B"
12. Dec 10, 2008
### FranzDiCoccio
I'm not sure I'm following you... What do you mean by "grid type energy"?
Probably it is a limit of mine, but your referring to protons and orbitals confuses me.
Plus, most of the papers I've seen ultimately deal with a simple "pure-hopping" tight-binding
model, assuming half filling.
I'd like to understand the (allegedly) cool relativistic effect in this framework.
Well, surely it has a quantum origin. And I'd say that here "relativistic" does not mean that
the speed of electrons is anywhere near c, since it is obviously not true.
I'm not even sure any more that the "relativistic" particle is the electron.
Perhaps it is something "more structured".
As far as I understand (but I am by no means sure) the pseudospin appearing in the Dirac
equations involves both of the sites in a graphene unit cell.
This might have something to do with what I say above... But perhaps it has not.. | {"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": 0.8184716105461121, "perplexity": 864.1862772815924}, "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/1529267860684.14/warc/CC-MAIN-20180618164208-20180618184208-00211.warc.gz"} |
http://tex.stackexchange.com/questions/73917/subtle-issue-when-changing-font-style-of-the-toc-in-connection-with-the-header-o/73931 | subtle issue when changing font style of the toc in connection with the header of the page
I am using the amsbook class and changed the font style of the title of the table of contents (toc) with the command
\renewcommand{\contentsname}{\textbf{\textsf{Contents}}}
So I want it in \sf style and bold face letters. The toc has two pages, and on the second page there appears a header line with CONTENTS written in smallcaps, also in \sf and bold face letters. I however do not want it to be bold face here. Is there a simple solution to change that? If it is complicated I guess I just live with the default amsbook style. Thanks anyway for any suggestions!
-
Redefining the formatting directly changing \contentsname is not a good idea since the changes will also affect the headers and (an eventual) entry in the ToC. Given the way \@starttoc is defined in amsbook, you need to redefine \@starttoc; the following example shows the necessary redefinition that will produce the desired effect (it will also apply the formatting to the titles of the LoF and the LoT):
\documentclass{amsbook}
\makeatletter
\def\@starttoc#1#2{%
\begingroup
\let\secdef\@gobbletwo \chapter
\let\@secnumber\@empty % for \@tocwrite and \chaptermark
\ifx\contentsname#2%
\else \@tocwrite{chapter}{#2}\fi
\typeout{#2}\@xp\chaptermark\@xp{#2}%
\makeatletter
\@input{\jobname.#1}%
\if@filesw
\@xp\newwrite\csname tf@#1\endcsname
\immediate\@xp\openout\csname tf@#1\endcsname \jobname.#1\relax
\fi
\global\@nobreakfalse \endgroup
\newpage
}
\makeatother
\begin{document}
\tableofcontents
\listoftables
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\chapter{Test}\section{test}\section{test}
\end{document}
The upper part of the first and second pages of the ToC:
-
Thanks for help! It works perfectly :) – Britzel Sep 25 '12 at 12:27
You should not subvert the \contentsname for changing the formatting, it is merely meant to hold the actual name of the table of contents, and as you experience it is used more than one place. What you see on the second page is the running head.
The formatting for the heading of tableofcontents, and other such lists, is controlled by an internal command called \@makeschapterhead. You can redefine as follows to get bold sans-serif for the headings of all of these lists:
\documentclass{amsbook}
\makeatletter
\begingroup
\fontsize{\@xivpt}{18}\bfseries\sffamily\centering
#1\par \endgroup
\vskip\skip@ }
\makeatother
\begin{document}
\tableofcontents
\chapter{Test}
\end{document}
Should you just wish to change the formatting for the table of contents then you can use the following which switches to a custom style just for the \tableofcontents command:
\documentclass{amsbook}
\makeatletter
\begingroup
\fontsize{\@xivpt}{18}\bfseries\sffamily\centering
#1\par \endgroup
\vskip\skip@ }
\makeatother
\begin{document}
\tableofcontents
\listoffigures
\chapter{Test}
\end{document}
-
The command \patchcmd{\@makeschapterhead}{\bfseries}{\bfseries\sffamily}{}{} (needs etoolbox and the usual \makeat...) is easier and perhaps more maintainable. For the second method you can \let\@maketochead\@makeschapterhead and patch \@maketochead, then redefine \tableofcontents in the same way as you already do. – egreg Sep 24 '12 at 20:01
@egreg That certainly an interesting variation. I am little wary of \patchcmd though, as obtaining the correct effect requires some stable knowledge of the definititon of the command being patched. – Andrew Swann Sep 25 '12 at 9:36
Hi and thanks for your answer! I adopted Gonzalo Medina's approach now. Your's might be useful as well for me in the future! Thanks! – Britzel Sep 25 '12 at 12:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8993186354637146, "perplexity": 1563.1221294999357}, "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-2015-48/segments/1448398446535.72/warc/CC-MAIN-20151124205406-00236-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://arxiv.org/abs/1902.04823 | # Nuclear Experiment
arXiv:1902.04823 (nucl-ex)
# Title:X-ray pumping of the Th-229 nuclear clock isomer
Abstract: Thorium-229 is a unique case in nuclear physics: it presents a metastable first excited state Th-229m, just a few electronvolts above the nuclear ground state. This so-called isomer is accessible by VUV lasers, which allows transferring the amazing precision of atomic laser spectroscopy to nuclear physics. Being able to manipulate the Th-229 nuclear states at will opens up a multitude of prospects, from studies of the fundamental interactions in physics to applications as a compact and robust nuclear clock. However, direct optical excitation of the isomer or its radiative decay back to the ground state has not yet been observed, and a series of key nuclear structure parameters such as the exact energies and half-lives of the low-lying nuclear levels of Th-229 are yet unknown. Here we present the first active optical pumping into Th-229m. Our scheme employs narrow-band 29 keV synchrotron radiation to resonantly excite the second excited state, which then predominantly decays into the isomer. We determine the resonance energy with 0.07 eV accuracy, measure a half-life of 82.2 ps, an excitation linewidth of 1.70 neV, and extract the branching ratio of the second excited state into the ground and isomeric state respectively. These measurements allow us to re-evaluate gamma spectroscopy data that have been collected over 40~years.
Comments: 14 pages with 9 figures and 3 tables Subjects: Nuclear Experiment (nucl-ex); Instrumentation and Detectors (physics.ins-det) DOI: 10.1038/s41586-019-1542-3 Cite as: arXiv:1902.04823 [nucl-ex] (or arXiv:1902.04823v1 [nucl-ex] for this version)
## Submission history
From: Noboru Sasao [view email]
[v1] Wed, 13 Feb 2019 09:58:46 UTC (1,195 KB) | {"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": 0.872541606426239, "perplexity": 3585.905383946047}, "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-2020-24/segments/1590347410745.37/warc/CC-MAIN-20200531023023-20200531053023-00115.warc.gz"} |
https://worldwidescience.org/topicpages/h/hydrocarbon-diffuse+interstellar+band.html | #### Sample records for hydrocarbon-diffuse interstellar band
1. Infrared diffuse interstellar bands
Science.gov (United States)
Galazutdinov, G. A.; Lee, Jae-Joon; Han, Inwoo; Lee, Byeong-Cheol; Valyavin, G.; Krełowski, J.
2017-05-01
We present high-resolution (R ˜ 45 000) profiles of 14 diffuse interstellar bands in the ˜1.45 to ˜2.45 μm range based on spectra obtained with the Immersion Grating INfrared Spectrograph at the McDonald Observatory. The revised list of diffuse bands with accurately estimated rest wavelengths includes six new features. The diffuse band at 15 268.2 Å demonstrates a very symmetric profile shape and thus can serve as a reference for finding the 'interstellar correction' to the rest wavelength frame in the H range, which suffers from a lack of known atomic/molecular lines.
2. Probing the diffuse interstellar medium with diffuse interstellar bands
Science.gov (United States)
Theodorus van Loon, Jacco; Bailey, Mandy; Farhang, Amin; Javadi, Atefeh; Khosroshahi, Habib
2015-08-01
For a century already, a large number of absorption bands have been known at optical wavelengths, called the diffuse interstellar bands (DIBs). While their carriers remain unidentified, the relative strengths of these bands in various environments make them interesting new probes of the diffuse interstellar medium (ISM). We present the results from two large, dedicated campaigns to map the ISM using DIBs measured in the high signal-to-noise spectra of hundreds of early-type stars: [1] in and around the Local Bubble using ESO's New Technology Telescope and the Isaac Newton Telescope, and [2] across both Magellanic Clouds using the Very Large Telescope and the Anglo-Australian Telescope. We discuss the implications for the structure and dynamics of the ISM, as well as the constraints these maps place on the nature of the carriers of the DIBs. Partial results have appeared in the recent literature (van Loon et al. 2013; Farhang et al. 2015a,b; Bailey, PhD thesis 2014) with the remainder being prepared for publication now.
3. VIBRONIC PROGRESSIONS IN SEVERAL DIFFUSE INTERSTELLAR BANDS
International Nuclear Information System (INIS)
Duley, W. W.; Kuzmin, Stanislav
2010-01-01
A number of vibronic progressions based on low-energy vibrational modes of a large molecule have been found in the diffuse interstellar band (DIB) spectrum of HD 183143. Four active vibrational modes have been identified with energies at 5.18 cm -1 , 21.41 cm -1 , 31.55 cm -1 , and 34.02 cm -1 . The mode at 34.02 cm -1 was previously recognized by Herbig. Four bands are associated with this molecule, with origins at 6862.61 A, 6843.64 A, 6203.14 A, and 5545.11 A (14589.1 cm -1 , 14608.08 cm -1 , 16116.41 cm -1 , and 18028.9 cm -1 , respectively). The progressions are harmonic and combination bands are observed involving all modes. The appearance of harmonic, rather than anharmonic, terms in these vibronic progressions is consistent with torsional motion of pendant rings, suggesting that the carrier is a 'floppy' molecule. Some constraints on the type and size of the molecule producing these bands are discussed.
4. The ESO Diffuse Interstellar Band Large Exploration Survey (EDIBLES)
Science.gov (United States)
Cami, J.; Cox, N. L.; Farhang, A.; Smoker, J.; Elyajouri, M.; Lallement, R.; Bacalla, X.; Bhatt, N. H.; Bron, E.; Cordiner, M. A.; de Koter, A..; Ehrenfreund, P.; Evans, C.; Foing, B. H.; Javadi, A.; Joblin, C.; Kaper, L.; Khosroshahi, H. G.; Laverick, M.; Le Petit, F..; Linnartz, H.; Marshall, C. C.; Monreal-Ibero, A.; Mulas, G.; Roueff, E.; Royer, P.; Salama, F.; Sarre, P. J.; Smith, K. T.; Spaans, M.; van Loon, J. T..; Wade, G.
2018-03-01
The ESO Diffuse Interstellar Band Large Exploration Survey (EDIBLES) is a Large Programme that is collecting high-signal-to-noise (S/N) spectra with UVES of a large sample of O and B-type stars covering a large spectral range. The goal of the programme is to extract a unique sample of high-quality interstellar spectra from these data, representing different physical and chemical environments, and to characterise these environments in great detail. An important component of interstellar spectra is the diffuse interstellar bands (DIBs), a set of hundreds of unidentified interstellar absorption lines. With the detailed line-of-sight information and the high-quality spectra, EDIBLES will derive strong constraints on the potential DIB carrier molecules. EDIBLES will thus guide the laboratory experiments necessary to identify these interstellar “mystery molecules”, and turn DIBs into powerful diagnostics of their environments in our Milky Way Galaxy and beyond. We present some preliminary results showing the unique capabilities of the EDIBLES programme.
5. PROPERTIES OF DIFFUSE INTERSTELLAR BANDS AT DIFFERENT PHYSICAL CONDITIONS OF THE INTERSTELLAR MEDIUM
International Nuclear Information System (INIS)
Kos, J.; Zwitter, T.
2013-01-01
Diffuse interstellar bands (DIBs) can trace different conditions of the interstellar medium (ISM) along the sightline toward the observed stars. A small survey was made in optical wavelengths, producing high-resolution and high signal-to-noise spectra. We present measurements of 19 DIBs' properties in 50 sightlines toward hot stars, distributed at a variety of galactic coordinates and interstellar reddening. Equivalent widths were obtained by fitting asymmetric Gaussian and variable continua to DIBs. Conditions of the ISM were calculated from eight atomic and molecular interstellar lines. Two distinctly different types of DIBs were identified by carefully comparing correlation coefficients between DIBs and reddening and by different behavior in UV-shielded (ζ) and nonshielded (σ) sightlines. A ratio of DIBs at 5780 Å and 5797 Å proved to be reliable enough to distinguish between two different sightline types. Based on the linear relations between DIB equivalent width and reddening for σ and ζ sightlines, we divide DIBs into type I (where both linear relations are similar) and type II (where they are significantly different). The linear relation for ζ type sightlines always shows a higher slope and larger x-intercept parameter than the relation for σ sightlines. Scatter around the linear relation is reduced after the separation, but it does not vanish completely. This means that UV shielding is the dominant factor of the DIB equivalent width versus reddening relation shape for ζ sightlines, but in σ sightlines other physical parameters play a major role. No similar dependency on gas density, electron density, or turbulence was observed. A catalog of all observed interstellar lines is made public
6. Empirical relationship of ultraviolet extinction and the interstellar diffuse bands
International Nuclear Information System (INIS)
Wu, C.; York, D.G.; Snow, T.P.
1981-01-01
New ultraviolet colors are presented for 110 hot stars. These data are combined with infrared colors and diffuse-band measurements to study the relationship of diffuse interstellar bands (lambdalambda4430, 5780, 6284) to the overall extinction curve. Equivalent widths of lambdalambda5780 and 6284 are not well correlated with infrared, visible, or ultraviolet extinction measurements for stars in our sample. The central depth of lambda4430 is well correlated with visible and infrared extinction, but less well correlated with UV extinction at 1800 A. lambda4430 is strongly correlated with the strength of the 2200-A bump. Our data suggest that if small grains account for the general rise in UV extinction, the diffuse bands are not formed in these grains. lambda4430 may well arise in large grains and/or in the material responsible for the 2200-A bump. Correlations with UV extinctions derived by other authors are discussed in detail. It is suggested that definitions of extinction parameters and band shapes, as well as selection effects in small samples of stars, may still compromise conclusions based on correlation studies such as we are attempting
7. The VLT-FLAMES Tarantula Survey. IX. The interstellar medium seen through diffuse interstellar bands and neutral sodium
NARCIS (Netherlands)
van Loon, J.Th.; Bailey, M.; Tatton, B.L.; Maíz Apellániz, J.; Crowther, P.A.; de Koter, A.; Evans, C.J.; Hénault-Brunet, V.; Howarth, I.D.; Richter, P.; Sana, H.; Simón-Díaz, S.; Taylor, W.; Walborn, N.R.
2013-01-01
Context. The Tarantula Nebula (a.k.a. 30 Dor) is a spectacular star-forming region in the Large Magellanic Cloud (LMC), seen through gas in the Galactic disc and halo. Diffuse interstellar bands (DIBs) offer a unique probe of the diffuse, cool-warm gas in these regions. Aims. The aim is to use DIBs
8. Using Machine Learning to classify the diffuse interstellar bands
Science.gov (United States)
Baron, Dalya; Poznanski, Dovi; Watson, Darach; Yao, Yushu; Cox, Nick L. J.; Prochaska, J. Xavier
2015-07-01
Using over a million and a half extragalactic spectra from the Sloan Digital Sky Survey we study the correlations of the diffuse interstellar bands (DIBs) in the Milky Way. We measure the correlation between DIB strength and dust extinction for 142 DIBs using 24 stacked spectra in the reddening range E(B - V) studied before. Most of the DIBs do not correlate with dust extinction. However, we find 10 weak and barely studied DIBs with correlations that are higher than 0.7 with dust extinction and confirm the high correlation of additional five strong DIBs. Furthermore, we find a pair of DIBs, 5925.9 and 5927.5 Å, which exhibits significant negative correlation with dust extinction, indicating that their carrier may be depleted on dust. We use Machine Learning algorithms to divide the DIBs to spectroscopic families based on 250 stacked spectra. By removing the dust dependence, we study how DIBs follow their local environment. We thus obtain six groups of weak DIBs, four of which are tightly associated with C2 or CN absorption lines.
9. Applicability of Broad-Band Photometry for Determining the Properties of Stars and Interstellar Extinction
Science.gov (United States)
Sichevskij, S. G.
2018-01-01
The feasibility of the determination of the physical conditions in star's atmosphere and the parameters of interstellar extinction from broad-band photometric observations in the 300-3000 nm wavelength interval is studied using SDSS and 2MASS data. The photometric accuracy of these surveys is shown to be insufficient for achieving in practice the theoretical possibility of estimating the atmospheric parameters of stars based on ugriz and JHK s photometry exclusively because such determinations result in correlations between the temperature and extinction estimates. The uncertainty of interstellar extinction estimates can be reduced if prior data about the temperature are available. The surveys considered can nevertheless be potentially valuable sources of information about both stellar atmospheric parameters and the interstellar medium.
10. PROBING THE LOCAL BUBBLE WITH DIFFUSE INTERSTELLAR BANDS. III. THE NORTHERN HEMISPHERE DATA AND CATALOG
Energy Technology Data Exchange (ETDEWEB)
Farhang, Amin; Khosroshahi, Habib G.; Javadi, Atefeh [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran (Iran, Islamic Republic of); Van Loon, Jacco Th., E-mail: [email protected] [Astrophysics Group, Lennard-Jones Laboratories, Keele University, Staffordshire ST5 5BG (United Kingdom)
2015-02-01
We present new high signal-to-noise ratio (S/N) observations of the diffuse interstellar bands (DIBs) in the Local Bubble and its surroundings. We observed 432 sightlines and obtain the equivalent widths of the λ5780 and λ5797 Å DIBs up to a distance of ∼200 pc. All of the observations were carried out using the Intermediate Dispersion Spectrograph on the 2.5 m Isaac Newton Telescope, during three years, to reach a minimum S/N of ∼2000. All of the λ5780 and λ5797 absorptions are presented in this paper and we tabulate the observed values of the interstellar parameters, λ5780, λ5797, Na ID{sub 1}, and Na ID{sub 2}, including the uncertainties.
11. PROBING THE LOCAL BUBBLE WITH DIFFUSE INTERSTELLAR BANDS. III. THE NORTHERN HEMISPHERE DATA AND CATALOG
International Nuclear Information System (INIS)
Farhang, Amin; Khosroshahi, Habib G.; Javadi, Atefeh; Van Loon, Jacco Th.
2015-01-01
We present new high signal-to-noise ratio (S/N) observations of the diffuse interstellar bands (DIBs) in the Local Bubble and its surroundings. We observed 432 sightlines and obtain the equivalent widths of the λ5780 and λ5797 Å DIBs up to a distance of ∼200 pc. All of the observations were carried out using the Intermediate Dispersion Spectrograph on the 2.5 m Isaac Newton Telescope, during three years, to reach a minimum S/N of ∼2000. All of the λ5780 and λ5797 absorptions are presented in this paper and we tabulate the observed values of the interstellar parameters, λ5780, λ5797, Na ID 1 , and Na ID 2 , including the uncertainties
12. Probing the Local Bubble with Diffuse Interstellar Bands. III. The Northern Hemisphere Data and Catalog
Science.gov (United States)
Farhang, Amin; Khosroshahi, Habib G.; Javadi, Atefeh; van Loon, Jacco Th.
2015-02-01
We present new high signal-to-noise ratio (S/N) observations of the diffuse interstellar bands (DIBs) in the Local Bubble and its surroundings. We observed 432 sightlines and obtain the equivalent widths of the λ5780 and λ5797 Å DIBs up to a distance of ~200 pc. All of the observations were carried out using the Intermediate Dispersion Spectrograph on the 2.5 m Isaac Newton Telescope, during three years, to reach a minimum S/N of ~2000. All of the λ5780 and λ5797 absorptions are presented in this paper and we tabulate the observed values of the interstellar parameters, λ5780, λ5797, Na ID1, and Na ID2, including the uncertainties.
13. Perspective: C60+ and laboratory spectroscopy related to diffuse interstellar bands
Science.gov (United States)
Campbell, E. K.; Maier, J. P.
2017-04-01
In the last 30 years, our research has focused on laboratory measurements of the electronic spectra of organic radicals and ions. Many of the species investigated were selected based on their potential astrophysical relevance, particularly in connection with the identification of appealing candidate molecules for the diffuse interstellar absorptions. Notably, carbon chains and derivatives containing hydrogen and nitrogen atoms in their neutral and ionic forms were studied. These data could be obtained after developing appropriate techniques to record spectra at low temperatures relevant to the interstellar medium. The measurement of gas phase laboratory spectra has enabled direct comparisons with astronomical data to be made and though many species were found to have electronic transitions in the visible where the majority of diffuse bands are observed, none of the absorptions matched the prominent interstellar features. In 2015, however, the first carrier molecule was identified: C60 + . This was achieved after the measurement of the electronic spectrum of C60 + -He at 6K in a radiofrequency ion trap.
14. EVIDENCE FOR DIACETYLENE CATION AS THE CARRIER OF A DIFFUSE INTERSTELLAR BAND
International Nuclear Information System (INIS)
Krelowski, J.; Beletsky, Y.; LoCurto, G.; Galazutdinov, G. A.; Kolos, R.; Gronowski, M.
2010-01-01
High-quality spectra acquired at three different observatories point to the presence of a new diffuse interstellar band (DIB) at 5069 A. The spectral profile of this DIB matches published laboratory measurements of the diacetylene cation A 2 Π u -X 2 Π g (0-0) low-temperature gas-phase optical absorption. HC 4 H + is approximately 60-80 times less abundant than CH along the analyzed lines of sight. Only an upper limit could presently be inferred from the search for an analogous band of the triacetylene cation HC 6 H + , expected at 6001.1 A, which implies the HC 6 H + to HC 4 H + ratio of less than ∼1/3.
15. FIRST INFRARED BAND STRENGTHS FOR AMORPHOUS CO{sub 2}, AN OVERLOOKED COMPONENT OF INTERSTELLAR ICES
Energy Technology Data Exchange (ETDEWEB)
Gerakines, Perry A.; Hudson, Reggie L., E-mail: [email protected] [Astrochemistry Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States)
2015-08-01
Solid carbon dioxide (CO{sub 2}) has long been recognized as a component of both interstellar and solar system ices, but a recent literature search has revealed significant qualitative and quantitative discrepancies in the laboratory spectra on which the abundances of extraterrestrial CO{sub 2} are based. Here we report new infrared (IR) spectra of amorphous CO{sub 2}-ice along with band intensities (band strengths) of four mid-IR absorptions, the first such results in the literature. A possible thickness dependence for amorphous-CO{sub 2} IR band shapes and positions also is investigated, and the three discordant reports of amorphous CO{sub 2} spectra in the literature are addressed. Applications of our results are discussed with an emphasis on laboratory investigations and results from astronomical observations. A careful comparison with earlier work shows that the IR spectra calculated from several databases for CO{sub 2} ices, all ices being made near 10 K, are not for amorphous CO{sub 2}, but rather for crystalline CO{sub 2} or crystalline-amorphous mixtures.
16. Probing the Local Bubble with diffuse interstellar bands. I. Project overview and southern hemisphere survey
Science.gov (United States)
Bailey, Mandy; van Loon, Jacco Th.; Farhang, Amin; Javadi, Atefeh; Khosroshahi, Habib G.; Sarre, Peter J.; Smith, Keith T.
2016-01-01
Context. The Sun traverses a low-density, hot entity called the Local Bubble. Despite its relevance to life on Earth, the conditions in the Local Bubble and its exact configuration are not very well known. Besides that, there is some unknown interstellar substance that causes a host of absorption bands across the optical spectrum, called diffuse interstellar bands (DIBs). Aims: We have started a project to chart the Local Bubble in a novel way and learn more about the carriers of the DIBs, by using DIBs as tracers of diffuse gas and environmental conditions. Methods: We conducted a high signal-to-noise spectroscopic survey of 670 nearby early-type stars to map DIB absorption in and around the Local Bubble. The project started with a southern hemisphere survey conducted at the European Southern Observatory's New Technology Telescope and has since been extended to an all-sky survey using the Isaac Newton Telescope. Results: In this first paper in the series, we introduce the overall project and present the results from the southern heiphere survey. We make aviable a catalogue of equivalent-width measurements of the DIBs at 5780, 5797, 5850, 6196, 6203, 6270, 6283, and 6614 Å, of the interstellar Na I D lines at 5890 and 5896 Å, and of the stellar He I line at 5876 Å. We find that the 5780 Å DIB is relatively strong throughout, as compared to the 5797 Å DIB, but especially within the Local Bubble and at the interface iwth a more neutral medium. The 6203 Å DIB shows similar behaviour with respect to the 6196 Å DIB. Some nearby stars show surprisingly strong DIBs, whereas some distant stars show very weak DIBs, indicating small-scale structure within, as well as outside, the Local Bubble. The sight lines with non-detections trace the extent of the Local Bubble especially clearly and show it opening out into the halo. Conclusions: The Local Bubble has a wall that is in contact with hot gas and/or a harsh interstellar radiation field. That wall is perforated
17. Exploring the diffuse interstellar bands with the Sloan Digital Sky Survey
Science.gov (United States)
Lan, Ting-Wen; Ménard, Brice; Zhu, Guangtun
2015-10-01
We use star, galaxy and quasar spectra taken by the Sloan Digital Sky Survey to map out the distribution of diffuse interstellar bands (DIBs) induced by the Milky Way. After carefully removing the intrinsic spectral energy distribution of each source, we show that by stacking thousands of spectra, it is possible to measure statistical flux fluctuations at the 10-3 level, detect more than 20 DIBs and measure their strength as a function of position on the sky. We create a map of DIB absorption covering about 5000 deg2 and measure correlations with various tracers of the interstellar medium: atomic and molecular hydrogen, dust and polycyclic aromatic hydrocarbons (PAHs). After recovering known correlations, we show that each DIB has a different dependence on atomic and molecular hydrogen: while they are all positively correlated with N_{H I}, they exhibit a range of behaviours with N_{H_2} showing positive, negative or no correlation. We show that a simple parametrization involving only N_{H I} and N_{H_2} applied to all the DIBs is sufficient to reproduce a large collection of observational results reported in the literature: it allows us to naturally describe the relations between DIB strength and dust reddening (including the so-called skin effect), the related scatter, DIB pair-wise correlations and families, the affinity for σ/ζ-type environments and other correlations related to molecules. Our approach allows us to characterize DIB dependencies in a simple manner and provides us with a metric to characterize the similarity between different DIBs.
18. PROBING THE LOCAL BUBBLE WITH DIFFUSE INTERSTELLAR BANDS. II. THE DIB PROPERTIES IN THE NORTHERN HEMISPHERE
Energy Technology Data Exchange (ETDEWEB)
Farhang, Amin; Khosroshahi, Habib G.; Javadi, Atefeh; Molaeinezhad, Alireza; Tavasoli, Saeed; Habibi, Farhang; Kourkchi, Ehsan; Rezaei, Sara; Saberi, Maryam [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746 Tehran (Iran, Islamic Republic of); Van Loon, Jacco Th.; Bailey, Mandy [Astrophysics Group, Lennard-Jones Laboratories, Keele University, Staffordshire ST5 5BG (United Kingdom); Hardy, Liam, E-mail: [email protected] [Isaac Newton Group, Apartado 321, E-38700 Santa Cruz de La Palma (Spain)
2015-02-10
We present a new high signal-to-noise ratio spectroscopic survey of the Northern hemisphere to probe the Local Bubble and its surroundings using the λ5780 Å and λ5797 Å diffuse interstellar bands (DIBs). We observed 432 sightlines to a distance of 200 pc over a duration of three years. In this study, we establish the λ5780 and λ5797 correlations with Na I, Ca II and E {sub B-V}, for both inside and outside the Local Bubble. The correlations show that among all neutral and ionized atoms, the correlation between Ca II and λ5780 is stronger than its correlation with λ5797, suggesting that λ5780 is more associated with regions where Ca{sup +} is more abundant. We study the λ5780 correlation with λ5797, which shows a tight correlation within and outside the Local Bubble. In addition, we investigate the DIB properties in UV irradiated and UV shielded regions. We find that, within and beyond the Local Bubble, λ5797 is located in denser parts of clouds, protected from UV irradiation, while λ5780 is located in the low-density regions of clouds.
19. PAHs and the Diffuse Interstellar Bands. What have we Learned from the New Generation of Laboratory and Observational Studies?
Science.gov (United States)
Salama, Farid
2005-01-01
Polycyclic Aromatic Hydrocarbons (PAHs) are an important and ubiquitous component of carbon-bearing materials in space. PAHs are the best-known candidates to account for the IR emission bands (UIR bands) and PAH spectral features are now being used as new probes of the ISM. PAHs are also thought to be among the carriers of the diffuse interstellar absorption bands (DIBs). In the model dealing with the interstellar spectral features, PAHs are present as a mixture of radicals, ions and neutral species. PAH ionization states reflect the ionization balance of the medium while PAH size, composition, and structure reflect the energetic and chemical history of the medium. A major challenge for laboratory astrophysics is to reproduce (in a realistic way) the physical conditions that exist in the emission and/or absorption interstellar zones, An extensive laboratory program has been developed at NASA Ames to characterize the physical and chemical properties of PAHs in astrophysical environments and to describe how they influence the radiation and energy balance in space and the interstellar chemistry. In particular, laboratory experiments provide measurements of the spectral characteristics of interstellar PAH analogs from the ultraviolet and visible range to the infrared range for comparison with astronomical data. This paper will focus on the recent progress made in the laboratory to measure the direct absorption spectra of neutral and ionized PAHs in the gas phase in the near-W and visible range in astrophysically relevant environments. These measurements provide data on PAHs and nanometer-sized particles that can now be directly compared to astronomical observations. The harsh physical conditions of the IS medium - characterized by a low temperature, an absence of collisions and strong V W radiation fields - are simulated in the laboratory by associating a molecular beam with an ionizing discharge to generate a cold plasma expansion. PAH ions are formed from the neutral
20. NEAR INFRARED DIFFUSE INTERSTELLAR BANDS TOWARD THE CYGNUS OB2 ASSOCIATION
Energy Technology Data Exchange (ETDEWEB)
Hamano, Satoshi; Kondo, Sohei; Sameshima, Hiroaki; Nakanishi, Kenshi; Kawakita, Hideyo [Laboratory of Infrared High-resolution Spectroscopy, Koyama Astronomical Observatory, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555 (Japan); Kobayashi, Naoto [Institute of Astronomy, School of Science, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015 (Japan); Ikeda, Yuji [Photocoding, 460-102 Iwakura-Nakamachi, Sakyo-ku, Kyoto, 606-0025 (Japan); Yasui, Chikako; Mizumoto, Misaki; Matsunaga, Noriyuki; Fukue, Kei; Yamamoto, Ryo; Izumi, Natsuko [Department of Astronomy, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Mito, Hiroyuki [Kiso Observatory, Institute of Astronomy, School of Science, The University of Tokyo, 10762-30 Mitake, Kiso-machi, Kiso-gun, Nagano, 397-0101 (Japan); Nakaoka, Tetsuya; Kawanishi, Takafumi; Kitano, Ayaka; Otsubo, Shogo [Department of Physics, Faculty of Sciences, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555 (Japan); Kinoshita, Masaomi, E-mail: [email protected] [Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi, 464-8601 (Japan)
2016-04-10
We obtained the near-infrared (NIR) high-resolution (R ≡ λ/Δλ ∼ 20,000) spectra of the seven brightest early-type stars in the Cygnus OB2 association for investigating the environmental dependence of diffuse interstellar bands (DIBs). The WINERED spectrograph mounted on the Araki 1.3 m telescope in Japan was used to collect data. All 20 of the known DIBs within the wavelength coverage of WINERED (0.91 < λ < 1.36 μm) were clearly detected along all lines of sight because of their high flux density in the NIR wavelength range and the large extinction. The equivalent widths (EWs) of DIBs were not correlated with the column densities of C{sub 2} molecules, which trace the patchy dense component, suggesting that the NIR DIB carriers are distributed mainly in the diffuse component. On the basis of the correlations among the NIR DIBs both for stars in Cyg OB2 and stars observed previously, λλ10780, 10792, 11797, 12623, and 13175 are found to constitute a “family,” in which the DIBs are correlated well over the wide EW range. In contrast, the EW of λ10504 is found to remain almost constant over the stars in Cyg OB2. The extinction estimated from the average EW of λ10504 (A{sub V} ∼ 3.6 mag) roughly corresponds to the lower limit of the extinction distribution of OB stars in Cyg OB2. This suggests that λ10504 is absorbed only by the foreground clouds, implying that the carrier of λ10504 is completely destroyed in Cyg OB2, probably by the strong UV radiation field. The different behaviors of the DIBs may be caused by different properties of the DIB carriers.
1. The ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES) . I. Project description, survey sample, and quality assessment
Science.gov (United States)
Cox, Nick L. J.; Cami, Jan; Farhang, Amin; Smoker, Jonathan; Monreal-Ibero, Ana; Lallement, Rosine; Sarre, Peter J.; Marshall, Charlotte C. M.; Smith, Keith T.; Evans, Christopher J.; Royer, Pierre; Linnartz, Harold; Cordiner, Martin A.; Joblin, Christine; van Loon, Jacco Th.; Foing, Bernard H.; Bhatt, Neil H.; Bron, Emeric; Elyajouri, Meriem; de Koter, Alex; Ehrenfreund, Pascale; Javadi, Atefeh; Kaper, Lex; Khosroshadi, Habib G.; Laverick, Mike; Le Petit, Franck; Mulas, Giacomo; Roueff, Evelyne; Salama, Farid; Spaans, Marco
2017-10-01
The carriers of the diffuse interstellar bands (DIBs) are largely unidentified molecules ubiquitously present in the interstellar medium (ISM). After decades of study, two strong and possibly three weak near-infrared DIBs have recently been attributed to the C60^+ fullerene based on observational and laboratory measurements. There is great promise for the identification of the over 400 other known DIBs, as this result could provide chemical hints towards other possible carriers. In an effort tosystematically study the properties of the DIB carriers, we have initiated a new large-scale observational survey: the ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES). The main objective is to build on and extend existing DIB surveys to make a major step forward in characterising the physical and chemical conditions for a statistically significant sample of interstellar lines-of-sight, with the goal to reverse-engineer key molecular properties of the DIB carriers. EDIBLES is a filler Large Programme using the Ultraviolet and Visual Echelle Spectrograph at the Very Large Telescope at Paranal, Chile. It is designed to provide an observationally unbiased view of the presence and behaviour of the DIBs towards early-spectral-type stars whose lines-of-sight probe the diffuse-to-translucent ISM. Such a complete dataset will provide a deep census of the atomic and molecular content, physical conditions, chemical abundances and elemental depletion levels for each sightline. Achieving these goals requires a homogeneous set of high-quality data in terms of resolution (R 70 000-100 000), sensitivity (S/N up to 1000 per resolution element), and spectral coverage (305-1042 nm), as well as a large sample size (100+ sightlines). In this first paper the goals, objectives and methodology of the EDIBLES programme are described and an initial assessment of the data is provided.
2. Laboratory determination of the infrared band strengths of pyrene frozen in water ice: Implications for the composition of interstellar ices
Energy Technology Data Exchange (ETDEWEB)
Hardegree-Ullman, E. E. [New York Center for Astrobiology and Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180 (United States); Gudipati, M. S.; Werner, M. [Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109 (United States); Boogert, A. C. A. [Infrared Processing and Analysis Center, Mail Code 100-22, California Institute of Technology, Pasadena, CA 91125 (United States); Lignell, H. [Department of Chemistry, University of California Irvine, Irvine, CA 92697-2025 (United States); Allamandola, L. J. [Space Science Division, Mail Stop 245-6, NASA Ames Research Center, Moffett Field, CA 94035 (United States); Stapelfeldt, K. R., E-mail: [email protected], E-mail: [email protected] [NASA Goddard Space Flight Center, Exoplanets and Stellar Astrophysics Laboratory, Code 667, Greenbelt, MD 20771 (United States)
2014-04-01
Broad infrared emission features (e.g., at 3.3, 6.2, 7.7, 8.6, and 11.3 μm) from the gas phase interstellar medium have long been attributed to polycyclic aromatic hydrocarbons (PAHs). A significant portion (10%-20%) of the Milky Way's carbon reservoir is locked in PAH molecules, which makes their characterization integral to our understanding of astrochemistry. In molecular clouds and the dense envelopes and disks of young stellar objects (YSOs), PAHs are expected to be frozen in the icy mantles of dust grains where they should reveal themselves through infrared absorption. To facilitate the search for frozen interstellar PAHs, laboratory experiments were conducted to determine the positions and strengths of the bands of pyrene mixed with H{sub 2}O and D{sub 2}O ices. The D{sub 2}O mixtures are used to measure pyrene bands that are masked by the strong bands of H{sub 2}O, leading to the first laboratory determination of the band strength for the CH stretching mode of pyrene in water ice near 3.25 μm. Our infrared band strengths were normalized to experimentally determined ultraviolet band strengths, and we find that they are generally ∼50% larger than those reported by Bouwman et al. based on theoretical strengths. These improved band strengths were used to reexamine YSO spectra published by Boogert et al. to estimate the contribution of frozen PAHs to absorption in the 5-8 μm spectral region, taking into account the strength of the 3.25 μm CH stretching mode. It is found that frozen neutral PAHs contain 5%-9% of the cosmic carbon budget and account for 2%-9% of the unidentified absorption in the 5-8 μm region.
3. Theoretical study of electronic absorption spectroscopy of propadienylidene molecule vis-â-vis the observed diffuse interstellar bands
International Nuclear Information System (INIS)
2012-01-01
Highlights: ► Theoretical study of spectroscopy and dynamics of electronically excited l-C 3 H 2 . ► Construction of ab initio electronic potential energy and diabatic coupling surfaces. ► First principles study of nuclear dynamics on excited electronic states. ► Findings reveal l-C 3 H 2 is a potential molecular carrier of diffuse interstellar bands. ► Electronically excited l-C 3 H 2 decays by ultrafast nonradiative internal conversion. -- Abstract: Observation of broad and diffuse interstellar bands (DIBs) at 4881 Å and 5440 Å assigned to the optical absorption spectrum of Y-shaped propadienylidene (H 2 C=C=C:) molecule is theoretically examined in this paper. This molecule apparently absorbs in the same wavelength region as the observed DIBs and was suggested to be a potential carrier of these DIBs. This assignment mostly relied on the experimental data from radioastronomy and laboratory measurements. Motivated by these available experimental data we attempt here a theoretical study and investigate the detailed electronic structure and nuclear dynamics underlying the electronic absorption bands of propadienylidene molecule. Our results show that this molecule indeed absorbs in the wavelength region of the recorded DIBs. Strong nonadiabatic coupling between its energetically low-lying electronic states plays major role, initiates ultrafast internal conversion and contributes to the spectral broadening. Theoretical findings are finally compared with the available experimental and theoretical data and discussed in connection with the recorded DIBs.
4. INTERACTION BETWEEN THE BROAD-LINED TYPE Ic SUPERNOVA 2012ap AND CARRIERS OF DIFFUSE INTERSTELLAR BANDS
International Nuclear Information System (INIS)
Milisavljevic, Dan; Margutti, Raffaella; Crabtree, Kyle N.; Soderberg, Alicia M.; Sanders, Nathan E.; Drout, Maria R.; Kamble, Atish; Chakraborti, Sayan; Kirshner, Robert P.; Foster, Jonathan B.; Fesen, Robert A.; Parrent, Jerod T.; Pickering, Timothy E.; Cenko, S. Bradley; Silverman, Jeffrey M.; Marion, G. H. Howie; Vinko, Jozsef; Filippenko, Alexei V.; Mazzali, Paolo; Maeda, Keiichi
2014-01-01
Diffuse interstellar bands (DIBs) are absorption features observed in optical and near-infrared spectra that are thought to be associated with carbon-rich polyatomic molecules in interstellar gas. However, because the central wavelengths of these bands do not correspond to electronic transitions of any known atomic or molecular species, their nature has remained uncertain since their discovery almost a century ago. Here we report on unusually strong DIBs in optical spectra of the broad-lined Type Ic supernova SN 2012ap that exhibit changes in equivalent width over short (≲ 30 days) timescales. The 4428 Å and 6283 Å DIB features get weaker with time, whereas the 5780 Å feature shows a marginal increase. These nonuniform changes suggest that the supernova is interacting with a nearby source of DIBs and that the DIB carriers possess high ionization potentials, such as small cations or charged fullerenes. We conclude that moderate-resolution spectra of supernovae with DIB absorptions obtained within weeks of outburst could reveal unique information about the mass-loss environment of their progenitor systems and provide new constraints on the properties of DIB carriers
5. INTERACTION BETWEEN THE BROAD-LINED TYPE Ic SUPERNOVA 2012ap AND CARRIERS OF DIFFUSE INTERSTELLAR BANDS
Energy Technology Data Exchange (ETDEWEB)
Milisavljevic, Dan; Margutti, Raffaella; Crabtree, Kyle N.; Soderberg, Alicia M.; Sanders, Nathan E.; Drout, Maria R.; Kamble, Atish; Chakraborti, Sayan; Kirshner, Robert P. [Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 (United States); Foster, Jonathan B. [Yale Center for Astronomy and Astrophysics, Yale University, New Haven, CT 06520 (United States); Fesen, Robert A.; Parrent, Jerod T. [Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Lab, Hanover, NH 03755 (United States); Pickering, Timothy E. [Southern African Large Telescope, P.O. Box 9, Observatory 7935, Cape Town (South Africa); Cenko, S. Bradley [Astrophysics Science Division, NASA Goddard Space Flight Center, Mail Code 661, Greenbelt, MD 20771 (United States); Silverman, Jeffrey M.; Marion, G. H. Howie; Vinko, Jozsef [University of Texas at Austin, 1 University Station C1400, Austin, TX 78712-0259 (United States); Filippenko, Alexei V. [Department of Astronomy, University of California, Berkeley, CA 94720-3411 (United States); Mazzali, Paolo [Astrophysics Research Institute, Liverpool John Moores University, Liverpool L3 5RF (United Kingdom); Maeda, Keiichi, E-mail: [email protected] [Department of Astronomy, Kyoto University Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); and others
2014-02-10
Diffuse interstellar bands (DIBs) are absorption features observed in optical and near-infrared spectra that are thought to be associated with carbon-rich polyatomic molecules in interstellar gas. However, because the central wavelengths of these bands do not correspond to electronic transitions of any known atomic or molecular species, their nature has remained uncertain since their discovery almost a century ago. Here we report on unusually strong DIBs in optical spectra of the broad-lined Type Ic supernova SN 2012ap that exhibit changes in equivalent width over short (≲ 30 days) timescales. The 4428 Å and 6283 Å DIB features get weaker with time, whereas the 5780 Å feature shows a marginal increase. These nonuniform changes suggest that the supernova is interacting with a nearby source of DIBs and that the DIB carriers possess high ionization potentials, such as small cations or charged fullerenes. We conclude that moderate-resolution spectra of supernovae with DIB absorptions obtained within weeks of outburst could reveal unique information about the mass-loss environment of their progenitor systems and provide new constraints on the properties of DIB carriers.
6. Infrared Spectra and Band Strengths of CH3SH, an Interstellar Molecule
Science.gov (United States)
Hudson, R. L.
2016-01-01
Three solid phases of CH3SH (methanethiol or methyl mercaptan) have been prepared and their mid-infrared spectra recorded at 10-110 degrees Kelvin, with an emphasis on the 17-100 degrees Kelvin region. Refractive indices have been measured at two temperatures and used to estimate ice densities and infrared band strengths. Vapor pressures for the two crystalline phases of CH3SH at 110 degrees Kelvin are estimated. The behavior of amorphous CH3SH on warming is presented and discussed in terms of Ostwald's step rule. Comparisons to CH3OH under similar conditions are made, and some inconsistencies and ambiguities in the CH3SH literature are examined and corrected.
7. THE SEARCH FOR THE DIFFUSE INTERSTELLAR BANDS AND OTHER MOLECULES IN COMETS 17P (HOLMES) AND C/2007 W1 (BOATTINI)
International Nuclear Information System (INIS)
O'Malia, K. K. J.; Snow, T. P.; Thorburn, J. A.; Hammergren, M.; Dembicky, J.; Hobbs, L. M.; York, D. G.
2010-01-01
We present the search for both diffuse interstellar bands (DIBs) and molecules in Comet 17P (Holmes) and Comet C/2007 W1 (Boattini) occultation observations. Absorption spectra were taken during stellar occultations by Comet Holmes of 31 and β Persei, and the occultation of BD+22 216 by Comet Boattini. While no signature of the comets was detected, we present upper limits for some common cometary molecules such as C 2 , C 3 , CH, CN and for the most common DIBs. We did not detect either comet in absorption, most likely because of the large distance between the line of sight to the star and the nucleus of the comet. Interstellar sight lines with comparable reddening to what was measured in Comet Holmes have DIB equivalent widths between 5 and 50 mA. However, future observations with closer approaches to a background star have great potential for spatially mapping molecule distributions in comets, and in discovering DIBs, if they are present, in comets. Future observations could detect DIBs and molecules if they are done: (1) less than ∼10 4 -10 3 km from the nucleus (2) with a signal to noise in the background star of ∼300 and (3) with a resolving power of at least 38,000.
8. BROAD BALMER WINGS IN BA HYPER/SUPERGIANTS DISTORTED BY DIFFUSE INTERSTELLAR BANDS: FIVE EXAMPLES IN THE 30 DORADUS REGION FROM THE VLT-FLAMES TARANTULA SURVEY
Energy Technology Data Exchange (ETDEWEB)
Walborn, Nolan R.; Sana, Hugues; Sabbi, Elena, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); and others
2015-08-10
Extremely broad emission wings at Hβ and Hα have been found in VLT-FLAMES Tarantula Survey data for five very luminous BA supergiants in or near 30 Doradus in the Large Magellanic Cloud. The profiles of both lines are extremely asymmetrical, which we have found to be caused by very broad diffuse interstellar bands (DIBs) in the longward wing of Hβ and the shortward wing of Hα. These DIBs are well known to interstellar but not to many stellar specialists, so that the asymmetries may be mistaken for intrinsic features. The broad emission wings are generally ascribed to electron scattering, although we note difficulties for that interpretation in some objects. Such profiles are known in some Galactic hyper/supergiants and are also seen in both active and quiescent Luminous Blue Variables (LBVs). No prior or current LBV activity is known in these 30 Dor stars, although a generic relationship to LBVs is not excluded; subject to further observational and theoretical investigation, it is possible that these very luminous supergiants are approaching the LBV stage for the first time. Their locations in the HRD and presumed evolutionary tracks are consistent with that possibility. The available evidence for spectroscopic variations of these objects is reviewed, while recent photometric monitoring does not reveal variability. A search for circumstellar nebulae has been conducted, with an indeterminate result for one of them.
9. Mapping diffuse interstellar bands in the local ISM on small scales via MUSE 3D spectroscopy. A pilot study based on globular cluster NGC 6397
Science.gov (United States)
Wendt, Martin; Husser, Tim-Oliver; Kamann, Sebastian; Monreal-Ibero, Ana; Richter, Philipp; Brinchmann, Jarle; Dreizler, Stefan; Weilbacher, Peter M.; Wisotzki, Lutz
2017-11-01
Context. We map the interstellar medium (ISM) including the diffuse interstellar bands (DIBs) in absorption toward the globular cluster NGC 6397 using VLT/MUSE. Assuming the absorbers are located at the rim of the Local Bubble we trace structures on the order of mpc (milliparsec, a few thousand AU). Aims: We aimed to demonstrate the feasibility to map variations of DIBs on small scales with MUSE. The sightlines defined by binned stellar spectra are separated by only a few arcseconds and we probe the absorption within a physically connected region. Methods: This analysis utilized the fitting residuals of individual stellar spectra of NGC 6397 member stars and analyzed lines from neutral species and several DIBs in Voronoi-binned composite spectra with high signal-to-noise ratio (S/N). Results: This pilot study demonstrates the power of MUSE for mapping the local ISM on very small scales which provides a new window for ISM observations. We detect small scale variations in Na I and K I as well as in several DIBs within few arcseconds, or mpc with regard to the Local Bubble. We verify the suitability of the MUSE 3D spectrograph for such measurements and gain new insights by probing a single physical absorber with multiple sight lines.
10. Interstellar Extinction
OpenAIRE
Gontcharov, George
2017-01-01
This review describes our current understanding of interstellar extinction. This differ substantially from the ideas of the 20th century. With infrared surveys of hundreds of millions of stars over the entire sky, such as 2MASS, SPITZER-IRAC, and WISE, we have looked at the densest and most rarefied regions of the interstellar medium at distances of a few kpc from the sun. Observations at infrared and microwave wavelengths, where the bulk of the interstellar dust absorbs and radiates, have br...
11. VizieR Online Data Catalog: Catalog of Eq.Widths of Interstellar 217nm Band (Friedemann 1992)
Science.gov (United States)
Friedemann, C.
2005-03-01
(from CDS Inf. Bull. 40, 31) The main task of the catalogue consists in a comprehensive collection of equivalent widths of the 217nm band derived from both spectrophotometric and filterphotometric measurements obtained with TD-1, OAO-2 and ANS satellites. These data concern reddened O, B stars with color excesses E(B-V) >= 0.02 mag. The extinction curve is approximated by the empirical formula introduced by Guertler et al. (1982AN....303..105G) e({lambda}) = A(i/{lambda} - 1/{lambda}o)n + B + C {kappa}({lambda}) The relative errors amount to about {delta}A/A = +/- 0.10, {delta}B/B = +/- 0.02 and {delta}C/C = +/- 0.03. (1 data file).
12. Interstellar ammonia
International Nuclear Information System (INIS)
Ho, P.T.P.; Townes, C.H.
1983-01-01
Investigations and results on interstellar NH3 are discussed. The physics of the molecule, its interstellar excitation, and its formation and dissociation mechanisms are reviewed. The observing techniques and instruments, including single-antenna facilities, infrared and submillimeter techniques, and interferometric studies using the Very Large Array are briefly considered. Spectral data analysis is discussed, including the derivation of optical depths, excitation measurements, ortho-para measurements, and cross sections. Progress achieved in understanding the properties and evolution of the interstellar medium through NH3 studies is reviewed, including observations of nearby dark clouds and of clumping effects in molecular clouds, as well as interferometric observations of hot molecular cores in Orion, W51, and Sagittarius A. Research results on extragalactic NH3, far-infrared, submillimeter, and midinfrared NH3 observations are described. 101 references
13. Interstellar holography
NARCIS (Netherlands)
Walker, M. A.; Koopmans, L. V. E.; Stinebring, D. R.; van Straten, W.
2008-01-01
The dynamic spectrum of a radio pulsar is an in-line digital hologram of the ionized interstellar medium. It has previously been demonstrated that such holograms permit image reconstruction, in the sense that one can determine an approximation to the complex electric field values as a function of
14. Interstellar matter
International Nuclear Information System (INIS)
Mezger, P.G.
1978-01-01
An overview of the formation of our galaxy is presented followed by a summary of recent work in star formation and related topics. Selected discussions are given on interstellar matter including absorption characteristics of dust, the fully ionised component of the ISM and the energy density of lyc-photons in the solar neighbourhood and the diffuse galactic IR radiation
15. Interstellar grains
Energy Technology Data Exchange (ETDEWEB)
Hoyle, F.; Wickramasinghe, N.C.
1980-11-01
Interstellar extinction of starlight was observed and plotted as a function of inverse wavelength. Agreement with the calculated effects of the particle distribution is shown. The main kinds of grain distinguished are: (1) graphite spheres of radius 0.02 microns, making up 10% of the total grain mass (2) small dielectric spheres of radius 0.04 microns making up 25% and (3) hollow dielectric cylinders containing metallic iron, with diameters of 2/3 microns making up 45%. The remaining 20% consists of other metals, metal oxides, and polysiloxanes. Absorption factor evidence suggests that the main dielectric component of the grains is organic material.
16. Interstellar chemistry.
Science.gov (United States)
Klemperer, William
2006-08-15
In the past half century, radioastronomy has changed our perception and understanding of the universe. In this issue of PNAS, the molecular chemistry directly observed within the galaxy is discussed. For the most part, the description of the molecular transformations requires specific kinetic schemes rather than chemical thermodynamics. Ionization of the very abundant molecular hydrogen and atomic helium followed by their secondary reactions is discussed. The rich variety of organic species observed is a challenge for complete understanding. The role and nature of reactions involving grain surfaces as well as new spectroscopic observations of interstellar and circumstellar regions are topics presented in this special feature.
17. PAHs in Translucent Interstellar Clouds
Science.gov (United States)
Salama, Farid; Galazutdinov, G.; Krelowski, J.; Biennier, L.; Beletsky, Y.; Song, I.
2011-05-01
We discuss the proposal of relating the origin of some of the diffuse interstellar bands (DIBs) to neutral polycyclic aromatic hydrocarbons (PAHs) present in translucent interstellar clouds. The spectra of several cold, isolated gas-phase PAHs have been measured in the laboratory under experimental conditions that mimic the interstellar conditions and are compared with an extensive set of astronomical spectra of reddened, early type stars. This comparison provides - for the first time - accurate upper limits for the abundances of specific PAH molecules along specific lines-of-sight. Something that is not attainable from IR observations alone. The comparison of these unique laboratory data with high resolution, high S/N ratio astronomical observations leads to two major findings: (1) a finding specific to the individual molecules that were probed in this study and, which leads to the clear and unambiguous conclusion that the abundance of these specific neutral PAHs must be very low in the individual translucent interstellar clouds that were probed in this survey (PAH features remain below the level of detection) and, (2) a general finding that neutral PAHs exhibit intrinsic band profiles that are similar to the profile of the narrow DIBs indicating that the carriers of the narrow DIBs must have close molecular structure and characteristics. This study is the first quantitative survey of neutral PAHs in the optical range and it opens the way for unambiguous quantitative searches of PAHs in a variety of interstellar and circumstellar environments. // Reference: F. Salama et al. (2011) ApJ. 728 (1), 154 // Acknowledgements: F.S. acknowledges the support of the NASA's Space Mission Directorate APRA Program. J.K. acknowledges the financial support of the Polish State (grant N203 012 32/1550). The authors are deeply grateful to the ESO archive as well as to the ESO staff members for their active support.
18. Interstellar Extinction in the Gaia Photometric Systems
Directory of Open Access Journals (Sweden)
Bridžius A.
2003-12-01
Full Text Available Three medium-band photometric systems proposed for the Gaia space mission are intercompared in determining color excesses for stars of spectral classes from O to M at V = 18 mag. A possibility of obtaining a three-dimensional map of the interstellar extinction is discussed.
19. The Interstellar Medium
CERN Document Server
Lequeux, James
2005-01-01
Describing interstellar matter in our galaxy in all of its various forms, this book also considers the physical and chemical processes that are occurring within this matter. The first seven chapters present the various components making up the interstellar matter and detail the ways that we are able to study them. The following seven chapters are devoted to the physical, chemical and dynamical processes that control the behaviour of interstellar matter. These include the instabilities and cloud collapse processes that lead to the formation of stars. The last chapter summarizes the transformations that can occur between the different phases of the interstellar medium. Emphasizing methods over results, "The Interstellar Medium" is written for graduate students, for young astronomers, and also for any researchers who have developed an interest in the interstellar medium.
20. Interstellar space: the astrochemist's laboratory
International Nuclear Information System (INIS)
Allen, M.A.
1976-01-01
A mechanism for the formation of molecules on small (radius less than or equal to 0.04 μ) interstellar grains is proposed. A simplified H 2 formation model is then presented that utilizes this surface reaction mechanism. This approach is further developed into an ab initio chemical model for dense interstellar clouds that incorporates 598 grain surface reactions, with small grains again providing the key reaction area. Gas-phase molecules are depleted through collisions with grains. The abundances of 372 chemical species are calculated as a function of time and are found to be of sufficient magnitude to explain most observations. The reaction rates for ion-molecule chemistry are approximately the same, therefore indicating that surface and gas-phase chemistry may be coupled in certain regions. The composition of grain mantles is shown to be a function of grain radius. In certain grain size ranges, large molecules containing two or more heavy atoms are more predominant than lighter ''ices''--H 2 O, NH 3 , and CH 4 . It is possible that absorption due to these large molecules in the mantles may contribute to the observed 3μ band in astronomical spectra. The second part of this thesis is an account of a radio astronomy observational program to detect new transitions of both previously observed and yet undetected interstellar molecules. The negative results yield order ofmagnitude upper limits to the column densities of the lower transition states of the various molecules. One special project was the search for the Λ-doublet transitions of the 2 H/sub 3 / 2 /, J = 3 / 2 state of OD. The resulting upper limit for the OD/OH column density ratio towards the galactic center is 1/400 and is discussed with reference to theories about deuterium enrichment in interstellar molecules
1. Search for interstellar methane
International Nuclear Information System (INIS)
Knacke, R.F.; Kim, Y.H.; Noll, K.S.; Geballe, T.R.
1990-01-01
Researchers searched for interstellar methane in the spectra of infrared sources embedded in molecular clouds. New observations of several lines of the P and R branches of the nu 3 band of CH4 near 3.3 microns give column densities in the range N less than 1(-2) times 10 to the minus 16th power cm(-2). Resulting abundance ratios are (CH4)/(CO) less than 3.3 times 10 to the minus 2nd power toward GL961 in NGC 2244 and less than 2.4 times 10 to the minus 3rd power toward GL989 in the NGC 2264 molecular cloud. The limits, and those determined in earlier observations of BN in Orion and GL490, suggest that there is little methane in molecular clouds. The result agrees with predictions of chemical models. Exceptions could occur in clouds where oxygen may be depleted, for example by H2O freezing on grains. The present observations probably did not sample such regions
2. Nature of interstellar turbulence
International Nuclear Information System (INIS)
Altunin, V.
1981-01-01
A significant role in producing the pattern of interstellar scintillation observed in discrete radio sources may be played by the magnetoacoustic turbulence that will be generated as shock waves are propagated at velocity V/sub sh/roughly-equal 20--100 km/sec through the interstellar medium, as well as by irregularities in stellar wind emanating from type OB stars
3. Interstellar hydrogen bonding
Science.gov (United States)
Etim, Emmanuel E.; Gorai, Prasanta; Das, Ankan; Chakrabarti, Sandip K.; Arunan, Elangannan
2018-06-01
This paper reports the first extensive study of the existence and effects of interstellar hydrogen bonding. The reactions that occur on the surface of the interstellar dust grains are the dominant processes by which interstellar molecules are formed. Water molecules constitute about 70% of the interstellar ice. These water molecules serve as the platform for hydrogen bonding. High level quantum chemical simulations for the hydrogen bond interaction between 20 interstellar molecules (known and possible) and water are carried out using different ab-intio methods. It is evident that if the formation of these species is mainly governed by the ice phase reactions, there is a direct correlation between the binding energies of these complexes and the gas phase abundances of these interstellar molecules. Interstellar hydrogen bonding may cause lower gas abundance of the complex organic molecules (COMs) at the low temperature. From these results, ketenes whose less stable isomers that are more strongly bonded to the surface of the interstellar dust grains have been observed are proposed as suitable candidates for astronomical observations.
4. NASA's interstellar probe mission
International Nuclear Information System (INIS)
Liewer, P.C.; Ayon, J.A.; Wallace, R.A.; Mewaldt, R.A.
2000-01-01
NASA's Interstellar Probe will be the first spacecraft designed to explore the nearby interstellar medium and its interaction with our solar system. As envisioned by NASA's Interstellar Probe Science and Technology Definition Team, the spacecraft will be propelled by a solar sail to reach >200 AU in 15 years. Interstellar Probe will investigate how the Sun interacts with its environment and will directly measure the properties and composition of the dust, neutrals and plasma of the local interstellar material which surrounds the solar system. In the mission concept developed in the spring of 1999, a 400-m diameter solar sail accelerates the spacecraft to ∼15 AU/year, roughly 5 times the speed of Voyager 1 and 2. The sail is used to first bring the spacecraft to ∼0.25 AU to increase the radiation pressure before heading out in the interstellar upwind direction. After jettisoning the sail at ∼5 AU, the spacecraft coasts to 200-400 AU, exploring the Kuiper Belt, the boundaries of the heliosphere, and the nearby interstellar medium
5. On Graphene in the Interstellar Medium
Science.gov (United States)
Chen, X. H.; Li, Aigen; Zhang, Ke
2017-11-01
The possible detection of C24, a planar graphene that was recently reported to be in several planetary nebulae by García-Hernández et al., inspires us to explore whether and how much graphene could exist in the interstellar medium (ISM) and how it would reveal its presence through its ultraviolet (UV) extinction and infrared (IR) emission. In principle, interstellar graphene could arise from the photochemical processing of polycyclic aromatic hydrocarbon (PAH) molecules, which are abundant in the ISM, due to the complete loss of their hydrogen atoms, and/or from graphite, which is thought to be a major dust species in the ISM, via fragmentation caused by grain–grain collisional shattering. Both quantum-chemical computations and laboratory experiments have shown that the exciton-dominated electronic transitions in graphene cause a strong absorption band near 2755 \\mathringA . We calculate the UV absorption of graphene and place an upper limit of ∼5 ppm of C/H (i.e., ∼1.9% of the total interstellar C) on the interstellar graphene abundance. We also model the stochastic heating of graphene C24 in the ISM, excited by single starlight photons of the interstellar radiation field and calculate its IR emission spectra. We also derive the abundance of graphene in the ISM to be <5 ppm of C/H by comparing the model emission spectra with that observed in the ISM.
6. The galactic interstellar medium
CERN Document Server
Burton, WB; Genzel, R
1992-01-01
This volume contains the papers of three extended lectures addressing advanced topics in astronomy and astrophysics. The topics discussed include the most recent observational data on interstellar matter outside our galaxy and the physics and chemistry of molecular clouds.
7. Dynamics of interstellar matter
International Nuclear Information System (INIS)
Kahn, F.D.
1975-01-01
A review of the dynamics of interstellar matter is presented, considering the basic equations of fluid flow, plane waves, shock waves, spiral structure, thermal instabilities and early star cocoons. (B.R.H.)
8. Interstellar organic chemistry.
Science.gov (United States)
Sagan, C.
1972-01-01
Most of the interstellar organic molecules have been found in the large radio source Sagittarius B2 toward the galactic center, and in such regions as W51 and the IR source in the Orion nebula. Questions of the reliability of molecular identifications are discussed together with aspects of organic synthesis in condensing clouds, degradational origin, synthesis on grains, UV natural selection, interstellar biology, and contributions to planetary biology.
9. SEARCHING FOR NAPHTHALENE CATION ABSORPTION IN THE INTERSTELLAR MEDIUM
International Nuclear Information System (INIS)
Searles, Justin M.; Destree, Joshua D.; Snow, Theodore P.; Salama, Farid; York, Donald G.; Dahlstrom, Julie
2011-01-01
Interstellar naphthalene cations (C 10 H + 8 ) have been proposed by a study to be the carriers of a small number of diffuse interstellar bands (DIBs). Using an archive of high signal-to-noise spectra obtained at the Apache Point Observatory, we used two methods to test the hypothesis. Both methods failed to detect significant absorption at lab wavelengths of interstellar spectra with laboratory spectra. We thereby conclude that C 10 H + 8 is not a DIB carrier in typical reddened sight lines.
10. Detection of organic matter in interstellar grains.
Science.gov (United States)
Pendleton, Y J
1997-06-01
Star formation and the subsequent evolution of planetary systems occurs in dense molecular clouds, which are comprised, in part, of interstellar dust grains gathered from the diffuse interstellar medium (DISM). Radio observations of the interstellar medium reveal the presence of organic molecules in the gas phase and infrared observational studies provide details concerning the solid-state features in dust grains. In particular, a series of absorption bands have been observed near 3.4 microns (approximately 2940 cm-1) towards bright infrared objects which are seen through large column densities of interstellar dust. Comparisons of organic residues, produced under a variety of laboratory conditions, to the diffuse interstellar medium observations have shown that aliphatic hydrocarbon grains are responsible for the spectral absorption features observed near 3.4 microns (approximately 2940 cm-1). These hydrocarbons appear to carry the -CH2- and -CH3 functional groups in the abundance ratio CH2/CH3 approximately 2.5, and the amount of carbon tied up in this component is greater than 4% of the cosmic carbon available. On a galactic scale, the strength of the 3.4 microns band does not scale linearly with visual extinction, but instead increases more rapidly for objects near the Galactic Center. A similar trend is noted in the strength of the Si-O absorption band near 9.7 microns. The similar behavior of the C-H and Si-O stretching bands suggests that these two components may be coupled, perhaps in the form of grains with silicate cores and refractory organic mantles. The ubiquity of the hydrocarbon features seen in the near infrared near 3.4 microns throughout out Galaxy and in other galaxies demonstrates the widespread availability of such material for incorporation into the many newly forming planetary systems. The similarity of the 3.4 microns features in any organic material with aliphatic hydrocarbons underscores the need for complete astronomical observational
11. Diffuse interstellar clouds
International Nuclear Information System (INIS)
Black, J.H.
1987-01-01
The author defines and discusses the nature of diffuse interstellar clouds. He discusses how they contribute to the general extinction of starlight. The atomic and molecular species that have been identified in the ultraviolet, visible, and near infrared regions of the spectrum of a diffuse cloud are presented. The author illustrates some of the practical considerations that affect absorption line observations of interstellar atoms and molecules. Various aspects of the theoretical description of diffuse clouds required for a full interpretation of the observations are discussed
12. Nebulae and interstellar matter
International Nuclear Information System (INIS)
1987-01-01
The South African Astronomical Observatory (SAAO) has investigated the IRAS source 1912+172. This source appears to be a young planetary nebula with a binary central star. During 1986 SAAO has also studied the following: hydrogen deficient planetary nebulae; high speed flows in HII regions, and the wavelength dependence of interstellar polarization. 2 figs
13. Ionization of Interstellar Hydrogen
Science.gov (United States)
Whang, Y. C.
1996-09-01
Interstellar hydrogen can penetrate through the heliopause, enter the heliosphere, and may become ionized by photoionization and by charge exchange with solar wind protons. A fluid model is introduced to study the flow of interstellar hydrogen in the heliosphere. The flow is governed by moment equations obtained from integration of the Boltzmann equation over the velocity space. Under the assumption that the flow is steady axisymmetric and the pressure is isotropic, we develop a method of solution for this fluid model. This model and the method of solution can be used to study the flow of neutral hydrogen with various forms of ionization rate β and boundary conditions for the flow on the upwind side. We study the solution of a special case in which the ionization rate β is inversely proportional to R2 and the interstellar hydrogen flow is uniform at infinity on the upwind side. We solve the moment equations directly for the normalized density NH/NN∞, bulk velocity VH/VN∞, and temperature TH/TN∞ of interstellar hydrogen as functions of r/λ and z/λ, where λ is the ionization scale length. The solution is compared with the kinetic theory solution of Lallement et al. The fluid solution is much less time-consuming than the kinetic theory solutions. Since the ionization rate for production of pickup protons is directly proportional to the local density of neutral hydrogen, the high-resolution solution of interstellar neutral hydrogen obtained here will be used to study the global distribution of pickup protons.
14. Interstellar extinction correlations
International Nuclear Information System (INIS)
Jones, A.P.; Williams, D.A.; Duley, W.W.
1987-01-01
A recently proposed model for interstellar grains in which the extinction arises from small silicate cores with mantles of hydrogenated amorphous carbon (HAC or α-C:H), and large, but thinly coated, silicate grains can successfully explain many of the observed properties of interstellar dust. The small silicate cores give rise to the 2200 A extinction feature. The extinction in the visual is produced by the large silicates and the HAC mantles on the small cores, whilst the far UV extinction arises in the HAC mantles with a small contribution form the silicate grains. The grain model requires that the silicate material is the more resilient component and that variations in the observed extinction from region to region are due to the nature and depletion of the carbon in the HAC mantles. (author)
15. Evolution of interstellar grains
International Nuclear Information System (INIS)
Greenberg, J.M.
1984-01-01
The principal aim of this chapter is to derive the properties of interstellar grains as a probe of local physical conditions and as a basis for predicting such properties as related to infrared emissivity and radiative transfer which can affect the evolution of dense clouds. The first sections will develop the criteria for grain models based directly on observations of gas and dust. A summary of the chemical evolution of grains and gas in diffuse and dense clouds follows. (author)
16. INTERSTELLAR EXTINCTION LAW TOWARD THE GALACTIC CENTER III: J, H, KS BANDS IN THE 2MASS AND THE MKO SYSTEMS, AND 3.6, 4.5, 5.8, 8.0 μm IN THE SPITZER/IRAC SYSTEM
International Nuclear Information System (INIS)
Nishiyama, Shogo; Nagata, Tetsuya; Tamura, Motohide; Hatano, Hirofumi; Kato, Daisuke; Tanabe, Toshihiko; Sugitani, Koji
2009-01-01
We have determined interstellar extinction law toward the Galactic center (GC) at the wavelength from 1.2 to 8.0 μm, using point sources detected in the IRSF/SIRIUS near-infrared (NIR) survey and those in the Two Micron All Sky Survey (2MASS) and Spitzer/IRAC/GLIMPSE II catalogs. The central region |l | ∼ 0 0 and |b | ∼ 0 0 has been surveyed in the J, H, and K S bands with the IRSF telescope and the SIRIUS camera whose filters are similar to the Mauna Kea Observatories (MKO) NIR photometric system. Combined with the GLIMPSE II point source catalog, we made K S versus K S - λ color-magnitude diagrams (CMDs) where λ=3.6, 4.5, 5.8, and 8.0 μm. The K S magnitudes of bulge red clump stars and the K S - λ colors of red giant branches are used as a tracer of the reddening vector in the CMDs. From these magnitudes and colors, we have obtained the ratios of total-to-selective extinction A K S /E K S -λ for the four IRAC bands. Combined with A λ /A K S for the J and H bands derived by Nishiyama et al., we obtain A J :A H :A K S :A [3.6] :A [4.5] :A [5.8] :A [8.0] = 3.02:1.73:1:0.50:0.39:0.36:0.43 for the line of sight toward the GC. This confirms the flattening of the extinction curve at λ ∼> 3 μm from a simple extrapolation of the power-law extinction at shorter wavelengths, in accordance with recent studies. The extinction law in the 2MASS J, H, and K S bands has also been calculated, and good agreement with that in the MKO system is found. Thus, it is established that the extinction in the wavelength range of J, H, and K S is well fitted by a power law of steep decrease A λ ∝ λ -2.0 toward the GC. In nearby molecular clouds and diffuse interstellar medium, the lack of reliable measurements of the total-to-selective extinction ratios hampers unambiguous determination of the extinction law; however, observational results toward these lines of sight cannot be reconciled with a single extinction law.
17. Wavelength dependence of interstellar polarization
International Nuclear Information System (INIS)
Mavko, G.E.
1974-01-01
The wavelength dependence of interstellar polarization was measured for twelve stars in three regions of the Milky Way. A 120A bandpass was used to measure the polarization at a maximum of sixteen wavelengths evenly spaced between 2.78μ -1 (3600A) and 1.28μ -1 (7800A). For such a wide wavelength range, the wavelength resolution is superior to that of any previously reported polarization measurements. The new scanning polarimeter built by W. A. Hiltner of the University of Michigan was used for the observations. Very broad structure was found in the wavelength dependence of the polarization. Extensive investigations were carried out to show that the structure was not caused by instrumental effects. The broad structure observed is shown to be in agreement with concurrent extinction measurements for the same stars. Also, the observed structure is of the type predicted when a homogeneous silicate grain model is fitted to the observed extinction. The results are in agreement with the hypothesis that the very broad band structure seen in the extinction is produced by the grains. (Diss. Abstr. Int., B)
18. Quenched carbonaceous composite (QCC): a likely candidate for interstellar grains
International Nuclear Information System (INIS)
Sakata, A.; Wada, S.; Tanabe, T.; Onaka, T.
1984-01-01
The authors have recently reported that a carbonaceous composite synthesized from a hydrocarbon plasma shows an extinction property quite resembling the observed average interstellar extinction curve around the 220 nm hump. This composite is synthesized by quenching the excited gas ejecting from a plasma of methane gas, so it is called 'quenched carbonaceous composite' or 'QCC'. A recent study of QCC in the infrared region has shown that QCC can also account for some of the unidentified bands in the infrared region detected in several celestial objects. These results suggest that most of the pronounced features of the interstellar grains originate from substances whose major constituent is carbon. (author)
19. Molecular diagnostics of interstellar shocks
International Nuclear Information System (INIS)
Hartquist, T.W.; Oppenheimer, M.; Dalgarno, A.
1980-01-01
The chemistry of molecules in shocked regions of the interstellar gas is considered and calculations are carried out for a region subjected to a shock at a velocity of 8 km s -1 Substantial enhancements are predicted in the concentrations of the molecules H 2 S, SO, and SiO compared to those anticipated in cold interstellar clouds
20. Molecular diagnostics of interstellar shocks
Science.gov (United States)
Hartquist, T. W.; Dalgarno, A.; Oppenheimer, M.
1980-02-01
The chemistry of molecules in shocked regions of the interstellar gas is considered and calculations are carried out for a region subjected to a shock at a velocity of 8 km/sec. Substantial enhancements are predicted in the concentrations of the molecules H2S, SO, and SiO compared to those anticipated in cold interstellar clouds.
1. Observational constraints on interstellar chemistry
International Nuclear Information System (INIS)
Winnewisser, G.
1984-01-01
The author points out presently existing observational constraints in the detection of interstellar molecular species and the limits they may cast on our knowledge of interstellar chemistry. The constraints which arise from the molecular side are summarised and some technical difficulties encountered in detecting new species are discussed. Some implications for our understanding of molecular formation processes are considered. (Auth.)
2. Molecular diagnostics of interstellar shocks
Science.gov (United States)
Hartquist, T. W.; Dalgarno, A.; Oppenheimer, M.
1980-01-01
The chemistry of molecules in shocked regions of the interstellar gas is considered and calculations are carried out for a region subjected to a shock at a velocity of 8 km/sec. Substantial enhancements are predicted in the concentrations of the molecules H2S, SO, and SiO compared to those anticipated in cold interstellar clouds.
3. Visualizing Interstellar's Wormhole
Science.gov (United States)
James, Oliver; von Tunzelmann, Eugénie; Franklin, Paul; Thorne, Kip S.
2015-06-01
Christopher Nolan's science fiction movie Interstellar offers a variety of opportunities for students in elementary courses on general relativity theory. This paper describes such opportunities, including: (i) At the motivational level, the manner in which elementary relativity concepts underlie the wormhole visualizations seen in the movie; (ii) At the briefest computational level, instructive calculations with simple but intriguing wormhole metrics, including, e.g., constructing embedding diagrams for the three-parameter wormhole that was used by our visual effects team and Christopher Nolan in scoping out possible wormhole geometries for the movie; (iii) Combining the proper reference frame of a camera with solutions of the geodesic equation, to construct a light-ray-tracing map backward in time from a camera's local sky to a wormhole's two celestial spheres; (iv) Implementing this map, for example, in Mathematica, Maple or Matlab, and using that implementation to construct images of what a camera sees when near or inside a wormhole; (v) With the student's implementation, exploring how the wormhole's three parameters influence what the camera sees—which is precisely how Christopher Nolan, using our implementation, chose the parameters for Interstellar's wormhole; (vi) Using the student's implementation, exploring the wormhole's Einstein ring and particularly the peculiar motions of star images near the ring, and exploring what it looks like to travel through a wormhole.
4. Interstellar molecules and masers
International Nuclear Information System (INIS)
Nguyen-Q-Rieu; Guibert, J.
1978-01-01
The study of dense and dark clouds, in which hydrogen is mostly in molecular form, became possible since the discovery of interstellar molecules, emitting in the centimeter and millimeter wavelengths. The molecular lines are generally not in local thermal equilibrium (LTE). Their intensity can often be explained by invoking a population inversion mechanism. Maser emission lines due to OH, H 2 O and SiO molecules are among the most intense molecular lines. The H 2 CO molecule, detected in absorption in front of the cold cosmic background radiation of 2.7 K, illustrates the inverse phenomenon, the antimaser absorption. For a radio transition of frequency v, the inversion rate Δn (relative population difference between the upper and lower level) as well as the maser gain can be determined from the radio observations. In the case of the OH lines in the 2 PIsub(3/2), J=3/2 state, the inversion rates approximately 1 to 2% derived from the observations, are comparable with those obtained in the laboratory. The determination of the excitation mechanisms of the masers, through the statistical equilibrium and radiative transfer equations, implies the knowledge of collisional and radiative transition probabilities. A pumping model, which can satisfactorily explain the radio observations of some interstellar OH clouds, will be discussed [fr
5. Interstellar dust and extinction
International Nuclear Information System (INIS)
Mathis, J.S.
1990-01-01
It is noted that the term interstellar dust refers to materials with rather different properties, and that the mean extinction law of Seaton (1979) or Savage and Mathis (1979) should be replaced by the expression given by Cardelli et al. (1989), using the appropriate value of total-to-selective extinction. The older laws were appropriate for the diffuse ISM but dust in clouds differs dramatically in its extinction law. Dust is heavily processed while in the ISM by being included within clouds and cycled back into the diffuse ISM many times during its lifetime. Hence, grains probably reflect only a trace of their origin, although meteoritic inclusions with isotopic anomalies demonstrate that some tiny particles survive intact from a supernova origin to the present. 186 refs
6. The diffuse interstellar medium
Science.gov (United States)
Cox, Donald P.
1990-01-01
The last 20 years of the efforts to understand the diffuse ISM are reviewed, with recent changes of fundamental aspects being highlighted. Attention is given to the interstellar pressure and its components, the weight of the ISM, the midplane pressure contributions, and pressure contributions at 1 kpc. What velocity dispersions, cosmic ray pressure, and magnetic field pressure that can be expected for a gas in a high magnetic field environment is addressed. The intercloud medium is described, with reference to the work of Cox and Slavin (1989). Various caveats are discussed and a number of areas for future investigation are identified. Steps that could be taken toward a successful phase segregation model are discussed.
7. Interstellar scattering and resolution limitations
International Nuclear Information System (INIS)
Dennison, B.
1987-01-01
Density irregularities in both the interplanetary medium and the ionized component of the interstellar medium scatter radio waves, resulting in limitations on the achievable resolution. Interplanetary scattering (IPS) is weak for most observational situations, and in principle the resulting phase corruption can be corrected for when observing with sufficiently many array elements. Interstellar scattering (ISS), on the other hand, is usually strong at frequencies below about 8 GHz, in which case intrinsic structure information over a range of angular scales is irretrievably lost. With the earth-space baselines now planned, it will be possible to search directly for interstellar refraction, which is suspected of modulating the fluxes of background sources. 14 references
8. The distribution of interstellar dust
International Nuclear Information System (INIS)
Clocchiatti, A.; Marraco, H.G.
1986-01-01
We propose the interstellar matter structural function as a tool to derive the features of the interstellar dust distribution. We study that function resolving some ideal dust distribution models. Later we describe the method used to find a reliable computing algorithm for the observational case. Finally, we describe the steps to build a model for the interstellar matter composed by spherically symmetrical clouds. The density distribution for each of these clouds is D(r) = D 0 .esup(-r/r 0 ) 2 . The preliminary results obtained are summarised. (author)
9. Recent interstellar molecular line work
International Nuclear Information System (INIS)
Winnewisser, G.
1975-01-01
A summary of recent interstellar molecular line work is presented. Transitions of the following molecules have been detected in Sgr B2: Vinylcyanide, H 2 C 2 HCN, formic acid, HCOOH, dimethyl ether (CH 3 ) 2 O and isotopically labelled cyanoacetylene- 13 C,HC 13 CCN and HCC 13 CN. The data on cyanoacetylene give an upper limit to the abundance ratio 12 C/ 13 C of 36 +- 5. A short discussion of the interstellar chemistry leads to the conclusion that hydrocarbons such as acetylene, HCCH, ethylen, H 2 CCH 2 and ethane H 3 CCH 3 should be present in interstellar clouds. 13 refs
10. Four Interstellar Dust Candidates from the Stardust Interstellar Dust Collector
Science.gov (United States)
Westphal, A. J.; Allen, C.; Bajt, S.; Bechtel, H. A.; Borg, J.; Brenker, F.; Bridges, J.; Brownlee, D. E.; Burchell, M.; Burghammer, M.;
2011-01-01
In January 2006, the Stardust sample return capsule returned to Earth bearing the first solid samples from a primitive solar system body, Comet 81P/Wild2, and a collector dedicated to the capture and return of contemporary interstellar dust. Both collectors were approx. 0.1 sq m in area and were composed of aerogel tiles (85% of the collecting area) and aluminum foils. The Stardust Interstellar Dust Collector (SIDC) was exposed to the interstellar dust stream for a total exposure factor of 20 sq m/day. The Stardust Interstellar Preliminary Examination (ISPE) is a consortium-based project to characterize the collection using nondestructive techniques. The goals and restrictions of the ISPE are described . A summary of analytical techniques is described.
11. OpenAIRE
Demyk K.
2012-01-01
Cosmic dust is omnipresent in the Universe. Its presence influences the evolution of the astronomical objects which in turn modify its physical and chemical properties. The nature of cosmic dust, its intimate coupling with its environment, constitute a rich field of research based on observations, modelling and experimental work. This review presents the observations of the different components of interstellar dust and discusses their evolution during the life cycle of the interstellar medium.
12. Riddling bifurcation and interstellar journeys
International Nuclear Information System (INIS)
Kapitaniak, Tomasz
2005-01-01
We show that riddling bifurcation which is characteristic for low-dimensional attractors embedded in higher-dimensional phase space can give physical mechanism explaining interstellar journeys described in science-fiction literature
13. The Interstellar Conspiracy
Science.gov (United States)
Johnson, Les; Matloff, Gregory L.
2005-01-01
If we were designing a human-carrying starship that could be launched in the not-too-distant future, it would almost certainly not use a warp drive to instantaneously bounce around the universe, as is done in Isaac Asimov's classic Foundation series or in episodes of Star Trek or Star Wars. Sadly, those starships that seem to be within technological reach could not even travel at high relativistic speeds, as does the interstellar ramjet in Poul Anderson's Tau Zero. Warp-speeds seem to be well outside the realm of currently understood physical law; proton-fusing ramjets may never be technologically feasible. Perhaps fortunately in our terrorist-plagued world, the economics of antimatter may never be attractive for large-scale starship propulsion. But interstellar travel will be possible within a few centuries, although it will certainly not be as fast as we might prefer. If humans learn how to hibernate, perhaps we will sleep our way to the stars, as do the crew in A. E. van Vogt's Far Centaurus. However, as discussed in a landmark paper in The Journal of the British Interplanetary Society, the most feasible approach to transporting a small human population to the planets (if any) of Alpha Centauri is the worldship. Such craft have often been featured in science fiction. See for example Arthur C. Clarke's Rendezvous with Rama, and Robert A. Heinlein's Orphans of the Sky. Worldships are essentially mobile versions of the O Neill free-space habitats. Constructed mostly from lunar and/or asteroidal materials, these solar-powered, multi-kilometer-dimension structures could house 10,000 to 100,000 humans in Earth-approximating environments. Artificial gravity would be provided by habitat rotation, and cosmic ray shielding would be provided by passive methods, such as habitat atmosphere and mass shielding, or magnetic fields. A late 21st century space-habitat venture might support itself economically by constructing large solar-powered satellites to beam energy back to
14. The 3 micron ice band
International Nuclear Information System (INIS)
Greenberg, J.M.; Bult, C.E.P.M. van de
1984-01-01
Ever since it was proposed that H 2 O could be a dominant constituent of interstellar grains, its detection, or lack thereof, has played a large role in theories of grains and their evolution. It now appears possible to provide a basic theoretical structure for the evolution of grains in molecular clouds based on current observational evidence and laboratory experiments on the ice band. Both band strengths and shapes can be reasonably predicted by grain models. (U.K.)
15. Detection of interstellar methylcyanoacetylene
International Nuclear Information System (INIS)
Broten, N.W.; MacLeod, J.M.; Avery, L.W.; Irvine, W.M.; Hoeglund, B.; Friberg, P.; Hjalmarson
1984-01-01
A new interstellar molecule, methylcyanoacetylene (CH 3 C 3 N), has been detected in the molecular cloud TMC-1. The J = 8 → 7, J = 7 → 6, J = 6 → 5, and J = 5 → 4 transitions have been observed. For the first three of these, both the K = 0 and K = 1 components are present, while for J = 5 → 4, only the K = 0 line has been detected. The observed frequencies were calculated by assuming a value of radial velocity V/sub lSR/ = 5.8 km s -1 for TMC-1, typical of other molecules in the cloud. All Observed frequencies are within 10 kHz of the calculated frequencies, which are based on the 1982 laboratory constants of Moises et al., so the identification is secure. The lines are broadened by hyperfine splitting, and the J = 5 → 4, K = 0 transition shows incipient resolution into three hyperfine components. The rotational temperature determined from these observations is quite low, with 2.7 K 12 cm -2
16. Interstellar Sweat Equity
Science.gov (United States)
Cohen, M. H.; Becker, R. E.; O'Donnell, D. J.; Brody, A. R.
So, you have just launched aboard the Starship, headed to an exoplanet light years from Earth. You will spend the rest of your natural life on this journey in the expectation and hope that your grandchildren will arrive safely, land, and build a new settlement. You will need to govern the community onboard the Starship. This system of governance must meet unique requirements for participation, representation, and decision-making. On a spaceship that can fly and operate by itself, what will the crewmembers do for their generations in transit? Certainly, they will train and train again to practice the skills they will need upon arrival at a new world. However, this vicarious practice neither suffices to prepare the future pioneers for their destiny at a new star nor will it provide them with the satisfaction in their own work. To hone the crewmembers' inventive and technical skills, to challenge and prepare them for pioneering, the crew would build and expand the interstellar ship in transit. This transstellar sweat equity'' gives a stake in the enterprise to all the people, providing meaningful and useful activity to the new generations of crewmembers. They build all the new segments of the vessel from raw materials - including atmosphere - stored on board. Construction of new pressure shell modules would be one option, but they also reconstruct or fill-in existing pressurized volumes. The crew makes new life support system components and develops new agricultural modules in anticipation of their future needs. Upon arrival at the new star or planet, the crew shall apply these robustly developed skills and self-sufficient spirit to their new home.
17. Comet Halley and interstellar chemistry
International Nuclear Information System (INIS)
Snyder, L.E.
1989-01-01
How complex is the chemistry of the interstellar medium? How far does it evolve and how has it interacted with the chemistry of the solar system? Are the galactic chemical processes destroyed, preserved, or even enhanced in comets? Are biogenic molecules formed in space and have the formation mechanisms interacted in any way with prebiotic organic chemical processes on the early earth? Radio molecular studies of comets are important for probing deep into the coma and nuclear region and thus may help answer these questions. Comets are believed to be pristine samples of the debris left from the formation of the solar system and may have been the carrier between interstellar and terrestrial prebiotic chemistries. Recent observations of Comet Halley and subsequent comets have given the author an excellent opportunity to study the relationship between interstellar molecular chemistry and cometary chemistry
18. Interstellar Matters: Neutral Hydrogen and the Galactic Magnetic Field
Science.gov (United States)
Verschuur, Gerrit; Schmelz, Joan T.; Asgari-Targhi asgari-Targhi, M.
2018-01-01
The physics of the interstellar medium was revolutionized by the observations of the Galactic Arecibo L-Band Feed Array (GALFA) HI survey done at the Arecibo Observatory. The high-resolution, high-sensitivity, high-dynamic- range images show complex, tangled, extended filaments, and reveal that the fabric of the neutral interstellar medium is deeply tied to the structure of the ambient magnetic field. This discovery prompts an obvious question – how exactly is the interstellar {\\it neutral} hydrogen being affected by the galactic magnetic field? We look into this question by examining a set of GALFA-HI data in great detail. We have chosen a long, straight filament in the southern galactic sky. This structure is both close by and isolated in velocity space. Gaussian analysis of profiles both along and across the filament reveal internal structure – braided strands that can be traced through the simplest part, but become tangled in more complex segments. These braids do not resemble in any way the old spherical HI clouds and rudimentary pressure balance models that were used to explain the pre-GALFA- HI interstellar medium. It is clear that these structures are created, constrained, and dominated by magnetic fields. Like many subfields of astronomy before it, e.g., physics of the solar coronal, extragalactic radio jets, and pulsar environment, scientists are confronted with observations that simply cannot be explained by simple hydrodynamics and are forced to consider magneto-hydrodynamics.
19. Formation of interstellar anions
Science.gov (United States)
Senent, Maria Luisa
2012-05-01
Formation of interstellar anions: M.L. Senent. The recent detection of negative charged species in the ISM1 has instigated enthusiasm for anions in the astrophysical community2. Many of these species are new and entail characterization. How they are formed in astrophysical sources is a question of major relevance. The anion presence in ISM was first predicted theoretically on the basis of electron affinities and on the negative linear chain molecular stabilities. Although very early, they were considered in astrochemical models3-4, their discovery is so recent because their abundances seem to be relatively low. These have to be understood in terms of molecular stabilities, reaction probabilities and radiative and collisional excitations. Then, we present our theoretical work on even carbon chains type Cn and CnH (n=2,4,6) focused to the understanding of anion abundances. We use highly correlated ab initio methods. We performed spectroscopic studies of various isomers that can play important roles as intermediates5-8. In previous papers9-10, we compared C2H and C2H- collisional rates responsible for observed line intensities. Actually, we study hydrogen attachment (Cn +H → CnH and Cn- +H → CnH-) and associative detachment processes (Cn- +H → CnH +e-) for 2, 4 and 6 carbon atom chains11. [1] M.C.McCarthy, C.A.Gottlieb, H.Gupta, P.Thaddeus, Astrophys.J, 652, L141 (2006) [2] V.M.Bierbaum, J.Cernicharo, R.Bachiller, eds., 2011, pp 383-389. [3] A. Dalgarno, R.A. Mc Cray, Astrophys.J,, 181, 95 (1973) [4] E. Herbst E., Nature, 289, 656 (1981); [5] H.Massó, M.L.Senent, P.Rosmus, M.Hochlaf, J.Chem.Phys., 124, 234304 (2006) [6] M.L.Senent, M.Hochlaf, Astrophys. J. , 708, 1452(2010) [7] H.Massó, M.L.Senent, J.Phys.Chem.A, 113, 12404 (2009) [8] D. Hammoutene, M.Hochlaf, M.L.Senent, submitted. [9] A. Spielfiedel, N. Feautrier, F. Najar, D. ben Abdallah, F. Dayou, M.L. Senent, F. Lique, Mon.Not.R.Astron.Soc., 421, 1891 (2012) [10] F.Dumouchel, A, Spielfieldel , M
20. Chemisputtering of interstellar graphite grains
International Nuclear Information System (INIS)
Draine, B.T.
1979-01-01
The rate of erosion of interstellar graphite grains as a result of chemical reaction with H, N, and O is estimated using the available experiment evidence. It is argued that ''chemical sputtering'' yields for interstellar graphite grains will be much less than unity, contrary to earlier estimates by Barlow and Silk. Chemical sputtering of graphite grains in evolving H II regions is found to be unimportant, except in extremely compact (n/sub H/> or approx. =10 5 cm -3 ) H II regions. Alternative explanations are considered for the apparent weakness of the lambda=2175 A extinction ''bump'' in the direction of several early type stars
1. Interstellar Initiative Web Page Design
Science.gov (United States)
Mehta, Alkesh
1999-01-01
This summer at NASA/MSFC, I have contributed to two projects: Interstellar Initiative Web Page Design and Lenz's Law Relative Motion Demonstration. In the Web Design Project, I worked on an Outline. The Web Design Outline was developed to provide a foundation for a Hierarchy Tree Structure. The Outline would help design a Website information base for future and near-term missions. The Website would give in-depth information on Propulsion Systems and Interstellar Travel. The Lenz's Law Relative Motion Demonstrator is discussed in this volume by Russell Lee.
2. Interstellar matter within elliptical galaxies
Science.gov (United States)
Jura, Michael
1988-01-01
Multiwavelength observations of elliptical galaxies are reviewed, with an emphasis on their implications for theoretical models proposed to explain the origin and evolution of the interstellar matter. Particular attention is given to interstellar matter at T less than 100 K (atomic and molecular gas and dust), gas at T = about 10,000 K, and gas at T = 10 to the 6th K or greater. The data are shown to confirm the occurrence of mass loss from evolved stars, significant accretion from companion galaxies, and cooling inflows; no evidence is found for large mass outflow from elliptical galaxies.
3. Experimental interstellar organic chemistry - Preliminary findings
Science.gov (United States)
Khare, B. N.; Sagan, C.
1973-01-01
Review of the results of some explicit experimental simulation of interstellar organic chemistry consisting in low-temperature high-vacuum UV irradiation of condensed simple gases known or suspected to be present in the interstellar medium. The results include the finding that acetonitrile may be present in the interstellar medium. The implication of this and other findings are discussed.
4. Laboratory Investigations into the Spectra and Origin of Propylene Oxide: A Chiral Interstellar Molecule
Science.gov (United States)
Hudson, R. L.; Loeffler, M. J.; Yocum, K. M.
2017-01-01
Propylene oxide was recently identified in the interstellar medium, but few laboratory results are available for this molecule to guide current and future investigations. To address this situation, here we report infrared spectra, absorption coefficients, and band strengths of solid propylene oxide along with the first measurement of its refractive index and a calculation of its density, all for the amorphous solid form of the compound. We present the first experimental results showing a low-temperature formation pathway for propylene oxide near 10 K in interstellar ice analogs. Connections are drawn between our new results and the interstellar molecules propanal and acetone, and predictions are made about several as yet unobserved vinyl alcohols and methylketene. Comparisons are given to earlier laboratory work and a few applications to interstellar and solar system astrochemistry are described.
5. Laboratory Investigations into the Spectra and Origin of Propylene Oxide: A Chiral Interstellar Molecule
Energy Technology Data Exchange (ETDEWEB)
Hudson, R. L.; Loeffler, M. J. [Astrochemistry Laboratory (Code 691), NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Yocum, K. M., E-mail: [email protected] [Department of Chemistry, Kutztown University, Kutztown, PA 19530 (United States)
2017-02-01
Propylene oxide was recently identified in the interstellar medium, but few laboratory results are available for this molecule to guide current and future investigations. To address this situation, here we report infrared spectra, absorption coefficients, and band strengths of solid propylene oxide along with the first measurement of its refractive index and a calculation of its density, all for the amorphous solid form of the compound. We present the first experimental results showing a low-temperature formation pathway for propylene oxide near 10 K in interstellar ice analogs. Connections are drawn between our new results and the interstellar molecules propanal and acetone, and predictions are made about several as yet unobserved vinyl alcohols and methylketene. Comparisons are given to earlier laboratory work and a few applications to interstellar and solar system astrochemistry are described.
6. Diamonds in dense molecular clouds - A challenge to the standard interstellar medium paradigm
Science.gov (United States)
Allamandola, L. J.; Sandford, S. A.; Tielens, A. G. G. M.; Herbst, T. M.
1993-01-01
Observations of a newly discovered infrared C-H stretching band indicate that interstellar diamond-like material appears to be characteristic of dense clouds. In sharp contrast, the spectral signature of dust in the diffuse interstellar medium is dominated by -CH2- and -CH3 groups. This dichotomy in the aliphatic organic component between the dense and diffuse media challenges standard assumptions about the processes occurring in, and interactions between, these two media. The ubiquity of this interstellar diamond-like material rules out models for meteoritic diamond formation in unusual circumstellar environments and implies that the formation of the diamond-like material is associated with common interstellar processes or stellar types.
7. Interstellar turbulence and shock waves
International Nuclear Information System (INIS)
Bykov, A.M.
1982-01-01
Random deflections of shock fronts propagated through the turbulent interstellar medium can produce the strong electro-density fluctuations on scales l> or approx. =10 13 cm inferred from pulsar radio scintillations. The development of turbulence in the hot-phase ISM is discussed
8. Stardust Interstellar Preliminary Examination (ISPE)
Science.gov (United States)
Westphal, A. J.; Allen, C.; Bajt, S.; Basset, R.; Bastien, R.; Bechtel, H.; Bleuet, P.; Borg, J.; Brenker F.; Bridges, J.
2009-01-01
In January 2006 the Stardust sample return capsule returned to Earth bearing the first solid samples from a primitive solar system body, C omet 81P/Wild2, and a collector dedicated to the capture and return o f contemporary interstellar dust. Both collectors were approximately 0.1m(exp 2) in area and were composed of aerogel tiles (85% of the co llecting area) and aluminum foils. The Stardust Interstellar Dust Col lector (SIDC) was exposed to the interstellar dust stream for a total exposure factor of 20 m(exp 2-) day during two periods before the co metary encounter. The Stardust Interstellar Preliminary Examination ( ISPE) is a three-year effort to characterize the collection using no ndestructive techniques. The ISPE consists of six interdependent proj ects: (1) Candidate identification through automated digital microsco py and a massively distributed, calibrated search (2) Candidate extr action and photodocumentation (3) Characterization of candidates thro ugh synchrotronbased FourierTranform Infrared Spectroscopy (FTIR), S canning XRay Fluoresence Microscopy (SXRF), and Scanning Transmission Xray Microscopy (STXM) (4) Search for and analysis of craters in f oils through FESEM scanning, Auger Spectroscopy and synchrotronbased Photoemission Electron Microscopy (PEEM) (5) Modeling of interstell ar dust transport in the solar system (6) Laboratory simulations of h ypervelocity dust impacts into the collecting media
9. Magnetite and the interstellar medium
International Nuclear Information System (INIS)
Landaberry, S.C.; Magalhaes, A.M.
1976-01-01
Recent observations concerning interstellar circular polarization are explained by a simple two-cloud model using magnetite (Fe 3 O 4 ) grains as polarizing agents. Three stars covering a wide range of linear polarization spectral shapes were selected. Reasonably low column densities are required in order to interpret polarization data [pt
10. Physical processes in the interstellar medium
CERN Document Server
Spitzer, Lyman
2008-01-01
Physical Processes in the Interstellar Medium discusses the nature of interstellar matter, with a strong emphasis on basic physical principles, and summarizes the present state of knowledge about the interstellar medium by providing the latest observational data. Physics and chemistry of the interstellar medium are treated, with frequent references to observational results. The overall equilibrium and dynamical state of the interstellar gas are described, with discussions of explosions produced by star birth and star death and the initial phases of cloud collapse leading to star formation.
11. ON ESTIMATING INTERSTELLAR POLYCYCLIC AROMATIC HYDROCARBON ABUNDANCES WITH CALCULATED OSCILLATOR STRENGTHS
International Nuclear Information System (INIS)
Tan Xiaofeng; Bernstein, Lawrence; Cami, Jan; Salama, Farid
2011-01-01
Vibronic bands of polycyclic aromatic hydrocarbons (PAHs) in the UV/visible range are often used to estimate the abundances of PAHs in the interstellar medium by comparing laboratory-measured spectra with astronomical observations. We investigate the errors introduced by associating theoretical electronic oscillator strengths with individual vibronic bands when estimating the abundances of interstellar PAHs. The vibronic oscillator strengths of the 0-0 bands of nine PAHs with two to seven benzene rings, spanning in the 2800-6700 A spectral range, have been calculated using the Franck-Condon approximation and compared to their electronic oscillator strengths. It is found that the use of calculated electronic oscillator strengths rather than the more physically relevant vibronic oscillator strengths underestimates interstellar abundances of the nine PAHs under study, on average by a factor of about 2.4. It is recommended that vibronic oscillator strengths should be systematically used to analyze the vibronic spectra of specific PAHs and to estimate their abundances in the interstellar medium. An empirical correcting factor is suggested for the cases where the vibronic oscillator strengths are unknown for more realistic estimation of interstellar PAH abundances.
12. Optical properties of likely constituents of interstellar dust
International Nuclear Information System (INIS)
Dayawansa, I.J.
1977-07-01
Optical properties of polyoxymethylene (POM) at room temperature have been measured from the near ultra-violet to infrared as an initial stage of a link between interstellar dust and organic matter, and the results, which are particularly relevant to interstellar extinction, are reported. There is a strong possibility of a more complex organic component which could significantly contribute to the interstellar extinction. Measurements have also been made of the effect of fast neutron bombardment on the optical properties of quartz (SiO 2 ). At a high total flux of neutrons the crystalline quartz will change to its amorphous form which has extinction properties that resemble the interstellar extinction. Extinction due to small particles of several forms of SiO 2 has been measured and among them the hydrated mineral, opal, behaved like an amorphous silica. Neutron irradiated olivine showed a stronger and a broader 10μm band in addition to weaker bands towards the longer wavelengths which indicated that atomic damage has been produced. At high fluxes more atomic damage is expected to change the crystalline structure and thereby cause changes in the infrared absorption properties. Extinction measurements were also made for smoke particles of MgO in the infrared. When the measurements were made with the particles deposited on substrates, in addition to a very broad surface mode absorption feature around 20μm an extinction maximum was observed typical of the bulk mode at 25μm. Extinction measurements for MgO smoke particles in air also showed similar results. However when the particles were dispersed in a non-absorbing medium, the bulk absorption mode was not observed. This implies that the appearance of the bulk mode is due to clumping. (author)
13. Modelling interstellar extinction: Pt. 1
International Nuclear Information System (INIS)
Jones, A.P.
1988-01-01
Several methods of calculating the extinction of porous silicate grains are discussed, these include effective medium theories and hollow spherical shells. Porous silicate grains are shown to produce enhanced infrared, ultraviolet and far-ultraviolet extinction and this effect can be used to reduce the abundance of carbon required to match the average interstellar extinction, however, matching the visual extinction is rather more problematical. We have shown that the enhanced extinction at long and short wavelengths have different origins, and have explained why the visual extinction is little affected by porosity. The implications of porous grains in the interstellar medium are discussed with particular reference to surface chemistry, the polarization of starlight, and their dynamical evolution. (author)
14. Interstellar Grains: 50 Years on
Science.gov (United States)
Wickramasinghe, N. C.
Our understanding of the nature of interstellar grains has evolved considerably over the past half century with the present author and Fred Hoyle being intimately involved at several key stages of progress. The currently fashionable graphite-silicate-organic grain model has all its essential aspects unequivocally traceable to original peer-reviewed publications by the author and/or Fred Hoyle. The prevailing reluctance to accept these clear-cut priorities may be linked to our further work that argued for interstellar grains and organics to have a biological provenance -- a position perceived as heretical. The biological model, however, continues to provide a powerful unifying hypothesis for a vast amount of otherwise disconnected and disparate astronomical data.
15. Why do interstellar grains exist
International Nuclear Information System (INIS)
Seab, C.G.; Hollenbach, D.J.; Mckee, C.F.; Tielens, A.G.G.M.
1986-01-01
There exists a discrepancy between calculated destruction rates of grains in the interstellar medium and postulated sources of new grains. This problem was examined by modelling the global life cycle of grains in the galaxy. The model includes: grain destruction due to supernovae shock waves; grain injection from cool stars, planetary nebulae, star formation, novae, and supernovae; grain growth by accretion in dark clouds; and a mixing scheme between phases of the interstellar medium. Grain growth in molecular clouds is considered as a mechanism or increasing the formation rate. To decrease the shock destruction rate, several new physical processes, such as partial vaporization effects in grain-grain collisions, breakdown of the small Larmor radius approximation for betatron acceleration, and relaxation of the steady-state shock assumption are included
16. Origins of amorphous interstellar grains
International Nuclear Information System (INIS)
Hasegawa, H.
1984-01-01
The existence of amorphous interstellar grains has been suggested from infrared observations. Some carbon stars show the far infrared emission with a lambda -1 wavelength dependence. Far infrared emission supposed to be due to silicate grains often show the lambda -1 wavelength dependence. Mid infrared spectra around 10 μm have broad structure. These may be due to the amorphous silicate grains. The condition that the condensed grains from the cosmic gas are amorphous is discussed. (author)
17. Representing culture in interstellar messages
Science.gov (United States)
Vakoch, Douglas A.
2008-09-01
As scholars involved with the Search for Extraterrestrial Intelligence (SETI) have contemplated how we might portray humankind in any messages sent to civilizations beyond Earth, one of the challenges they face is adequately representing the diversity of human cultures. For example, in a 2003 workshop in Paris sponsored by the SETI Institute, the International Academy of Astronautics (IAA) SETI Permanent Study Group, the International Society for the Arts, Sciences and Technology (ISAST), and the John Templeton Foundation, a varied group of artists, scientists, and scholars from the humanities considered how to encode notions of altruism in interstellar messages . Though the group represented 10 countries, most were from Europe and North America, leading to the group's recommendation that subsequent discussions on the topic should include more globally representative perspectives. As a result, the IAA Study Group on Interstellar Message Construction and the SETI Institute sponsored a follow-up workshop in Santa Fe, New Mexico, USA in February 2005. The Santa Fe workshop brought together scholars from a range of disciplines including anthropology, archaeology, chemistry, communication science, philosophy, and psychology. Participants included scholars familiar with interstellar message design as well as specialists in cross-cultural research who had participated in the Symposium on Altruism in Cross-cultural Perspective, held just prior to the workshop during the annual conference of the Society for Cross-cultural Research . The workshop included discussion of how cultural understandings of altruism can complement and critique the more biologically based models of altruism proposed for interstellar messages at the 2003 Paris workshop. This paper, written by the chair of both the Paris and Santa Fe workshops, will explore the challenges of communicating concepts of altruism that draw on both biological and cultural models.
18. Interstellar Grains: 50 Years On
OpenAIRE
Wickramasinghe, N. Chandra
2011-01-01
Our understanding of the nature of interstellar grains has evolved considerably over the past half century with the present author and Fred Hoyle being intimately involved at several key stages of progress. The currently fashionable graphite-silicate-organic grain model has all its essential aspects unequivocally traceable to original peer-reviewed publications by the author and/or Fred Hoyle. The prevailing reluctance to accept these clear-cut priorities may be linked to our further work tha...
19. JHK photometric study of the variable interstellar extinction in the direction of open star cluster NGC 654
International Nuclear Information System (INIS)
Sagar, Ram; Qianzhong Yu
1989-01-01
JHK magnitudes have been determined for 18 stars in the field of NGC 654. Study of the interstellar extinction law in the cluster direction indicates an anomalous distribution of interstellar grains causing more extinction in U and B pass-bands compared to that obtained from the colour excesses E(V-J), E(V-H) and E(V-K) using a normal reddening law. This implies a small shift in the grain-size distribution towards smaller than normal sized particles. Patchy distribution of interstellar matter seems to be responsible for the non-uniform extinction in the cluster region. (author)
20. Observations of interstellar C2 toward Chi Oph, HD 154368, 147889 and 149404
NARCIS (Netherlands)
Dishoeck, van E.F.; Zeeuw, de P.T.
1984-01-01
Interstellar absorption lines of the C2 (2-0) Phillips band at 8750 A have been searched for in the spectra of southern stars. Seventeen lines originating from the lowest eight rotational levels have been detected toward Chi Oph, and eleven lines originating from the lowest five rotational levels
1. On the ionization of interstellar magnesium
International Nuclear Information System (INIS)
1977-01-01
It has been shown that two concentric ionization zones of interstellar magnesium must exist around each star: internal, with a radius coinciding with that of the zone of hydrogen ionization Ssub(H); and external, with a radius greater than Ssub(H), by one order. Unlike interstellar hydrogen, interstellar magnesium is ionized throughout the Galaxy. It also transpires that the ionizing radiation of ordinary hot stars cannot provide for the observed high degree of ionization of interstellar magnesium. The discrepance can be eliminated by assuming the existence of circumstellar clouds or additional ionization sources of interstellar magnesium (X-ray background radiation, high-energy particles, etc.). Stars of the B5 and BO class play the main role in the formation of ionization zones of interstellar magnesium; the contribution of O class stars is negligible (<1%). (Auth.)
2. Mechanisms of heating the interstellar matter
International Nuclear Information System (INIS)
Lequeux, J.
1975-01-01
The knowledge of the interstellar medium has been considerably improved in the recent years, thanks in particular to Radioastronomy and Ultraviolet Space Astronomy. This medium is a natural laboratory where the conditions and various and very different to what can be realised in terrestrial laboratories. To illustrate its interest for physicists here one of the most interesting but controversial points of interstellar astronomy is discussed: the mechanisms for heating and cooling the interstellar medium [fr
3. Variations in the Peak Position of the 6.2 micron Interstellar Emission Feature: A Tracer of N in the Interstellar Polycyclic Aromatic Hydrocarbon Population
Science.gov (United States)
Hudgins, Douglas M.; Bauschlicher, Charles W.; Allamandola, L. J.
2005-01-01
This paper presents the results of an investigation of the molecular characteristics that underlie the observed peak position and profile of the nominal 6.2 micron interstellar emission band generally attributed to the CC stretching vibrations of polycyclic aromatic hydrocarbons (PAHs). It begins with a summary of recent experimental and theoretical studies ofthe spectroscopic properties of large (>30 carbon atoms) PAH cations as they relate to this aspect of the astrophysical problem. It then continues with an examination of the spectroscopic properties of a number of PAH variants within the context of the interstellar 6.2 micron emission, beginning with a class of compounds known as polycyclic aromatic nitrogen heterocycles (PANHs; PAHs with one or more nitrogen atoms substituted into their carbon skeleton). In this regard, we summarize the results of recent relevant experimental studies involving a limited set of small PANHs and their cations and then report the results of a comprehensive computational study that extends that work to larger PANH cations including many nitrogen-substituted variants of coronene(+) (C24H12(+)), ovalene(+) (C32H14(+)), circumcoronene(+) (C54H18(+)), and circum-circumcoronene(+) (C96H24(+)). Finally, we report the results of more focused computational studies of selected representatives from a number of other classes of PAH variants that share one or more of the key attributes of the PANH species studied. These alternative classes of PAH variants include (1) oxygen- and silicon-substituted PAH cations; (2) PAH-metal ion complexes (metallocenes) involving the cosmically abundant elements magnesium and iron; and (3) large, asymmetric PAH cations. Overall, the studies reported here demonstrate that increasing PAH size alone is insuEcient to account for the position of the shortest wavelength interstellar 6.2 micron emission bands, as had been suggested by earlier studies. On the other hand, this work reveals that substitution of one or
4. Parameterizing the interstellar dust temperature
Science.gov (United States)
Hocuk, S.; Szűcs, L.; Caselli, P.; Cazaux, S.; Spaans, M.; Esplugues, G. B.
2017-08-01
The temperature of interstellar dust particles is of great importance to astronomers. It plays a crucial role in the thermodynamics of interstellar clouds, because of the gas-dust collisional coupling. It is also a key parameter in astrochemical studies that governs the rate at which molecules form on dust. In 3D (magneto)hydrodynamic simulations often a simple expression for the dust temperature is adopted, because of computational constraints, while astrochemical modelers tend to keep the dust temperature constant over a large range of parameter space. Our aim is to provide an easy-to-use parametric expression for the dust temperature as a function of visual extinction (AV) and to shed light on the critical dependencies of the dust temperature on the grain composition. We obtain an expression for the dust temperature by semi-analytically solving the dust thermal balance for different types of grains and compare to a collection of recent observational measurements. We also explore the effect of ices on the dust temperature. Our results show that a mixed carbonaceous-silicate type dust with a high carbon volume fraction matches the observations best. We find that ice formation allows the dust to be warmer by up to 15% at high optical depths (AV> 20 mag) in the interstellar medium. Our parametric expression for the dust temperature is presented as Td = [ 11 + 5.7 × tanh(0.61 - log 10(AV) ]χuv1/5.9, where χuv is in units of the Draine (1978, ApJS, 36, 595) UV field.
5. Grain destruction in interstellar shocks
International Nuclear Information System (INIS)
Seab, C.G.; Shull, J.M.
1984-01-01
One of the principal methods for removing grains from the Interstellar Medium is to destroy them in shock waves. Previous theoretical studies of shock destruction have generally assumed only a single size and type of grain; most do not account for the effect of the grain destruction on the structure of the shock. Earlier calculations have been improved in three ways: first, by using a ''complete'' grain model including a distribution of sizes and types of grains; second, by using a self-consistent shock structure that incorporates the changing elemental depletions as the grains are destroyed; and third, by calculating the shock-processed ultraviolet extinction curves for comparison with observations. (author)
6. The Identification of Complex Organic Molecules in the Interstellar Medium: Using Lasers and Matrix Isolation Spectroscopy to Simulate the Interstellar Environment
Science.gov (United States)
1998-01-01
The Astrochemistry Group at NASA Ames Research Center is interested in the identification of large organic molecules in the interstellar medium Many smaller organic species (e.g. hydrocarbons, alcohols, etc.) have been previously identified by their radiofrequency signature due to molecular rotations. However, this becomes increasingly difficult to observe as the size of the molecule increases. Our group in interested in the identification of the carriers of the Diffuse Interstellar Bands (absorption features observed throughout the visible and near-infrared in the spectra of stars, due to species in the interstellar medium). Polycyclic Aromatic Hydrocarbons (PAHs) and related molecules are thought to be good candidates for these carriers. Laboratory experiments am performed at Ames to simulate the interstellar environment, and to compare spectra obtained from molecules in the laboratory to those derived astronomically. We are also interested in PAHs with respect to their possible connection to the UIR (Unidentified infrared) and ERE (Extended Red Emission) bands - emission features found to emanate from particular regions of our galaxy (e.g. Orion nebula, Red Rectangle, etc.). An old, "tried and proven spectroscopic technique, matrix isolation spectroscopy creates molecular conditions ideal for performing laboratory astrophysics.
7. THE POSSIBLE INTERSTELLAR ANION CH2CN–: SPECTROSCOPIC CONSTANTS, VIBRATIONAL FREQUENCIES, AND OTHER CONSIDERATIONS
International Nuclear Information System (INIS)
Fortenberry, Ryan C.; Lee, Timothy J.; Crawford, T. Daniel
2013-01-01
The A 1 B 1 ⇽ X-tilde 1 A' excitation into the dipole-bound state of the cyanomethyl anion (CH 2 CN – ) has been hypothesized as the carrier for one diffuse interstellar band. However, this particular molecular system has not been detected in the interstellar medium even though the related cyanomethyl radical and the isoelectronic ketenimine molecule have been found. In this study, we are employing the use of proven quartic force fields and second-order vibrational perturbation theory to compute accurate spectroscopic constants and fundamental vibrational frequencies for X-tilde 1 A' CH 2 CN – in order to assist in laboratory studies and astronomical observations.
8. Identifying specific interstellar polycyclic aromatic hydrocarbons
International Nuclear Information System (INIS)
Mulas, Giacomo; Malloci, Giuliano; Porceddu, Ignazio
2005-01-01
Interstellar Polycyclic Aromatic Hydrocarbons (PAHs) have been thought to be ubiquitous for more than twenty years, yet no single species in this class has been identified in the Interstellar Medium (ISM) to date. The unprecedented sensitivity and resolution of present Infrared Space Observatory (ISO) and forthcoming Herschel observations in the far infrared spectral range will offer a unique way out of this embarrassing impasse
9. Can spores survive in interstellar space
Energy Technology Data Exchange (ETDEWEB)
Weber, P.; Greenberg, J.M.
1985-08-01
Inactivation of spores (Bacillus subtilis) has been investigated in the laboratory by vacuum ultraviolet radiation in simulated interstellar conditions. Damage produced at the normal interstellar particle temperature of 10 K is less than at higher temperatures: the major damage being produced by radiation in the 2,000-3,000 A range. The results place constraints on the panspermia hypothesis. (author).
10. MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
NARCIS (Netherlands)
VOGELAAR, MGR; WAKKER, BP
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
11. MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
NARCIS (Netherlands)
VOGELAAR, MGR; WAKKER, BP
1994-01-01
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
12. Interstellar grains - the 75th anniversary
International Nuclear Information System (INIS)
Li Aigen
2005-01-01
The year of 2005 marks the 75th anniversary since Trumpler (1930) provided the first definitive proof of interstellar grains by demonstrating the existence of general absorption and reddening of starlight in the galactic plane. This article reviews our progressive understanding of the nature of interstellar dust
13. THERMODYNAMICS AND CHARGING OF INTERSTELLAR IRON NANOPARTICLES
Energy Technology Data Exchange (ETDEWEB)
Hensley, Brandon S. [Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109 (United States); Draine, B. T., E-mail: [email protected] [Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (United States)
2017-01-10
Interstellar iron in the form of metallic iron nanoparticles may constitute a component of the interstellar dust. We compute the stability of iron nanoparticles to sublimation in the interstellar radiation field, finding that iron clusters can persist down to a radius of ≃4.5 Å, and perhaps smaller. We employ laboratory data on small iron clusters to compute the photoelectric yields as a function of grain size and the resulting grain charge distribution in various interstellar environments, finding that iron nanoparticles can acquire negative charges, particularly in regions with high gas temperatures and ionization fractions. If ≳10% of the interstellar iron is in the form of ultrasmall iron clusters, the photoelectric heating rate from dust may be increased by up to tens of percent relative to dust models with only carbonaceous and silicate grains.
14. Interstellar Probe: First Step to the Stars
Science.gov (United States)
McNutt, R. L., Jr.
2017-12-01
The idea of an "Interstellar Probe," a robotic spacecraft traveling into the nearby interstellar medium for the purpose of scientific investigation, dates to the mid-1960s. The Voyager Interstellar Mission (VIM), an "accidental" 40-year-old by-product of the Grand Tour of the solar system, has provided initial answers to the problem of the global heliospheric configuration and the details of its interface with interstellar space. But the twin Voyager spacecraft have, at most, only another decade of lifetime, and only Voyager 1 has emerged from the heliosheath interaction region. To understand the nature of the interaction, a near-term mission to the "near-by" interstellar medium with modern and focused instrumentation remains a compelling priority. Imaging of energetic neutral atoms (ENAs) by the Ion Neutral CAmera (INCA) on Cassini and from the Interstellar Boundary Explorer (IBEX) in Earth orbit have provided significant new insights into the global interaction region but point to discrepancies with our current understanding. Exploring "as far as possible" into "pristine" interstellar space can resolve these. Hence, reaching large heliocentric distances rapidly is a driver for an Interstellar Probe. Such a mission is timely; understanding the interstellar context of exoplanet systems - and perhaps the context for the emergence of life both here and there - hinges upon what we can discover within our own stellar neighborhood. With current spacecraft technology and high-capability launch vehicles, such as the Space Launch System (SLS), a small, but extremely capable spacecraft, could be dispatched to the near-by interstellar medium with at least twice the speed of the Voyagers. Challenges remain with payload mass and power constraints for optimized science measurements. Mission longevity, as experienced by, but not designed into, the Voyagers, communications capability, and radioisotope power system performance and lifetime are solvable engineering challenges. Such
15. From interstellar dust to comets - A unification of observational constraints
International Nuclear Information System (INIS)
Greenberg, J.M.; Hage, J.I.
1990-01-01
The interstellar dust model of comets is numerically worked out to satisfy simultaneously several basic constraints provided by observations of Comet Halley, and to derive the porosity of coma dust. The observational constraints are (1) the strengths of the 3.4 and 9.7 micron emission bands, (2) the shape of the 9.7 micron band, (3) the amount of silicates relative to organic materials, and (4) the mass distribution of the dust. The method used involves precise calculations of temperatures and the emission characteristics of porous aggregates of interstellar dust as a function of their mass, porosity, and distance to the sun and the wavelength. The results indicate that coma dust has a porosity in the range 0.93-0.975, i.e., a packing factor of 0.07 or less, consistent with independent observations of comet densities of 0.6 to 0.26 g/cu cm and meteor densities of less than 0.2 g/cu cm. 63 refs
16. Infrared absorption and emission characteristics of interstellar PAHs [Polycyclic Aromatic Hydrocarbon
International Nuclear Information System (INIS)
Allamandola, L.J.; Tielens, A.G.G.M.; Barker, J.R.
1986-01-01
The mid-infrared interstellar emission spectrum with features at 3050, 1610, 1300, 1150, and 885 cm -1 (3.28, 6.2, 7.7, 8.7 and 11.3 microns) is discussed in terms of the Polycyclic Aromatic Hydrocarbon (PAH) hypothesis. This hypothesis is based on the suggestive, but inconclusive comparison between the interstellar emission spectrum with the infrared absorption and Raman spectra of a few PAHs. The fundamental vibrations of PAHs and PAH-like species which determine the ir and Raman properties are discussed. Interstellar ir band emission is due to relaxation from highly vibrationally excited PAHs which have been excited by ultraviolet photons. The excitation/emission process is described in general and the ir fluorescence from one PAH, chrysene, is traced in detail. Generally, there is sufficient energy to populate several vibrational levels in each mode. Molecular vibrational potentials are anharmonic and emission from these higher levels will fall at lower frequencies and produce weak features to the red of the stronger fundamentals. This process is also described and can account for some spectroscopic details of the interstellar emission spectra previously unexplained. Analysis of the interstellar spectrum shows that PAHs containing between 20 and 30 carbon atoms are responsible for the emission. 43 refs., 11 figs
17. Infrared absorption and emission characteristics of interstellar PAHs (Polycyclic Aromatic Hydrocarbon)
Energy Technology Data Exchange (ETDEWEB)
Allamandola, L.J.; Tielens, A.G.G.M.; Barker, J.R.
1986-01-01
The mid-infrared interstellar emission spectrum with features at 3050, 1610, 1300, 1150, and 885 cm/sup -1/ (3.28, 6.2, 7.7, 8.7 and 11.3 microns) is discussed in terms of the Polycyclic Aromatic Hydrocarbon (PAH) hypothesis. This hypothesis is based on the suggestive, but inconclusive comparison between the interstellar emission spectrum with the infrared absorption and Raman spectra of a few PAHs. The fundamental vibrations of PAHs and PAH-like species which determine the ir and Raman properties are discussed. Interstellar ir band emission is due to relaxation from highly vibrationally excited PAHs which have been excited by ultraviolet photons. The excitation/emission process is described in general and the ir fluorescence from one PAH, chrysene, is traced in detail. Generally, there is sufficient energy to populate several vibrational levels in each mode. Molecular vibrational potentials are anharmonic and emission from these higher levels will fall at lower frequencies and produce weak features to the red of the stronger fundamentals. This process is also described and can account for some spectroscopic details of the interstellar emission spectra previously unexplained. Analysis of the interstellar spectrum shows that PAHs containing between 20 and 30 carbon atoms are responsible for the emission. 43 refs., 11 figs.
18. Radio propagation through the turbulent interstellar plasma
International Nuclear Information System (INIS)
Rickett, B.J.
1990-01-01
The current understanding of interstellar scattering is reviewed, and its impact on radio astronomy is examined. The features of interstellar plasma turbulence are also discussed. It is concluded that methods involving the investigation of the flux variability of pulsars and extragalactic sources and the VLBI visibility curves constitute new techniques for probing the ISM. However, scattering causes a seeing limitation in radio observations. It is now clear that variation due to RISS (refractive interstellar scintillations) is likely to be important for several classes of variable sources, especially low-frequency variables and centimeter-wave flickering. 168 refs
19. Physics of the galaxy and interstellar matter
International Nuclear Information System (INIS)
Scheffler, H.; Elsasser, H.
1988-01-01
This book is based on the authors' long standing experience in teaching astronomy courses. It presents in a modern and complete way our present picture of the physics of the Milky Way system. The first part of the book deals with topics of more empirical character, such as the positions and motions of stars, the structure and kinetics of the stellar systems and interstellar phenomena. The more advanced second part is devoted to the interpretation of observational results, i.e. to the physics of interstellar gas and dust, to stellar dynamics, to the theory of spiral structures and the dynamics of interstellar gas
20. Structure and evolution of the interstellar medium
International Nuclear Information System (INIS)
Chieze, J.P.
1985-10-01
We give a two dimensional hydrodynamical analysis of HI clouds collisions in order to determine the mass spectrum of diffuse interstellar clouds. We have taken into account evaporation and abrasion by supernovae blast waves. The conditions for cloud merging or fragmentation are precised. Applications to the model of the interstellar medium of Mc Kee and Ostriker are also discussed. On the other hand, we show that molecular clouds belong to a one parameter family which can be identified to the sequence of the gravitationally unstable states of clouds bounded by the uniform pressure of the coronal phase of the interstellar medium. Hierarchical fragmentation of molecular clouds is analysed in this context [fr
1. Abundances in the diffuse interstellar medium
International Nuclear Information System (INIS)
Harris, A.W.
1988-04-01
The wealth of interstellar absorption line data obtained with the Copernicus and IUE satellites has opened up a new era in studies of the interstellar gas. It is now well established that certain elements, generally those with high condensation temperatures, are substantially under-abundant in the gas-phase relative to total solar or cosmic abundances. This depletion of elements is due to the existence of solid material in the form of dust grains in the interstellar medium. Surprisingly, however, recent surveys indicate that even volatile elements such as Zn and S are significantly depleted in many sight lines. Developments in this field which have been made possible by the large base of UV interstellar absorption line data built up over recent years are reviewed and the implications of the results for our understanding of the physical processes governing depletion are discussed. (author)
2. The composition of circumstellar and interstellar dust
NARCIS (Netherlands)
Tielens, AGGM; Woodward, CE; Biscay, MD; Shull, JM
2001-01-01
A large number of solid dust components have been identified through analysis of stardust recovered from meteorites, and analysis of IR observations of circumstellar shells and the interstellar medium. These include graphite, hydrogenated amorphous carbon, diamond, PAHs, silicon-, iron-, and
3. Experimental interstellar organic chemistry: Preliminary findings
Science.gov (United States)
Khare, B. N.; Sagan, C.
1971-01-01
In a simulation of interstellar organic chemistry in dense interstellar clouds or on grain surfaces, formaldehyde, water vapor, ammonia and ethane are deposited on a quartz cold finger and ultraviolet-irradiated in high vacuum at 77K. The HCHO photolytic pathway which produces an aldehyde radical and a superthermal hydrogen atom initiates solid phase chain reactions leading to a range of new compounds, including methanol, ethanol, acetaldehyde, acetonitrile, acetone, methyl formate, and possibly formic acid. Higher nitriles are anticipated. Genetic relations among these interstellar organic molecules (e.g., the Cannizzaro and Tischenko reactions) must exist. Some of them, rather than being synthesized from smaller molecules, may be degradation products of larger organic molecules, such as hexamethylene tetramine, which are candidate consitituents of the interstellar grains. The experiments reported here may also be relevant to cometary chemistry.
4. Update on an Interstellar Asteroid
Science.gov (United States)
Kohler, Susanna
2018-01-01
Whats the news coming from the research world on the interstellar asteroid visitor, asteroid 1I/Oumuamua? Read on for an update from a few of the latest studies.What is Oumuamua?In lateOctober2017, the discovery of minor planet 1I/Oumuamua was announced. This body which researchers first labeled asa comet and later revised to an asteroid had just zipped around the Sun and was already in the process of speeding away whenwe trained our telescopes on it. Its trajectory, however, marked it as being a visitor from outside our solar system: the first knownvisitorof its kind.Since Oumuamuasdiscovery, scientists have been gathering as many observations of this bodyas possible before it vanishes into the distance. Simultaneously, theorists have leapt at the opportunity to explain its presence and the implications its passage has on our understanding of our surroundings. Here we present just a few of the latest studies that have been published on this first detected interstellar asteroid including several timelystudies published in our new journal, Research Notes of the AAS.The galactic velocity of Oumuamua does not coincide with any of the nearest stars to us. [Mamajek 2018]Where Did Oumuamua Come From?Are we sure Oumuamua didnt originate in our solar system andget scattered into a weird orbit? Jason Wright (The Pennsylvania State University) demonstrates via a series of calculations that no known solar system body could have scattered Oumuamua onto its current orbit nor could any stillunknown object bound to our solar system.Eric Mamajek (Caltech and University of Rochester) showsthat thekinematics of Oumuamua areconsistent with what we might expect of interstellar field objects, though he argues that its kinematics suggest its unlikely to have originated from many of the neareststellar systems.What AreOumuamuas Properties?Oumuamuas light curve. [Bannister et al. 2017]A team of University of Maryland scientists led by Matthew Knight captured a light curve of Oumuamua using
5. Newly detected molecules in dense interstellar clouds
Science.gov (United States)
Irvine, William M.; Avery, L. W.; Friberg, P.; Matthews, H. E.; Ziurys, L. M.
Several new interstellar molecules have been identified including C2S, C3S, C5H, C6H and (probably) HC2CHO in the cold, dark cloud TMC-1; and the discovery of the first interstellar phosphorus-containing molecule, PN, in the Orion "plateau" source. Further results include the observations of 13C3H2 and C3HD, and the first detection of HCOOH (formic acid) in a cold cloud.
6. Carbon chain molecules in interstellar clouds
International Nuclear Information System (INIS)
Winnewisser, G.; Walmsley, C.M.
1979-01-01
A survey of the distribution of long carbon chain molecules in interstellar clouds shows that their abundance is correlated. The various formation schemes for these molecules are discussed. It is concluded that the ion-molecule type formation mechanisms are more promising than their competitors. They have also the advantage of allowing predictions which can be tested by observations. Acetylene C 2 H 2 and diacetylene HCCCCH, may be very abundant in interstellar clouds. (Auth.)
7. Plasma generation and processing of interstellar carbonaceous dust analogs
Science.gov (United States)
Peláez, R. J.; Maté, B.; Tanarro, I.; Molpeceres, G.; Jiménez-Redondo, M.; Timón, V.; Escribano, R.; Herrero, V. J.
2018-03-01
Interstellar (IS) dust analogs, based on amorphous hydrogenated carbon (a-C:H) were generated by plasma deposition in radio frequency discharges of CH4 + He mixtures. The a-C:H samples were characterized by means of secondary electron microscopy, infrared (IR) spectroscopy and UV-visible reflectivity. DFT calculations of structure and IR spectra were also carried out. From the experimental data, atomic compositions were estimated. Both IR and reflectivity measurements led to similar high proportions (≈50%) of H atoms, but there was a significant discrepancy in the sp2/sp3 hybridization ratios of C atoms (sp2/sp3 = 1.5 from IR and 0.25 from reflectivity). Energetic processing of the samples with 5 keV electrons led to a decay of IR aliphatic bands and to a growth of aromatic bands, which is consistent with a dehydrogenation and graphitization of the samples. The decay of the CH aliphatic stretching band at 3.4 μm upon electron irradiation is relatively slow. Estimates based on the absorbed energy and on models of cosmic ray (CR) flux indicate that CR bombardment is not enough to justify the observed disappearance of this band in dense IS clouds.
8. Enabling the First Interstellar Missions
Science.gov (United States)
Lubin, P.
2017-12-01
All propulsion systems that leave the Earth are based on chemical reactions. Chemical reactions, at best, have an efficiency compared to rest mass of 10-10 (or about 1eV per bond). All the mass in the universe converted to chemical reactions would not propel even a single proton to relativistic speeds. While chemistry will get us to Mars it will not allow interstellar capability in any reasonable mission time. Barring new physics we are left with few realistic solutions. None of our current propulsion systems, including nuclear, are capable of the relativistic speeds needed for exploring the many nearby stellar systems and exo-planets. However recent advances in photonics and directed energy systems now allow us to realize what was only a decade ago, simply science fiction, namely the ability to seriously conceive of and plan for relativistic flight. From fully-functional gram-level wafer-scale spacecraft capable of speeds greater than c/4 that could reach the nearest star in 20 years to spacecraft for large missions capable of supporting human life with masses more than 105 kg (100 tons) for rapid interplanetary transit that could reach speeds of greater than 1000 km/s can be realized. With this technology spacecraft can be propelled to speeds currently unimaginable. Photonics, like electronics, and unlike chemical propulsion is an exponential technology with a current double time of about 20 months. This is the key. The cost of such a system is amortized over the essentially unlimited number of launches. In addition, the same photon driver can be used for many other purposes including beamed energy to power high Isp ion engines, remote asteroid composition analysis and planetary defense. This would be a profound change in human capability with enormous implications. Known as Starlight we are now in a NASA Phase II study. The FY 2017 congressional appropriations request directs NASA to study the feasibility of an interstellar mission to coincide with the 100th
9. Components in the interstellar medium
International Nuclear Information System (INIS)
Martin, E.R.
1981-01-01
An analysis is made of the lines of sight toward 32 stars with a procedure that gives velocity components for various interstellar ions. The column densities found for species expected to be relatively undepleted are used to estimate the column density of neutral hydrogen in each component. Whenever possible, the molecular hydrogen excitation temperature, abundances (relative to S II), electron density, and hydrogen volume density are calculated for each component. The results for each star are combined to give total HI column density as a function of (LSR) velocity. The derived velocities correspond well with those found in optical studies. The mean electron density is found to be approximately constant with velocity, but the mean hydrogen volume density is found to vary. The data presented here are consistent with the assumption that some of the velocity components are due to circumstellar material. The total HI column density toward a given star is generally in agreement with Lyman alpha measurements, but ionization and abundance effects are important toward some stars. The total HI column density is found to vary exponentially with velocity (for N(HI)> 10 17 cm -2 ), with an indication that the velocity dispersion at low column densities (N(HI) 17 cm -2 ) is approximately constant. An estimate is made of the kinetic energy density due to cloud motion which depends only on the total HI column density as a function of velocity. The value of 9 x 10 42 erg/pc 3 is in good agreement with a theoretical prediction
10. Characterization of Interstellar Organic Molecules
International Nuclear Information System (INIS)
Gencaga, Deniz; Knuth, Kevin H.; Carbon, Duane F.
2008-01-01
Understanding the origins of life has been one of the greatest dreams throughout history. It is now known that star-forming regions contain complex organic molecules, known as Polycyclic Aromatic Hydrocarbons (PAHs), each of which has particular infrared spectral characteristics. By understanding which PAH species are found in specific star-forming regions, we can better understand the biochemistry that takes place in interstellar clouds. Identifying and classifying PAHs is not an easy task: we can only observe a single superposition of PAH spectra at any given astrophysical site, with the PAH species perhaps numbering in the hundreds or even thousands. This is a challenging source separation problem since we have only one observation composed of numerous mixed sources. However, it is made easier with the help of a library of hundreds of PAH spectra. In order to separate PAH molecules from their mixture, we need to identify the specific species and their unique concentrations that would provide the given mixture. We develop a Bayesian approach for this problem where sources are separated from their mixture by Metropolis Hastings algorithm. Separated PAH concentrations are provided with their error bars, illustrating the uncertainties involved in the estimation process. The approach is demonstrated on synthetic spectral mixtures using spectral resolutions from the Infrared Space Observatory (ISO). Performance of the method is tested for different noise levels.
11. The photoevaporation of interstellar clouds
International Nuclear Information System (INIS)
Bertoldi, F.
1989-01-01
The dynamics of the photoevaporation of interstellar clouds and its consequences for the structure and evolution of H II regions are studied. An approximate analytical solution for the evolution of photoevaporating clouds is derived under the realistic assumption of axisymmetry. The effects of magnetic fields are taken into account in an approximate way. The evolution of a neutral cloud subjected to the ionizing radiation of an OB star has two distinct stages. When a cloud is first exposed to the radiation, the increase in pressure due to the ionization at the surface of the cloud leads to a radiation-driven implosion: an ionization front drives a shock into the cloud, ionizes part of it and compresses the remaining into a dense globule. The initial implosion is followed by an equilibrium cometary stage, in which the cloud maintains a semistationary comet-shaped configuration; it slowly evaporates while accelerating away from the ionizing star until the cloud has been completely ionized, reaches the edge of the H II region, or dies. Expressions are derived for the cloud mass-loss rate and acceleration. To investigate the effect of the cloud photoevaporation on the structure of H II regions, the evolution of an ensemble of clouds of a given mass distribution is studied. It is shown that the compressive effect of the ionizing radiation can induce star formation in clouds that were initially gravitationally stable, both for thermally and magnetically supported clouds
12. The interstellar medium in galaxies
CERN Document Server
1997-01-01
It has been more than five decades ago that Henk van de Hulst predicted the observability of the 21-cm line of neutral hydrogen (HI ). Since then use of the 21-cm line has greatly improved our knowledge in many fields and has been used for galactic structure studies, studies of the interstellar medium (ISM) in the Milky Way and other galaxies, studies of the mass distribution of the Milky Way and other galaxies, studies of spiral struc ture, studies of high velocity gas in the Milky Way and other galaxies, for measuring distances using the Tully-Fisher relation etc. Regarding studies of the ISM, there have been a number of instrumen tal developments over the past decade: large CCD's became available on optical telescopes, radio synthesis offered sensitive imaging capabilities, not only in the classical 21-cm HI line but also in the mm-transitions of CO and other molecules, and X-ray imaging capabilities became available to measure the hot component of the ISM. These developments meant that Milky Way was n...
13. THE STRUCTURE, ORIGIN, AND EVOLUTION OF INTERSTELLAR HYDROCARBON GRAINS
Energy Technology Data Exchange (ETDEWEB)
Chiar, J. E.; Ricca, A. [SETI Institute, Carl Sagan Center, 189 Bernardo Avenue, Mountain View, CA 94043 (United States); Tielens, A. G. G. M. [Leiden Observatory, P.O. Box 9513, NL-2300 RA Leiden (Netherlands); Adamson, A. J., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Gemini Observatory, Northern Operations Center, 670 North A' ohoku Place, Hilo, HI 96729 (United States)
2013-06-10
Many materials have been considered for the carrier of the hydrocarbon absorption bands observed in the diffuse interstellar medium (ISM). In order to refine the model for ISM hydrocarbon grains, we analyze the observed aromatic (3.28, 6.2 {mu}m) and aliphatic (3.4 {mu}m) hydrocarbon absorption features in the diffuse ISM along the line of sight toward the Galactic center Quintuplet Cluster. Observationally, sp {sup 2} bonds can be measured in astronomical spectra using the 6.2 {mu}m CC aromatic stretch feature, whereas the 3.4 {mu}m aliphatic feature can be used to quantify the fraction of sp {sup 3} bonds. The fractional abundance of these components allows us to place the Galactic diffuse ISM hydrocarbons on a ternary phase diagram. We conclude that the Galactic hydrocarbon dust has, on average, a low H/C ratio and sp {sup 3} content and is highly aromatic. We have placed the results of our analysis within the context of the evolution of carbon dust in the ISM. We argue that interstellar carbon dust consists of a large core of aromatic carbon surrounded by a thin mantle of hydrogenated amorphous carbon (a-C:H), a structure that is a natural consequence of the processing of stardust grains in the ISM.
14. THE STRUCTURE, ORIGIN, AND EVOLUTION OF INTERSTELLAR HYDROCARBON GRAINS
International Nuclear Information System (INIS)
Chiar, J. E.; Ricca, A.; Tielens, A. G. G. M.; Adamson, A. J.
2013-01-01
Many materials have been considered for the carrier of the hydrocarbon absorption bands observed in the diffuse interstellar medium (ISM). In order to refine the model for ISM hydrocarbon grains, we analyze the observed aromatic (3.28, 6.2 μm) and aliphatic (3.4 μm) hydrocarbon absorption features in the diffuse ISM along the line of sight toward the Galactic center Quintuplet Cluster. Observationally, sp 2 bonds can be measured in astronomical spectra using the 6.2 μm CC aromatic stretch feature, whereas the 3.4 μm aliphatic feature can be used to quantify the fraction of sp 3 bonds. The fractional abundance of these components allows us to place the Galactic diffuse ISM hydrocarbons on a ternary phase diagram. We conclude that the Galactic hydrocarbon dust has, on average, a low H/C ratio and sp 3 content and is highly aromatic. We have placed the results of our analysis within the context of the evolution of carbon dust in the ISM. We argue that interstellar carbon dust consists of a large core of aromatic carbon surrounded by a thin mantle of hydrogenated amorphous carbon (a-C:H), a structure that is a natural consequence of the processing of stardust grains in the ISM.
15. Organic chemistry and biology of the interstellar medium
Science.gov (United States)
Sagan, C.
1973-01-01
Interstellar organic chemistry is discussed as the field of study emerging from the discovery of microwave lines of formaldehyde and of hydrogen cyanide in the interstellar medium. The reliability of molecular identifications and comparisons of interstellar and cometary compounds are considered, along with the degradational origin of simple organics. It is pointed out that the contribution of interstellar organic chemistry to problems in biology is not substantive but analogical. The interstellar medium reveals the operation of chemical processes which, on earth and perhaps on vast numbers of planets throughout the universe, led to the origin of life, but the actual molecules of the interstellar medium are unlikely to play any significant biological role.
16. Hydrocarbons on Saturns Satellites: Relationship to Interstellar Dust and the Solar Nebula
Science.gov (United States)
Cruikshank, D. P.
2012-01-01
To understand the origin and evolution of our Solar System, and the basic components that led to life on Earth, we study interstellar and planetary spectroscopic signatures. The possible relationship of organic material detected in carbonaceous meteorites, interplanetary dust particles (IDPs), comets and the interstellar medium have been the source of speculation over the years as the composition and processes that governed the early solar nebula have been explored to understand the extent to which primitive material survived or became processed. The Cassini VIMS has provided new data relevant to this problem. Three of Saturn's satellites, Phoebe, Iapetus, and Hyperion, are found to have aromatic and aliphatic hydrocarbons on their surfaces. The aromatic hydrocarbon signature (C-H stretching mode at 3.28 micrometers) is proportionally significantly stronger (relative to the aliphatic bands) than that seen in other Solar System bodies (e.g., comets) and materials (Stardust samples, IDPs, meteorites) and the distinctive sub-features of the 3.4 micrometer aliphatic band (CH2 and CH3 groups) are reminiscent of those widely detected throughout the diffuse ISM. Phoebe may be a captured object that originated in the region beyond the present orbit of Neptune, where the solar nebula contained a large fraction of original interstellar ice and dust that was less processed than material closer to the Sun. Debris from Phoebe now resident on Iapetus and Hyperion, as well as o Phoebe itself, thus presents a unique blend of hydrocarbons, amenable to comparisons with interstellar hydrocarbons and other Solar System materials. The dust ring surrounding Saturn, in which Phoebe is embedded, probably originated from a collision with Phoebe. Dust ring particles are the likely source of the organic-bearing materials, and perhaps the recently identified small particles of Fe detected on Saturn's satellites. Lab measurements of the absolute band strengths of representative aliphatic and
17. The Interstellar Boundary Explorer (IBEX) - Time to Launch!
Science.gov (United States)
McComas, David
The Interstellar Boundary Explorer (IBEX) mission is scheduled to launch in mid-July 2008, right around the time of this COSPAR meeting. IBEX will make the first global observations of the heliosphere's interaction with the interstellar medium. IBEX achieves these breakthrough observations by traveling outside of the Earth's magnetosphere in a highly elliptical orbit and taking global Energetic Neutral Atoms (ENA) images with two very large aperture single pixel ENA cameras. IBEX-Lo makes measurements in 8 contiguous energy pass bands covering from ˜10 eV to 2 keV; IBEX-Hi similarly covers from ˜300 eV to 6 keV in 6 contiguous pass bands. IBEX's high-apogee (˜50RE ) orbit enables heliospheric ENA measurements by providing viewing from far outside the earth's relatively bright magnetospheric ENA emissions. The IBEX cameras view perpendicular to the spacecraft's sun-pointed spin axis. Each six months, the spacecraft spin and progression of the sun-pointing spin axis as the Earth moves around the Sun lead naturally to global, all-sky images. IBEX is the first mission to achieve a high altitude from a standard Pegasus launch vehicle. We accomplish this by adding the propulsion from an IBEX-supplied solid rocket motor and the spacecraft's hydrazine propulsion system. Additional information on IBEX is available at www.ibex.swri.edu. This talk, on behalf of the IBEX science and engineering teams, will summarize the IBEX science and mission and will provide an up-to-the-minute update on the status of the mission, including any new information on the launch and commissioning status.
18. Photodissociation and excitation of interstellar molecules
International Nuclear Information System (INIS)
Dishoeck, E.F. van.
1984-01-01
Apart from a rather long introduction containing some elementary astrophysics, quantum chemistry and spectroscopy and an incomplete, historical review of molecular observations, this thesis is divided into three sections. In part A, a rigorous quantum chemical and dynamical study is made of the photodissociation processes in the OH and HCl molecules. In part B, the cross sections obtained in part A are used in various astrophysical problems such as the study of the abundances of the OH and HCl molecules in interstellar clouds, the use of the OH abundance as a measure of the cosmic ray ionization rate, the lifetime of the OH radical in comets and the abundance of OH in the solar photosphere. Part C discusses the excitation of the C 2 molecule under interstellar conditions, its use as a diagnostic probe of the temperature, density and strength of the radiation field in interstellar clouds. Quadrupole moments and oscillator strengths are analyzed. (Auth.)
19. On the nature of interstellar turbulence
International Nuclear Information System (INIS)
Altunin, V.I.
1981-01-01
Possible reasons of interstellar medium turbulence manifested in pulsar scintillation and radio-frequency emission scattering of extragalactic sources near by the Galaxy plane, are discussed. Sources and conditions of turbulence emergence in HII region shells, supernova, residue and in stellar wind giving observed scattering effects are considered. It is shown that in the formation of the interstellar scintillation pattern of discrete radio-frequency emission sources a certain role can be played by magnetosound turbulence, which arises due to shock-waves propagating in the interstellar medium at a velocity Vsub(sh) approximately 20-100 km/s as well as by stellar-wind inhomogeneity of OB classes stars [ru
20. Physics of the interstellar and intergalactic medium
CERN Document Server
Draine, Bruce T
2010-01-01
This is a comprehensive and richly illustrated textbook on the astrophysics of the interstellar and intergalactic medium--the gas and dust, as well as the electromagnetic radiation, cosmic rays, and magnetic and gravitational fields, present between the stars in a galaxy and also between galaxies themselves. Topics include radiative processes across the electromagnetic spectrum; radiative transfer; ionization; heating and cooling; astrochemistry; interstellar dust; fluid dynamics, including ionization fronts and shock waves; cosmic rays; distribution and evolution of the interstellar medium; and star formation. While it is assumed that the reader has a background in undergraduate-level physics, including some prior exposure to atomic and molecular physics, statistical mechanics, and electromagnetism, the first six chapters of the book include a review of the basic physics that is used in later chapters. This graduate-level textbook includes references for further reading, and serves as an invaluable resourc...
1. Investigating nearby exoplanets via interstellar radar
Science.gov (United States)
Scheffer, Louis K.
2014-01-01
Interstellar radar is a potential intermediate step between passive observation of exoplanets and interstellar exploratory missions. Compared with passive observation, it has the traditional advantages of radar astronomy. It can measure surface characteristics, determine spin rates and axes, provide extremely accurate ranges, construct maps of planets, distinguish liquid from solid surfaces, find rings and moons, and penetrate clouds. It can do this even for planets close to the parent star. Compared with interstellar travel or probes, it also offers significant advantages. The technology required to build such a radar already exists, radar can return results within a human lifetime, and a single facility can investigate thousands of planetary systems. The cost, although too high for current implementation, is within the reach of Earth's economy.
2. Experiments on chemical and physical evolution of interstellar grain mantles
International Nuclear Information System (INIS)
Greenberg, J.M.
1984-01-01
The Astrophysical Laboratory at the University of Leiden is the first to succeed in simulating the essential conditions in interstellar space as they affect the evolution of interstellar grains. (author)
3. 3D distribution of interstellar medium in the Galaxy: Preparation for analysis of Gaia observations
Energy Technology Data Exchange (ETDEWEB)
Puspitarini, Lucky, E-mail: [email protected] [GEPI Observatoire de Paris, CNRS, Paris Diderot University, 5 Place Jules Janssen, 92190, Meudon (France); Bosscha Observatory and Department of Astronomy, FMIPA, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 (Indonesia); Lallement, Rosine, E-mail: [email protected] [GEPI Observatoire de Paris, CNRS, Paris Diderot University, 5 Place Jules Janssen, 92190, Meudon (France)
2015-09-30
Accurate and detailed three-dimensional (3D) maps of Galactic interstellar medium (ISM) are still lacking. One way to obtain such 3D descriptions is to record a large set of individual absorption or reddening measurements toward target stars located at various known distances and directions. The inversion of these measurements using a tomographic method can produce spatial distribution of the ISM. Until recently absorption data were very limited and distances to the target stars are still uncertain, but the situation will greatly improve thanks to current and future massive stellar surveys from ground, and to Gaia mission. To prepare absorption data for inversion from a huge number of stellar spectra, automated tools are needed. We have developed various spectral analysis tools adapted to different type of spectra, early- or late- type star. We also have used diffuse interstellar bands (DIBs) to trace IS structures and kinematics. Although we do not know yet their carriers, they can be a promising tool to trace distant interstellar clouds or Galactic arms. We present some examples of the interstellar fitting and show the potentiality of DIBs in tracing the ISM. We will also briefly show and comment the latest 3D map of the local ISM which reveal nearby cloud complexes and cavities.
4. 3D distribution of interstellar medium in the Galaxy: Preparation for analysis of Gaia observations
International Nuclear Information System (INIS)
Puspitarini, Lucky; Lallement, Rosine
2015-01-01
Accurate and detailed three-dimensional (3D) maps of Galactic interstellar medium (ISM) are still lacking. One way to obtain such 3D descriptions is to record a large set of individual absorption or reddening measurements toward target stars located at various known distances and directions. The inversion of these measurements using a tomographic method can produce spatial distribution of the ISM. Until recently absorption data were very limited and distances to the target stars are still uncertain, but the situation will greatly improve thanks to current and future massive stellar surveys from ground, and to Gaia mission. To prepare absorption data for inversion from a huge number of stellar spectra, automated tools are needed. We have developed various spectral analysis tools adapted to different type of spectra, early- or late- type star. We also have used diffuse interstellar bands (DIBs) to trace IS structures and kinematics. Although we do not know yet their carriers, they can be a promising tool to trace distant interstellar clouds or Galactic arms. We present some examples of the interstellar fitting and show the potentiality of DIBs in tracing the ISM. We will also briefly show and comment the latest 3D map of the local ISM which reveal nearby cloud complexes and cavities
5. Surface chemistry on interstellar oxide grains
International Nuclear Information System (INIS)
Denison, P.; Williams, D.A.
1981-01-01
Detailed calculations are made to test the predictions of Duley, Millar and Williams (1978) concerning the chemical reactivity of interstellar oxide grains. A method is established for calculating interaction energies between atoms and the perfect crystal with or without surface vacancy sites. The possibility of reactions between incident atoms and absorbed atoms is investigated. It is concluded that H 2 formation can occur on the perfect crystal surfaces, and that for other diatomic molecules the important formation sites are the Fsub(s)- and V 2- sub(s)-centres. The outline by Duley, Millar and Williams (1979) of interstellar oxide grain growth and destruction is justified by these calculations. (author)
6. REVISITING ULYSSES OBSERVATIONS OF INTERSTELLAR HELIUM
International Nuclear Information System (INIS)
Wood, Brian E.; Müller, Hans-Reinhard; Witte, Manfred
2015-01-01
We report the results of a comprehensive reanalysis of Ulysses observations of interstellar He atoms flowing through the solar system, the goal being to reassess the interstellar He flow vector and to search for evidence of variability in this vector. We find no evidence that the He beam seen by Ulysses changes at all from 1994-2007. The direction of flow changes by no more than ∼0.°3 and the speed by no more than ∼0.3 km s –1 . A global fit to all acceptable He beam maps from 1994-2007 yields the following He flow parameters: V ISM = 26.08 ± 0.21 km s –1 , λ = 75.54 ± 0.°19, β = –5.44 ± 0.°24, and T = 7260 ± 270 K; where λ and β are the ecliptic longitude and latitude direction in J2000 coordinates. The flow vector is consistent with the original analysis of the Ulysses team, but our temperature is significantly higher. The higher temperature somewhat mitigates a discrepancy that exists in the He flow parameters measured by Ulysses and the Interstellar Boundary Explorer, but does not resolve it entirely. Using a novel technique to infer photoionization loss rates directly from Ulysses data, we estimate a density of n He = 0.0196 ± 0.0033 cm –3 in the interstellar medium
7. REVISITING ULYSSES OBSERVATIONS OF INTERSTELLAR HELIUM
Energy Technology Data Exchange (ETDEWEB)
Wood, Brian E. [Naval Research Laboratory, Space Science Division, Washington, DC 20375 (United States); Müller, Hans-Reinhard [Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 (United States); Witte, Manfred, E-mail: [email protected] [Max-Planck-Institute for Solar System Research, Katlenburg-Lindau D-37191 (Germany)
2015-03-01
We report the results of a comprehensive reanalysis of Ulysses observations of interstellar He atoms flowing through the solar system, the goal being to reassess the interstellar He flow vector and to search for evidence of variability in this vector. We find no evidence that the He beam seen by Ulysses changes at all from 1994-2007. The direction of flow changes by no more than ∼0.°3 and the speed by no more than ∼0.3 km s{sup –1}. A global fit to all acceptable He beam maps from 1994-2007 yields the following He flow parameters: V {sub ISM} = 26.08 ± 0.21 km s{sup –1}, λ = 75.54 ± 0.°19, β = –5.44 ± 0.°24, and T = 7260 ± 270 K; where λ and β are the ecliptic longitude and latitude direction in J2000 coordinates. The flow vector is consistent with the original analysis of the Ulysses team, but our temperature is significantly higher. The higher temperature somewhat mitigates a discrepancy that exists in the He flow parameters measured by Ulysses and the Interstellar Boundary Explorer, but does not resolve it entirely. Using a novel technique to infer photoionization loss rates directly from Ulysses data, we estimate a density of n {sub He} = 0.0196 ± 0.0033 cm{sup –3} in the interstellar medium.
8. Interstellar propagation of low energy cosmic rays
International Nuclear Information System (INIS)
Cesarsky, C.J.
1975-01-01
Wave particles interactions prevent low energy cosmic rays from propagating at velocities much faster than the Alfven velocity, reducing their range by a factor of order 50. Therefore, supernovae remnants cannot fill the neutral portions of the interstellar medium with 2 MeV cosmic rays [fr
9. SILICATE COMPOSITION OF THE INTERSTELLAR MEDIUM
Energy Technology Data Exchange (ETDEWEB)
Fogerty, S.; Forrest, W.; Watson, D. M.; Koch, I. [Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627 (United States); Sargent, B. A., E-mail: [email protected] [Center for Imaging Science and Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology, 54 Lomb Memorial Drive, Rochester, NY 14623 (United States)
2016-10-20
The composition of silicate dust in the diffuse interstellar medium and in protoplanetary disks around young stars informs our understanding of the processing and evolution of the dust grains leading up to planet formation. An analysis of the well-known 9.7 μ m feature indicates that small amorphous silicate grains represent a significant fraction of interstellar dust and are also major components of protoplanetary disks. However, this feature is typically modeled assuming amorphous silicate dust of olivine and pyroxene stoichiometries. Here, we analyze interstellar dust with models of silicate dust that include non-stoichiometric amorphous silicate grains. Modeling the optical depth along lines of sight toward the extinguished objects Cyg OB2 No. 12 and ζ Ophiuchi, we find evidence for interstellar amorphous silicate dust with stoichiometry intermediate between olivine and pyroxene, which we simply refer to as “polivene.” Finally, we compare these results to models of silicate emission from the Trapezium and protoplanetary disks in Taurus.
10. THE AGE OF THE LOCAL INTERSTELLAR BUBBLE
International Nuclear Information System (INIS)
Abt, Helmut A.
2011-01-01
The Local Interstellar Bubble is an irregular region from 50 to 150 pc from the Sun in which the interstellar gas density is 10 -2 -10 -3 of that outside the bubble and the interstellar temperature is 10 6 K. Evidently most of the gas was swept out by one or more supernovae. I explored the stellar contents and ages of the region from visual double stars, spectroscopic doubles, single stars, open clusters, emission regions, X-ray stars, planetary nebulae, and pulsars. The bubble has three sub-regions. The region toward the galactic center has stars as early as O9.5 V and with ages of 2-4 M yr. It also has a pulsar (PSRJ1856-3754) with a spin-down age of 3.76 Myr. That pulsar is likely to be the remnant of the supernova that drove away most of the gas. The central lobe has stars as early as B7 V and therefore an age of about 160 Myr or less. The Pleiades lobe has stars as early as B3 and therefore an age of about 50 Myr. There are no obvious pulsars that resulted from the supernovae that cleared out those areas. As found previously by Welsh and Lallement, the bubble has five B stars along its perimeter that show high-temperature ions of O VI and C II along their lines of sight, confirming its high interstellar temperature.
11. Fluorescent excitation of interstellar H2
NARCIS (Netherlands)
Black, J.H.; Dishoeck, van E.F.
1987-01-01
The infrared emission spectrum of H2 excited by ultraviolet absorption, followed by fluorescence, was investigated using comprehensive models of interstellar clouds for computing the spectrum and to assess the effects on the intensity to various cloud properties, such as density, size, temperature,
12. Organics in meteorites - Solar or interstellar?
Science.gov (United States)
Alexander, Conel M. O'D.; Cody, George D.; Fogel, Marilyn; Yabuta, Hikaru
2008-10-01
The insoluble organic material (IOM) in primitive meteorites is related to the organic material in interplanetary dust particles and comets, and is probably related to the refractory organic material in the diffuse interstellar medium. If the IOM is representative of refractory ISM organics, models for how and from what it formed will have to be revised.
13. Optical observations of nearby interstellar gas
Science.gov (United States)
Frisch, P. C.; York, D. G.
1984-11-01
Observations indicated that a cloud with a heliocentric velocity of approximately -28 km/s and a hydrogen column density that possibly could be on the order of, or greater than, 5 x 10 to the 19 power/square cm is located within the nearest 50 to 80 parsecs in the direction of Ophiuchus. This is a surprisingly large column density of material for this distance range. The patchy nature of the absorption from the cloud indicates that it may not be a feature with uniform properties, but rather one with small scale structure which includes local enhancements in the column density. This cloud is probably associated with the interstellar cloud at about the same velocity in front of the 20 parsec distant star alpha Oph (Frisch 1981, Crutcher 1982), and the weak interstellar polarization found in stars as near as 35 parsecs in this general region (Tinbergen 1982). These data also indicate that some portion of the -14 km/s cloud also must lie within the 100 parsec region. Similar observations of both Na1 and Ca2 interstellar absorption features were performed in other lines of sight. Similar interstellar absorption features were found in a dozen stars between 20 and 100 parsecs of the Sun.
14. SILICATE COMPOSITION OF THE INTERSTELLAR MEDIUM
International Nuclear Information System (INIS)
Fogerty, S.; Forrest, W.; Watson, D. M.; Koch, I.; Sargent, B. A.
2016-01-01
The composition of silicate dust in the diffuse interstellar medium and in protoplanetary disks around young stars informs our understanding of the processing and evolution of the dust grains leading up to planet formation. An analysis of the well-known 9.7 μ m feature indicates that small amorphous silicate grains represent a significant fraction of interstellar dust and are also major components of protoplanetary disks. However, this feature is typically modeled assuming amorphous silicate dust of olivine and pyroxene stoichiometries. Here, we analyze interstellar dust with models of silicate dust that include non-stoichiometric amorphous silicate grains. Modeling the optical depth along lines of sight toward the extinguished objects Cyg OB2 No. 12 and ζ Ophiuchi, we find evidence for interstellar amorphous silicate dust with stoichiometry intermediate between olivine and pyroxene, which we simply refer to as “polivene.” Finally, we compare these results to models of silicate emission from the Trapezium and protoplanetary disks in Taurus.
15. MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
NARCIS (Netherlands)
VOGELAAR, MGR; WAKKER, BP; SCHWARZ, UJ
1991-01-01
To study the structure of interstellar clouds we used the so-called perimeter-area relation to estimate fractal dimensions. We studied the reliability of the method by applying it to artificial fractals and discuss some of the problems and pitfalls. Results for two different cloud types
16. INTERSTELLAR MAGNETIC FIELD SURROUNDING THE HELIOPAUSE
International Nuclear Information System (INIS)
Whang, Y. C.
2010-01-01
This paper presents a three-dimensional analytical solution, in the limit of very low plasma β-ratio, for the distortion of the interstellar magnetic field surrounding the heliopause. The solution is obtained using a line dipole method that is the integration of point dipole along a semi-infinite line; it represents the magnetic field caused by the presence of the heliopause. The solution allows the variation of the undisturbed magnetic field at any inclination angle. The heliosphere is considered as having blunt-nosed geometry on the upwind side and it asymptotically approaches a cylindrical geometry having an open exit for the continuous outflow of the solar wind on the downwind side. The heliopause is treated as a magnetohydrodynamic tangential discontinuity; the interstellar magnetic field lines at the boundary are tangential to the heliopause. The interstellar magnetic field is substantially distorted due to the presence of the heliopause. The solution shows the draping of the field lines around the heliopause. The magnetic field strength varies substantially near the surface of the heliopause. The effect on the magnetic field due to the presence of the heliopause penetrates very deep into the interstellar space; the depth of penetration is of the same order of magnitude as the scale length of the heliosphere.
17. The influence of the interstellar medium on climate and life
International Nuclear Information System (INIS)
Talbot, R.J. Jr.
1980-01-01
Recent studies of the gas and dust between the stars, the interstellar medium, reveal a complex chemistry which indicates that prebiotic organic chemistry is ubiquitous. The relationship between this interstellar chemistry and the organic chemistry of the early solar system and the Earth is explored. The interstellar medium is also considered as likely to have a continuing influence upon the climate of the Earth and other planets. Life forms as known are not only descendants of the organic evolution begun in the interstellar medium, but their continuing evolution is also molded through occasional interactions between the interstellar medium, the Sun and the climate on Earth. (author)
18. Ultraviolet extinction properties of grains in the interstellar medium
International Nuclear Information System (INIS)
Seab, C.G.
1982-01-01
The IUE satellite has been used to derive UV extinction curves for 58 stars, ranging in spectral type from 06 the A5, and with E(B-V) reddenings from 0.09 to 1.59 mag. The average reddening is 0.63 mag. Anomalous extinction curves were particularly sought in the project. The most striking discovery was the near absence of the 2175 Angstrom extinction feature from the line of sight towards HD 29647 in the Taurus dark cloud. The collection of data has been analyzed in several ways. Patterns are sought in the collection as a whole, in homogeneous subsets of the data, and in relation to diffuse band strengths. Apart from some well-known correlations, only a few weak relationships are found, including a quasi-relationship between the 2175 Angstrom bump and the 4430 Angstrom diffuse band that persists after the basic E(B-V) dependencies have been removed. A search for diffuse bands in the UV was done by stacking 48 of the extinction curves to reduce the noise. The stacked curve showed no evidence of new diffuse bands. To help interpret the anomalous extinction curves, a theoretical simulation of grain processing in interstellar shocks was undertaken. Shock processing was found to cause strong 2175 angstorm bumps and high far UV extinction. Comparison to extinction curves associated with supernova remnants confirms the predictions of strong 2175 Angstrom bumps, and partially confirms the prediction of high far UV extinction. The implications of all of these results are considered for the two most prominent grain models
19. TRIANGULATION OF THE INTERSTELLAR MAGNETIC FIELD
Energy Technology Data Exchange (ETDEWEB)
Schwadron, N. A.; Moebius, E. [University of New Hampshire, Durham, NH 03824 (United States); Richardson, J. D. [Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Burlaga, L. F. [Goddard Space Flight Center, Greenbelt, MD 20771 (United States); McComas, D. J. [Southwest Research Institute, San Antonio, TX 78228 (United States)
2015-11-01
Determining the direction of the local interstellar magnetic field (LISMF) is important for understanding the heliosphere’s global structure, the properties of the interstellar medium, and the propagation of cosmic rays in the local galactic medium. Measurements of interstellar neutral atoms by Ulysses for He and by SOHO/SWAN for H provided some of the first observational insights into the LISMF direction. Because secondary neutral H is partially deflected by the interstellar flow in the outer heliosheath and this deflection is influenced by the LISMF, the relative deflection of H versus He provides a plane—the so-called B–V plane in which the LISMF direction should lie. Interstellar Boundary Explorer (IBEX) subsequently discovered a ribbon, the center of which is conjectured to be the LISMF direction. The most recent He velocity measurements from IBEX and those from Ulysses yield a B–V plane with uncertainty limits that contain the centers of the IBEX ribbon at 0.7–2.7 keV. The possibility that Voyager 1 has moved into the outer heliosheath now suggests that Voyager 1's direct observations provide another independent determination of the LISMF. We show that LISMF direction measured by Voyager 1 is >40° off from the IBEX ribbon center and the B–V plane. Taking into account the temporal gradient of the field direction measured by Voyager 1, we extrapolate to a field direction that passes directly through the IBEX ribbon center (0.7–2.7 keV) and the B–V plane, allowing us to triangulate the LISMF direction and estimate the gradient scale size of the magnetic field.
20. Dust in the Diffuse Neutral Interstellar Medium
Science.gov (United States)
Sofia, Ulysses J.
2008-05-01
Studies of interstellar dust have always relied heavily upon Laboratory Astrophysics for interpretation. Laboratory values, in the broad sense that includes theory, are needed for the most basic act of measuring interstellar abundances, to the more complex determination of what grains are responsible for particular extinction. The symbiotic relationship between astronomical observations and Laboratory Astrophysics has prompted both fields to move forward, especially in the era of high-resolution ultraviolet spectroscopy when new elemental species could be interpreted and observations were able to show the limits of laboratory determinations. Thanks to this synergy, we currently have a good idea of the quantity of the most abundant elements incorporated into dust in diffuse neutral interstellar clouds: carbon, oxygen, iron, silicon and magnesium. Now the task is to figure out how, chemically and physically, those elements are integrated into interstellar grains. We can do this by comparing extinction curves to grain populations in radiative transfer models. The limitation at the present time is the availability of optical constants in the infrared through ultraviolet for species that are likely to exist in dust, i.e., those that are easy to form in the physical environments around stars and in molecular clouds. Extinction in some lines of sight can be fit within current abundance limits and with the optical constants that are available. However the inability to reproduce other extinction curves suggests that optical constants can be improved, either in quality for compounds that have been measured, or quantity in the sense of providing data for more materials. This talk will address the current state and the future of dust studies in the diffuse neutral interstellar medium. This work is supported by the grant HST-AR-10979.01-A from the Space Telescope Science Institute to Whitman College.
1. Laboratory Anion Chemistry: Implications for the DIBs, and a Potential Formation Mechanism for a Known Interstellar Molecule
Science.gov (United States)
Eichelberger, B.; Barckholtz, C.; Stepanovic, M.; Bierbaum, V.; Snow, T.
2002-01-01
Due to recent interest in molecular anions as possible interstellar species, we have carried out several laboratory studies of anion chemistry. The reactions of the series C(sub n)(sup -); and C(sub n)H(sup -) with H and H2 were studied to address the viability of such species in the diffuse interstellar medium and to address their ability to be carriers of the diffuse interstellar bands (DIBs). These same molecules were also reacted with N and O to show possible heteroatomic products. C(sub m)N(sup - was a particularly stable product from the reaction of C(sub n)(sup -) + N. C3N(sup -) was further reacted with H to study chemistry that could produce HC3N, a known interstellar species. The reactions were done in a flowing afterglow selected ion flow tube apparatus (FA-SIFT). The anions were generated in an electron impact or cold cathode discharge source and the anion of interest was then selected by a quadrupole mass filter. The selected ion was then reacted with the atomic or molecular species in the flow tube and products were detected by another quadrupole. While the C(sub n)(sup -) species do not appear to be viable DIB carriers, their possible presence could provide a mechanism for the formation of known heteroatomic neutral molecules detected in the interstellar medium (ISM).
2. The loop I superbubble and the local interstellar magnetic field
International Nuclear Information System (INIS)
Frisch, Priscilla Chapman
2014-01-01
Recent data on the interstellar magnetic field in the low density nearby interstellar medium suggest a new perspective for understanding interstellar clouds within 40 pc. The directions of the local interstellar magnetic field found from measurements of optically polarized starlight and the very local field found from the Ribbon of energetic neutral atoms discovered by IBEX nearly agree. The geometrical relation between the local magnetic field, the positions and kinematics of local interstellar clouds, and the Loop I S1 superbubble, suggest that the Sun is located in the boundary of this evolved superbubble. The quasiperpendicular angle between the bulk kinematics and magnetic field of the local ISM indicates that a complete picture of low density interstellar clouds needs to include information on the interstellar magnetic field.
3. The Possible Interstellar Anion CH2CN-: Spectroscopic Constants, Vibrational Frequencies, and Other Considerations
Science.gov (United States)
Fortenberry, Ryan C.; Crawford, T. Daniel; Lee, Timothy J.
2013-01-01
The A\\ ^1B_1 \\leftarrow \\tilde{X}\\ ^1A^{\\prime } excitation into the dipole-bound state of the cyanomethyl anion (CH2CN-) has been hypothesized as the carrier for one diffuse interstellar band. However, this particular molecular system has not been detected in the interstellar medium even though the related cyanomethyl radical and the isoelectronic ketenimine molecule have been found. In this study, we are employing the use of proven quartic force fields and second-order vibrational perturbation theory to compute accurate spectroscopic constants and fundamental vibrational frequencies for \\tilde{X}\\ ^1A^{\\prime } CH2CN- in order to assist in laboratory studies and astronomical observations.
4. C60+ - looking for the bucky-ball in interstellar space
Science.gov (United States)
Galazutdinov, G. A.; Shimansky, V. V.; Bondar, A.; Valyavin, G.; Krełowski, J.
2017-03-01
The laboratory gas-phase spectrum recently published by Campbell et al. has reinvigorated attempts to confirm the presence of the C_{60}^+ cation in the interstellar medium, through an analysis of the spectra of hot, reddened stars. This search is hindered by at least two issues that need to be addressed: (I) the wavelength range of interest is severely polluted by strong water-vapour lines coming from the Earth's atmosphere; (II) one of the major bands attributed to C_{60}^+, at 9633 Å, is blended with the stellar Mg II line, which is susceptible to non-local thermodynamic equilibrium effects in hot stellar atmospheres. Both these issues are carefully considered here for the first time, based on high-resolution and high signal-to-noise ratio echellé spectra for 19 lines of sight. The result is that the presence of C_{60}^+ in interstellar clouds is brought into question.
5. Interstellar C2 molecules in a Taurus dark cloud
International Nuclear Information System (INIS)
Hobbs, L.M.; Black, J.H.; van Dishoeck, E.F.
1983-01-01
Five relatively strong interstellar absorption lines of the 2--0) Phillips band of C 2 near lambda8760 are detected in the spectrum of HD 29647, a late B star which lies behind a substantial part of the Taurus molecular cloud complex about 20triangle-solid from TMC-1. In combination with newly determined oscillator strengths, the observations yield a column density N(C 2 )roughly-equal9 x 10 13 cm -2 , which is comparable to those of widely distributed molecules like CH and H 2 O. Theoreticl models of the observed C 2 rotational level populations indicate a kinetic temperature T = 14 +8 /sub -/ 5 K and a mean density n 3 cm -3 . A narrow, anomalous strong, stellar Mn II line yields for HD 29647 a project rotational velocity v sin i -1 and is explained by previous identifications HD 29647 as a Hg-Mn peculiar star. Similar spectra of ν Cyg and omicron And give an upper limit W/sub lambda/ 2 lines in the 2--0) band, toward both stars
6. Scientists Toast the Discovery of Vinyl Alcohol in Interstellar Space
Science.gov (United States)
2001-10-01
Astronomers using the National Science Foundation's 12 Meter Telescope at Kitt Peak, AZ, have discovered the complex organic molecule vinyl alcohol in an interstellar cloud of dust and gas near the center of the Milky Way Galaxy. The discovery of this long-sought compound could reveal tantalizing clues to the mysterious origin of complex organic molecules in space. Vinyl Alcohol and its fellow isomers "The discovery of vinyl alcohol is significant," said Barry Turner, a scientist at the National Radio Astronomy Observatory (NRAO) in Charlottesville, Va., "because it gives us an important tool for understanding the formation of complex organic compounds in interstellar space. It may also help us better understand how life might arise elsewhere in the Cosmos." Vinyl alcohol is an important intermediary in many organic chemistry reactions on Earth, and the last of the three stable members of the C2H4O group of isomers (molecules with the same atoms, but in different arrangements) to be discovered in interstellar space. Turner and his colleague A. J. Apponi of the University of Arizona's Steward Observatory in Tucson detected the vinyl alcohol in Sagittarius B -- a massive molecular cloud located some 26,000 light-years from Earth near the center of our Galaxy. The astronomers were able to detect the specific radio signature of vinyl alcohol during the observational period of May and June of 2001. Their results have been accepted for publication in the Astrophysical Journal Letters. Of the approximately 125 molecules detected in interstellar space, scientists believe that most are formed by gas-phase chemistry, in which smaller molecules (and occasionally atoms) manage to "lock horns" when they collide in space. This process, though efficient at creating simple molecules, cannot explain how vinyl alcohol and other complex chemicals are formed in detectable amounts. For many years now, scientists have been searching for the right mechanism to explain how the building
7. Organic Synthesis in Simulated Interstellar Ice Analogs
Science.gov (United States)
Dworkin, Jason P.; Bernstein, Max P.; Sandford, Scott A.; Allamandola, Louis J.; Deamer, David W.; Elsila, Jamie; Zare, Richard N.
2001-01-01
Comets and carbonaceous micrometeorites may have been significant sources of organic compounds on the early Earth. Ices on grains in interstellar dense molecular clouds contain a variety of simple molecules as well as aromatic molecules of various sizes. While in these clouds the icy grains are processed by ultraviolet light and cosmic radiation which produces more complex organic molecules. We have run laboratory simulations to identify the types of molecules which could have been generated photolytically in pre-cometary ices. Experiments were conducted by forming various realistic interstellar mixed-molecular ices with and without polycyclic aromatic hydrocarbons (PAHs) at approx. 10 K under high vacuum irradiated with UV light from a hydrogen plasma lamp. The residue that remained after warming to room temperature was analyzed by HPLC, and by laser desorption mass spectrometry. The residue contains several classes of compounds which may be of prebiotic significance.
8. Diffuse interstellar gas in disk galaxies
International Nuclear Information System (INIS)
1989-01-01
The physical properties of the diffuse gas in our Galaxy are reviewed and considered as a starting point for interstellar (IS) studies of disk galaxies. Attention is focussed on the atomic and ionic component, detected through radio, optical, ultraviolet (UV) and X-ray observations. The cooling and heating processes in the IS gas are briefly recalled in order to introduce current models of disk and halo gas. Observations of nearby galaxies critical to test IS models are considered, including 21-cm surveys, optical and UV absorptions of bright, extragalactic sources, and X-ray emission from hot halos. Finally, further steps necessary to develop a global model for the structure and evolution of the interstellar medium are indicated. (author)
9. Glaciations and dense interstellar clouds; and reply
Energy Technology Data Exchange (ETDEWEB)
McCrea, W H [Sussex Univ., Brighton (UK); Dennison, B; Mansfield, V N
1976-09-16
Reference is made to Dennison and Mansfield (Nature 261:32 (1976)) who offered comments on a previous paper by the author (Nature 255:607 (1975)), in which he suggested that a possible cause of an ice age on the Earth was the passage of the solar system through an interstellar matter compression region bordering a spiral arm of the Galaxy. Dennison and Mansfield criticised this suggestion because it led them to expect to find a dense cloud of interstellar matter still very close to the Earth, whereas no such cloud is known. It is stated here that this criticism ignores the structure of the Galaxy, that provided the basis of the suggestion. A reply by Dennison and Mansfield is appended.
10. Fast Neutral reactions in cold interstellar clouds
International Nuclear Information System (INIS)
Graff, M.M.
1989-01-01
The dynamics of exothermic neutral reactions between radical species have been examined, with particular attention to reactivity at the very low energies characteristic of cold interstellar clouds. Long-range interactions (electrostatic and spin-orbit) were considered within in the adiabatic capture-infinite order sudden approximation (ACIOSA). Analytic expressions have been developed for cross sections and rate constants of exothermic reactions between atoms and dipolar radicals at low temperatures. A method for approximating the adiabatic potential surface for the reactive state will be presented. The reaction systems O+OH and O+CH are both predicted to be fast at low temperatures. The systems C+CH and C+OH are expected to be nonreactive at low temperatures, and upper limits of rate constants for these reactions have been estimated. General predictions are made for other reaction systems. Implications for interstellar chemistry will be discussed
11. Identification of interstellar polysaccharides and related hydrocarbons
International Nuclear Information System (INIS)
Hoyle, F.; Olavesen, A.H.; Wickramasinghe, N.C.
1978-01-01
A discussion is presented on the infrared transmittance spectra of several polysaccharides that may be of interest as possible interstellar candidates. It is stated that a 2.5 to 15 μm spectrum computed from the author's measurements is remarkably close to that required to explain a wide range of astronomical data, except for two points. First the required relative opacity at the 3 μm absorption dip is a factor of about 1.5 lower than was found in laboratory measurements; this difference may arise from the presence of water in terrestrial polysaccharide samples. Secondly, in the 9.5 to 12 μm waveband an additional source of opacity appears to be necessary. Close agreement between the spectrum of this additional opacity and the absorption spectrum of propene, C 3 H 6 , points strongly to the presence of hydrocarbons of this type, which may be associated with polysaccharide grains in interstellar space. (U.K.)
12. Polarization of submillimetre lines from interstellar medium
Science.gov (United States)
Zhang, Heshou; Yan, Huirong
2018-04-01
Magnetic fields play important roles in many astrophysical processes. However, there is no universal diagnostic for the magnetic fields in the interstellar medium (ISM) and each magnetic tracer has its limitation. Any new detection method is thus valuable. Theoretical studies have shown that submillimetre fine-structure lines are polarized due to atomic alignment by ultraviolet photon-excitation, which opens up a new avenue to probe interstellar magnetic fields. We will, for the first time, perform synthetic observations on the simulated three-dimensional ISM to demonstrate the measurability of the polarization of submillimetre atomic lines. The maximum polarization for different absorption and emission lines expected from various sources, including star-forming regions are provided. Our results demonstrate that the polarization of submillimetre atomic lines is a powerful magnetic tracer and add great value to the observational studies of the submilimetre astronomy.
13. Absorption and emission characteristics of interstellar dust
International Nuclear Information System (INIS)
Allamandola, L.J.
1984-01-01
Molecular transitions which occur in the middle infrared region of the spectrum correspond with the characteristic frequencies of molecular vibrations. Thus, moderate resolution spectroscopy of the interstellar medium offers unique evidence about the molecules in the condensed and gaseous phases and their distribution. The author discusses the spectral properties of the condensed phase. However, in the astrophysical literature, it is difficult to find a qualitative description of the effects the solid state has on molecular vibrations, and since it is these which largely determine the spectroscopic properties of the interstellar dust, this discussion begins with a general description of these effects and then is directed toward describing the optical characteristics of the molecular ice component of the dust. The properties of this component of the dust are stressed, rather than those expected from more homogeneous components such as silicates, graphite, or amorphous carbon since these have been discussed in considerable detail elsewhere. (Auth.)
14. CN radical in diffuse interstellar clouds
International Nuclear Information System (INIS)
Federman, S.R.; Danks, A.C.; Lambert, D.L.
1984-01-01
A survey of 15 lines of sight for the CN B 2 Σ + --X 2 Σ + interstellar absorption lines shows that the CN column density in diffuse interstellar clouds follows the relation log N(CN)proportionalm log N(H 2 ), where mroughly-equal3. This result is reproduced by a reaction network in which CN is produced primarily from C 2 by the neutral-neutral reaction C 2 +N → CN+C, and photodissociation is the main destruction pathway for the neutral molecules CH, C 2 , and CN. The CN radical is the first molecular species observed in diffuse clouds that requires a neutral-neutral reaction for its formation in the gas phase. The network also reproduces the observed ratio N(CN)/N(H 2 )
15. The Rosseland mean opacity of interstellar grain
International Nuclear Information System (INIS)
Ali, A.; El Shalaby, M.A.; El-Nawawy, M.S.
1990-10-01
We have calculated the opacity of interstellar grains in the temperature range 10 deg. K - 1500 deg. K. Two composite grain models have been considered. One of them consists of silicate coated with ice mantle and the second has a graphite core coated also with ice mantle. These models are compared with isolated grain models. An exact analytical and computational development of Guettler's formulae for composite grain models has been used to calculate the extinction coefficient. It has been found that the thickness of the mantle affects the opacity of the interstellar grains. The opacity of composite models differs from that of the isolated models. The effect of the different species (ice, silicate and graphite) is also clear. (author). 22 refs, 4 figs, 1 tab
16. Human factors issues for interstellar spacecraft
Science.gov (United States)
Cohen, Marc M.; Brody, Adam R.
1991-01-01
Developments in research on space human factors are reviewed in the context of a self-sustaining interstellar spacecraft based on the notion of traveling space settlements. Assumptions about interstellar travel are set forth addressing costs, mission durations, and the need for multigenerational space colonies. The model of human motivation by Maslow (1970) is examined and directly related to the design of space habitat architecture. Human-factors technology issues encompass the human-machine interface, crew selection and training, and the development of spaceship infrastructure during transtellar flight. A scenario for feasible instellar travel is based on a speed of 0.5c, a timeframe of about 100 yr, and an expandable multigenerational crew of about 100 members. Crew training is identified as a critical human-factors issue requiring the development of perceptual and cognitive aids such as expert systems and virtual reality.
17. The composition of interstellar grain mantles
International Nuclear Information System (INIS)
Tielens, A.G.G.M.
1984-01-01
The molecular composition of interstellar grain mantles employing gas phase as well as grain surface reactions has been calculated. The calculated mixtures consist mainly of the molecules H 2 O H 2 CO, N 2 , CO, O 2 , CO 2 , H 2 O 2 , NH 3 , and their deuterated counterparts in varying ratios. The exact compositions depend strongly on the physical conditions in the gas phase. The calculated mixtures are compared to the observations by using laboratory spectra of grain mantle analogs. (author)
18. Kinetic chemistry of dense interstellar clouds
International Nuclear Information System (INIS)
Graedel, T.E.; Langer, W.D.; Frerking, M.A.
1982-01-01
A detailed model of the time-dependent chemistry of dense interstellar clouds has been developed to study the dominant chemical processes in carbon and oxygen isotope fractionation, formation of nitrogen-containing molecules, evolution of product molecules as a function of cloud density and temperature, and other topics of interest. The full computation involves 328 individual reactions (expanded to 1067 to study carbon and oxygen isotope chemistry); photodegradation processes are unimportant in these dense clouds and are excluded
19. An investigation of the interstellar extinction
International Nuclear Information System (INIS)
Roche, P.F.; Aitken, D.K.; Melbourne Univ., Point Cook
1984-01-01
The 10 μm extinction towards six WC8 or WC9 Wolf-Rayet stars is investigated. All objects show smooth dust emission suffering silicate absorption with depths well correlated with the extinction in the visible. The de-reddened spectra are well represented by emission from featureless grain components, possibly from iron or carbon grains. The extinction to the stars is found to be dominantly interstellar in origin with little extinction from the circumstellar shell. (author)
20. Stochastic histories of refractory interstellar dust
International Nuclear Information System (INIS)
Liffman, K.; Chayton, D.D.
1988-01-01
The authors calculate histories for refractory dust particles in the interstellar medium. The double purposes are to learn something of the properties of interstellar dust as a system and to evaluate with specific assumptions the cosmic chemical memory interpretation of a specific class of isotopic anomalies. They assemble the profile of a particle population from a large number of stochastic, or Monte Carlo, histories of single particles, which are necessarily taken to be independent with this approach. They specify probabilities for each of the events that may befall a given particle and unfold its history by a sequence of random numbers. They assume that refractory particles are created only by thermal condensation within stellar material during its ejection from stars, and that these refractory particles can be destroyed only by being sputtered to a size too small for stability or by being incorporated into the formation of new stars. In order to record chemical detail, the authors take each new refractory particle to consist of a superrefractory core plus a more massive refractory mantle. They demonstrate that these superrefractory cores have effective lifetimes much longer than the turnover time of dust mass against sputtering. As examples of cosmic chemical memory they evaluate the 16 O-richness of interstellar aluminum and mechanisms for the 48 Ca/ 50 Ti correlation. Several related consequences of this approach are discussed
1. Design for minimum energy in interstellar communication
Science.gov (United States)
Messerschmitt, David G.
2015-02-01
Microwave digital communication at interstellar distances is the foundation of extraterrestrial civilization (SETI and METI) communication of information-bearing signals. Large distances demand large transmitted power and/or large antennas, while the propagation is transparent over a wide bandwidth. Recognizing a fundamental tradeoff, reduced energy delivered to the receiver at the expense of wide bandwidth (the opposite of terrestrial objectives) is advantageous. Wide bandwidth also results in simpler design and implementation, allowing circumvention of dispersion and scattering arising in the interstellar medium and motion effects and obviating any related processing. The minimum energy delivered to the receiver per bit of information is determined by cosmic microwave background alone. By mapping a single bit onto a carrier burst, the Morse code invented for the telegraph in 1836 comes closer to this minimum energy than approaches used in modern terrestrial radio. Rather than the terrestrial approach of adding phases and amplitudes increases information capacity while minimizing bandwidth, adding multiple time-frequency locations for carrier bursts increases capacity while minimizing energy per information bit. The resulting location code is simple and yet can approach the minimum energy as bandwidth is expanded. It is consistent with easy discovery, since carrier bursts are energetic and straightforward modifications to post-detection pattern recognition can identify burst patterns. Time and frequency coherence constraints leading to simple signal discovery are addressed, and observations of the interstellar medium by transmitter and receiver constrain the burst parameters and limit the search scope.
2. Chemical reactivities of some interstellar molecules
Energy Technology Data Exchange (ETDEWEB)
1980-01-01
Work in the area of chemical evolution during the last 25 years has revealed the formation of a large number of biologically important molecules produced from simple starting materials under relatively simple experimental conditions. Much of this work has resulted from studies under atmospheres simulating that of the primitive earth or other planets. During the last decade, progress has also been made in the identification of chemical constituents of interstellar medium. A number of these molecules are the same as those identified in laboratory experiments. Even though the conditions of the laboratory experiments are vastly different from those of the cool, low-density interstellar medium, some of the similarities in composition are too obvious to go unnoticed. The present paper highlights some of the similarities in the composition of prebiotic molecules and those discovered in the interstellar medium. Also the chemical reactions which some of the common molecules e.g., NH3, HCN, H2CO, HC(triple bond)-C-CN etc. can undergo are surveyed.
3. Gamma rays from the interstellar medium
International Nuclear Information System (INIS)
Bloemen, J.B.G.M.
1985-01-01
This thesis describes new gamma-ray views on cosmic rays and the interstellar medium. The author describes the COS-B data base and the pre-launch and in-flight calibration data used for all analyses. Diffuse galactic gamma radiation (> 50 MeV) may be either a result of cosmic-ray-matter interactions, or of the cosmic-ray electrons with the interstellar radiation field (mainly at optical and infrared wavelengths), through the inverse-Compton process. A detailed comparison between the gamma-ray observations of the large complex of interstellar clouds in Orion and Monoceros and the CO and HI surveys of this region is given. It gives insight into the cloud penetration of cosmic rays and in the relation between CO detections and molecular hydrogen column densities. Next, the radial distribution of gamma rays in the Galaxy is studied, as well as the galactic centre (more precisely, the central 400 pc), which contains a large concentration of CO molecules. The H 2 /CO abundance and the cosmic-ray density in the galactic centre are discussed and compared to the findings for the galactic disk. In various analyses in this thesis a likelihood-ratio method is applied for parameter estimation and hypothesis testing. A general description of this method is added as an appendix. (Auth.)
4. Properties of interstellar dust in reflection nebulae
International Nuclear Information System (INIS)
Sellgren, K.
1988-01-01
Observations of interstellar dust in reflection nebulae are the closest analog in the interstellar medium to studies of cometary dust in our solar system. The presence of a bright star near the reflection nebula dust provides the opportunity to study both the reflection and emission characteristics of interstellar dust. At 0.1 to 1 micrometer, the reflection nebula emission is due to starlight scattered by dust. The albedo and scattering phase function of the dust is determined from observations of the scattered light. At 50 to 200 micrometers, thermal emission from the dust in equilibrium with the stellar radiation field is observed. The derived dust temperature determines the relative values of the absorption coefficient of the dust at wavelengths where the stellar energy is absorbed and at far infrared wavelengths where the absorbed energy is reradiated. These emission mechanisms directly relate to those seen in the near and mid infrared spectra of comets. In a reflection nebula the dust is observed at much larger distances from the star than in our solar system, so that the equilibrium dust temperature is 50 K rather than 300 K. Thus, in reflection nebulae, thermal emission from dust is emitted at 50 to 200 micrometer
5. Interstellar matrices: the chemical composition and evolution of interstellar ices as observed by ISO.
Science.gov (United States)
d'Hendecourt, L; Dartois, E
2001-03-15
Matrix isolation techniques have been developed in the early sixties as a tool for studying the spectroscopic properties of out of equilibrium species (atoms, radicals, ions, reactive molecules), embedded in rare gas inert matrices at low temperatures. Cold interstellar grains surfaces are able to condense out gas phase molecules, routinely observed by radioastronomy. These grain 'mantles' can be considered as 'interstellar matrices'. However, these matrices are not clean and unreactive. They are made principally of dirty ices whose composition must be determined carefully to assess the importance of the solid state chemistry that takes place in the Interstellar Medium. Infrared spectroscopy, both in astronomy and in the laboratory, is the unique tool to determine the chemical composition of these ices. Astronomical spectra can directly be compared with laboratory ones obtained using classical matrix isolation techniques. Furthermore, dedicated experiments may be undertaken to further improve the understanding of the basic physico-chemical processes that take place in cosmic ices.
6. The Ingenious Theory of Interstellar Trade
Science.gov (United States)
This paper extends interplanetary trade theory to an interstellar setting. It is chiefly concerned with the following question: How should interest charges on goods in transit be computed when the goods travel at speeds close to the actual speed of light? This is a problem because the time taken in transit will appear less to an observer travelling with the goods than to a stationary observer. An innovative and ingenious solution is derived from the economic theory, and two useless but TRUE theorems are proved. The interstellar trade would happen in such a way that two time frames must be considered namely that of the stationary observer whose time runs faster compared to the time frame of the observer in transit The interest in a given trade is purely based on the time taken for the debtor to pay the amount, once the goods have been delivered by the seller. But, in case of interstellar trade, the interest to be calculated in between two time frames would lead to the question of which time frame to be considered and moreover, the time taken for the goods to reach the destination is signicantly prolonged compared to the interplanetary trade, which means, even the slightest variations in the interest rate would be magnied. Apart from this, various new factors arise while calculating the interest. The factors include the time value of money, and the risk of variation in demand for goods, the risk of interspace accidents causing loss of the goods and the rate of perish-ability in case of organic goods. The first two factors considered, for which the time frame of the stationary observer is considered and the factors such as the risk of accidents and the rate of perish-ability of the goods are considered based on the time frame of the observer in transit's point of view. The reasons for such considerations and various assumptions on these concepts are dealt in this paper. The theorems that are formulated in this paper would provide the interstellar traders a basic
7. Interstellar propulsion using a pellet stream for momentum transfer
International Nuclear Information System (INIS)
Singer, C.E.
1979-10-01
A pellet-stream concept for interstellar propulsion is described. Small pellets are accelerated in the solar system and accurately guided to an interstellar probe where they are intercepted and transfer momentum. This propulsion system appears to offer orders-of-magnitude improvements in terms of engineering simplicity and power requirements over any other known feasible system for transport over interstellar distance in a time comparable to a human lifespan
8. An introduction to the physics of interstellar dust
CERN Document Server
Krugel, Endrik
2007-01-01
Streamlining the extensive information from the original, highly acclaimed monograph, this new An Introduction to the Physics of Interstellar Dust provides a concise reference and overview of interstellar dust and the interstellar medium. Drawn from a graduate course taught by the author, a highly regarded figure in the field, this all-in-one book emphasizes astronomical formulae and astronomical problems to give a solid foundation for the further study of interstellar medium. Covering all phenomena associated with cosmic dust, this inclusive text eliminates the need to consult special physica
9. Synthesis of molecules in interstellar clouds and star formation
International Nuclear Information System (INIS)
Ghosh, K.K.; Ghosh, S.N.
1981-01-01
Study of the formation and destruction processes of interstellar molecules may throw certain light on interstellar medium. Formation and destruction processes of some interstellar molecules are proposed on the basis of laboratory data. The abundances of these molecules are calculated under steady-state condition. The calculated values are then compared with the observed values, obtained by different investigators. It appears that gas phase ion-neutral reactions are capable of synthesizing most interstellar molecules. The role of ion-neutral reactions to star formation has also been discussed. (author)
10. Analysis of "Midnight" Tracks in the Stardust Interstellar Dust Collector: Possible Discovery of a Contemporary Interstellar Dust Grain
Science.gov (United States)
Westphal, A. J.; Allen, C.; Bajit, S.; Bastien, R.; Bechtel, H.; Bleuet, P.; Borg, J.; Brenker, F.; Bridges, J.; Brownlee, D. E.;
2010-01-01
In January 2006, the Stardust sample return capsule returned to Earth bearing the first solid samples from a primitive solar system body, Comet 81P/Wild2, and a collector dedicated to the capture and return of contemporary interstellar dust. Both collectors were approximately 0.1m(exp 2) in area and were composed of aerogel tiles (85% of the collecting area) and aluminum foils. The Stardust Interstellar Dust Collector (SIDC) was exposed to the interstellar dust stream for a total exposure factor of 20 m(exp 2) day. The Stardust Interstellar Preliminary Examination (ISPE) is a three-year effort to characterize the collection using nondestructive techniques.
11. Science.gov (United States)
Salama, Farid; Galazutdinov, G.; Biennier, L.; Krelowski, J.
2012-05-01
We describe and discuss the laboratory experiments that were designed to test the proposal of relating the origin of some of the diffuse interstellar bands (DIBs) to neutral and ionized polycyclic aromatic hydrocarbons (PAHs) present in diffuse interstellar clouds. The spectra of several cold, isolated gas-phase PAH ions and neutral molecules have been measured using the COSmIC laboratory facility at NASA-Ames and are compared with an extensive set of astronomical spectra of reddened, early type stars. The COSmIC facility combines a supersonic free jet expansion with discharge plasma and high-sensitivity cavity ringdown spectroscopy to provide experimental conditions that closely mimic the interstellar conditions. This comparison provides - for the first time - accurate upper limits for the abundances of specific PAH molecules and ions along specific lines-of-sight. Something that is not attainable from infrared observations alone. The comparison of these unique laboratory data with high resolution, high S/N ratio astronomical observations leads to major findings regarding the column densities of the individual PAH molecules and ions that are probed in this survey and leads to clear and unambiguous conclusions regarding the expected abundances for PAHs of various sizes and charge states in these environments. This quantitative survey of neutral and ionized PAHs in the optical range opens the way for unambiguous quantitative searches of PAHs and complex organics in a variety of interstellar and circumstellar environments. Acknowledgements: F.S. acknowledges the support of the NASA’s Space Mission Directorate APRA Program. The authors are deeply grateful to the ESO archive as well as to the ESO staff members for their active support.
12. PAHs molecules and heating of the interstellar gas
Science.gov (United States)
Verstraete, Laurent; Leger, Alain; Dhendecourt, Louis B.; Dutuit, O.; Defourneau, D.
1989-01-01
Until now it has remained difficult to account for the rather high temperatures seen in many diffuse interstellar clouds. Various heating mechanisms have been considered: photoionization of minor species, ionization of H by cosmic rays, and photoelectric effect on small grains. Yet all these processes are either too weak or efficient under too restricting conditions to balance the observed cooling rates. A major heat source is thus still missing in the thermal balance of the diffuse gas. Using photoionization cross sections measured in the lab, it was shown that in order to balance the observed cooling rates in cold diffuse clouds (T approx. 80 K) the PAHs would have to contain 15 percent of the cosmic abundance of carbon. This value does not contradict the former estimation of 6 percent deduced from the IR emission bands since this latter is to be taken as a lower limit. Further, it was estimated that the contribution to the heating rate due to PAH's in a warm HI cloud, assuming the same PAH abundance as for a cold HI cloud, would represent a significant fraction of the value required to keep the medium in thermal balance. Thus, photoionization of PAHs might well be a major heat source for the cold and warm HI media.
13. Interstellar depletions and the filling factor of the hot interstellar medium
International Nuclear Information System (INIS)
Dwek, E.; Scalo, J.M.
1979-01-01
We have examined theoretically the evolution of refractory interstellar grain abundances and corresponding metal deplections in the solar neighborhood. The calculations include a self-consistent treatment of red-giant winds, planetary nebulae, protostellar nebulae, and suprnovae as sources of grains and star formation, and of encounters with supernova blast waves as sinks. We find that in the standard two-phase model for the interstellar medium (ISM), grain destruction is very efficient, and the abundance of refractory grains should be negligible, contrary to observations. In a cloudy three-phase ISM most grains reside in the warm and cold phases of the medium. Supernova blast waves expand predominantly in the hot and tenuous phase of the medium and are showed down as they propagate through a cloud. In order to obtain significant (approx.3) depletions of metals presubably locked up in refractory grain cores, the destruction of grains that reside in the clouds must be minimal. This requires that (a) the density contrast between the cloud and intercloud medium be sufficiently high, and (b) the filling factor of the hot and tenuous gas of the interstellar medium, which presumably gives rise to the O VI absorption and soft X-ray emission, be nearly unity. Much larger depletions (> or approx. =10) must reflect accretion of mantles within interstellar clouds
14. Magnetic Fields in the Interstellar Medium
Science.gov (United States)
Clark, Susan
2017-01-01
The Milky Way is magnetized. Invisible magnetic fields thread the Galaxy on all scales and play a vital but still poorly understood role in regulating flows of gas in the interstellar medium and the formation of stars. I will present highlights from my thesis work on magnetic fields in the diffuse interstellar gas and in accretion disks. At high Galactic latitudes, diffuse neutral hydrogen is organized into an intricate network of slender linear features. I will show that these neutral hydrogen “fibers” are extremely well aligned with the ambient magnetic field as traced by both starlight polarization (Clark et al. 2014) and Planck 353 GHz polarized dust emission (Clark et al. 2015). The structure of the neutral interstellar medium is more tightly coupled to the magnetic field than previously known. Because the orientation of neutral hydrogen is an independent predictor of the local dust polarization angle, our work provides a new tool in the search for inflationary gravitational wave B-mode polarization in the cosmic microwave background, which is currently limited by dust foreground contamination. Magnetic fields also drive accretion in astrophysical disks via the magnetorotational instability (MRI). I analytically derive the behavior of this instability in the weakly nonlinear regime and show that the saturated state of the instability depends on the geometry of the background magnetic field. The analytical model describes the behavior of the MRI in a Taylor-Couette flow, a set-up used by experimentalists in the ongoing quest to observe MRI in the laboratory (Clark & Oishi 2016a, 2016b).
15. Observing Interstellar and Intergalactic Magnetic Fields
Science.gov (United States)
Han, J. L.
2017-08-01
Observational results of interstellar and intergalactic magnetic fields are reviewed, including the fields in supernova remnants and loops, interstellar filaments and clouds, Hii regions and bubbles, the Milky Way and nearby galaxies, galaxy clusters, and the cosmic web. A variety of approaches are used to investigate these fields. The orientations of magnetic fields in interstellar filaments and molecular clouds are traced by polarized thermal dust emission and starlight polarization. The field strengths and directions along the line of sight in dense clouds and cores are measured by Zeeman splitting of emission or absorption lines. The large-scale magnetic fields in the Milky Way have been best probed by Faraday rotation measures of a large number of pulsars and extragalactic radio sources. The coherent Galactic magnetic fields are found to follow the spiral arms and have their direction reversals in arms and interarm regions in the disk. The azimuthal fields in the halo reverse their directions below and above the Galactic plane. The orientations of organized magnetic fields in nearby galaxies have been observed through polarized synchrotron emission. Magnetic fields in the intracluster medium have been indicated by diffuse radio halos, polarized radio relics, and Faraday rotations of embedded radio galaxies and background sources. Sparse evidence for very weak magnetic fields in the cosmic web is the detection of the faint radio bridge between the Coma cluster and A1367. Future observations should aim at the 3D tomography of the large-scale coherent magnetic fields in our Galaxy and nearby galaxies, a better description of intracluster field properties, and firm detections of intergalactic magnetic fields in the cosmic web.
16. Long Term Perspective On Interstellar Flight
Science.gov (United States)
Millis, M. G.
2017-12-01
The process and interim findings of a broad interstellar flight assessment is presented. In contrast to precursor mission studies, this assessment takes a longer view and also considers factors that have been underrepresented in prior studies. The goal is to chart a conceptual roadmap for interstellar flight development that takes all the factors into account and ultimately identifies which research options, today, might have the greatest overall impact on future progress. Three envisioned flight eras are examined, the "era of precursors," the "era of infrastructure," and the "unforeseeable future." Several influential factors have typically been missing from prior studies that will now be assessed; a) the impact of different, often implicit, motivations, b) the interdependency of infrastructure with vehicle design, c) the pace of different developments, and d) the enormous energy required for any interstellar mission. Regarding motivations for example, if the driving motivation is to launch soon, then the emphasis is on existing technologies. In contrast, if the motivation is the survival of humanity, then the emphasis would be on 'world ships.' Infrastructure considerations are included in a broader system-level context. Future infrastructure will support multiple in-space activities, not just one mission-vehicle development. Though it may be too difficult to successfully assess, the study will attempt to compare the rates of different developments, such as the pace of Earth-based astronomy, miniaturization, artificial intelligence, infrastructure development, transhumanism, and others. For example, what new information could be acquired after 30 years of further advances in astronomy compared to a space probe with current technology and a 30 year flight time? The final factor of the study is to assess the pace and risks of the enormous energy levels required for interstellar flight. To compare disparate methods, a set of 'meta measures' will be defined and
17. Planetary nebulae and the interstellar magnetic field
International Nuclear Information System (INIS)
Heiligman, G.M.
1980-01-01
Previous workers have found a statistical correlation between the projected directions of the interstellar magnetic field and the major axes of planetary nebulae. This result has been examined theoretically using a numerical hydromagnetic model of a cold plasma nebula expanding into a uniform vacuum magnetic field, with nebular gas accreting on the surface. It is found that magnetic pressure alone is probably not sufficient to shape most planetary nebulae to the observed degree. Phenomena are discussed which could amplify simple magnetic pressure, alter nebular morphology and account for the observed correlation. (author)
18. Interstellar extinction in the Taurus dark clouds
International Nuclear Information System (INIS)
Meistas, E.; Straizys, V.
1981-01-01
The results of photoelectric photometry of 89 stars in the Vilnius seven-color system in the area of the Taurus dark clouds with corrdinates (1950) 4sup(h)16sup(m)-4sup(h)33sup(m), +16 0 -+20 0 are presented. Photometric spectral types, absolute magnitude, color excesses, interstellar extinctions and distances of the stars are determined. The distance of the dark nebula is found to be 140 pc and is in a good agreement with the distance determined for the dark nebula Khavtassi 286, 278. The average extinction Asub(v) in the investigated area is of the order of 1.4. (author)
19. Interstellar colonization and the zoo hypothesis
International Nuclear Information System (INIS)
Jones, E.M.
1978-01-01
Michael Hart and others have pointed out that current estimates of the number of technological civilizations arisen in the Galaxy since its formation is in fundamental conflict with the expectation that such a civilization could colonize and utilize the entire Galaxy in 10 to 20 million years. This dilemma can be called Hart's paradox. Resolution of the paradox requires that one or more of the following are true: we are the Galaxy's first technical civilization; interstellar travel is immensely impractical or simply impossible; technological civilizations are very short-lived; or we inhabit a wildnerness preserve. The latter is the zoo hypothesis
20. The interstellar medium in galaxies - An overview
Science.gov (United States)
Knapp, G. R.
1990-01-01
Recent observational developments on the subject of the interstellar medium in galaxies are summarized, with emphasis placed on global properties. The properties and distribution of the ISM in the solar neighborhood and in the Galactic plane are examined and a number of results from the most important observational probes (HI, CO, and infrared) are described. A recent development is the observation of the ISM in galaxies of all morphological types, early to late. These developments are summarized and the properties of different types of galaxies are compared to one another. The origin of radio galaxies, the effect of environment, and the prospects for direct observations of ISM evolution in galaxies are discussed.
1. OH radiation from the interstellar cloud medium
Energy Technology Data Exchange (ETDEWEB)
Nguyen-Q-Rieu,; Winnberg, A [Max-Planck-Institut fuer Radioastronomie, Bonn (F.R. Germany); Guibert, J [Observatoire de Paris, Section de Meudon, 92 (France); Lepine, J R.D. [Universidade Mackenzie, Sao Paulo (Brazil). Centro de Radio-Astronomia et Astrofisica; Johansson, L E.B. [Rymdobservatoriet, Onsala (Sweden); Goss, W M [Commonwealth Scientific and Industrial Research Organization, Epping (Australia). Div. of Radiophysics
1976-02-01
We have detected OH in the direction of about 50% of the continuum sources investigated. The OH abundance is one order of magnitude less than usually found in dust clouds. Most of the OH features have HI counterparts. This suggests that the OH radiation arises from the HI interstellar cold clouds. Our observations allowed in some cases the determination of the excitation temperatures in all four lines. A pumping model involving far-infrared radiation and collisions with neutral and charged particles has been proposed. It explains the observed excitation temperatures.
2. IMAGINE: Interstellar MAGnetic field INference Engine
Science.gov (United States)
Steininger, Theo
2018-03-01
IMAGINE (Interstellar MAGnetic field INference Engine) performs inference on generic parametric models of the Galaxy. The modular open source framework uses highly optimized tools and technology such as the MultiNest sampler (ascl:1109.006) and the information field theory framework NIFTy (ascl:1302.013) to create an instance of the Milky Way based on a set of parameters for physical observables, using Bayesian statistics to judge the mismatch between measured data and model prediction. The flexibility of the IMAGINE framework allows for simple refitting for newly available data sets and makes state-of-the-art Bayesian methods easily accessible particularly for random components of the Galactic magnetic field.
3. Chemical equilibrium models of interstellar gas clouds
International Nuclear Information System (INIS)
Freeman, A.
1982-10-01
This thesis contains work which helps towards our understanding of the chemical processes and astrophysical conditions in interstellar clouds, across the whole range of cloud types. The object of the exercise is to construct a mathematical model representing a large system of two-body chemical reactions in order to deduce astrophysical parameters and predict molecular abundances and chemical pathways. Comparison with observations shows that this type of model is valid but also indicates that our knowledge of some chemical reactions is incomplete. (author)
4. Interstellar extinction in the Large Magellanic Cloud
International Nuclear Information System (INIS)
Nandy, K.; Morgan, D.H.; Willis, A.J.; Wilson, R.; Gondhalekar, P.M.; Houziaux, L.
1980-01-01
Recent UV observations together with complementary visible data of several reddened and comparison stars of similar spectral types in the Large Magellanic Cloud have been used to study the interstellar extinction in that galaxy. Most of the reddened stars studied here are located within 2 0 of 30 Doradus and show remarkably high extinction in the far UV, suggesting a large abundance of small particles. From the optical wavelength to 2,600 A the normalised extinction curves of the LMC stars are similar to the mean galactic extinction law. (author)
5. Structural, chemical and isotopic examinations of interstellar organic matter extracted from meteorites and interstellar dust particles
Science.gov (United States)
Busemann, Henner; Alexander, Conel M. O'D.; Nittler, Larry R.; Stroud, Rhonda M.; Zega, Tom J.; Cody, George D.; Yabuta, Hikaru; Kilcoyne, A. L. David
2008-10-01
Meteorites and Interplanetary Dust Particles (IDPs) are supposed to originate from asteroids and comets, sampling the most primitive bodies in the Solar System. They contain abundant carbonaceous material. Some of this, mostly insoluble organic matter (IOM), likely originated in the protosolar molecular cloud, based on spectral properties and H and N isotope characteristics. Together with cometary material returned with the Stardust mission, these samples provide a benchmark for models aiming to understand organic chemistry in the interstellar medium, as well as for mechanisms that secured the survival of these fragile molecules during Solar System formation. The carrier molecules of the isotope anomalies are largely unknown, although amorphous carbonaceous spheres, so-called nanoglobules, have been identified as carriers. We are using Secondary Ion Mass Spectrometry to identify isotopically anomalous material in meteoritic IOM and IDPs at a ~100-200 nm scale. Organics of most likely interstellar origin are then extracted with the Focused-Ion-Beam technique and prepared for synchrotron X-ray and Transmission Electron Microscopy. These experiments yield information on the character of the H- and N-bearing interstellar molecules: While the association of H and N isotope anomalies with nanoglobules could be confirmed, we have also identified amorphous, micron-sized monolithic grains. D-enrichments in meteoritic IOM appear not to be systematically associated with any specific functional groups, whereas 15N-rich material can be related to imine and nitrile functionality. The large 15N- enrichments observed here (δ15N > 1000 ‰) cannot be reconciled with models using interstellar ammonia ice reactions, and hence, provide new constraints for understanding the chemistry in cold interstellar clouds.
6. Abundances of Neutral and Ionized PAH Along The Lines-of-Sight of Diffuse and Translucent Interstellar Clouds
Science.gov (United States)
Salama, Farid; Galazutdinov, Gazinur; Krewloski, Jacek; Biennier, Ludovic; Beletsky, Yuri; Song, In-Ok
2013-01-01
The spectra of neutral and ionized PAHs isolated in the gas phase at low temperature have been measured in the laboratory under conditions that mimic interstellar conditions and are compared with a set of astronomical spectra of reddened, early type stars. The comparisons of astronomical and laboratory data provide upper limits for the abundances of neutral PAH molecules and ions along specific lines-of-sight. Something that is not attainable from infrared observations. We present the characteristics of the laboratory facility (COSmIC) that was developed for this study and discuss the findings resulting from the comparison of the laboratory data with high resolution, high S/N ratio astronomical observations. COSmIC combines a supersonic jet expansion with discharge plasma and cavity ringdown spectroscopy and provides experimental conditions that closely mimic the interstellar conditions. The column densities of the individual PAH molecules and ions probed in these surveys are derived from the comparison of the laboratory data with high resolution, high S/N ratio astronomical observations. The comparisons of astronomical and laboratory data lead to clear conclusions regarding the expected abundances for PAHs in the interstellar environments probed in the surveys. Band profile comparisons between laboratory and astronomical spectra lead to information regarding the molecular structures and characteristics associated with the DIB carriers in the corresponding lines-of-sight. These quantitative surveys of neutral and ionized PAHs in the optical range open the way for quantitative searches of PAHs and complex organics in a variety of interstellar and circumstellar environments.
7. Distribution of Interstellar Reddening Material in the Galactic Plane
Directory of Open Access Journals (Sweden)
Chulhee Kim
1987-12-01
Full Text Available By using the recently determined color excess and distance data of classical cepheids by Kim(1985, the distribution of interstellar reddening material was studied to see the general picture of the average rate of interstellar absorption out to about 7-8kpc in the Galactic plane in various directions from the sun.
8. Streaming of interstellar grains in the solar system
Science.gov (United States)
Gustafson, B. A. S.; Misconi, N. Y.
1979-01-01
Results of a theoretical study of the interactions between interstellar grains streaming through the solar system and the solar wind are presented. It is shown that although elongated core-mantle interstellar particles of a characteristic radius of about 0.12 microns are subject to a greater force due to radiation pressure than to gravitational attraction, they are still able to penetrate deep inside the solar system. Calculations of particle trajectories within the solar system indicate substantial effects of the solar activity cycle as reflected in the interplanetary magnetic field on the distribution of 0.12- and 0.0005-micron interstellar grains streaming through the solar system, leading to a 50-fold increase in interstellar grain densities 3 to 4 AU ahead of the sun during years 8 to 17 of the solar cycle. It is noted that during the Solar Polar Mission, concentrations are expected which will offer the opportunity of detecting interstellar grains in the solar system.
9. A Search for Interstellar Monohydric Thiols
Energy Technology Data Exchange (ETDEWEB)
Gorai, Prasanta; Das, Ankan; Das, Amaresh; Chakrabarti, Sandip K. [Indian Centre for Space Physics, 43 Chalantika, Garia Station Rd., Kolkata, 700084 (India); Sivaraman, Bhalamurugan [Atomic Molecular and Optical Physics Division, Physical Research Laboratory, Ahmedabad, 380009 (India); Etim, Emmanuel E., E-mail: [email protected] [Indian Institute of Science Bangalore, 560012 (India)
2017-02-10
It has been pointed out by various astronomers that a very interesting relationship exists between interstellar alcohols and the corresponding thiols (sulfur analog of alcohols) as far as the spectroscopic properties and chemical abundances are concerned. Monohydric alcohols such as methanol and ethanol are widely observed and 1-propanol was recently claimed to have been seen in Orion KL. Among the monohydric thiols, methanethiol (chemical analog of methanol) has been firmly detected in Orion KL and Sgr B2(N2) and ethanethiol (chemical analog of ethanol) has been observed in Sgr B2(N2), though the confirmation of this detection is yet to come. It is very likely that higher order thiols could be observed in these regions. In this paper, we study the formation of monohydric alcohols and their thiol analogs. Based on our quantum chemical calculation and chemical modeling, we find that the Tg conformer of 1-propanethiol is a good candidate of astronomical interest. We present various spectroscopically relevant parameters of this molecule to assist in its future detection in the interstellar medium.
10. 26Al in the interstellar medium
International Nuclear Information System (INIS)
Clayton, D.D.; Leising, M.D.
1987-01-01
Several different lines of physical reasoning have converged on the importance of the radioactive nucleus 26 Al. The sciences of meteoritics, nucleosynthesis, gamma-ray astronomy, galactic chemical evolution, solar system formation, and interstellar chemistry all place this nucleus in a central position with possible profound implications. Perhaps more importantly the study of this radioactivity can unite these diverse fields in a complicated framework which will benefit all of them. This review traces the evolution of ideas concerning 26 Al in the context of these disciplines. 26 Al was first discussed for the possibility that its decay energy could melt meteorite parent bodies, and its daughter, 26 Mg, was later found in meteorites with enhanced abundance. It was also among the first radioactivities expected to be synthesized in interestingly large quantities in nulceosynthetic events. The first definitive detection of gamma-rays from an interstellar radioactivity is that of 1.809 MeV gamma-rays from 26 Al. This discovery has many implications, some of which are outlined here. The whole problem of isotopic anomalies in meteorites is greatly influenced by the specific issues surrounding excess 26 Mg, whether it represents in situ decay of 26 Al or memory of conditions of the ISM. The relationships among these ideas and their implications are examined. (orig.)
11. UV observations of local interstellar medium.
Science.gov (United States)
Kurt, V.; Mironova, E.; Fadeev, E.
2008-12-01
The methods of the interstellar matter study are described. The brief information of space missions aimed at observations in the unreachable for ground based telescopes UV spectral range (IUE, As- tron, HST and GALEX.) is presented. The history of discovery of H and He atoms entering the Solar System from the local interstellar medium (LISM) is given in brief. The results of observations performed by the group from Stern- berg Astronomical Institute (SAI MSU) and Space Research Institute (IKI RAS) performed with the help of the missions Prognoz-5, Prognoz-6 and the stations Zond-1, Venera and Mars and aimed at estimation of all basic LISM parameters (the velocity of the Sun in relation to LISM, directions of movement, densities of H and He atoms, LISM temperature) are presented. We also describe the present-day investigations of LISM performed with SOHO and ULYSSES mis- sions including the direct registration of He atoms entering the Solar System. The problem of interaction between the incoming flow of the ISM atoms ("in- terstellar wind") and the area of two shocks at the heliopause border (100-200 AU) is discussed. The LISM parameters obtained using the available data are presented in two tables.
12. Interstellar dehydrogenated PAH anions: vibrational spectra
Science.gov (United States)
Buragohain, Mridusmita; Pathak, Amit; Sarre, Peter; Gour, Nand Kishor
2018-03-01
Interstellar polycyclic aromatic hydrocarbon (PAH) molecules exist in diverse forms depending on the local physical environment. Formation of ionized PAHs (anions and cations) is favourable in the extreme conditions of the interstellar medium (ISM). Besides in their pure form, PAHs are also likely to exist in substituted forms; for example, PAHs with functional groups, dehydrogenated PAHs etc. A dehydrogenated PAH molecule might subsequently form fullerenes in the ISM as a result of ongoing chemical processes. This work presents a density functional theory (DFT) calculation on dehydrogenated PAH anions to explore the infrared emission spectra of these molecules and discuss any possible contribution towards observed IR features in the ISM. The results suggest that dehydrogenated PAH anions might be significantly contributing to the 3.3 μm region. Spectroscopic features unique to dehydrogenated PAH anions are highlighted that may be used for their possible identification in the ISM. A comparison has also been made to see the size effect on spectra of these PAHs.
13. PRECURSORS TO INTERSTELLAR SHOCKS OF SOLAR ORIGIN
Energy Technology Data Exchange (ETDEWEB)
Gurnett, D. A.; Kurth, W. S. [University of Iowa, Department of Physics and Astronomy, Iowa City, IA 52242 (United States); Stone, E. C.; Cummings, A. C. [California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125 (United States); Krimigis, S. M.; Decker, R. B. [Applied Physics Laboratory/JHU, 11100 Johns Hopkins Road, Laurel, MD 20723 (United States); Ness, N. F. [Catholic University of America, 620 Michigan Avenue NE, Washington, DC 20064 (United States); Burlaga, L. F., E-mail: [email protected] [NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771 (United States)
2015-08-20
On or about 2012 August 25, the Voyager 1 spacecraft crossed the heliopause into the nearby interstellar plasma. In the nearly three years that the spacecraft has been in interstellar space, three notable particle and field disturbances have been observed, each apparently associated with a shock wave propagating outward from the Sun. Here, we present a detailed analysis of the third and most impressive of these disturbances, with brief comparisons to the two previous events, both of which have been previously reported. The shock responsible for the third event was first detected on 2014 February 17 by the onset of narrowband radio emissions from the approaching shock, followed on 2014 May 13 by the abrupt appearance of intense electron plasma oscillations generated by electrons streaming outward ahead of the shock. Finally, the shock arrived on 2014 August 25, as indicated by a jump in the magnetic field strength and the plasma density. Various disturbances in the intensity and anisotropy of galactic cosmic rays were also observed ahead of the shock, some of which are believed to be caused by the reflection and acceleration of cosmic rays by the magnetic field jump at the shock, and/or by interactions with upstream plasma waves. Comparisons to the two previous weaker events show somewhat similar precursor effects, although differing in certain details. Many of these effects are very similar to those observed in the region called the “foreshock” that occurs upstream of planetary bow shocks, only on a vastly larger spatial scale.
14. THE NANOGRAV NINE-YEAR DATA SET: MONITORING INTERSTELLAR SCATTERING DELAYS
Energy Technology Data Exchange (ETDEWEB)
Levin, Lina; McLaughlin, Maura A.; Palliyaguru, Nipuni; Jones, Megan L. [Department of Physics and Astronomy, West Virginia University, P.O. Box 6315, Morgantown, WV 26505 (United States); Jones, Glenn [Department of Physics, Columbia University, 550 W. 120th Street, New York, NY 10027 (United States); Cordes, James M.; Chatterjee, Shami; Dolch, Timothy; Lam, Michael T. [Department of Astronomy, Cornell University, Ithaca, NY 14853 (United States); Stinebring, Daniel R. [Department of Physics and Astronomy, Oberlin College, Oberlin, OH 44074 (United States); Lazio, T. Joseph W.; Ellis, Justin A. [Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91106 (United States); Arzoumanian, Zaven [Center for Research and Exploration in Space Science and Technology and X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771 (United States); Crowter, Kathryn; Fonseca, Emmanuel; Gonzalez, Marjorie E. [Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1 (Canada); Demorest, Paul B. [National Radio Astronomy Observatory, P.O. Box 0, Socorro, NM, 87801 (United States); Ferdman, Robert D. [Department of Physics, McGill University, 3600 rue Universite, Montreal, QC H3A 2T8 (Canada); Nice, David J. [Department of Physics, Lafayette College, Easton, PA 18042 (United States); Pennucci, Timothy T. [University of Virginia, Department of Astronomy, P.O. Box 400325 Charlottesville, VA 22904-4325 (United States); and others
2016-02-20
We report on an effort to extract and monitor interstellar scintillation parameters in regular timing observations collected for the North American Nanohertz Observatory for Gravitational Waves pulsar timing array. Scattering delays are measured by creating dynamic spectra for each pulsar and observing epoch of wide-band observations centered near 1500 MHz and carried out at the Green Bank Telescope and the Arecibo Observatory. The ∼800 MHz wide frequency bands imply dramatic changes in scintillation bandwidth across the bandpass, and a stretching routine has been included to account for this scaling. For most of the 10 pulsars for which the scaling has been measured, the bandwidths scale with frequency less steeply than expected for a Kolmogorov medium. We find estimated scattering delay values that vary with time by up to an order of magnitude. The mean measured scattering delays are similar to previously published values and are slightly higher than predicted by interstellar medium models. We investigate the possibility of increasing the timing precision by mitigating timing errors introduced by the scattering delays. For most of the pulsars, the uncertainty in the time of arrival of a single timing point is much larger than the maximum variation of the scattering delay, suggesting that diffractive scintillation remains as only a negligible part of their noise budget.
15. Methods for Detection of Families of Molecules in the Interstellar Medium
Science.gov (United States)
Langston, Glen
2014-06-01
We present a high velocity resolution (0.04 km/sec) molecular line survey of the Taurus Molecular Cloud in the frequency range 39 to 48 GHz with NSF's Robert C. Byrd Green Bank telescope (GBT). The observing method and data reduction process are outlined. We describe the method of obtaining the calibrated, averaged spectral line data online. The RMS survey sensitivity was slightly different for each 200MHz frequency band, and ranged from 0.02 to 0.15 K (T_B) for the different bands. A large number of molecular lines are detected, most of which have previously been associated with already known interstellar molecules. We present a summary processes to combine a number of lines of molecular species in order to identify new species.
16. Interstellar Mapping and Acceleration Probe (IMAP)
International Nuclear Information System (INIS)
Schwadron, N. A.; Moebius, E.; Spence, H. E.; Opher, M.; Kasper, J.; Zurbuchen, T. H.; Mewaldt, R.
2016-01-01
Our piece of cosmic real estate, the heliosphere, is the domain of all human existence – an astrophysical case history of the successful evolution of life in a habitable system. By exploring our global heliosphere and its myriad interactions, we develop key physical knowledge of the interstellar interactions that influence exoplanetary habitability as well as the distant history and destiny of our solar system and world. IBEX is the first mission to explore the global heliosphere and in concert with Voyager 1 and Voyager 2 is discovering a fundamentally new and uncharted physical domain of the outer heliosphere. In parallel, Cassini/INCA maps the global heliosphere at energies (∼5-55 keV) above those measured by IBEX. The enigmatic IBEX ribbon and the INCA belt were unanticipated discoveries demonstrating that much of what we know or think we understand about the outer heliosphere needs to be revised. This paper summarizes the next quantum leap enabled by IMAP that will open new windows on the frontier of Heliophysics at a time when the space environment is rapidly evolving. IMAP with 100 times the combined resolution and sensitivity of IBEX and INCA will discover the substructure of the IBEX ribbon and will reveal, with unprecedented resolution, global maps of our heliosphere. The remarkable synergy between IMAP, Voyager 1 and Voyager 2 will remain for at least the next decade as Voyager 1 pushes further into the interstellar domain and Voyager 2 moves through the heliosheath. Voyager 2 moves outward in the same region of sky covered by a portion of the IBEX ribbon. Voyager 2’s plasma measurements will create singular opportunities for discovery in the context of IMAP's global measurements. IMAP, like ACE before, will be a keystone of the Heliophysics System Observatory by providing comprehensive measurements of interstellar neutral atoms and pickup ions, the solar wind distribution, composition, and magnetic field, as well as suprathermal ion
17. Interstellar depletion anomalies and ionization potentials
International Nuclear Information System (INIS)
Tabak, R.G.
1979-01-01
Satellite observations indicate that (1) most elements are depleted from the gas phase when compared to cosmic abundances, (2) some elements are several orders of magnitude more depleted than others, and (3) these depletions vary from cloud to cloud. Since the most likely possibility is that the 'missing' atoms are locked into grains, depletions occur either by accretion onto core particles in interstellar clouds or earlier, during the period of primary grain formation. If the latter mechanism is dominant, then the most important depletion parameter is the condensation temperature of the elements and their various compounds. However, this alone is not sufficient to explain all the observed anomalies. It is shown that electrostatic effects - under a wide variety of conditions- can enormously enhance the capture cross-section of the grain. It is suggested that this mechanism can also account for such anomalies as the apparent 'overabundance' of the alkali metals in the gas phase. (orig.)
18. Interstellar scattering of pulsar radiation. Pt. 1
International Nuclear Information System (INIS)
Backer, D.C.
1975-01-01
An investigation of the intensity fluctuations of 28 pulsars near 0.4 GHz indicates that spectra of interstellar scintillation are consistent with a gaussian shape, that scintillation indices are near unity, and that scintillation bandwidth depends linearly on dispersion measure. Observations at cm wavelengths show that the observer is in the near field of the scattering medium for objects with the lowest dispersion measures, and confirm the step dependence of correlation bandwidth on dispersion measure found by Sutton (1971). The variation of scattering parameters with dispersion measure may indicate that the rms deviation of thermal electron density on the scale of 10 11 cm grows with path length through the galaxy. (orig.) [de
19. Hot interstellar matter in elliptical galaxies
CERN Document Server
Kim, Dong-Woo
2012-01-01
Based on a number of new discoveries resulting from 10 years of Chandra and XMM-Newton observations and corresponding theoretical works, this is the first book to address significant progress in the research of the Hot Interstellar Matter in Elliptical Galaxies. A fundamental understanding of the physical properties of the hot ISM in elliptical galaxies is critical, because they are directly related to the formation and evolution of elliptical galaxies via star formation episodes, environmental effects such as stripping, infall, and mergers, and the growth of super-massive black holes. Thanks to the outstanding spatial resolution of Chandra and the large collecting area of XMM-Newton, various fine structures of the hot gas have been imaged in detail and key physical quantities have been accurately measured, allowing theoretical interpretations/predictions to be compared and tested against observational results. This book will bring all readers up-to-date on this essential field of research.
20. The mass spectrum of interstellar clouds
International Nuclear Information System (INIS)
Dickey, J.M.; Garwood, R.W.
1989-01-01
The abundances of diffuse clouds and molecular clouds in the inner Galaxy and at the solar circle are compared. Using results of recent low-latitude 21 cm absorption studies, the number of diffuse clouds per kiloparsec along the line of sight is derived as a function of the cloud column density, under two assumptions relating cloud densities and temperatures. The density of clouds is derived as a function of cloud mass. The results are consistent with a single, continuous mass spectrum for interstellar clouds from less than 1 solar mass to 1,000,000 solar masses, with perhaps a change of slope at masses where the atomic and molecular mass fractions are roughly equal. 36 refs
1. Structure and characteristics of diffuse interstellar clouds
International Nuclear Information System (INIS)
Arshutkin, L.N.; Kolesnik, I.G.
1978-01-01
The results of model calculations for spherically symmetrical interstellar clouds being under external pressure are given. Thermal balance of gas clouds is considered. Ultraviolet radiation fields in clouds and equilibrium for chemical elements are calculated for this purpose. Calculations were carried out in the case when cooling is under way mainly by carbon atoms and ions. The clouds with mass up to 700 Msub(sun) under external pressure from 800 to 3000 K cm -3 are considered. In typical for Galactic disk conditions, clouds have dense n > or approximately 200 cm -3 , and cold T approximately 20-30 K state clouds depending on external pressure is given. The critical mass for clouds at the Galactic disk is approximately 500-600 Msub(sun). It is less than the isothermal solution by a factor of approximately 1.5. The massive gas-dust cloud formation problem is discussed
2. Interstellar Silicon Depletion and the Ultraviolet Extinction
Science.gov (United States)
Mishra, Ajay; Li, Aigen
2018-01-01
Spinning small silicate grains were recently invoked to account for the Galactic foreground anomalous microwave emission. These grains, if present, will absorb starlight in the far ultraviolet (UV). There is also renewed interest in attributing the enigmatic 2175 Å interstellar extinction bump to small silicates. To probe the role of silicon in the UV extinction, we explore the relations between the amount of silicon required to be locked up in silicates [Si/H]dust and the 2175 Å bump or the far-UV extinction rise, based on an analysis of the extinction curves along 46 Galactic sightlines for which the gas-phase silicon abundance [Si/H]gas is known. We derive [Si/H]dust either from [Si/H]ISM - [Si/H]gas or from the Kramers- Kronig relation which relates the wavelength-integrated extinction to the total dust volume, where [Si/H]ISM is the interstellar silicon reference abundance and taken to be that of proto-Sun or B stars. We also derive [Si/H]dust from fi�tting the observed extinction curves with a mixture of amorphous silicates and graphitic grains. We fi�nd that in all three cases [Si/H]dust shows no correlation with the 2175 Å bump, while the carbon depletion [C/H]dust tends to correlate with the 2175 Å bump. This supports carbon grains instead of silicates as the possible carrier of the 2175 Å bump. We also �find that neither [Si/H]dust nor [C/H]dust alone correlates with the far-UV extinction, suggesting that the far-UV extinction is a combined effect of small carbon grains and silicates.
3. Searching for Cost-Optimized Interstellar Beacons
Science.gov (United States)
Benford, Gregory; Benford, James; Benford, Dominic
2010-06-01
What would SETI beacon transmitters be like if built by civilizations that had a variety of motives but cared about cost? In a companion paper, we presented how, for fixed power density in the far field, a cost-optimum interstellar beacon system could be built. Here, we consider how we should search for a beacon if it were produced by a civilization similar to ours. High-power transmitters could be built for a wide variety of motives other than the need for two-way communication; this would include beacons built to be seen over thousands of light-years. Extraterrestrial beacon builders would likely have to contend with economic pressures just as their terrestrial counterparts do. Cost, spectral lines near 1 GHz, and interstellar scintillation favor radiating frequencies substantially above the classic "water hole." Therefore, the transmission strategy for a distant, cost-conscious beacon would be a rapid scan of the galactic plane with the intent to cover the angular space. Such pulses would be infrequent events for the receiver. Such beacons built by distant, advanced, wealthy societies would have very different characteristics from what SETI researchers seek. Future searches should pay special attention to areas along the galactic disk where SETI searches have seen coherent signals that have not recurred on the limited listening time intervals we have used. We will need to wait for recurring events that may arriarrive in intermittent bursts. Several new SETI search strategies have emerged from these ideas. We propose a new test for beacons that is based on the Life Plane hypotheses.
4. Studies of interstellar vibrationally-excited molecules
International Nuclear Information System (INIS)
Ziurys, L.M.; Snell, R.L.; Erickson, N.R.
1986-01-01
Several molecules thus far have been detected in the ISM in vibrationally-excited states, including H 2 , SiO, HC 3 N, and CH 3 CN. In order for vibrational-excitation to occur, these species must be present in unusually hot and dense gas and/or where strong infrared radiation is present. In order to do a more thorough investigation of vibrational excitation in the interstellar medium (ISM), studies were done of several mm-wave transitions originating in excited vibrational modes of HCN, an abundant interstellar molecule. Vibrationally-excited HCN was recently detected toward Orion-KL and IRC+10216, using a 12 meter antenna. The J=3-2 rotational transitions were detected in the molecule's lowest vibrational state, the bending mode, which is split into two separate levels, due to l-type doubling. This bending mode lies 1025K above ground state, with an Einstein A coefficient of 3.6/s. The J=3-2 line mode of HCN, which lies 2050K above ground state, was also observed toward IRC+10216, and subsequently in Orion-KL. Further measurements of vibrationally-excited HCN were done using a 14 meter telescope, which include the observations of the (0,1,0) and (0,2,0) modes towards Orion-KL, via their J=3-2 transitions at 265-267 GHz. The spectrum of the J=3-2 line in Orion taken with the 14 meter telescope, is shown, along with a map, which indicates that emission from vibrationally-excited HCN arises from a region probably smaller than the 14 meter telescope's 20 arcsec beam
5. THE POSSIBLE INTERSTELLAR ANION CH{sub 2}CN{sup -}: SPECTROSCOPIC CONSTANTS, VIBRATIONAL FREQUENCIES, AND OTHER CONSIDERATIONS
Energy Technology Data Exchange (ETDEWEB)
Fortenberry, Ryan C.; Lee, Timothy J. [NASA Ames Research Center, Moffett Field, CA 94035-1000 (United States); Crawford, T. Daniel, E-mail: [email protected], E-mail: [email protected] [Department of Chemistry, Virginia Tech, Blacksburg, VA 24061 (United States)
2013-01-10
The A {sup 1}B{sub 1} Leftwards-Open-Headed-Arrow X-tilde{sup 1}A' excitation into the dipole-bound state of the cyanomethyl anion (CH{sub 2}CN{sup -}) has been hypothesized as the carrier for one diffuse interstellar band. However, this particular molecular system has not been detected in the interstellar medium even though the related cyanomethyl radical and the isoelectronic ketenimine molecule have been found. In this study, we are employing the use of proven quartic force fields and second-order vibrational perturbation theory to compute accurate spectroscopic constants and fundamental vibrational frequencies for X-tilde{sup 1} A' CH{sub 2}CN{sup -} in order to assist in laboratory studies and astronomical observations.
6. Developing Automated Spectral Analysis Tools for Interstellar Features Extractionto Support Construction of the 3D ISM Map
Science.gov (United States)
Puspitarini, L.; Lallement, R.; Monreal-Ibero, A.; Chen, H.-C.; Malasan, H. L.; Aprilia; Arifyanto, M. I.; Irfan, M.
2018-04-01
One of the ways to obtain a detailed 3D ISM map is by gathering interstellar (IS) absorption data toward widely distributed background target stars at known distances (line-of-sight/LOS data). The radial and angular evolution of the LOS measurements allow the inference of the ISM spatial distribution. For a better spatial resolution, one needs a large number of the LOS data. It requires building fast tools to measure IS absorption. One of the tools is a global analysis that fit two different diffuse interstellar bands (DIBs) simultaneously. We derived the equivalent width (EW) ratio of the two DIBs recorded in each spectrum of target stars. The ratio variability can be used to study IS environmental conditions or to detect DIB family.
7. Gitting of infrared data to the interstellar polarization law
Energy Technology Data Exchange (ETDEWEB)
Clarke, D
1984-02-15
The ability of Serkowski's law describing the wavelength dependence of interstellar polarization to encompass new infrared measurements in combination with optical data has been examined. Fitting by least-squares procedures reveals departures from the law in various wavelength zones or at specific wavelength points across the optical and infrared spectrum. These structures may be caused by a combination of effects such as normal experimental noise, complex interstellar clouds or systematic errors in the polarimetry but the possibility remains that some, particularly in the infrared, reflect the scattering properties of interstellar grains. 8 references.
8. Fitting of infrared data to the interstellar polarization law
Energy Technology Data Exchange (ETDEWEB)
Clarke, D [Glasgow Univ., Great Britain
1984-02-15
The ability of Serkowski's law describing the wavelength dependence of interstellar polarization to encompass new infrared measurements in combination with optical data has been examined. Fitting by least-squares procedures reveals departures from the law in various wavelength zones or at specific wavelength points across the optical and infrared spectrum. These structures may be caused by a combination of effects such as normal experimental noise, complex interstellar clouds or systematic errors in the polarimetry but the possibility remains that some, particularly in the infrared, reflect the scattering properties of interstellar grains.
9. Interstellar Ices and Radiation-induced Oxidations of Alcohols
Science.gov (United States)
Hudson, R. L.; Moore, M. H.
2018-04-01
Infrared spectra of ices containing alcohols that are known or potential interstellar molecules are examined before and after irradiation with 1 MeV protons at ∼20 K. The low-temperature oxidation (hydrogen loss) of six alcohols is followed, and conclusions are drawn based on the results. The formation of reaction products is discussed in terms of the literature on the radiation chemistry of alcohols and a systematic variation in their structures. The results from these new laboratory measurements are then applied to a recent study of propargyl alcohol. Connections are drawn between known interstellar molecules, and several new reaction products in interstellar ices are predicted.
10. Chemistry in interstellar space. [environment characteristics influencing reaction dynamics
Science.gov (United States)
Donn, B.
1973-01-01
The particular characteristics of chemistry in interstellar space are determined by the unique environmental conditions involved. Interstellar matter is present at extremely low densities. Large deviations from thermodynamic equilibrium are, therefore, to be expected. A relatively intense ultraviolet radiation is present in many regions. The temperatures are in the range from 5 to 200 K. Data concerning the inhibiting effect of small activation energies in interstellar clouds are presented in a table. A summary of measured activation energies or barrier heights for exothermic exchange reactions is also provided. Problems of molecule formation are discussed, taking into account gas phase reactions and surface catalyzed processes.
11. Interstellar and ejecta dust in the cas a supernova remnant
Energy Technology Data Exchange (ETDEWEB)
Arendt, Richard G. [CRESST, University of Maryland, Baltimore County, Baltimore, MD 21250 (United States); Dwek, Eli; Kober, Gladys [NASA Goddard Space Flight Center, Code 665, Greenbelt, MD 20771 (United States); Rho, Jeonghee [SETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043 (United States); Hwang, Una, E-mail: [email protected] [NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771 (United States)
2014-05-01
Infrared continuum observations provide a means of investigating the physical composition of the dust in the ejecta and swept up medium of the Cas A supernova remnant (SNR). Using low-resolution Spitzer IRS spectra (5-35 μm), and broad-band Herschel PACS imaging (70, 100, and 160 μm), we identify characteristic dust spectra, associated with ejecta layers that underwent distinct nuclear burning histories. The most luminous spectrum exhibits strong emission features at ∼9 and 21 μm and is closely associated with ejecta knots with strong Ar emission lines. The dust features can be reproduced by magnesium silicate grains with relatively low Mg to Si ratios. Another dust spectrum is associated with ejecta having strong Ne emission lines. It has no indication of any silicate features and is best fit by Al{sub 2}O{sub 3} dust. A third characteristic dust spectrum shows features that are best matched by magnesium silicates with a relatively high Mg to Si ratio. This dust is primarily associated with the X-ray-emitting shocked ejecta, but it is also evident in regions where shocked interstellar or circumstellar material is expected. However, the identification of dust composition is not unique, and each spectrum includes an additional featureless dust component of unknown composition. Colder dust of indeterminate composition is associated with emission from the interior of the SNR, where the reverse shock has not yet swept up and heated the ejecta. Most of the dust mass in Cas A is associated with this unidentified cold component, which is ≲ 0.1 M {sub ☉}. The mass of warmer dust is only ∼0.04 M {sub ☉}.
12. Growing interstellar molecules with ion-molecule reactions
International Nuclear Information System (INIS)
Bohme, D.K.
1989-01-01
Laboratory measurements of gas-phase ion-molecule reactions continue to provide important insights into the chemistry of molecular growth in interstellar environments. It is also true that the measurements are becoming more demanding as larger molecules capture our interest. While some of these measurements are motivated by current developments in chemical models of interstellar environments or by new molecular observations by astronomers, others explore novel chemistry which can lead to predictions of new interstellar molecules. Here the author views the results of some recent measurements, taken in the Ion Chemistry Laboratory at York University with the SIFT technique, which address some of the current needs of modellers and observers and which also provide some new fundamental insight into molecular growth, particularly when it occurs in the presence of large molecules such as PAH molecules which are now thought to have a major influence on the chemistry of interstellar environments in which they are present
13. The Interstellar Medium in External Galaxies: Summaries of contributed papers
Science.gov (United States)
Hollenbach, David J. (Editor); Thronson, Harley A., Jr. (Editor)
1990-01-01
The Second Wyoming Conference entitled, The Interstellar Medium in External Galaxies, was held on July 3 to 7, 1989, to discuss the current understanding of the interstellar medium in external galaxies and to analyze the basic physical processes underlying interstellar phenomena. The papers covered a broad range of research on the gas and dust in external galaxies and focused on such topics as the distribution and morphology of the atomic, molecular, and dust components; the dynamics of the gas and the role of the magnetic field in the dynamics; elemental abundances and gas depletions in the atomic and ionized components; cooling flows; star formation; the correlation of the nonthermal radio continuum with the cool component of the interstellar medium; the origin and effect of hot galactic halos; the absorption line systems seen in distant quasars; and the effect of galactic collisions.
14. Electromagnetic Forces on a Relativistic Spacecraft in the Interstellar Medium
Energy Technology Data Exchange (ETDEWEB)
Hoang, Thiem [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Loeb, Abraham, E-mail: [email protected], E-mail: [email protected] [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA (United States)
2017-10-10
A relativistic spacecraft of the type envisioned by the Breakthrough Starshot initiative will inevitably become charged through collisions with interstellar particles and UV photons. Interstellar magnetic fields would therefore deflect the trajectory of the spacecraft. We calculate the expected deflection for typical interstellar conditions. We also find that the charge distribution of the spacecraft is asymmetric, producing an electric dipole moment. The interaction between the moving electric dipole and the interstellar magnetic field is found to produce a large torque, which can result in fast oscillation of the spacecraft around the axis perpendicular to the direction of motion, with a period of ∼0.5 hr. We then study the spacecraft rotation arising from impulsive torques by dust bombardment. Finally, we discuss the effect of the spacecraft rotation and suggest several methods to mitigate it.
15. The local interstellar medium and gamma-ray astronomy
International Nuclear Information System (INIS)
Lebrun, F.; Paul, J.
1985-08-01
The recent improvement of the calibration of the galaxy counts used as an interstellar-absorption tracer modifies significantly the picture of the local interstellar medium (ISM). Consequently, previous analyses of the γ-ray emission from the local ISM involving galaxy counts have to be revised. In this paper, we consider the implications regarding the cosmic-ray (CR) density in the local ISM, and in particular within Loop I, a nearby supernova remnant (SNR)
16. Stellar and interstellar K lines - Gamma Pegasi and iota Herculis.
Science.gov (United States)
Hobbs, L. M.
1973-01-01
High-resolution scans show that the relatively strong (about 90 mA) K lines of Ca II in the early B stars gamma-Peg and iota-Her are almost entirely stellar in origin, although the latter case includes a small interstellar contribution. Such stellar lines can be of great importance in augmenting the interstellar absorption, up through the earliest of the B stars.
17. The Turbulent Interstellar Medium: Insights and Questions from Numerical Models
OpenAIRE
Mac Low, Mordecai-Mark; de Avillez, Miguel A.; Korpi, Maarit J.
2003-01-01
"The purpose of numerical models is not numbers but insight." (Hamming) In the spirit of this adage, and of Don Cox's approach to scientific speaking, we discuss the questions that the latest generation of numerical models of the interstellar medium raise, at least for us. The energy source for the interstellar turbulence is still under discussion. We review the argument for supernovae dominating in star forming regions. Magnetorotational instability has been suggested as a way of coupling di...
18. New look at radiative association in dense interstellar clouds
International Nuclear Information System (INIS)
Herbst, E.
1980-01-01
A corrected statistical theory of radiative association reactions is presented and discussed. Calculations are undertaken to determine the rate coefficients of a variety of radiative association reactions of possible importance in dense interstellar clouds. Our results confirm the suggestion of Smith and Adams that certain radiative association reactions occur quite rapidly at low temperature and are probably important in the synthesis of complex interstellar molecules
19. Interstellar medium structure and content and gamma ray astronomy
International Nuclear Information System (INIS)
Lebrun, F.
1982-05-01
A general description of gamma-ray astronomy is presented with special emphasis on the study of diffuse gamma-ray emission. This is followed by a collection of reflections and observations on the structure and the gas and dust content of the local interstellar medium. Results of gamma-ray observations on the local interstellar medium are given. The last part is devoted to the whole of the galactic gamma-ray emission and its interpretation [fr
20. Interstellar Organics, the Solar Nebula, and Saturn's Satellite Phoebe
Science.gov (United States)
Pendleton, Y. J.; Cruikshank, D. P.
2014-01-01
The diffuse interstellar medium inventory of organic material (Pendleton et al. 1994, Pendleton & Allamandola 2002) was likely incorporated into the molecular cloud in which the solar nebula condensed. This provided the feedstock for the formation of the Sun, major planets, and the smaller icy bodies in the region outside Neptune's orbit (transneptunian objects, or TNOs). Saturn's satellites Phoebe, Iapetus, and Hyperion open a window to the composition of one class of TNO as revealed by the near-infrared mapping spectrometer (VIMS) on the Cassini spacecraft at Saturn. Phoebe (mean diameter 213 km) is a former TNO now orbiting Saurn. VIMS spaectral maps of PHoebe's surface reveal a complex organic spectral signature consisting of prominent aromatic (CH) and alophatic hydrocarbon (CH2, CH3) absorption bands (3.2-3.6 micrometers). Phoebe is the source of a huge debris ring encircling Saturn, and from which particles (approximately 5-20 micrometer size) spiral inward toward Saturn. They encounter Iapetus and Hperion where they mix with and blanket the native H2O ice of those two bodies. Quantitative analysis of the hydrocarbon bands on Iapetus demonstrates that aromatic CH is approximately 10 times as abundant as aliphatic CH2+CH3, significantly exceeding the strength of the aromatic signature in interplanetary dust particles, comet particles, ad in carbonaceous meteorites (Cruikshank et al. 2013). A similar excess of aromatics over aliphatics is seen in the qualitative analysis of Hyperion and Phoebe itself (Dalle Ore et al. 2012). The Iapetus aliphatic hydrocarbons show CH2/CH3 approximately 4, which is larger than the value found in the diffuse ISM (approximately 2-2.5). In so far as Phoebe is a primitive body that formed in the outer regions of the solar nebula and has preserved some of the original nebula inventory, it can be key to understanding the content and degree of procesing of the nebular material. There are other Phoebe-like TNOs that are presently
1. THE EFFICIENCY AND WAVELENGTH DEPENDENCE OF NEAR-INFRARED INTERSTELLAR POLARIZATION TOWARD THE GALACTIC CENTER
Energy Technology Data Exchange (ETDEWEB)
Hatano, Hirofumi; Kurita, Mikio; Kanai, Saori; Sato, Shuji [Department of Astrophysics, Nagoya University, Chikusa-ku, Nagoya 464-8602 (Japan); Nishiyama, Shogo; Nakajima, Yasushi; Tamura, Motohide; Kandori, Ryo [National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8858 (Japan); Nagata, Tetsuya; Yoshikawa, Tatsuhito [Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto 606-8502 (Japan); Kato, Daisuke [Department of Astronomy, School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Sato, Yaeko; Suenaga, Takuya, E-mail: [email protected], E-mail: [email protected] [Department of Astronomical Sciences, Graduate University for Advanced Studies (Sokendai), Mitaka, Tokyo 181-8858 (Japan)
2013-04-15
Near-infrared polarimetric imaging observations toward the Galactic center (GC) have been carried out to examine the efficiency and wavelength dependence of interstellar polarization. A total area of about 5.7 deg{sup 2} is covered in the J, H, and K{sub S} bands. We examined the polarization efficiency, defined as the ratio of the degree of polarization to color excess. The interstellar medium between the GC and us shows a polarization efficiency lower than that in the Galactic disk by a factor of three. Moreover we investigated the spatial variation of the polarization efficiency by comparing it with that of the color excess, degree of polarization, and position angle. The spatial variations of color excess and degree of polarization depend on the Galactic latitude, while the polarization efficiency varies independently of the Galactic structure. Position angles are nearly parallel to the Galactic plane, indicating a longitudinal magnetic field configuration between the GC and us. The polarization efficiency anticorrelates with dispersions of position angles. The low polarization efficiency and its spatial variation can be explained by the differences in the magnetic field directions along the line of sight. From the lower polarization efficiency, we suggest a higher strength of a random component relative to a uniform component of the magnetic field between the GC and us. We also derived the ratios of degree of polarization p{sub H} /p{sub J} = 0.581 {+-} 0.004 and p{sub K{sub S}}/p{sub H} = 0.620 {+-} 0.002. The power-law indices of the wavelength dependence of polarization are {beta}{sub JH} = 2.08 {+-} 0.02 and {beta}{sub HK{sub S}} = 1.76 {+-} 0.01. Therefore, the wavelength dependence of interstellar polarization exhibits flattening toward longer wavelengths in the range of 1.25-2.14 {mu}m. The flattening would be caused by aligned large-size dust grains.
2. The hydrogen coverage of interstellar PAHs [Polycyclic Aromatic Hydrocarbons
International Nuclear Information System (INIS)
Tielens, A.G.G.M.; Allamandola, L.J.; Barker, J.R.; Cohen, M.
1986-02-01
The rate at which the CH bond in interstellar Polycyclic Aromatic Hydrocarbons (PAHs) rupture due to the absorption of a uv photon has been calculated. The results show that small PAHs (less than or equal to 25 carbon atoms) are expected to be partially dehydrogenated in regions with intense uv fields, while large PAHs (greater than or equal to 25 atoms) are expected to be completely hydrogenated in those regions. Because estimate of the carbon content of interstellar PAHs lie in the range of 20 to 25 carbon atoms, dehydrogenation is probably not very important. Because of the absence of other emission features besides the 11.3 micrometer feature in ground-based 8 to 13 micrometer spectra, it has been suggested that interstellar PAHs are partially dehydrogenated. However, IRAS 8 to 22 micrometer spectra of most sources that show strong 7.7 and 11.2 micrometer emission features also show a plateau of emission extending from about 11.3 to 14 micrometer. Like the 11.3 micrometer feature, this new feature is attributed to the CH out of plane bending mode in PAHs. This new feature shows that interstellar PAHs are not as dehydrogenated as estimated from ground-based 8 to 13 micrometer spectra. It also constrains the molecular structure of interstellar PAHs. In particular, it seems that very condensed PAHs, such as coronene and circumcoronene, dominate the interstellar PAH mixture as expected from stability arguments
3. Small-scale structure in the diffuse interstellar medium
International Nuclear Information System (INIS)
Meyer, D.M.
1990-01-01
The initial results of a study to probe the small-scale structure in the diffuse interstellar medium (ISM) through IUE and optical observations of interstellar absorption lines toward both components of resolvable binary stars is reported. The binaries (Kappa CrA, 57 Aql, 59 And, HR 1609/10, 19 Lyn, and Theta Ser) observed with IUE have projected linear separations ranging from 5700 to 700 Au. Except for Kappa CrA, the strengths of the interstellar absorption lines toward both components of these binaries agree to within 10 percent. In the case of Kappa CrA, the optically thin interstellar Mg I and Mn II lines are about 50 percent stronger toward Kappa-2 CrA than Kappa-1 CrA. Higher resolution observations of interstellar Ca II show that this difference is concentrated in the main interstellar component at V(LSR) = 9 + or - 2 km/s. Interestingly, this velocity corresponds to an intervening cloud that may be associated with the prominent Loop I shell in the local ISM. Given the separation (23 arcsec) and distance (120 pc) of Kappa CrA, the line strength variations indicate that this cloud has structure on scales of 2800 AU or less. 21 refs
4. Matrix isolation as a tool for studying interstellar chemical reactions
Science.gov (United States)
Ball, David W.; Ortman, Bryan J.; Hauge, Robert H.; Margrave, John L.
1989-01-01
Since the identification of the OH radical as an interstellar species, over 50 molecular species were identified as interstellar denizens. While identification of new species appears straightforward, an explanation for their mechanisms of formation is not. Most astronomers concede that large bodies like interstellar dust grains are necessary for adsorption of molecules and their energies of reactions, but many of the mechanistic steps are unknown and speculative. It is proposed that data from matrix isolation experiments involving the reactions of refractory materials (especially C, Si, and Fe atoms and clusters) with small molecules (mainly H2, H2O, CO, CO2) are particularly applicable to explaining mechanistic details of likely interstellar chemical reactions. In many cases, matrix isolation techniques are the sole method of studying such reactions; also in many cases, complexations and bond rearrangements yield molecules never before observed. The study of these reactions thus provides a logical basis for the mechanisms of interstellar reactions. A list of reactions is presented that would simulate interstellar chemical reactions. These reactions were studied using FTIR-matrix isolation techniques.
5. Absorption of X-rays in the interstellar medium
International Nuclear Information System (INIS)
Ride, S.K.; Stanford Univ., Calif.; Walker, A.B.C. Jr.; Stanford Univ., Calif.
1977-01-01
In order to interpret soft X-ray spectra of cosmic X-ray sources, it is necessary to know the photoabsorption cross-section of the intervening interstellar material. Current models suggest that the interstellar medium contains two phases which make a substantial contribution to the X-ray opacity: cool, relatively dense clouds that exist in pressure equilibrium with hot, tenuous intercloud regions. We have computed the soft X-ray photoabsorption cross-section (per hydrogen atom) of each of these two phases. The calculation are based on a model of the interstellar medium which includes chemical evolution of the galaxy, the formation of molecules and grains, and the ionization structure of each of each phase. These cross-sections of clouds and of intercloud regions can be combined to yield the total soft X-ray photoabsorption cross-section of the interstellar medium. By choosing the appropriate linear combination of cloud and intercloud cross-sections, we can tailor the total cross-section to a particular line-of-sight. This approach, coupled with our interstellar model, enables us to better describe a wide range of interstellar features such as H II regions, dense (molecular) clouds, or the ionized clouds which may surround binary X-ray sources. (orig.) [de
6. Starry messages: Searching for signatures of interstellar archaeology
Energy Technology Data Exchange (ETDEWEB)
Carrigan, Richard A., Jr.; /Fermilab
2009-12-01
Searching for signatures of cosmic-scale archaeological artifacts such as Dyson spheres or Kardashev civilizations is an interesting alternative to conventional SETI. Uncovering such an artifact does not require the intentional transmission of a signal on the part of the original civilization. This type of search is called interstellar archaeology or sometimes cosmic archaeology. The detection of intelligence elsewhere in the Universe with interstellar archaeology or SETI would have broad implications for science. For example, the constraints of the anthropic principle would have to be loosened if a different type of intelligence was discovered elsewhere. A variety of interstellar archaeology signatures are discussed including non-natural planetary atmospheric constituents, stellar doping with isotopes of nuclear wastes, Dyson spheres, as well as signatures of stellar and galactic-scale engineering. The concept of a Fermi bubble due to interstellar migration is introduced in the discussion of galactic signatures. These potential interstellar archaeological signatures are classified using the Kardashev scale. A modified Drake equation is used to evaluate the relative challenges of finding various sources. With few exceptions interstellar archaeological signatures are clouded and beyond current technological capabilities. However SETI for so-called cultural transmissions and planetary atmosphere signatures are within reach.
7. Infrared spectra of interstellar deuteronated PAHs
Science.gov (United States)
Buragohain, Mridusmita; Pathak, Amit; Sarre, Peter
2015-08-01
Polycyclic Aromatic Hydrocarbon (PAH) molecules have emerged as a potential constituent of the ISM that emit strong features at 3.3, 6.2, 7.7, 8.6, 11.2 and 12.7 μm with weaker and blended features in the 3-20μm region. These features are proposed to arise from the vibrational relaxation of PAH molecules on absorption of background UV photons (Tielens 2008). These IR features have been observed towards almost all types of astronomical objects; say H II regions, photodissociation regions, reflection nebulae, planetary nebulae, young star forming regions, external galaxies, etc. A recent observation has proposed that interstellar PAHs are major reservoir for interstellar deuterium (D) (Peeters et al. 2004). According to the deuterium depletion model' as suggested by Draine (2006), some of the Ds formed in the big bang are depleted in PAHs, which can account for the present value of D/H in the ISM. Hence, study of deuterated PAHs (PADs) is essential in order to measure D/H in the ISM.In this work, we consider another probable category of the large PAH family, i.e. Deuteronated PAHs (DPAH+). Onaka et al. have proposed a D/H ratio which is an order of magnitude smaller than the proposed value of D/H by Draine suggesting that if Ds are depleted in PAHs, they might be accommodated in large PAHs (Onaka et al. 2014). This work reports a Density Functional Theory' calculation of large deuteronated PAHs (coronene, ovalene, circumcoronene and circumcircumcoronene) to determine the expected region of emission features and to find a D/H ratio that is comparable to the observational results. We present a detailed analysis of the IR spectra of these molecules and discuss the possible astrophysical implications.ReferencesDraine B. T. 2006, in ASP Conf. Ser. 348, Proc. Astrophysics in the Far Ultraviolet: Five Years of Discovery with FUSE, ed. G. Sonneborn, H. Moos, B-G Andersson (San Francisco, CA:ASP) 58Onaka T., Mori T. I., Sakon I., Ohsawa R., Kaneda H., Okada Y., Tanaka M
8. Interstellar clouds and the formation of stars
International Nuclear Information System (INIS)
Alfen, H.; Carlqvist, P.
1977-12-01
The 'pseudo-plasma formalism' which up to now has almost completely dominated theoretical astrophysics must be replaced by an experimentally based approach, involving the introduction of a number of neglected plasma phenomena, such as electric double layers, critical velocity, and pinch effect. The general belief that star light is the main ionizer is shown to be doubtful; hydromagnetic conversion of gravitational and kinetic energy may often be much more important. The revised plasma physics is applied to dark clouds and star formation. Magnetic fields do not necessarily counteract the contraction of a cloud, they may just as well 'pinch' the cloud. Magnetic compression may be the main mechanism for forming interstellar clouds and keeping them together. Star formation is due to an instability, but it is very unlikely that it has anything to do with the Jeans instablility. A reasonable mechanism is that the sedimentation of 'dust' (including solid bodies of different size) is triggering off a gravitationally assisted accretion. The study of the evolution of a dark cloud leads to a scenario of planet formation which is reconcilable with the results obtained from studies based on solar system data. This means that the new approach to cosmical plasma physics discussed logically leads to a consistent picture of the evolution of dark clouds and the formation of solar systems
9. Stability of interstellar clouds containing magnetic fields
International Nuclear Information System (INIS)
Langer, W.D.; and Bell Laboratories, Crawford Hill Laboratory, Holmdel, NJ)
1978-01-01
The stability of interstellar clouds against gravitational collapse and fragmentation in the presence of magnetic fields is investigated. A magnetic field can provide pressure support against collapse if it is strongly coupled to the neutral gas; this coupling is mediated by ion-neutral collisions in the gas. The time scale for the growth of perturbations in the gas is found to be a sensitive function of the fractional ion abundance of the gas. For a relatively large fractional ion abundance, corresponding to strong coupling, the collapse of the gas is retarded. Star formation is inhibited in dense clouds and the collapse time for diffuse clouds cn exceed the limit on their lifetime set by disruptive processes. For a small fractional ion abundance, the magnetic fields do not inhibit collapse and the distribution of the masses of collapsing fragments are likely to be quite different in regions of differing ion abundance. The solutions also predict the existence of large-scale density waves corresponding to two gravitational-magnetoacoustic modes. The conditions which best support these modes correspond to those found in the giant molecular clouds
10. Three-Dimensional Messages for Interstellar Communication
Science.gov (United States)
Vakoch, Douglas A.
One of the challenges facing independently evolved civilizations separated by interstellar distances is to communicate information unique to one civilization. One commonly proposed solution is to begin with two-dimensional pictorial representations of mathematical concepts and physical objects, in the hope that this will provide a foundation for overcoming linguistic barriers. However, significant aspects of such representations are highly conventional, and may not be readily intelligible to a civilization with different conventions. The process of teaching conventions of representation may be facilitated by the use of three-dimensional representations redundantly encoded in multiple formats (e.g., as both vectors and as rasters). After having illustrated specific conventions for representing mathematical objects in a three-dimensional space, this method can be used to describe a physical environment shared by transmitter and receiver: a three-dimensional space defined by the transmitter--receiver axis, and containing stars within that space. This method can be extended to show three-dimensional representations varying over time. Having clarified conventions for representing objects potentially familiar to both sender and receiver, novel objects can subsequently be depicted. This is illustrated through sequences showing interactions between human beings, which provide information about human behavior and personality. Extensions of this method may allow the communication of such culture-specific features as aesthetic judgments and religious beliefs. Limitations of this approach will be noted, with specific reference to ETI who are not primarily visual.
11. X-ray scattering by interstellar dust
International Nuclear Information System (INIS)
Rolf, D.
1980-10-01
This thesis reports work carried out to make a first observation of x-rays scattered by interstellar dust grains. Data about the dust, obtained at wavelengths ranging from the infrared to ultra-violet spectral regions, are discussed in order to establish a useful description of the grains themselves. This is then used to estimate the magnitude and form of the expected x-ray scattering effect which is shown to manifest itself as a diffuse halo accompanying the image of a celestial x-ray source. Two x-ray imaging experiments are then discussed. The first, specifically proposed to look for this effect surrounding a point x-ray source, was the Skylark 1611 project, and comprised an imaging proportional counter coupled to an x-ray mirror. This is described up to its final calibration when the basis for a concise model of its point response function was established. The experiment was not carried out but its objective and the experience gained during its testing were transferred to the second of the x-ray imaging experiments, the Einstein Observatory. The new instrumental characteristics are described and a model for its point response function is developed. Using this, image data for the point x-ray source GX339-4 is shown to exhibit the sought after scattering phenomenon. (author)
12. Interstellar Extinction in 20 Open Star Clusters
Science.gov (United States)
Rangwal, Geeta; Yadav, R. K. S.; Durgapal, Alok K.; Bisht, D.
2017-12-01
The interstellar extinction law in 20 open star clusters namely, Berkeley 7, Collinder 69, Hogg 10, NGC 2362, Czernik 43, NGC 6530, NGC 6871, Bochum 10, Haffner 18, IC 4996, NGC 2384, NGC 6193, NGC 6618, NGC 7160, Collinder 232, Haffner 19, NGC 2401, NGC 6231, NGC 6823, and NGC 7380 have been studied in the optical and near-IR wavelength ranges. The difference between maximum and minimum values of E(B - V) indicates the presence of non-uniform extinction in all the clusters except Collinder 69, NGC 2362, and NGC 2384. The colour excess ratios are consistent with a normal extinction law for the clusters NGC 6823, Haffner 18, Haffner 19, NGC 7160, NGC 6193, NGC 2401, NGC 2384, NGC 6871, NGC 7380, Berkeley 7, Collinder 69, and IC 4996. We have found that the differential colour-excess ΔE(B - V), which may be due to the occurrence of dust and gas inside the clusters, decreases with the age of the clusters. A spatial variation of colour excess is found in NGC 6193 in the sense that it decreases from east to west in the cluster region. For the clusters Berkeley 7, NGC 7380, and NGC 6871, a dependence of colour excess E(B - V) with spectral class and luminosity is observed. Eight stars in Collinder 232, four stars in NGC 6530, and one star in NGC 6231 have excess flux in near-IR. This indicates that these stars may have circumstellar material around them.
13. DYNAMIC SPECTRAL MAPPING OF INTERSTELLAR PLASMA LENSES
Energy Technology Data Exchange (ETDEWEB)
Tuntsov, Artem V.; Walker, Mark A. [Manly Astrophysics, 3/22 Cliff Street, Manly 2095 (Australia); Koopmans, Leon V. E. [Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, NL-9700 AV Groningen (Netherlands); Bannister, Keith W.; Stevens, Jamie; Johnston, Simon [CSIRO Astronomy and Space Science, P.O. Box 76, Epping NSW 1710 (Australia); Reynolds, Cormac; Bignall, Hayley E., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [International Centre for Radio Astronomy Research—Curtin University, Perth (Australia)
2016-02-01
Compact radio sources sometimes exhibit intervals of large, rapid changes in their flux density, due to lensing by interstellar plasma crossing the line of sight. A novel survey program has made it possible to discover these “Extreme Scattering Events” (ESEs) in real time, resulting in a high-quality dynamic spectrum of an ESE observed in PKS 1939–315. Here we present a method for determining the column-density profile of a plasma lens, given only the dynamic radio spectrum of the lensed source, under the assumption that the lens is either axisymmetric or totally anisotropic. Our technique relies on the known, strong frequency dependence of the plasma refractive index in order to determine how points in the dynamic spectrum map to positions on the lens. We apply our method to high-frequency (4.2–10.8 GHz) data from the Australia Telescope Compact Array of the PKS 1939–315 ESE. The derived electron column-density profiles are very similar for the two geometries we consider, and both yield a good visual match to the data. However, the fit residuals are substantially above the noise level, and deficiencies are evident when we compare the predictions of our model to lower-frequency (1.6–3.1 GHz) data on the same ESE, thus motivating future development of more sophisticated inversion techniques.
14. Detection of interstellar vibrationally excited HCN
International Nuclear Information System (INIS)
Ziurys, L.M.; Turner, B.E.
1986-01-01
Vibrationally excited HCN has been observed for the first time in the interstellar medium. The J = 3-2 rotational transitions of the l-doubled (0,1/sup 1d/,1c, 0) bending mode of HCN have been detected toward Orion-KL and IRC +10216. In Orion, the overall column density in the (0,1,0) mode, which exclusively samples the ''hot core,'' is 1.7-10 16 cm -2 and can be understood in terms of the ''doughnut'' model for Orion. The ground-state HCN column density implied by the excited-state observations is 2.3 x 10 18 cm -2 in the hot core, at least one order of magnitude greater than the column densities derived for HCN in its spike and plateau/doughnut components. Radiative excitation by 14 μm flux from IRc2 accounts for the (0,1,0) population provided the hot core is approx.6-7 x 10 16 cm distant from IRc2, in agreement with the ''cavity'' model for KL. Toward IRC +10216 we have detected J = 3-2 transitions of both (0,1/sup 1c/,/sup 1d/,0) and (0,2 0 ,0) excited states. The spectral profiles have been modeled to yield abundances and excitation conditions throughout the expanding envelope
15. Interstellar rendezvous missions employing fission propulsion systems
International Nuclear Information System (INIS)
Lenard, Roger X.; Lipinski, Ronald J.
2000-01-01
There has been a conventionally held nostrum that fission system specific power and energy content is insufficient to provide the requisite high accelerations and velocities to enable interstellar rendezvous missions within a reasonable fraction of a human lifetime. As a consequence, all forms of alternative mechanisms that are not yet, and may never be technologically feasible, have been proposed, including laser light sails, fusion and antimatter propulsion systems. In previous efforts, [Lenard and Lipinski, 1999] the authors developed an architecture that employs fission power to propel two different concepts: one, an unmanned probe, the other a crewed vehicle to Alpha Centauri within mission times of 47 to 60 years. The first portion of this paper discusses employing a variant of the ''Forward Resupply Runway'' utilizing fission systems to enable both high accelerations and high final velocities necessary for this type of travel. The authors argue that such an architecture, while expensive, is considerably less expensive and technologically risky than other technologically advanced concepts, and, further, provides the ability to explore near-Earth stellar systems out to distances of 8 light years or so. This enables the ability to establish independent human societies which can later expand the domain of human exploration in roughly eight light-year increments even presuming that no further physics or technology breakthroughs or advances occur. In the second portion of the paper, a technology requirement assessment is performed. The authors argue that reasonable to extensive extensions to known technology could enable this revolutionary capability
16. Interstellar extinction in the Large Magellanic Cloud
International Nuclear Information System (INIS)
Nandy, K.; Morgan, D.H.; Willis, A.J.; Wilson, R.; Gondhalekar, P.M.
1981-01-01
A systematic investigation of interstellar extinction in the ultraviolet as a function of position in the Large Magellanic Cloud has been made from an enlarged sample of reddened and comparison stars distributed throughout the cloud. Except for one star SK-69-108, the most reddened star of our sample, the shape of the extinction curves for the LMC stars do not show significant variations. All curves show an increase in extinction towards 2200 A, but some have maxima near 2200 A, some near 1900 A. It has been shown that the feature of the extinction curve near 1900 A is caused by the mismatch of the stellar F III 1920 A feature. The strength of this 1920 A feature as a function of luminosity and spectral type has been determined. The extinction curves have been corrected for the mismatch of the 1920 feature and a single mean extinction curve for the LMC normalized to Asub(V) = 0 and Esub(B-V) = 1 is presented. For the same value of Esub(B-V) the LMC stars show the 2200 A feature weaker by a factor 2 as compared with the galactic stars. Higher extinction shortward of 2000 A in the LMC extinction curves than that in our Galaxy, as reported in earlier papers, is confirmed. (author)
17. Interstellar clouds and the formation of stars
Energy Technology Data Exchange (ETDEWEB)
Alfven, H; Carlqvist, P [Kungliga Tekniska Hoegskolan, Stockholm (Sweden). Institutionen foer Plasmafysik
1978-05-01
Part I gives a survey of the drastic revision of cosmic plasma physics which is precipitated by the exploration of the magnetosphere through in situ measurements. The 'pseudo-plasma formalism', which until now has almost completely dominated theoretical astrophysics, must be replaced by an experimentally based approach involving the introduction of a number of neglected plasma phenomena, such as electric double layers, critical velocity, and pinch effect. The general belief that star light is the main ionizer is shown to be doubtful; hydromagnetic conversion of gravitational and kinetic energy may often be much more important. In Part II the revised plasma physics is applied to dark clouds and star formation. Magnetic fields do not necessarily counteract the contraction of a cloud; they may just as well 'pinch' the cloud. Magnetic compression may be the main mechanism for forming interstellar clouds and keeping them together. Part III treats the formation of stars in a dusty cosmic plasma cloud. Star formation is due to an instability, but it is very unlikely that it has anything to do with the Jeans instability. A reasonable mechanism is that the sedimentation of 'dust' (including solid bodies of different size) is triggering off a gravitationally assisted accretion. A 'stellesimal' accretion analogous to the planetesimal accretion leads to the formation of a star surrounded by a very low density hollow in the cloud. Matter falling in from the cloud towards the star is the raw material for the formation of planets and satellites.
18. Interstellar extinction and polarization in the infrared
International Nuclear Information System (INIS)
Martin, P.G.; Whittet, D.C.B.
1990-01-01
The wavelength dependences of interstellar continuum extinction and polarization in the range 0.35-5 microns are examined. The existence of a universal extinction curve with power law index of about 1.8 extending from the near-IR to at least 5 microns appears to be established for both diffuse and dense cloud dust. The polarization yields evidence for some degree of universality in the 1.6-5 micron regime which may be represented by a power law with index 1.5-2.0, encompassing that for extinction. The form of the polarization curve in the IR seems independent of the wavelength at which the degree of polarization peaks in the optical, implying that variations in that wavelength are caused by changes in the optical properties of the particle at blue-visible rather than IR wavelengths. It is argued that the more significant alterations of the grain size distribution from one environment to another occur for the smaller particles. 47 refs
19. Modelling interstellar structures around Vela X-1
Science.gov (United States)
Gvaramadze, V. V.; Alexashov, D. B.; Katushkina, O. A.; Kniazev, A. Y.
2018-03-01
We report the discovery of filamentary structures stretched behind the bow-shock-producing high-mass X-ray binary Vela X-1 using the SuperCOSMOS H-alpha Survey and present the results of optical spectroscopy of the bow shock carried out with the Southern African Large Telescope. The geometry of the detected structures suggests that Vela X-1 has encountered a wedge-like layer of enhanced density on its way and that the shocked material of the layer partially outlines a wake downstream of Vela X-1. To substantiate this suggestion, we carried out 3D magnetohydrodynamic simulations of interaction between Vela X-1 and the layer for three limiting cases. Namely, we run simulations in which (i) the stellar wind and the interstellar medium (ISM) were treated as pure hydrodynamic flows, (ii) a homogeneous magnetic field was added to the ISM, while the stellar wind was assumed to be unmagnetized, and (iii) the stellar wind was assumed to possess a helical magnetic field, while there was no magnetic field in the ISM. We found that although the first two simulations can provide a rough agreement with the observations, only the third one allowed us to reproduce not only the wake behind Vela X-1, but also the general geometry of the bow shock ahead of it.
20. Deuterium fractionation in dense interstellar clouds
International Nuclear Information System (INIS)
Millar, T.J.; Bennett, A.; Herbst, E.
1989-01-01
The time-dependent gas-phase chemistry of deuterium fractionation in dense interstellar clouds ranging in temperature between 10 and 70 K was investigated using a pseudo-time-dependent model similar to that of Brown and Rice (1986). The present approach, however, considers much more complex species, uses more deuterium fractionation reactions, and includes the use of new branching ratios for dissociative recombinations reactions. Results indicate that, in cold clouds, the major and most global source of deuterium fractionation is H2D(+) and ions derived from it, such as DCO(+) and H2DO(+). In warmer clouds, reactions of CH2D(+), C2HD(+), and associated species lead to significant fractionation even at 70 K, which is the assumed Orion temperature. The deuterium abundance ratios calculated at 10 K are consistent with those observed in TMC-1 for most species. However, a comparison between theory and observatiom for Orion, indicates that, for species in the ambient molecular cloud, the early-time results obtained with the old dissociative recombination branching ratios are superior if a temperature of 70 K is utilized. 60 refs
1. Deuterium fractionation in dense interstellar clouds
Science.gov (United States)
Millar, T. J.; Bennett, A.; Herbst, Eric
1989-05-01
The time-dependent gas-phase chemistry of deuterium fractionation in dense interstellar clouds ranging in temperature between 10 and 70 K was investigated using a pseudo-time-dependent model similar to that of Brown and Rice (1986). The present approach, however, considers much more complex species, uses more deuterium fractionation reactions, and includes the use of new branching ratios for dissociative recombinations reactions. Results indicate that, in cold clouds, the major and most global source of deuterium fractionation is H2D(+) and ions derived from it, such as DCO(+) and H2DO(+). In warmer clouds, reactions of CH2D(+), C2HD(+), and associated species lead to significant fractionation even at 70 K, which is the assumed Orion temperature. The deuterium abundance ratios calculated at 10 K are consistent with those observed in TMC-1 for most species. However, a comparison between theory and observatiom for Orion, indicates that, for species in the ambient molecular cloud, the early-time results obtained with the old dissociative recombination branching ratios are superior if a temperature of 70 K is utilized.
2. PRESSURE EQUILIBRIUM BETWEEN THE LOCAL INTERSTELLAR CLOUDS AND THE LOCAL HOT BUBBLE
Energy Technology Data Exchange (ETDEWEB)
Snowden, S. L.; Chiao, M.; Collier, M. R.; Porter, F. S.; Thomas, N. E. [NASA/Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Cravens, T.; Robertson, I. P. [Department of Physics and Astronomy, University of Kansas, 1251 Wescoe Hall Drive, Lawrence, KS 66045 (United States); Galeazzi, M.; Uprety, Y.; Ursino, E. [Department of Physics, University of Miami, 1320 Campo Sano Drive, Coral Gables, FL 33146 (United States); Koutroumpa, D. [Université Versailles St-Quentin, Sorbonne Universités, UPMC Univ. Paris 06, CNRS/INSU, LATMOS-IPSL, 11 Boulevard d' Alembert, F-78280 Guyancourt (France); Kuntz, K. D. [The Henry A. Rowland Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218 (United States); Lallement, R.; Puspitarini, L. [GEPI, Observatoire de Paris, CNRS UMR8111, Université Paris Diderot, 5 Place Jules Janssen, F-92190 Meudon (France); Lepri, S. T. [University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109 (United States); McCammon, D.; Morgan, K. [Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706 (United States); Walsh, B. M., E-mail: [email protected] [Space Sciences Laboratory, 7 Gauss Way, Berkeley, CA 94720 (United States)
2014-08-10
Three recent results related to the heliosphere and the local interstellar medium (ISM) have provided an improved insight into the distribution and conditions of material in the solar neighborhood. These are the measurement of the magnetic field outside of the heliosphere by Voyager 1, the improved mapping of the three-dimensional structure of neutral material surrounding the Local Cavity using extensive ISM absorption line and reddening data, and a sounding rocket flight which observed the heliospheric helium focusing cone in X-rays and provided a robust estimate of the contribution of solar wind charge exchange emission to the ROSAT All-Sky Survey 1/4 keV band data. Combining these disparate results, we show that the thermal pressure of the plasma in the Local Hot Bubble (LHB) is P/k = 10, 700 cm{sup –3} K. If the LHB is relatively free of a global magnetic field, it can easily be in pressure (thermal plus magnetic field) equilibrium with the local interstellar clouds, eliminating a long-standing discrepancy in models of the local ISM.
3. Modern Progress and Modern Problems in High Resolution X-ray Absorption from the Cold Interstellar Medium
Science.gov (United States)
Corrales, Lia; Li, Haochuan; Heinz, Sebastian
2018-01-01
With accurate cross-sections and higher signal-to-noise, X-ray spectroscopy can directly measure Milky Way gas and dust-phase metal abundances with few underlying assumptions. The X-ray energy band is sensitive to absorption by all abundant interstellar metals — carbon, oxygen, neon, silicon, magnesium, and iron — whether they are in gas or dust form. High resolution X-ray spectra from Galactic X-ray point sources can be used to directly measure metal abundances from all phases of the interstellar medium (ISM) along singular sight lines. We show our progress for measuring the depth of photoelectric absorption edges from neutral ISM metals, using all the observations of bright Galactic X-ray binaries available in the Chandra HETG archive. The cross-sections we use take into account both the absorption and scattering effects by interstellar dust grains on the iron and silicate spectral features. However, there are many open problems for reconciling X-ray absorption spectroscopy with ISM observations in other wavelengths. We will review the state of the field, lab measurements needed, and ways in which the next generation of X-ray telescopes will contribute.
4. Congenital Constriction Band Syndrome
OpenAIRE
Rajesh Gupta, Fareed Malik, Rishabh Gupta, M.A.Basit, Dara Singh
2008-01-01
Congenital constriction bands are anomalous bands that encircle a digit or an extremity. Congenitalconstriction band syndrome is rare condition and is mostly associated with other musculoskeletaldisorders.We report such a rare experience.
5. INTERPRETATION OF INFRARED VIBRATION-ROTATION SPECTRA OF INTERSTELLAR AND CIRCUMSTELLAR MOLECULES
International Nuclear Information System (INIS)
Lacy, John H.
2013-01-01
Infrared vibration-rotation lines can be valuable probes of interstellar and circumstellar molecules, especially symmetric molecules, which have no pure rotational transitions. But most such observations have been interpreted with an isothermal absorbing slab model, which leaves out important radiative transfer and molecular excitation effects. A more realistic non-LTE and non-isothermal radiative transfer model has been constructed. The results of this model are in much better agreement with the observations, including cases where lines in one branch of a vibration-rotation band are in absorption and another in emission. In general, conclusions based on the isothermal absorbing slab model can be very misleading, but the assumption of LTE may not lead to such large errors, particularly if the radiation field temperature is close to the gas temperature.
6. Mid-infrared emission from the local and extragalactic interstellar medium: the Isocam view
International Nuclear Information System (INIS)
Tran, Quang-Dan
1998-01-01
This research thesis is an attempt to identify the properties of different physical components (UIB, VSG, and so on) which can be observed by the camera embarked in the ISO satellite (ISOCAM), and to use these properties to understand the emission of galaxies in the middle infrared. In the first part, the author addresses dusts as they can be seen in the Galaxy interstellar medium. The objective is to obtain some elements of understanding on the different contributions in the middle infrared. This comprised the study of the impulse mechanism, the study of properties of non-identified infrared bands, and the discussion of very small grains visible in the H II regions. The second part reports the interpretation of the emission of galaxies in the middle infrared. This comprises the interpretation of the infrared emission of starburst galaxies, and the discussion of the emission of spiral galaxies and of the way this emission can be understood [fr
7. Observations of the interstellar ice grain feature in the Taurus molecular clouds
International Nuclear Information System (INIS)
Whittet, D.C.B.; Bode, H.F.; Longmore, A.J.; Baines, D.W.T.; Evans, A.
1983-01-01
Although water ice was originally proposed as a major constituent of the interstellar grain population (e.g. Oort and van de Hulst, 1946), the advent of infrared astronomy has shown that the expected absorption due to O-H stretching vibrations at 3 μm is illusive. Observations have in fact revealed that the carrier of this feature is apparently restricted to regions deep within dense molecular clouds (Merrill et al., 1976; Willner et al., 1982). However, the exact carrier of this feature is still controversial, and many questions remain as to the conditions required for its appearance. It is also uncertain whether it is restricted to circumstellar shells, rather than the general cloud medium. Detailed discussion of the 3 μm band properties is given elsewhere in this volume. 15 references, 4 figures
8. INTERSTELLAR ABUNDANCES TOWARD X Per, REVISITED
International Nuclear Information System (INIS)
Valencic, Lynne A.; Smith, Randall K.
2013-01-01
The nearby X-ray binary X Per (HD 24534) provides a useful beacon with which to examine dust grain types and measure elemental abundances in the local interstellar medium (ISM). The absorption features of O, Fe, Mg, and Si along this line of sight were measured using spectra from the Chandra X-Ray Observatory's LETG/ACIS-S and XMM-Newton's RGS instruments, and the Spex software package. The spectra were fit with dust analogs measured in the laboratory. The O, Mg, and Si abundances were compared to those from standard references, and the O abundance was compared to that along lines of sight toward other X-ray binaries. The results are as follows. First, it was found that a combination of MgSiO 3 (enstatite) and Mg 1.6 Fe 0.4 SiO 4 (olivine) provided the best fit to the O K edge, with N(MgSiO 3 )/N(Mg 1.6 Fe 0.4 SiO 4 ) = 3.4. Second, the Fe L edge could be fit with models that included metallic iron, but it was not well described by the laboratory spectra currently available. Third, the total abundances of O, Mg, and Si were in very good agreement with that of recently re-analyzed B stars, suggesting that they are good indicators of abundances in the local ISM, and the depletions were also in agreement with expected values for the diffuse ISM. Finally, the O abundances found from X-ray binary absorption spectra show a similar correlation with Galactocentric distances as seen in other objects.
9. Surfatron accelerator in the local interstellar cloud
Energy Technology Data Exchange (ETDEWEB)
Loznikov, V. M., E-mail: [email protected]; Erokhin, N. S.; Zol’nikova, N. N.; Mikhailovskaya, L. A. [Russian Academy of Sciences, Space Research Institute (Russian Federation)
2017-01-15
Taking into account results of numerous experiments, the variability of the energy spectra of cosmic rays (protons and helium nuclei) in the energy range of 10 GeV to ~10{sup 7} GeV is explained on the basis of a hypothesis of the existence of two variable sources close to the Sun. The first (soft) surfatron source (with a size of ~100 AU) is located at the periphery of the heliosphere. The second (hard) surfatron source (with a size of ~1 pc) is situated in the Local Interstellar Cloud (LIC) at a distance of <1 pc. The constant background is described by a power-law spectrum with a slope of ~2.75. The variable heliospheric surfatron source is described by a power-law spectrum with a variable amplitude, slope, and cutoff energy, the maximum cutoff energy being in the range of E{sub CH}/Z < 1000 GeV. The variable surfatron source in the LIC is described by a power-law spectrum with a variable amplitude, slope, and cut-off energy, the maximum cut-off energy being E{sub Ð}¡{sub L}/Z ≤ 3 × 10{sup 6} GeV. The proposed model is used to approximate data from several experiments performed at close times. The energy of each cosmic-ray component is calculated. The possibility of surfatron acceleration of Fe nuclei (Z = 26) in the LIC up to an energy of E{sub CL} ~ 10{sup 17} eV and electron and positrons to the “knee” in the energy spectrum is predicted. By numerically solving a system of nonlinear equations describing the interaction between an electromagnetic wave and a charged particle with an energy of up to E/Z ~ 3 × 10{sup 6} GeV, the possibility of trapping, confinement, and acceleration of charged cosmic-ray particles by a quasi-longitudinal plasma wave is demonstrated.
10. Organic compounds in circumstellar and interstellar environments.
Science.gov (United States)
Kwok, Sun
2015-06-01
Recent research has discovered that complex organic matter is prevalent throughout the Universe. In the Solar System, it is found in meteorites, comets, interplanetary dust particles, and planetary satellites. Spectroscopic signatures of organics with aromatic/aliphatic structures are also found in stellar ejecta, diffuse interstellar medium, and external galaxies. From space infrared spectroscopic observations, we have found that complex organics can be synthesized in the late stages of stellar evolution. Shortly after the nuclear synthesis of the element carbon, organic gas-phase molecules are formed in the stellar winds, which later condense into solid organic particles. This organic synthesis occurs over very short time scales of about a thousand years. In order to determine the chemical structures of these stellar organics, comparisons are made with particles produced in the laboratory. Using the technique of chemical vapor deposition, artificial organic particles have been created by injecting energy into gas-phase hydrocarbon molecules. These comparisons led us to believe that the stellar organics are best described as amorphous carbonaceous nanoparticles with mixed aromatic and aliphatic components. The chemical structures of the stellar organics show strong similarity to the insoluble organic matter found in meteorites. Isotopic analysis of meteorites and interplanetary dust collected in the upper atmospheres have revealed the presence of pre-solar grains similar to those formed in old stars. This provides a direct link between star dust and the Solar System and raises the possibility that the early Solar System was chemically enriched by stellar ejecta with the potential of influencing the origin of life on Earth.
11. Solid H2 in the interstellar medium
Science.gov (United States)
Füglistaler, A.; Pfenniger, D.
2018-06-01
Context. Condensation of H2 in the interstellar medium (ISM) has long been seen as a possibility, either by deposition on dust grains or thanks to a phase transition combined with self-gravity. H2 condensation might explain the observed low efficiency of star formation and might help to hide baryons in spiral galaxies. Aims: Our aim is to quantify the solid fraction of H2 in the ISM due to a phase transition including self-gravity for different densities and temperatures in order to use the results in more complex simulations of the ISM as subgrid physics. Methods: We used molecular dynamics simulations of fluids at different temperatures and densities to study the formation of solids. Once the simulations reached a steady state, we calculated the solid mass fraction, energy increase, and timescales. By determining the power laws measured over several orders of magnitude, we extrapolated to lower densities the higher density fluids that can be simulated with current computers. Results: The solid fraction and energy increase of fluids in a phase transition are above 0.1 and do not follow a power law. Fluids out of a phase transition are still forming a small amount of solids due to chance encounters of molecules. The solid mass fraction and energy increase of these fluids are linearly dependent on density and can easily be extrapolated. The timescale is below one second, the condensation can be considered instantaneous. Conclusions: The presence of solid H2 grains has important dynamic implications on the ISM as they may be the building blocks for larger solid bodies when gravity is included. We provide the solid mass fraction, energy increase, and timescales for high density fluids and extrapolation laws for lower densities.
12. SECONDARY POPULATION OF INTERSTELLAR NEUTRALS seems deflected to the side
Science.gov (United States)
Nakagawa, H.; Bzowski, M.; Yamazaki, A.; Fukunishi, H.; Watanabe, S.; Takahashi, Y.; Taguchi, M.
Recently the neutral hydrogen flow in the inner heliosphere was found to be deflected relative to the helium flow by about 4 degrees Lallement et al 2005 The explanation of this delfection offered was a distortion of the heliosphere under the action of an ambient interstellar magnetic field In a separate study a number of data sets pertaining to interstellar neutral atoms obtained with various techniques were compiled and interpreted as due to an inflow of interstellar gas from an ecliptic longitude shifted by 10 - 40 degrees from the canonical upstream interstellar neutral flow direction at 254 degrees Collier et al 2004 The origin and properties of such a flow is still under debate We have performed a cross-experiment analysis of the heliospheric hydrogen and helium photometric observations performed simltaneously by the Nozomi spacecraft between the Earth and Mars orbit and explored possible deflection of hydrogen and helium flows with respect to the canonical upwind direction For the interpretation we used predictions of a state of the art 3D and fully time-dependent model of the neutral gas in the heliosphere with the boundary conditions ionization rates and radiation pressure taken from literature The model includes two populations of the thermal interstellar hydrogen predicted by the highly-reputed Moscow Monte Carlo model of the heliosphere The agreement between the data and simulations is not satifactory when one assumes that the upwind direction is the same for both populations and identical with the direction derived from inerstellar helium
13. The distribution of interstellar dust in CALIFA edge-on galaxies via oligochromatic radiative transfer fitting
Science.gov (United States)
De Geyter, Gert; Baes, Maarten; Camps, Peter; Fritz, Jacopo; De Looze, Ilse; Hughes, Thomas M.; Viaene, Sébastien; Gentile, Gianfranco
2014-06-01
We investigate the amount and spatial distribution of interstellar dust in edge-on spiral galaxies, using detailed radiative transfer modelling of a homogeneous sample of 12 galaxies selected from the Calar Alto Legacy Integral Field Area survey. Our automated fitting routine, FITSKIRT, was first validated against artificial data. This is done by simultaneously reproducing the Sloan Digital Sky Survey g-, r-, i- and z-band observations of a toy model in order to combine the information present in the different bands. We show that this combined, oligochromatic fitting has clear advantages over standard monochromatic fitting especially regarding constraints on the dust properties. We model all galaxies in our sample using a three-component model, consisting of a double-exponential disc to describe the stellar and dust discs and using a Sérsic profile to describe the central bulge. The full model contains 19 free parameters, and we are able to constrain all these parameters to a satisfactory level of accuracy without human intervention or strong boundary conditions. Apart from two galaxies, the entire sample can be accurately reproduced by our model. We find that the dust disc is about 75 per cent more extended but only half as high as the stellar disc. The average face-on optical depth in the V band is 0.76 and the spread of 0.60 within our sample is quite substantial, which indicates that some spiral galaxies are relatively opaque even when seen face-on.
14. PAHs in the Ices of Saturn's Satellites: Connections to the Solar Nebula and the Interstellar Medium
Science.gov (United States)
Cruikshank, Dale P.; Pendleton, Yvonne J.
2015-01-01
Aliphatic hydrocarbons and PAHs have been observed in the interstellar medium (e.g., Allamandola et al. 1985, Pendleton et al. 1994, Pendleton & Allamandola 2002, Tielens 2013, Kwok 2008, Chiar & Pendleton 2008) The inventory of organic material in the ISM was likely incorporated into the molecular cloud in which the solar nebula condensed, contributing to the feedstock for the formation of the Sun, major planets, and the smaller icy bodies in the region outside Neptune's orbit (transneptunian objects, or TNOs). Additional organic synthesis occurred in the solar nebula (Ciesla & Sandford 2012). Saturn's satellites Phoebe, Iapetus, and Hyperion open a window to the composition of one class of TNO as revealed by the near-infrared mapping spectrometer (VIMS) on the Cassini spacecraft at Saturn. Phoebe (mean diameter 213 km) is a former TNO now orbiting Saturn (Johnson & Lunine 2005). VIMS spectral maps of Phoebe's surface reveal a complex organic spectral signature consisting of prominent aromatic (CH) and aliphatic hydrocarbon (=CH2, -CH3) absorption bands (3.2-3.6 micrometers). Phoebe is the source of a huge debris ring encircling Saturn, and from which particles ((is) approximately 5-20 micrometers size) spiral inward toward Saturn (Verbiscer et al. 2009). They encounter Iapetus and Hyperion where they mix with and blanket the native H2O ice of those two bodies. Quantitative analysis of the hydrocarbon bands on Iapetus demonstrates that aromatic CH is approximately 10 times as abundant as aliphatic CH2+CH3, significantly exceeding the strength of the aromatic signature in interplanetary dust particles, comet particles, and in carbonaceous meteorites (Cruikshank et al. 2014). A similar excess of aromatics over aliphatics is seen in the qualitative analysis of Hyperion and Phoebe itself (Dalle Ore et al. 2012). The Iapetus aliphatic hydrocarbons show CH2/CH3 (is) approximately 4, which is larger than the value found in the diffuse ISM ((is) approximately 2
15. Dust clouds in Orion and the interstellar neutral hydrogen distribution
International Nuclear Information System (INIS)
Bystrova, N.V.
1989-01-01
According to published examples of the far IR observations in the Orion and its surroundings, several well defined dust clouds of different sizes and structure are present. For comparison of these clouds with the neutral hydrogen distribution on the area of approx. 1000 sq degs, the data from Pulkovo Sky Survey in the interstellar neutral Hydrogen Radio Line as well as special observations with the RATAN-600 telescope in 21 cm line were used. From the materials of Pulkovo HI Survey, the data were taken near the line emission at ten velocities between -21.8 and +25.6 km/s LSR for the structural component of the interstellar hydrogen emission. The results given concern mainly the Orion's Great Dust Cloud and the Lambda Orionis region where the information about the situation with the dust and interstellar hydrogen is very essential for interpretation
16. Cosmic ray diffusion in a violent interstellar medium
International Nuclear Information System (INIS)
Bykov, A.M.; Toptygin, I.N.
1985-01-01
A variety of the avaiable observational data on the cosmic ray (CR) spectrum, anisotropy and composition are in good agreement with a suggestion on the diffusion propagation of CR with energy below 10(15) eV in the interstellar medium. The magnitude of the CR diffusion coefficient and its energy dependence are determined by interstellar medium (ISM) magnetic field spectra. Direct observational data on magnetic field spectra are still absent. A theoretical model to the turbulence generation in the multiphase ISM is resented. The model is based on the multiple generation of secondary shocks and concomitant large-scale rarefactions due to supernova shock interactions with interstellar clouds. The distribution function for ISM shocks are derived to include supernova statistics, diffuse cloud distribution, and various shock wave propagation regimes. This permits calculation of the ISM magnetic field fluctuation spectrum and CR diffusion coefficient for the hot phase of ISM
17. A scenario for interstellar exploration and its financing
CERN Document Server
Bignami, Giovanni F
2013-01-01
This book develops a credible scenario for interstellar exploration and colonization. In so doing, it examines: • the present situation and prospects for interstellar exploration technologies; • where to go: the search for habitable planets; • the motivations for space travel and colonization; • the financial mechanisms required to fund such enterprises. The final section of the book analyzes the uncertainties surrounding the presented scenario. The purpose of building a scenario is not only to pinpoint future events but also to highlight the uncertainties that may propel the future in different directions. Interstellar travel and colonization requires a civilization in which human beings see themselves as inhabitants of a single planet and in which global governance of these processes is conducted on a cooperative basis. The key question is, then, whether our present civilization is ready for such an endeavor, reflecting the fact that the critical uncertainties are political and cultural in nature. I...
18. Magnetic seismology of interstellar gas clouds: Unveiling a hidden dimension.
Science.gov (United States)
Tritsis, Aris; Tassis, Konstantinos
2018-05-11
Stars and planets are formed inside dense interstellar molecular clouds by processes imprinted on the three-dimensional (3D) morphology of the clouds. Determining the 3D structure of interstellar clouds remains challenging because of projection effects and difficulties measuring the extent of the clouds along the line of sight. We report the detection of normal vibrational modes in the isolated interstellar cloud Musca, allowing determination of the 3D physical dimensions of the cloud. We found that Musca is vibrating globally, with the characteristic modes of a sheet viewed edge on, not the characteristics of a filament as previously supposed. We reconstructed the physical properties of Musca through 3D magnetohydrodynamic simulations, reproducing the observed normal modes and confirming a sheetlike morphology. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
19. Necessity for non-standard models of interstellar turbulence. The 'Champagne bottle' model
Energy Technology Data Exchange (ETDEWEB)
Bonazzola, S; Celnikier, L M; Chevreton, M [Observatoire de Paris, Section de Meudon, 92 (France)
1978-01-01
A complete treatment of interstellar pulsar scintillation by the Physically Thin Screen phase changing model allows one to obtain better agreement with observation and thereby extract new information about the turbulence structure of the interstellar plasma.
20. On the necessity for non-standard models of interstellar turbulence. The 'Champagne bottle' model
International Nuclear Information System (INIS)
Bonazzola, S.; Celnikier, L.M.; Chevreton, M.
1978-01-01
A complete treatment of interstellar pulsar scintillation by the Physically Thin Screen phase changing model allows one to obtain better agreement with observation and thereby extract new information about the turbulence structure of the interstellar plasma
1. The existence and nature of the interstellar bow shock
Energy Technology Data Exchange (ETDEWEB)
Ben-Jaffel, Lotfi [UPMC Univ Paris 06, UMR7095, Institut d' Astrophysique de Paris, F-75014, Paris (France); Strumik, M.; Ratkiewicz, R.; Grygorczuk, J., E-mail: [email protected] [Space Research Centre, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw (Poland)
2013-12-20
We report a new diagnosis of two different states of the local interstellar medium (LISM) near our solar system by using a sensitivity study constrained by several distinct and complementary observations of the LISM, solar wind, and inner heliosphere. Assuming the Interstellar Boundary Explorer (IBEX) He flow parameters for the LISM, we obtain a strength of ∼2.7 ± 0.2 μG and a direction pointing away from galactic coordinates (28, 52) ± 3° for the interstellar magnetic field as a result of fitting Voyager 1 and Voyager 2 in situ plasma measurements and IBEX energetic neutral atoms ribbon. When using Ulysses parameters for the LISM He flow, we recently reported the same direction but with a strength of 2.2 ± 0.1 μG. First, we notice that with Ulysses He flow, our solution is in the expected hydrogen deflection plane (HDP). In contrast, for the IBEX He flow, the solution is ∼20° away from the corresponding HDP plane. Second, the long-term monitoring of the interplanetary H I flow speed shows a value of ∼26 km s{sup –1} measured upwind from the Doppler shift in the strong Lyα sky background emission line. All elements of the diagnosis seem therefore to support Ulysses He flow parameters for the interstellar state. In that frame, we argue that reliable discrimination between superfast, subfast, or superslow states of the interstellar flow should be based on most existing in situ and remote observations used together with global modeling of the heliosphere. For commonly accepted LISM ionization rates, we show that a fast interstellar bow shock should be standing off upstream of the heliopause.
2. Interstellar Propulsion Research: Realistic Possibilities and Idealistic Dreams
Science.gov (United States)
Johnson, Les
2009-01-01
Though physically possible, interstellar travel will be exceedingly difficult. Both the known laws of physics and the limits of our current understanding of engineering place extreme limits on what may actually be possible. Our remote ancestors looked at the night sky and assumed those tiny points of light were campfires around which other tribes were gathered -- and they dreamed of someday making the trip to visit them. In our modern era, we've grown accustomed to humans regularly traveling into space and our robots voyaging ever-deeper into the outer edges of our solar system. Traveling to those distant campfires (stars) has been made to look easy by the likes of Captains Kirk and Picard as well as Han Solo and Commander Adama. Our understanding of physics and engineering has not kept up with our imaginations and many are becoming frustrated with the current pace at which we are exploring the universe. Fortunately, there are ideas that may one day lead to new physical theories about how the universe works and thus potentially make rapid interstellar travel possible -- but many of these are just ideas and are not even close to being considered a scientific theory or hypothesis. Absent any scientific breakthroughs, we should not give up hope. Nature does allow for interstellar travel, albeit slowly and requiring an engineering capability far beyond what we now possess. Antimatter, fusion and photon sail propulsion are all candidates for relatively near-term interstellar missions. The plenary lecture will discuss the dreams and challenges of interstellar travel, our current understanding of what may be possible and some of the "out of the box" ideas that may allow us to become an interstellar species someday in the future.
3. The Interstellar Ethics of Self-Replicating Probes
Science.gov (United States)
Cooper, K.
Robotic spacecraft have been our primary means of exploring the Universe for over 50 years. Should interstellar travel become reality it seems unlikely that humankind will stop using robotic probes. These probes will be able to replicate themselves ad infinitum by extracting raw materials from the space resources around them and reconfiguring them into replicas of themselves, using technology such as 3D printing. This will create a colonising wave of probes across the Galaxy. However, such probes could have negative as well as positive consequences and it is incumbent upon us to factor self-replicating probes into our interstellar philosophies and to take responsibility for their actions.
4. Interstellar Scintillation and Scattering of Micro-arc-second AGN
Directory of Open Access Journals (Sweden)
David L. Jauncey
2016-11-01
Full Text Available The discovery of the first quasar 3C 273 led directly to the discovery of their variability at optical and radio wavelengths. We review the radio variability observations, in particular the variability found at frequencies below 1 GHz, as well as those exhibiting intra-day variability (IDV at cm wavelengths. Observations have shown that IDV arises principally from scintillation caused by scattering in the ionized interstellar medium of our Galaxy. The sensitivity of interstellar scintillation towards source angular sizes has provided a powerful tool for studying the most compact components of radio-loud AGN at microarcsecond and milliarcsecond scale resolution.
5. Thermoluminescence of Simulated Interstellar Matter after Gamma-ray Irradiation
OpenAIRE
Koike, K.; Nakagawa, M.; Koike, C.; Okada, M.; Chihara, H.
2002-01-01
Interstellar matter is known to be strongly irradiated by radiation and several types of cosmic ray particles. Simulated interstellar matter, such as forsterite $\\rm Mg_{2}SiO_{4}$, enstatite $\\rm MgSiO_{3}$ and magnesite $\\rm MgCO_{3}$ has been irradiated with the $\\rm ^{60}Co$ gamma-rays in liquid nitrogen, and also irradiated with fast neutrons at 10 K and 70 K by making use of the low-temperature irradiation facility of Kyoto University Reactor (KUR-LTL. Maximum fast neutron dose is \$10^{...
6. A photometric map of interstellar reddening within 100 PC
Science.gov (United States)
Perry, C. L.; Johnston, L.; Crawford, D. L.
1982-12-01
Color excesses and distances are calculated for 300 bright, northern, late F stars using uvby beta photometric indices. The data allow an extension of the earlier maps by Perry and Johnston of the spatial distribution of interstellar reddening into the local (r less than 100 pc) solar neighborhood. Some definite conclusions are made regarding the distribution of interstellar dust in the northern hemisphere and within 300 pc of the sun by merging these results and the polarimetric observations by Tinbergen (1982) for 180 stars within 35 pc of the sun.
7. Rotational Spectra in 29 Vibrationally Excited States of Interstellar Aminoacetonitrile
Energy Technology Data Exchange (ETDEWEB)
Kolesniková, L.; Alonso, E. R.; Mata, S.; Alonso, J. L. [Grupo de Espectroscopia Molecular (GEM), Edificio Quifima, Área de Química-Física, Laboratorios de Espectroscopia y Bioespectroscopia, Parque Científico UVa, Unidad Asociada CSIC, Universidad de Valladolid, E-47011 Valladolid (Spain)
2017-04-01
We report a detailed spectroscopic investigation of the interstellar aminoacetonitrile, a possible precursor molecule of glycine. Using a combination of Stark and frequency-modulation microwave and millimeter wave spectroscopies, we observed and analyzed the room-temperature rotational spectra of 29 excited states with energies up to 1000 cm{sup −1}. We also observed the {sup 13}C isotopologues in the ground vibrational state in natural abundance (1.1%). The extensive data set of more than 2000 new rotational transitions will support further identifications of aminoacetonitrile in the interstellar medium.
8. UV IRRADIATION OF AROMATIC NITROGEN HETEROCYCLES IN INTERSTELLAR ICE ANALOGS
Science.gov (United States)
Elsila, J. E.; Bernstein, M. P.; Sanford, S. A.
2005-01-01
Here, we present information on the properties of the ANH quinoline frozen in interstellar water-ice analogs. Quinoline is a two-ring compound structurally analogous to the PAH naphthalene. In this work, binary mixtures of water and quinoline were frozen to create interstellar ice analogs, which were then subjected to ultraviolet photolysis. We will present the infrared spectra of the resulting ices at various temperatures, as well as chromatographic analysis of the residues remaining upon warm-up of these ices to room temperature.
9. Interstellar gas near and within the solar system
International Nuclear Information System (INIS)
Burgin, M.S.
1981-01-01
The picture of the interaction between the local interstellar medium (LISM) and the solar environment developed in recent years is described, and prospects are discussed for obtaining complete information about the LISM. Special attention is given to the neutral component of the LISM, particularly to the results of observations of the uv radiation scattered from hydrogen and helium atoms penetrating the solar system from interstellar space. The properties of the LISM plasma are considered only as they pertain to the interaction with the neutral component
10. Stochastic evolution of refractory interstellar dust during the chemical evolution of a two-phase interstellar medium
International Nuclear Information System (INIS)
Liffman, K.; Clayton, D.D.
1989-01-01
The evolution course of refractory interstellar dust during the chemical evolution of a two-phase interstellar medium (ISM) is studied using a simple model of the chemical evolution of ISM. It is assumed that, in this medium, the stars are born in molecular clouds, but new nucleosynthesis products and stellar return are entered into a complementary diffuse medium; the well-mixed matter of each interstellar phase is repeatedly cycled stochastically through the complementary phase and back. The dust is studied on a particle-by-particle bases as it is sputtered by shock waves in the diffuse medium, accretes an amorphous mantle of gaseous refractory atoms while its local medium joins the molecular cloud medium, and encounters the possibility of astration within molecular clouds. Results are presented relevant to the size spectrum of accreted mantles, its age spectrum and the distinction among its several lifetimes, depletion factors of refractory atoms in the diffuse gas, and isotopic anomalies. 26 refs
11. Surface science studies of ethene containing model interstellar ices
Science.gov (United States)
Puletti, F.; Whelan, M.; Brown, W. A.
2011-05-01
The formation of saturated hydrocarbons in the interstellar medium (ISM) is difficult to explain only by taking into account gas phase reactions. This is mostly due to the fact that carbonium ions only react with H_2 to make unsaturated hydrocarbons, and hence no viable route to saturated hydrocarbons has been postulated to date. It is therefore likely that saturation processes occur via surface reactions that take place on interstellar dust grains. One of the species of interest in this family of reactions is C_2H_4 (ethene) which is an intermediate in several molecular formation routes (e.g. C_2H_2 → C_2H_6). To help to understand some of the surface processes involving ethene, a study of ethene deposited on a dust grain analogue surface (highly oriented pyrolytic graphite) held under ultra-high vacuum at 20 K has been performed. The adsorption and desorption of ethene has been studied both in water-free and water-dominated model interstellar ices. A combination of temperature programmed desorption (TPD) and reflection absorption infrared spectroscopy (RAIRS) have been used to identify the adsorbed and trapped species and to determine the kinetics of the desorption processes. In all cases, ethene is found to physisorb on the carbonaceous surface. As expected water has a very strong influence on the desorption of ethene, as previously observed for other model interstellar ice systems.
12. Interstellar C2, CH, and CN in translucent molecular clouds
NARCIS (Netherlands)
Dishoeck, van E.F.; Black, J.H.
1989-01-01
Optical absorption-line techniques have been applied to the study of a number of translucent molecular clouds in which the total column densities are large enough that substantial molecular abundances can be maintained. Results are presented for a survey of absorption lines of interstellar C2, CH,
13. Three-Component Dust Models for Interstellar Extinction C ...
without standard' method were used to constrain the dust characteristics in the mean ISM (RV = 3.1), ... Interstellar dust models have evolved as the observational data have advanced, and the most popular dust ... distribution comes from the IRAS observation which shows an excess of 12 μ and. 25 μ emission from the ISM ...
14. The Stardust Interstellar Dust Collector and Stardust@home
Science.gov (United States)
Westphal, A. J.; Anderson, D.; Bastien, R.; Butterworth, A.; Frank, D.; Gainsforth, Z.; Kelley, N.; Lettieri, R.; Mendez, B.; Prasad, R.; Tsitrin, S.; von Korff, J.; Warren, J.; Wertheimer, D.; Zhang, A.; Zolensky, M.
2006-12-01
The Stardust sample return mission is effectively two missions in one. Stardust brought back to earth for analytical study the first solid samples from a known solar system body beyond the moon, comet Wild2. The first results of the analyses of these samples are reported elsewhere in this session. In a separate aerogel collector, Stardust also captured and has returned the first samples of contemporary interstellar dust. Landgraf et al. [1] has estimated that ~ 50 interstellar dust particles in the micron size range have been captured in the Stardust Interstellar Dust Collector. Their state after capture is unknown. Before analysis of these particles can begin, they must be located in the collector. Here we describe the current status of Stardust@home, the massively distributed public search for these tiny interstellar dust particles. So far more than 13,000 volunteers have collectively performed more than 10,000,000 searches in stacks of digital images of ~10% of the collector. We report new estimates of the flux of interplanetary dust at ~2 AU based on the results of this search, and will compare with extant models[2]. References: [1] Landgraf et al., (1999) Planet. Spac. Sci. 47, 1029. [2] Staubach et al. (2001) in Interplanetary Dust, E. Grün, ed., Astron. &Astro. Library, Springer, 2001.
15. Rapid interstellar scintillation of quasar PKS 1257-326
NARCIS (Netherlands)
Bignall, Hayley E.; Jauncey, David L.; Lovell, James E. J.; Tzioumis, Anastasios K.; Macquart, Jean-Pierre; Kedziora-Chudczer, Lucyna; Engvold, O
2005-01-01
PKS 1257-326 is one of three quasars known to show unusually large and rapid, intra-hour intensity variations, as a result of scintillation in the turbulent Galactic interstellar medium. We have measured time delays in the variability pattern arrival times at the VLA and the ATCA, as well as an
16. Project Icarus: Stakeholder Scenarios for an Interstellar Exploration Program
Science.gov (United States)
Hein, A. M.; Tziolas, A. C.; Osborne, R.
The Project Icarus Study Group's objective is to design a mainly fusion-propelled interstellar probe. The starting point are the results of the Daedalus study, which was conducted by the British Interplanetary Society during the 1970's. As the Daedalus study already indicated, interstellar probes will be the result of a large scale, decade-long development program. To sustain a program over such long periods, the commitment of key stakeholders is vital. Although previous publications identified political and societal preconditions to an interstellar exploration program, there is a lack of more specific scientific and political stakeholder scenarios. This paper develops stakeholder scenarios which allow for a more detailed sustainability assessment of future programs. For this purpose, key stakeholder groups and their needs are identified and scientific and political scenarios derived. Political scenarios are based on patterns of past space programs but unprecedented scenarios are considered as well. Although it is very difficult to sustain an interstellar exploration program, there are scenarios in which this seems to be possible, e.g. the discovery of life within the solar system and on an exoplanet, a global technology development program, and dual-use of technologies for defence and security purposes. This is a submission of the Project Icarus Study Group.
17. Radiation-pressure-driven dust waves inside bursting interstellar bubbles
NARCIS (Netherlands)
Ochsendorf, B.B.; Verdolini, S.; Cox, N.L.J.; Berné, O.; Kaper, L.; Tielens, A.G.G.M.
2014-01-01
Massive stars drive the evolution of the interstellar medium through their radiative and mechanical energy input. After their birth, they form "bubbles" of hot gas surrounded by a dense shell. Traditionally, the formation of bubbles is explained through the input of a powerful stellar wind, even
18. Band structure of semiconductors
CERN Document Server
Tsidilkovski, I M
2013-01-01
Band Structure of Semiconductors provides a review of the theoretical and experimental methods of investigating band structure and an analysis of the results of the developments in this field. The book presents the problems, methods, and applications in the study of band structure. Topics on the computational methods of band structure; band structures of important semiconducting materials; behavior of an electron in a perturbed periodic field; effective masses and g-factors for the most commonly encountered band structures; and the treatment of cyclotron resonance, Shubnikov-de Haas oscillatio
19. Influence of the interstellar medium on climate and life: the Black Cloud revisited
Energy Technology Data Exchange (ETDEWEB)
Talbot, Jr, R J
1980-06-01
Recent studies of the gas and dust between the stars, the interstellar medium, reveal a complex chemistry which indicates that prebiotic organic chemistry is ubiquitous. The relationship between this interstellar chemistry and the organic chemistry of the early solar system and the earth is explored. The interstellar medium is also considered as likely to have a continuing influence upon the climate of the earth and other planets. Life forms as we know them are not only descendants of the organic evolution begun in the interstellar medium, but their continuing evolution is also molded through occasional interactions between the interstellar medium, the sun and the climate on earth.
20. Influence of the interstellar medium on climate and life. The black cloud revisited
Energy Technology Data Exchange (ETDEWEB)
Talbot, Jr, R J [Rice Univ., Houston, TX (USA). Dept. of Space Physics and Astronomy
1980-06-01
Recent studies of the gas and dust between the stars, the interstellar medium, reveal a complex chemistry which indicates that prebiotic organic chemistry is ubiquitous. The relationship between this interstellar chemistry and the organic chemistry of the early solar system and the Earth is explored. The interstellar medium is also considered as likely to have a continuing influence upon the climate of the Earth and other planets. Life forms as known are not only descendants of the organic evolution begun in the interstellar medium, but their continuing evolution is also molded through occasional interactions between the interstellar medium, the Sun and the climate on Earth.
1. Stardust Interstellar Preliminary Examination X: Impact Speeds and Directions of Interstellar Grains on the Stardust Dust Collector
Science.gov (United States)
Sterken, Veerle J.; Westphal, Andrew J.; Altobelli, Nicolas; Grun, Eberhard; Hillier, Jon K.; Postberg, Frank; Allen, Carlton; Stroud, Rhonda M.; Sandford, S. A.; Zolensky, Michael E.
2014-01-01
On the basis of an interstellar dust model compatible with Ulysses and Galileo observations, we calculate and predict the trajectories of interstellar dust (ISD) in the solar system and the distribution of the impact speeds, directions, and flux of ISD particles on the Stardust Interstellar Dust Collector during the two collection periods of the mission. We find that the expected impact velocities are generally low (less than 10 km per second) for particles with the ratio of the solar radiation pressure force to the solar gravitational force beta greater than 1, and that some of the particles will impact on the cometary side of the collector. If we assume astronomical silicates for particle material and a density of 2 grams per cubic centimeter, and use the Ulysses measurements and the ISD trajectory simulations, we conclude that the total number of (detectable) captured ISD particles may be on the order of 50. In companion papers in this volume, we report the discovery of three interstellar dust candidates in the Stardust aerogel tiles. The impact directions and speeds of these candidates are consistent with those calculated from our ISD propagation model, within the uncertainties of the model and of the observations.
2. Organic Compounds Produced by Photolysis of Realistic Interstellar and Cometary Ice Analogs Containing Methanol
Science.gov (United States)
Bernstein, Max P.; Sandford, Scott A.; Allamandola, Louis J.; Chang, Sherwood; Scharberg, Maureen A.
1995-01-01
The InfraRed (IR) spectra of UltraViolet (UV) and thermally processed, methanol-containing interstellar / cometary ice analogs at temperatures from 12 to 300 K are presented. Infrared spectroscopy, H-1 and C-13 Nuclear Magnetic Resonance (NMR) spectroscopy, and gas chromatography-mass spectrometry indicate that CO (carbon monoxide), CO2 (carbon dioxide), CH4 (methane), HCO (the formyl radical), H2CO (formaldehyde), CH3CH2OH (ethanol), HC([double bond]O)NH2 (formamide), CH3C([double bond]O)NH2 (acetamide), and R[single bond]C[triple bond]N (nitriles) are formed. In addition, the organic materials remaining after photolyzed ice analogs have been warmed to room temperature contain (in rough order of decreasing abundance), (1) hexamethylenetetramine (HMT, C6H12N4), (2) ethers, alcohols, and compounds related to PolyOxyMethylene (POM, ([single bond]CH2O[single bond](sub n)), and (3) ketones (R[single bond]C([double bond]O)[single bond]R') and amides (H2NC([double bond]O)[single bond]R). Most of the carbon in these residues is thought to come from the methanol in the original ice. Deuterium and C-13 isotopic labeling demonstrates that methanol is definitely the source of carbon in HMT. High concentrations of HMT in interstellar and cometary ices could have important astrophysical consequences. The ultraviolet photolysis of HMT frozen in H2O ice readily produces the 'XCN' band observed in the spectra of protostellar objects and laboratory ices, as well as other nitriles. Thus, HMT may be a precursor of XCN and a source of CN in comets and the interstellar medium. Also, HMT is known to hydrolyze under acidic conditions to yield ammonia, formaldehyde, and amino acids. Thus, HMT may be a significant source of prebiogenic compounds on asteroidal parent bodies. A potential mechanism for the radiative formation of HMT in cosmic ices is outlined.
3. HD 62542: Probing the Bare, Dense Core of an Interstellar Cloud
Science.gov (United States)
Welty, Daniel; Sonnentrucker, Paule G.; Rachford, Brian; Snow, Theodore; York, Donald G.
2018-01-01
We discuss the interstellar absorption from many atomic and molecular species seen in high-resolution HST/STIS UV spectra of the moderately reddened B3-5 V star HD 62542 [E(B-V) ~ 0.35; AV ~ 1.2]. This remarkable sight line exhibits both very steep far-UV extinction and a high fraction of hydrogen in molecular form -- with strong absorption from CH, C2, CN, and CO but weak absorption from CH+ and most of the commonly observed diffuse interstellar bands. Most of the material appears to reside in a single narrow velocity component -- thus offering a rare opportunity to probe the relatively dense, primarily molecular core of a single interstellar cloud, with little associated diffuse atomic gas.Detailed analyses of the absorption-line profiles seen in the UV spectra reveal a number of properties of the main diffuse molecular cloud toward HD 62542:1) The depletions of Mg, Si, and Fe are more severe than those seen in any other sight line, but the depletions of Cl and Kr are very mild; the overall pattern of depletions differs somewhat from those derived from larger samples of Galactic sight lines.2) The rotational excitation of H2 and C2 indicates that the gas is fairly cold (Tk = 40-45 K) and moderately dense (nH > 420 cm-3) somewhat higher densities are suggested by the fine-structure excitation of neutral carbon.3) The excitation temperatures characterizing the rotational populations of both 12CO (11.7 K) and 13CO (7.7 K) are higher than those typically found for Galactic diffuse molecular clouds.4) Carbon is primarily singly ionized -- N(C+) > N(CO) > N(C).5) The relative abundances of various trace neutral atomic species reflect the effects of both the steep far-UV extinction and the severe depletions of some elements.6) Differences in line widths for the various atomic and molecular species are suggestive of differences in spatial distribution within the main cloud.Support for this study was provided by NASA, via STScI grant GO-12277.008-A.
4. Three-dimensional mapping of the local interstellar medium with composite data
Science.gov (United States)
Capitanio, L.; Lallement, R.; Vergely, J. L.; Elyajouri, M.; Monreal-Ibero, A.
2017-10-01
Context. Three-dimensional maps of the Galactic interstellar medium are general astrophysical tools. Reddening maps may be based on the inversion of color excess measurements for individual target stars or on statistical methods using stellar surveys. Three-dimensional maps based on diffuse interstellar bands (DIBs) have also been produced. All methods benefit from the advent of massive surveys and may benefit from Gaia data. Aims: All of the various methods and databases have their own advantages and limitations. Here we present a first attempt to combine different datasets and methods to improve the local maps. Methods: We first updated our previous local dust maps based on a regularized Bayesian inversion of individual color excess data by replacing Hipparcos or photometric distances with Gaia Data Release 1 values when available. Secondly, we complemented this database with a series of ≃5000 color excess values estimated from the strength of the λ15273 DIB toward stars possessing a Gaia parallax. The DIB strengths were extracted from SDSS/APOGEE spectra. Third, we computed a low-resolution map based on a grid of Pan-STARRS reddening measurements by means of a new hierarchical technique and used this map as the prior distribution during the inversion of the two other datasets. Results: The use of Gaia parallaxes introduces significant changes in some areas and globally increases the compactness of the structures. Additional DIB-based data make it possible to assign distances to clouds located behind closer opaque structures and do not introduce contradictory information for the close structures. A more realistic prior distribution instead of a plane-parallel homogeneous distribution helps better define the structures. We validated the results through comparisons with other maps and with soft X-ray data. Conclusions: Our study demonstrates that the combination of various tracers is a potential tool for more accurate maps. An online tool makes it possible to
5. Elaboration, organisation and optical properties of carbon nano-particles as interstellar dust models
International Nuclear Information System (INIS)
Galvez, Aymeric
1999-01-01
Astrophysical and space observations from ultraviolet to infrared (IR) wavelengths provide the only signatures of carbon cosmic dust which is formed in the vicinity of old stars by molecular species condensation around 1000 K. Despite numerous models developed, a fundamental question concerns the exact nature of these grains in space. Their sampling being impossible, a better knowledge of these objects requires earth analogues obtained in conditions as close as possible of those met in space. Implying synthesis mechanism similar to those postulated for carbon cosmic dust, infrared laser pyrolysis (IRLP) appears as a versatile method in order to produce a wide variety of nanoparticles able to reproduce the main signatures characteristics of the interstellar carbon dust. We checked that the synthesised particles by this method showed strong analogies with carbon dust from the point of view of their infrared spectroscopy. The majority of the bands observed by the astrophysicists are present in spectra. Nevertheless defects exist and can be connected to the too small size of the poly-aromatic units present in such deposits. In order to confirm this size effect and to refine the spectroscopic agreement, we chose two different way by acting either directly on the synthesis by modifying the most relevant experimental parameters (temperature of flame, residence time of the reagent in the reactional zone) or indirectly by the means of post-processing (annealing, irradiation). In order to follow the optical, structural and micro-textural evolutions, the deposits thus formed or treated were characterised by infrared spectroscopy, Transmission electron Microscopy (TeM) and by image analysis of the TeM patterns in order to correlate, their organisation multi-scales and in particular the diameter of the aromatic units, with their aptitude to reproduce the spectral characteristics of interstellar carbonaceous dust. (author) [fr
6. The correlation between the ultraviolet lambda 220 feature and the diffuse lambda 4430 band
International Nuclear Information System (INIS)
Nandy, K.; Thompson, G.I.
1975-01-01
Observations of the ultraviolet feature which occurs close to 2200 A are presented for over 60 stars for which interstellar lambda 4430 data are available in the literature. Observational material used here is obtained from the ultraviolet spectra taken with the Sky Survey telescope (S2/68) in the ESRO TD1 satellite. The equivalent widths of the lambda 2200 feature have been determined from ultraviolet extinction at 2190 and 2500 A, and the relation between the equivalent width of the ultraviolet feature and the central depth of the lambda 4430 band has been determined. It is found that they are well correlated and the correlation coefficient, including allowance for errors, is greater than 0.9; this indicates that the carriers for the lambda 2200 feature and diffuse band lambda 4430 coexist in the interstellar medium. (author)
7. Observations of Carbon Isotopic Fractionation in Interstellar Formaldehyde
Science.gov (United States)
Wirstrom, E. S.; Charnley, S. B.; Geppert, W. D.; Persson, C. M.
2012-01-01
Primitive Solar System materials (e.g. chondrites. IDPs, the Stardust sample) show large variations in isotopic composition of the major volatiles (H, C, N, and O ) even within samples, witnessing to various degrees of processing in the protosolar nebula. For ex ample. the very pronounced D enhancements observed in IDPs [I] . are only generated in the cold. dense component of the interstellar medium (ISM), or protoplanetary disks, through ion-molecule reactions in the presence of interstellar dust. If this isotopic anomaly has an interstellar origin, this leaves open the possibility for preservation of other isotopic signatures throughout the form ation of the Solar System. The most common form of carbon in the ISM is CO molecules, and there are two potential sources of C-13 fractionation in this reservoir: low temperature chemistry and selective photodissociation. While gas-phase chemistry in cold interstellar clouds preferentially incorporates C-13 into CO [2], the effect of self-shielding in the presence of UV radiation instead leads to a relative enhancement of the more abundant isotopologue, 12CO. Solar System organic material exhibit rather small fluctuations in delta C-13 as compared to delta N-15 and delta D [3][1], the reason for which is still unclear. However, the fact that both C-13 depleted and enhanced material exists could indicate an interstellar origin where the two fractionation processes have both played a part. Formaldehyde (H2CO) is observed in the gas-phase in a wide range of interstellar environments, as well as in cometary comae. It is proposed as an important reactant in the formation of more complex organic molecules in the heated environments around young stars, and formaldehyde polymers have been suggested as the common origin of chondritic insoluable organic matter (IOM) and cometary refractory organic solids [4]. The relatively high gas-phase abundance of H2CO observed in molecular clouds (10(exp- 9) - 10(exp- 8) relative to H2) makes
8. Interstellar Molecules in K-12 Education
Science.gov (United States)
Kuiper, T. B. H.; Hofstadter, M. D.; Levin, S. M.; MacLaren, D.
2006-12-01
The Lewis Center for Educational Research (LCER) and the Jet Propulsion Laboratory (JPL) collaborate in a K-12 educational project in which students conduct observations for several research programs led by radio astronomers. The Goldstone-Apple Valley Radio Telescope (GAVRT) program provides participating teachers with curriculum elements, based on the students' observing experiences, which support national and state academic standards. The current program is based on 2.2-GHz and 8.4-GHz radiometric observations of variable sources. The research programs monitor Jupiter, Uranus, and a selected set of quasars. The telescope is a decommissioned NASA Deep Space Network antenna at Goldstone, California. In the next three years, a second telescope will be added. This telescope will at least operate at the above frequencies as well as 6 GHz and 12 GHz. Possibly, it will operate in a continuous band from 1.2 GHz to 14 GHz. In either case, the telescope will be able to observe at least the 6.6-GHz and 12.2-GHz methanol maser lines. The success of the GAVRT program depends critically on the participation of scientists committed to the research who have the ability and enthusiasm for interacting with K-12 students, typically through teleconferences. The scientists will initially work with the LCER staff to create curriculum elements around their observing program.
9. Interstellar PAH in the Laboratory and in Space. What have we Learned from the New Generation of Laboratory and Observational Studies?
Science.gov (United States)
Salama, Farid
2005-01-01
Polycyclic Aromatic Hydrocarbons (PAHs) are an important and ubiquitous component of carbon-bearing materials in space. PAHs are the best-known candidates to account for the IR emission bands (UIR bands) and PAH spectral features are now being used as new probes of the ISM. PAHs are also thought to be among the carriers of the diffuse interstellar absorption bands (DIBs). In the model dealing with the interstellar spectral features, PAHs are present as a mixture of radicals, ions and neutral species. PAH ionization states reflect the ionization balance of the medium while PAH size, composition, and structure reflect the energetic and chemical history of the medium. A major challenge for laboratory astrophysics is to reproduce (in a realistic way) the physical conditions that exist in the emission and/or absorption interstellar zones. An extensive laboratory program has been developed at NASA Ames to assess the physical and chemical properties of PAHs in such environments and to describe how they influence the radiation and energy balance in space and the interstellar chemistry. In particular, laboratory experiments provide measurements of the spectral characteristics of interstellar PAH analogs from the ultraviolet and visible range to the infrared range for comparison with astronomical data. This paper will focus on the recent progress made in the laboratory to measure the direct absorption spectra of neutral and ionized PAHs in the gas phase in the near-UV and visible range in astrophysically relevant environments. These measurements provide data on PAHs and nanometer-sized particles that can now be directly compared to astronomical observations. The harsh physical conditions of the IS medium - characterized by a low temperature, an absence of collisions and strong VUV radiation fields - are simulated in the laboratory by associating a molecular beam with an ionizing discharge to generate a cold plasma expansion. PAH ions are formed from the neutral precursors in
10. Interstellar extinction in the dark Taurus clouds. Pt. 1
International Nuclear Information System (INIS)
Straizys, V.; Meistas, E.
1980-01-01
The results of photoelectric photometry of 74 stars in the Vilnius seven-color system in the area of Taurus dark clouds with coordinates (1950) 4sup(h)20sup(m)-4sup(h)48sup(m)+24 0 .5-+27 0 are presented. Photometric spectral types, absolute magnitudes, color excesses, interstellar extinctions and distances of the stars are determined. The dark cloud Khavtassi 286, 278 and the surrounding absorbing nebulae are found to extend from 140 to 175 pc from the sun. The average interstellar extinction Asub(V) on both sides of the dark cloud is of the order of 1sup(m).5. We find no evidence of the existence of several absorbing clouds situated at various distances. (author)
11. Molecular Diagnostics of the Interstellar Medium and Star Forming Regions
Science.gov (United States)
Hartquist, T. W.; Dalgarno, A.
1996-03-01
Selected examples of the use of observationally inferred molecular level populations and chemical compositions in the diagnosis of interstellar sources and processes important in them (and in other diffuse astrophysical sources) are given. The sources considered include the interclump medium of a giant molecular cloud, dark cores which are the progenitors of star formation, material responding to recent star formation and which may form further stars, and stellar ejecta (including those of supernovae) about to merge with the interstellar medium. The measurement of the microwave background, mixing of material between different nuclear burning zones in evolved stars and turbulent boundary layers (which are present in and influence the structures and evolution of all diffuse astrophysical sources) are treated.
12. Optical Polarization as a Probe of the Local Interstellar Medium
Science.gov (United States)
Tinbergen, J.
1984-01-01
The use of interstellar polarization as a tool for measuring interstellar dust is discussed. Problems resulting from dust and magnetic field configurations becoming mixed up are discussed, as is the availability of sufficiently bright stars to obtain the photons needed for precision measurements. It is proposed that: (1) on the scale of several hundred parsec, there is a preferential magnetic field direction, as evidenced by observations at the Galactic poles and selected longitudes in the Galactic plane; (2) the local (r 50 pc) region is devoid of dust, as evidenced by the mean square degree of polarization as a function of distance; and, less certainly, that (3) at a distance of less than 5 pc, there is a patch of dust which may be of interest in connection with cloud models.
13. The synthesis of complex molecules in interstellar clouds
Science.gov (United States)
Huntress, W. T., Jr.; Mitchell, G. F.
1979-01-01
The abundances of polyatomic molecules that may be formed by CH3(+) radiative association reactions in dense interstellar molecular clouds are reevaluated. The formation of a number of complex interstellar molecules via radiative association reactions involving ionic precursors other than CH3(+) is also investigated; these additional precursors include CH3O(+), CH3CO(+), CH5(+), HCO(+), NO(+), H2CN(+), C2H2(+), and NH3(+). The results indicate that the postulated gas-phase ion-molecule radiative association reactions could potentially explain the synthesis of most of the more complex species observed in dense molecular clouds such as Sgr B2. It is concluded, however, that in order to be conclusive, laboratory data are needed to show whether or not these reactions proceed at the required rates at low temperatures.
14. On the carbon enrichment of the interstellar medium
International Nuclear Information System (INIS)
Sarmiento, A.; Peimbert, M.
1985-01-01
The contribution of novae, IMS, and massive stars to the 12 C and 13 C enrichment of the interstellar medium is evaluated. The following results are obtained: a) novae are not important contributors to the 12 C abundance but contribute significantly to 13 C, b) limits to the ratio of the mixing length to the pressure scale height,α, and to the mass loss rate parameter, eta, are derived for IMS, c) IMS are the main contributors to the 12 C and 13 C enrichment of the interstellar medium, d) it is easier to explain the solar vicinity 12 C/ 13 C ratio than the solar system ratio, e) to explain the 12 C/ 13 C ratio in the ISM the mass ejected per nova outburst has to be approx. 1 x 10 -5 M sub(sun). (author)
15. The nature of interstellar dust as revealed by light scattering
Directory of Open Access Journals (Sweden)
D. A. Williams
2011-09-01
Full Text Available Interstellar dust was first identified through the extinction that it causes of optical starlight. Initially, observational and theoretical studies of extinction were made to identify simple ways of removing the effect of extinction. Over the last few decades it has become clear that dust has a number of very important roles in interstellar physics and chemistry, and that through these roles dust affects quite fundamentally the evolution of the Milky Way and other galaxies. However, our detailed knowledge of the actual material of dust remains relatively poor. The use of accurate models for the interaction of electromagnetic radiation with particles of arbitrary shape and composition remains vital, if our description of dust is to improve.
16. Fission-Based Electric Propulsion for Interstellar Precursor Missions
International Nuclear Information System (INIS)
HOUTS, MICHAEL G.; LENARD, ROGER X.; LIPINSKI, RONALD J.; PATTON, BRUCE; POSTON, DAVID; WRIGHT, STEVEN A.
1999-01-01
This paper reviews the technology options for a fission-based electric propulsion system for interstellar precursor missions. To achieve a total ΔV of more than 100 km/s in less than a decade of thrusting with an electric propulsion system of 10,000s Isp requires a specific mass for the power system of less than 35 kg/kWe. Three possible configurations are described: (1) a UZrH-fueled,NaK-cooled reactor with a steam Rankine conversion system,(2) a UN-fueled gas-cooled reactor with a recuperated Brayton conversion system, and (3) a UN-fueled heat pipe-cooled reactor with a recuperated Brayton conversion system. All three of these systems have the potential to meet the specific mass requirements for interstellar precursor missions in the near term. Advanced versions of a fission-based electric propulsion system might travel as much as several light years in 200 years
17. Interstellar material in front of chi ophiuchi. I. Optical observations
International Nuclear Information System (INIS)
Frisch, P.C.
1979-01-01
Optical observations of the interstellar material in front of chi Oph are discussed. The main interstellar cloud is made up of several regions with velocities between -6 and -12 km s -1 (heliocentric). Both CH and CH + are found within this feature, but with central velocities which differ by 2 km s -1 . Another cloud, with a velocity of -26 km s -1 , contains relatively strong Ca + lines. It has a ratio between Ca + and Na 0 column densities that is appropriate for ''high-velocity'' clouds. Calcium, iron, and sodium column densities are used to estimate an average electron density for the line of sight as well as for each cloud. The abundances of CH and CH + , and the absence of CN, are analyzed in terms of current theories about their origin
18. Energetic Processing of Interstellar Silicate Grains by Cosmic Rays
Energy Technology Data Exchange (ETDEWEB)
Bringa, E M; Kucheyev, S O; Loeffler, M J; Baragiola, R A; Tielens, A G Q M; Dai, Z R; Graham, G; Bajt, S; Bradley, J; Dukes, C A; Felter, T E; Torres, D F; van Breugel, W
2007-03-28
While a significant fraction of silicate dust in stellar winds has a crystalline structure, in the interstellar medium nearly all of it is amorphous. One possible explanation for this observation is the amorphization of crystalline silicates by relatively 'low' energy, heavy ion cosmic rays. Here we present the results of multiple laboratory experiments showing that single-crystal synthetic forsterite (Mg{sub 2}SiO{sub 4}) amorphizes when irradiated by 10 MeV Xe{sup ++} ions at large enough fluences. Using modeling, we extrapolate these results to show that 0.1-5.0 GeV heavy ion cosmic rays can rapidly ({approx}70 Million yrs) amorphize crystalline silicate grains ejected by stars into the interstellar medium.
Science.gov (United States)
Löhmer, O.; Mitra, D.; Gupta, Y.; Kramer, M.; Ahuja, A.
2004-10-01
Using radio pulsars as probes of the interstellar medium (ISM) we study the frequency evolution of interstellar scattering. The frequency dependence of scatter broadening times, τsc, for most of the pulsars with low and intermediate dispersion measures (DM ≲ 400 pc cm-3) is consistent with the Kolmogorov spectrum of electron density fluctuations in a turbulent medium. In contrast, the measured τsc's for highly dispersed pulsars in the central region of the Galaxy are larger than expected and show a spectrum which is flatter than the Kolmogorov law. We analyse the first measurements of spectral indices of scatter broadening over the full known DM range and discuss possible explanations for the anomalous scattering behaviour along peculiar lines of sight (LOS).
20. Spiral arms and a supernova-dominated interstellar medium
International Nuclear Information System (INIS)
Brand, P.W.J.L.; Heathcote, S.R.
1982-01-01
Models of the interstellar medium (ISM) utilizing the large energy output of supernovae to determine the average kinematical properties of the gas, are subjected to an imposed (spiral) density wave. The consequent appearance of the ISM is considered. In particular the McKee-Ostriker model with cloud evaporation is used, but it is shown that the overall appearance of the galaxy model does not change significantly if a modification of Cox's mechanism, with no cloud evaporation, is incorporated. It is found that a spiral density wave shock can only be self-sustaining if quite restrictive conditions are imposed on the values of the galactic supernova rate and the mean interstellar gas density. (author)
1. Tholins - Organic chemistry of interstellar grains and gas
Science.gov (United States)
Sagan, C.; Khare, B. N.
1979-01-01
The paper discusses tholins, defined as complex organic solids formed by the interaction of energy - for example, UV light or spark discharge - with various mixtures of cosmically abundant gases - CH4, C2H6, NH3, H2O, HCHO, and H2S. It is suggested that tholins occur in the interstellar medium and are responsible for some of the properties of the interstellar grains and gas. Additional occurrences of tholins are considered. Tholins have been produced experimentally; 50 or so pyrolytic fragments of the brown, sometimes sticky substances have been identified by gas chromatography-mass spectrometry, and the incidence of these fragments in tholins produced by different procedures is reported.
2. Chemical Evolution in the Interstellar Medium: From Astrochemistry to Astrobiology
Science.gov (United States)
Allamandola, Louis J.
2009-01-01
Great strides have been made in our understanding of interstellar material thanks to advances in infrared astronomy and laboratory astrophysics. Ionized polycyclic aromatic hydrocarbons (PAHs), shockingly large molecules by earlier astrochemical standards, are widespread and very abundant throughout much of the Universe. In cold molecular clouds, the birthplace of planets and stars, interstellar molecules freeze onto dust and ice particles forming mixed molecular ices dominated by simple species such as water, methanol, ammonia, and carbon monoxide. Within these clouds, and especially in the vicinity of star and planet forming regions, these ices and PAHs are processed by ultraviolet light and cosmic rays forming hundreds of far more complex species, some of biogenic interest. Eventually, these are delivered to primordial planets by comets and meteorites. Astrochemical evolution, highlights of this field from a chemist's perspective, and the astronomer's infrared toolbox will be reviewed.
3. High-sensitivity Raman spectrometer to study pristine and irradiated interstellar ice analogs.
Science.gov (United States)
Bennett, Chris J; Brotton, Stephen J; Jones, Brant M; Misra, Anupam K; Sharma, Shiv K; Kaiser, Ralf I
2013-06-18
We discuss the novel design of a sensitive, normal-Raman spectrometer interfaced to an ultra-high vacuum chamber (5 × 10(-11) Torr) utilized to investigate the interaction of ionizing radiation with low temperature ices relevant to the solar system and interstellar medium. The design is based on a pulsed Nd:YAG laser which takes advantage of gating techniques to isolate the scattered Raman signal from the competing fluorescence signal. The setup incorporates innovations to achieve maximum sensitivity without detectable heating of the sample. Thin films of carbon dioxide (CO2) ices of 10 to 396 nm thickness were prepared and characterized using both Fourier transform infrared (FT-IR) spectroscopy and HeNe interference techniques. The ν+ and ν- Fermi resonance bands of CO2 ices were observed by Raman spectroscopy at 1385 and 1278 cm(-1), respectively, and the band areas showed a linear dependence on ice thickness. Preliminary irradiation experiments are conducted on a 450 nm thick sample of CO2 ice using energetic electrons. Both carbon monoxide (CO) and the infrared inactive molecular oxygen (O2) products are readily detected from their characteristic Raman bands at 2145 and 1545 cm(-1), respectively. Detection limits of 4 ± 3 and 6 ± 4 monolayers of CO and O2 were derived, demonstrating the unique power to detect newly formed molecules in irradiated ices in situ. The setup is universally applicable to the detection of low-abundance species, since no Raman signal enhancement is required, demonstrating Raman spectroscopy as a reliable alternative, or complement, to FT-IR spectroscopy in space science applications.
4. SYSTEMATIC THEORETICAL STUDY ON THE INTERSTELLAR CARBON CHAIN MOLECULES
Energy Technology Data Exchange (ETDEWEB)
Etim, Emmanuel E.; Arunan, Elangannan [Inorganic and Physical Chemistry Department, Indian Institute of Science Bangalore, 560012 (India); Gorai, Prasanta; Das, Ankan [Indian Centre for Space Physics, 43 Chalantika, Garia Station Road, Kolkata 700 084 (India); Chakrabarti, Sandip K., E-mail: [email protected] [Department of Chemical Sciences, Federal University Wukari, Katsina-Ala Road, P.M.B. 1020 Wukari, Taraba State (Nigeria)
2016-12-01
In an effort to further our interest in understanding the basic chemistry of interstellar molecules, here we carry out an extensive investigation of the stabilities of interstellar carbon chains; C{sub n}, H{sub 2}C{sub n}, HC{sub n}N and C{sub n}X (X = N, O, Si, S, H, P, H{sup −}, N{sup −}). These sets of molecules account for about 20% of all the known interstellar and circumstellar molecules. Their high abundances, therefore, demand serious attention. High-level ab initio quantum chemical calculations are employed to accurately estimate the enthalpy of formation, chemical reactivity indices, global hardness and softness, and other chemical parameters of these molecules. Chemical modeling of the abundances of these molecular species has also been performed. Of the 89 molecules considered from these groups, 47 have been astronomically observed, and these observed molecules are found to be more stable with respect to other members of the group. Of the 47 observed molecules, 60% are odd-numbered carbon chains. Interstellar chemistry is not actually driven by thermodynamics, but it is primarily dependent on various kinetic parameters. However, we found that the detectability of the odd-numbered carbon chains could be correlated due to the fact that they are more stable than the corresponding even-numbered carbon chains. Based on this aspect, the next possible carbon chain molecule for astronomical observation in each group is proposed. The effect of kinetics in the formation of some of these carbon chain molecules is also discussed.
5. Superconducting ion scoop and its application to interstellar flight
Energy Technology Data Exchange (ETDEWEB)
Matloff, G L; Fennelly, A J
1974-09-01
Physical and engineering aspects of a superconducting ion scoop with an effective field radius of 10/sup 4/ km are discussed. Application of the system to interstellar ramjet travel is considered. Used in conjunction with a large boron sail towed behind the spacecraft, the scoop could be applied as a deceleration mechanism for thermonuclear-rocket-boosted vehicles moving at least as fast as 0.2C.
6. Hot interstellar tunnels. I. Simulation of interacting supernova remnants
International Nuclear Information System (INIS)
Smith, B.W.
1977-01-01
Reexamining a suggestion of Cox and Smith, we find that intersecting supernova remnants can indeed generate and maintain hot interstellar regions with napproximately-less-than10 -2 cm -3 and Tapprox.10 6 K. These regions are likely to occupy at least 30% of the volume of a spiral arm near the midplane of the gaseous disk if the local supernova rate there is greater than 1.5 x 10 -7 Myr -1 pc -3 . Their presence in the interstellar medium is supported by observations of the soft X-ray background. The theory required to build a numerical simulation of interacting supernova remnants is developed. The hot cavities within a population of remnants will become connected for a variety of assumed conditions in the outer shells of old remnants. Extensive hot cavity regions or tunnels are built and enlarged by supernovae occurring in relatively dense gas which produce connections, but tunnels are kept hot primarily by supernovae occurring within the tunnels. The latter supernovae initiate fast shock waves which apparently reheat tunnels faster than they are destroyed by thermal conduction in a galactic magnetic field or by radiative cooling. However, the dispersal of these rejuvenating shocks over a wide volume is inhibited by motions of cooler interstellar gas in the interval between shocks. These motions disrupt the contiguity of the component cavities of a tunnel and may cause its death.The Monte Carlo simulations indicate that a quasi-equilibrium is reached within 10 7 years of the first supernova in a spiral arm. This equilibrium is characterized by a constant average filling fraction for cavities in the interstellar volume. Aspects of the equilibrium are discussed for a range of supernova rates. Two predictions of Cox and Smith are not confirmed within this range: critical growth of hot regions to encompass the entire medium, and the efficient quenching of a remnant's expansion by interaction with other cavities
7. The Abundance of Mg in the Interstellar Medium
Science.gov (United States)
Fitzpatrick, Edward L.
1997-06-01
An empirical determination of the f-values of the far-UV Mg II λλ1239, 1240 lines is reported. The strong near-UV Mg II λλ2796, 2803 lines are generally highly saturated along most interstellar sight lines outside the local interstellar medium (ISM) and usually yield extremely uncertain estimates of Mg+ column densities in interstellar gas. Since Mg+ is the dominant form of Mg in the neutral ISM, and since Mg is expected to be a significant constituent of interstellar dust grains, the far-UV lines are critical for assessing the role of this important element in the ISM. This study consists of complete component analyses of the absorption along the lines of sight toward HD 93521 in the Galactic halo and ξ Persei and ζ Ophiuchi in the Galactic disk, including all four UV Mg+ lines and numerous other transitions. The three analyses yield consistent determinations of the λλ1239, 1240 f-values, with weighted means of (6.4 +/- 0.4) × 10-4 and (3.2 +/- 0.2) × 10-4, respectively. These results are a factor of ~2.4 larger than a commonly used theoretical estimate, and a factor of ~2 smaller than a recently suggested empirical revision. The effects of this result on gas- and dust-phase abundance measurements of Mg are discussed. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, under NASA contract NAS5-2655. This Letter is dedicated to the memory of Professor Lyman Spitzer Jr. He was a great guy.
8. Plasma Diagnostics of the Interstellar Medium with Radio Astronomy
OpenAIRE
Haverkorn, Marijke; Spangler, Steven R.
2013-01-01
We discuss the degree to which radio propagation measurements diagnose conditions in the ionized gas of the interstellar medium (ISM). The "signal generators" of the radio waves of interest are extragalactic radio sources (quasars and radio galaxies), as well as Galactic sources, primarily pulsars. The polarized synchrotron radiation of the Galactic non-thermal radiation also serves to probe the ISM, including space between the emitting regions and the solar system. Radio propagation measurem...
9. The variation of interstellar element abundances with hydrogen density
International Nuclear Information System (INIS)
Keenan, F.P.; Hibbert, A.; Dufton, P.L.; Murray, M.J.
1986-01-01
The variation of the interstellar nitrogen, oxygen and magnesium abundances with mean line-of-sight hydrogen density is analysed in terms of a two-component model, which consists of warm, low-density neutral gas and cold clouds. In all cases the gas-phase abundances have been deduced using reliable oscillator strengths specifically calculated for this purpose. Depletions in the warm and cold gas, are derived from non-linear least-squares fits to the data. (author)
10. A chemical model for the interstellar medium in galaxies
OpenAIRE
Bovino, S.; Grassi, Tommaso; Capelo, P. R.; Schleicher, D. R. G.; Banerjee, R.
2016-01-01
Aims: We present and test chemical models for three-dimensional hydrodynamical simulations of galaxies. We explore the effect of changing key parameters such as metallicity, radiation, and non-equilibrium versus equilibrium metal cooling approximations on the transition between the gas phases in the interstellar medium. Methods: The microphysics was modelled by employing the public chemistry package KROME, and the chemical networks were tested to work in a wide range of densities and temp...
11. HERSCHEL/HIFI DISCOVERY OF HCL+ IN THE INTERSTELLAR MEDIUM
International Nuclear Information System (INIS)
De Luca, M.; Gerin, M.; Falgarone, E.; Gupta, H.; Drouin, B. J.; Pearson, J. C.; Neufeld, D.; Teyssier, D.; Lis, D. C.; Monje, R.; Phillips, T. G.; Goicoechea, J. R.; Godard, B.; Bell, T. A.; Coutens, A.
2012-01-01
The radical ion HCl + , a key intermediate in the chlorine chemistry of the interstellar gas, has been identified for the first time in the interstellar medium with the Herschel Space Observatory's Heterodyne Instrument for the Far-Infrared. The ground-state rotational transition of H 35 Cl + , 2 Π 3/2 J = 5/2-3/2, showing Λ-doubling and hyperfine structure, is detected in absorption toward the Galactic star-forming regions W31C (G10.6-0.4) and W49N. The complex interstellar absorption features are modeled by convolving in velocity space the opacity profiles of other molecular tracers toward the same sources with the fine and hyperfine structure of HCl + . This structure is derived from a combined analysis of optical data from the literature and new laboratory measurements of pure rotational transitions, reported in the accompanying Letter by Gupta et al. The models reproduce well the interstellar absorption, and the frequencies inferred from the astronomical observations are in exact agreement with those calculated using spectroscopic constants derived from the laboratory data. The detection of H 37 Cl + toward W31C, with a column density consistent with the expected 35 Cl/ 37 Cl isotopic ratio, provides additional evidence for the identification. A comparison with the chemically related molecules HCl and H 2 Cl + yields an abundance ratio of unity with both species (HCl + : H 2 Cl + : HCl ∼ 1). These observations also yield the unexpected result that HCl + accounts for 3%-5% of the gas-phase chlorine toward W49N and W31C, values several times larger than the maximum fraction (∼1%) predicted by chemical models.
12. Source of the 26Al observed in the interstellar medium
International Nuclear Information System (INIS)
Dearborn, D.S.P.; Blake, J.B.
1985-01-01
Recent HEAO 3 observations have been interpreted by Mahoney and colleagues as requiring approximately 3 M/sub sun/ of 26 Al alive in the interstellar medium. Calculations briefly discussed in this Letter indicate that there is substantial production and dispersal of 26 Al in the stellar winds of O and W-R stars and suggest that the stellar winds of very massive stars are a significant source of 26 Al
13. Numerical study of rotating interstellar clouds: equilibrium and collapse
International Nuclear Information System (INIS)
Norman, M.L.
1980-06-01
Equilibrium and collapse of rotating, axisymmetric, idealized interstellar gas clouds is calculated with a 2D hydrodynamics code. The hydrodynamics features an improved angular momentum advection algorithm. Angular momentum is advected consistently with mass by deriving angular momentum fluxes from mass fluxes and the local distribution of specific angular momentum. Local conservation is checked by a graph of mass versus specific angular momentum for the cloud as a whole
14. Skating on thin ice: surface chemistry under interstellar conditions
Science.gov (United States)
Fraser, H.; van Dishoeck, E.; Tielens, X.
Solid CO2 has been observed towards both active star forming regions and quiescent clouds (Gerakines et. al. (1999)). The high abundance of CO2 in the solid phase, and its low abundance in the gas phase, support the idea that CO2 is almost exclusively formed in the solid state. Several possible formation mechanisms have been postulated (Ruffle &Herbst (2001): Charnley &Kaufman (2000)), and the detection of CO2 towards quiescent sources such as Elias 16 (Whittet et. al. (1998)) clearly suggests that CO2 can be produced in the absence of UV or electron mediated processes. The most likely route is via the surface reactions between O atoms, or OH radicals, and CO. The tools of modern surface- science offer us the potential to determine many of the physical and chemical attributes of icy interstellar grain mantles under highly controlled conditions, that closely mimic interstellar environments. The Leiden Surface Reaction Simulation Device ( urfreside) combines UHV (UltraS High Vacuum) surface science techniques with an atomic beam to study chemical reactions occurring on the SURFACE and in the BULK of interstellar ice grain mimics. By simultaneously combining two or more surface analysis techniques, the chemical kinetics, reaction mechanisms and activation energies can be determined directly. The experiment is aimed at identifying the key barrierless reactions and desorption pathways on and in H2 O and CO ices under interstellar conditions. The results from traditional HV (high vacuum) and UHV studies of the CO + O and CO + OH reactions will be presented in this paper. Charnley, S.B., & Kaufman, M.J., 2000, ApJ, 529, L111 Gerakines, P.A., 1999, ApJ, 522, 357 Ruffle, D.P., & Herbst, E., 2001, MNRAS, 324, 1054 Whittet, D.C.B., et.al., 1998, ApJ, 498, L159
15. Dissociative recombination of interstellar ions: electronic structure calculations for HCO+
International Nuclear Information System (INIS)
Kraemer, W.P.; Hazi, A.U.
1985-01-01
The present study of the interstellar formyl ion HCO + is the first attempt to investigate dissociative recombination for a triatomic molecular ion using an entirely theoretical approach. We describe a number of fairly extensive electronic structure calculations that were performed to determine the reaction mechanism of the e-HCO + process. Similar calculations for the isoelectronic ions HOC + and HN 2 + are in progress. 60 refs
16. Interstellar scattering in the inner parts of the galaxy
International Nuclear Information System (INIS)
Rao, A.P.; Ananthakrishnan, S.
1984-01-01
A new survey of the galactic plane for sources with size less than 1 arc s at 327 MHz shows that towards the inner parts of the galaxy for galactic latitudes less than 5deg, interstellar scattering is much larger than expected from data at higher latitudes. The enhanced scattering varies both with galactic latitude and longitude. A two-component model for the distribution of scattering matter in the Galaxy is proposed to interpret the observations. (author)
17. Interaction of Interstellar Shocks with Dense Obstacles: Formation of Bullets''
Science.gov (United States)
The so-called cumulative effect take place in converging conical shock waves arising behind dense obstacles overtaken by incident interstellar shock. A significant part of energy of converging flow of matter swept-up by a radiative conical shock can be transferred to a dense jet-like ejection (bullet'') directed along the cone axis. Possible applications of this effect for star-forming regions (e.g., OMC-1) and supernova remnants (e.g., Vela SNR) are discussed.
18. THz Time-Domain Spectroscopy of Interstellar Ice Analogs
Science.gov (United States)
Ioppolo, Sergio; McGuire, Brett A.; de Vries, Xander; Carroll, Brandon; Allodi, Marco; Blake, Geoffrey
2015-08-01
The unambiguous identification of nearly 200 molecular species in different astronomical environments proves that our cosmos is a ‘Molecular Universe’. The cumulative outcome of recent observations, laboratory studies, and astrochemical models indicates that there is a strong interplay between the gas and the solid phase throughout the process of forming molecules in space. Observations of interstellar ices are generally limited to lines-of-sight along which infrared absorption spectroscopy is possible. Therefore, the identification of more complex prebiotic molecules in the mid-IR is difficult because of their low expected interstellar abundances and the overlap of their absorption features with those from the more abundant species. In the THz region, telescopes can detect Interstellar ices in emission or absorption against dust continuum. Thus, THz searches do not require a background point source. Moreover, since THz spectra are the fingerprint of inter- and intramolecular forces, complex species can present unique modes that do not overlap with those from simpler, more abundant molecules. THz modes are also sensitive to temperature and phase changes in the ice. Therefore, spectroscopy at THz frequencies has the potential to better characterize the physics and chemistry of the ISM. Currently, the Herschel Space Telescope, SOFIA, and ALMA databases contain a vast amount of new THz spectral data that require THz laboratory spectra for interpretation. The latter, however, are largely lacking. We have recently constructed a new THz time-domain spectroscopy system operating in the range between 0.3 - 7.5 THz. This work focuses on the laboratory investigation of the composition and structure of the most abundant interstellar ice analogs compared to some more complex species. Different temperatures, mixing ratios, and matrix isolation experiments will be shown. The ultimate goal of this research is to provide the scientific community with an extensive THz ice
19. INTERSTELLAR PICKUP ION PRODUCTION IN THE GLOBAL HELIOSPHERE AND HELIOSHEATH
Energy Technology Data Exchange (ETDEWEB)
Wu, Y.; Florinski, V.; Guo, X., E-mail: [email protected] [Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL 35805 (United States)
2016-11-20
Interstellar pickup ions (PUIs) play a significant part in mediating the solar wind (SW) interaction with the interstellar medium. In this paper, we examine the details of spatial variation of the PUI velocity distribution function (VDF) in the SW by solving the PUI transport equation. We assume the PUI distribution is isotropic resulting from strong pitch-angle scattering by wave–particle interaction. A three-dimensional model combining the MHD treatment of the background SW and neutrals with a kinetic treatment of PUIs throughout the heliosphere and the surrounding local interstellar medium has been developed. The model generates PUI power-law tails via second-order Fermi process. We analyze how PUIs transform across the heliospheric termination shock and obtain the PUI phase space distribution in the inner heliosheath including continuing velocity diffusion. Our simulated PUI spectra are compared with observations made by New Horizons , Ulysses , Voyager 1, 2 , and Cassini , and a satisfactory agreement is demonstrated. Some specific features in the observations, for example, a cutoff of PUI VDF at v = V {sub SW} and a f ∝ v {sup -5} tail in the reference frame of the SW, are well represented by the model.
20. The Starflight Handbook: A Pioneer's Guide to Interstellar Travel
Science.gov (United States)
Mallove, Eugene F.; Matloff, Gregory L.
1989-06-01
The Starflight Handbook A Pioneer's Guide to Interstellar Travel "The Starflight Handbook is an indispensable compendium of the many and varied methods for traversing the vast interstellar gulf--don't leave the Solar System without it!" --Robert Forward "Very sensible, very complete and useful. Its good use of references and technical sidebars' adds to the book and allows the nontechnical text to be used by ordinary readers in an easy fashion. I certainly would recommend this book to anyone doing any thinking at all about interstellar flight or the notion of possibilities of contacts between hypothetical civilizations in different stat systems." --Louis Friedman Executive Director, The Planetary Society The Starflight Handbook is the first and only compendium on planet Earth of the radical new technologies now on the drawing boards of some of our smartest and most imaginative space scientists and engineers. Scientists and engineers as well as general readers will be captivated by its: In-depth discussions of everything from nuclear pulse propulsion engines to in-flight navigation, in flowing, non-technical language Sidebars and appendices cover technical and mathematical concepts in detail Seventy-five elegant and enlightening illustrations depicting starships and their hardware
1. Laboratory studies of ion-molecule reactions and interstellar chemistry
International Nuclear Information System (INIS)
Koyano, Inosuke
1989-01-01
Several types of laboratory studies have been performed on ion-molecule reactions relevant to the formation of the interstellar molecules. Special emphasis is placed on the formation, structure, and reactivity of the C 3 H 3 + ions, which are believed to play a key role in interstellar chemistry. When these ions are produced by the reaction of C 3 H 4+ with C 3 H 4 in a beam-gas arrangement, their times-of-flight (TOF) show abnormally broad distributions regardless of the sources of the reactant C 3 H 4 + ion (photoionization of allene, propyne, the cyclopropene) and the nature of the neutral reactant, while all other product ions from the same reaction show sharp TOF distributions. On the other hand, all C 3 H 3 + ions produced by unimolecular decomposition of energetic C 3 H 4 + ions show sharp TOF distribution. The peculiarity of the C 3 H 3 + ions manifested in these and other experiments is discussed in conjunction with interstellar chemistry
2. INTERSTELLAR GAS FLOW PARAMETERS DERIVED FROM INTERSTELLAR BOUNDARY EXPLORER-Lo OBSERVATIONS IN 2009 AND 2010: ANALYTICAL ANALYSIS
International Nuclear Information System (INIS)
Möbius, E.; Bochsler, P.; Heirtzler, D.; Kucharek, H.; Lee, M. A.; Leonard, T.; Schwadron, N. A.; Wu, X.; Petersen, L.; Valovcin, D.; Wurz, P.; Bzowski, M.; Kubiak, M. A.; Fuselier, S. A.; Crew, G.; Vanderspek, R.; McComas, D. J.; Saul, L.
2012-01-01
Neutral atom imaging of the interstellar gas flow in the inner heliosphere provides the most detailed information on physical conditions of the surrounding interstellar medium (ISM) and its interaction with the heliosphere. The Interstellar Boundary Explorer (IBEX) measured neutral H, He, O, and Ne for three years. We compare the He and combined O+Ne flow distributions for two interstellar flow passages in 2009 and 2010 with an analytical calculation, which is simplified because the IBEX orientation provides observations at almost exactly the perihelion of the gas trajectories. This method allows separate determination of the key ISM parameters: inflow speed, longitude, and latitude, as well as temperature. A combined optimization, as in complementary approaches, is thus not necessary. Based on the observed peak position and width in longitude and latitude, inflow speed, latitude, and temperature are found as a function of inflow longitude. The latter is then constrained by the variation of the observed flow latitude as a function of observer longitude and by the ratio of the widths of the distribution in longitude and latitude. Identical results are found for 2009 and 2010: an He flow vector somewhat outside previous determinations (λ ISM∞ = 79. 0 0+3. 0 0(–3. 0 5), β ISM∞ = –4. 0 9 ± 0. 0 2, V ISM∞ 23.5 + 3.0(–2.0) km s –1 , T He = 5000-8200 K), suggesting a larger inflow longitude and lower speed. The O+Ne temperature range, T O+Ne = 5300-9000 K, is found to be close to the upper range for He and consistent with an isothermal medium for all species within current uncertainties.
3. Spectral Study of A 1Π–X 1Σ+ Transitions of CO Relevant to Interstellar Clouds
Science.gov (United States)
Cheng, Junxia; Zhang, Hong; Cheng, Xinlu
2018-05-01
Highly correlated ab initio calculations were performed for an accurate determination of the A 1Π–X 1Σ+ system of the CO molecule. A highly accurate multi-reference configuration interaction approach was used to investigate the potential energy curves (PECs) and the transition dipole moment curve (TDMC). The resultant PECs and TDMC found by using the aug-cc-pV5Z (aV5Z) basis set and 5330 active spaces are in good agreement with the experimental data. Moreover, the Einstein A coefficients, lifetimes, ro-vibrational intensities, absorption oscillator strengths, and integrated cross sections are calculated so that the vibrational bands include v″ = 0–39 \\to v‧ = 0–23. For applications in the atmosphere and interstellar clouds, we studied the transition lineshapes to Gaussian and Lorentzian profiles at different temperatures and pressures. The intensities were calculated at high temperature that was used to satisfy some astrophysical applications, such as in planetary atmospheres. The results are potentially useful for important SAO/NASA Astrophysics Data System and databases such as HITRAN, HITEMP, and the National Institute of Standards and Technology. Because the results from many laboratory techniques and our calculations now agree, analyses of interstellar CO based on absorption from A 1Π–X 1Σ+ are no longer hindered by present spectral parameters.
4. The third flight of CHESS: Preliminary analysis of interstellar H2 on the β1 Sco sightline
Science.gov (United States)
Kruczek, Nick; France, Kevin
2018-01-01
We describe the scientific motivation and technical development of the Colorado High-resolution Echelle Stellar Spectrograph (CHESS), focusing on the preliminary science results for the third launch of the payload (CHESS-3). CHESS is a far ultraviolet rocket-borne instrument designed to study the atomic-to-molecular transitions within translucent cloud regions in the interstellar medium. CHESS is an objective echelle spectrograph, which uses a mechanically-ruled echelle and a powered (f/12.4) cross-dispersing grating, and is designed to achieve a resolving power R > 100,000 over the band pass λλ 1000-1600 Å. CHESS-3 launched on 14 June 2017 aboard NASA/CU sounding rocket mission 36.323 UG. The target for the flight was β1 Sco, a B1V star with a sightline that is likely sampling translucent material. We present flight results of interstellar molecular hydrogen excitation, including initial measurements of the column density and temperature, on the sightline.
5. Wide Band to ''Double Band'' upgrade
International Nuclear Information System (INIS)
Kasper, P.; Currier, R.; Garbincius, P.; Butler, J.
1988-06-01
The Wide Band beam currently uses electrons obtained from secondary photon conversions to produce the photon beam incident on the experimental targets. By transporting the positrons produced in these conversions as well as the electrons it is possible to almost double the number of photons delivered to the experiments per primary beam proton. 11 figs
6. Interstellar and Solar Nebula Materials in Cometary Dust
Science.gov (United States)
Messenger, Scott; Nakamura-Messenger, Keiko; Keller, Lindsay; Nguyen, Ann; Clemett, Simon
2017-01-01
Laboratory studies of cometary dust collected in the stratosphere and returned from comet 81P/Wild 2 by the Stardust spacecraft have revealed ancient interstellar grains and molecular cloud organic matter that record a range of astrophysical processes and the first steps of planetary formation. Presolar materials are rarer meteorites owing to high temperature processing in the solar nebula and hydrothermal alteration on their asteroidal parent bodies. The greater preservation of presolar materials in comets is attributed to their low accretion temperatures and limited planetary processing. Yet, comets also contain a large complement of high temperature materials from the inner Solar System. Owing to the limited and biased sampling of comets to date, the proportions of interstellar and Solar System materials within them remains highly uncertain. Interstellar materials are identified by coordinated isotopic, mineralogical, and chemical measurements at the scale of individual grains. Chondritic porous interplanetary dust particles (CP IDPs) that likely derive from comets are made up of 0.1 - 10 micron-sized silicates, Fe-Ni-sulfides, oxides, and other phases bound by organic material. As much as 1% of the silicates are interstellar grains that have exotic isotopic compositions imparted by nucleosynthetic processes in their parent stars. Crystalline silicates in CP IDPs dominantly have normal isotopic compositions and probably formed in the Solar System. 81P samples include isotopically normal refractory minerals that resemble Ca-Al rich inclusions and chondrules common in meteorites. The origins of sub-micron amorphous silicates in IDPs are not certain, but at least a few % of them are interstellar grains. The remainder have isotopic compositions consistent with Solar System origins and elemental compositions that are inconsistent with interstellar grain properties, thus favoring formation in the solar nebula [4]. The organic component in comets and primitive
7. Amniotic constriction bands
Science.gov (United States)
... Supplements Videos & Tools Español You Are Here: Home → Medical Encyclopedia → Amniotic band sequence URL of this page: //medlineplus.gov/ency/ ... birth. The baby should be delivered in a medical center that has specialists experienced in caring for babies ... or partial loss of function of a body part. Congenital bands affecting large parts of the body cause the ...
8. Stardust Interstellar Preliminary Examination VII: Synchrotron X-Ray Fluorescence Analysis of Six Stardust Interstellar Candidates Measured with the Advanced Photon Source 2-ID-D Microprobe
Science.gov (United States)
Allen, Carlton C.; Anderson, David; Bastien, Ron K.; Brenker, Frank E.; Flynn, George J.; Frank, David; Gainsforth, Zack; Sandford, Scott A.; Simionovici, Alexandre S.; Zolensky, Michael E.
2014-01-01
The NASA Stardust spacecraft exposed an aerogel collector to the interstellar dust passing through the solar system. We performed X-ray fluorescence element mapping and abundance measurements, for elements 19 < or = Z < or = 30, on six "interstellar candidates," potential interstellar impacts identified by Stardust@Home and extracted for analyses in picokeystones. One, I1044,3,33, showed no element hot-spots within the designated search area. However, we identified a nearby surface feature, consistent with the impact of a weak, high-speed particle having an approximately chondritic (CI) element abundance pattern, except for factor-of-ten enrichments in K and Zn and an S depletion. This hot-spot, containing approximately 10 fg of Fe, corresponds to an approximately 350 nm chondritic particle, small enough to be missed by Stardust@Home, indicating that other techniques may be necessary to identify all interstellar candidates. Only one interstellar candidate, I1004,1,2, showed a track. The terminal particle has large enrichments in S, Ti, Cr, Mn, Ni, Cu, and Zn relative to Fe-normalized CI values. It has high Al/Fe, but does not match the Ni/Fe range measured for samples of Al-deck material from the Stardust sample return capsule, which was within the field-of-view of the interstellar collector. A third interstellar candidate, I1075,1,25, showed an Al-rich surface feature that has a composition generally consistent with the Al-deck material, suggesting that it is a secondary particle. The other three interstellar candidates, I1001,1,16, I1001,2,17, and I1044,2,32, showed no impact features or tracks, but allowed assessment of submicron contamination in this aerogel, including Fe hot-spots having CI-like Ni/Fe ratios, complicating the search for CI-like interstellar/interplanetary dust.
9. ON THE FORMATION OF BENZOIC ACID AND HIGHER-ORDER BENZENE CARBOXYLIC ACIDS IN INTERSTELLAR MODEL ICE GRAINS
Energy Technology Data Exchange (ETDEWEB)
McMurtry, Brandon M.; Saito, Sean E. J.; Turner, Andrew M.; Chakravarty, Harish K.; Kaiser, Ralf I. [W. M. Keck Research Laboratory in Astrochemistry, University of Hawaii at Manoa, Honolulu, HI 96822 (United States)
2016-11-10
With a binary ice mixture of benzene (C{sub 6}H{sub 6}) and carbon dioxide (CO{sub 2}) at 10 K under contamination-free ultrahigh vacuum conditions, the formation of benzene carboxylic acids in interstellar ice grains was studied. Fourier transform infrared spectroscopy was used to probe for the formation of new species during the chemical processing of the ice mixture and during the following temperature-programmed desorption. Newly formed benzene carboxylic acid species, i.e., benzoic acid, as well as meta - and para -benzene dicarboxylic acid, were assigned using newly emerging bands in the infrared spectrum; a reaction mechanism, along with rate constants, was proposed utilizing the kinetic fitting of the coupled differential equations.
10. On the Formation of Interstellar Water Ice: Constraints from a Search for Hydrogen Peroxide Ice in Molecular Clouds
Science.gov (United States)
Smith, R. G.; Charnely, S. B.; Pendleton, Y. J.; Wright, C. M.; Maldoni, M. M.; Robinson, G.
2011-01-01
Recent surface chemistry experiments have shown that the hydrogenation of molecular oxygen on interstellar dust grains is a plausible formation mechanism, via hydrogen peroxide (H2O2), for the production of water (H2O) ice mantles in the dense interstellar medium. Theoretical chemistry models also predict the formation of a significant abundance of H2O2 ice in grain mantles by this route. At their upper limits, the predicted and experimental abundances are sufficiently high that H2O2 should be detectable in molecular cloud ice spectra. To investigate this further, laboratory spectra have been obtained for H2O2/H2O ice films between 2.5 and 200 micron, from 10 to 180 K, containing 3%, 30%, and 97% H2O2 ice. Integrated absorbances for all the absorption features in low-temperature H2O2 ice have been derived from these spectra. For identifying H2O2 ice, the key results are the presence of unique features near 3.5, 7.0, and 11.3 micron. Comparing the laboratory spectra with the spectra of a group of 24 protostars and field stars, all of which have strong H2O ice absorption bands, no absorption features are found that can definitely be identified with H2O2 ice. In the absence of definite H2O2 features, the H2O2 abundance is constrained by its possible contribution to the weak absorption feature near 3.47 micron found on the long-wavelength wing of the 3 micron H2O ice band. This gives an average upper limit for H2O2, as a percentage of H2O, of 9% +/- 4%. This is a strong constraint on parameters for surface chemistry experiments and dense cloud chemistry models.
11. On the formation of niacin (vitamin B3) and pyridine carboxylic acids in interstellar model ices
Energy Technology Data Exchange (ETDEWEB)
McMurtry, Brandon M.; Turner, Andrew M.; Saito, Sean E.J.; Kaiser, Ralf I. [W. M. Keck Research Laboratory in Astrochemistry, University of Hawaii at Manoa, Honolulu, Hawaii, HI 96822 (United States); Department of Chemistry, University of Hawaii at Manoa, Honolulu, Hawaii, HI 96822 (United States)
2016-06-15
The formation of pyridine carboxylic acids in interstellar ice grains was simulated by electron exposures of binary pyridine (C{sub 5}H{sub 5}N)-carbon dioxide (CO{sub 2}) ice mixtures at 10 K under contamination-free ultrahigh vacuum conditions. Chemical processing of the pristine ice and subsequent warm-up phase was monitored on line and in situ via Fourier transform infrared spectroscopy to probe for the formation of new radiation induced species. In the infrared spectra of the irradiated ice, bands assigned to nicotinic acid (niacin; vitamin B3; m-C{sub 5}H{sub 4}NCOOH) along with 2,3-, 2,5-, 3,4-, and 3,5-pyridine dicarboxylic acid (C{sub 5}H{sub 3}N(COOH){sub 2}) were unambiguously identified along with the hydroxycarbonyl (HOCO) radical. Our study suggests that the reactive pathway responsible for pyridine carboxylic acids formation involves a HOCO intermediate, which forms through the reaction of suprathermal hydrogen ejected from pyridine with carbon dioxide. The newly formed pyridinyl radical may then undergo radical–radical recombination with a hydroxycarbonyl radical to form a pyridine carboxylic acid.
12. DETAILED INTERSTELLAR POLARIMETRIC PROPERTIES OF THE PIPE NEBULA AT CORE SCALES
International Nuclear Information System (INIS)
Franco, G. A. P.; Alves, F. O.; Girart, J. M.
2010-01-01
We use R-band CCD linear polarimetry collected for about 12,000 background field stars in 46 fields of view toward the Pipe nebula to investigate the properties of the polarization across this dark cloud. Based on archival Two Micron All Sky Survey data, we estimate that the surveyed areas present total visual extinctions in the range 0.6 mag ≤ A V ≤ 4.6 mag. While the observed polarizations show a well-ordered large-scale pattern, with polarization vectors almost perpendicularly aligned to the cloud's long axis, at core scales one sees details that are characteristics of each core. Although many observed stars present degrees of polarization that are unusual for the common interstellar medium (ISM), our analysis suggests that the dust grains constituting the diffuse parts of the Pipe nebula seem to have the same properties as the normal Galactic ISM. Estimates of the second-order structure function of the polarization angles suggest that most of the Pipe nebula is magnetically dominated and that turbulence is sub-Alvenic. The Pipe nebula is certainly an interesting region to investigate the processes that prevailed during the initial phases of low-mass stellar formation.
13. Large scale features of the hot component of the interstellar medium
International Nuclear Information System (INIS)
Garmire, G.P.
1983-01-01
The interstellar medium contains identifiable hot plasma clouds occupying up to about 35% of the volume of the local galactic disc. The temperature of these clouds is not uniform but ranges from 10 5 up to 4 x 10 6 K. Besides the high temperature which places the emission spectrum in the soft X-ray band, the implied pressure of the hot plasma compared to the cooler gas reveals the importance of this component in determining the motions and evolution of the cooler gas in the disc, as well as providing a source of hot gas which may extend above the galactic disc to form a corona. The author presents data from the A-2 soft X-ray experiment on the HEAO-1 spacecraft concerning the large scale features of this gas. These features are interpreted in terms of the late phases of supernovae expansion, multiple supernovae and the possible creation of a hot halo surrounding the region of the galactic nucleus. (Auth.)
14. Consequences of the Solar System passage through dense interstellar clouds
Directory of Open Access Journals (Sweden)
A. G. Yeghikyan
2003-06-01
Full Text Available Several consequences of the passage of the solar system through dense interstellar molecular clouds are discussed. These clouds, dense (more than 100 cm-3, cold (10–50 K and extended (larger than 1 pc, are characterized by a gas-to-dust mass ratio of about 100, by a specific power grain size spectrum (grain radii usually cover the range 0.001–3 micron and by an average dust-to-gas number density ratio of about 10-12. Frequently these clouds contain small-scale (10–100 AU condensations with gas concentrations ranging up to 10 5 cm-3. At their casual passage over the solar system they exert pressures very much enhanced with respect to today’s standards. Under these conditions it will occur that the Earth is exposed directly to the interstellar flow. It is shown first that even close to the Sun, at 1 AU, the cloud’s matter is only partly ionized and should mainly interact with the solar wind by charge exchange processes. Dust particles of the cloud serve as a source of neutrals, generated by the solar UV irradiation of dust grains, causing the evaporation of icy materials. The release of neutral atoms from dust grains is then followed by strong influences on the solar wind plasma flow. The behavior of the neutral gas inflow parameters is investigated by a 2-D hydrodynamic approach to model the interaction processes. Because of a reduction of the heliospheric dimension down to 1 AU, direct influence of the cloud’s matter to the terrestrial environment and atmosphere could be envisaged.Key words. Interplanetary physics (heliopause and solar wind termination; interplanetary dust; interstellar gas
15. Consequences of the Solar System passage through dense interstellar clouds
Directory of Open Access Journals (Sweden)
A. G. Yeghikyan
Full Text Available Several consequences of the passage of the solar system through dense interstellar molecular clouds are discussed. These clouds, dense (more than 100 cm-3, cold (10–50 K and extended (larger than 1 pc, are characterized by a gas-to-dust mass ratio of about 100, by a specific power grain size spectrum (grain radii usually cover the range 0.001–3 micron and by an average dust-to-gas number density ratio of about 10-12. Frequently these clouds contain small-scale (10–100 AU condensations with gas concentrations ranging up to 10 5 cm-3. At their casual passage over the solar system they exert pressures very much enhanced with respect to today’s standards. Under these conditions it will occur that the Earth is exposed directly to the interstellar flow. It is shown first that even close to the Sun, at 1 AU, the cloud’s matter is only partly ionized and should mainly interact with the solar wind by charge exchange processes. Dust particles of the cloud serve as a source of neutrals, generated by the solar UV irradiation of dust grains, causing the evaporation of icy materials. The release of neutral atoms from dust grains is then followed by strong influences on the solar wind plasma flow. The behavior of the neutral gas inflow parameters is investigated by a 2-D hydrodynamic approach to model the interaction processes. Because of a reduction of the heliospheric dimension down to 1 AU, direct influence of the cloud’s matter to the terrestrial environment and atmosphere could be envisaged.
Key words. Interplanetary physics (heliopause and solar wind termination; interplanetary dust; interstellar gas
16. Rocket and satellite observations of the local interstellar medium
International Nuclear Information System (INIS)
Jelinsky, P.N.
1988-01-01
The purpose of the study described in this thesis was to obtained new information on the structure of the local interstellar medium (ISM). Two separate experiments using different instruments were used in this study. The first experiment employed a spectrometer with a spectral bandpass from 350-1150 angstrom which was placed at the focus of a 95 cm, f/2.8 normal incidence telescope flown on an Aries sounding rocket. The purpose of this experiment was to measure the interstellar absorption edges, due to neutral helium and neutral hydrogen, in the spectrum of a hot white dwarf. The hot white dwarf G191-B2B was observed for 87 seconds during the flight. Unfortunately, due to high pressure in the rocket, no scientifically useful data was obtained during the flight. The second experiment utilized the high resolution spectrometer on the International Ultraviolet Explorer satellite. The purpose of the experiment was to observe interstellar absorption lines in the spectrum of hot white dwarfs. A new method of determining the equivalent widths of absorption lines and their uncertainties was developed. The neutral hydrogen column density is estimated from the N I, Si II, and C II columns. Unfortunately, the uncertainties in the neutral hydrogen columns are very large, only two are constrained to better than an order of magnitude. High ionization species (N V, Si IV, and C IV) are seen in five of the stars. Upper limits to the temperature of the ISM are determined from the velocity dispersions. The temperature of the low ionization gas toward four of the stars is constrained to be less than 50,000 K
17. Stochastic histories of dust grains in the interstellar medium
International Nuclear Information System (INIS)
Liffman, K.; Clayton, D.D.
1989-01-01
The purpose is to study an evolving system of refractory dust grains within the Interstellar Medium (ISM). This is done via a combination of Monte Carlo processes and a system of partial differential equations, where refractory dust grains formed within supernova remnants and ejecta from high mass loss stars are subjected to the processes of sputtering and collisional fragmentation in the diffuse media and accretion within the cold molecular clouds. In order to record chemical detail, the authors take each new particle to consist of a superrefractory core plus a more massive refractory mantle. The particles are allowed to transfer to and fro between the different phases of the interstellar medium (ISM) - on a time scale of 10(exp 8) years - until either the particles are destroyed or the program finishes at a Galaxy time of 6x10(exp 9) years. The resulting chemical and size spectrum(s) are then applied to various astrophysical problems with the following results. For an ISM which has no collisional fragmentation of the dust grains, roughly 10 percent by mass of the most refractory material survives the rigors of the ISM intact, which leaves open the possibility that fossilized isotopically anomalous material may have been present within the primordial solar nebula. Stuctured or layered refractory dust grains within the model cannot explain the observed interstellar depletions of refractory material. Fragmentation due to grain-grain collisions in the diffuse phase plus the accretion of material in the molecular cloud phase can under certain circumstances cause a bimodal distribution in grain size
18. OBSERVATIONAL CONSTRAINTS ON METHANOL PRODUCTION IN INTERSTELLAR AND PREPLANETARY ICES
International Nuclear Information System (INIS)
Whittet, D. C. B.; Cook, A. M.; Herbst, Eric; Chiar, J. E.; Shenoy, S. S.
2011-01-01
Methanol (CH 3 OH) is thought to be an important link in the chain of chemical evolution that leads from simple diatomic interstellar molecules to complex organic species in protoplanetary disks that may be delivered to the surfaces of Earthlike planets. Previous research has shown that CH 3 OH forms in the interstellar medium predominantly on the surfaces of dust grains. To enhance our understanding of the conditions that lead to its efficient production, we assemble a homogenized catalog of published detections and limiting values in interstellar and preplanetary ices for both CH 3 OH and the other commonly observed C- and O-bearing species, H 2 O, CO, and CO 2 . We use this catalog to investigate the abundance of ice-phase CH 3 OH in environments ranging from dense molecular clouds to circumstellar envelopes around newly born stars of low and high mass. Results show that CH 3 OH production arises during the CO freezeout phase of ice-mantle growth in the clouds, after an ice layer rich in H 2 O and CO 2 is already in place on the dust, in agreement with current astrochemical models. The abundance of solid-phase CH 3 OH in this environment is sufficient to account for observed gas-phase abundances when the ices are subsequently desorbed in the vicinity of embedded stars. CH 3 OH concentrations in the ices toward embedded stars show order-of-magnitude object-to-object variations, even in a sample restricted to stars of low mass associated with ices lacking evidence of thermal processing. We hypothesize that the efficiency of CH 3 OH production in dense cores and protostellar envelopes is mediated by the degree of prior CO depletion.
19. Evolution of interstellar organic compounds under asteroidal hydrothermal conditions
Science.gov (United States)
Vinogradoff, V.; Bernard, S.; Le Guillou, C.; Remusat, L.
2018-05-01
Carbonaceous chondrites (CC) contain a diversity of organic compounds. No definitive evidence for a genetic relationship between these complex organic molecules and the simple organic molecules detected in the interstellar medium (ISM) has yet been reported. One of the many difficulties arises from the transformations of organic compounds during accretion and hydrothermal alteration on asteroids. Here, we report results of hydrothermal alteration experiments conducted on a common constituent of interstellar ice analogs, Hexamethylenetetramine (HMT - C6H12N4). We submitted HMT to asteroidal hydrothermal conditions at 150 °C, for various durations (up to 31 days) and under alkaline pH. Organic products were characterized by gas chromatography mass spectrometry, infrared spectroscopy and synchrotron-based X-ray absorption near edge structure spectroscopy. Results show that, within a few days, HMT has evolved into (1) a very diverse suite of soluble compounds dominated by N-bearing aromatic compounds (> 150 species after 31 days), including for instance formamide, pyridine, pyrrole and their polymers (2) an aromatic and N-rich insoluble material that forms after only 7 days of experiment and then remains stable through time. The reaction pathways leading to the soluble compounds likely include HMT dissociation, formose and Maillard-type reactions, e.g. reactions of sugar derivatives with amines. The present study demonstrates that, if interstellar organic compounds such as HMT had been accreted by chondrite parent bodies, they would have undergone chemical transformations during hydrothermal alteration, potentially leading to the formation of high molecular weight insoluble organic molecules. Some of the diversity of soluble and insoluble organic compounds found in CC may thus result from asteroidal hydrothermal alteration.
20. Band parameters of phosphorene
International Nuclear Information System (INIS)
Lew Yan Voon, L C; Wang, J; Zhang, Y; Willatzen, M
2015-01-01
Phosphorene is a two-dimensional nanomaterial with a direct band-gap at the Brillouin zone center. In this paper, we present a recently derived effective-mass theory of the band structure in the presence of strain and electric field, based upon group theory. Band parameters for this theory are computed using a first-principles theory based upon the generalized-gradient approximation to the density-functional theory. These parameters and Hamiltonian will be useful for modeling physical properties of phosphorene. (paper)
1. Band parameters of phosphorene
DEFF Research Database (Denmark)
Lew Yan Voon, L. C.; Wang, J.; Zhang, Y.
2015-01-01
Phosphorene is a two-dimensional nanomaterial with a direct band-gap at the Brillouin zone center. In this paper, we present a recently derived effective-mass theory of the band structure in the presence of strain and electric field, based upon group theory. Band parameters for this theory...... are computed using a first-principles theory based upon the generalized-gradient approximation to the density-functional theory. These parameters and Hamiltonian will be useful for modeling physical properties of phosphorene....
2. The Optical-Mid-infrared Extinction Law of the l = 165° Sightline in the Galactic Plane: Diversity of the Extinction Law in the Diffuse Interstellar Medium
Science.gov (United States)
Wang, Shu; Jiang, B. W.; Zhao, He; Chen, Xiaodian; de Grijs, Richard
2017-10-01
Understanding the effects of dust extinction is important to properly interpret observations. The optical total-to-selective extinction ratio, {R}V={A}V/E(B-V), is widely used to describe extinction variations in ultraviolet and optical bands. Since the {R}V=3.1 extinction curve adequately represents the average extinction law of diffuse regions in the Milky Way, it is commonly used to correct observational measurements along sightlines toward diffuse regions in the interstellar medium. However, the {R}V value may vary even along different diffuse interstellar medium sightlines. In this paper, we investigate the optical-mid-infrared (mid-IR) extinction law toward a very diffuse region at l=165^\\circ in the Galactic plane, which was selected based on a CO emission map. Adopting red clump stars as extinction tracers, we determine the optical-mid-IR extinction law for our diffuse region in two APASS bands (B,V), three XSTPS-GAC bands (g,r,I), three 2MASS bands (J,H,{K}s), and two WISE bands (W1,W2). Specifically, 18 red clump stars were selected from the APOGEE-RC catalog based on spectroscopic data in order to explore the diversity of the extinction law. We find that the optical extinction curves exhibit appreciable diversity. The corresponding {R}V ranges from 1.7 to 3.8, while the mean {R}V value of 2.8 is consistent with the widely adopted average value of 3.1 for Galactic diffuse clouds. There is no apparent correlation between {R}V value and color excess E(B-V) in the range of interest, from 0.2 to 0.6 mag, or with specific visual extinction per kiloparsec, {A}V/d.
3. Strategic Roadmap for the Development of an Interstellar Space Program
Science.gov (United States)
Gifra, M.; Peeters, W.
Recent technological advances and scientific discoveries, particularly in astronomy and space technology, are opening our minds into the deepest realms of the universe, and also they are bringing a new era of space exploration and development. This sense of entering into a new era of space exploration is being boosted by the permanent discovery of new planets - to date, there are 684 confirmed extrasolar planets [1] - outside our solar system. The possibility that astronomers may soon find a habitable extrasolar planet near Earth and the recent advances in space propulsion that could reduce travel times have stimulated the space community to consider the development of an interstellar manned mission. But this scenario of entering into a new era of space development is ultimately contingent on the outcome of the actual world's economic crisis. The current financial crisis, on top of recent national and sovereign debts problems, could have serious consequences for space exploration and development as the national budgets for space activities are to freeze [2].This paper proposes a multi-decade space program for an interstellar manned mission. It designs a roadmap for the achievement of interstellar flight capability within a timeframe of 40 years, and also considers different scenarios where various technological and economical constraints are taken into account in order to know if such a space endeavour could be viable. It combines macro-level scenarios with a strategic roadmap to provide a framework for condensing all information in one map and timeframe, thus linking decision-making with plausible scenarios. The paper also explores the state of the art of space technologies 20 to 40 years in the future and its potential economic impact. It estimates the funding requirements, possible sources of funds, and the potential returns.The Interstellar Space Program proposed in this paper has the potential to help solve the global crisis by bringing a new landscape of
4. Ketene Formation in Interstellar Ices: A Laboratory Study
Science.gov (United States)
Hudson, Reggie L.; Loeffler, Mark Josiah
2013-01-01
The formation of ketene (H2CCO, ethenone) in polar and apolar ices was studied with in situ 0.8 MeV proton irradiation, far-UVphotolysis, and infrared spectroscopic analyses at 10-20 K. Using isotopically enriched reagents, unequivocal evidencewas obtained for ketene synthesis in H2O-rich and CO2-rich ices, and several reaction products were identified. Results from scavenging experiments suggested that ketene was formed by free-radical pathways, as opposed to acid-base processes or redox reactions. Finally, we use our results to draw conclusions about the formation and stability of ketene in the interstellar medium.
5. Use of Laboratory Data to Model Interstellar Chemistry
Science.gov (United States)
Vidali, Gianfranco; Roser, J. E.; Manico, G.; Pirronello, V.
2006-01-01
Our laboratory research program is about the formation of molecules on dust grains analogues in conditions mimicking interstellar medium environments. Using surface science techniques, in the last ten years we have investigated the formation of molecular hydrogen and other molecules on different types of dust grain analogues. We analyzed the results to extract quantitative information on the processes of molecule formation on and ejection from dust grain analogues. The usefulness of these data lies in the fact that these results have been employed by theoreticians in models of the chemical evolution of ISM environments.
6. Recommended rest frequencies for observed interstellar molecular transitions
International Nuclear Information System (INIS)
Lovas, F.J.; Snyder, I.E.; Johnson, D.R.
1979-01-01
The most accurate values presently available for the rest frequencies of all known interstellar molecular transitions are presented and recommended for reference in future astronomical observations in the radio and microwave regions. The recommended values have been carefully selected after critical evaluation of the spectroscopic literature. Probable error limits along with the proper molecular and quantum mechanical labels are presented for each observed transition. Representative line antenna temperatures are also presented for a typical source as a convenience to users. References are cited to both the astronomical and the laboratory literature
7. Study of the interstellar medium towards RCW 103
OpenAIRE
Paron, Sergio Ariel; Reynoso, Estela Marta; Dubner, Gloria Mabel; Castelletti, Gabriela Marta
2017-01-01
RCW 103 is a shell type supernova remnant (SNR) that, according to near infrared observations, is interacting with a molecular cloud, specially to the south. In this paper we report on the study of the interstellar medium in an extended region towards RCW 103 based on HI 21 cm data acquired with the ATCA radiotelescope. Also, we report on the detection of HCO+ and CO emission in the rotational transition J=1-0 associated with the remnant. These observations were carried out with the millimete...
8. Interstellar ice grains in the Taurus molecular clouds
International Nuclear Information System (INIS)
Whittet, D.C.B.; Bode, M.F.; Baines, D.W.T.; Evans, A.
1983-01-01
Observations made in November 1981 using the United Kingdom Infrared Telescope (UKIRT) at Mauna Kea of the 3 μm ice absorption feature in the spectra of several obscured stars in the Taurus interstellar clouds are reported. The feature correlated in strength with extinction at visual wavelengths (Asub(v)), and is present in stars with Asub(v) as low as 4-6 mag. Ice may be widespread in the Taurus clouds, vindicating ideas on grain composition and growth first reported nearly 50 yr ago. (author)
9. Dense interstellar cloud chemistry: Basic issues and possible dynamical solution
International Nuclear Information System (INIS)
Prasad, S.S.; Heere, K.R.; Tarafdar, S.P.
1989-01-01
Standing at crossroad of enthusiasm and frustration, dense intertellar cloud chemistry has a squarely posed fundamental problem: Why do the grains appear to play at best a minor role in the chemistry? Grain surface chemistry creates considerable difficulties when the authors treat dense clouds as static objects and ignore the implications of the processes by which the clouds became dense in the first place. A new generation of models which treat chemical and dynamical evolutions concurrently are therefore presented as possible solution to the current frustrations. The proposed modeling philosophy and agenda could make the next decade quite exciting for interstellar chemistry
10. Spectroscopy of the earth's atmosphere and interstellar medium
CERN Document Server
Rao, KN
1992-01-01
Spectroscopy of the Earth's Atmosphere and Interstellar Medium focuses on the characteristics of the electromagnetic spectrum of the Earth's atmosphere in the far-infrared and microwave regions. It discusses the modes of observation in field measurements and reviews the two techniques used in the spectral region. Organized into six chapters, this volume begins with an overview of the effect of water-vapor absorption, followed by a discussion on the two frequently used method for deriving atmospheric parameters from high-resolution infrared atmospheric spectra, namely, the equivalent width
11. Physical conditions in CaFe interstellar clouds
OpenAIRE
Gnacinski, P.; Krogulec, M.
2007-01-01
Interstellar clouds that exhibit strong Ca I and Fe I lines were called CaFe clouds. The ionisation equilibrium equations were used to model the column densities of Ca II, Ca I, K I, Na I, Fe I and Ti II in CaFe clouds. The chemical composition of CaFe clouds is that of the Solar System and no depletion of elements onto dust grains is seen. The CaFe clouds have high electron densities n=1 cm^-3 that leads to high column densities of neutral Ca and Fe.
12. CSF oligoclonal banding - slideshow
Science.gov (United States)
... this page: //medlineplus.gov/ency/presentations/100145.htm CSF oligoclonal banding - series—Normal anatomy To use the ... 5 out of 5 Overview The cerebrospinal fluid (CSF) serves to supply nutrients to the central nervous ...
13. Decay of superdeformed bands
International Nuclear Information System (INIS)
Carpenter, M.P.; Khoo, T.L.; Lauritsen, T.
1995-01-01
One of the major challenges in the study of superdeformation is to directly connect the large number of superdeformed bands now known to the yrast states. In this way, excitation energies, spins and parities can be assigned to the levels in the second well which is essential to establish the collective and single-particle components of these bands. This paper will review some of the progress which has been made to understand the decay of superdeformed bands using the new arrays including the measurement of the total decay spectrum and the establishment of direct one-step decays from the superdeformed band to the yrast line in 194 Hg. 42 refs., 5 figs
14. Laparoscopic gastric banding
Science.gov (United States)
... eat by making you feel full after eating small amounts of food. After surgery, your doctor can adjust the band ... You will feel full after eating just a small amount of food. The food in the small upper pouch will ...
15. Equation of Motion of an Interstellar Bussard Ramjet with Radiation and Mass Losses
Science.gov (United States)
Semay, Claude; Silvestre-Brac, Bernard
2008-01-01
An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In recent papers, it was shown that the relativistic equation of motion of an ideal ramjet and that of a ramjet with radiation loss are analytical. When a mass loss appears, the limit speed of the ramjet is more strongly…
16. Electronic Spectroscopy of Organic Cations in Gas-Phase at 6 K:IDENTIFICATION of C60/^+ in the Interstellar Medium
Science.gov (United States)
Maier, John P.
2016-06-01
After the discovery of C60, the question of its relevance to the diffuse interstellar bands was raised. In 1987 H. W. Kroto wrote: The present observations indicate that C60 might survive in the general interstellar medium (probably as the ion C60/^+)''. In 1994 two diffuse interstellar bands (DIBs) at 9632 and 9577 Å/ were detected and proposed to be the absorption features of C60/^+. This was based on the proximity of these wavelengths to the two prominent absorption bands of C60/^+ measured by us in a neon matrix in 1993. Confirmation of the assignment required the gas phase spectrum of C60/^+ and has taken 20 years. The approach which succeeded confines C60/^+ ions in a radiofrequency trap, cools them by collisions with high density helium allowing formation of the weakly bound C60/^+--He complexes below 10 K. The photofragmentation spectrum of this mass-selected complex is then recorded using a cw laser. In order to infer the position of the absorption features of the bare C60/^+ ion, measurements on C60/^+--He_2 were also made. The spectra show that the presence of a helium atom shifts the absorptions by less than 0.2 Å, much less than the accuracy of the astronomical measurements. The two absorption features in the laboratory have band maxima at 9632.7(1) and 9577.5(1) Å, exactly the DIB wavelengths, and the widths and relative intensities agree. This leads to the first definite identification of now five bands among the five hundred or so DIBs known and proves the presence of gaseous C60/^+ in the interstellar medium. The absorption of cold C70/^+ has also been obtained by this approach. In addition the electronic spectra of a number of cations of astrophysical interest ranging from those of carbon chains including oxygen to larger polycyclic aromatic hydrocarbon could be measured in the gas phase at around 10 K in the ion trap but using an excitation-dissociation approach. The implications of these laboratory spectra in relation to the diffuse
17. The effect of catastrophic collisional fragmentation and diffuse medium accretion on a computational interstellar dust system
Science.gov (United States)
Liffman, Kurt
1990-01-01
The effects of catastrophic collisional fragmentation and diffuse medium accretion on a the interstellar dust system are computed using a Monte Carlo computer model. The Monte Carlo code has as its basis an analytic solution of the bulk chemical evolution of a two-phase interstellar medium, described by Liffman and Clayton (1989). The model is subjected to numerous different interstellar processes as it transfers from one interstellar phase to another. Collisional fragmentation was found to be the dominant physical process that shapes the size spectrum of interstellar dust. It was found that, in the diffuse cloud phase, 90 percent of the refractory material is locked up in the dust grains, primarily due to accretion in the molecular medium. This result is consistent with the observed depletions of silicon. Depletions were found to be affected only slightly by diffuse cloud accretion.
18. A dirty window diffuse and translucent molecular gas in the interstellar medium
CERN Document Server
Magnani, Loris
2017-01-01
This book provides an introduction to the physics of interstellar gas in the Galaxy. It deals with the diffuse interstellar medium which supplies a complex environment for exploring the neutral gas content of a galaxy like the Milky Way and the techniques necessary for studying this non-stellar component. After an initial exposition of the phases of the interstellar medium and the role of gas in a spiral galaxy, the authors discuss the transition from atomic to molecular gas. They then consider basic radiative transfer and molecular spectroscopy with particular emphasis on the molecules useful for studying low-density molecular gas. Observational techniques for investigating the gas and the dust component of the diffuse interstellar medium throughout the electromagnetic spectrum are explored emphasizing results from the recent Herschel and Planck missions. A brief exposition on dust in the diffuse interstellar medium is followed by a discussion of molecular clouds in general and high-latitude molecular clouds...
19. Determination of interstellar pickup ion distributions in the solar wind with SOHO and Cluster
Directory of Open Access Journals (Sweden)
E. Möbius
1996-05-01
Full Text Available Over the last 10 years, the experimental basis for the study of the local interstellar medium has been substantially enhanced by the direct detection of interstellar pickup ions and of interstellar neutral helium within the heliosphere. Pickup ions can be studied for a wide range of interstellar species. However, currently the accuracy of the method to determine the parameters of the interstellar medium, namely neutral density, temperature and relative velocity, is hampered by two problems: (1 In most cases the crucial ionization rates are not available from simultaneous measurements and (2 the transport of the pickup ions in the interplanetary medium substantially modifies the measured spatial distribution of the ions. In this study we will discuss how the enhanced capabilities of the instrumentation on SOHO and Cluster in combination with ongoing efforts to model the pickup ion distributions will lead to a significant improvement over the coming years.
20. BENZENE FORMATION ON INTERSTELLAR ICY MANTLES CONTAINING PROPARGYL ALCOHOL
Energy Technology Data Exchange (ETDEWEB)
Sivaraman, B.; Mukherjee, R.; Subramanian, K. P.; Banerjee, S. B., E-mail: [email protected] [Space and Atmospheric Sciences Division, Physical Research Laboratory, Ahmedabad (India)
2015-01-10
Propargyl alcohol (CHCCH{sub 2}OH) is a known stable isomer of the propenal (CH{sub 2}CHCHO) molecule that was reported to be present in the interstellar medium (ISM). At astrochemical conditions in the laboratory, icy layers of propargyl alcohol grown at 85 K were irradiated by 2 keV electrons and probed by a Fourier Transform InfraRed spectrometer in the mid-infrared (IR) region, 4000-500 cm{sup –1}. Propargyl alcohol ice under astrochemical conditions was studied for the first time; therefore, IR spectra of reported amorphous (85 K) and crystalline (180 K) propargyl alcohol ices can be used to detect its presence in the ISM. Moreover, our experiments clearly show benzene (C{sub 6}H{sub 6}) formation to be the major product from propargyl alcohol irradiation, confirming the role of propargyl radicals (C{sub 3}H{sub 3}) formed from propargyl alcohol dissociation that was long expected based on theoretical modeling to effectively synthesize C{sub 6}H{sub 6} in the interstellar icy mantles.
1. Effects of time-dependent photoionization on interstellar pickup atoms
International Nuclear Information System (INIS)
Isenberg, P.A.; Lee, M.A.
1995-01-01
We present an analytical model for the density variations of interstellar pickup ions in the solar wind due to a time-dependent variation in the photoionization rate, our model predicts a pickup ion density enhancement lasting for a time of the order of the duration of the increase plus the solar wind convection time to the observation point. If the photoionization rate returns to its initial value, this enhancement is followed by a decreased pickup ion density resulting from a depleted interstellar neutral particle density. In the absence of further variations in the photoionization rate, the pickup ion density recovers on a time which scales as the radial position of the observation point divided by the inflow speed of the neutral particles. Gradual variations in the photoionization rate result in a pickup ion density which tends to track the ionization rate, though the density variations are smoothed and delayed in time due to the solar wind convection of ions picked up at points closer to the Sun. 27 refs., 4 figs
2. TRAJECTORIES AND DISTRIBUTION OF INTERSTELLAR DUST GRAINS IN THE HELIOSPHERE
International Nuclear Information System (INIS)
Slavin, Jonathan D.; Frisch, Priscilla C.; Müller, Hans-Reinhard; Heerikhuisen, Jacob; Pogorelov, Nikolai V.; Reach, William T.; Zank, Gary
2012-01-01
The solar wind carves a bubble in the surrounding interstellar medium (ISM) known as the heliosphere. Charged interstellar dust grains (ISDG) encountering the heliosphere may be diverted around the heliopause or penetrate it depending on their charge-to-mass ratio. We present new calculations of trajectories of ISDG in the heliosphere, and the dust density distributions that result. We include up-to-date grain charging calculations using a realistic UV radiation field and full three-dimensional magnetohydrodynamic fluid + kinetic models for the heliosphere. Models with two different (constant) polarities for the solar wind magnetic field (SWMF) are used, with the grain trajectory calculations done separately for each polarity. Small grains a gr ∼ gr ∼> 1.0 μm, pass into the inner solar system and are concentrated near the Sun by its gravity. Trajectories of intermediate size grains depend strongly on the SWMF polarity. When the field has magnetic north pointing to ecliptic north, the field de-focuses the grains resulting in low densities in the inner heliosphere, while for the opposite polarity the dust is focused near the Sun. The ISDG density outside the heliosphere inferred from applying the model results to in situ dust measurements is inconsistent with local ISM depletion data for both SWMF polarities but is bracketed by them. This result points to the need to include the time variation in the SWMF polarity during grain propagation. Our results provide valuable insights for interpretation of the in situ dust observations from Ulysses.
3. ACCURATE MODELING OF X-RAY EXTINCTION BY INTERSTELLAR GRAINS
International Nuclear Information System (INIS)
Hoffman, John; Draine, B. T.
2016-01-01
Interstellar abundance determinations from fits to X-ray absorption edges often rely on the incorrect assumption that scattering is insignificant and can be ignored. We show instead that scattering contributes significantly to the attenuation of X-rays for realistic dust grain size distributions and substantially modifies the spectrum near absorption edges of elements present in grains. The dust attenuation modules used in major X-ray spectral fitting programs do not take this into account. We show that the consequences of neglecting scattering on the determination of interstellar elemental abundances are modest; however, scattering (along with uncertainties in the grain size distribution) must be taken into account when near-edge extinction fine structure is used to infer dust mineralogy. We advertise the benefits and accuracy of anomalous diffraction theory for both X-ray halo analysis and near edge absorption studies. We present an open source Fortran suite, General Geometry Anomalous Diffraction Theory (GGADT), that calculates X-ray absorption, scattering, and differential scattering cross sections for grains of arbitrary geometry and composition
4. ACCURATE MODELING OF X-RAY EXTINCTION BY INTERSTELLAR GRAINS
Energy Technology Data Exchange (ETDEWEB)
Hoffman, John; Draine, B. T., E-mail: [email protected], E-mail: [email protected] [Princeton University Observatory, Peyton Hall, Princeton, NJ 08544-1001 (United States)
2016-02-01
Interstellar abundance determinations from fits to X-ray absorption edges often rely on the incorrect assumption that scattering is insignificant and can be ignored. We show instead that scattering contributes significantly to the attenuation of X-rays for realistic dust grain size distributions and substantially modifies the spectrum near absorption edges of elements present in grains. The dust attenuation modules used in major X-ray spectral fitting programs do not take this into account. We show that the consequences of neglecting scattering on the determination of interstellar elemental abundances are modest; however, scattering (along with uncertainties in the grain size distribution) must be taken into account when near-edge extinction fine structure is used to infer dust mineralogy. We advertise the benefits and accuracy of anomalous diffraction theory for both X-ray halo analysis and near edge absorption studies. We present an open source Fortran suite, General Geometry Anomalous Diffraction Theory (GGADT), that calculates X-ray absorption, scattering, and differential scattering cross sections for grains of arbitrary geometry and composition.
5. Stochastic histories of dust grains in the interstellar medium
International Nuclear Information System (INIS)
Liffman, K.
1988-01-01
The purpose of this thesis is to study an evolving system of SU-perNOva CONdensateS (SUNOCONS) within the Interstellar Medium (ISM). This is done via a Monte Carlo process where refractory dust grains formed within supernova remnants are subjected to the processes of sputtering and collisional fragmentation in the diffuse phase and accretion within the cold molecular cloud phase. In order to record chemical detail, we take each new particle to consist of a superrefractory core plus a more massive refractory mantle. The particles are allowed to transfer to and from between the different phases of the ISM until either the particles are destroyed or the program finishes. The resulting chemical and size spectrum(s) are then applied to various astrophysical problems with the following results: (1) after six thousand million years roughly 10 to 20% by mass of the most refractory material (Al 2 O 3 ) survives the rigors of the ISM intact, which leaves open the possibility that fossilized isotopically anomalous material may have been present within the primordial solar nebula. (2) structured or layered refractory dust grains within our model cannot explain the observed interstellar depletions of refractory material. (3) fragmentation due to grain-grain collisions in the diffuse phase plus the accretion of material in the molecular cloud phase can under certain circumstances cause a biomodal distribution in grain size
6. Nuclear abundances and evolution of the interstellar medium
International Nuclear Information System (INIS)
Wannier, P.G.
1980-01-01
Observations of molecular and elemental abundances in the interstellar medium (ISM) are reviewed, with special attention given to isotope ratios. The derivation of molecular isotope abundances for the ISM is discussed, along with H and C fractionation. Millimeter- and centimeter-wave spectra of giant clouds are examined with respect to isotope abundances of C, O, N, Si, S, and D. Evidence for the current enrichment of the ISM by mass loss from evolved stars is considered, together with chemical abundance gradients in H II regions and planetary nebulae. Cosmic-ray observations pertaining to abundances in the ISM are summarized, with emphasis on available results for Ne, Mg, Si, Fe, and Ni. The observations reviewed are shown to support arguments in favor of: (1) the cosmological production of D and He-3 (2) the production of the CNO elements by hydrostatic hydrogen burning (3) the nucleosynthesis of Ne, Mg, Si, S, Fe, and Ni as a result of He burning (4) solar abundances of interstellar S, Fe, and Ni and (5) a direct association between observed inhomogeneities in the ISM and mass loss from evolved stellar objects
7. An infrared measurement of chemical desorption from interstellar ice analogues
Science.gov (United States)
Oba, Y.; Tomaru, T.; Lamberts, T.; Kouchi, A.; Watanabe, N.
2018-03-01
In molecular clouds at temperatures as low as 10 K, all species except hydrogen and helium should be locked in the heterogeneous ice on dust grain surfaces. Nevertheless, astronomical observations have detected over 150 different species in the gas phase in these clouds. The mechanism by which molecules are released from the dust surface below thermal desorption temperatures to be detectable in the gas phase is crucial for understanding the chemical evolution in such cold clouds. Chemical desorption, caused by the excess energy of an exothermic reaction, was first proposed as a key molecular release mechanism almost 50 years ago1. Chemical desorption can, in principle, take place at any temperature, even below the thermal desorption temperature. Therefore, astrochemical network models commonly include this process2,3. Although there have been a few previous experimental efforts4-6, no infrared measurement of the surface (which has a strong advantage to quantify chemical desorption) has been performed. Here, we report the first infrared in situ measurement of chemical desorption during the reactions H + H2S → HS + H2 (reaction 1) and HS + H → H2S (reaction 2), which are key to interstellar sulphur chemistry2,3. The present study clearly demonstrates that chemical desorption is a more efficient process for releasing H2S into the gas phase than was previously believed. The obtained effective cross-section for chemical desorption indicates that the chemical desorption rate exceeds the photodesorption rate in typical interstellar environments.
8. Magnetic field amplification in interstellar collisionless shock waves
International Nuclear Information System (INIS)
Chevalier, R.A.
1977-01-01
It is stated that it is commonly assumed that a simple compression of the magnetic field occurs in interstellar shock waves. Recent space observations of the Earth's bow shock have shown that turbulent amplification of the magnetic field can occur in a collisionless shock. It is shown here that radio observations of Tycho's supernova remnant indicate the presence of a shock wave with such magnetic field amplification. There is at present no theory for the microinstabilities that give rise to turbulent amplification of the magnetic field. Despite the lack of theoretical understanding the possibility of field amplification in interstellar shock waves is here considered. In Tycho's supernova remnant there is evidence for the presence of a collisionless shock, and this is discussed. On the basis of observations of the Earth's bow shock, it is expected that turbulent magnetic field amplification occurs in the shock wave of this remnant, and this is supported by radio observations of the remnant. Consideration is given as to what extent the magnetic field is amplified in the shock wave on the basis of the non-thermal radio flux. (U.K.)
9. Polarimetric study of the interstellar medium in Taurus Dark Clouds
International Nuclear Information System (INIS)
Hsu, J.
1985-01-01
An optical linear polarimetric survey was completed for more than 300 stars in an area of 6.5 0 x 10 0 toward the Taurus Dark Clouds Complex. It was found that the orientation of the magnetic field is roughly perpendicular to the elongation direction of the dust lanes, indicating cloud contraction along the magnetic field lines. The distance to the front edge of the dark clouds in Taurus is determined to be 126 pc. There is only insignificant amount of obscuring material between the cloud complex and the Sun. Besides the polarization data, the reddenings of about 250 stars were also obtained from the UBV photometry. The mean polarization to reddening ratio in the Taurus region is 4.6, which is similar to that of the general interstellar matter. The wavelengths of maximum polarization were determined for 30 stars in Taurus. They show an average value of lambda/sub max/ = 0.57 μm, which is only slightly higher than the mean value of the general interstellar medium, lambda/sub max/ = 0.55 μm. A few stars that show higher values of lambda/sub max/ are found near the small isolated regions of very high extinction. One such highly obscured small region where very complex long chain molecules have been discovered in the ratio spectra, is the Taurus Molecular Cloud 1
10. VARIATIONS BETWEEN DUST AND GAS IN THE DIFFUSE INTERSTELLAR MEDIUM
International Nuclear Information System (INIS)
Reach, William T.; Heiles, Carl; Bernard, Jean-Philippe
2015-01-01
Using the Planck far-infrared and Arecibo GALFA 21 cm line surveys, we identified a set of isolated interstellar clouds (approximately degree-sized on the sky and comprising 100 solar masses) and assessed the ratio of gas mass to dust mass. Significant variations of the gas/dust ratio are found both from cloud to cloud and within regions of individual clouds; within the clouds, the atomic gas per unit dust decreases by more than a factor of 3 compared with the standard gas/dust ratio. Three hypotheses are considered. First, the apparently low gas/dust ratio could be due to molecular gas. Comparing to Planck CO maps, the brightest clouds have a H 2 /CO ratio comparable to Galactic plane clouds, but a strong lower limit is placed on the ratio for other clouds, such that the required amount of molecular gas is far higher than would be expected based on the CO upper limits. Second, we consider self-absorbed 21 cm lines and find that the optical depth must be ∼3, significantly higher than found from surveys of radio sources. Third, grain properties may change within the clouds: they become more emissive when they are colder, while not utilizing heavy elements that already have their cosmic abundance fully locked into grains. It is possible that all three processes are active, and follow-up studies will be required to disentangle them and measure the true total gas and dust content of interstellar clouds
11. ON THE FORMATION OF DIPEPTIDES IN INTERSTELLAR MODEL ICES
International Nuclear Information System (INIS)
Kaiser, R. I.; Kim, Y. S.; Stockton, A. M.; Jensen, E. C.; Mathies, R. A.
2013-01-01
The hypothesis of an exogenous origin and delivery of biologically important molecules to early Earth presents an alternative route to their terrestrial in situ formation. Dipeptides like Gly-Gly detected in the Murchison meteorite are considered as key molecules in prebiotic chemistry because biofunctional dipeptides present the vital link in the evolutionary transition from prebiotic amino acids to early proteins. However, the processes that could lead to the exogenous abiotic synthesis of dipeptides are unknown. Here, we report the identification of two proteinogenic dipeptides—Gly-Gly and Leu-Ala—formed via electron-irradiation of interstellar model ices followed by annealing the irradiated samples to 300 K. Our results indicate that the radiation-induced, non-enzymatic formation of proteinogenic dipeptides in interstellar ice analogs is facile. Once synthesized and incorporated into the ''building material'' of solar systems, biomolecules at least as complex as dipeptides could have been delivered to habitable planets such as early Earth by meteorites and comets, thus seeding the beginning of life as we know it.
12. Protostellar formation in rotation interstellar clouds. III. Nonaxisymmetric collapse
International Nuclear Information System (INIS)
Boss, A.P.
1980-01-01
A full three spatial-dimension gravitational hydrodynamics code has been used to follow the collapse of isothermal rotating clouds subjected to various nonaxialy symmetric perturbations (NAP). An initially axially symmetric cloud collapsed to form a ring which then fragmented into a binary protostellar system. A low thermal energy cloud with a large bar-shaped NAP collapsed and fragmented directly into a binary; higher thermal energy clouds damp out such NAPs while higher rotational rotational energy clouds produce binaries with wider separations. Fragmentation into single and binary systems has been seen. The tidal effects of other nearby protostellar clouds are shown to have an important effect upon the collapse and should not be neglected. The three-dimensional calculations indicate that isothermal interstellar clouds may fragment (with or without passing through a transitory ring phase) into protostellar objects while still in the isothermal regime. The fragments obtained have masses and specific spin angular momenta roughly a 10th that of the original cloud. Interstellar clouds and their fragments may pass through successive collapse phases with fragmentation and reduction of spin angular momentum (by conversion to orbital angular momentum and preferential accretion of low angular momentum matter) terminating in the formation of pre--main-sequence stars with the observed pre--main-sequence rotation rates
13. Dark matter properties implied by gamma ray interstellar emission models
Energy Technology Data Exchange (ETDEWEB)
Balázs, Csaba; Li, Tong, E-mail: [email protected], E-mail: [email protected] [ARC Centre of Excellence for Particle Physics at the Tera-scale, School of Physics and Astronomy, Monash University, Melbourne, Victoria 3800 (Australia)
2017-02-01
We infer dark matter properties from gamma ray residuals extracted using eight different interstellar emission scenarios proposed by the Fermi-LAT Collaboration to explain the Galactic Center gamma ray excess. Adopting the most plausible simplified ansatz, we assume that the dark matter particle is a Majorana fermion interacting with standard fermions via a scalar mediator. To trivially respect flavor constraints, we only couple the mediator to third generation fermions. Using this theoretical hypothesis, and the Fermi residuals, we calculate Bayesian evidences, including Fermi-LAT exclusion limits from 15 dwarf spheroidal galaxies as well. Our evidence ratios single out one of the Fermi scenarios as most compatible with the simplified dark matter model. In this scenario the dark matter (mediator) mass is in the 25-200 (1-1000) GeV range and its annihilation is dominated by bottom quark final state. Our conclusion is that the properties of dark matter extracted from gamma ray data are highly sensitive to the modeling of the interstellar emission.
14. RUSTY OLD STARS: A SOURCE OF THE MISSING INTERSTELLAR IRON?
International Nuclear Information System (INIS)
McDonald, I.; Zijlstra, A. A.; Markwick, A. J.; Sloan, G. C.; Bernard-Salas, J.; Matsunaga, N.; Matsuura, M.; Kraemer, K. E.
2010-01-01
Iron, the universe's most abundant refractory element, is highly depleted in both circumstellar and interstellar environments, meaning it exists in solid form. The nature of this solid is unknown. In this Letter, we provide evidence that metallic iron grains are present around oxygen-rich asymptotic giant branch stars, where it is observationally manifest as a featureless mid-infrared excess. This identification is made using Spitzer Space Telescope observations of evolved globular cluster stars, where iron dust production appears ubiquitous and in some cases can be modeled as the only observed dust product. In this context, FeO is examined as the likely carrier for the 20 μm feature observed in some of these stars. Metallic iron appears to be an important part of the dust condensation sequence at low metallicity, and subsequently plays an influential role in the interstellar medium. We explore the stellar metallicities and luminosities at which iron formation is observed, and how the presence of iron affects the outflow and its chemistry. The conditions under which iron can provide sufficient opacity to drive a wind remain unclear.
15. MAD with aliens? Interstellar deterrence and its implications
Science.gov (United States)
Korhonen, Janne M.
2013-05-01
The possibility that extraterrestrial intelligences (ETIs) could be hostile to humanity has been raised as a reason to avoid even trying to contact ETIs. However, there is a distinct shortage of analytical discussion about the risks of an attack, perhaps because of an implicit premise that we cannot analyze the decision making of an alien civilization. This paper argues that we can draw some inferences from the history of the Cold War and nuclear deterrence in order to show that at least some attack scenarios are likely to be exaggerated. In particular, it would seem to be unlikely that the humanity would be attacked simply because it might, sometime in the future, present a threat to the ETI. Even if communication proves to be difficult, rational decision-makers should avoid unprovoked attacks, because their success would be very difficult to assure. In general, it seems believable that interstellar conflicts between civilizations would remain rare. The findings advise caution for proposed interstellar missions, however, as starfaring capability itself might be seen as a threat. On the other hand, attempting to contact ETIs seems to be a relatively low-risk strategy: paranoid ETIs must also consider the possibility that the messages are a deception designed to lure out hostile civilizations and preemptively destroy them.
16. Interstellar communication. II. Application to the solar gravitational lens
Science.gov (United States)
Hippke, Michael
2018-01-01
We have shown in paper I of this series [1] that interstellar communication to nearby (pc) stars is possible at data rates of bits per second per Watt between a 1 m sized probe and a large receiving telescope (E-ELT, 39 m), when optimizing all parameters such as frequency at 300-400 nm. We now apply our framework of interstellar extinction and quantum state calculations for photon encoding to the solar gravitational lens (SGL), which enlarges the aperture (and thus the photon flux) of the receiving telescope by a factor of >109 . For the first time, we show that the use of the SGL for communication purposes is possible. This was previously unclear because the Einstein ring is placed inside the solar coronal noise, and contributing factors are difficult to determine. We calculate point-spread functions, aperture sizes, heliocentric distance, and optimum communication frequency. The best wavelength for nearby (meter-sized telescopes, an improvement of 107 compared to using the same receiving telescope without the SGL. A 1 m telescope in the SGL can receive data at rates comparable to a km-class "normal" telescope.
17. Effects of noise on the interstellar polarization law
International Nuclear Information System (INIS)
Clarke, D.; Al-Roubaie, A.
1983-01-01
A re-appraisal has been made of catalogued four- and seven-colour polarimetric data in terms of the Serkowski law P(lambda)/Psub(max)=exp(-K ln 2 (lambdasub(max)/lambda)) for the wavelength dependence of interstellar polarization. It has been found that the parameter (K) controlling the peakiness of the p(lambda) curve is not a constant at 1.15 but that it is correlated with the value of lambdasub(max), the wavelength corresponding to the maximum value of p(lambda). It has also been found the the form of the correlation depends significantly on the choice of the wavelength values used to measure p(lambda). A numerical exercise involving data simulation shows that the correlations found in the real data could be an artifact of the random noise on the p(lambda) measurements. It is also suggested that a recent proposal to refine the interstellar law reflects, at least partly, the effects of random noise associated with polarimetric measurements. (author)
18. Analysis of ensembles of moderately saturated interstellar lines
International Nuclear Information System (INIS)
Jenkins, E.B.
1986-01-01
It is shown that the combined equivalent widths for a large population of Gaussian-like interstellar line components, each with different central optical depths tau(0) and velocity dispersions b, exhibit a curve of growth (COG) which closely mimics that of a single, pure Gaussian distribution in velocity. Two parametric distributions functions for the line populations are considered: a bivariate Gaussian for tau(0) and b and a power law distribution for tau(0) combined with a Gaussian dispersion for b. First, COGs for populations having an extremely large number of nonoverlapping components are derived, and the implications are shown by focusing on the doublet-ratio analysis for a pair of lines whose f-values differ by a factor of two. The consequences of having, instead of an almost infinite number of lines, a relatively small collection of components added together for each member of a doublet are examined. The theory of how the equivalent widths grow for populations of overlapping Gaussian profiles is developed. Examples of the composite COG analysis applied to existing collections of high-resolution interstellar line data are presented. 39 references
19. Interstellar scintillation of the double pulsar J0737–3039
Energy Technology Data Exchange (ETDEWEB)
Rickett, B. J.; Coles, W. A.; Nava, C. F. [ECE Dept., University of California San Diego, La Jolla, CA 92093-0407 (United States); McLaughlin, M. A. [West Virginia University, Morgantown, WV 26505 (United States); Ransom, S. M. [National Radio Astronomy Observatory, Charlottesville, VA 22903 (United States); Camilo, F. [National Astronomy and Ionosphere Center, Arecibo, PR 00612-8346 (United States); Ferdman, R. D.; Kramer, M.; Lyne, A. G. [Jodrell Bank Center for Astrophysics, University of Manchester, M13 9PL (United Kingdom); Freire, P. C. C. [Dept. of Physics, McGill University, Montréal, QC H3A 2T8 (Canada); Stairs, I. H., E-mail: [email protected] [Dept. of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1 (Canada)
2014-06-01
We report a series of observations of the interstellar scintillation (ISS) of the double pulsar J0737–3039 over the course of 18 months. As in earlier work, the basic phenomenon is the variation in the ISS caused by the changing transverse velocities of each pulsar, the ionized interstellar medium (IISM), and the Earth. The transverse velocity of the binary system can be determined both by very long baseline interferometry and timing observations. The orbital velocity and inclination is almost completely determined from timing observations, but the direction of the orbital angular momentum is not known. Since the Earth's velocity is known, and can be compared with the orbital velocity by its effect on the timescale of the ISS, we can determine the orientation Ω of the pulsar orbit with respect to equatorial coordinates (Ω = 65 ± 2°). We also resolve the ambiguity (i = 88.°7 or 91.°3) in the inclination of the orbit deduced from the measured Shapiro delay by our estimate i = 88.°1 ± 0.°5. This relies on the analysis of the ISS over both frequency and time, and provides a model for the location, anisotropy, turbulence level, and transverse phase gradient of the IISM. We find that the IISM can be well-modeled during each observation, typically of a few orbital periods, but its turbulence level and mean velocity vary significantly over the 18 months.
20. Solar neutrinos and solar accretion of interstellar matter
International Nuclear Information System (INIS)
Newman, M.J.; Talbot, R.J. Jr.
1976-01-01
It is argued that if the Hoyle-Lyttleton mass accretion rate applies (Proc. Camb. Phil. Soc., Math. Phys. Sci. 35: 405 (1939)) the accretion of interstellar matter by the Sun is sufficient to enhance the surface heavy element abundances. This will also apply to other solar-type stars. The enhancement may be sufficient to allow the construction of consistent solar models with an interior heavy element abundance significantly lower than the observed surface abundance. This state of affairs lowers the predicted solar neutrino flux. It has been suggested that a similar enhancement of surface abundances might occur due to accretion of 'planetesimals' left over after formation of the solar system, and both processes may occur, thereby increasing the effect. The simple accretion model of Hoyle and Lyttleton is discussed mathematically. A crucial question to be answered by future research, however, is whether or not accretion on to the solar surface actually occurs. One of the most obvious obstacles is the outward flowing solar wind, and this is discussed. It appears that the outward flow can be reversed to an inward flow for certain interstellar cloud densities. (U.K.)
1. THE INTERSTELLAR MAGNETIC FIELD CLOSE TO THE SUN. II
International Nuclear Information System (INIS)
Frisch, P. C.; Andersson, B-G; Berdyugin, A.; Piirola, V.; DeMajistre, R.; Funsten, H. O.; Magalhaes, A. M.; Seriacopi, D. B.; McComas, D. J.; Schwadron, N. A.; Slavin, J. D.; Wiktorowicz, S. J.
2012-01-01
The magnetic field in the local interstellar medium (ISM) provides a key indicator of the galactic environment of the Sun and influences the shape of the heliosphere. We have studied the interstellar magnetic field (ISMF) in the solar vicinity using polarized starlight for stars within 40 pc of the Sun and 90° of the heliosphere nose. In Frisch et al. (Paper I), we developed a method for determining the local ISMF direction by finding the best match to a group of interstellar polarization position angles obtained toward nearby stars, based on the assumption that the polarization is parallel to the ISMF. In this paper, we extend the analysis by utilizing weighted fits to the position angles and by including new observations acquired for this study. We find that the local ISMF is pointed toward the galactic coordinates l, b =47° ± 20°, 25° ± 20°. This direction is close to the direction of the ISMF that shapes the heliosphere, l, b =33° ± 4°, 55° ± 4°, as traced by the center of the 'Ribbon' of energetic neutral atoms discovered by the Interstellar Boundary Explorer (IBEX) mission. Both the magnetic field direction and the kinematics of the local ISM are consistent with a scenario where the local ISM is a fragment of the Loop I superbubble. A nearby ordered component of the local ISMF has been identified in the region l ≈0° → 80° and b ≈0° → 30°, where PlanetPol data show a distance-dependent increase of polarization strength. The ordered component extends to within 8 pc of the Sun and implies a weak curvature in the nearby ISMF of ∼0. 0 25 pc –1 . This conclusion is conditioned on the small sample of stars available for defining this rotation. Variations from the ordered component suggest a turbulent component of ∼23°. The ordered component and standard relations between polarization, color excess, and H o column density predict a reasonable increase of N(H) with distance in the local ISM. The similarity of the ISMF directions traced
2. THE INTERSTELLAR MAGNETIC FIELD CLOSE TO THE SUN. II
Energy Technology Data Exchange (ETDEWEB)
Frisch, P. C. [Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637 (United States); Andersson, B-G [SOFIA Science Center, Universities Space Research Association, NASA Ames Research Center, M.S. N232-12 Moffett Field, CA 94035 (United States); Berdyugin, A.; Piirola, V. [Finnish Centre for Astronomy with ESO, University of Turku (Finland); DeMajistre, R. [The Johns Hopkins University Applied Physics Laboratory, Laurel, MD (United States); Funsten, H. O. [Los Alamos National Laboratory, Los Alamos, NM (United States); Magalhaes, A. M.; Seriacopi, D. B. [Inst. de Astronomia, Geofisica e Ciencias Atmosfericas, Universidade de Sao Paulo (Brazil); McComas, D. J. [Southwest Research Institute, San Antonio, TX (United States); Schwadron, N. A. [Space Science Center, University of New Hampshire, Durham, NH (United States); Slavin, J. D. [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States); Wiktorowicz, S. J. [Department of Astronomy, University of California at Santa Cruz, Santa Cruz, CA (United States)
2012-12-01
The magnetic field in the local interstellar medium (ISM) provides a key indicator of the galactic environment of the Sun and influences the shape of the heliosphere. We have studied the interstellar magnetic field (ISMF) in the solar vicinity using polarized starlight for stars within 40 pc of the Sun and 90 Degree-Sign of the heliosphere nose. In Frisch et al. (Paper I), we developed a method for determining the local ISMF direction by finding the best match to a group of interstellar polarization position angles obtained toward nearby stars, based on the assumption that the polarization is parallel to the ISMF. In this paper, we extend the analysis by utilizing weighted fits to the position angles and by including new observations acquired for this study. We find that the local ISMF is pointed toward the galactic coordinates l, b =47 Degree-Sign {+-} 20 Degree-Sign , 25 Degree-Sign {+-} 20 Degree-Sign . This direction is close to the direction of the ISMF that shapes the heliosphere, l, b =33 Degree-Sign {+-} 4 Degree-Sign , 55 Degree-Sign {+-} 4 Degree-Sign , as traced by the center of the 'Ribbon' of energetic neutral atoms discovered by the Interstellar Boundary Explorer (IBEX) mission. Both the magnetic field direction and the kinematics of the local ISM are consistent with a scenario where the local ISM is a fragment of the Loop I superbubble. A nearby ordered component of the local ISMF has been identified in the region l Almost-Equal-To 0 Degree-Sign {yields} 80 Degree-Sign and b Almost-Equal-To 0 Degree-Sign {yields} 30 Degree-Sign , where PlanetPol data show a distance-dependent increase of polarization strength. The ordered component extends to within 8 pc of the Sun and implies a weak curvature in the nearby ISMF of {approx}0.{sup 0}25 pc{sup -1}. This conclusion is conditioned on the small sample of stars available for defining this rotation. Variations from the ordered component suggest a turbulent component of {approx}23 Degree-Sign . The
3. Simulating STARDUST: Reproducing Impacts of Interstellar Dust in the Laboratory
Science.gov (United States)
Postberg, F.; Srama, R.; Hillier, J. K.; Sestak, S.; Green, S. F.; Trieloff, M.; Grün, E.
2008-09-01
Our experiments are carried out to support the analysis of interstellar dust grains, ISDGs, brought to earth by the STARDUST mission. Since the very first investigations, it has turned out that the major problem of STARDUST particle analysis is the modification (partly even the destruction) during capture when particles impact the spacecraft collectors with a velocity of up to 20 km/s. While it is possible to identify, extract, and analyse cometary grains larger than a few microns in aerogel and on metal collector plates, the STARDUST team is not yet ready for the identification, extraction, and analysis of sub-micron sized ISDGs with impact speeds of up to 20 km/s. Reconstructing the original particle properties requires a simulation of this impact capture process. Moreover, due to the lack of laboratory studies of high speed impacts of micron scale dust into interstellar STARDUST flight spares, the selection of criteria for the identification of track candidates is entirely subjective. Simulation of such impact processes is attempted with funds of the FRONTIER program within the framework of the Heidelberg University initiative of excellence. The dust accelerator at the MPI Kernphysik is a facility unique in the world to perform such experiments. A critical point is the production of cometary and interstellar dust analogue material and its acceleration to very high speeds of 20 km/s, which has never before been performed in laboratory experiments. Up to now only conductive material was successfully accelerated by the 2 MV Van de Graaf generator of the dust accelerator facility. Typical projectile materials are Iron, Aluminium, Carbon, Copper, Silver, and the conducting hydrocarbon Latex. Ongoing research now enables the acceleration of any kind of rocky planetary and interstellar dust analogues (Hillier et al. 2008, in prep.). The first batch of dust samples produced with the new method consists of micron and submicron SiO2 grains. Those were successfully
4. Laboratory Studies of Stabilities of Heterocyclic Aromatic Molecules: Suggested Gas Phase Ion-Molecule Routes to Production in Interstellar Gas Clouds
Science.gov (United States)
Adams, Nigel G.; Fondren, L. Dalila; McLain, Jason L.; Jackson, Doug M.
2006-01-01
Several ring compounds have been detected in interstellar gas clouds, ISC, including the aromatic, benzene. Polycyclic aromatic hydrocarbons, PAHs, have been implicated as carriers of diffuse interstellar bands (DIBs) and unidentified infrared (UIR) bands. Heterocyclic aromatic rings of intermediate size containing nitrogen, possibly PreLife molecules, were included in early searches but were not detected and a recent search for Pyrimidine was unsuccessful. Our laboratory investigations of routes to such molecules could establish their existence in ISC and suggest conditions under which their concentrations would be maximized thus aiding the searches. The stability of such ring compounds (C5H5N, C4H4N2, C5H11N and C4H8O2) has been tested in the laboratory using charge transfer excitation in ion-molecule reactions. The fragmentation paths, including production of C4H4(+), C3H3N(+) and HCN, suggest reverse routes to the parent molecules, which are presently under laboratory investigation as production sources.
5. Visible and ultraviolet (800--130 nm) extinction of vapor-condensed silicate, carbon, and silicon carbide smokes and the interstellar extinction curve
International Nuclear Information System (INIS)
Stephens, J.R.
1980-01-01
The extinction curves from 800 to 130 nm (1.25--7.7 μm -1 ) of amorphous silicate smokes nominally of olivine and pyroxene composition, carbon smokes, and crystalline SiC smokes are presented. The SiC smoke occurred in the low-temperature (β) cubic structural form. The mean grain radius ranged from 5 to 13 nm. The extinction profiles of the amorphous olivine smokes were similar in the ultraviolet to the measured extinction curves of crystalline olivine of nearly the same grain size. The SiC smoke showed an absorption edge which occurred at significantly longer wavelengths than the calculated extinction profile of the hexagonal SiC form previously used to calculate the interstellar extinction profile. Neither SiC nor amorphous silicates show an extinction band similar to the observed 6.6 μm -1 astronomical extinction band
6. Ultra wide band antennas
CERN Document Server
Begaud, Xavier
2013-01-01
Ultra Wide Band Technology (UWB) has reached a level of maturity that allows us to offer wireless links with either high or low data rates. These wireless links are frequently associated with a location capability for which ultimate accuracy varies with the inverse of the frequency bandwidth. Using time or frequency domain waveforms, they are currently the subject of international standards facilitating their commercial implementation. Drawing up a complete state of the art, Ultra Wide Band Antennas is aimed at students, engineers and researchers and presents a summary of internationally recog
7. Interstellar Gas Flow Vector and Temperature Determination over 5 Years of IBEX Observations
International Nuclear Information System (INIS)
Möbius, E; Heirtzler, D; Kucharek, H; Lee, M A; Leonard, T; Schwadron, N; Bzowski, M; Kubiak, M A; Sokół, J M; Fuselier, S A; McComas, D J; Wurz, P
2015-01-01
The Interstellar Boundary Explorer (IBEX) observes the interstellar neutral gas flow trajectories at their perihelion in Earth's orbit every year from December through early April, when the Earth's orbital motion is into the oncoming flow. These observations have defined a narrow region of possible, but very tightly coupled interstellar neutral flow parameters, with inflow speed, latitude, and temperature as well-defined functions of inflow longitude. The best- fit flow vector is different by ≈ 3° and lower by ≈ 3 km/s than obtained previously with Ulysses GAS, but the temperature is comparable. The possible coupled parameter space reaches to the previous flow vector, but only for a substantially higher temperature (by ≈ 2000 K). Along with recent pickup ion observations and including historical observations of the interstellar gas, these findings have led to a discussion, whether the interstellar gas flow into the solar system has been stable or variable over time. These intriguing possibilities call for more detailed analysis and a longer database. IBEX has accumulated observations over six interstellar flow seasons. We review key observations and refinements in the analysis, in particular, towards narrowing the uncertainties in the temperature determination. We also address ongoing attempts to optimize the flow vector determination through varying the IBEX spacecraft pointing and discuss related implications for the local interstellar cloud and its interaction with the heliosphere
8. KETENE FORMATION IN INTERSTELLAR ICES: A LABORATORY STUDY
Energy Technology Data Exchange (ETDEWEB)
Hudson, Reggie L.; Loeffler, Mark J., E-mail: [email protected] [Astrochemistry Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States)
2013-08-20
The formation of ketene (H{sub 2}CCO, ethenone) in polar and apolar ices was studied with in situ 0.8 MeV proton irradiation, far-UV photolysis, and infrared spectroscopic analyses at 10-20 K. Using isotopically enriched reagents, unequivocal evidence was obtained for ketene synthesis in H{sub 2}O-rich and CO{sub 2}-rich ices, and several reaction products were identified. Results from scavenging experiments suggested that ketene was formed by free-radical pathways, as opposed to acid-base processes or redox reactions. Finally, we use our results to draw conclusions about the formation and stability of ketene in the interstellar medium.
9. An interstellar origin for Jupiter's retrograde co-orbital asteroid
Science.gov (United States)
Namouni, F.; Morais, M. H. M.
2018-06-01
Asteroid (514107) 2015 BZ509 was discovered recently in Jupiter's co-orbital region with a retrograde motion around the Sun. The known chaotic dynamics of the outer Solar system have so far precluded the identification of its origin. Here, we perform a high-resolution statistical search for stable orbits and show that asteroid (514107) 2015 BZ509 has been in its current orbital state since the formation of the Solar system. This result indicates that (514107) 2015 BZ509 was captured from the interstellar medium 4.5 billion years in the past as planet formation models cannot produce such a primordial large-inclination orbit with the planets on nearly coplanar orbits interacting with a coplanar debris disc that must produce the low-inclination small-body reservoirs of the Solar system such as the asteroid and Kuiper belts. This result also implies that more extrasolar asteroids are currently present in the Solar system on nearly polar orbits.
10. Characteristics of old neutron stars in dense interstellar clouds
International Nuclear Information System (INIS)
Boehringer, H.; Morfill, G.E.; Zimmermann, H.U.
1987-01-01
The forms observable radiation will assume as old neutron stars pass through interstellar clouds and accrete material are examined theoretically. The radiation, mainly X-rays and gamma rays, will be partially absorbed by the surrounding dust and gas, which in turn produces far-IR radiation from warm dust and line radiation from the gas. Adiabatic compression of the accretion flow and the accretion shock are expected to produce cosmic rays, while gamma rays will be emitted by interaction of the energetic particles with the cloud material. The calculations indicate that the stars will then be identified as X-ray sources, some of which may be unidentified sources in the COS-B database. 37 references
11. The formation of molecules in contracting interstellar clouds
International Nuclear Information System (INIS)
Suzuki, Hiroko; Miki, Satoshi; Sato, Katsuhiko; Kiguchi, Masayoshi; Nakagawa, Yoshitsugu
1976-01-01
The abundances of atoms, molecules and ions in contracting interstellar clouds are investigated in the wide ranges of density (from 10 cm -3 to 10 7 cm -3 ) and optical depth. Abundances of molecules are not in a steady state in optically thick stages because their reaction time scales are very long (10sup(12.5)-10sup(13.5) sec) compared with the contraction time scales. At some stage of contraction the abundances of neutral molecules become frozen, and the frozen abundances are considerably different from the steady-state abundances. The frozen abundances are mainly determined by the contraction time scale of the cloud. Especially, molecules containing carbon except for CO are less abundant for the cloud contracting more slowly. (auth.)
12. Investigating the dynamical history of the interstellar object 'Oumuamua
Science.gov (United States)
Dybczyński, Piotr A.; Królikowska, Małgorzata
2018-02-01
Here we try to find the origin of 1I/2017 U1 'Oumuamua, the first interstellar object recorded inside the solar system. To this aim, we searched for close encounters between 'Oumuamua and all nearby stars with known kinematic data during their past motion. We had checked over 200 thousand stars and found just a handful of candidates. If we limit our investigation to within a 60 pc sphere surrounding the Sun, then the most probable candidate for the 'Oumuamua parent stellar habitat is the star UCAC4 535-065571. However GJ 876 is also a favourable candidate. However, the origin of 'Oumuamua from a much more distant source is still an open question. Additionally, we found that the quality of the original orbit of 'Oumuamua is accurate enough for such a study and that none of the checked stars had perturbed its motion significantly. All numerical results of this research are available in the appendix.
13. Interstellar clouds toward 3C 154 and 3C 353
International Nuclear Information System (INIS)
Federman, S.R.; Evans, N.J. II; Willson, R.F.; Falgarone, E.; Combes, F.; Texas Univ., Austin; Tufts Univ., Medford, MA; Meudon, Observatoire, France)
1987-01-01
Molecular observations of the interstellar clouds toward the radio sources 3C 154 and 3C 353 were obtained in order to elucidate the physical conditions within the clouds. Maps of (C-12)O emission in the J = 1-0 and J = 2-1 lines were compared with observations of the (C-13)O, CH, and OH molecules. The peak emission in the (C-12)O transitions does not occur in the direction of the continuum sources, and thus, an incomplete picture arises when only one line of sight in the two clouds is analyzed. The cloud toward 3C 154 appears to have a low extinction, but a relatively high CO abundance, suggesting that it is similar to high-latitude clouds and CO-rich diffuse clouds. The cloud toward 3C 353 is considerably denser than that toward 3C 154 and may be more like a dark cloud. 32 references
14. Formation of buckminsterfullerene (C60) in interstellar space
Science.gov (United States)
Berné, Olivier; Tielens, Alexander G. G. M.
2012-01-01
Buckminsterfullerene (C60) was recently confirmed to be the largest molecule identified in space. However, it remains unclear how, and where this molecule is formed. It is generally believed that C60 is formed from the build up of small carbonaceous compounds, in the hot and dense envelopes of evolved stars. Analyzing infrared observations, obtained by Spitzer and Herschel, we found that C60 is efficiently formed in the tenuous and cold environment of an interstellar cloud illuminated by strong ultraviolet (UV) radiation fields. This implies that another formation pathway, efficient at low densities, must exist. Based on recent laboratory and theoretical studies, we argue that Polycyclic Aromatic Hydrocarbons are converted into graphene, and subsequently C60, under UV irradiation from massive stars. This shows that alternative - top-down - routes are key to understanding the organic inventory in space.
15. Physical model for the 2175 A interstellar extinction feature
International Nuclear Information System (INIS)
Hecht, J.H.
1986-01-01
Recent IUE observations have shown that the 2175 A interstellar extinction feature is constant in wavelength but varies in width. A model has been constructed to explain these results. It is proposed that the 2175 A feature will only be seen when there is extinction due to carbon grains which have lost their hydrogen. In particular, the feature is caused by a separate population of small (less than 50 A radius), hydrogen-free carbon grains. The variations in width would be due to differences in either their temperature, size distribution, or impurity content. All other carbon grains retain hydrogen, which causes the feature to be suppressed. If this model is correct, then it implies that the grains responsible for the unidentified IR emission features would not generally cause the 2175 A feature. 53 references
16. Thermal emission from interstellar dust in and near the Pleiades
International Nuclear Information System (INIS)
White, R.E.
1989-01-01
IRAS survey coadds for a 8.7 deg x 4.3 deg field near the Pleiades provide evidence for dynamical interaction between the cluster and the surrounding interstellar medium. The far-infrared images show large region of faint emission with bright rims east of the cluster, suggestive of a wake. Images of the far-infrared color temperature and 100 micron optical depth reveal temperature maxima and optical depth minima near the bright cluster stars, as well as a strong optical depth peak at the core of the adjacent CO cloud. Models for thermal dust emission near the stars indicate that most of the apparent optical depth minima near stars are illusory, but also provide indirect evidence for small interaction between the stars and the encroaching dust cloud
17. Thermal emission from interstellar dust in and near the Pleiades
Science.gov (United States)
White, Richard E.
1989-01-01
IRAS survey coadds for a 8.7 deg x 4.3 deg field near the Pleiades provide evidence for dynamical interaction between the cluster and the surrounding interstellar medium. The far-infrared images show large region of faint emission with bright rims east of the cluster, suggestive of a wake. Images of the far-infrared color temperature and 100 micron optical depth reveal temperature maxima and optical depth minima near the bright cluster stars, as well as a strong optical depth peak at the core of the adjacent CO cloud. Models for thermal dust emission near the stars indicate that most of the apparent optical depth minima near stars are illusory, but also provide indirect evidence for small interaction between the stars and the encroaching dust cloud.
18. Study of the diffuse interstellar gas near the Pleiades
International Nuclear Information System (INIS)
Federman, S.R.
1982-01-01
The interstellar gas toward the Pleiades was studied by observing lines of CH, CH + , and K I. New detections of CH and K I, and of CH + and K I in the directions of 20 Tau and eta Tau, respectively, are reported. Evidence for a moderately strong shock of velocity 10--15 km -1 was found for the line of sight toward 20 Tau, where the CH line is blueshifted by 3--4 km s -1 was respect to the CH + line. The relative weakness of the K I features, as well as the weakness of the other previously observed atomic species, requires the gas to be approx.0.3 pc from the stars. A reexamination of the observed distribution of H 2 among its rotational levels indicates that collisions occurring in the shock are largely responsible for populating levels with J>2
19. Rocket propulsion by nuclear microexplosions and the interstellar paradox
Energy Technology Data Exchange (ETDEWEB)
Winterberg, F
1979-11-01
Magnetic insulation is discussed with regard to generating ultra-intense ion beams (IIBs) for thermonuclear microexplosion ignition. With energies up to 10 to the 9th Joule reached by IIB pulses or target staging, the ignition of the hydrogen/boron-11 (HB-11) thermonuclear reaction by the addition of DT and fissionable material is considered. In addition, the possibility of HB-11 as a rocket propulsion system utilizing a magnetic mirror whose magnetic field is generated with high field superconductors is discussed in terms of interstellar travel at up to 1/10 the velocity of light. Attention is also given to the possibility of a relatively unique advanced civilization on earth caused by a rare, near-Roche limit capture of the moon and the subsequent tidal effects resulting in a land/water combination favorable for rapid evolution of life forms.
20. Organic Chemistry: From the Interstellar Medium to the Solar System
Science.gov (United States)
Sandford, Scott; Witteborn, Fred C. (Technical Monitor)
1997-01-01
This talk will review the various types of organic materials observed in different environments in the interstellar medium, discuss the processes by which these materials may have formed and been modified, and present the evidence supporting the contention that at least a fraction of this material survived incorporation, substantially unaltered, into our Solar System during its formation. The nature of this organic material is of direct interest to issues associated with the origin of life, both because this material represents a large fraction of the Solar System inventory of the biogenically-important elements, and because many of the compounds in this inventory have biogenic implications. Several specific examples of such molecules will be briefly discussed.
1. On the effects of rotation on interstellar molecular line profiles
International Nuclear Information System (INIS)
1988-01-01
Theoretical models are constructed to study the effects of systematic gas rotation on the emergent profiles of interstellar molecular lines, in particular the effects of optical depth and different velocity laws. Both rotational and radial motions (expansion or contraction) may produce similar asymmetric profiles, but the behaviour of the velocity centroid of the emergent profile over the whole cloud (iso-centroid maps) can be used to distinguish between these motions. Iso-centroid maps can also be used to determine the location and orientation of the rotation axis and of the equatorial axis. For clouds undergoing both radial and rotational motion, the component of the centroid due to the rotational motion can be separated from that due to the radial motion. Information on the form of the rotational velocity law can also be derived. (author)
2. PRESSURE PULSES AT VOYAGER 2 : DRIVERS OF INTERSTELLAR TRANSIENTS?
Energy Technology Data Exchange (ETDEWEB)
Richardson, J. D. [Kavli Center for Astrophysics and Space Science, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Wang, C.; Liu, Y. D. [State Key Laboratory for Space Weather, Chinese Academy of Sciences, Beijing (China); Šafránková, J.; Němeček, Z. [Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, 180 00 Prague 8 (Czech Republic); Kurth, W. S., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [University of Iowa, Iowa City, IA 52242 (United States)
2017-01-10
Voyager 1 ( V1 ) crossed the heliopause into the local interstellar medium (LISM) in 2012. The LISM is a dynamic region periodically disturbed by solar transients with outward-propagating shocks, cosmic-ray intensity changes and anisotropies, and plasma wave oscillations. Voyager 2 ( V2 ) trails V1 and thus may observe the solar transients that are later observed at V1. V2 crossed the termination shock in 2007 and is now in the heliosheath. Starting in 2012, when solar maximum conditions reached V2 , five possible merged interaction regions (MIRs) have been observed by V2 in the heliosheath. The timing is consistent with these MIRs driving the transients observed by V1 in the LISM. The largest heliosheath MIR was observed by V2 in late 2015 and should reach V1 in 2018.
3. Challenges in the determination of the interstellar flow longitude from the pickup ion cutoff
Science.gov (United States)
Taut, A.; Berger, L.; Möbius, E.; Drews, C.; Heidrich-Meisner, V.; Keilbach, D.; Lee, M. A.; Wimmer-Schweingruber, R. F.
2018-03-01
Context. The interstellar flow longitude corresponds to the Sun's direction of movement relative to the local interstellar medium. Thus, it constitutes a fundamental parameter for our understanding of the heliosphere and, in particular, its interaction with its surroundings, which is currently investigated by the Interstellar Boundary EXplorer (IBEX). One possibility to derive this parameter is based on pickup ions (PUIs) that are former neutral ions that have been ionized in the inner heliosphere. The neutrals enter the heliosphere as an interstellar wind from the direction of the Sun's movement against the partially ionized interstellar medium. PUIs carry information about the spatial variation of their neutral parent population (density and flow vector field) in their velocity distribution function. From the symmetry of the longitudinal flow velocity distribution, the interstellar flow longitude can be derived. Aim. The aim of this paper is to identify and eliminate systematic errors that are connected to this approach of measuring the interstellar flow longitude; we want to minimize any systematic influences on the result of this analysis and give a reasonable estimate for the uncertainty. Methods: We use He+ data measured by the PLAsma and SupraThermal Ion Composition (PLASTIC) sensor on the Solar TErrestrial RElations Observatory Ahead (STEREO A) spacecraft. We analyze a recent approach, identify sources of systematic errors, and propose solutions to eliminate them. Furthermore, a method is introduced to estimate the error associated with this approach. Additionally, we investigate how the selection of interplanetary magnetic field angles, which is closely connected to the pickup ion velocity distribution function, affects the result for the interstellar flow longitude. Results: We find that the revised analysis used to address part of the expected systematic effects obtains significantly different results than presented in the previous study. In particular
4. ON THE FORMATION OF CO2 AND OTHER INTERSTELLAR ICES
International Nuclear Information System (INIS)
Garrod, R. T.; Pauly, T.
2011-01-01
We investigate the formation and evolution of interstellar dust-grain ices under dark-cloud conditions, with a particular emphasis on CO 2 . We use a three-phase model (gas/surface/mantle) to simulate the coupled gas-grain chemistry, allowing the distinction of the chemically active surface from the ice layers preserved in the mantle beneath. The model includes a treatment of the competition between barrier-mediated surface reactions and thermal-hopping processes. The results show excellent agreement with the observed behavior of CO 2 , CO, and water ice in the interstellar medium. The reaction of the OH radical with CO is found to be efficient enough to account for CO 2 ice production in dark clouds. At low visual extinctions, with dust temperatures ∼>12 K, CO 2 is formed by direct diffusion and reaction of CO with OH; we associate the resultant CO 2 -rich ice with the observational polar CO 2 signature. CH 4 ice is well correlated with this component. At higher extinctions, with lower dust temperatures, CO is relatively immobile and thus abundant; however, the reaction of H and O atop a CO molecule allows OH and CO to meet rapidly enough to produce a CO:CO 2 ratio in the range ∼2-4, which we associate with apolar signatures. We suggest that the observational apolar CO 2 /CO ice signatures in dark clouds result from a strongly segregated CO:H 2 O ice, in which CO 2 resides almost exclusively within the CO component. Observed visual-extinction thresholds for CO 2 , CO, and H 2 O are well reproduced by depth-dependent models. Methanol formation is found to be strongly sensitive to dynamical timescales and dust temperatures.
5. TRAJECTORIES AND DISTRIBUTION OF INTERSTELLAR DUST GRAINS IN THE HELIOSPHERE
Energy Technology Data Exchange (ETDEWEB)
Slavin, Jonathan D. [Harvard-Smithsonian Center for Astrophysics, MS 83, 60 Garden Street, Cambridge, MA 02138 (United States); Frisch, Priscilla C. [Department of Astronomy and Astrophysics, University of Chicago, 5460 S. Ellis Avenue, Chicago, IL 60637 (United States); Mueller, Hans-Reinhard [Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 (United States); Heerikhuisen, Jacob; Pogorelov, Nikolai V. [Department of Physics and Center for Space Physics and Aeronomic Research, University of Alabama, Huntsville, AL 35899 (United States); Reach, William T. [Universities Space Research Association, MS 211-3, Moffett Field, CA 94035 (United States); Zank, Gary [Department of Physics and Center for Space Plasma and Aeronomic Research, University of Alabama, Huntsville, AL 35805 (United States)
2012-11-20
The solar wind carves a bubble in the surrounding interstellar medium (ISM) known as the heliosphere. Charged interstellar dust grains (ISDG) encountering the heliosphere may be diverted around the heliopause or penetrate it depending on their charge-to-mass ratio. We present new calculations of trajectories of ISDG in the heliosphere, and the dust density distributions that result. We include up-to-date grain charging calculations using a realistic UV radiation field and full three-dimensional magnetohydrodynamic fluid + kinetic models for the heliosphere. Models with two different (constant) polarities for the solar wind magnetic field (SWMF) are used, with the grain trajectory calculations done separately for each polarity. Small grains a {sub gr} {approx}< 0.01 {mu}m are completely excluded from the inner heliosphere. Large grains, a {sub gr} {approx}> 1.0 {mu}m, pass into the inner solar system and are concentrated near the Sun by its gravity. Trajectories of intermediate size grains depend strongly on the SWMF polarity. When the field has magnetic north pointing to ecliptic north, the field de-focuses the grains resulting in low densities in the inner heliosphere, while for the opposite polarity the dust is focused near the Sun. The ISDG density outside the heliosphere inferred from applying the model results to in situ dust measurements is inconsistent with local ISM depletion data for both SWMF polarities but is bracketed by them. This result points to the need to include the time variation in the SWMF polarity during grain propagation. Our results provide valuable insights for interpretation of the in situ dust observations from Ulysses.
6. Are CO Observations of Interstellar Clouds Tracing the H2?
Science.gov (United States)
Federrath, Christoph; Glover, S. C. O.; Klessen, R. S.; Mac Low, M.
2010-01-01
Interstellar clouds are commonly observed through the emission of rotational transitions from carbon monoxide (CO). However, the abundance ratio of CO to molecular hydrogen (H2), which is the most abundant molecule in molecular clouds is only about 10-4. This raises the important question of whether the observed CO emission is actually tracing the bulk of the gas in these clouds, and whether it can be used to derive quantities like the total mass of the cloud, the gas density distribution function, the fractal dimension, and the velocity dispersion--size relation. To evaluate the usability and accuracy of CO as a tracer for H2 gas, we generate synthetic observations of hydrodynamical models that include a detailed chemical network to follow the formation and photo-dissociation of H2 and CO. These three-dimensional models of turbulent interstellar cloud formation self-consistently follow the coupled thermal, dynamical and chemical evolution of 32 species, with a particular focus on H2 and CO (Glover et al. 2009). We find that CO primarily traces the dense gas in the clouds, however, with a significant scatter due to turbulent mixing and self-shielding of H2 and CO. The H2 probability distribution function (PDF) is well-described by a log-normal distribution. In contrast, the CO column density PDF has a strongly non-Gaussian low-density wing, not at all consistent with a log-normal distribution. Centroid velocity statistics show that CO is more intermittent than H2, leading to an overestimate of the velocity scaling exponent in the velocity dispersion--size relation. With our systematic comparison of H2 and CO data from the numerical models, we hope to provide a statistical formula to correct for the bias of CO observations. CF acknowledges financial support from a Kade Fellowship of the American Museum of Natural History.
7. THE INTERSTELLAR MEDIUM IN THE KEPLER SEARCH VOLUME
Energy Technology Data Exchange (ETDEWEB)
Johnson, Marshall C. [Department of Astronomy, University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712 (United States); Redfield, Seth [Astronomy Department, Van Vleck Observatory, Wesleyan University, Middletown, CT 06459 (United States); Jensen, Adam G., E-mail: [email protected] [Department of Physics and Physical Science, University of Nebraska-Kearney, Bruner Hall of Science, 2401 11th Ave, Kearney, NE 68849 (United States)
2015-07-10
The properties of the interstellar medium (ISM) surrounding a planetary system can impact planetary climate through a number of mechanisms, including changing the size of the astrosphere (one of the major shields for cosmic rays) as well as direct deposition of material into planetary atmospheres. In order to constrain the ambient ISM conditions for exoplanetary systems, we present observations of interstellar Na i and K i absorption toward seventeen early type stars in the Kepler prime mission field of view (FOV). We identify 39 Na i and 8 K i velocity components, and attribute these to 11 ISM clouds. Six of these are detected toward more than one star, and for these clouds we put limits on the cloud properties, including distance and hydrogen number density. We identify one cloud with significant (≳1.5 cm{sup −3}) hydrogen number density located within the nominal ∼100 pc boundary of the Local Bubble. We identify systems with confirmed planets within the Kepler FOV that could lie within these ISM clouds, and estimate upper limits on the astrosphere sizes of these systems under the assumption that they do lie within these clouds. Under this condition, the Kepler-20, 42, and 445 multiplanet systems could have compressed astrospheres much smaller than the present-day heliosphere. Among the known habitable zone planet hosts, Kepler-186 could have an astrosphere somewhat smaller than the heliosphere, while Kepler-437 and KOI-4427 could have astrospheres much larger than the heliosphere. The thick disk star Kepler-444 may have an astrosphere just a few AU in radius.
8. Relative amounts of stars and interstellar matter in the local Milky Way
International Nuclear Information System (INIS)
Jura, M.
1987-01-01
This paper considers the balance between star formation and mass loss from evolved stars in the region within 1 kpc of the sun. There is considerably more mass in stars than in the interstellar medium, and more material is being incorporated into new stars than is being returned by evolved stars. In the simplest interpretation of the data, it appears that unless there is some infall of new interstellar gas, the era of substantial star formation out of interstellar gas will be over in a few (perhaps 3) billion years. 34 references
9. Cometary and interstellar dust grains - Analysis by ion microprobe mass spectrometry and other techniques
Science.gov (United States)
Zinner, Ernst
1991-01-01
A survey of microanalytical measurements on interplanetary dust particles (IDPs) and interstellar dust grains from primitive meteorites is presented. Ion-microprobe mass spectrometry with its capability to determine isotopic compositions of many elements on a micron spatial scale has played a special role. Examples are measurements of H, N, and O isotopes and refractory trace elements in IDPs; C, N, Mg, and Si isotopes in interstellar SiC grains; and C and N isotopes and H, N, Al, and Si concentrations in interstellar graphite grains.
10. The evolution of interstellar medium mass probed by dust emission: Alma observations at z = 0.3-2
International Nuclear Information System (INIS)
Scoville, N.; Manohar, S.; Aussel, H.; Sheth, K.; Scott, K. S.; Sanders, D.; Ivison, R.; Pope, A.; Capak, P.; Vanden Bout, P.; Kartaltepe, J.; Robertson, B.; Lilly, S.
2014-01-01
The use of submillimeter dust continuum emission to probe the mass of interstellar dust and gas in galaxies is empirically calibrated using samples of local star-forming galaxies, Planck observations of the Milky Way, and high-redshift submillimeter galaxies. All of these objects suggest a similar calibration, strongly supporting the view that the Rayleigh-Jeans tail of the dust emission can be used as an accurate and very fast probe of the interstellar medium (ISM) in galaxies. We present ALMA Cycle 0 observations of the Band 7 (350 GHz) dust emission in 107 galaxies from z = 0.2 to 2.5. Three samples of galaxies with a total of 101 galaxies were stellar-mass-selected from COSMOS to have M * ≅ 10 11 M ☉ : 37 at z ∼ 0.4, 33 at z ∼ 0.9, and 31 at z = 2. A fourth sample with six infrared-luminous galaxies at z = 2 was observed for comparison with the purely mass-selected samples. From the fluxes detected in the stacked images for each sample, we find that the ISM content has decreased by a factor ∼6 from 1 to 2 × 10 10 M ☉ at both z = 2 and 0.9 down to ∼2 × 10 9 M ☉ at z = 0.4. The infrared-luminous sample at z = 2 shows a further ∼4 times increase in M ISM compared with the equivalent non-infrared-bright sample at the same redshift. The gas mass fractions are ∼2% ± 0.5%, 12% ± 3%, 14% ± 2%, and 53% ± 3% for the four subsamples (z = 0.4, 0.9, and 2 and infrared-bright galaxies).
11. Band-notched spiral antenna
Science.gov (United States)
Jeon, Jae; Chang, John
2018-03-13
A band-notched spiral antenna having one or more spiral arms extending from a radially inner end to a radially outer end for transmitting or receiving electromagnetic radiation over a frequency range, and one or more resonance structures positioned adjacent one or more segments of the spiral arm associated with a notch frequency band or bands of the frequency range so as to resonate and suppress the transmission or reception of electromagnetic radiation over said notch frequency band or bands.
12. Physical Conditions of the Interstellar Medium in Star-forming Galaxies at z1.5
Science.gov (United States)
Hayashi, Masao; Ly, Chun; Shimasaku, Kazuhiro; Motohara, Kentaro; Malkan, Matthew A.; Nagao, Tohru; Kashikawa, Nobunari; Goto, Ryosuke; Naito, Yoshiaki
2015-01-01
We present results from Subaru/FMOS near-infrared (NIR) spectroscopy of 118 star-forming galaxies at z approximately equal to 1.5 in the Subaru Deep Field. These galaxies are selected as [O II] lambda 3727 emitters at z approximately equal to 1.47 and 1.62 from narrow-band imaging. We detect H alpha emission line in 115 galaxies, [O III] lambda 5007 emission line in 45 galaxies, and H Beta, [N II] lambda 6584, and [S II]lambda lambda 6716, 6731 in 13, 16, and 6 galaxies, respectively. Including the [O II] emission line, we use the six strong nebular emission lines in the individual and composite rest-frame optical spectra to investigate physical conditions of the interstellar medium in star-forming galaxies at z approximately equal to 1.5. We find a tight correlation between H alpha and [O II], which suggests that [O II] can be a good star formation rate (SFR) indicator for galaxies at z approximately equal to 1.5. The line ratios of H alpha / [O II] are consistent with those of local galaxies. We also find that [O II] emitters have strong [O III] emission lines. The [O III]/[O II] ratios are larger than normal star-forming galaxies in the local Universe, suggesting a higher ionization parameter. Less massive galaxies have larger [O III]/[O II] ratios. With evidence that the electron density is consistent with local galaxies, the high ionization of galaxies at high redshifts may be attributed to a harder radiation field by a young stellar population and/or an increase in the number of ionizing photons from each massive star.
13. Measurements of the millimeter-wave spectrum of interstellar dust emission
Science.gov (United States)
Fischer, M. L.; Clapp, A.; Devlin, M.; Gundersen, J. O.; Lange, A. E.; Lubin, P. M.; Meinhold, P. R.; Richards, P. L.; Smoot, G. F.
1995-01-01
We report measurements of the differential brightness of interstellar dust emission near the Galactic plane and at high Galactic latitudes. The data were obtained as part of a program to measure anisotropy in the cosmic microwave background (CMB). The measurements were made with a 0.5 deg beam size and a 1.3 deg sinusoidal chop, in broad bands (Delta nu/nu approximately 0.3) centered near frequencies of 6, 9, and 12 cm(exp -1). A measurement made toward the Galactic plane, at longitude 1 = 23.7 deg, is compared with the contrast observed in the 100 micrometers IRAS data. Assuming the dust emission has a brightness I(sub nu) proportional to nu(sup n)B(sub nu)(T(sub d)), where B(sub nu) is the Planck function, a best fit yields n = 1.6 +/- 0.4, T(sub d) = 24 +/- 5 K. In a region near the star mu Pegasi (mu PEG l = 91 deg, b = -31 deg), the comparison of our data with the 100 micrometers IRAS data yields n = 1.4 +/- 0.4, and T(sub d) = 18 +/- 3 K. In a second region near the star gamma Ursa Minoris (GUM l = 108 deg, b = 41 deg), an upper limit is placed on contrast in dust emission. This upper limit is consistent with spectrum measured at mu PEG and the IRAS 100 micrometer emission contrast at GUM, which is approximately 8 times lower than mu PEG.
14. INTERSTELLAR-MEDIUM MAPPING IN M82 THROUGH LIGHT ECHOES AROUND SUPERNOVA 2014J
Energy Technology Data Exchange (ETDEWEB)
Yang, Yi; Wang, Lifan; Brown, Peter J. [George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A. and M. University, Department of Physics and Astronomy, 4242 TAMU, College Station, TX 77843 (United States); Baade, Dietrich; Patat, Ferdinando; Spyromilio, Jason [European Organisation for Astronomical Research in the Southern Hemisphere (ESO), Karl-Schwarzschild-Straße 2, D-85748 Garching b. München (Germany); Cracraft, Misty; Sparks, William B. [Space Telescope Science Institute, Baltimore, MD 21218 (United States); Höflich, Peter A. [Department of Physics, Florida State University, Tallahassee, Florida 32306-4350 (United States); Maund, Justyn; Stevance, Heloise F. [Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Wang, Xiaofeng [Physics Department and Tsinghua Center for Astrophysics (THCA), Tsinghua University, Beijing, 100084 (China); Wheeler, J. Craig, E-mail: [email protected] [Department of Astronomy and McDonald Observatory, The University of Texas at Austin, Austin, TX 78712 (United States)
2017-01-01
We present multiple-epoch measurements of the size and surface brightness of the light echoes from supernova (SN) 2014J in the nearby starburst galaxy M82. Hubble Space Telescope ( HST ) ACS/WFC images were taken ∼277 and ∼416 days after B -band maximum in the filters F 475 W , F 606 W , and F 775 W . Observations with HST WFC3/UVIS images at epochs ∼216 and ∼365 days are included for a more complete analysis. The images reveal the temporal evolution of at least two major light-echo components. The first one exhibits a filled ring structure with position-angle-dependent intensity. This radially extended, diffuse echo indicates the presence of an inhomogeneous interstellar dust cloud ranging from ∼100 to ∼500 pc in the foreground of the SN. The second echo component appears as an unresolved luminous quarter-circle arc centered on the SN. The wavelength dependence of scattering measured in different dust components suggests that the dust producing the luminous arc favors smaller grain sizes, while that causing the diffuse light echo may have sizes similar to those of the Milky Way dust. Smaller grains can produce an optical depth consistent with that along the supernova-Earth line of sight measured by previous studies around maximum light. Therefore, it is possible that the dust slab from which the luminous arc arises is also responsible for most of the extinction toward SN 2014J. The optical depths determined from the Milky Way-like dust in the scattering matters are lower than the optical depth produced by the dust slab.
15. Observations of the impact of starbursts on the interstellar medium in dwarf galaxies
Science.gov (United States)
Marlowe, Amanda T.; Heckman, Timothy M.; Wyse, Rosemary F. G.; Schommer, Robert
1995-01-01
Dwarf galaxies play a crucial role in our understanding of the formation and evolution of galaxies, and the concept of supernova-driven mass outflows is a vital ingredient in theories of the structure and evolution of dwarf galaxies. Despite the theoretical importance of these outflows, there is a very limited amount of direct observational evidence for their existence. We have therefore begun a detailed multi-wave-band search for outflows in dwarf (MB greater than or = -18) galaxies with extensive recent or ongoing centrally concentrated star formation. We report the first results of this search in the present paper. Observations of the ionized gas in dwarf amorphous galaxies with centrally concentrated populations of massive stars provide evidence for the large-scale expansion of their expansion of their ionized interstellar media. Fabry-Perot H alpha images reveal the presence of kiloparsec-scale 'superbubbles' and filaments which tend to be oriented along the galaxy minor axis. These structures are comparable in size to the chracteristic optical sizes of the galaxies, and dominate the morphology of the galaxies at low surface brightness in H alpha. Since expanding structure of this size and velocity are not observed in all low-mass galaxies with recent or ongoing star formation, we suggest that we are witnessing transient events that likely have a relatively low 'duty cycle' in such galaxies. That is, we argue that the particular galaxies in the present paper have had significantly elevated star formation rates over the past 107-108 yr (i.e., these are starburst or young poststarburst systems). This interpretation is consistent with the optical colors and emission-line properties of these galaxies.
16. AN ESTIMATE OF THE NEARBY INTERSTELLAR MAGNETIC FIELD USING NEUTRAL ATOMS
International Nuclear Information System (INIS)
Heerikhuisen, J.; Pogorelov, N. V.
2011-01-01
The strength and orientation of the magnetic field in the nearby interstellar medium have remained elusive, despite continual improvements in observations and models. Data from NASA's Voyager mission and the Solar Wind ANisotropies (SWAN) experiment on board Solar and Heliospheric Observatory (SOHO) have placed observational constraints on the magnetic field, and the more recent Interstellar Boundary Explorer (IBEX) data appear to also bear an imprint of the interstellar magnetic field (ISMF). In this paper, we combine computational models of the heliosphere with data from Voyager, SOHO/SWAN, and IBEX to estimate both the strength and direction of the nearby ISMF. On the basis of our simulations, we find that a field strength of 2-3 μG pointing from ecliptic coordinates (220-224, 39-44), combined with an interstellar hydrogen density of ∼0.15 cm -3 , produces results most consistent with observations.
17. Attenuation of VHE Gamma Rays by the Milky Way Interstellar Radiation Field
Energy Technology Data Exchange (ETDEWEB)
Moskalenko, Igor V.; /Stanford U., HEPL; Porter, Troy A.; /Louisiana State U.; Strong, Andrew W.; /Garching, Max Planck Inst., MPE
2006-04-19
The attenuation of very high energy gamma rays by pair production on the Galactic interstellar radiation field has long been thought of as negligible. However, a new calculation of the interstellar radiation field consistent with multi-wavelength observations by DIRBE and FIRAS indicates that the energy density of the Galactic interstellar radiation field is higher, particularly in the Galactic center, than previously thought. We have made a calculation of the attenuation of very high energy gamma rays in the Galaxy using this new interstellar radiation field which takes into account its nonuniform spatial and angular distributions. We find that the maximum attenuation occurs around 100 TeV at the level of about 25% for sources located at the Galactic center, and is important for both Galactic and extragalactic sources.
18. Spiral model of the Galaxy from observations of the interstellar light attenuation
International Nuclear Information System (INIS)
Urasin, L.A.
1987-01-01
The model of two arms spiral structure of the Galaxy is made from the observations of space distribution of the interstellar dust matter. This model is the logarithmic spiral with characteristic angle (pith) 6.5 deg
19. Detailed investigation of proposed gas-phase syntheses of ammonia in dense interstellar clouds
International Nuclear Information System (INIS)
Herbst, E.; Defrees, D.J.; Mclean, A.D.; Molecular Research Institute, Palo Alto, CA; IBM Almaden Research Center, San Jose, CA)
1987-01-01
The initial reactions of the Herbst and Klemperer (1973) and the Dalgarno (1974) schemes (I and II, respectively) for the gas-phase synthesis of ammonia in dense interstellar clouds were investigated. The rate of the slightly endothermic reaction between N(+) and H2 to yield NH(+) and H (scheme I) under interstellar conditions was reinvestigated under thermal and nonthermal conditions based on laboratory data. It was found that the relative importance of this reaction in synthesizing ammonia is determined by how the laboratory data at low temperature are interpreted. On the other hand, the exothermic reaction between N and H3(+) to form NH2(+) + H (scheme II) was calculated to possess significant activation energy and, therefore, to have a negligible rate coefficient under interstellar conditions. Consequently, this reaction cannot take place appreciably in interstellar clouds. 41 references
20. The hierarchically organized splitting of chromosome bands into sub-bands analyzed by multicolor banding (MCB).
Science.gov (United States)
Lehrer, H; Weise, A; Michel, S; Starke, H; Mrasek, K; Heller, A; Kuechler, A; Claussen, U; Liehr, T
2004-01-01
To clarify the nature of chromosome sub-bands in more detail, the multicolor banding (MCB) probe-set for chromosome 5 was hybridized to normal metaphase spreads of GTG band levels at approximately 850, approximately 550, approximately 400 and approximately 300. It could be observed that as the chromosomes became shorter, more of the initial 39 MCB pseudo-colors disappeared, ending with 18 MCB pseudo-colored bands at the approximately 300-band level. The hierarchically organized splitting of bands into sub-bands was analyzed by comparing the disappearance or appearance of pseudo-color bands of the four different band levels. The regions to split first are telomere-near, centromere-near and in 5q23-->q31, followed by 5p15, 5p14, and all GTG dark bands in 5q apart from 5q12 and 5q32 and finalized by sub-band building in 5p15.2, 5q21.2-->q21.3, 5q23.1 and 5q34. The direction of band splitting towards the centromere or the telomere could be assigned to each band separately. Pseudo-colors assigned to GTG-light bands were resistant to band splitting. These observations are in concordance with the recently proposed concept of chromosome region-specific protein swelling. Copyright 2003 S. Karger AG, Basel
1. Structure in the interstellar polarization curve and the nature of the polarizing grains
International Nuclear Information System (INIS)
Wolstencroft, R.D.; Smith, R.J.
1984-01-01
At this workshop the emphasis is on divining the nature of the interstellar grains by using infrared spectral features as the principal diagnostic. Nevertheless other approaches are also contributing to an understanding of the grains and deserve some attention. This paper describes the structure recently found in the interstellar polarization curve, and discusses its relation to the structure seen in the extinction curve and the nature of the grains producing the spectral features. (author)
2. Ultraviolet interstellar linear polarization. I - Applicability of current dust grain models
Science.gov (United States)
Wolff, Michael J.; Clayton, Geoffrey C.; Meade, Marilyn R.
1993-01-01
UV spectropolarimetric observations yielding data on the wavelength-dependence of interstellar polarization along eight lines of sight facilitate the evaluation of dust grain models previously used to fit the extinction and polarization in the visible and IR. These models pertain to bare silicate/graphite grains, silicate cores with organic refractory mantles, silicate cores with amorphous carbon mantles, and composite grains. The eight lines-of-sight show three different interstellar polarization dependences.
3. Cataclysmic variables as probes of x-ray properties of interstellar grains
International Nuclear Information System (INIS)
Bode, M.F.; Evans, A.; Norwell, G.A.
1983-01-01
Interstellar-grain properties have previously been probed at wavelengths ranging from the infrared to the ultraviolet. Recent work by other authors has shown that we may also observe the effects of scattering by such grains at x-ray wavelengths. In this paper we suggest that investigations of the x-ray properties of interstellar grains may profitably be conducted in sight lines to variable sources. Particular emphasis is given in this context to cataclysmic variables and related objects
4. Science From Beyond: NASA's Pioneer Plaque and the History of Interstellar Communication, 1957- 1972
Science.gov (United States)
Macauley, William
2012-05-01
In the late twentieth century, science and technology facilitated exploration beyond the Solar System and extended human knowledge through messages comprised of pictures and mathematical symbols, transmitted from radio telescopes and inscribed on material artifacts attached to spacecraft. ‘Interstellar communication' refers to collective efforts by scientists and co-workers to detect and transmit intelligible messages between humans and supposed extraterrestrial intelligence in remote star systems. Interstellar messages are designed to communicate universal knowledge without recourse to text, human linguistic systems or anthropomorphic content because it is assumed that recipients have no prior knowledge of humankind or the planet we inhabit. Scientists must therefore imagine how extraterrestrials will relate to human knowledge and culture. The production and transmission of interstellar messages became interdisciplinary design problems that involved collaboration and exchange of ideas between scientists, visual artists, and others. My proposed paper will review sociocultural aspects of interstellar communication since the late 1950s and focus on key issues regarding conception, design and production of a specific interstellar message launched into space during the early 1970s - NASA's Pioneer plaque. The paper will explore how research on the history of interstellar communication relates to previous historical and sociological studies on rhetorical aspects of visual representation and mathematics in scientific practice. In particular, I will explain how the notion of ‘inscription' is an appropriate conceptual tool for analyzing how scientists have used pictures to articulate and validate knowledge claims and scientific facts. I argue that scientific knowledge carried on interstellar messages such as the Pioneer plaque is constituted in material practices and inscription technologies that translate natural objects, agency and culture into legible forms
5. A New, Large-scale Map of Interstellar Reddening Derived from H I Emission
Science.gov (United States)
Lenz, Daniel; Hensley, Brandon S.; Doré, Olivier
2017-09-01
We present a new map of interstellar reddening, covering the 39% of the sky with low H I column densities ({N}{{H}{{I}}}Peek and Graves based on observed reddening toward passive galaxies. We therefore argue that our H I-based map provides the most accurate interstellar reddening estimates in the low-column-density regime to date. Our reddening map is made publicly available at doi.org/10.7910/DVN/AFJNWJ.
6. A new component of the interstellar matter - Small grains and large aromatic molecules
International Nuclear Information System (INIS)
Puget, J.L.
1989-01-01
Predictions from dust models constructed to account for the interstellar extinction curve are in conflict with emission data. This paper shows that the introduction of small grains and large aromatic molecules as a new component of the interstellar matter can resolve this conflict. Observational evidence for the existence of very small grains is also reviewed, along with the physics of IR emission by thermal fluctuations and its relation to very small particles. 99 refs
7. The inventory of interstellar materials available for the formation of the solar system
Science.gov (United States)
Sandford, Scott A.
1996-07-01
Tremendous progress has been made in the field of interstellar dust in recent years through the use of telescopic observations, theoretical studies, laboratory studies of analogs, and the study of actual interstellar samples found in meteorites. It is increasingly clear that the interstellar medium (ISM) contains an enormous diversity of materials created by a wide range of chemical and physical processes. This understanding is a far cry from the picture of interstellar materials held as recently as two decades ago, a picture which incorporated only a few generic types of grains and few molecules. In this paper, I attempt to review some of our current knowledge of the more abundant materials thought to exist in the ISM. The review concentrates on matter in interstellar dense molecular clouds since it is the materials in these environments from which new stars and planetary systems are formed. However, some discussion is reserved for materials in circumstellar environments and in the diffuse ISM. The paper also focuses largely on solid materials as opposed to gases since solids contain a major fraction of the heavier elements in clouds and because solids are most likely to survive incorporation into new planetary systems in identifiable form. The paper concludes with a discussion of some of the implications resulting from the recent growth of our knowledge about interstellar materials and also considers a number of areas in which future work might be expected to yield important results.
8. Probing the Spatial Distribution of the Interstellar Dust Medium by High Angular Resolution X-ray Halos of Point Sources
Science.gov (United States)
Xiang, Jingen
X-rays are absorbed and scattered by dust grains when they travel through the interstellar medium. The scattering within small angles results in an X-ray `halo''. The halo properties are significantly affected by the energy of radiation, the optical depth of the scattering, the grain size distributions and compositions, and the spatial distribution of dust along the line of sight (LOS). Therefore analyzing the X-ray halo properties is an important tool to study the size distribution and spatial distribution of interstellar grains, which plays a central role in the astrophysical study of the interstellar medium, such as the thermodynamics and chemistry of the gas and the dynamics of star formation. With excellent angular resolution, good energy resolution and broad energy band, the Chandra ACIS is so far the best instrument for studying the X-ray halos. But the direct images of bright sources obtained with ACIS usually suffer from severe pileup which prevents us from obtaining the halos in small angles. We first improve the method proposed by Yao et al to resolve the X-ray dust scattering halos of point sources from the zeroth order data in CC-mode or the first order data in TE mode with Chandra HETG/ACIS. Using this method we re-analyze the Cygnus X-1 data observed with Chandra. Then we studied the X-ray dust scattering halos around 17 bright X-ray point sources using Chandra data. All sources were observed with the HETG/ACIS in CC-mode or TE-mode. Using the interstellar grain models of WD01 model and MRN model to fit the halo profiles, we get the hydrogen column densities and the spatial distributions of the scattering dust grains along the line of sights (LOS) to these sources. We find there is a good linear correlation not only between the scattering hydrogen column density from WD01 model and the one from MRN model, but also between N_{H} derived from spectral fits and the one derived from the grain models WD01 and MRN (except for GX 301-2 and Vela X-1): N
9. Noise exposure in marching bands
Science.gov (United States)
Keefe, Joseph
2005-09-01
Previous studies involving orchestras have shown that music ensembles can produce hazardous noise levels. There are no similar data for marching bands and pep bands. In order to evaluate the noise levels produced by marching and pep bands, 1/3-octave-band sound-pressure levels were measured while these groups rehearsed and performed. Data were collected while marching with the bands to ensure a realistic environment. Comparing these data to OSHA and NIOSH criteria, marching and pep band exposures often exceed safe values. For typical exposures, OSHA doses range from 11% to 295%, while NIOSH doses range from 35% to 3055%. Exposures that would be considered hazardous in the workplace are common in marching and pep bands; students and band directors should take steps to recognize the risk posed by various instruments and various locations, and should implement hearing conservation efforts.
10. Organic Signature of Dust from the Interstellar Medium (ISM)
Science.gov (United States)
Freund, Friedemann; Freund, Minoru; Staple, Aaron; Scoville, John
2001-01-01
Dust in the ISM carries an "organic" signature in form of a distinct group of C-H stretching bands, both in emission and absorption, around 3.4 micrometers. These bands agree with the symmetrical and asymmetrical C-H stretching vibrations of aliphatic -CH2- entities and are thought to be associated with organic molecules on the surface of dust grains. We show that this interpretation is inconsistent with laboratory experiments. Synthetic MgO and natural olivine single crystals, grown from a CO/CO2/H2O-saturated melt, exhibit the same C-H stretching bands but those bands are clearly associated with C-H entities inside the dense mineral matrix. The multitude of C-H stretching bands suggests that the C-H bonds arise from polyatomic C(sub n) entities. We heated the MgO and olivine crystals to temperatures between 550-1000 K to pyrolyze the C-H bonds and to cause the C-H stretching bands to disappear. Upon annealing at moderate temperatures between 300-390 K the C-H stretching bands reappear within a few days to weeks. The C-H stretching band intensity increases linearly with the square root of time. Thus, while the pyrolysis broke the C-H bonds and caused the H to disperse in the mineral matrix, the H atoms (or H2 molecules) are sufficiently mobile to return during annealing and reestablish the C-H bonds. Dust grains that condense in a gas-laden environment (outflow of late-stage stars or in dense molecular clouds) probably incorporate the same type of Cn-H entities. Imbedded in and in part bonded to the surrounding mineral matrix, the Cn-H entities display C-H stretching bands in the 3.4 micrometer region, but their lower frequency librational modes are so strongly coupled to the lattice modes that they broaden excessively and thus become unobservable.
11. ON THE FORMATION OF INTERSTELLAR WATER ICE: CONSTRAINTS FROM A SEARCH FOR HYDROGEN PEROXIDE ICE IN MOLECULAR CLOUDS
Energy Technology Data Exchange (ETDEWEB)
Smith, R. G.; Wright, C. M.; Robinson, G. [School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600 (Australia); Charnley, S. B. [Astrochemistry Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Pendleton, Y. J. [NASA Lunar Science Institute, NASA Ames Research Center, Moffett Field, CA 94035 (United States); Maldoni, M. M., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Geoscience Australia, Canberra, ACT 2601 (Australia)
2011-12-20
Recent surface chemistry experiments have shown that the hydrogenation of molecular oxygen on interstellar dust grains is a plausible formation mechanism, via hydrogen peroxide (H{sub 2}O{sub 2}), for the production of water (H{sub 2}O) ice mantles in the dense interstellar medium. Theoretical chemistry models also predict the formation of a significant abundance of H{sub 2}O{sub 2} ice in grain mantles by this route. At their upper limits, the predicted and experimental abundances are sufficiently high that H{sub 2}O{sub 2} should be detectable in molecular cloud ice spectra. To investigate this further, laboratory spectra have been obtained for H{sub 2}O{sub 2}/H{sub 2}O ice films between 2.5 and 200 {mu}m, from 10 to 180 K, containing 3%, 30%, and 97% H{sub 2}O{sub 2} ice. Integrated absorbances for all the absorption features in low-temperature H{sub 2}O{sub 2} ice have been derived from these spectra. For identifying H{sub 2}O{sub 2} ice, the key results are the presence of unique features near 3.5, 7.0, and 11.3 {mu}m. Comparing the laboratory spectra with the spectra of a group of 24 protostars and field stars, all of which have strong H{sub 2}O ice absorption bands, no absorption features are found that can definitely be identified with H{sub 2}O{sub 2} ice. In the absence of definite H{sub 2}O{sub 2} features, the H{sub 2}O{sub 2} abundance is constrained by its possible contribution to the weak absorption feature near 3.47 {mu}m found on the long-wavelength wing of the 3 {mu}m H{sub 2}O ice band. This gives an average upper limit for H{sub 2}O{sub 2}, as a percentage of H{sub 2}O, of 9% {+-} 4%. This is a strong constraint on parameters for surface chemistry experiments and dense cloud chemistry models.
12. Semiconductors bonds and bands
CERN Document Server
Ferry, David K
2013-01-01
As we settle into this second decade of the twenty-first century, it is evident that the advances in micro-electronics have truly revolutionized our day-to-day lifestyle. The technology is built upon semiconductors, materials in which the band gap has been engineered for special values suitable to the particular application. This book, written specifically for a one semester course for graduate students, provides a thorough understanding of the key solid state physics of semiconductors. It describes how quantum mechanics gives semiconductors unique properties that enabled the micro-electronics revolution, and sustain the ever-growing importance of this revolution.
13. Toroidal Plasma Thruster for Interplanetary and Interstellar Space Flights
International Nuclear Information System (INIS)
Gorelenkov, N.N.; Zakharov, L.E.; Gorelenkova, M.V.
2001-01-01
This work involves a conceptual assessment for using the toroidal fusion reactor for deep space interplanetary and interstellar missions. Toroidal thermonuclear fusion reactors, such as tokamaks and stellarators, are unique for space propulsion, allowing for a design with the magnetic configuration localized inside toroidal magnetic field coils. Plasma energetic ions, including charged fusion products, can escape such a closed configuration at certain conditions, a result of the vertical drift in toroidal rippled magnetic field. Escaping particles can be used for direct propulsion (since toroidal drift is directed one way vertically) or to create and heat externally confined plasma, so that the latter can be used for propulsion. Deuterium-tritium fusion neutrons with an energy of 14.1 MeV also can be used for direct propulsion. A special design allows neutrons to escape the shield and the blanket of the tokamak. This provides a direct (partial) conversion of the fusion energy into the directed motion of the propellant. In contrast to other fusion concepts proposed for space propulsion, this concept utilizes the natural drift motion of charged particles out of the closed magnetic field configuration
14. Cometary Materials Originating from Interstellar Ices: Clues from Laboratory Experiments
Energy Technology Data Exchange (ETDEWEB)
Fresneau, A.; Mrad, N. Abou; LS d’Hendecourt, L.; Duvernay, F.; Chiavassa, T.; Danger, G. [Aix-Marseille Université, PIIM UMR-CNRS 7345, F-13397 Marseille (France); Flandinet, L.; Orthous-Daunay, F.-R.; Vuitton, V.; Thissen, R., E-mail: [email protected] [Université Grenoble Alpes, CNRS, IPAG, Grenoble F-38000 (France)
2017-03-10
We use laboratory experiments to derive information on the chemistry occurring during the evolution of astrophysical ices from dense molecular clouds to interplanetary objects. Through a new strategy that consists of coupling very high resolution mass spectrometry and infrared spectroscopy (FT-IR), we investigate the molecular content of the organic residues synthesized from different initial ice compositions. We also obtain information on the evolution of the soluble part of the residues after their over-irradiation. The results give insight into the role of water ice as a trapping and diluting agent during the chemical evolution. They also give information about the importance of the amount of ammonia in such ices, particularly regarding its competition with the carbon chemistry. All of these results allow us to build a first mapping of the evolution of soluble organic matter based on its chemical and physical history. Furthermore, our results suggest that interstellar ices should lead to organic materials enriched in heteroatoms that present similarities with cometary materials but strongly differ from meteoritic organic material, especially in their C/N ratios.
15. The Implications of Interstellar Dust for the Cosmic Microwave Background
Science.gov (United States)
Schmelz, Joan T.; Verschuur, Gerrit
2018-01-01
A detailed comparison of the full range of PLANCK and WMAP data for small (2 deg by 2 deg) areas of sky and the Cosmic Microwave Background (CMB) ILC maps reveals that the structure of foreground dust may be more complex than previously thought. If 857 and 353 GHz emission is dominated by galactic dust at a distance data also show that there is no single answer for the question, “To what extent does dust contaminate the cosmologically important 143 GHz data?” In some directions, the contamination appears to be quite strong, but in others, it is less of an issue. This complexity needs to be taken in account in order to derive an accurate foreground mask in the quest to understand the CMB small-scale structure. We hope that a continued investigation of these data will lead to a definitive answer to the question above and, possibly, to new scientific insights on interstellar matter, the CMB, or both.
16. Detection of interstellar (C-13)N toward Zeta Ophiuchi
International Nuclear Information System (INIS)
Crane, P.; Hegyi, D.J.
1988-01-01
Observations of a diffuse interstellar cloud toward Zeta Oph, obtained with resolution 100,000-150,000 near the 3874.608-A R(0) line of (C-12)N using a coude echelle spectrograph on the 1.4-m telescope at ESO during 1984 and 1985, are reported. Data from 54 20-min runs were fitted to Gaussian line shapes using the line center, depth, and width of the R(0) and R(1) lines of (C-12)N and the line center and depth of the R(0) line of (C-13)N as fitting parameters. The (C-13)N R(0) line, with equivalent width 0.190 + or - 0.020 mA, was detected 173.7 + or - 0.8 mA to the red of (C-12)N R(0); the corresponding isotope abundance ratio, (C-12)N/(C-13)N = 47.3 + 5.5 or -4.4, is shown to be in good agreement with previous measurements for CH(+) (Hawkins et al., 1985). 13 references
17. NEW ULTRAVIOLET EXTINCTION CURVES FOR INTERSTELLAR DUST IN M31
Energy Technology Data Exchange (ETDEWEB)
Clayton, Geoffrey C. [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Gordon, Karl D.; Bohlin, R. C. [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Bianchi, Luciana C. [Department of Physics and Astronomy, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218 (United States); Massa, Derck L.; Wolff, Michael J. [Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301 (United States); Fitzpatrick, Edward L., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Department of Astronomy and Astrophysics, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085 (United States)
2015-12-10
New low-resolution UV spectra of a sample of reddened OB stars in M31 were obtained with the Hubble Space Telescope/STIS to study the wavelength dependence of interstellar extinction and the nature of the underlying dust grain populations. Extinction curves were constructed for four reddened sightlines in M31 paired with closely matching stellar atmosphere models. The new curves have a much higher signal-to-noise ratio than previous studies. Direct measurements of N(H i) were made using the Lyα absorption lines enabling gas-to-dust ratios to be calculated. The sightlines have a range in galactocentric distance of 5–14 kpc and represent dust from regions of different metallicities and gas-to-dust ratios. The metallicities sampled range from solar to 1.5 solar. The measured curves show similarity to those seen in the Milky Way and the Large Magellanic Cloud. The Maximum Entropy Method was used to investigate the dust composition and size distribution for the sightlines observed in this program, finding that the extinction curves can be produced with the available carbon and silicon abundances if the metallicity is super-solar.
18. The destruction and growth of dust grains in interstellar space
International Nuclear Information System (INIS)
Barlow, M.J.
1978-01-01
The processes governing the destruction and growth of dust grains in interstellar space are investigated with a view to establishing the conditions required for the existence of ice mantles. In this paper sputtering by particles with energies in the eV to GeV range is considered. Previous sputtering yield estimates which were based on theoretical considerations are shown to be greatly in error for incident particle energies of less than 1 keV. Empirical formulae for the sputtering threshold energy and the sputtering yield are derived from the extensive experimental data available. The sputtering of grains in H II regions, in the inter-cloud medium, and in shock waves produced by cloud-cloud collisions and by supernova remnants, is investigated. Of these, supernova remnants are shown to be the most important, leading to lifetimes of approximately 2 x 10 8 yr for ice grains and between 5 to 20 x 10 8 yr for refractory grains. Destruction rates are estimated for grains bombarded by MeV and GeV cosmic rays. It is shown that collision cascade sputtering dominates evaporative sputtering produced by thermal spikes. It is also shown that even if all electron excitation energy loss in a grain material could be transferred to the lattice particles, the observed cosmic ray flux spectrum could not cause significant destruction of ice grains. (author)
19. DESTRUCTION OF INTERSTELLAR DUST IN EVOLVING SUPERNOVA REMNANT SHOCK WAVES
International Nuclear Information System (INIS)
Slavin, Jonathan D.; Dwek, Eli; Jones, Anthony P.
2015-01-01
Supernova generated shock waves are responsible for most of the destruction of dust grains in the interstellar medium (ISM). Calculations of the dust destruction timescale have so far been carried out using plane parallel steady shocks, however, that approximation breaks down when the destruction timescale becomes longer than that for the evolution of the supernova remnant (SNR) shock. In this paper we present new calculations of grain destruction in evolving, radiative SNRs. To facilitate comparison with the previous study by Jones et al., we adopt the same dust properties as in that paper. We find that the efficiencies of grain destruction are most divergent from those for a steady shock when the thermal history of a shocked gas parcel in the SNR differs significantly from that behind a steady shock. This occurs in shocks with velocities ≳200 km s −1 for which the remnant is just beginning to go radiative. Assuming SNRs evolve in a warm phase dominated ISM, we find dust destruction timescales are increased by a factor of ∼2 compared to those of Jones et al., who assumed a hot gas dominated ISM. Recent estimates of supernova rates and ISM mass lead to another factor of ∼3 increase in the destruction timescales, resulting in a silicate grain destruction timescale of ∼2–3 Gyr. These increases, while not able to resolve the problem of the discrepant timescales for silicate grain destruction and creation, are an important step toward understanding the origin and evolution of dust in the ISM
20. General physical characteristics of the interstellar molecular gas
International Nuclear Information System (INIS)
Turner, B.E.
1979-01-01
The interstellar medium may be characterized by several physically rather distinct regimes: coronal gas, intercloud gas, diffuse clouds, isolated dark clouds and globules (of small to modest mass), more massive molecular clouds containing OB (and later) stars, and giant molecular clouds. Values of temperature, density, ionization fraction, mass, size, and velocity field are discussed for each regime. Heating and cooling mechanisms are reviewed. Nearly all molecular clouds exceed the Jeans criteria for gravitational instability, yet detailed models reveal no cases where observations can be interpreted unambiguously in terms of rapid collapse. The possibility that clouds are supported by turbulence, rotation, or magnetic fields is discussed, and it is concluded that none of these agencies suffice. Comments are made about fragmentation and star formation in molecular clouds, with possible explanations for why only low mass stars form in low mass clouds, why early-type stars form only in clouds with masses > approximately 10 3 M solar masses, and why O-stars seem to form near edges of clouds. Finally, large-scale interactions between molecular clouds and the galactic disk stellar population are discussed. (Auth.)
1. On Al-26 and other short-lived interstellar radioactivity
Science.gov (United States)
Clayton, Donald D.; Hartmann, Dieter H.; Leising, Mark D.
1993-01-01
Several authors have shown that massive stars exploding at a rate of about three per century can account for a large portion, if not all, of the observed interstellar Al-26. In a separate argument using models of Galactic chemical evolution, Clayton (1984) showed that the Al-26/Al-27 production ratio was not large enough to maintain enough Al-26 in the Galactic disk gas of about 10 exp 10 solar masses having solar composition. We present a resolution of those conflicting arguments. A past history of Galactic infall growing the Galactic disk so dilutes the stable Al-27 concentration that the two approaches can be brought into near agreement. If massive stars dominate the production of Al-26, we suggest that the apparent shortfall of their Al-26/Al-27 yield ratio is to be interpreted as evidence for significant growth of the Galactic disk. We also discuss the implications of these arguments for other extinct radioactivities in meteorites, using I-129 and Sm-146 as examples.
2. Chemical Simulations of Prebiotic Molecules: Interstellar Ethanimine Isomers
Science.gov (United States)
Quan, Donghui; Herbst, Eric; Corby, Joanna F.; Durr, Allison; Hassel, George
2016-06-01
The E- and Z-isomers of ethanimine (CH3CHNH) were recently detected toward the star-forming region Sagittarius (Sgr) B2(N) using the Green Bank Telescope PRIMOS cm-wave spectral data, and imaged by the Australia Telescope Compact Array. Ethanimine is not reported in the hot cores of Sgr B2, but only in gas that absorbs at +64 and +82 km s-1 in the foreground of continuum emission generated by H II regions. The ethanimine isomers can serve as precursors of the amino acid alanine and may play important roles in forming biological molecules in the interstellar medium. Here we present a study of the chemistry of ethanimine using a gas-grain simulation based on rate equations, with both isothermal and warm-up conditions. In addition, the density, kinetic temperature, and cosmic ray ionization rate have been varied. For a variety of physical conditions in the warm-up models for Sgr B2(N) and environs, the simulations show reasonable agreement with observationally obtained abundances. Isothermal models of translucent clouds along the same line of sight yield much lower abundances, so that ethanimine would be much more difficult to detect in these sources despite the fact that other complex molecules have been detected there.
3. Extragalactic interstellar extinction curves: Indicators of local physical conditions
Energy Technology Data Exchange (ETDEWEB)
Cecchi-Pestellini, Cesare [INAF-Osservatorio Astronomico di Palermo, P.zza Parlamento 1, I-90134 Palermo (Italy); Viti, Serena; Williams, David A., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Department of Physics and Astronomy, University College London Gower Street, London WC1E 6BT (United Kingdom)
2014-06-20
Normalized interstellar extinction curves (ISECs) in the Milky Way and other galaxies show a variety of shapes. This variety is attributed to differences along different sight lines in the abundances of the several dust and gas components contributing to extinction. In this paper we propose that these abundance differences are not arbitrary but are a specific consequence of the physical conditions on those sight lines. If this proposal is correct, then it implies that ISECs contain information about physical conditions in the regions generating extinction. This may be particularly important for high redshift galaxies where information on the conditions may be difficult to obtain. We adopt a model of extinction carriers in which the solid and gaseous components are not immutable but respond time-dependently to the local physics. We validate this model by fitting extinction curves measured on sight lines in the Magellanic Clouds and obtained for the gamma-ray burst afterglow GRB 080605. We present results for this model as follows: (1) we show that computed ISECs are controlled by a small number of physical parameters, (2) we demonstrate the sensitivity of computed ISECs to these parameters, (3) we compute as examples ISECs for particular galaxy types, and (4) we note that different galaxy types have different shapes of ISEC.
4. Cometary Materials Originating from Interstellar Ices: Clues from Laboratory Experiments
Science.gov (United States)
Fresneau, A.; Abou Mrad, N.; d'Hendecourt, L. LS; Duvernay, F.; Flandinet, L.; Orthous-Daunay, F.-R.; Vuitton, V.; Thissen, R.; Chiavassa, T.; Danger, G.
2017-03-01
We use laboratory experiments to derive information on the chemistry occurring during the evolution of astrophysical ices from dense molecular clouds to interplanetary objects. Through a new strategy that consists of coupling very high resolution mass spectrometry and infrared spectroscopy (FT-IR), we investigate the molecular content of the organic residues synthesized from different initial ice compositions. We also obtain information on the evolution of the soluble part of the residues after their over-irradiation. The results give insight into the role of water ice as a trapping and diluting agent during the chemical evolution. They also give information about the importance of the amount of ammonia in such ices, particularly regarding its competition with the carbon chemistry. All of these results allow us to build a first mapping of the evolution of soluble organic matter based on its chemical and physical history. Furthermore, our results suggest that interstellar ices should lead to organic materials enriched in heteroatoms that present similarities with cometary materials but strongly differ from meteoritic organic material, especially in their C/N ratios.
5. CHEMICAL SIMULATIONS OF PREBIOTIC MOLECULES: INTERSTELLAR ETHANIMINE ISOMERS
Energy Technology Data Exchange (ETDEWEB)
Quan, Donghui; Durr, Allison [Department of Chemistry, Eastern Kentucky University, Richmond, KY 40475 (United States); Herbst, Eric [Departments of Chemistry and Astronomy, University of Virginia, Charlottesville, VA 22904 (United States); Corby, Joanna F. [Department of Astronomy, University of Virginia, Charlottesville, VA 22904 (United States); Hassel, George [Physics and Astronomy Department, Siena College, Loudonville, NY 12211 (United States)
2016-06-20
The E- and Z- isomers of ethanimine (CH{sub 3}CHNH) were recently detected toward the star-forming region Sagittarius (Sgr) B2(N) using the Green Bank Telescope PRIMOS cm-wave spectral data, and imaged by the Australia Telescope Compact Array. Ethanimine is not reported in the hot cores of Sgr B2, but only in gas that absorbs at +64 and +82 km s{sup −1} in the foreground of continuum emission generated by H ii regions. The ethanimine isomers can serve as precursors of the amino acid alanine and may play important roles in forming biological molecules in the interstellar medium. Here we present a study of the chemistry of ethanimine using a gas-grain simulation based on rate equations, with both isothermal and warm-up conditions. In addition, the density, kinetic temperature, and cosmic ray ionization rate have been varied. For a variety of physical conditions in the warm-up models for Sgr B2(N) and environs, the simulations show reasonable agreement with observationally obtained abundances. Isothermal models of translucent clouds along the same line of sight yield much lower abundances, so that ethanimine would be much more difficult to detect in these sources despite the fact that other complex molecules have been detected there.
6. Estimating Stellar Parameters and Interstellar Extinction from Evolutionary Tracks
Directory of Open Access Journals (Sweden)
Sichevsky S.
2016-03-01
Full Text Available Developing methods for analyzing and extracting information from modern sky surveys is a challenging task in astrophysical studies. We study possibilities of parameterizing stars and interstellar medium from multicolor photometry performed in three modern photometric surveys: GALEX, SDSS, and 2MASS. For this purpose, we have developed a method to estimate stellar radius from effective temperature and gravity with the help of evolutionary tracks and model stellar atmospheres. In accordance with the evolution rate at every point of the evolutionary track, star formation rate, and initial mass function, a weight is assigned to the resulting value of radius that allows us to estimate the radius more accurately. The method is verified for the most populated areas of the Hertzsprung-Russell diagram: main-sequence stars and red giants, and it was found to be rather precise (for main-sequence stars, the average relative error of radius and its standard deviation are 0.03% and 3.87%, respectively.
7. Small Body Exploration Technologies as Precursors for Interstellar Robotics
Energy Technology Data Exchange (ETDEWEB)
Noble, Robert; /SLAC; Sykes, Mark V.; /PSI, Tucson
2012-02-15
The scientific activities undertaken to explore our Solar System will be the same as required someday at other stars. The systematic exploration of primitive small bodies throughout our Solar System requires new technologies for autonomous robotic spacecraft. These diverse celestial bodies contain clues to the early stages of the Solar System's evolution as well as information about the origin and transport of water-rich and organic material, the essential building blocks for life. They will be among the first objects studied at distant star systems. The technologies developed to address small body and outer planet exploration will form much of the technical basis for designing interstellar robotic explorers. The Small Bodies Assessment Group, which reports to NASA, initiated a Technology Forum in 2011 that brought together scientists and technologists to discuss the needs and opportunities for small body robotic exploration in the Solar System. Presentations and discussions occurred in the areas of mission and spacecraft design, electric power, propulsion, avionics, communications, autonomous navigation, remote sensing and surface instruments, sampling, intelligent event recognition, and command and sequencing software. In this paper, the major technology themes from the Technology Forum are reviewed, and suggestions are made for developments that will have the largest impact on realizing autonomous robotic vehicles capable of exploring other star systems.
8. REACTIVITY OF ANIONS IN INTERSTELLAR MEDIA: DETECTABILITY AND APPLICATIONS
Energy Technology Data Exchange (ETDEWEB)
Senent, M. L. [Departamento de Quimica y Fisica Teoricas, Instituto de Estructura de la Materia, IEM-C.S.I.C., Serrano 121, Madrid E-28006 (Spain); Hochlaf, M., E-mail: [email protected], E-mail: [email protected] [Laboratoire de Modelisation et Simulation Multi Echelle, Universite Paris-Est, MSME UMR 8208 CNRS, 5 boulevard Descartes, F-77454 Marne-la-Vallee (France)
2013-05-01
We propose a general rule to distinguish between detectable and undetectable astronomical anions. We believe that only few anions live long enough in the interstellar medium and thus can be detected. Our method is based on quantum mechanical calculations capable of describing accurately the evolution of electronic states during chemical processes. The still not fully understood reactivity at low temperatures is discussed considering non-adiabatic effects. The role of excited states has usually been neglected in previous works which basically focused on the ground electronic state for interpretations of experimental observations. Here, we deal with unsaturated carbon chains (e.g., C{sub n} H{sup -}), which show a high density of electronic states close to their corresponding ground electronic states, complex molecular dynamics, and non-adiabatic phenomena. Our general rule shows that it is not sufficient that anions exist in the gas phase (in the laboratory) to be present in media such as astrophysical media, since formation and decomposition reactions of these anions may allow the population of anionic electronic states to autodetach, forming neutrals. For C{sub n} H, reactivity depends strongly on n, where long and short chains behave differently. Formation of linear chains is relevant.
9. COMET SHOWERS ARE NOT INDUCED BY INTERSTELLAR CLOUDS
Energy Technology Data Exchange (ETDEWEB)
Morris, D.E.
1985-11-01
Encounters with interstellar clouds (IC) have been proposed by Rampino and Stothers as a cause of quasi-periodic intense comet showers leading to earth impacts, in order to explain the periodicity in marine mass extinctions found by Raup and Sepkoski. The model was described further, criticized and defended. The debate has centered on the question of whether the scale height of the clouds is small enough (in comparison to the amplitude of the oscillation of the solar system about the plane of the Galaxy) to produce a modulation in the rate of encounters. We wish to point out another serious, we believe fatal, defect in this model - the tidal fields of ICs are not strong enough to produce intense comet showers leading to earth impacts by bringing comets of the postulated inner Oort cloud into earth crossing orbits, except possibly during very rare encounters with very dense clouds. We will show that encounters with abundant clouds of low density cannot produce comet showers; cloud density N > 10{sup 3} atoms cm{sup -3} is needed to produce an intense comet shower leading to earth impacts. Furthermore, the tidal field of a dense cloud during a distant encounter is too weak to produce such showers. As a consequence, comet showers induced by ICs will be far less frequent than showers caused by passing stars. This conclusion is independent of assumptions about the radial distribution of comets in the inner Oort cloud.
10. Atomic and molecular excitation mechanisms in the interstellar medium
International Nuclear Information System (INIS)
Sternberg, A.
1986-01-01
The detailed infrared response of dense molecular hydrogen gas to intense ultraviolet radiation fields in photodissociation regions is presented. The thermal and chemical structures of photodissociation regions are analyzed, and the relationship between the emission by molecular hydrogen and trace atomic and molecular species is explored. The ultraviolet spectrum of radiation generated by cosmic rays inside dense molecular clouds is presented, and the resulting rates of photodissociation for a variety of interstellar molecules are calculated. Effects of this radiation on the chemistry of dense molecular clouds are discussed, and it is argued that the cosmic ray induced photons will significantly inhibit the production of complex molecular species. It is argued that the annihilation of electrons and positrons at the galactic center may result in observable infrared line emission by atomic hydrogen. A correlation between the intensity variations of the 511 keV line and the hydrogen infrared lines emitted by the annihilation region is predicted. The observed infrared fluxes from compact infrared sources at the galactic center may be used to constrain theories of pair production there
11. A NETWORK-THEORETICAL APPROACH TO UNDERSTANDING INTERSTELLAR CHEMISTRY
International Nuclear Information System (INIS)
Jolley, Craig C.; Douglas, Trevor
2010-01-01
Recent years have seen dramatic advances in computational models of chemical processes in the interstellar medium (ISM). Typically, these models have been used to calculate changes in chemical abundances with time; the calculated abundances can then be compared with chemical abundances derived from observations. In this study, the output from an astrochemical simulation has been used to generate directed graphs with weighted edges; these have been analyzed with the tools of network theory to uncover whole-network properties of reaction systems in dark molecular clouds. The results allow the development of a model in which global network properties can be rationalized in terms of the basic physical properties of the reaction system. The ISM network exhibits an exponential degree distribution, which is likely to be a generic feature of chemical networks involving a broad range of reaction rate constants. While species abundances span several orders of magnitude, the formation and destruction rates for most species are approximately balanced-departures from this rule indicate species (such as CO) that play a critical role in shaping the dynamics of the system. Future theoretical or observational studies focusing on individual molecular species will be able to situate them in terms of their role in the complete system or quantify the degree to which they deviate from the typical system behavior.
12. Black hole feedback in a multiphase interstellar medium
Science.gov (United States)
Bourne, Martin A.; Nayakshin, Sergei; Hobbs, Alexander
2014-07-01
Ultrafast outflows (UFOs) from supermassive black holes (SMBHs) are thought to regulate the growth of SMBHs and host galaxies, resulting in a number of observational correlations. We present high-resolution numerical simulations of the impact of a thermalized UFO on the ambient gas in the inner part of the host galaxy. Our results depend strongly on whether the gas is homogeneous or clumpy. In the former case all of the ambient gas is driven outward rapidly as expected based on commonly used energy budget arguments, while in the latter the flows of mass and energy de-couple. Carrying most of the energy, the shocked UFO escapes from the bulge via paths of least resistance, taking with it only the low-density phase of the host. Most of the mass is however in the high-density phase, and is affected by the UFO much less strongly, and may even continue to flow inwards. We suggest that the UFO energy leakage through the pores in the multiphase interstellar medium (ISM) may explain why observed SMBHs are so massive despite their overwhelmingly large energy production rates. The multiphase ISM effects reported here are probably under-resolved in cosmological simulations but may be included in prescriptions for active galactic nuclei feedback in future simulations and in semi-analytical models.
13. Degenerate band edge laser
Science.gov (United States)
Veysi, Mehdi; Othman, Mohamed A. K.; Figotin, Alexander; Capolino, Filippo
2018-05-01
We propose a class of lasers based on a fourth-order exceptional point of degeneracy (EPD) referred to as the degenerate band edge (DBE). EPDs have been found in parity-time-symmetric photonic structures that require loss and/or gain; here we show that the DBE is a different kind of EPD since it occurs in periodic structures that are lossless and gainless. Because of this property, a small level of gain is sufficient to induce single-frequency lasing based on a synchronous operation of four degenerate Floquet-Bloch eigenwaves. This lasing scheme constitutes a light-matter interaction mechanism that leads also to a unique scaling law of the laser threshold with the inverse of the fifth power of the laser-cavity length. The DBE laser has the lowest lasing threshold in comparison to a regular band edge laser and to a conventional laser in cavities with the same loaded quality (Q ) factor and length. In particular, even without mirror reflectors the DBE laser exhibits a lasing threshold which is an order of magnitude lower than that of a uniform cavity laser of the same length and with very high mirror reflectivity. Importantly, this novel DBE lasing regime enforces mode selectivity and coherent single-frequency operation even for pumping rates well beyond the lasing threshold, in contrast to the multifrequency nature of conventional uniform cavity lasers.
14. The empirical Gaia G-band extinction coefficient
Science.gov (United States)
Danielski, C.; Babusiaux, C.; Ruiz-Dern, L.; Sartoretti, P.; Arenou, F.
2018-06-01
Context. The first Gaia data release unlocked the access to photometric information for 1.1 billion sources in the G-band. Yet, given the high level of degeneracy between extinction and spectral energy distribution for large passbands such as the Gaia G-band, a correction for the interstellar reddening is needed in order to exploit Gaia data. Aims: The purpose of this manuscript is to provide the empirical estimation of the Gaia G-band extinction coefficient kG for both the red giants and main sequence stars in order to be able to exploit the first data release DR1. Methods: We selected two samples of single stars: one for the red giants and one for the main sequence. Both samples are the result of a cross-match between Gaia DR1 and 2MASS catalogues; they consist of high-quality photometry in the G-, J- and KS-bands. These samples were complemented by temperature and metallicity information retrieved from APOGEE DR13 and LAMOST DR2 surveys, respectively. We implemented a Markov chain Monte Carlo method where we used (G - KS)0 versus Teff and (J - KS)0 versus (G - KS)0, calibration relations to estimate the extinction coefficient kG and we quantify its corresponding confidence interval via bootstrap resampling. We tested our method on samples of red giants and main sequence stars, finding consistent solutions. Results: We present here the determination of the Gaia extinction coefficient through a completely empirical method. Furthermore we provide the scientific community with a formula for measuring the extinction coefficient as a function of stellar effective temperature, the intrinsic colour (G - KS)0, and absorption.
15. Wide band ENDOR spectrometer
International Nuclear Information System (INIS)
Mendonca Filho, C.
1973-01-01
The construction of an ENDOR spectrometer operating from 0,5 to 75 MHz within a single band, with ore Klystron and homodine detection, and no fundamental changes on the electron spin resonance spectrometer was described. The ENDOR signal can be detected both by amplitude modulation of the frequency field, or direct detection of the ESR output, which is taken to a signal analyser. The signal-to-noise ratio is raised by averaging rather than filtering avoiding the use of long time constants, providing natural line widths. The experimental apparatus and the spectra obtained are described. A discussion, relating the ENDOR line amplitudes with the experimental conditions is done and ENDOR mechanism, in which there is a relevant presence of cross relaxation is proposed
16. Electronic band structure
International Nuclear Information System (INIS)
Grosso, G.
1986-01-01
The aim of this chapter is to present, in detail, some theoretical methods used to calculate electronic band structures in crystals. The basic strategies employed to attack the problem of electronic-structure calculations are presented. Successive sections present the basic formulations of the tight-binding, orthogonalized-plane-wave, Green'sfunction, and pseudopotential methods with a discussion of their application to perfect solids. Exemplifications in the case of a few selected problems provide further insight by the author into the physical aspects of the different methods and are a guide to the use of their mathematical techniques. A discussion is offered of completely a priori Hartree-Fock calculations and attempts to extend them. Special aspects of the different methods are also discussed in light of recently published related work
17. Planck intermediate results. XXI. Comparison of polarized thermal emission from Galactic dust at 353 GHz with interstellar polarization in the visible
DEFF Research Database (Denmark)
Cardoso, J.F.; Delabrouille, J.; Ganga, K.
2015-01-01
The Planck survey provides unprecedented full-sky coverage of the submillimetre polarized emission from Galactic dust. In addition to the information on the direction of the Galactic magnetic field, this also brings new constraints on the properties of dust. The dust grains that emit the radiation...... with the spectral dependence in the submillimetre from Planck, will be important for constraining and understanding the full complexity of the grain models, and for interpreting the Planck thermal dust polarization and refinement of the separation of this contamination of the cosmic microwave background....... of dust, and therefore of the important dust model parameters, composition, size, and shape. Using ancillary catalogues of interstellar polarization and extinction of starlight, we obtain the degree of polarization, pV, and the optical depth in the V band to the star, τV. Toward these stars we measure...
18. The interstellar extinction in the open clusters Tr 14, Tr 15, Tr 16/Cr 232 and Cr 228 in NGC 3372. New near-infrared photometry
International Nuclear Information System (INIS)
Tapia, M.; Roth, M.; Ruiz, M.T.
1988-01-01
Near-infrared JHKL photometry of more than 200 stars, members of the open clusters Tr14, Tr15, Tr16, Cr228 and Cr232 in the Carina Nebula are presented. From comparing these results with the available visual photometry and spectroscopy, it is found that, except in Tr15, the intracluster reddening is characterized by a 'normal' extinction law at λ > 0.5μm but is highly anomalous and variable in the U- and B-bands. This behaviour may be explained by the presence of intracluster interstellar grains 'processed' by shock waves presumably associated with the explosive history of η Carinae. All clusters are found to be at the same distance from the Sun at d = 2.4 ± 0.2 kpc or Vsub(o) - Msub(v) 11.9 ± 0.2. The total amount of reddening, though, differs significantly from cluster to cluster. (author)
19. Physics and Chemistry of the Interstellar Medium. General Colloquium, 19-21 November 2012, Paris
International Nuclear Information System (INIS)
Aguillon, Francois; Alata, Ivan; Alcaraz, Christian; Alves, Marta; Andre, Philippe; Bachiller, Rafael; Bacmann, Aurore; Baklouti, Donia; Bernard, Jean-Philippe; Berne, Olivier; Beroff, Karine; Bertin, Mathieu; Biennier, Ludovic; Bocchio, Marco; Bonal, Lydie; Bontemps, Sylvain; Bouchez Giret, Aurelia; Boulanger, Francois; Bracco, Andrea; Bron, Emeric; Brunetto, Rosario; Cabrit, Sylvie; Canosa, Andre; Capron, Michael; Ceccarelli, Cecilia; Cernicharo, Jose; Chaabouni, Henda; Chabot, Marin; Chen, Hui-Chen; Chiavassa, Thierry; Cobut, Vincent; Commercon, Benoit; Congiu, Emanuele; Coutens, Audrey; Danger, Gregoire; Daniel, Fabien; Dartois, Emmanuel; Demyk, Karine; Denis, Alpizar; Despois, Didier; D'hendecourt, Louis; Dontot, Leo; Doronin, Mikhail; Dubernet, Marie-Lise; Dulieu, Francois; Dumouchel, Fabien; Duvernay, Fabrice; Ellinger, Yves; Falgarone, Edith; Falvo, Cyril; Faure, Alexandre; Fayolle, Edith; Feautrier, Nicole; Feraud, Geraldine; Fillion, Jean-Hugues; Gamboa, Antonio; Gardez, Aline; Gavilan, Lisseth; Gerin, Maryvonne; Ghesquiere, Pierre; Godard, Benjamin; Godard, Marie; Gounelle, Matthieu; Gratier, Pierre; Grenier, Isabelle; Gruet, Sebastien; Gry, Cecile; Guillemin, Jean-Claude; Guilloteau, Stephane; Gusdorf, Antoine; Guzman, Viviana; Habart, Emilie; Hennebelle, Patrick; Herrera, Cinthya; Hily-Blant, Pierre; Hincelin, Ugo; Hochlaf, Majdi; Huet, Therese; Iftner, Christophe; Jallat, Aurelie; Joblin, Christine; Kahane, Claudine; Kalugina, Yulia; Kleiner, Isabelle; Koehler, Melanie; Kokkin, Damian; Koutroumpa, Dimitra; Krim, Lahouari; Lallement, Rosine; Lanza, Mathieu; Lattelais, Marie; Le Bertre, Thibaut; Le Gal, Romane; Le Petit, Franck; Le Picard, Sebastien; Lefloch, Bertrand; Lemaire, Jean Louis; Lesaffre, Pierre; Lique, Francois; Loison, Jean-Christophe; Lopez Sepulcre, Ana; Maillard, Jean-Pierre; Margules, Laurent; Martin, Celine; Mascetti, Joelle; Michaut, Xavier; Minissale, Marco; Miville-Deschenes, Marc-Antoine; Mokrane, Hakima; Momferratos, Georgios; Montillaud, Julien; Montmerle, Thierry; Moret-Bailly, Jacques; Motiyenko, Roman; Moudens, Audrey; Noble, Jennifer; Padovani, Marco; Pagani, Laurent; Pardanaud, Cedric; Parisel, Olivier; Pauzat, Francoise; Pernet, Amelie; Pety, Jerome; Philippe, Laurent; Piergiorgio, Casavecchia; Pilme, Julien; Pinto, Cecilia; Pirali, Olivier; Pirim, Claire; Puspitarini, Lucky; Rist, Claire; Ristorcelli, Isabelle; Romanzin, Claire; Roueff, Evelyne; Rousseau, Patrick; Sabbah, Hassan; Saury, Eleonore; Schneider, Ioan; Schwell, Martin; Sims, Ian; Spielfiedel, Annie; Stoecklin, Thierry; Talbi, Dahbia; Taquet, Vianney; Teillet-Billy, Dominique; Theule, Patrice; Thi, Wing-Fai; Trolez, Yann; Valdivia, Valeska; Van Dishoeck, Ewine; Verstraete, Laurent; Vinogradoff, Vassilissa; Wiesenfeld, Laurent; Ysard, Nathalie; Yvart, Walter; Zicler Eleonore
2012-11-01
This document publishes the oral contributions and the 66 posters presented during a colloquium on physics and chemistry of interstellar medium. The following themes have been addressed: New views on the interstellar medium with Herschel, Planck and Alma, Cycle of interstellar dusts, Physics and Dynamics of the interstellar medium, Molecular complexifying and the link towards pre-biotic chemistry. More precisely, the oral contributions addressed the following topics: Interstellar medium with Herschel and Planck; The anomalous microwave emission: a new window on the physics of small grains; Sub-millimetre spectroscopy of complex molecules and of radicals for ALMA and Herschel missions; Analysing observations of molecules in the ISM: theoretical and experimental studies of energy transfer; Unravelling the labyrinth of star formation with Herschel; Star formation regions with Herschel and Alma: astro-chemistry in the Netherlands; Physical structure of gas and dust in photo-dissociation regions observed with Herschel; Photo-desorption of analogues of interstellar ices; Formation of structures in the interstellar medium: theoretical and numerical aspects; Towards a 3D mapping of the galactic ISM by inversion of absorption individual measurements; Low velocity shocks as signatures of turbulent dissipation in diffuse irradiated gas; Early phases of solar system formation: 3D physical and chemical modelling of the collapse of pre-stellar dense core; Cosmic-ray propagation in molecular clouds; Protostellar shocks in the time of Herschel; A new PDR model of the physics and chemistry of the interstellar gas; Molecular spectroscopy in the ALMA era and laboratory Astrophysics in Spain; Which molecules to be searched for in the interstellar medium; Physics and chemistry of UV illuminated neutral gas: the Horsehead case; Nitrogen fractionation in dark clouds; Molecular spectral surveys from millimetre range to far infrared; Mechanisms and synthesis at the surface of cold grains
20. TIMESCALES ON WHICH STAR FORMATION AFFECTS THE NEUTRAL INTERSTELLAR MEDIUM
Energy Technology Data Exchange (ETDEWEB)
Stilp, Adrienne M.; Dalcanton, Julianne J.; Weisz, Daniel R.; Williams, Benjamin F. [Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 (United States); Warren, Steven R. [Department of Astronomy, University of Maryland, CSS Building, Room 1024, Stadium Drive, College Park, MD 20742-2421 (United States); Skillman, Evan [Minnesota Institute for Astrophysics, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455 (United States); Ott, Juergen [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville Road, Socorro, NM 87801 (United States); Dolphin, Andrew E. [Raytheon Company, 1151 East Hermans Road, Tucson, AZ 85756 (United States)
2013-08-01
Turbulent neutral hydrogen (H I) line widths are often thought to be driven primarily by star formation (SF), but the timescale for converting SF energy to H I kinetic energy is unclear. As a complication, studies on the connection between H I line widths and SF in external galaxies often use broadband tracers for the SF rate, which must implicitly assume that SF histories (SFHs) have been constant over the timescale of the tracer. In this paper, we compare measures of H I energy to time-resolved SFHs in a number of nearby dwarf galaxies. We find that H I energy surface density is strongly correlated only with SF that occurred 30-40 Myr ago. This timescale corresponds to the approximate lifetime of the lowest mass supernova progenitors ({approx}8 M{sub Sun }). This analysis suggests that the coupling between SF and the neutral interstellar medium is strongest on this timescale, due either to an intrinsic delay between the release of the peak energy from SF or to the coherent effects of many supernova explosions during this interval. At {Sigma}{sub SFR} > 10{sup -3} M{sub Sun} yr{sup -1} kpc{sup -2}, we find a mean coupling efficiency between SF energy and H I energy of {epsilon} = 0.11 {+-} 0.04 using the 30-40 Myr timescale. However, unphysical efficiencies are required in lower {Sigma}{sub SFR} systems, implying that SF is not the primary driver of H I kinematics at {Sigma}{sub SFR} < 10{sup -3} M{sub Sun} yr{sup -1} kpc{sup -2}.
1. Topology in Synthetic Column Density Maps for Interstellar Turbulence
Science.gov (United States)
Putko, Joseph; Burkhart, B. K.; Lazarian, A.
2013-01-01
We show how the topology tool known as the genus statistic can be utilized to characterize magnetohydrodyanmic (MHD) turbulence in the ISM. The genus is measured with respect to a given density threshold and varying the threshold produces a genus curve, which can suggest an overall ‘‘meatball,’’ neutral, or ‘‘Swiss cheese’’ topology through its integral. We use synthetic column density maps made from three-dimensional 5123 compressible MHD isothermal simulations performed for different sonic and Alfvénic Mach numbers (Ms and MA respectively). We study eight different Ms values each with one sub- and one super-Alfvénic counterpart. We consider sight-lines both parallel (x) and perpendicular (y and z) to the mean magnetic field. We find that the genus integral shows a dependence on both Mach numbers, and this is still the case even after adding beam smoothing and Gaussian noise to the maps to mimic observational data. The genus integral increases with higher Ms values (but saturates after about Ms = 4) for all lines of sight. This is consistent with greater values of Ms resulting in stronger shocks, which results in a clumpier topology. We observe a larger genus integral for the sub-Alfvénic cases along the perpendicular lines of sight due to increased compression from the field lines and enhanced anisotropy. Application of the genus integral to column density maps should allow astronomers to infer the Mach numbers and thus learn about the environments of interstellar turbulence. This work was supported by the National Science Foundation’s REU program through NSF Award AST-1004881.
2. DAMPING OF ELECTRON DENSITY STRUCTURES AND IMPLICATIONS FOR INTERSTELLAR SCINTILLATION
International Nuclear Information System (INIS)
Smith, K. W.; Terry, P. W.
2011-01-01
The forms of electron density structures in kinetic Alfven wave (KAW) turbulence are studied in connection with scintillation. The focus is on small scales L ∼ 10 8 -10 10 cm where the KAW regime is active in the interstellar medium, principally within turbulent H II regions. Scales at 10 times the ion gyroradius and smaller are inferred to dominate scintillation in the theory of Boldyrev et al. From numerical solutions of a decaying KAW turbulence model, structure morphology reveals two types of localized structures, filaments and sheets, and shows that they arise in different regimes of resistive and diffusive damping. Minimal resistive damping yields localized current filaments that form out of Gaussian-distributed initial conditions. When resistive damping is large relative to diffusive damping, sheet-like structures form. In the filamentary regime, each filament is associated with a non-localized magnetic and density structure, circularly symmetric in cross section. Density and magnetic fields have Gaussian statistics (as inferred from Gaussian-valued kurtosis) while density gradients are strongly non-Gaussian, more so than current. This enhancement of non-Gaussian statistics in a derivative field is expected since gradient operations enhance small-scale fluctuations. The enhancement of density gradient kurtosis over current kurtosis is not obvious, yet it suggests that modest density fluctuations may yield large scintillation events during pulsar signal propagation. In the sheet regime the same statistical observations hold, despite the absence of localized filamentary structures. Probability density functions are constructed from statistical ensembles in both regimes, showing clear formation of long, highly non-Gaussian tails.
3. PROPERTIES OF INTERSTELLAR TURBULENCE FROM GRADIENTS OF LINEAR POLARIZATION MAPS
International Nuclear Information System (INIS)
Burkhart, Blakesley; Lazarian, A.; Gaensler, B. M.
2012-01-01
Faraday rotation of linearly polarized radio signals provides a very sensitive probe of fluctuations in the interstellar magnetic field and ionized gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set of statistical tools to analyze images of the spatial gradient of linearly polarized radio emission (|∇P|) for both observational data from a test image of the Southern Galactic Plane Survey (SGPS) and isothermal three-dimensional simulations of MHD turbulence. Visually, in both observations and simulations, a complex network of filamentary structures is seen. Our analysis shows that the filaments in |∇P| can be produced both by interacting shocks and random fluctuations characterizing the non-differentiable field of MHD turbulence. The latter dominates for subsonic turbulence, while the former is only present in supersonic turbulence. We show that supersonic and subsonic turbulence exhibit different distributions as well as different morphologies in the maps of |∇P|. Particularly, filaments produced by shocks show a characteristic 'double jump' profile at the sites of shock fronts resulting from delta function-like increases in the density and/or magnetic field, while those produced by subsonic turbulence show a single jump profile. In order to quantitatively characterize these differences, we use the topology tool known as the genus curve as well as the probability distribution function moments of the image distribution. We find that higher values for the moments correspond to cases of |∇P| with larger sonic Mach numbers. The genus analysis of the supersonic simulations of |∇P| reveals a 'swiss cheese' topology, while the subsonic cases have characteristics of a 'clump' topology. Based on the analysis of the genus and the higher order moments, the SGPS test region data have a distribution and morphology that match subsonic- to transonic-type turbulence, which confirms what is now expected for the warm ionized medium.
4. THE HOT INTERSTELLAR MEDIUM OF THE INTERACTING GALAXY NGC 4490
International Nuclear Information System (INIS)
Richings, A. J.; Fabbiano, G.; Wang Junfeng; Roberts, T. P.
2010-01-01
We present an analysis of the hot interstellar medium (ISM) in the spiral galaxy NGC 4490, which is interacting with the irregular galaxy NGC 4485, using ∼100 ks of Chandra ACIS-S observations. The high angular resolution of Chandra enables us to remove discrete sources and perform spatially resolved spectroscopy for the star-forming regions and associated outflows, allowing us to look at how the physical properties of the hot ISM such as temperature, hydrogen column density, and metal abundances vary throughout these galaxies. We find temperatures of >0.41 keV and 0.85 +0.59 -0.12 keV, electron densities of >1.87η -1/2 x 10 -3 cm -3 and 0.21 +0.03 -0.04 η -1/2 x 10 -3 cm -3 , and hot gas masses of >1.1η 1/2 x 10 7 M sun and ∼3.7η 1/2 x 10 7 M sun in the plane and halo of NGC 4490, respectively, where η is the filling factor of the hot gas. The abundance ratios of Ne, Mg, and Si with respect to Fe are found to be consistent with those predicted by theoretical models of type II supernovae (SNe). The thermal energy in the hot ISM is ∼5% of the total mechanical energy input from SNe, so it is likely that the hot ISM has been enriched and heated by type II SNe. The X-ray emission is anticorrelated with the Hα and mid-infrared emission, suggesting that the hot gas is bounded by filaments of cooler ionized hydrogen mixed with warm dust.
5. Widespread rotationally hot hydronium ion in the galactic interstellar medium
International Nuclear Information System (INIS)
Lis, D. C.; Phillips, T. G.; Schilke, P.; Comito, C.; Higgins, R.
2014-01-01
We present new Herschel observations of the (6,6) and (9,9) inversion transitions of the hydronium ion toward Sagittarius B2(N) and W31C. Sensitive observations toward Sagittarius B2(N) show that the high, ∼500 K, rotational temperatures characterizing the population of the highly excited metastable H 3 O + rotational levels are present over a wide range of velocities corresponding to the Sagittarius B2 envelope, as well as the foreground gas clouds between the Sun and the source. Observations of the same lines toward W31C, a line of sight that does not intersect the Central Molecular Zone but instead traces quiescent gas in the Galactic disk, also imply a high rotational temperature of ∼380 K, well in excess of the kinetic temperature of the diffuse Galactic interstellar medium. While it is plausible that some fraction of the molecular gas may be heated to such high temperatures in the active environment of the Galactic center, characterized by high X-ray and cosmic-ray fluxes, shocks, and high degree of turbulence, this is unlikely in the largely quiescent environment of the Galactic disk clouds. We suggest instead that the highly excited states of the hydronium ion are populated mainly by exoergic chemical formation processes and the temperature describing the rotational level population does not represent the physical temperature of the medium. The same arguments may be applicable to other symmetric top rotors, such as ammonia. This offers a simple explanation of the long-standing puzzle of the presence of a pervasive, hot molecular gas component in the central region of the Milky Way. Moreover, our observations suggest that this is a universal process not limited to the active environments associated with galactic nuclei.
6. Aspects of the interstellar medium in starburst galaxies
International Nuclear Information System (INIS)
Fanelli, M.N.
1990-01-01
Researchers are engaged in a multifaceted program to investigate the stellar content and star formation history of actively star-forming galaxies. A large body of stellar spectra have been examined to identify spectral features characteristic of specific stellar types. These spectral diagnostics are then calibrated in terms of temperature (spectral type), gravity (luminosity class) and metallicity. The spectral data is compiled into a stellar library whose members represent specific locations in the HR diagram. Through the use of population synthesis techniques, both optimizing and evolutionary approaches, the stellar luminosity function in composite populations can be determined. Researchers have concentrated on the ultraviolet wavelength region (lambda lambda 1200 to 3200). In the optical, virtually all stars will contribute to the integrated light. In the ultraviolet however, cool stars will produce negligible flux due to their steep ultraviolet-to-visual continua, greatly simplifying the investigation of the hot component in a composite population. The researchers' initial stellar library has been applied to several blue compact galaxies, (BCGs), a class of starburst galaxy which is UV luminous. BCGs possess a complex interstellar medium which affects the emergent stellar continuum in several ways. This presents a challenge to the stellar analysis but affords insight into the properties of the gas and dust from which the massive OB stars have formed. The optimizing synthesis method solves for the stellar luminosity function and extinction simultaneously. This therefore provides an independent measure of the extinction affecting the hot population component. Despite the rise of the reddening law towards the ultraviolet, BCGs are found to be brighter in the ultraviolet than expected
7. PROPERTIES OF INTERSTELLAR TURBULENCE FROM GRADIENTS OF LINEAR POLARIZATION MAPS
Energy Technology Data Exchange (ETDEWEB)
Burkhart, Blakesley; Lazarian, A. [Astronomy Department, University of Wisconsin, Madison, 475 N. Charter St., WI 53711 (United States); Gaensler, B. M. [Sydney Institute for Astronomy, School of Physics, University of Sydney, NSW 2006 (Australia)
2012-04-20
Faraday rotation of linearly polarized radio signals provides a very sensitive probe of fluctuations in the interstellar magnetic field and ionized gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set of statistical tools to analyze images of the spatial gradient of linearly polarized radio emission (|{nabla}P|) for both observational data from a test image of the Southern Galactic Plane Survey (SGPS) and isothermal three-dimensional simulations of MHD turbulence. Visually, in both observations and simulations, a complex network of filamentary structures is seen. Our analysis shows that the filaments in |{nabla}P| can be produced both by interacting shocks and random fluctuations characterizing the non-differentiable field of MHD turbulence. The latter dominates for subsonic turbulence, while the former is only present in supersonic turbulence. We show that supersonic and subsonic turbulence exhibit different distributions as well as different morphologies in the maps of |{nabla}P|. Particularly, filaments produced by shocks show a characteristic 'double jump' profile at the sites of shock fronts resulting from delta function-like increases in the density and/or magnetic field, while those produced by subsonic turbulence show a single jump profile. In order to quantitatively characterize these differences, we use the topology tool known as the genus curve as well as the probability distribution function moments of the image distribution. We find that higher values for the moments correspond to cases of |{nabla}P| with larger sonic Mach numbers. The genus analysis of the supersonic simulations of |{nabla}P| reveals a 'swiss cheese' topology, while the subsonic cases have characteristics of a 'clump' topology. Based on the analysis of the genus and the higher order moments, the SGPS test region data have a distribution and morphology that match subsonic- to transonic-type turbulence, which confirms what is now
8. THE YOUNG INTERSTELLAR BUBBLE WITHIN THE ROSETTE NEBULA
International Nuclear Information System (INIS)
Bruhweiler, F. C.; Bourdin, M. O.; Freire Ferrero, R.; Gull, T. R.
2010-01-01
We use high-resolution International Ultraviolet Explorer (IUE) data and the interstellar (IS) features of highly ionized Si IV and C IV seen toward the young, bright OB stars of NGC 2244 in the core of the Rosette Nebula to study the physics of young IS bubbles. Two discrete velocity components in Si IV and C IV are seen toward stars in the 6.2 pc radius central cavity, while only a single velocity component is seen toward those stars in the surrounding H II region, at the perimeter and external to this cavity. The central region shows characteristics of a very young, windblown bubble. The shell around the central hot cavity is expanding at 56 km s -1 with respect to the embedded OB stars, while the surrounding H II region of the Rosette is expanding at ∼13 km s -1 . Even though these stars are quite young (∼2-4 Myr), both the radius and expansion velocity of the 6.2 pc inner shell point to a far younger age; t age ∼ 6.4 x 10 4 years. These results represent a strong contradiction to theory and present modeling, where much larger bubbles are predicted around individual O stars and O associations. Specifically, the results for this small bubble and its deduced age extend the 'missing wind luminosity problem' to young evolving bubbles. These results indicate that OB star winds mix the surrounding H II regions and the wind kinetic energy is converted to turbulence and radiated away in the dense H II regions. These winds do not form hot, adiabatically expanding cavities. True IS bubbles appear only to form at later evolutionary times, perhaps triggered by increased mass loss rates or discrete ejection events. Means for rectifying discrepancies between theory and observations are discussed.
9. Very local interstellar spectra for galactic electrons, protons and helium
Energy Technology Data Exchange (ETDEWEB)
Potgieter, Marius S., E-mail: [email protected] [Centre for Space Research, North-West University (South Africa)
2014-07-01
The local interstellar spectra (LIS) for cosmic rays at energies below ∼30 GeV/nuc are increasingly obscured from view at Earth by solar modulation, the lower the energy becomes. These charged particles encounter significant changes in the heliosphere, over an 11-year cycle, which include processes such as convection, diffusion, adiabatic energy losses and gradient, curvature and current sheet drifts. Particle drifts cause charge-sign-dependent modulation and a 22-year cycle, adding complexity to determining the respective very LIS from observations only at Earth. However, with measurements now made by the Voyager 1 spacecraft in the vicinity of the helio pause, it is possible to determine a very LIS for galactic electrons between ∼5 and ∼120 MeV. At these low energies, also galactic protons observed in the outer heliosphere had been completely obscured by the so-called anomalous component which is accelerated inside the helio sheath. Since August 2012, these anomalous cosmic rays are substantially depleted at Voyager 1 so that for cosmic ray ions, it is now possible to obtain a lower limit to their very LIS. Combining numerical modelling of solar modulation with the accurate measurements by the PAMELA mission and with Voyager observations, the lower limit of the very LIS for electrons, protons and helium and other ions can be determined from ∼5 MeV and above. These spectra are called helio pause spectra which is considered to be the lowest possible very LIS. Also, from an astrophysics point of view, the determination of what can be called a very LIS, not just an averaged galactic spectrum, is encouraging. The mentioned aspects are discussed, focusing on a comparison of recent heliospheric observations and corresponding solar modulation modelling. (author)
10. Manifestations of electric currents in interstellar molecular clouds
International Nuclear Information System (INIS)
Carlqvist, P.; Gahm, G.F.
1991-12-01
We draw the attention to filamentary structures in molecular clouds and point out the existence of subfilaments of sinusoidal shape and also of helix-like structures. For two dark clouds, the Lynds 204 complex and the Sandqvist 187-188 complex (The Norma 'sword') we make a detailed study of such shapes and in addition we find the possible existence of helices wound around the main filaments. All these features are highly reminiscent of morphologies encountered in solar ascending prominences and in experiments in plasma physics and suggest the existence of electric currents and magnetic fields in these clouds. On the basis of a generalization of the Bennett pinch model, we derive the magnitudes of the currents expected to flow in the filaments. Values of column densities, magnetic field strengths, and direction of the fields are derived from observations. Magnetic fields with both toroidal and axial components are considered. This study shows that axial currents of the order of a few times 10 13 A are necessary for the clouds to be in equilibrium. The corresponding mean current densities are very small and even at the very low values of the fractional abundance of electrons encountered in these clouds, the mean electron velocities are of the order of 10 -2 -10 -5 m s -1 , much lower than the thermal velocities in the clouds. We suggest that helical structures may evolve as a result of various instabilities in the pinched clouds. We also call the attention to the kink intability in connection with the sinusoidal shapes. The existence of electromagnetically controlled features in the interstellar clouds can be tested by further observations. (au)
11. Gas-Grain Models for Interstellar Anion Chemistry
Science.gov (United States)
Cordiner, M. A.; Charnely, S. B.
2012-01-01
Long-chain hydrocarbon anions C(sub n) H(-) (n = 4, 6, 8) have recently been found to be abundant in a variety of interstellar clouds. In order to explain their large abundances in the denser (prestellar/protostellar) environments, new chemical models are constructed that include gas-grain interactions. Models including accretion of gas-phase species onto dust grains and cosmic-ray-induced desorption of atoms are able to reproduce the observed anion-to-neutral ratios, as well as the absolute abundances of anionic and neutral carbon chains, with a reasonable degree of accuracy. Due to their destructive effects, the depletion of oxygen atoms onto dust results in substantially greater polyyne and anion abundances in high-density gas (with n(sub H2) approx > / cubic cm). The large abundances of carbon-chain-bearing species observed in the envelopes of protostars such as L1527 can thus be explained without the need for warm carbon-chain chemistry. The C6H(-) anion-to-neutral ratio is found to be most sensitive to the atomic O and H abundances and the electron density. Therefore, as a core evolves, falling atomic abundances and rising electron densities are found to result in increasing anion-to-neutral ratios. Inclusion of cosmic-ray desorption of atoms in high-density models delays freeze-out, which results in a more temporally stable anion-to-neutral ratio, in better agreement with observations. Our models include reactions between oxygen atoms and carbon-chain anions to produce carbon-chain-oxide species C6O, C7O, HC6O, and HC7O, the abundances of which depend on the assumed branching ratios for associative electron detachment
12. The Inventory of Interstellar Materials Available for the Formation of the Solar System
Science.gov (United States)
Sandford, Scott A.; Witteborn, Fred C. (Technical Monitor)
1996-01-01
Dr. Derek Sears, the editor of the journal Meteoritics and Planetary Science, has established a policy of having each issue of the journal contain an invited review of an area that he deems to be of special cur-rent importance. Typically 20 to 25 pages of the beginning of the journal are devoted to each review. He has asked me to prepare such a review summarizing what we know about the composition and structure of interstellar materials. The attached paper is the result. This is a good time for such a review since tremendous progress has been made in the field of interstellar dust in recent years through the use of telescopic observations, theoretical studies, laboratory studies of analogs, and the study of actual interstellar samples found in meteorites. It is increasing clear that the interstellar medium (ISM) contains an enormous diversity of materials created by a wide range of chemical and physical processes. This understanding is a far cry from the picture of interstellar materials held as recently as two decades ago, a picture which incorporated only a few generic types of grains and few molecules. In the paper I review our current knowledge of the more abundant materials thought to exist in the ISM. The review concentrates on matter in interstellar dense molecular clouds since it is the materials in these environments from which new stars and planetary systems are formed, although materials in circumstellar environments and in the diffuse ISM are also discussed. The paper focuses largely on solid materials since they contain a major fraction of the heavier elements in clouds and because solids are most likely to survive incorporation into new planetary systems in identifiable form. The paper concludes with discussion of some of the implications resulting from the identification of these interstellar materials. I also present some new thoughts, the most intriguing being that meteoritic 'microdiamonds' may be the same material that modelers of the
13. Role of 'core' and 'halo' solar electrons in ionization of the interstellar medium
International Nuclear Information System (INIS)
Askew, S.D.; Kunc, J.A.; University of Southern California, Los Angeles
1984-01-01
The probability of the interstellar wind atoms (H and He) to survive ionization by solar wind electrons is presented. For the first time a dual temperature electron distribution is used to model the effects of ''core'' (10 eV) and ''halo'' (60 eV) solar electrons on the probabilities. Survival probability distributions as a function of heliocentric distance were calculated for variations in the electron temperature, solar radiation force, and the interstellar wind flow velocity. These probabilities are important in determining the radial density distributions of the interstellar atoms. It has been found that the interstellar wind has a distinctively higher probability of surviving ''halo'' rather than ''core'' electron ionization only at heliocentric distances, rho, smaller than about 0.5 a.u. For distances larger than 0.5 a.u., the probabilities of surviving ''halo'' electrons are close to the probabilities of surviving ''core'' electrons. Also, the probabilities for both ''core'' and ''halo'' electrons are relatively insensitive to changes in μsub(proportional to) (interstellar wind velocity at infinity), μ(the solar ratio of radiation to gravitational force) and α (a model parameter for solar electron temperature) for rho > 0.5. For distances smaller than that, the sensitivity increases significantly. (author)
14. Iron: A Key Element for Understanding the Origin and Evolution of Interstellar Dust
Science.gov (United States)
Dwek, Eli
2016-01-01
The origin and depletion of iron differ from all other abundant refractory elements that make up the composition of the interstellar dust. Iron is primarily synthesized in Type Ia supernovae (SNe Ia) and in core collapse supernovae (CCSN), and is present in the outflows from AGB (Asymptotic Giant Branch) stars. Only the latter two are observed to be sources of interstellar dust, since searches for dust in SN Ia have provided strong evidence for the absence of any significant mass of dust in their ejecta. Consequently, more than 65 percent of the iron is injected into the ISM (Inter-Stellar Matter) in gaseous form. Yet, ultraviolet and X-ray observations along many lines of sight in the ISM show that iron is severely depleted in the gas phase compared to expected solar abundances. The missing iron, comprising about 90 percent of the total, is believed to be locked up in interstellar dust. This suggests that most of the missing iron must have precipitated from the ISM gas by cold accretion onto preexisting silicate, carbon, or composite grains. Iron is thus the only element that requires most of its growth to occur outside the traditional stellar condensation sources. This is a robust statement that does not depend on our evolving understanding of the dust destruction efficiency in the ISM. Reconciling the physical, optical, and chemical properties of such composite grains with their many observational manifestations is a major challenge for understanding the nature and origin of interstellar dust.
15. CARBON DIOXIDE INFLUENCE ON THE THERMAL FORMATION OF COMPLEX ORGANIC MOLECULES IN INTERSTELLAR ICE ANALOGS
Energy Technology Data Exchange (ETDEWEB)
Vinogradoff, V.; Fray, N.; Bouilloud, M.; Cottin, H. [LISA Laboratoire Interuniversitaire des Systèmes Atmosphériques, UMR CNRS 7583, Université Paris Est Créteil (UPEC), Université Paris Diderot (UPD), Institut Pierre Simon Laplace, Labex ESEP, Paris (France); Duvernay, F.; Chiavassa, T., E-mail: [email protected] [PIIM, Laboratoire de Physique des Interactions Ioniques et Moléculaires, Université Aix-Marseille, UMR CNRS 7345, Marseille (France)
2015-08-20
Interstellar ices are submitted to energetic processes (thermal, UV, and cosmic-ray radiations) producing complex organic molecules. Laboratory experiments aim to reproduce the evolution of interstellar ices to better understand the chemical changes leading to the reaction, formation, and desorption of molecules. In this context, the thermal evolution of an interstellar ice analogue composed of water, carbon dioxide, ammonia, and formaldehyde is investigated. The ice evolution during the warming has been monitored by IR spectroscopy. The formation of hexamethylenetetramine (HMT) and polymethylenimine (PMI) are observed in the organic refractory residue left after ice sublimation. A better understanding of this result is realized with the study of another ice mixture containing methylenimine (a precursor of HMT) with carbon dioxide and ammonia. It appears that carbamic acid, a reaction product of carbon dioxide and ammonia, plays the role of catalyst, allowing the reactions toward HMT and PMI formation. This is the first time that such complex organic molecules (HMT, PMI) are produced from the warming (without VUV photolysis or irradiation with energetic particles) of abundant molecules observed in interstellar ices (H{sub 2}O, NH{sub 3}, CO{sub 2}, H{sub 2}CO). This result strengthens the importance of thermal reactions in the ices’ evolution. HMT and PMI, likely components of interstellar ices, should be searched for in the pristine objects of our solar system, such as comets and carbonaceous chondrites.
16. Boundary Conditions for the Paleoenvironment: Chemical and Physical Processes in Dense Interstellar Clouds: Summary of Research
Science.gov (United States)
Irvine, William M.
1999-01-01
The basic theme of this program was the study of molecular complexity and evolution for the biogenic elements and compounds in interstellar clouds and in primitive solar system objects. Research included the detection and study of new interstellar and cometary molecules and investigation of reaction pathways for astrochemistry from a comparison of theory and observed molecular abundances. The latter includes studies of cold, dark clouds in which ion-molecule chemistry should predominate, searches for the effects of interchange of material between the gas and solid phases in interstellar clouds, unbiased spectral surveys of particular sources, and systematic investigation of the interlinked chemistry and physics of dense interstellar clouds. In addition, the study of comets has allowed a comparison between the chemistry of such minimally thermally processed objects and that of interstellar clouds, shedding light on the evolution of the biogenic elements during the process of solar system formation. One PhD dissertation on this research was completed by a graduate student at the University of Massachusetts. An additional 4 graduate students at the University of Massachusetts and 5 graduate students from other institutions participated in research supported by this grant, with 6 of these thus far receiving PhD degrees from the University of Massachusetts or their home institutions. Four postdoctoral research associates at the University of Massachusetts also participated in research supported by this grant, receiving valuable training.
17. EXPERIMENTAL AND COMPUTATIONAL STUDIES OF THE FORMATION MECHANISM OF PROTONATED INTERSTELLAR DIAZINES
Energy Technology Data Exchange (ETDEWEB)
Wang, Zhe-Chen; Cole, Callie A.; Bierbaum, Veronica M. [Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO 80309 (United States); Snow, Theodore P., E-mail: [email protected] [Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309 (United States)
2015-01-10
Studies of interstellar chemistry have grown in number and complexity by both observations and laboratory measurements, and nitrogen-containing aromatics have been implicated as important interstellar molecules. In this paper, the gas-phase collision induced dissociation (CID) processes of protonated pyridazine (1,2-diazine), pyrimidine (1,3-diazine), and pyrazine (1,4-diazine) cations (C{sub 4}H{sub 5}N{sub 2} {sup +}) are investigated in detail both experimentally and theoretically. The major neutral loss for all three CID processes is HCN, leading to the formation of C{sub 3}H{sub 4}N{sup +} isomers; our density functional theory (DFT) calculations support and elucidate our experimental results. The formation of C{sub 3}H{sub 4}N{sup +} isomers from the reaction of abundant interstellar acrylonitrile (CH{sub 2}CHCN) and H{sup +}is also studied employing DFT calculations. Our results lead to a novel mechanism for interstellar protonated diazine formation from the consecutive reactions of CH{sub 2}CHCN+ H{sup +} + HCN. Moreover, our results motivate the continuing search for interstellar C{sub 3}H{sub 4}N{sup +} isomers as well as polycyclic aromatic N-containing hydrocarbons (PANHs)
18. CARBON DIOXIDE INFLUENCE ON THE THERMAL FORMATION OF COMPLEX ORGANIC MOLECULES IN INTERSTELLAR ICE ANALOGS
International Nuclear Information System (INIS)
Vinogradoff, V.; Fray, N.; Bouilloud, M.; Cottin, H.; Duvernay, F.; Chiavassa, T.
2015-01-01
Interstellar ices are submitted to energetic processes (thermal, UV, and cosmic-ray radiations) producing complex organic molecules. Laboratory experiments aim to reproduce the evolution of interstellar ices to better understand the chemical changes leading to the reaction, formation, and desorption of molecules. In this context, the thermal evolution of an interstellar ice analogue composed of water, carbon dioxide, ammonia, and formaldehyde is investigated. The ice evolution during the warming has been monitored by IR spectroscopy. The formation of hexamethylenetetramine (HMT) and polymethylenimine (PMI) are observed in the organic refractory residue left after ice sublimation. A better understanding of this result is realized with the study of another ice mixture containing methylenimine (a precursor of HMT) with carbon dioxide and ammonia. It appears that carbamic acid, a reaction product of carbon dioxide and ammonia, plays the role of catalyst, allowing the reactions toward HMT and PMI formation. This is the first time that such complex organic molecules (HMT, PMI) are produced from the warming (without VUV photolysis or irradiation with energetic particles) of abundant molecules observed in interstellar ices (H 2 O, NH 3 , CO 2 , H 2 CO). This result strengthens the importance of thermal reactions in the ices’ evolution. HMT and PMI, likely components of interstellar ices, should be searched for in the pristine objects of our solar system, such as comets and carbonaceous chondrites
19. Historical Reveiw of Interstellar Probe Concepts and Examination of Payload Mass Considerations for Different System Architectures
Science.gov (United States)
Long, K.
2017-12-01
The ability to send a space probe beyond the Voyager probes, through the interstellar medium and towardsthe distant stars, has long been the ambition of both the science ction literature but also a small community ofadvocates that have argued for a broader and deeper vision of space exploration that goes outside of our SolarSystem. In this paper we discuss some of the historical interstellar probe concepts which are propelled usingdierent types of propulsion technology, from energetic reaction engines to directed energy beaming, and considerthe payload mass associated with such concepts. We compare and contrast the dierent design concepts, payloadmass fractions, powers and energies and discuss the implications for robotic space exploration within the stellarneighbourhood. Finally, we consider the Breakthrough Starshot initiative, which proposes to send a Gram-scalelaser driven spacecraft to the Alpha Centauri system in a 20 year mission travelling at v 0.2c. We show howthis is a good start in pushing our robotic probes towards interstellar destinations, but also discuss the potentialfor scaling up this systems architecture to missions closer at home, or higher mass missions wider aeld. This is apresentation for the American Geophysical Union at the AGU Fall meeting, New Orleans, 11-15 December 2017,Special Session on the Interstellar Probe Missions.Keywords: Interstellar Probe, Breakthrough Starshot
20. Anisotropies in TeV Cosmic Rays Related to the Local Interstellar Magnetic Field from the IBEX Ribbon
International Nuclear Information System (INIS)
Schwadron, N A; Moebius, E; Adams, F C; Christian, E; Desiati, P; Frisch, P; Funsten, H O; Jokipii, J R; McComas, D J; Zank, G P
2015-01-01
The Interstellar Boundary Explorer (IBEX) observes enhanced Energetic Neutral Atoms (ENAs) emission in the keV energy range from a narrow (∼20° wide) ''ribbon'' in the sky that appears to be centered on the direction of the local interstellar (LIS) magnetic field. The Milagro collaboration, the Asγ collaboration and the IceCube observatory have recently made global maps of cosmic ray fluxes in the TeV energy range, revealing anisotropic structures ordered in part by the local interstellar magnetic field and the interstellar flow. This paper following from a recent publication in Science makes the link between these disparate observations by developing a simple model of the magnetic structure surrounding the heliosphere in the Local Interstellar Medium (LISM) that is consistent with both IBEX ENA fluxes and TeV cosmic ray anisotropies. The model also employs the revised velocity direction of the LIC derived from neutral He observations by IBEX. By modeling the propagation of cosmic rays through this magnetic field structure, we specifically show that (1) the large-scale TeV anisotropy provides a roughly consistent orientation for the local interstellar magnetic field at the center of the IBEX Ribbon and corroborates the ∼ 3 μG magnitude of the local interstellar magnetic field derived from IBEX observations of the global heliosphere; (2) and small-scale structures in cosmic rays (over < 30° angular scales) are influenced by the interstellar field interaction with the heliosphere at energies < 10 TeV. Thus, we provide a link between IBEX ENA observations, IBEX neutral observations of interstellar He, and TeV cosmic ray anisotropies, which are strongly influenced by the interactions between the local interstellar magnetic field, the flow of the local interstellar plasma, and the global heliosphere | {"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": 0.8759472370147705, "perplexity": 3456.8277984370106}, "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-2020-24/segments/1590347399830.24/warc/CC-MAIN-20200528170840-20200528200840-00202.warc.gz"} |
https://cstheory.stackexchange.com/questions/38950/easy-instances-for-coset-intersection-problem?noredirect=1 | Easy instances for coset intersection problem
Coset Intersection Problem
Given : $K,H \le S_n$, and $\sigma \in S_n$
Find : $K \cap H\sigma$
Known results are :
• $n^{O(\sqrt n )}$ time algorithm by L.Babai.
• $n^{O(1)} m^{O(\sqrt m )}$, where $m$ is the length of the longest orbits of the two groups by L.Babai.
• exp ($O(\sqrt n \ log n))$ by L.Babai.
Problem is in $\mathsf{P\text{}}$, if subgroup $K$ is a $S_n$ or just identity element. My question is what are the other cases, where problem is easy to solve i.e. is in $\mathsf{P\text{}}$. | {"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": 0.9603542685508728, "perplexity": 676.3491240191178}, "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/1566027319155.91/warc/CC-MAIN-20190823235136-20190824021136-00364.warc.gz"} |
https://www.emathhelp.net/notes/differential-equations/laplace-transform/solving-ivps-with-laplace-transform/ | # Solving IVP's with Laplace Transform
You probably asked yourself why Laplace transform is in Differential Equations section. Answer is simple. Because we can solve initial-value problems with the help of Laplace transform.
Let's see how it is done.
Example 1. Solve y''+4y=t, y(0)=0, y'(0)=0
First step always is to take Laplace transform of both sides.
L(y''+4y)=L(t)
Or
L(y'')+4L(y)=1/s^2
Now, since L(y'')=s^2Y(s)-sy(0)-y'(0) (see table of Laplace transforms) then we obtain that
s^2Y(s)-sy(0)-y'(0)+4Y(s)=1/s^2 or using initial conditions
s^2Y(s)-s*0-0+4Y(s)=1/s^2 which yields Y(s)=1/(s^2(s^2+4)) .
So, to find y(t) we must find inverse Laplace transform.
Partial fraction decomposition is A/s+B/s^2+(Cs+D)/(s^2+4)=(As(s^2+4)+B(s^2+4)+(Cs+D)s^2)/(s^2(s^2+4))=((A+C)s^3+(B+D)s^2+4As+4B)/(s^2(s^2+4))=1/(s^2(s^2+4))
So, the following system is obtained
{(A+C=0),(B+D=0), (4A=0),(4B=1):} which has solution A=0, B=1/4, C=0, D=-1/4
So,
y(t)=L^-1(Y(s))=L^(-1)(1/(s^2(s^2+4)))=L^-1(1/4 1/(s^2)-1/4 1/(s^2+4))=1/4 L^-1(1/s^2)-1/4 L^-1(1/(s^2+4))=1/4 t -1/8 L^-1(2/(s^2+4))=1/4t-1/8 sin(2t)
That's all. For the linear differential equations it is always the case that we take Laplace transform, algebraically find Y(s) and take inverse transform to obtain solution.
Also, it is easier to solve IVP's that involve step function or dirac function with Laplace transforms.
Example 2. Solve y''+y'=u_1(t) , y(0)=0, y'(0)=0
Take Laplace transform
L(y'')+L(y')=L(u_1(t))
Or
(s^2Y(s)-sy(0)-y'(0))+(sY(s)-y(0))=(e^-s)/s
Applying initial conditions gives
s^2Y(s)+sY(s)=e^(-s)/s or Y(s)=e^(-s) 1/(s^2(s+1))
Partical fraction decomposition for 1/(s^2(s+1)) is 1/s^2-1/s+1/(s+1) .
So,
y(t)=L^-1(e^(-s) 1/s^2)-L^-1(e^(-s) 1/s)+L^-1(e^(-s) 1/(s+1))=u_1(t)(t-1)-u_1(t)1+u_1(t)e^(-(t-1))=u_1(t)(t-2+e^(1-t))
Of course we could rewrite Heaviside function by definition and solve differential equation on each interval separately, but this requires more amount of work.
Example 3. Calculate y''+y'=t , y(2)=0, y'(2)=0
Notice that initial conditions are not at 0. In order to use Laplace transform we need initial conditions to be at 0. For this use change of variable: let a=t-2 then :
y''(a+2)+y'(a+2)=a+2 , y(0)=0, y'(0)=0
To simplify expression let y(a+2)=u(a) then y'(a+2)=u'(a) and y''(a+2)=u''(a) , so equation can be rewritten as
u''+u'=a+2 , u(0)=0, u'(0)=0
Now we can use Laplace transform:
L(u'')+L(u')=L(a)+L(2)
s^2U(s)-su(0)-u'(0)+sU(s)-u(0)=1/s^2+2/s
Applying initial conditions gives
U(s)=(1/s^2+2/s)/(s^2+s)=(2s+1)/(s^3(s+1))
Partial fraction decomposition is (verify!) 1/s^3+1/s^2+1/(s+1)-1/s
So, u(a)=L^-1(1/s^3+1/s^2+1/(s+1)-1/s)=L^-1(1/2 2/s^3+1/s^2+1/(s+1)-1/s)=1/2a^2+a+e^(-a)-1
However we need y(t) , not u(a) . Recall, that y(t)=y(a+2)=u(a)=u(t-2) , so
y(t)=1/2 (t-2)^2+t-2+e^(-(t-2))-1=1/2 t^2-t-1+e^(2-t)
Laplace transform can be used to solve linear equations with non-constant coefficients, but in general it is very hard to solve them and Laplace transform can rearely help, however such cases exist. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9941073656082153, "perplexity": 4372.212826209937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371883359.91/warc/CC-MAIN-20200410012405-20200410042905-00506.warc.gz"} |
http://physics.stackexchange.com/questions/61848/motivation-for-the-deformed-nekrasov-partition-function | # Motivation for the Deformed Nekrasov Partition Function
I have recently been doing research on the AGT Correspondence between the Nekrasov Instanton Partition Function and Louiville Conformal Blocks (http://arxiv.org/abs/0906.3219). When looking at the Nekrasov Partition Function one defines a deformed metric in terms of the "deformation parameters" $\epsilon_1, \epsilon_2$ which seem to define a $SO(4)$ action on a standard Euclidean Metric, breaking translational symmetry. Much of the literature on these functions seems to be in the math department, defining the functions categorically in terms of sheaves and what-not (http://arxiv.org/abs/math/0311058) and even the original paper (http://arxiv.org/abs/hep-th/0206161) approaches the subject from a cohomological perspective.
Is there any obvious physical motivation for looking at partition functions in this strange deformed spacetime? Or should I view it as simply a mathematical manipulation?
-
mitchell.physics.tamu.edu/Conference/string2010/documents/… ... I think its chief utility lies somewhere in the space between M-theory and SQCD. – Mitchell Porter Apr 22 '13 at 10:21
The deformation parameters have a meaning in topological string theory, see for example arxiv.org/abs/arXiv:1302.6993 by Antoniadis et al. for a recent perspective. – Vibert Apr 22 '13 at 10:59
I think the paper by Nekrasov and Witten gives a nice picture. I don't understand it well enough myself to give an answer but you could take a look at it. arxiv.org/abs/1002.0888 – Siva May 12 '13 at 9:00
The most physical and understandable definition of Nekrasov's partition function to me uses five-dimensional gauge theories. Namely, any 4d N=2 susy gauge theory has a 5d version with the same matter content, so that compactifying it on a small $S^1$ brings it back to the original 4d theory.
Then we put the theory on the so-called Omega background: it is $\mathbb{R}^4 \times [0,\beta]$, but $(\vec{x},0)$ and $(\vec{x'},\beta)$ are identified by a rotation $$\vec x'=\begin{pmatrix} \cos \beta\epsilon_1 & \sin\beta\epsilon_1 & 0 & 0\\ -\sin \beta\epsilon_1 & \cos\beta\epsilon_1 & 0 & 0\\ 0& 0 &\cos \beta\epsilon_2 & \sin\beta\epsilon_2\\ 0& 0 &-\sin \beta\epsilon_2 & \cos\beta\epsilon_2 \end{pmatrix}\vec x.$$
Then we take the limit $\beta\to 0$, keeping $\epsilon_{1,2}$ fixed. (Strictly speaking we also need to add a background $SU(2)_R$ symmetry gauge field, so that some of the susy is preserved.) | {"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": 0.8951787948608398, "perplexity": 458.9378993571202}, "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-2016-22/segments/1464049275429.29/warc/CC-MAIN-20160524002115-00218-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.arxiv-vanity.com/papers/1311.4286/ | # Angular averaged consistency relations of large-scale structures
Patrick Valageas Institut de Physique Théorique,
CEA, IPhT, F-91191 Gif-sur-Yvette, Cédex, France
CNRS, URA 2306, F-91191 Gif-sur-Yvette, Cédex, France
July 13, 2021
###### Abstract
The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives rise to angular averaged consistency relations for the matter density correlations. This allows one to write the density correlation, with large-scale linear wave numbers that are integrated over angles, and fixed small-scale nonlinear wave numbers, in terms of the small-scale -point density correlation and prefactors that involve the linear power spectra at the large-scale wave numbers. These relations, which do not vanish for equal-time statistics, go beyond the already known kinematic consistency relations. They could be used to detect primordial non-Gaussianities, modifications of gravity, limitations of galaxy biasing schemes, or to help designing analytical models of gravitational clustering.
Cosmology and large scale structure of the Universe
98.80.-k
## I Introduction
After the results of the WMAP and Planck missions Komatsu et al. (2011); Planck Collaboration et al. (2013), which have already uncovered a lot of information from the cosmic microwave background data, surveys of the large-scale structure of the Universe promise to be an important and complementary probe of cosmological scenarios Albrecht et al. (2006); Laureijs et al. (2011). In particular, they should shed light on the properties of the dark matter and dark energy components. Unfortunately, even without considering the very complex processes of galaxy and star formation Scannapieco et al. (2012); Bryan et al. (2013); Semboloni et al. (2013); Martizzi et al. (2013) and focusing on the large-scale properties where gravity is the dominant driver, exact or well-controled predictions for the statistical properties of the density and velocity fields are difficult. Large scales can be described by standard perturbative approaches Goroff et al. (1986); Bernardeau et al. (2002), which can be improved to some degree by using resummation schemes Crocce and Scoccimarro (2006a); Valageas (2007a); Pietroni (2008); Bernardeau et al. (2008); Taruya et al. (2012); Pietroni et al. (2012); Crocce et al. (2012); Bernardeau et al. (2013); Valageas et al. (2013). However, these methods cannot reach the truly nonlinear regime where shell-crossing effects become important Pueblas and Scoccimarro (2009); Valageas (2011, 2013a). Small scales are studied through numerical simulations or phenomenological models Cooray and Sheth (2002) that rely on informations gained through these simulations. However, these scales are difficult to model with a high accuracy, even with simulations, and it would be useful to have analytical results that go beyond low-order perturbation theory.
Some exact results have recently been obtained Kehagias and Riotto (2013); Peloso and Pietroni (2013a); Creminelli et al. (2013); Kehagias et al. (2013); Peloso and Pietroni (2013b); Creminelli et al. (2013); Valageas (2013b) in the form of “kinematic consistency relations”. They relate the -density correlation, with large-scale wave numbers and small-scale wave numbers, to the -point small-scale density correlation, with prefactors that involve the linear power spectrum at the large-scale wave numbers. These relations, obtained at the leading order over the large-scale wave numbers , arise from the equivalence principle (in standard scenarios). It ensures that small-scale structures respond to a large-scale perturbation (which at leading order corresponds to a constant gravitational force over the extent of the small-size object) by a uniform displacement. Therefore, these relations express a kinematic effect, due to the displacement of small-scale structures between different times. This also means that (at this order) they vanish for equal-time statistics, as a uniform displacement has no impact on the statistical properties of the density field observed at a given time.
In practice, it is difficult to measure different-time density correlations, as correlations between different redshift planes along our light cone (hence over distances of order ) are very small. Therefore, it would be useful to obtain similar relations that apply to single-time density correlations. This means that we must go beyond the kinematic effect and investigate how small-scale density fluctuations respond to non-uniform gravitational forces. At leading order over the large-scale wave numbers, this is given by the response to a change of the background density, which also corresponds to a large-scale curvature of the gravitational potential.
In this paper, we show how this problem can be addressed by using an approximate symmetry of the cosmological gravitational dynamics.
In Sec. II, we recall how most of the dependence on cosmological parameters can be absorbed by a remapping of the time-coordinate, , where is the linear growing mode. This is a well-know approximate symmetry of the cosmological gravitational dynamics that is often used in analytical methods (e.g., perturbative schemes) to simplify the computations. Then, in Sec. III we show how this invariance dictates the response of density fluctuations to a small change of the background density, which corresponds to a change of the cosmological parameters and . This allows us to derive consistency relations that go beyond the kinematic effect and remain nontrivial for the equal-time density correlations. In Sec. IV, we explicitly check this relation for the matter density bispectrum, at leading order of perturbation theory. We also present a fully nonlinear check in 1D (using the fact that the Zel’dovich approximation becomes an exact solution), which provides a check for all many-body density correlations or polyspectra up to all orders of perturbation theory (and beyond the shell crossing regime if we consider the system as defined by the Zel’dovich solution). We discuss our results and conclude in Sec. V.
## Ii Approximate symmetry of the cosmological gravitational dynamics
On scales much smaller than the horizon, where the Newtonian approximation is valid, the equations of motion read as Peebles (1980)
∂δ∂t+1a∇⋅[(1+δ)v]=0, (1)
∂v∂t+Hv+1a(v⋅∇)v=−1a∇ϕ, (2)
∇2ϕ=4πG¯¯¯ρa2δ, (3)
where is the scale factor, the Hubble expansion rate, the density contrast, and the peculiar velocity. Here, we use the single-stream approximation to simplify the presentation, but the results remain valid beyond shell crossing. Linearizing these equations over , one obtains the linear growth rates , which are the independent solutions of Peebles (1980); Bernardeau et al. (2002)
¨D+2H˙D−4πG¯¯¯ρD=0. (4)
For an Einstein-de Sitter universe, where , the linear growing mode is and the linear decaying mode is . For a generic cosmology, with a nonzero cosmological constant and curvature, one must numerically solve Eq.(4).
As usual Crocce and Scoccimarro (2006a); Crocce et al. (2006); Valageas (2008), it is convenient to make the change of variables
η=lnD+,v=˙afu,ϕ=(˙af)2φ, (5)
where . Then, the equations of motion read as
∂δ∂η+∇⋅[(1+δ)u]=0, (6)
∂u∂η+(3Ωm2f2−1)u+(u⋅∇)u=−∇φ, (7)
∇2φ=3Ωm2f2δ, (8)
where is the matter density cosmological parameter as a function of time, which obeys .
It happens that for standard cosmologies (i.e., within General Relativity), is always very close to (which is exact for the Einstein-de Sitter case) Peebles (1980). Then, making the approximation removes all explicit time dependence in the equations of motion (6)-(8) and simplifies the analytical computations. This also removes all explicit dependence on the cosmological parameters. In particular, within a perturbative framework, one can use the results obtained for the Einstein-de Sitter case by making the replacement Nusser and Colberg (1998); Scoccimarro (1998). The accuracy of this approximation was investigated by Refs.Pietroni (2008); Crocce et al. (2012), who find that it performs to better than at redshift for Mpc, and at on these scales. The approximation performs increasingly well at high redshift in the matter era (where we recover the Einstein-de Sitter cosmology). Although it degrades on small scales at , this approximation is used by most perturbative approaches Crocce and Scoccimarro (2006a); Valageas (2007a); Pietroni (2008); Bernardeau et al. (2008); Taruya et al. (2012); Pietroni et al. (2012); Crocce et al. (2012); Bernardeau et al. (2013); Valageas et al. (2013) to simplify computations (in particular, it allows one to use the explicit exponential form of the linear response function or propagator adapted from the Einstein - de Sitter case, with factors and Crocce and Scoccimarro (2006a, b); Valageas (2007a)). Thus, it provides a sufficient approximation on perturbative scales and in the highly nonlinear regime at low redshift it is not the main source of inaccuracy, as uncertainties on the halo mass function for instance lead to greater error bars Valageas (2013a).
This approximate symmetry does not rely on the single-stream approximation, and instead of the Euler equations (2) and (7), we can use the equation of motion of the trajectories of the particles. It reads as
∂2x∂t2+2H∂x∂t=−1a2∇ϕ, (9)
which becomes with the time coordinate
∂2x∂η2+(3Ωm2f2−1)∂x∂η=−∇φ, (10)
where is the rescaled gravitational potential (8). This explicitly shows that it satisfies the same approximate symmetry. Therefore, our results are not restricted to the perturbative regime and also apply to small nonlinear scales governed by shell-crossing effects, as long as the approximation is sufficiently accurate (but this also means that we are restricted to scales dominated by gravity).
This standard approximation means that all the dependence on cosmological parameters is encapsulated in the linear growing mode . In this paper, we investigate the consequences of this approximate symmetry of the equations of motion, in terms of the “squeezed” limit of density correlations. This corresponds to Fourier space density correlations , where the wave numbers are much smaller than all other wavenumbers and within the linear regime. Our method relies on the fact that a large-scale spherically symmetric perturbation of the initial density contrast is similar to a change of the mean density , whence of the cosmological parameters, from the point of view of a much smaller region at the center of this initial perturbation.
## Iii Angular averaged consistency relations
We first consider the case of a single large-scale wave number and we generalize to several large-scale wave numbers in Sec. III.3.3.
### iii.1 Correlation and response functions
Because the cosmological density and velocity fields are statistically homogeneous and isotropic, it is often convenient to work in Fourier space. In this paper, we denote with a tilde Fourier-space fields, defining the Fourier transform as
δ(x)=∫dkeik⋅x~δ(k). (11)
To compare theoretical predictions with observations, one often computes correlation functions, , or multispectra, . In particular, the power spectrum is defined as
⟨~δ(k1)~δ(k2)⟩=δD(k1+k2)P(k1), (12)
where the Dirac factor arises from statistical homogeneity. We also denote with the subscript “L” the linear fields obtained by linearizing the equations of motion (1)-(3), and with the subscript “L0” the linear fields today, at . Throughout this paper, we assume as usual that the linear decaying modes have had time to become negligible by the times of interest. Then, the initial conditions are fully defined by the linear growing mode, which is also set by the linear density field today , which we assume to be Gaussian.
In analytical approaches, especially in perturbative schemes that use field-theoretic tools Crocce and Scoccimarro (2006a, b); Valageas (2007a, b); Taruya and Hiramatsu (2008); Bernardeau et al. (2008); Anselmi et al. (2011); Bernardeau et al. (2012), it is convenient to introduce response functions (also called propagators or Green functions), that we define in real space as
Rℓ,n(x′1,..,x′ℓ;x1,t1,..,xn,tn) = (13) ⟨Dℓ[δ(x1,t1)..δ(xn,tn)]DδL0(x′1)..DδL0(x′ℓ)⟩,
and similarly in Fourier space (throughout this paper, we denote by the letter the functional derivative). These quantities (13) describe how the nonlinear density field, at positions and times , responds to changes of the initial conditions [defined by ] at positions .
As described for instance in Valageas (2013b), for Gaussian initial conditions, correlations between the nonlinear density contrast and the linear density contrast that defines the initial conditions can be written in terms of response functions. This gives in Fourier space Valageas (2013b)
⟨~δL0(k′)~δ(k1,t1)..~δ(kn,tn)⟩ = PL0(k′) (14) ×⟨D[~δ(k1,t1)..~δ(kn,tn)]D~δL0(−k′)⟩,
where is the linear power spectrum of the initial conditions . This provides a simple method to obtain consistency relations for the density correlations by computing the response function [i.e., the last term in Eq.(14)] associated with a large-scale perturbation of the initial condition.
The leading-order effect that arises in the large-scale limit, , is a constant force, , and velocity, , over the small-scale region of size , with . This also corresponds to a zero local density perturbation, because in the linear regime we have (up to time-dependent factors), as seen from the continuity equation (1). This leads to a uniform displacement of small-scale structures. Then, one obtains kinematic consistency relations Kehagias and Riotto (2013); Peloso and Pietroni (2013a); Creminelli et al. (2013); Peloso and Pietroni (2013b); Creminelli et al. (2013); Kehagias et al. (2013); Valageas (2013b) that express a correlation of the form , with low wave numbers and high wave numbers, as a product of linear power spectra with the small-scale nonlinear correlation , at lowest order over . Because this corresponds to a uniform displacement, this leading-order result vanishes at equal times, , and the results obtained for different times simply describe how small-scale patches have moved in-between these times because of the force exerted by a large-scale perturbation.
In this paper, we go beyond the kinematic effect recalled above and we consider the effect of a nonzero large-scale density fluctuation, that is, a nonzero curvature of the gravitational potential. This higher-order effect does not vanish for equal-time statistics because the large-scale perturbation of the gravitational potential curvature leads to a deformation of the small-scale structure (mostly a space-time dilatation, as the overall collapse is accelerated or decelerated). This leads to consistency relations for density correlations that remain nontrivial for single-time correlations. To remove constant gradients, which are absorbed by the kinematic effect and do not contribute to equal-time statistics, and to mimic a constant large-scale density fluctuation (and isotropic curvature of the gravitational potential), we consider spherical averages that write in configuration space as
CnW=∫dx′W(x′)⟨δL0(x′)δ(x1,t1)..δ(xn,tn)⟩, (15)
and in Fourier space as
~CnW=(2π)3∫dk′~W(k′)⟨~δL0(k′)~δ(k1,t1)..δ(kn,tn)⟩, (16)
where , and its Fourier transform , is a large-scale window function. Using Eq.(14) and its configuration-space counterpart, Eqs.(15) and (16) read as
CnW=∫dxdx′W(x)CL0(x,x′)⟨D[δ(x1,t1)..δ(xn,tn)]DδL0(x′)⟩, (17)
where is the linear density correlation of the initial conditions, and
~CnW=(2π)3∫dk′~W(k′)PL0(k′)⟨D[~δ(k1,t1)..~δ(kn,tn)]D~δL0(−k′)⟩. (18)
By definition of the functional derivatives, these expressions also mean that we must consider the change of the small-scale density correlation at linear order over a perturbation , as
CnW=ddε∣∣∣ε=0⟨δ(x1,t1)..δ(xn,tn)⟩ε (19)
and
~CnW=ddε∣∣∣ε=0⟨~δ(k1,t1)..~δ(kn,tn)⟩ε, (20)
where is the statistical average with respect to the Gaussian initial conditions , when the linear density field is modified as
δL(x)→δL(x)+εD+(t)∫dx′W(x′)CL0(x,x′) (21)
or
~δL(k)→~δL(k)+εD+(t)(2π)3~W(k)PL0(k). (22)
Here and in the following, we normalize the linear growth rate and the linear density field as . The spherical average over a much larger scale than the region of interest of size in Eq.(21) ensures that over this small patch the density perturbation is constant (at leading order over ).
A similar idea was investigated in Ref. Creminelli et al. (2013) in the context of single-field inflation, noticing that the effect of a large-scale fluctuation is similar to changing the curvature of the universe, from the point of view of a small-scale region. However, this leads to a consistency relation between a correlation such as Eq.(15) and a small-scale -point correlation in a different universe. As such, it cannot be directly measured because we have access to only one universe (unless one compares different large-scale regions characterized by different large-scale mean densities). In this paper, focusing on the late-time universe during the matter and dark energy epochs, we show in the next section how the approximate symmetry recalled in Sec. II allows us to derive consistency relations between correlations measured in the same universe. This is because this symmetry provides a link between the cosmological gravitational dynamics in different Friedmann-Lemaitre-Robertson-Walker cosmologies.
### iii.2 Effect of a large-scale density perturbation
From the point of view of a small region, a much larger-scale almost uniform perturbation to the initial density contrast is similar to a change of the background density . Then, following Peebles (1980), we first recall that such a small change of the background also corresponds to a linear growing mode of the density contrast. Thus, we consider two universes with close cosmological parameters, defined at the background level by the functions and . The dynamics of the reference universe (i.e., our Universe) is given by the Friedmann equations,
˙a2a2=8πG3(¯¯¯ρ+¯¯¯ρΛ)−Ka2, (23)
¨aa=−4πG3¯¯¯ρ+8πG3¯¯¯ρΛ, (24)
where we included the contributions from a cosmological constant and a curvature term and the dot denotes a derivative with respect to the time . The auxiliary universe , denoted with a prime, obeys the same equations with the change (the constant dark energy density is not changed). It only differs from the reference universe by a small amount, of order , with
¯¯¯ρa3=¯¯¯ρ′a′3=¯¯¯ρ0,a′=a[1−ϵ(t)],¯¯¯ρ′=¯¯¯ρ[1+3ϵ(t)]. (25)
Here and in the following, we only keep terms up to linear order over . Substituting Eq.(25) into the second Friedmann equation (24) written for the auxiliary universe, we obtain
¨ϵ+2H˙ϵ−4πG¯¯¯ρϵ=0. (26)
As is well known Peebles (1980), we recover the evolution equation (4) of the linear growth rates . This is because spherically symmetric shells evolve independently as separate universes (before shell crossing), thanks to Birkhoff’s theorem, and their density difference behaves as the linear growth rate (in the linear regime). Thus, we write
ϵ(t)=D+(t)ϵ0. (27)
We now turn to the density and velocity fluctuations. In the reference universe, they follow the equations of motion (1)-(3). In the auxiliary universe, we have the same equations of motion with primed variables. For our purpose, these two sets of variables actually describe the same physical system, with two different choices for the background density around which we study fluctuations. For instance, in the case , a density contrast with a zero mean in the primed frame appears as a density contrast with a nonzero positive mean. Thus, a large-scale uniform density fluctuation in the reference frame is absorbed by going to the primed frame. This will allow us to study the effect of a large scale density fluctuation as in Eqs.(21)-(22).
Because both frames refer to the same physical system, we have
r′=r=a′x′=ax,¯¯¯ρ′(1+δ′)=¯¯¯ρ(1+δ), (28)
where is the physical coordinate. Thus, we have the relations
x′=(1+ϵ)x,δ′=δ−3ϵ(1+δ),v′=v+˙ϵax, (29)
where we used Eq.(25) and only kept terms up to linear order over . Then, we can check that if the fields satisfy the equations of motion (1)-(3) in the primed frame, the fields satisfy the equations of motion (1)-(3) in the unprimed frame, with the gravitational potential transforming as
ϕ′=ϕ−a2(¨ϵ+2H˙ϵ)x2/2. (30)
This remains valid beyond shell crossing: if the trajectories satisfy the equation of motion (9) in the primed frame, the trajectories satisfy the equation of motion (9) in the unprimed frame, the gravitational potentials transforming as in Eq.(30).
Linearizing over the density contrast, the peculiar velocity, and the perturbation , we have
δL=δ′L+3ϵ,vL=v′L−˙ϵax,ϕL=ϕ′L+a2(¨ϵ+2H˙ϵ)x22. (31)
In agreement with the remark above, we can again check that if is a valid linear growing mode in the primed frame, is a valid linear growing mode in the unprimed frame. Moreover, the density contrast is equal to , up to the dilatation (29), to which is added the uniform contribution that corresponds to a homogeneous linear growing mode, as seen from Eq.(27).
We can now compute the dependence of small-scale density correlations on , that is, on changes of the background density. Thus, we consider the response function
(32)
As described above, adding a nonzero background corresponds to changing the initial background density from the reference to the primed density . This modifies the growth of large-scale structures, as the latter evolve in a new cosmology, defined by a new set of cosmological parameters. In particular, starting from a concordance -CDM flat cosmology with , the change of the background density generates a curvature term . For a given set of initial conditions , the new field , measured in the reference frame with the added background , can be expressed in terms of the density contrast in the primed frame, where has been absorbed by the change , through the mapping (29). This gives
δϵ0(x,t)=(1+3ϵ)δ′[(1+ϵ)x,t]+3ϵ, (33)
which reads in Fourier space as
~δϵ0(k,t)=~δ′[(1−ϵ)k,t]+3ϵδD(k). (34)
Next, we use the approximate symmetry described in Sec. II to write that the density contrast only depends on the cosmological parameters through the linear growth rate , whence , where is the functional that gives the nonlinear density contrast for any set of cosmological parameters, for a given initial condition of the zero-mean linear density contrast. Thus, Eq.(34) writes as
~δϵ0(k,t)=~δ[(1−ϵ)k,D+ϵ0]+3ϵδD(k), (35)
where is the linear growth rate that is modified with respect to the initial by the perturbation . Then, the derivative of the density contrast with respect to reads as
∂~δ(k,t)∂ϵ0∣∣ ∣∣ϵ0=0=∂D+ϵ0∂ϵ0∣∣∣0∂~δ∂D+−D+(t)k⋅∂~δ∂k, (36)
where we disregarded the Dirac factor that does not contribute for wave numbers .
We need to compute the dependence of the linear growing mode on . The linear growth rates and obey Eq.(4), with unprimed and primed Hubble and density factors. Writing , where is of order , we obtain at linear order
¨y+2H˙y−4πG¯¯¯ρy=2˙D+˙ϵ+12πG¯¯¯ρD+ϵ. (37)
By definition of the matter density cosmological parameter , the mean density also obeys
4πG¯¯¯ρ=32ΩmH2≃32˙D2+D2+, (38)
where in the last expression we again used the approximation associated with the approximated symmetry discussed in Sec. II. Then, using as the time coordinate, Eq.(37) becomes
d2ydη2+12dydη−32y=132ϵ0e2η, (39)
which gives
y(t)=137ϵ0D+(t)2,∂D+ϵ0∂ϵ0∣∣∣0=137D+(t)2. (40)
This result was also obtained in App.D of Baldauf et al. (2011). Then, Eq.(36) also writes as
∂~δ(k,t)∂ϵ0∣∣ ∣∣ϵ0=0=D+(t)[137∂~δ∂lnD+−k⋅∂~δ∂k], (41)
which corresponds in configuration space to
∂δ(x,t)∂ϵ0∣∣∣ϵ0=0=D+(t)[3δ+137∂δ∂lnD++x⋅∂δ∂x]. (42)
Eq.(42) also follows from Eq.(33), where we disregard the constant factor because we consider small-scale wave numbers . In configuration space, this means that these relations are valid up to a constant density, which is irrelevant because we consider small-scale structures and disregard zero-mode (infinitely large-scale) normalizations.
This gives the impact of a large-scale uniform density perturbation, or a change of the background density, on the small-scale nonlinear density field. Indeed, from Eq.(31), the variable corresponds to a change of the linear density contrast of
ΔδL0=3ϵ0. (43)
### iii.3 Consistency relations
#### iii.3.1 One large-scale wave number
The comparison of Eq.(43) with Eq.(21) gives
ϵ0=ε3∫dx′W(x′)CL0(x′), (44)
where we used the fact that is a large-scale window and the integral over is independent of the position in the small-scale region, at leading order in the ratio of scales. This gives
CnW=13∫dx′W(x′)CL0(x′)∂⟨δ(x1,t1)..δ(xn,tn)⟩ϵ0∂ϵ0, (45)
and using Eq.(42), we obtain
CnW → ∫dx′W(x′)CL0(x′)n∑i=1D+i3(3+137∂∂lnD+i (46)
The small-scale correlation is invariant through translations, thanks to statistical homogeneity. However, the dilatation operators break this invariance when the times are not identical. Indeed, as described in Sec. III.2, the change of the background density due to the uniform density fluctuation (43) leads to a modified Hubble flow. This breaks the translation invariance for different-time statistics, as defining a different Hubble flow selects the origin from which comoving particles separate along with the global expansion. This is due to the large-scale approximation for the filter where we considered that the small-scale region has a zero-width at the center of the larger-scale fluctuation. To explicitly enforce this configuration, we set the center of the modified Hubble flow at the center of the small-scale region by writing
CnW = ∫dx′W(x′)CL0(x′)n∑i=1D+i3[3+137∂∂lnD+i (47)
which is explicitly invariant through uniform translations of , as all terms only depend on relative distances. In agreement with the remark above, Eq.(47) is identical to Eq.(46) when all times are equal, . Using the definition (15), this gives the configuration-space consistency relation
∫dx′W(x′)⟨δL0(x′)δ(x1,t1)..δ(xn,tn)⟩ = ∫dx′WCL0(x′) (48) ×n∑i=1D+i3[3+137∂∂lnD+i+(xi−1nn∑j=1xj)⋅∂∂xi] ×⟨δ(x1,t1)..δ(xn,tn)⟩.
As explained above, this relation holds in the large-scale limit for the filter , and up to uniform offsets for the density contrasts [i.e., the equality is valid when one integrates both sides with arbitrary weights that have a zero mean, ].
It is often more convenient to work in Fourier space (because the linearized equations of motion become diagonal). Because of statistical homogeneity, multispectra contain a Dirac factor that we explicitly factor out by defining
⟨~δ(k1)..~δ(kn)⟩=⟨~δ(k1)..~δ(kn)⟩′δD(k1+..+kn). (49)
To simplify the analysis, it is convenient to consider in Eq.(49) as a function of only, by substituting for . Using the invariance through translations of , which gives , we can write the dilatation factors of Eq.(48) (denoted as the overall operator D, without the factor ) as
{D}⋅⟨δ1..δn⟩ = {n−1∑i=1[D+i(xi−xn)+D+n−D+in (50) ×n−1∑j=1(xj−xn)]⋅∂∂xi}⟨δ1..δn⟩.
Using the Fourier transform of the density correlation as in Eq.(49) and integrating over , this yields
{D}⋅⟨δ1..δn⟩ = ∫dk1..dkn−1{[n−1∑i=1D+iki⋅∂∂ki (51) +n−1∑i,j=1D+n−D+inki⋅∂kj]ei∑n−1i=1ki⋅(xi−xn)} ×⟨~δ1..~δn⟩′.
Integrating by parts, using and , this also writes as
{D}⋅⟨δ1..δn⟩ = −∫dk1..dkn−1ei∑n−1i=1ki⋅(xi−xn)[3n−1n (52)
where is the Kronecker symbol. Therefore, Eq.(48) reads in Fourier space as
∫dΩk′4π⟨~δL0(k′)~δ(k1,t1)..~δ(kn,tn)⟩′k′→0=PL0(k′) (53) ×n∑i=1D+i[1n+1321∂∂lnD+i−n∑j=1(δKi,j−1n)ki3⋅∂∂kj] ×⟨~δ(k1,t1)..~δ(kn,tn)⟩′,
where is the unit vector along the direction of . On large scales we recover the linear theory, with . Thus, Eq.(53) also writes as
∫dΩk′4π⟨~δ(k′,t′)~δ(k1,t1)..~δ(kn,tn)⟩′k′→0=PL(k′,t′) (54) ×n∑i=1D+iD+(t′)[1n+1321∂∂lnD+i−n∑j=1(δKi,j−1n)ki3⋅∂∂kj] ×⟨~δ(k1,t1)..~δ(kn,tn)⟩′.
Because we wrote the operator that acts over in a symmetric form, in Eqs.(53)-(54) we can use any appropriate form for [i.e., we can write the point correlation as a function of , as can be replaced by for any index , or keep it as a function of the wavenumbers , because of the constraint ].
In contrast with the kinematic consistency relations that express the transport of small-scale structures by large-scale fluctuations Kehagias and Riotto (2013); Peloso and Pietroni (2013a); Creminelli et al. (2013); Kehagias et al. (2013); Peloso and Pietroni (2013b); Creminelli et al. (2013); Valageas (2013b), the angular averaged relations (54) do not vanish when all times are equal. Indeed, they go beyond this kinematic effect and express the deformation of small-scale structures by a large-scale isotropic curvature of the gravitational potential. When all times are equal, , Eq.(54) becomes
∫dΩk′4π⟨~δ(k′,t)~δ(k1,t)..~δ(kn,t)⟩′k′→0=PL(k′,t) (55) ×[1+1321∂∂lnD+−13n∑i=1∂∂lnki] ×⟨~δ(k1,t)..~δ(kn,t)⟩′,
where we used .
A nice property of the single-time consistency relation (55) is that it only involves single-time correlations on both sides (as opposed for instance to a relation that would involve the partial time derivative with respect to only one time in the right hand side). Moreover, thanks to the approximate symmetry discussed in Sec. II, both sides involve density correlations in the same (our) universe. This is because, although the effect of a large-scale curvature is similar to a change of cosmological parameters, the approximate symmetry allows us to express the density correlations in the modified cosmology in terms of the correlations measured in the original universe, through a rescaling of space and time coordinates. Therefore, the angular averaged consistency relations (55) can be measured and tested in our Universe. However, this requires measuring the evolution with time of the density correlations to estimate the time derivative in the right hand side.
#### iii.3.2 Bispectrum
In practice, one does not measure density correlations up to very high orders, which become increasingly noisy, and most observational constraints from density correlations come from the 2-point and 3-point correlations. This corresponds in Fourier space to the power spectrum and bispectrum . (In practice, one measures single-time statistics, but for completeness we also consider the different-time statistics.) Taking into account the constraint by writing and , with some arbitrary wave number , Eq.(54) reads for as
∫dΩk′4πB(k′,k−k′2,−k−k′2;t′,t1,t2)k′→0= (56) PL(k′,t′)D+(t′)[D+1+D+22(1−13∂∂lnk) +1321(D2+1∂∂D+1+D2+2∂∂D+2)]P(k;t1,t2).
When all times are equal to , this becomes, in agreement with Eq.(55),
∫dΩk′4πB(k′,k−k′2,−k−k′2;t)k′→0=PL(k′,t) (57) ×[1+1321∂∂lnD+−13∂∂lnk]P(k,t).
#### iii.3.3 Several large-scale wave numbers
It is possible to generalize the single-time consistency relation (55) to large-scale wave numbers by an iterative procedure, as long as they follow a hierarchy , because the angular average and the derivative commute. This gives
k′j≪k′j+1:∫ℓ∏j=1dΩk′j4π⟨ℓ∏j=1~δ(k′j) | {"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": 0.9687293767929077, "perplexity": 1004.1276546578778}, "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-2021-39/segments/1631780056392.79/warc/CC-MAIN-20210918093220-20210918123220-00142.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/72229-maximum-likehood-estimator-print.html | Maximum Likehood Estimator
• Feb 6th 2009, 06:12 PM
eigenvector11
Maximum Likehood Estimator
If f_Y(y;theta) = (theta*k^theta)*(1/y)^(theta+1), y>=k, theta>=1,
a) Find the maximum likelihood estimator for theta if information has been collected on a random sample of 25 people.
b) Find the method of moments estimator for theta if information has been collected on a random sample of 25 people.
Assume k is unknown.
Any help would be appreciated.
• Feb 7th 2009, 02:24 AM
mr fantastic
Quote:
Originally Posted by eigenvector11
If f_Y(y;theta) = (theta*k^theta)*(1/y)^(theta+1), y>=k, theta>=1,
a) Find the maximum likelihood estimator for theta if information has been collected on a random sample of 25 people.
[snip]
Assume k is unknown.
Any help would be appreciated.
For an example of what to do, read this: http://www.mathhelpforum.com/math-he...estimator.html
• Feb 7th 2009, 02:27 AM
mr fantastic
Quote:
Originally Posted by eigenvector11
If f_Y(y;theta) = (theta*k^theta)*(1/y)^(theta+1), y>=k, theta>=1,
[snip]
b) Find the method of moments estimator for theta if information has been collected on a random sample of 25 people.
Assume k is unknown.
Any help would be appreciated.
The only thought I have at the moment is that $E(Y) = \frac{k \theta}{\theta - 1}$ and so let $\frac{k \theta}{\theta - 1} = \overline{y}$ and solve for $\theta$.
• Feb 7th 2009, 11:53 AM
eigenvector11
1 Attachment(s)
For question a), I attached what I am getting so far. Am I on the right track here? I'm not sure where to go now.
Edit merge: Actually I already spotted an error, it should be 25lnk in the derivative..oops.
• Feb 7th 2009, 12:40 PM
eigenvector11
How did you come up with that expected value in question b)? And if you solve for theta in that equation, won't you get theta=(ybar-ybar)/k, which means that theta equals zero?
• Feb 7th 2009, 12:57 PM
mr fantastic
Quote:
Originally Posted by eigenvector11
How did you come up with that expected value in question b)? And if you solve for theta in that equation, won't you get theta=(ybar-ybar)/k, which means that theta equals zero?
$\overline{y}$ is the sample mean. $E(Y)$ is NOT the same as $\overline{y}$. I had thought this would be clear. So you get $\theta$ in terms of the sample eman.
I found E(Y) using the usual formula: $E(Y) = \int_k^{+\infty} y \, f_Y (y, \theta) \, dy$. Again, this is something that I thought would be clear. | {"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": 8, "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": 0.9331675171852112, "perplexity": 1043.8439476666645}, "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-2016-40/segments/1474738661905.96/warc/CC-MAIN-20160924173741-00077-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://en.universaldenker.org/illustrations/634 | # Illustration Helmholtz Coil with Dimensions
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A Helmholtz coil consists of two round loops with $$N$$ windings and with radius $$R$$, which are placed at a distance $$d$$ from each other. If an electric current $$I$$ is now sent through these coils, a magnetic field is created around the loops.
If the current in both coils has the same orientation and the radius is the same as the distance between the coils, then the magnetic field between the coils is homogeneous. | {"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": 0.9137347340583801, "perplexity": 536.5911346360949}, "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/1656104244535.68/warc/CC-MAIN-20220703134535-20220703164535-00051.warc.gz"} |
http://templgvinstructorregister.com.rtitb.info/okkcep/fixed-beam-deflection.php | # Fixed beam deflection
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Multiple point loads, distributed loads and concentrated moments can be defined as input There is also a considerable difference in the deflection of a beam, for a given force, depending on how it is supported and fixed and whether it is supported at one end only or at both ends. Fully restrained beam moment diagram. BEAM FIXED AT ONE END, SUPPORTED AT OTHER-CONCENTRATED LOAD AT CENTER The follow web pages contain engineering design calculators will determine the amount of deflection a beam of know Stress, Bending calculator for a Beam Fixed Mechanics of Materials CIVL 3322 / MECH 3322 Deflection of Beams The right end of the beam is supported by a fixed end support therefore the slope of the Common Beam Formulas FREE-FIXED BEAM WITH POINT LOAD Let's use this fact to solve for the deflection of the beam under the load. - References for Built in Beams with worked examples Fixed-Fixed Beam with Point Load is a beam type that has fixed supports on both ends and transverse point load located in the middle. Following calculator has been developed to find forces, moments, stresses BEAM DESIGN FORMULAS WITH SHEAR AND MOMENT DIAGRAMS R = span length of the bending member, in. The beam dimensions are 200mm long, 10mm Define fixed beam: a restrained or built-in beam fixed in place. Sponsored FIXED STRUCTURAL BEAM DEFLECTION AND STRESS CALCULATOR FOR MULTIPLE LOADS AND MOMENTS. l x. Welcome to the Beam Bending Calculator. The beam in the The cantilever beam will experience a greater bending moment the farther the Essay about Beam Deflection Experiment The experiment methods, and fixed point to the beam are the differences between these four small experiments. 3. Step 4: Substitute the deflections from Steps 2 and 3 into the Five Beam Deflection Calculators (Solid/Hollow, Round,Rectangular,Triangular ) I mostly use these calculators for leaf spring design. BEAMS: DEFORMATION BY SUPERPOSITION (9. 7 – 9. 3 LECTURE 19. Deflection of the beam: The deflection is obtained by integrating Free online Calculator for civil and mechanical engineers to determine bending moment and shear force values for Fixed beams and draw the diagram Figure 1 : Three-Span Beam Structure. SLOPE AT FREE END DEFLECTION AT ANY SECTION IN TERMS OF x. 7. Cantilever Beam – Concentrated load P at the free end. By applying an edge load on the beam I would expect to observe a deflection Sep 16, 2013 · The end of fixed beam Compare the fixing moments and theoretical deflections for the propped cantilever and the fixed beams Deflection of Beam. 3 max. = −. 8. AF&PA is the national trade association of the forest, paper, and wood products industry, representing member companies engaged in growing, harvesting, and processing wood and wood fiber,. American Forest & Paper Association (AF&PA). 1 The bending of Built in Beams fixed at both ends. Deflections due to Bending 269 Couple, End-loaded Simply-Supported Beam Point Load, Simply-Supported Beam The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a Cantilever beams have one end fixed, Beam Design and Deflections = actual beam deflection allowable = allowable beam deflection limit At Fixed Supports: = 0 THE DEFLECTION OF BEAMS This is the third tutorial on the bending of beams. The Deflection of any point between the Fixed end and the Load is: 1 Chapter 9 Deflections of Beams 9. 4 Deflection by Superposition ENES 220 ©Assakkaf Method of Superposition Beam Bending Calculator Powered by WebStructural. Following calculator has been developed to find forces, moments, stresses, deflections and slopes in a fixed beam. It is suggested that design should be based on a given deflection of a hornblock, and then determine what length, thickness and style of To find the shear force and bending moment over the length of a beam, first solve for the external reactions at the boundary conditions. Beam Deflection Equations are easy to apply and allow engineers to make simple and quick calculations for deflection. Determining Deflections of Hinge-Connected Beams Using and the bending moment M for the beam ab in Fig. Closed-form solutions to simple beam bending problems. The equation 6 APPENDIX C Example Consider a fixed-free beam made from aluminum. A fixed support or BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. The relation obtained is the equation of the points in a beam, the deflection and the slope of the beam cannot be discon- Fixed end moment The member under certain load conditions with both ends fixed. - fixed end beam: therefore LESS bending moment than a simple beam and LESS deflection than a simple beam. Summary for the value of end moments and deflection of perfectly restrained beam carrying various loadings. 20 pages (464 KB PDF) This document provides a handy series of shear and moment diagrams with accompanying formulas for design of beams under various static loading THE DEFLECTION OF BEAMS This is the third tutorial on the bending of beams. = 2. A beam with both ends fixed is deflection method; Matrix Relation between curvature and beam deflection the beam which is adjusted in such a way as to fix the position of the beam at that point. Related Topics. limit the maximum deflection of a beam to about 1/360 th of its spans. EI θ = (. I think I should use the superposition principle but I am not very sure how Mechanics of Materials-Deflection Beam Deflections The deformation of a beam is usually expressed in terms of its deflection from its fixed or hinge supports). Beam formulas may be used to determine the deflection, shear and bending moment in a beam based on the applied loading and boundary conditions. 9 Fixed-end moments 104 or beam (bending moment response Stress in a bending beam can be expressed as. I am simulating the deflectiopn of a beam with fixed supports at each end with a concentrated load at the middle. What differences exist on the use between fixed end support and hinged end support in beam This reflects reduction in the bending moment in a fixed ended beam. For example, the cantilever beam below has an applied force shown in red, and the reactions are shown in blue at the fixed boundary condition: Cantilever Beam. Figure 15 Beam Fixed at One End, some fixed origin (Fig. fixed beam deflectionCantilever beam with a force on the free end. The beam is 24 inches long. Elastic Beam Deflection Calculator simply enter in the 'component' situations and sum up the deflection. BEAM DEFLECTION FORMULAE. ) So, the last two constants vanish because of the fixed What i observed was the bending of the beam to a deflection in that the beam was fixed Method but not 100% how to apply it to a fixed end beam with 2 Fixed-connected joint How will this beam deflect? Deflections Deflection Diagrams and the Elastic Curve How will this frame deflect? How will this frame deflect? beam deflection under the anticipated design load and compare this figure with the allowable value fixed, the beam stiffness can be maximised by ma. Cantilever Beams. Beams - Fixed at Both Ends - Continuous and Point Loads ; Beam Fixed at Both Ends Beams and Columns - Deflection and stress, Define fixed beam: a restrained or built-in beam Stress in a bending beam can be expressed as. Compute the deflection for the beam DSUL. Px y. Beam Formulas. The shape of the deflected beam is defined by v(x); it is the A beam with a moment of inertia I and with Young's modulus E will have a bending stress f at a distance from the Neutral Axis Fixed Beam . » Deflection In addition to bending stresses, internal and external loads cause beams to DEFLECT. the deflection is zero and at a fixed support both the deflection and the slope are zero. 3 Fixed –circled beam Knowledge on theory of deflection in beams is used in analyzing for magnitudes of deflection resulting from a given loads. EI. 4 show the normal stress and deflection one would expect when a beam bends downward. Beams - Fixed at Both Ends - Continuous and Point Loads - Support loads, stress and deflections ; The equations necessary to calculate the deflection of a reinforced concrete beam be fixed at their far ends, as is the beam to beam deflection THE DEFLECTION OF A RECTANGULAR PLATE FIXED AT THE EDGES* BY H. Cantilever, End Load, Cantilever, End Load. 8) Slide No. Fixed End Beam with UDL | {"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": 0.949773371219635, "perplexity": 1403.9332218819334}, "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-2018-05/segments/1516084887077.23/warc/CC-MAIN-20180118071706-20180118091706-00475.warc.gz"} |
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# 12.E: Introduction to Calculus (Exercises)
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## 12.1: Finding Limits - Numerical and Graphical Approaches
In this section, we will examine numerical and graphical approaches to identifying limits.
#### Verbal
Explain the difference between a value at $$x=a$$ and the limit as $$x$$ approaches $$a$$.
The value of the function, the output, at $$x=a$$ is $$f(a)$$. When the $$\lim \limits_{x \to a}f(x)$$ is taken, the values of $$x$$ get infinitely close to $$a$$ but never equal $$a$$. As the values of $$x$$ approach $$a$$ from the left and right, the limit is the value that the function is approaching.
Explain why we say a function does not have a limit as $$x$$ approaches $$a$$ if, as $$x$$ approaches $$a$$, the left-hand limit is not equal to the right-hand limit.
#### Graphical
For the following exercises, estimate the functional values and the limits from the graph of the function $$f$$ provided in Figure.
$$\lim \limits_{x \to −2^−} f(x)$$
–4
$$\lim \limits_{x \to −2^+ }f(x)$$
$$\lim \limits_{x \to −2 f(x)}$$
–4
$$f(−2)$$
$$\lim \limits_{x \to −1^− f(x)}$$
2
$$\lim \limits_{x \to 1^+} f(x)$$
$$\lim \limits_{x \to 1} f(x)$$
does not exist
$$f(1)$$
$$\lim \limits_{x \to 4^−} f(x)$$
4
$$\lim \limits_{x \to 4^+} f(x)$$
$$\lim \limits_{x \to 4} f(x)$$
does not exist
$$f(4)$$
For the following exercises, draw the graph of a function from the functional values and limits provided.
$$\lim \limits_{x \to 0^−} f(x)=2, \lim \limits_{x \to 0^+} f(x)=–3, \lim \limits_{x \to 2} f(x)=2, f(0)=4, f(2)=–1, f(–3) \text{ does not exist.}$$
$$\lim \limits_{x \to 2^−} f(x)=0,\lim \limits_{x \to 2^+} =–2,\lim \limits_{x \to 0} f(x)=3, f(2)=5, f(0)$$
$$\lim \limits_{ x \to 2^−} f(x)=2, \lim \limits_{ x \to 2^+} f(x)=−3, \lim \limits_{x \to 0} f(x)=5, f(0)=1, f(1)=0$$
$$\lim \limits_{x \to 3^−} f(x)=0, \lim \limits_{x \to 3^+} f(x)=5, \lim \limits_{x \to 5} f(x)=0, f(5)=4, f(3) \text{ does not exist.}$$
$$\lim \limits_{ x \to 4} f(x)=6, \lim \limits_{ x \to 6^+} f(x)=−1, \lim \limits_{ x \to 0} f(x)=5, f(4)=6, f(2)=6$$
$$\lim \limits_{ x \to −3} f(x)=2, \lim \limits_{ x \to 1^+} f(x)=−2, \lim \limits_{ x \to 3} f(x)=–4, f(–3)=0, f(0)=0$$
$$\lim \limits_{ x \to π} f(x)=π^2, \lim \limits_{ x \to –π} f(x)=\frac{π}{2}, \lim \limits_{ x \to 1^-} f(x)=0, f(π)=\sqrt{2}, f(0) \text{ does not exist}.$$
For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as $$x$$ approaches 0.
$$f(x)=(1+x)^{\frac{1}{x}}$$
$$g(x)=(1+x)^{\frac{2}{x}}$$
7.38906
$$h(x)=(1+x)^{\frac{3}{x}}$$
$$i(x)=(1+x)^{\frac{4}{x}}$$
54.59815
$$j(x)=(1+x)^{\frac{5}{x}}$$
Based on the pattern you observed in the exercises above, make a conjecture as to the limit of $$f(x)=(1+x)^{\frac{6}{x}}, g(x)=(1+x)^{\frac{7}{x}},$$ and $$h(x)=(1+x)^{\frac{n}{x}}.$$
$$e^6≈403.428794,e^7≈1096.633158, e^n$$
For the following exercises, use a graphing utility to find graphical evidence to determine the left- and right-hand limits of the function given as $$x$$ approaches $$a$$. If the function has a limit as $$x$$ approaches $$a$$,state it. If not, discuss why there is no limit.
$$(x)= \begin{cases} |x|−1, && \text{if }x≠1 \\ x^3, && \text{if }x=1 \end{cases} a=1$$
$$(x)= \begin{cases} \frac{1}{x+1}, && \text{if } x=−2 \\ (x+1)^2, && \text{if } x≠−2 \end{cases} a=−2$$
$$\lim \limits_{x \to −2} f(x)=1$$
#### Numeric
For the following exercises, use numerical evidence to determine whether the limit exists at $$x=a$$. If not, describe the behavior of the graph of the function near $$x=a$$. Round answers to two decimal places.
$$f(x)=\frac{x^2−4x}{16−x^2};a=4$$
$$f(x)=\frac{x^2−x−6}{x^2−9};a=3$$
$$\lim \limits_{x \to 3} (\frac{x^2−x−6}{x^2−9})=\frac{5}{6}≈0.83$$
$$f(x)=\frac{x^2−6x−7}{x^2– 7x};a=7$$
$$f(x)=\frac{x^2–1}{x^2–3x+2};a=1$$
$$\lim \limits_{x \to 1}(\frac{x^2−1}{x^2−3x+2})=−2.00$$
$$f(x)=\frac{1−x^2}{x^2−3x+2};a=1$$
$$f(x)=\frac{10−10x^2}{x^2−3x+2};a=1$$
$$\lim \limits_{x \to 1}(\frac{10−10x^2}{x^2−3x+2})=20.00$$
$$f(x)=\frac{x}{6x^2−5x−6};a=\frac{3}{2}$$
$$f(x)=\frac{x}{4x^2+4x+1};a=−\frac{1}{2}$$
$$\lim \limits_{x \to \frac{−1}{2}}(\frac{x}{4x^2+4x+1})$$ does not exist. Function values decrease without bound as $$x$$ approaches –0.5 from either left or right.
$$f(x)=\frac{2}{x−4}; a=4$$
For the following exercises, use a calculator to estimate the limit by preparing a table of values. If there is no limit, describe the behavior of the function as $$x$$ approaches the given value.
$$\lim \limits_{x \to 0} \frac{7 \tan x}{3x}$$
$$\lim \limits_{x \to 0} \frac{7 \tan x}{3x}=\frac{7}{3}$$
$$\lim \limits_{x \to 4} \frac{x^2}{x−4}$$
$$\lim \limits_{x \to 0}\frac{2 \sin x}{4 \tan x}$$
$$\lim \limits_{x \to 0} \frac{2 \sin x}{4 \tan x}=\frac{1}{2}$$
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as $$x$$ approaches $$a$$. If the function has a limit as $$x$$ approaches $$a$$, state it. If not, discuss why there is no limit.
$$\lim \limits_{x \to 0}e^{e^{\frac{1}{x}}}$$
$$\lim \limits_{x \to 0}e^{e^{− \frac{1}{x^2}}}$$
$$\lim \limits_{x \to 0}e^{e^{− \frac{1}{x^2}}}=1.0$$
$$\lim \limits_{x \to 0} \frac{|x|}{x}$$
$$\lim \limits_{x \to −1} \frac{|x+1|}{x+1}$$
$$\lim \limits_{ x→−1^−}\frac{| x+1 |}{x+1}=\frac{−(x+1)}{(x+1)}=−1$$ and $$\lim \limits_{ x \to −1^+}\frac{| x+1 |}{x+1}=\frac{(x+1)}{(x+1)}=1$$; since the right-hand limit does not equal the left-hand limit, $$\lim \limits_{ x to −1}\frac{|x+1|}{x+1}$$ does not exist.
$$\lim \limits_{ x \to 5} \frac{| x−5 |}{5−x}$$
$$\lim \limits_{ x \to −1}\frac{1}{(x+1)^2}$$
$$\lim \limits_{ x \to −1} \frac{1}{(x+1)^2}$$ does not exist. The function increases without bound as $$x$$ approaches $$−1$$ from either side.
$$\lim \limits_{ x \to 1} \frac{1}{(x−1)^3}$$
$$\lim \limits_{ x \to 0} \frac{5}{1−e^{\frac{2}{x}}}$$
$$\lim \limits_{ x \to 0} \frac{5}{1−e^{\frac{2}{x}}}$$ does not exist. Function values approach 5 from the left and approach 0 from the right.
Use numerical and graphical evidence to compare and contrast the limits of two functions whose formulas appear similar: $$f(x)=| \frac{1−x}{x} |$$ and $$g(x)=| \frac{1+x}{x} |$$ as $$x$$ approaches 0. Use a graphing utility, if possible, to determine the left- and right-hand limits of the functions $$f(x)$$ and $$g(x)$$ as $$x$$ approaches 0. If the functions have a limit as $$x$$ approaches 0, state it. If not, discuss why there is no limit.
#### Extensions
According to the Theory of Relativity, the mass m m of a particle depends on its velocity $$v$$. That is
$m=\dfrac{m_o}{\sqrt{1−(v^2/c^2)}}$
where $$m_o$$ is the mass when the particle is at rest and $$c$$ is the speed of light. Find the limit of the mass, $$m$$, as $$v$$ approaches $$c^−.$$
Through examination of the postulates and an understanding of relativistic physics, as $$v→c, m→∞.$$Take this one step further to the solution,
$\lim \limits_{v \to c^−}m=\lim \limits_{v \to c^−} \dfrac{m_o}{\sqrt{1−(v^2/c^2)}}=∞$
Allow the speed of light, $$c$$, to be equal to 1.0. If the mass, $$m$$, is 1, what occurs to $$m$$ as $$v \to c$$? Using the values listed in Table, make a conjecture as to what the mass is as $$v$$ approaches 1.00.
$$v$$ $$m$$ 0.5 1.15 0.9 2.29 0.95 3.20 0.99 7.09 0.999 22.36 0.99999 223.61
## 12.2: Finding Limits - Properties of Limits
Graphing a function or exploring a table of values to determine a limit can be cumbersome and time-consuming. When possible, it is more efficient to use the properties of limits, which is a collection of theorems for finding limits. Knowing the properties of limits allows us to compute limits directly.
#### Verbal
Give an example of a type of function $$f$$ whose limit, as $$x$$ approaches $$a,$$ is $$f(a)$$.
If $$f$$ is a polynomial function, the limit of a polynomial function as $$x$$ approaches $$a$$ will always be $$f(a)$$.
When direct substitution is used to evaluate the limit of a rational function as $$x$$ approaches $$a$$ and the result is $$f(a)=\frac{0}{0}$$,does this mean that the limit of $$f$$ does not exist?
What does it mean to say the limit of $$f(x)$$, as $$x$$ approaches $$c$$, is undefined?
It could mean either (1) the values of the function increase or decrease without bound as $$x$$ approaches $$c,$$ or (2) the left and right-hand limits are not equal.
#### Algebraic
For the following exercises, evaluate the limits algebraically.
$$\lim \limits_{x \to 0} (3)$$
$$\lim \limits_{x \to 2}(\frac{−5x}{x^2−1})$$
$$\frac{−10}{3}$$
$$\lim \limits_{x \to 2}(\frac{x^2−5x+6}{x+2})$$
$$\lim \limits_{x \to 3}(\frac{x^2−9}{x−3})$$
6
$$\lim \limits_{x \to −1}(\frac{x^2−2x−3}{x+1})$$
$$\lim \limits_{x \to \frac{3}{2}}(\frac{6x^2−17x+12}{2x−3})$$
$$\frac{1}{2}$$
$$\lim \limits_{ x \to −\frac{7}{2}}(\frac{8x^2+18x−35}{2x+7})$$
$$\lim \limits_{ x \to 3}(\frac{x^2−9}{x−5x+6})$$
6
$$\lim \limits_{ x \to −3} (\frac{−7x^4−21x^3}{−12x^4+108x^2})$$
$$\lim \limits_{ x \to 3} (\frac{x^2+2x−3}{x−3})$$
does not exist
$$\lim \limits_{ h \to 0} (\frac{(3+h)^3−27}{h})$$
$$\lim \limits_{ h \to 0} (\frac{(2−h)^3−8}{h})$$
$$−12$$
$$\lim \limits_{ h \to 0}(\frac{(h+3)^2−9}{h})$$
$$\lim \limits_{ h \to 0} (\frac{\sqrt{5−h}−\sqrt{5}}{h})$$
$$−\frac{\sqrt{5}}{10}$$
$$\lim \limits_{ x \to 0} (\frac{\sqrt{3−x}−\sqrt{3}}{x})$$
$$\lim \limits_{ x \to 9}(\frac{x^2−81}{3−x})$$
$$−108$$
$$\lim \limits_{ x \to 1}(\frac{\sqrt{x}−x^2}{1−\sqrt{x}})$$
$$\lim \limits_{ x \to 0}(\sqrt{x1+2x}−1)$$
1
$$\lim \limits_{ x \to \frac{1}{2}}(\frac{x^2−\frac{1}{4}}{2x−1})$$
$$\lim \limits_{ x \to 4} (\frac{x^3−64}{x^2−16})$$
6
$$\lim \limits_{ x \to 2^−} (\frac{|x−2|}{x−2})$$
$$\lim \limits_{ x \to 2^+} (\frac{| x−2 |}{x−2})$$
1
$$\lim \limits_{ x \to 2}(\frac{| x−2 |}{x−2})$$
$$\lim \limits_{ x \to 4^−}(\frac{| x−4 |}{4−x})$$
1
$$\lim \limits_{ x \to 4^+}(\frac{| x−4 |}{4−x})$$
$$\lim \limits_{ x \to 4}(\frac{| x−4 |}{4−x})$$
does not exist
$$\lim \limits_{ x \to 2}(\frac{−8+6x−x^2}{x−2})$$
For the following exercise, use the given information to evaluate the limits: $$\lim \limits_{x \to c}f(x)=3, \lim \limits_{x \to c} g(x)=5$$
$$\lim \limits_{x \to c} [ 2f(x)+\sqrt{g(x)} ]$$
$$6+\sqrt{5}$$
$$\lim \limits_{x \to c} [ 3f(x)+\sqrt{g(x)} ]$$
$$\lim \limits_{x \to c}\frac{f(x)}{g(x)}$$
$$\frac{3}{5}$$
For the following exercises, evaluate the following limits.
$$\lim \limits_{x \to 2} \cos (πx)$$
$$\lim \limits_{x \to 2} \sin (πx)$$
0
$$\lim \limits_{x \to 2} \sin (\frac{π}{x})$$
$$f(x)= \begin{cases} 2x^2+2x+1, && x≤0 \\ x−3, && x>0 ; \end{cases} \lim \limits_{x \to 0^+}f(x)$$
$$−3$$
$$f(x)= \begin{cases} 2x^2+2x+1, && x≤0 \\ x−3, && x>0 ; \end{cases} \lim \limits_{x \to 0^−} f(x)$$
$$f(x)= \begin{cases} 2x^2+2x+1, && x≤0 \\ x−3, && x>0 ; \end{cases} \lim \limits_{x \to 0}f(x)$$
does not exist; right-hand limit is not the same as the left-hand limit.
$$\lim \limits_{x \to 4} \frac{\sqrt{x+5}−3}{x−4}$$
$$\lim \limits_{x \to 2^+} (2x−〚x〛)$$
2
$$\lim \limits_{x \to 2} \frac{\sqrt{x+7}−3}{x^2−x−2}$$
$$\lim \limits_{x \to 3^+}\frac{x^2}{x^2−9}$$
Limit does not exist; limit approaches infinity.
For the following exercises, find the average rate of change$$\frac{f(x+h)−f(x)}{h}$$.
$$f(x)=x+1$$
$$f(x)=2x^2−1$$
$$4x+2h$$
$$f(x)=x^2+3x+4$$
$$f(x)=x^2+4x−100$$
$$2x+h+4$$
$$f(x)=3x^2+1$$
$$f(x)= \cos (x)$$
$$\frac{\cos (x+h)− \cos (x)}{h}$$
$$f(x)=2x^3−4x$$
$$f(x)=\frac{1}{x}$$
$$\frac{−1}{x(x+h)}$$
$$f(x)=\frac{1}{x^2}$$
$$f(x)=\sqrt{x}$$
$$\frac{−1}{\sqrt{x+h}+\sqrt{x}}$$
#### Graphical
Find an equation that could be represented by Figure.
Find an equation that could be represented by Figure.
$$f(x)=\frac{x^2+5x+6}{x+3}$$
For the following exercises, refer to Figure.
What is the right-hand limit of the function as $$x$$ approaches 0?
What is the left-hand limit of the function as $$x$$ approaches 0?
does not exist
#### Real-World Applications
The position function $$s(t)=−16t^2+144t$$ gives the position of a projectile as a function of time. Find the average velocity (average rate of change) on the interval $$[ 1,2 ]$$.
The height of a projectile is given by $$s(t)=−64t^2+192t$$ Find the average rate of change of the height from $$t=1$$ second to $$t=1.5$$ seconds.
52
The amount of money in an account after $$t$$ years compounded continuously at 4.25% interest is given by the formula $$A=A_0e^{0.0425t}$$,where $$A_0$$ is the initial amount invested. Find the average rate of change of the balance of the account from $$t=1$$ year to $$t=2$$ years if the initial amount invested is \$1,000.00.
## 12.3: Continuity
A function that remains level for an interval and then jumps instantaneously to a higher value is called a stepwise function. This function is an example. A function that has any hole or break in its graph is known as a discontinuous function. A stepwise function, such as parking-garage charges as a function of hours parked, is an example of a discontinuous function. We can check three different conditions to decide if a function is continuous at a particular number.
### Section Exercises
#### Verbal
State in your own words what it means for a function $$f$$ to be continuous at $$x=c$$.
Informally, if a function is continuous at $$x=c$$, then there is no break in the graph of the function at $$f(c)$$, and $$f(c)$$ is defined.
State in your own words what it means for a function to be continuous on the interval $$(a,b)$$.
#### Algebraic
For the following exercises, determine why the function $$f$$ is discontinuous at a given point $$a$$ on the graph. State which condition fails.
$f(x)=ln | x+3 |,a=−3$
discontinuous at $$a=−3$$; $$f(−3)$$ does not exist
$f(x)= \ln | 5x−2 |,a=\dfrac{2}{5}$
$$f(x)=\frac{x^2−16}{x+4},a=−4$$
removable discontinuity at $$a=−4; f(−4)$$ is not defined
$$f(x)=\frac{x^2−16x}{x},a=0$$
$$f(x)= \begin{cases} x, && x≠3 \\ 2x, && x=3 \end{cases} a=3$$
Discontinuous at $$a=3; \lim \limits_{x \to 3} f(x)=3,$$ but $$f(3)=6,$$ which is not equal to the limit.
$$f(x) = \begin{cases} 5, &&x≠0 \\ 3, && x=0 \end{cases} a=0$$
$$f(x)= \begin{cases} \frac{1}{2−x}, && x≠2 \\ 3, &&x=2 \end{cases} a=2$$
$$\lim \limits_{x \to 2}f(x)$$ does not exist.
$$f(x)= \begin{cases} \frac{1}{x+6}, && x=−6 \\ x^2, && x≠−6 \end{cases} a=−6$$
$$f(x)=\begin{cases} 3+x, &&x<1 \\ x, &&x=1 \\ x^2, && x>1 \end{cases} a=1$$
$$\lim \limits_{x \to 1^−}f(x)=4;\lim \limits_{x \to 1^+}f(x)=1.$$ Therefore, $$\lim \limits_{x \to 1}f(x)$$ does not exist.
$$f(x)= \begin{cases} 3−x, && x<1 \\ x, && x=1 \\ 2x^2, && x>1 \end{cases} a=1$$
$$f(x)= \begin{cases} 3+2x, && x<1 \\ x, && x=1 \\ −x^2, && x>1 \end{cases} a=1$$
$$\lim \limits_{x \to 1^−} f(x)=5≠ \lim \limits_{x \to 1^+}f(x)=−1$$. Thus $$\lim \limits_{x \to 1}f(x)$$ does not exist.
$$f(x)= \begin{cases} x^2, &&x<−2 \\ 2x+1, && x=−2 \\ x^3, && x>−2 \end{cases} a=−2$$
$$f(x)= \begin{cases} \frac{x^2−9}{x+3}, && x<−3 \\ x−9, && x=−3 \\ \frac{1}{x}, && x>−3 \end{cases} a=−3$$
$$\lim \limits_{x to −3^+}f(x)=−\frac{1}{3}$$
Therefore, $$\lim \limits_{x \to −3} f(x)$$ does not exist.
$$f(x)= \begin{cases} \frac{x^2−9}{x+3}, && x<−3 \\ x−9, && x=−3\\ −6, && x>−3 \end{cases} a=3$$
$$f(x)=\frac{x^2−4}{x−2}, a=2$$
$$f(2)$$ is not defined.
$$f(x)=\frac{25−x^2}{x^2−10x+25}, a=5$$
$$f(x)=\frac{x^3−9x}{x^2+11x+24}, a=−3$$
$$f(−3)$$ is not defined.
$$f(x)=\frac{x^3−27}{x^2−3x}, a=3$$
$$f(x)=\frac{x}{|x|}, a=0$$
$$f(0)$$ is not defined.
$$f(x)=\frac{2|x+2|}{x+2}, a=−2$$
For the following exercises, determine whether or not the given function $$f$$ is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.
$$f(x)=x^3−2x−15$$
Continuous on $$(−∞,∞)$$
$$f(x)=\frac{x^2−2x−15}{x−5}$$
$$f(x)=2⋅3^{x+4}$$
Continuous on $$(−∞,∞)$$
$$f(x)=− \sin (3x)$$
$$f(x)=\frac{|x−2|}{x^2−2x}$$
Discontinuous at $$x=0$$ and$$x=2$$
$$f(x)= \tan (x)+2$$
$$f(x)=2x+\frac{5}{x}$$
Discontinuous at $$x=0$$
$$f(x)=\log _2 (x)$$
$$f(x)= \ln x^2$$
Continuous on $$(0,∞)$$
$$f(x)=e^{2x}$$
$$f(x)=\sqrt{x−4}$$
Continuous on $$[4,∞)$$
$$f(x)= \sec (x)−3$$
$$f(x)=x^2+ \sin (x)$$
Continuous on $$(−∞,∞)$$.
Determine the values of $$b$$ and $$c$$ such that the following function is continuous on the entire real number line.
$f(x)= \begin{cases}x+1, && 1<x<3 \\ x^2+bx+c, &&|x−2|≥1 \end{cases}$
#### Graphical
For the following exercises, refer to Figure. Each square represents one square unit. For each value of $$a$$, determine which of the three conditions of continuity are satisfied at $$x=a$$ and which are not.
$$x=−3$$
1, but not 2 or 3
$$x=2$$
$$x=4$$
1 and 2, but not 3
For the following exercises, use a graphing utility to graph the function $$f(x)= \sin (\frac{12π}{x})$$ as in Figure. Set the x-axis a short distance before and after 0 to illustrate the point of discontinuity.
Which conditions for continuity fail at the point of discontinuity?
Evaluate $$f(0)$$.
$$f(0)$$ is undefined.
Solve for $$x$$ if $$f(x)=0$$.
What is the domain of $$f(x)$$?
$$(−∞,0)∪(0,∞)$$
For the following exercises, consider the function shown in Figure.
At what x-coordinates is the function discontinuous?
What condition of continuity is violated at these points?
At $$x=−1$$, the limit does not exist. At $$x=1, f(1)$$ does not exist.
At $$x=2$$, there appears to be a vertical asymptote, and the limit does not exist.
Consider the function shown in Figure. At what x-coordinates is the function discontinuous? What condition(s) of continuity were violated?
Construct a function that passes through the origin with a constant slope of 1, with removable discontinuities at $$x=−7$$ and $$x=1$$.
$$\frac{x^3+6x^2−7x}{(x+7)(x−1)}$$
The function $$f(x)=\frac{x^3−1}{x−1}$$ is graphed in Figure. It appears to be continuous on the interval $$[−3,3]$$, but there is an x-value on that interval at which the function is discontinuous. Determine the value of $$x$$ at which the function is discontinuous, and explain the pitfall of utilizing technology when considering continuity of a function by examining its graph.
Find the limit limx→1f(x) limx→1f(x) and determine if the following function is continuous at $$x=1$$:
$fx= \begin{cases} x^2+4 && x≠1 \\ 2 && x=1\end{cases}$
The function is discontinuous at $$x=1$$ because the limit as $$x$$ approaches 1 is 5 and $$f(1)=2$$.
The graph of $$f(x)= \frac{\sin (2x)}{x}$$ is shown in Figure. Is the function $$f(x)$$ continuous at $$x=0?$$ Why or why not?
## 12.4: Derivatives
Change divided by time is one example of a rate. The rates of change in the previous examples are each different. In other words, some changed faster than others. If we were to graph the functions, we could compare the rates by determining the slopes of the graphs. | {"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": 0.9342215061187744, "perplexity": 252.2899998487558}, "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-2019-13/segments/1552912201996.61/warc/CC-MAIN-20190319143502-20190319165502-00235.warc.gz"} |
https://mathoverflow.net/questions/318854/superintuitionistic-logics-which-are-not-hereditary-monotonic-impossible-or-pos/318878 | # Superintuitionistic logics which are not hereditary/monotonic: impossible or possible?
An intuitionistic Kripke model is a triple $$\langle W,\leq, \Vdash \rangle$$, where $$\langle W,\leq \rangle$$ is a preordered Kripke frame, and $$\Vdash$$ satisfies the following condition of hereditariness (or monotonicity):
if $$P$$ is a propositional variable, $$w\leq u$$, and $$w\Vdash P$$, then $$u\Vdash P$$.
• Are there intermediate logics (excluding classical logic), including intermediate modal logics (i.e intermediate logics which contain modalities) for which there are no Kripke models in the above sense?
• (If so,) what is the smallest such intermediate logic?
• If there are no such intermediate logics, what is the proof of this claim?
I was thinking particularly of intuitionistic logics to which is adjoined some modality $$\bigcirc$$ which does not obey hereditariness. I.e, for which we have:
$$P$$ is a propositional variable, $$w\leq u$$, $$w\Vdash \bigcirc P$$ and $$u\not\Vdash \bigcirc P$$.
Edit
It has been observed below that classical logic can be given a Kripke model in the above sense. Does this entail that any intermediate logic can be given a Kripke model?
• It is not clear what you are asking. The term "Kripke model" means a certain interpretation of propositional calculus, namely in the Heyting algebra generated as the upper sets of a partial order (or a preorder). Every such interpretation will satisfy monotonicity by design. If you are looking for something that is not a Kripke model, then it's not clear what monotonicity means (ok, as long as it's a sheaf model we'll be able to guess). In other words, it sounds like your question is a terminological question masquerading as a mathematical question. – Andrej Bauer Dec 17 '18 at 13:50
• I can put it in another way: monotonicity is a property of semantics of propositional logic. It therefore makes no sense to ask whether there are logics which violate it. Even classical logic satisfies the monotonicity requirement, trivially so because there aren't any interesting Kripke models of classical logic. (But there are Kripke models of classical logic!) – Andrej Bauer Dec 17 '18 at 13:56
• I am asking whether there are intermediate logic for which there are no standard Kripke models. There are modal logics for which there is no Kripke model. – user65526 Dec 17 '18 at 14:02
• I have edited my question – user65526 Dec 17 '18 at 14:03
• But even classical logics have Kripke models (consider the discrete preorder), so what are you asking? – Andrej Bauer Dec 17 '18 at 14:13
## 1 Answer
Every propositional logic $$L$$ weaker than classical logic (i.e., any logic whose provable propositions are a subset of classically provable propositions) has a Kripke model. Just take $$W = \{\star\}$$, the frame with a single element, and the trivial preorder. The model is equivalent to the boolean algebra $$\{\bot, \top\}$$, therefore it validates all classically provable propositions and is a model of $$L$$.
I should also note that monotonicity is a property of Kripke models, not of logics. A Kripke model is just the Heyting algebra of the upper sets of a preorder, by design. Of course the upper sets are upward closed.
You mention modal logics, but for those we need to augment Kripke models with an accessibility relation, and in any case, monotonicity still holds by virtue of what a Kripke model is.
• Thank you. :) But I did not mean to exclude predicate logics. Is this the case also for intermediate predicate logics? – user65526 Dec 17 '18 at 14:48
• Everything I said applies to predicate logics as well. In fact, we can generalize to higher-order intuitionistic logic by expanding Kripke models to presheaf toposes on preorders. – Andrej Bauer Dec 17 '18 at 14:53
• The reason I asked the question was because I found a logic with a modal operator which was not hereditary. It was suggested to me that this showed that we could not define the operator intuitionistically. But is this line of thought therefore mistaken? – user65526 Dec 17 '18 at 15:33
• That depends on pesky details. – Andrej Bauer Dec 17 '18 at 15:47 | {"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": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9177025556564331, "perplexity": 342.4864286885767}, "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-2020-34/segments/1596439738603.37/warc/CC-MAIN-20200810012015-20200810042015-00167.warc.gz"} |
http://mathhelpforum.com/calculus/28080-integration-couple-questions.html | # Thread: Integration: couple of questions
1. ## Integration: couple of questions
Hi, I have a couple of questions on integration:
1.) Expressing the derivative of a function f(x) from the limit gives you:
lim_Δx->0 [f(x+Δx) - f(x)] / Δx = d/dx f(x)
..so that you essentially have a small change in f(x) divided by a small change in x, to give you the gradient of a secant line, which approches the actual value of the gradient at a point, when Δx approaches 0. I find this easy to follow, and like to think of the gradient in terms of a 'rate of change' of one variable, y, with another, x, when thinking about physical applications...e.g. the rate of change of distance with time, or velocity with pressure.
When it comes to integration, you have:
lim_Δx->0 Σ_n f(x_n)Δx = ∫f(x)dx
..so that for each 'n', you have a value f(x_n)Δx for the area of a narrow column, and by adding these up you get a total value for the area under the curve, which gets closer and closer to the real value of this area, as Δx approaches 0.
What I don't get is the multiplication by the term dx. if the value of dx is infinitessimally small, then musn't the product of dx, and the integrand be infinitesimally small also? For the derivative, dy/dx, It still doesn't make much sense to divide two infinitesimally small values, but I can at least understand this as the ratio of Δy and Δx (gradient) becoming more accurate, as the lengths approach 0. For the integral, I'm struggling for a nicer interpretaion of what it means.
It's all good knowing that integration gives you a function describing "the area under a graph", but in a physical sense is there a better interpretation?..for example, I can think of derivatives as a rate of change of one quantity with another, which is very easily translated to physical applications, but integrals seem harder to place.
2.) If integration and differentiation are opposite processes, can someone show me the proof of this for an arbitrary function? Do you have to do this from the limit or something?
2. Originally Posted by Greengoblin
Hi, I have a couple of questions on integration:
1.) Expressing the derivative of a function f(x) from the limit gives you:
lim_Δx->0 [f(x+Δx) - f(x)] / Δx = d/dx f(x)
..so that you essentially have a small change in f(x) divided by a small change in x, to give you the gradient of a secant line, which approches the actual value of the gradient at a point, when Δx approaches 0. I find this easy to follow, and like to think of the gradient in terms of a 'rate of change' of one variable, y, with another, x, when thinking about physical applications...e.g. the rate of change of distance with time, or velocity with pressure.
nice explanation. your thoughts are more or less accurate.
When it comes to integration, you have:
lim_Δx->0 Σ_n f(x_n)Δx = ∫f(x)dx
your definition of the integral is off. it is $\lim_{n \to \infty} \sum_{i = 1}^{n} f(x_i) \Delta x = \int f(x)~dx$
..so that for each 'n', you have a value f(x_n)Δx for the area of a narrow column, and by adding these up you get a total value for the area under the curve, which gets closer and closer to the real value of this area, as Δx approaches 0.
yes, something like that. however, $\Delta x$ depends on n. so we think of it as a function of n, and consider when $n \to \infty$.
What I don't get is the multiplication by the term dx. if the value of dx is infinitessimally small, then musn't the product of dx, and the integrand be infinitesimally small also?
not necessarily.
For the derivative, dy/dx, It still doesn't make much sense to divide two infinitesimally small values, but I can at least understand this as the ratio of Δy and Δx (gradient) becoming more accurate, as the lengths approach 0. For the integral, I'm struggling for a nicer interpretaion of what it means.
well, to really get into the meaning of the integral, you have to do analysis. what math are you doing now?
It's all good knowing that integration gives you a function describing "the area under a graph", but in a physical sense is there a better interpretation?
mmmm, not really... that is a good conceptualization of what the integral does, but in terms of physical applications, it is perhaps better to interpret the integral in terms of the derivative. that is, it is the reverse of the derivative (which happens to have many applications).
for example, I can think of derivatives as a rate of change of one quantity with another, which is very easily translated to physical applications, but integrals seem harder to place.
this is true, see above
2.) If integration and differentiation are opposite processes, can someone show me the proof of this for an arbitrary function? Do you have to do this from the limit or something?
the proof of this in general is really a proof for the fundamental theorem of calculus. it should be in your text as well as countless sites on the net. some sites make a distinction between "the fundamental theorem of calculus" and "the second fundamental theorem of calculus." so look that up as well. based on your questions before, i believe you'd be more interested in "the second fundamental theorem..."
for an arbitrary function, it is easy to see this is true.
say f(x) = x
differentiate it we get 1
integrate it, we get back x
so it works.
however, there is what we call the indefinate integral and the definate integral. in the indefinate, we add a constant C to cover the possibility there was a part of the function lost in differentiating, such as constants.
for instance, if the function was f(x) = x + 1, the derivative would again be 1 and the integral would again be x, but you see we lost a 1. so we write the integral as x + C, to account for the possibility of a lost constant. so look out for that as well
3. Thanks. Are you saying that for an integral, Δx=f(n)? I don't understand why Δx would be a function of n, and why you can consider n approaching infinity to mean Δx approaching 0 - and Δx must approach 0 for the width of each column to become infinitesimally small?
well, to really get into the meaning of the integral, you have to do analysis. what math are you doing now?
I've just finished learning about differentiation, and now I'm trying to learn about integration too. By "Analysis" are you talking about things like sequences and series or more advanced? I've just started looking at sequences and series too, with arithmetic progression and stuff. Actually I'm not sure where the formula for an arithmetic series comes from. I understand that nth term = a + (n-1)d, but I don't understand how this can lead to the formula for the series:
Sn = n/2[2a + (n-1)d]
for an arbitrary function, it is easy to see this is true.
say f(x) = x
But f(x)=x isn't a general function is it? I mean like a proof for any function f(x), that could prove it true no matter what the function is. For example it could aslo be trig, or exponential or polynomial etc. Thanks for the reply
4. Originally Posted by Greengoblin
Thanks. Are you saying that for an integral, Δx=f(n)? I don't understand why Δx would be a function of n, and why you can consider n approaching infinity to mean Δx approaching 0 - and Δx must approach 0 for the width of each column to become infinitesimally small?
yes, $\Delta x \to 0$ as $n \to \infty$, but it is just apart of the definition of the integral to use only the limit with respect to n (imagine having to use a double limit in the definition! one as $\Delta x \to 0$ and one as $n \to \infty$). it is easier to do one. and it is easy to write $\Delta x$ in terms of n and the end points of the interval we are considering, so why not do it that way?
I've just finished learning about differentiation, and now I'm trying to learn about integration too. By "Analysis" are you talking about things like sequences and series or more advanced?
more advanced. analysis is something you do after your elementary calculus sequence (calculus 1,2, and 3).
I've just started looking at sequences and series too, with arithmetic progression and stuff. Actually I'm not sure where the formula for an arithmetic series comes from. I understand that nth term = a + (n-1)d, but I don't understand how this can lead to the formula for the series:
Sn = n/2[2a + (n-1)d]
you can see here for how the sum is derived.
you can also try do derive the formula using the intuitive approach it talks about.
say you want to sum the first n terms, that is, find:
$S_n = 1 + 2 + 3 + \cdots + (n - 2) + (n - 1) + n$
notice that if we add the first and last terms, and then the second and second to last terms, and third and third to last terms, we get n + 1 in each case, as illustrated below:
$1 + n = n + 1$
$2 + (n - 1) = n + 1$
$3 + (n - 2) = n + 1$
.
.
.
and so on
so the sum of the n terms amounts to summing all these (n + 1)'s. how many are there? well, they result from us pairing off terms, so there must be half the number of (n + 1)'s as there are the number of terms. there are n terms, so there are $\frac n2$ (n + 1)'s. thus:
$S_n = \frac n2(n + 1)$
here 1 is the first term, analogous therefore to $a_1$ and n is the nth term, analogous therefore to $a_n$. so we can replace them.
so, $S_n = \frac n2(a_1 + a_n)$
replacing $a_n$ with the formula for an arithmetic series yields the formula you mentioned earlier.
by no means is this a rigorous proof. here i showed this for a particular kind of arithmetic series (one in which the first term was 1 and the common difference is 1). however, this procedure can be generalized to any term. i was merely trying to give you an intuitive feel for how the formula came about. the link i gave you shows another way to derive the formula as well.
But f(x)=x isn't a general function is it? I mean like a proof for any function f(x), that could prove it true no matter what the function is. For example it could aslo be trig, or exponential or polynomial etc. Thanks for the reply
as i said, what you are asking for, in general, is the proof to the fundamental theorem of calculus. you can look it up on wikipedia or in your text. every calculus text has it. if yours doesn't, it should be burnt. | {"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": 18, "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": 0.94364994764328, "perplexity": 308.79778180828066}, "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-2016-40/segments/1474738661768.10/warc/CC-MAIN-20160924173741-00169-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://micromath.wordpress.com/2011/05/14/donald-knuth-and-his-notation-for-multiplicative-inverses/?like=1&source=post_flair&_wpnonce=e60e0e8ee0 | Posted by: Alexandre Borovik | May 14, 2011
## Donald Knuth and his notation for multiplicative inverses
Please help me to find a reference to Donald Knuth‘s suggestion to denote inverses as $x^-$ rather than $x^{-1}$. I remember Knuth commenting somewhere that $^1$ is redundant because $x^{-1}$ could be easily understood as $(x^-)^1$. | {"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": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.945655882358551, "perplexity": 1740.691299839402}, "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/1529267867095.70/warc/CC-MAIN-20180624215228-20180624235228-00555.warc.gz"} |
https://xianblog.wordpress.com/2017/11/21/the-hyvarinen-score-is-back/ | the Hyvärinen score is back
Stéphane Shao, Pierre Jacob and co-authors from Harvard have just posted on arXiv a new paper on Bayesian model comparison using the Hyvärinen score
$\mathcal{H}(y, p) = 2\Delta_y \log p(y) + ||\nabla_y \log p(y)||^2$
which thus uses the Laplacian as a natural and normalisation-free penalisation for the score test. (Score that I first met in Padova, a few weeks before moving from X to IX.) Which brings a decision-theoretic alternative to the Bayes factor and which delivers a coherent answer when using improper priors. Thus a very appealing proposal in my (biased) opinion! The paper is mostly computational in that it proposes SMC and SMC² solutions to handle the estimation of the Hyvärinen score for models with tractable likelihoods and tractable completed likelihoods, respectively. (Reminding me that Pierre worked on SMC² algorithms quite early during his Ph.D. thesis.)
A most interesting remark in the paper is to recall that the Hyvärinen score associated with a generic model on a series must be the prequential (predictive) version
$\mathcal{H}_T (M) = \sum_{t=1}^T \mathcal{H}(y_t; p_M(dy_t|y_{1:(t-1)}))$
rather than the version on the joint marginal density of the whole series. (Followed by a remark within the remark that the logarithm scoring rule does not make for this distinction. And I had to write down the cascading representation
$\log p(y_{1:T})=\sum_{t=1}^T \log p(y_t|y_{1:t-1})$
to convince myself that this unnatural decomposition, where the posterior on θ varies on each terms, is true!) For consistency reasons.
This prequential decomposition is however a plus in terms of computation when resorting to sequential Monte Carlo. Since each time step produces an evaluation of the associated marginal. In the case of state space models, another decomposition of the authors, based on measurement densities and partial conditional expectations of the latent states allows for another (SMC²) approximation. The paper also establishes that for non-nested models, the Hyvärinen score as a model selection tool asymptotically selects the closest model to the data generating process. For the divergence induced by the score. Even for state-space models, under some technical assumptions. From this asymptotic perspective, the paper exhibits an example where the Bayes factor and the Hyvärinen factor disagree, even asymptotically in the number of observations, about which mis-specified model to select. And last but not least the authors propose and assess a discrete alternative relying on finite differences instead of derivatives. Which remains a proper scoring rule.
I am quite excited by this work (call me biased!) and I hope it can induce following works as a viable alternative to Bayes factors, if only for being more robust to the [unspecified] impact of the prior tails. As in the above picture where some realisations of the SMC² output and of the sequential decision process see the wrong model being almost acceptable for quite a long while…
15 Responses to “the Hyvärinen score is back”
1. Funny that you may think all proper priors acceptable as true distributions! For instance, some proper priors lead to inadmissible estimators while some improper priors produce admissible ones…
• Dan Simpson Says:
I obviously don’t think that! A prior is appropriate for a given circumstance. So it’s never true that all proper priors could be used for any problem.
Regarding admissibility, my understanding is that there are essentially two types of inadmissible priors: the howlingly inadmissible and the ones that are only just beaten.
I guess this view comes from my background in numerics. I just don’t trust computers with big numbers or small number, so if the maths is dichotomizing estimators based on properties way out in the tails, then I think it’s hard to take the dichotomy seriously.
For instance, if you can beat my prior when |theta| > 10^10, but it performs better for more reasonable values, I’m not enormously concerned with the resulting estimator being inadmissible.
You know the maths of this much better than I do, but it was always my impression that the improper priors come from playing those sorts of games with infinity and infinitesimals.
For a lot of models, such as a poisson-glm withif a log-link, parameter values in [-20,20] cover well beyond the reasonable range (if your data has a mean of 10^8, you should rescale it before doing things in a computer!), so arguments around infinity are not very meaningful. And priors that put non-trivial mass outside that interval (or that are defined as the limit of things that put non-trivial mass outside that interval) seem a-statistical.
2. Fabrizio Leisen Says:
First of all, congratulations to Pierre and coauthors for the nice paper. As usual, Pierre writes interesting papers. Apparently, scoring rules are stalking me recently :) . At a first quick look, I don’t see problems with the limiting argument but I have to admit that my reading was superficial. Hope Pierre will answer to my emails when I’ll properly read the paper. :-)
3. Pierre Jacob Says:
In a nutshell, the marginal log-likelihood might indeed be ill-defined when a prior becomes vaguer, while its derivatives with respect to the observation ‘y’ might admit a limit. This explains the appeal of using a scoring rule based on derivatives of the (incremental) log-likelihoods, such as the Hyvärinen scoring rule.
This is well-explained in Dawid and Musio’s 2015 paper.
• Dan Simpson Says:
All Dawid and Musio do is say that you can still compute it even if the distribution is improper. They don’t seem to talk about what that means. The theory in Hyvärinen’s paper (which deals with unknown normalizations not unnormalisable densities) that shows propriety of the score all assumes that the density is normalisable. It might still be proper against sigma-finite measures, but someone needs to prove it somewhere…
• Pierre Jacob Says:
If you look at their case study in linear models, you’ll see that they consider improper priors as limits of sequences of proper priors. Then, if you agree that the score has a meaning for any proper prior, and that its limit (as the prior becomes improper) is well-defined, this immediately “gives a meaning” to this score when using improper priors.
We have a similar toy example on page 2 of our paper, with a simple Normal-Normal conjugate model.
Or maybe it’s the idea of giving meaning through a limit argument that makes you incomfortable? If so, then there’s not much to argue about, it’s a conceptual disagreement. I’m happy e.g. with derivatives being defined as limits of finite differences, and integrals as limits of averages.
• Dan Simpson Says:
I don’t agree that, for complicated nonlinear functions of the prior, things that work when the prior is proper still work when the prior is at its improper limit. If that were true we could safely use gamma(epsilon,epsilon) priors.
I really don’t want to say it doesn’t work. I have literally no idea. But I’ve been burnt before. That’s why we have maths. And no one seems to have done it.
4. Dan Simpson Says:
I didn’t think p(y) was well defined for improper priors, so I’m not sure how this can be interpreted as a score (which would require p to be a probability distribution). Isn’t it only known up to a multiplicative constant? In that case how does the scoring rule stuff work? Or am I missing something obvious?
Full disclosure: I haven’t hit this paper on my pile yet and I am looking forward to it. But that seems like a key challenge.
• The first and second differentials of log p(y) are clearly independent from the constant.
• Pierre Jacob Says:
Thanks Dan for putting this on your pile, and thanks Christian for the supportive comments!
• Dan Simpson Says:
Yes, but what does this mean to the score. P(y) is clearly not a probability in general, it’s just an integral of things. Does the wnole scoring rule machine still run?
• Dan Simpson Says:
Just to be clear, it’s not the case that there is a constant and we know it (which would be fine for this score), it’s that any constant could be used.
This problem goes away if you use the posterior predictive density rather than the prior predictive density.
• I still do not get the argument why a finite measure has more meaning than a sigma-finite measure. Limits are necessary “evils” in a topological world…
• Dan Simpson Says:
The problem (or potential problem) is that the set of sigma finite measures is strictly bigger than the set of finite measures. So you might be able to “game” the scoring rule on the larger set (find a minimum that isn’t at the true distribution) or the rule may no longer be strictly proper (because there is an unnormalisable measure that has the same score as the true distribution).
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https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.713030 | Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.713030
Title: On the theory of dissipative extensions
Author: Fischbacher, Christoph Stefan
ISNI: 0000 0004 6349 1089
Awarding Body: University of Kent
Current Institution: University of Kent
Date of Award: 2017
Availability of Full Text:
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Abstract:
We consider the problem of constructing dissipative extensions of given dissipative operators. Firstly, we discuss the dissipative extensions of symmetric operators and give a suffcient condition for when these extensions are completely non-selfadjoint. Moreover, given a closed and densely defined operator A, we construct its closed extensions which we parametrize by suitable subspaces of D(A^*). Then, we consider operators A and \widetilde{A} that form a dual pair, which means that A\subset \widetilde{A}^*, respectively \widetilde{A}\subset A^* Assuming that A and (-\widetilde{A}) are dissipative, we present a method of determining the proper dissipative extensions \widehat{A} of this dual pair, i.e. we determine all dissipative operators \widehat{A} such that A\subset \subset\widehat{A}\subset\widetilde{A}^* provided that D(A)\cap D(\widetilde{A}) is dense in H. We discuss applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators. Also, we investigate the stability of the numerical ranges of the various proper dissipative extensions of the dual pair (A,\widetilde{A}). Assuming that zero is in the field of regularity of a given dissipative operator A, we then construct its Krein-von Neumann extension A_K, which we show to be maximally dissipative. If there exists a dissipative operator (-\widetilde{A}) such that A and \widetilde{A} form a dual pair, we discuss when A_K is a proper extension of the dual pair (A,\widetilde{A}) and if this is not the case, we propose a construction of a dual pair (A_0,\widetilde{A}_0), where A_0\subset A and \widetilde{A}_0\subset\widetilde{A} such that A_K is a proper extension of (A_0,\widetilde{A}_0). After this, we consider dual pairs (A, \widetilde{A}) of sectorial operators and construct proper sectorial extensions that satisfy certain conditions on their numerical range. We apply this result to positive symmetric operators, where we recover the theory of non-negative selfadjoint and sectorial extensions of positive symmetric operators as described by Birman, Krein, Vishik and Grubb. Moreover, for the case of proper extensions of a dual pair (A_0,\widetilde{A}_0)of sectorial operators, we develop a theory along the lines of the Birman-Krein-Vishik theory and define an order in the imaginary parts of the various proper dissipative extensions of (A,\widetilde{A}). We finish with a discussion of non-proper extensions: Given a dual pair (A,\widetilde{A}) that satisfies certain assumptions, we construct all dissipative extensions of A that have domain contained in D(\widetilde{A}^*). Applying this result, we recover Crandall and Phillip's description of all dissipative extensions of a symmetric operator perturbed by a bounded dissipative operator. Lastly, given a dissipative operator A whose imaginary part induces a strictly positive closable quadratic form, we find a criterion for an arbitrary extension of A to be dissipative.
Supervisor: Wood, Ian Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.713030 DOI: Not available
Keywords: QA Mathematics (inc Computing science)
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http://support.sas.com/documentation/cdl/en/statug/67523/HTML/default/statug_loess_syntax06.htm | # The LOESS Procedure
### MODEL Statement
• MODEL dependents = regressors </ options>;
The MODEL statement names the dependent variables and the independent variables. Variables specified in the MODEL statement must be numeric variables in the data set being analyzed.
Table 59.2 summarizes the options available in the MODEL statement.
Table 59.2: Summary of MODEL Statement Options
Option
Description
Fit Options
specifies the number of points in k-d tree buckets
specifies the degree of local polynomials (1 or 2)
specifies the method of computing lookup degrees of freedom
specifies direct fitting at every data point
specifies the variables whose squares are to be dropped from local quadratic polynomials
specifies the interpolating polynomials (linear or cubic)
specifies the number of reweighting iterations
specifies the method used to scale the regressor variables
specifies that automatic smoothing parameter selection be done
specifies the list of smoothing values
Output Statistics Table Options
requests CLM , RESIDUAL , SCALEDINDEP , STD , and T options
displays confidence limits for mean predictions
displays residuals
displays scaled independent variable coordinates
displays standard errors of the mean predicted values
displays t statistics
Other options
sets significance level for confidence intervals
specifies which tables are to be displayed
displays the trace of the smoothing matrix
The following options are available in the MODEL statement after a slash (/).
ALL
requests all these options: CLM, RESIDUAL, SCALEDINDEP, STD, and T.
ALPHA=number
sets the significance level used for the construction of confidence intervals for the current MODEL statement. The value must be between 0 and 1; the default value of 0.05 results in 95% intervals.
BUCKET=number
specifies the maximum number of points in the leaf nodes of the k-d tree. The default value used is , where s is a smoothing parameter value specified using the SMOOTH= option and n is the number of observations being used in the current BY group. The BUCKET= option is ignored if the DIRECT option is specified.
CLM
requests that % confidence limits on the mean predicted value be added to the "Output Statistics" table. By default, 95% limits are computed; the ALPHA= option in the MODEL statement can be used to change the significance level. The use of this option implicitly selects the model option DFMETHOD=EXACT if the DFMETHOD= option has not been explicitly used.
DEGREE=1 | 2
sets the degree of the local polynomials to use for each local regression. The valid values are 1 for local linear fitting and 2 for local quadratic fitting, with 1 being the default.
DETAILS <( tables )>
selects which tables to display, where tables is one or more of the specifications KDTREE, MODELSUMMARY, OUTPUTSTATISTICS, and PREDATVERTICES:
• KDTREE displays the k-d tree structure.
• MODELSUMMARY displays the fit criteria for all smoothing parameter values that are specified in the SMOOTH= option in the MODEL statement, or that are fit with automatic smoothing parameter selection.
• OUTPUTSTATISTICS displays the predicted values and other requested statistics at the points in the input data set.
• PREDATVERTICES displays fitted values and coordinates of the k-d tree vertices where the local least squares fitting is done.
The KDTREE and PREDATVERTICES specifications are ignored if the DIRECT option is specified in the MODEL statement. Specifying the option DETAILS with no qualifying list outputs all tables.
DFMETHOD=NONE | EXACT | APPROX <(approx-options)>
specifies the method used to calculate the lookup degrees of freedom used in performing statistical inference. The default is DFMETHOD=NONE, unless you specify any of the MODEL statement options ALL, CLM, STD, and T, or any SCORE statement CLM option, in which case the default is DFMETHOD=EXACT.
You can specify the following approx-options in parentheses after the DFMETHOD=APPROX option:
QUANTILE=number
specifies that the smallest 100(number)% of the nonzero coefficients in the smoothing matrix be set to zero in computing the approximate lookup degrees of freedom. The default value is QUANTILE=0.9.
CUTOFF=number
specifies that coefficients in the smoothing matrix whose magnitude is less than the specified value be set to zero in computing the approximate lookup degrees of freedom. Using the CUTOFF= option overrides the QUANTILE= option.
See the section Sparse and Approximate Degrees of Freedom Computation for a description of the method used when the DFMETHOD=APPROX option is specified.
DIRECT
specifies that local least squares fits are to be done at every point in the input data set. When the direct option is not specified, a computationally faster method is used. This faster method performs local fitting at vertices of a k-d tree decomposition of the predictor space followed by blending of the local polynomials to obtain a regression surface.
DROPSQUARE=(variables)
specifies the quadratic monomials to exclude from the local quadratic fits. This option is ignored unless the DEGREE=2 option has been specified.
For example,
model z=x y / degree=2 dropsquare=(y)
uses the monomials 1, x, y, , and in performing the local fitting.
INTERP=LINEAR | CUBIC
specifies the degree of the interpolating polynomials used for blending local polynomial fits at the k-d tree vertices. This option is ignored if the DIRECT option is specified in the model statement. INTERP=CUBIC is not supported for models with more than two regressors. The default is INTERP=LINEAR.
ITERATIONS=number
specifies the total number of iterations to be done. The first iteration performs an initial LOESS fit. Subsequent iterations perform iterative reweighting. Such iterations are appropriate when there are outliers in the data or when the error distribution is a symmetric long-tailed distribution. The default number of iterations is 1.
RESIDUAL | R
specifies that residuals be included in the "Output Statistics" table.
SCALE=NONE | SD < (number) >
specifies the scaling method to be applied to scale the regressors. The default is NONE, in which case no scaling is applied. A specification of SD(number) indicates that a trimmed standard deviation is to be used as a measure of scale, where number is the trimming fraction. A specification of SD with no qualification defaults to 10% trimmed standard deviation.
SCALEDINDEP
specifies that scaled regressor coordinates be included in the output tables. This option is ignored if the SCALE= model option is not used or if SCALE=NONE is specified.
SELECT=criterion <(<GLOBAL> <PRESEARCH> <STEPS> <RANGE(lower,upper)> )>
SELECT=DFCriterion <(target <GLOBAL> <PRESEARCH> <STEPS> <RANGE(lower,upper)> )>
specifies that automatic smoothing parameter selection be done using the named criterion or DFCriterion. Valid values for the criterion are as follows:
AICC
specifies the criterion (Hurvich, Simonoff, and Tsai, 1998).
AICC1
specifies the criterion (Hurvich, Simonoff, and Tsai, 1998).
GCV
specifies the generalized cross validation criterion (Craven and Wahba, 1979).
The DFCriterion specifies the measure used to estimate the model degrees of freedom. The measures implemented in PROC LOESS all depend on prediction matrix relating the observed and predicted values of the dependent variable. Valid values for the DFCriterion are as follows:
DF1
specifies .
DF2
specifies .
DF3
specifies .
For both types of selection, the smoothing parameter value is selected to yield a minimum of an optimization criterion. If you specify criterion as one of AICC, AICC1, or GCV, the optimization criterion is the specified criterion. If you specify DFCriterion as one of DF1, DF2, or DF3, the optimization criterion is , where target is a specified target degree of freedom value. Note that if you specify a DFCriterion, then you must also specify a target value. See the section Automatic Smoothing Parameter Selection for definitions and properties of the selection criteria.
The selection is done as follows:
• If you specify the SMOOTH=value-list option, then PROC LOESS selects the largest value in this list that yields the global minimum of the specified optimization criterion.
• If you do not specify the SMOOTH= option, then PROC LOESS finds a local minimum of the specified optimization criterion by using a golden section search of values less than or equal to one.
You can specify the following suboptions in parentheses after the specified criterion to alter the behavior of the SELECT= option:
GLOBAL
specifies that a global minimum be found within the range of smoothing parameter values examined. This suboption has no effect if you also specify the SMOOTH= option in the MODEL statement.
PRESEARCH
requests an initial grid search to find a smoothing parameter range within which the subsequent golden section search is done. The initial point in this grid is the smoothing parameter value corresponding to the smallest number of points, n, in the local neighborhoods that yields a fit that does not interpolate all the data points. Subsequent fits with number of local points n + 1, n + 2, n + 4, n + 8, ... are evaluated until either the number of local points exceeds the number of fitting points or the SELECT=criterion starts increasing. This suboption is ignored if you additionally specify the GLOBAL suboption of the SELECT= option or if you specify the SMOOTH= option in the MODEL statement. If you additionally specify the RANGE= suboption, then the golden section search is done on the intersection of the range found by this grid search and the range that you specify in the RANGE= suboption. This option is useful for data exhibiting features at multiple scales, because in such cases the SELECT= criterion often has multiple local minima. Using the PRESEARCH option increases the likelihood that the golden section search will find the global minimum of the SELECT= criterion. See Example 59.4 for such an example.
RANGE(lower,upper)
specifies that only smoothing parameter values greater than or equal to lower and less than or equal to upper be examined.
STEPS
specifies that all models evaluated in the selection process be displayed.
For models with one dependent variable, if you specify neither the SELECT= nor the SMOOTH= options in the MODEL statement, then PROC LOESS uses SELECT=AICC.
The following table summarizes how the smoothing parameter values are chosen for various combinations of the SMOOTH= option, the SELECT= option, and the SELECT= option modifiers.
Table 59.3: Smoothing Parameter Value(s) Used for Combinations of SMOOTH= and SELECT= OPTIONS for Models with One Dependent Variable
Syntax
Search Method
Search Domain
default
golden section using AICC
SMOOTH=list
no selection
values in list
SMOOTH=list SELECT=criterion
global
values in list
SMOOTH=list SELECT=criterion ( RANGE() )
global
values in list within
SELECT=criterion
golden section
SELECT=criterion (RANGE(l,u) )
golden section
SELECT=criterion ( GLOBAL )
global
SELECT=criterion ( GLOBAL RANGE() )
global
Some examples of using the SELECT= option follow:
SELECT=GCV
specifies selection that uses the GCV criterion.
SELECT=DF1(6.3)
specifies selection that uses the DF1 DFCriterion with target value 6.3.
SELECT=AICC(STEPS)
specifies selection that uses the AICC criterion, showing all step details.
SELECT=DF2(7 GLOBAL)
specifies selection that uses a global search algorithm to find the smoothing parameter that yields the DF2 DFCriterion closest to the target value 7.
Note: The SELECT= option cannot be used for models with more than one dependent variable.
SMOOTH=value-list
specifies a list of positive smoothing parameter values. If you do not specify the SELECT= option in the MODEL statement, then a separate fit is obtained for each SMOOTH= value specified. If you do specify the SELECT= option, then models with all values specified in the SMOOTH= list are examined, and PROC LOESS selects the value that minimizes the criterion specified in the SELECT= option.
For models with two or more dependent variables, if the SMOOTH= option is not specified in the MODEL statement, then SMOOTH=0.5 is used as a default.
STD
specifies that standard errors of the mean predicted values be included in the "Output Statistics" table. The use of this option implicitly selects the model option DFMETHOD=EXACT if the DFMETHOD= option has not been explicitly used.
T
specifies that t statistics are to be included in the "Output Statistics" table. The use of this option implicitly selects the model option DFMETHOD=EXACT if the DFMETHOD= option has not been explicitly used.
TRACEL
specifies that the trace of the prediction matrix as well as the GCV and AICC statistics be included in the "Fit Summary" table. The use of any of the MODEL statement options ALL, CLM, DFMETHOD=EXACT, DIRECT, SELECT=, STD, and T implicitly selects the TRACEL option. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8134583830833435, "perplexity": 1914.2994351676077}, "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-2019-43/segments/1570986655735.13/warc/CC-MAIN-20191015005905-20191015033405-00493.warc.gz"} |
https://www.math.snu.ac.kr/board/index.php?mid=seminars&sort_index=date&order_type=desc&page=20&document_srl=812483 | ※ Zoom ID: 553 119 4205
We review the notions of buildings for projective general linear groups and give a geometric description of the arithmetic quotient of PGL(3). We further discuss dynamical and combinatorial properties of diagonal action on the arithmetic quotient. | {"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": 0.9679527282714844, "perplexity": 548.3917292781562}, "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-2022-49/segments/1669446710690.85/warc/CC-MAIN-20221129064123-20221129094123-00733.warc.gz"} |
https://asu.pure.elsevier.com/en/publications/spin-orbit-interaction-and-spin-selectivity-for-tunneling-electro | # Spin-orbit interaction and spin selectivity for tunneling electron transfer in DNA
Solmar Varela, Iskra Zambrano, Bertrand Berche, Vladimiro Mujica, Ernesto Medina
Research output: Contribution to journalArticlepeer-review
2 Scopus citations
## Abstract
Electron transfer (ET) in biological molecules, such as peptides and proteins, consists of electrons moving between well-defined localized states (donors to acceptors) through a tunneling process. Here, we present an analytical model for ET by tunneling in DNA in the presence of spin-orbit (SO) interaction to produce a strong spin asymmetry with the intrinsic atomic SO strength in the meV range. We obtain a Hamiltonian consistent with charge transport through π orbitals on the DNA bases and derive the behavior of ET as a function of the injection state momentum, the spin-orbit coupling, and barrier length and strength. Both tunneling energies, deep below the barrier and close to the barrier height, are considered. A highly consistent scenario arises where two concomitant mechanisms for spin selection arises; spin interference and differential spin amplitude decay. High spin filtering can take place at the cost of reduced amplitude transmission assuming realistic values for the SO coupling. The spin filtering scenario is completed by addressing the spin-dependent torque under the barrier with a consistent conserved definition for the spin current.
Original language English (US) 241410 Physical Review B 101 24 https://doi.org/10.1103/PhysRevB.101.241410 Published - Jun 15 2020
## ASJC Scopus subject areas
• Electronic, Optical and Magnetic Materials
• Condensed Matter Physics
## Fingerprint
Dive into the research topics of 'Spin-orbit interaction and spin selectivity for tunneling electron transfer in DNA'. Together they form a unique fingerprint. | {"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": 0.9071572422981262, "perplexity": 4857.156171754786}, "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/1634323585290.83/warc/CC-MAIN-20211019233130-20211020023130-00103.warc.gz"} |
http://cms.math.ca/10.4153/CMB-2003-036-9 | location: Publications → journals → CMB
Abstract view
# Gauss and Eisenstein Sums of Order Twelve
Let $q=p^{r}$ with $p$ an odd prime, and $\mathbf{F}_{q}$ denote the finite field of $q$ elements. Let $\Tr\colon\mathbf{F}_{q} \to\mathbf{F}_{p}$ be the usual trace map and set $\zeta_{p} =\exp(2\pi i/p)$. For any positive integer $e$, define the (modified) Gauss sum $g_{r}(e)$ by $$g_{r}(e) =\sum_{x\in \mathbf{F}_{q}}\zeta_{p}^{\Tr x^{e}}$$ Recently, Evans gave an elegant determination of $g_{1}(12)$ in terms of $g_{1}(3)$, $g_{1}(4)$ and $g_{1}(6)$ which resolved a sign ambiguity present in a previous evaluation. Here I generalize Evans' result to give a complete determination of the sum $g_{r}(12)$. | {"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": 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": 0.9821350574493408, "perplexity": 309.58004565322994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860111612.51/warc/CC-MAIN-20160428161511-00214-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://chem.libretexts.org/Ancillary_Materials/Worksheets/Worksheets%3A_General_Chemistry/Worksheets%3A_General_Chemistry_(Traditional)/Building_Atoms_with_Quantum_Leaps_(Worksheet) | # Building Atoms with Quantum Leaps (Worksheet)
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Name: ______________________________
Section: _____________________________
Student ID#:__________________________
Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.
"Physicists Put Atom in Two Places at Once." This was the headline in the science section of the New York Times on May 28, 1996. “Impossible!” you say. “How could they do that?” you wonder. This event is impossible at the macroscopic level at which classical mechanics governs the world. But it is entirely possible according to quantum mechanics, which governs the particulate world of atoms, protons, and electrons. The physicists who caused a single beryllium atom to exist in two states at the same time, separated by a distance of 83 nanometers, made use of a quantum mechanical trait called spin.
## Quantum Numbers
The spin attribute is one of the four quantum mechanical characteristics needed to describe an electron completely. Each of these characteristics is described by what is known as a quantum number. If we consider quantum numbers to be the “address” of each electron within an atom, each address has four parts, and no two electrons have the exact same address.
The Bohr model of the hydrogen atom gave us our first understanding that electrons were governed by non-classical mechanics, and this model worked well for explaining the properties of the electron in the hydrogen atom. However, it failed for all other atoms. In 1926, Erwin Schrödinger devised a new model of the atom which is now known as the quantum mechanical model.
The Quantum Mechanical Model of the Atom Schrödinger’s atomic model is framed mathematically in terms of what is known as a wave equation. Solutions of wave equations are called wave functions. The solutions to a wave equation define the volume in space where an electron with a particular energy is likely to be found. This volume in space is called an orbital. Each orbital is characterized by three quantum numbers.
## The Pauli Exclusion Principle
This principle states that no two electrons in an atom can have the same four quantum numbers. If two electrons occupy the same orbital, they must have different spins.
The four quantum numbers (for electronic wavefunctions) are:
1. The principal quantum number, n.
The allowed values of the principal quantum number are n = 1, 2, 3, ..., 7. Electrons with the same value of n are said to have the same principal energy level.
2. The angular momentum quantum number, l.
Angular momentum quantum numbers depend on principal quantum numbers. For n = 1, l = 0. For n = 2, l = 0 or 1. For n = 3, l = 0, 1, or 2. For n = 4 (and higher), l = 0, 1, 2, or 3. This pattern can be summarized as l = 0, 1, ..., n – 1. Notice that all principal energy levels are divided into one or more sublevels.
Angular momentum quantum numbers are often referred to by using letter designations which correspond with the numerical values. l = 0 is also called the s sublevel, l = 1 is p, l = 2 is d, and l = 3 is f. Electron energies are described by the principal energy level and the sublevel. Thus an electron with n = 3 and l = 1 is referred to as a 3p electron.
3. The magnetic quantum number, ml.
Magnetic quantum numbers depend on angular momentum quantum numbers. The pattern is ml = –l, ..., 0, ..., +l. Thus for l = 0, the only allowed value of ml is 0. When l = 1, ml can be –1, 0, or +1. For l = 2, ml = –2, –1, 0, +1, and +2. When this pattern is followed for l = 3, there are seven possible ml values (can you write them?).
4. The electron spin quantum number, ms.
The values of ms are +½ and –½ . Electrons can be thought of as spinning on an axis, where one ms value corresponds to a clockwise rotation and the other value corresponds to a counterclockwise rotation.
## The Periodic Table
The periodic table serves as a guide to both order of increasing electron energies and the order in which electrons fill orbitals. Electrons occupy the lowest energy orbitals available, and as the numbers of electrons in an atom increases, the outermost electrons occupy higher and higher energy levels. The periodic table below illustrates the correspondence of electron energy levels and position on the periodic table.
Note:
s orbitals are being filled in Groups 1A–2A, p orbitals are being filled in groups 3A–8A, d orbitals fill in the B Groups, and f orbitals fill in the lanthanide and actinide series.
For s and p orbitals, the period number corresponds with the principal energy level. For d orbitals, the fourth period corresponds to n = 3, the fifth period to n = 4, and so on. The lanthanides correspond to n = 4, and the actinides have n = 5.
This page titled Building Atoms with Quantum Leaps (Worksheet) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Mark Draganjac via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. | {"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": 0.8328415155410767, "perplexity": 447.14901321577673}, "config": {"markdown_headings": true, "markdown_code": false, "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-2023-14/segments/1679296950383.8/warc/CC-MAIN-20230402043600-20230402073600-00092.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/a-0500-kg-sphere-moving-with-a-velocity-200-260-100-m-s-strikes-another-sphere-of-mass-150-q3364806 | A 0.500 kg sphere moving with a velocity (2.00 - 2.60 + 1.00) m/s strikes another sphere of mass 1.50 kg moving with a velocity (-1.00 + 2.00 - 3.00) m/s. (a) If the velocity of the 0.500 kg sphere after the collision is (-1.00 + 3.00 - 8.00) m/s, find the velocity of the 1.50 kg sphere and identify the kind of collision (elastic, inelastic, or perfectly inelastic). ( + + ) m/s This is ______ collision. an elastic an inelastic a perfectly inelastic (b) If the velocity of the 0.500 kg sphere after the collision is (-0.250 + 0.850 - 2.00) m/s, find the final velocity of the 1.50 kg sphere and identify the kind of collision. ( + + ) m/s This is ______ collision. an elastic an inelastic a perfectly inelastic (c) What if? If the velocity of the 0.500 kg sphere after the collision is (-1.00 + 3.40 + a) m/s, find the value of a and the velocity of the 1.50 kg sphere after an elastic collision. (Two values of a are possible, a negative value and a positive value. Report each with their corresponding final velocities.) a (positive value) m/s2 v2f = m/s a (negative value) m/s2 v2f = m/s | {"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": 0.8430772423744202, "perplexity": 1364.8769663553792}, "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-2013-20/segments/1368705502703/warc/CC-MAIN-20130516115822-00089-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/61039/a-cycle-which-is-the-product-of-disjoint-m-cycles-does-not-necessarily-have-or | # A cycle which is the product of disjoint $m$-cycles does not necessarily have order $m$?
Suppose a cycle $\sigma\in S_n$ has decomposition a product of disjoint $p$-cycles, for $p$ a prime. So each cycle has order $p$, and thus $\sigma^p=id$, so $\sigma$ has order dividing $p$, and thus order $p$ when $\sigma\neq id$.
What if $\sigma$ has a decomposition into a product of disjoint $m$-cycles, for $m$ composite. I know $\sigma^m=id$, and thus has order dividing $m$. In every example I've tried, it seems $\sigma$ still has order $m$. Is it possible for $\sigma$ to have order smaller than $m$ (when not the identity of course)? If so, is there an example?
Much thanks,
-
exercise: the order of a product of disjoint cycles is the lcm of the cycle lengths – yoyo Aug 31 '11 at 23:05
A permutation that is the product of disjoint permutations that all have the same order, has the same order as its factors. So your $\sigma$ will have order $m$, guaranteed.
(It must have order at most $m$ because the disjoint factors commute, so $\sigma^m = (xy\cdots z)^m = x^m y^m \cdots z^m = 1\cdot 1\cdots 1 = 1$. On the other hand, by the same argument, if it had order less than $m$, each factor would also have that order, because the only way a product of disjoint permutations can be the identity is if each of the factors are).
(By the way $\sigma$ is not itself a "cycle" if it is the product of two or more disjoint permutations). | {"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": 0.9757288694381714, "perplexity": 79.01619570285335}, "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/1454701158811.82/warc/CC-MAIN-20160205193918-00248-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/rotational-motion.150668/ | # Rotational Motion
1. Jan 9, 2007
### elitespart
1. I need some ideas on how to demonstrate angular velocity and angular acceleration in the class.
3. We have some wheels w/ handles on either side that we can use to show rotation. We're going to apply the equations of angular velocity and acceleration to that. Does anyone have any input on how we can prove to the class how these two concepts work and some ideas on how to apply a constant acceleration to the rotating wheel
2. Jan 9, 2007
### BobG
The bicycle wheels can also be used to let people 'feel' angular momentum. Hold one handle and move the tire around. As long as the direction of the axis doesn't change, there's not much resistance. Try changing the direction of the axis, though. The greater the angular velocity, the greater the angular momentum.
Applying constant angular acceleration to the tire's rotation will be a little tough, but showing the effects of constant acceleration on the tires motion is pretty easy since gravity will do the trick for you. If you suspend one end of the tire from a loop of rope, gravity will cause the tire to precess about the rope. If you think about the torque caused by one of the handles being supported by the rope and the other end being accelerated by gravity, you can detemine the direction of the torque vector using the right hand screw rule. Using right hand screw rule for the angular momentum vector, you have two vectors. Comparing them, you ought to be able to guess which direction the tire will rotate around the rope.
Edit: Probably not quite what you're looking for since it doesn't deal directly with angular velocity and angular acceleration, but fun none the less.
Last edited: Jan 9, 2007
3. Jan 9, 2007
### chemhelper
In order to get constant acceleration, you need to apply a constant force. A great example of this is a gyroscope. As you pull on the string that is wrapped around the axis (i.e. the force), the gyroscope wheel will accelerate.
To show angular velocity, take the bike wheel and tape one of the spokes. Count every time the piece of tape passes a marked point for 10 seconds. You can then deduce, the wheel rotated "X" times in 10 seconds and the angular velocity is (X/10) rev / sec
Hope this helps
Last edited by a moderator: Jan 20, 2007
4. Jan 9, 2007
### elitespart
Hey thanks guys. appreciate the help.
Similar Discussions: Rotational Motion | {"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": 0.8489358425140381, "perplexity": 496.01539697802286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607960.64/warc/CC-MAIN-20170525010046-20170525030046-00015.warc.gz"} |
http://clay6.com/qa/14968/the-selection-in-a-population-subject-to-rapidly-changing-environments-with | # The selection in a population subject to rapidly changing environments with highly fluctuating food sources is called
$\begin {array} {1 1} (1)\;Stabilizing\: selection & \quad (2)\;K-selection \\ (3)\;r-selection & \quad (4)\;Disruptive\: selection \end {array}$
(3) r-selection | {"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": 0.9359930157661438, "perplexity": 4828.9906197588025}, "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-2018-13/segments/1521257647600.49/warc/CC-MAIN-20180321082653-20180321102653-00417.warc.gz"} |
https://www.physicsforums.com/threads/newtons-laws-blocks-and-pulleys-problem-with-friction.934780/ | # Newton's laws -- Blocks and pulleys problem with friction...
1. Dec 18, 2017
### Eitan Levy
1. The problem statement, all variables and given/known data
The coefficient of friction between A and the table is μA.
The coefficient of friction between A and B is μB.
A, B, C and D all move with an acceleration of 2m/s^2 (A and B move to the left).
Find the force that the friction between the bodies apply on B.
Find the tension of the yarn that connects A and C.
Find the mass of D.
At a certain moment, the yarn which connects A and D is torn. Will A and B still move together? (Show with calculations)
mA=1.4kg ,mB=0.6kg, mC=2kg, μA=0.2, μB=0.75, a=2m/s^2
*Both times the static and dynamic coefficients are equal.
2. Relevant equations
F=ma
3. The attempt at a solution
The last question is what I am stuck in, but I don't have the answers so I will show my calculations prior to that.
Forces on A and B: (I hope everything is clear)
mBg=6N so NB=6N, now we could see that according to ma=F, 1.2=F, so the force is 1.2N.
Now if we look at C we could see that 4=TC-20, TC=24N.
Now if we look at A we could see that: mAg=14N, so NA=20N.
Using ma=F: 2.8=TD-1.2-24-0.2*20 so 2.8=TD-29.2, TD=32N
Looking at D: 2mD=10mD-TD, mD=4kg.
Now I am not sure what to do, I tried to draw the forces again, but from there I don't really know what to do. How can I know if C moves now? If it doesn't then A and B doesn't move, but if it does I don't know how to reach the answer.
2. Dec 18, 2017
### TSny
In your diagram you have assumed that the friction force between A and B is given by μN.
Is this friction force static or dynamic (kinetic)? Can you see why you should not assume that the friction force is μN? Fortunately, in your calculations you never used this assumption. Your results so far look correct to me.
At the instant the yarn breaks, I think they want you to assume the system is in motion according to the setup of the first part of the problem. So, all the blocks have the same speed at the instant the yarn breaks. You'll need to draw new free body diagrams.
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3. Dec 18, 2017
### Eitan Levy
I can see why I should not assume this, I just used it to draw the diagram but I admit it wasn't clever to do.
I will try what you said, I just never assume anything and due to that it quite often I can't solve problems. I wish those things would be clearer...
4. Dec 18, 2017
### scottdave
If a block is in static condition with the surface (for example block B moves with block A), then the frictional force is enough to keep it in that condition, which may be less than μstaticN. If the amount of force necessary to keep it static (not sliding) is greater than μstaticN, then the block is sliding and the amount of force is equal to μkineticN. Note that the problem statement assigns μkinetic equal to μstatic for each of the surfaces.
I would recommend finding some practice problems where they have the block on an incline and you have to figure out "will is slide" or "how fast does it slide".
5. Dec 18, 2017
### haruspex
... And anyway, in this part of the question, using g=10m/s2, it happens that the assumption is correct.
Does that matter? It doesn't affect the accelerations and forces, does it?
Even if the static coefficient at the table were greater than the kinetic, it would have to "pass through" the static condition to reverse direction.
That said, there can be a very subtle snag with these "cut string" questions. Any real string has some elasticity. A proper treatment would allow some string constant k, but having solved for the general case take the limit as k tends to infinity.
A consequence is that the tension in the uncut string does not instantly change. It can only change by virtue of the attached object, newly freed from its other string, yielding to that tension. So to answer the question above strictly, whether the two blocks remain in a static relationship, the unchanged tension in the uncut string should be used.
That is clearly not the intent of the problem setter, though.
Last edited: Dec 18, 2017
6. Dec 18, 2017
### TSny
The force of friction on B is 1.2 N. But μBNB = (0.75)(6.0N) = 4.5 N
No, it doesn't matter. Any speed that the blocks have at the instant the yarn snaps does not affect the forces and accelerations. But, I think it's a good part of the exercise for the student to think through this.
Interesting. Would this affect whether or not the blocks are in a static relationship 1 second, say, after the yarn breaks?
7. Dec 19, 2017
### haruspex
I should have magnified the diagram. I read the A subscript on μA as a B.
It depends. If the initially high tension makes it enough to overcome static friction and the asymptotic tension overcomes kinetic but not static, then yes, it will make a long term difference to the outcome.
8. Dec 19, 2017
### Eitan Levy
So, after the yarn is torn I am getting this:
So that basically means that they won't move together because their acceleration are different, correct?
9. Dec 19, 2017
### Eitan Levy
I don't understand how this can be solved without this assumption. If it doesn't matter how can you know how the forces would look like, and if it would be enough to get A moving?
10. Dec 19, 2017
### haruspex
Just treat it as though mass D were never present. Somebody was holding A in place then let go.
11. Dec 19, 2017
### Eitan Levy
From what I understand TSny was correct when he said I should make this assumption because of the way the question is written. If that's the case, are my diagram and explanation above correct?
12. Dec 19, 2017
### haruspex
What assumption do you mean?
I am not at all certain what your diagrams in post #8 indicate. Looks to me like you have the two blocks accelerating in opposite directions, but that makes no sense.
13. Dec 19, 2017
### Eitan Levy
This: (what TSny wrote)
At the instant the yarn breaks, I think they want you to assume the system is in motion according to the setup of the first part of the problem. So, all the blocks have the same speed at the instant the yarn breaks. You'll need to draw new free body diagrams.
This diagram is supposed to show the forces on each block after the yarn is torn.
14. Dec 19, 2017
### haruspex
You are perhaps confusing direction of movement with direction of acceleration.
Since A is moving left, with some inertia, you are right that after the cut the friction from the table still acts to the right on A at first. (I was wrong to say the the initial leftward movement was completely irrelevant.) But think carefully about the interaction between A and B.
Before the cut, friction acts to the left on B because A is accelerating leftwards. After the cut, which way does A accelerate? What does that mean for the contact between A and B?
15. Dec 19, 2017
### Eitan Levy
Wait, so the direction of the friction between A and B on each block would be determined by the direction of A's acceleration and not by the direction of its movement?
16. Dec 19, 2017
### haruspex
It is determined by the relative movement, or tendency to relative movement, of the two surfaces in contact.
Just before the yarn is cut, A and B are moving at the same velocity, but because A is being accelerated left there is friction between the surfaces opposing the tendency for A to move left faster than B. Thus the friction acts to the left on B and to the right on A.
When the yarn has been cut, there is no leftward force on A, except possibly from B. So friction between A and B no longer has to oppose A's tendency to move left faster than B. Indeed, except for B, all the forces on A are now to the right, so the tendency is for A to accelerate to the right. That means it will tend to have a rightward movement relative to B, and the frictional forces between the two reverse.
17. Jan 1, 2018
### Eitan Levy
Now I am not actually sure how to calculate if they will be able to move together. I understood how the forces act, and what I did is to assume that they move together and then check if μB is smaller or equal to 0.75. However I am not sure if I am allowed to make this assumption, how would you solve it?
18. Jan 1, 2018
### haruspex
That is a valid method since it is, in effect, what the masses will do; they will move together until the static friction is inadequate.
Draft saved Draft deleted
Similar Discussions: Newton's laws -- Blocks and pulleys problem with friction... | {"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": 0.8290570378303528, "perplexity": 653.5496467458513}, "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-2018-05/segments/1516084890928.82/warc/CC-MAIN-20180121234728-20180122014728-00270.warc.gz"} |
http://math.stackexchange.com/questions/163612/distance-between-2-random-points-in-a-segment | # Distance between $2$ random points in a segment.
On a straight line of length $10$ cm, two points A, B are selected at random uniformly and independently. What is the probability that the distance $AB > 4$ cm?
Edit: I edited the question to make it more clear. Note that apart from the clear answer to this question from mjqxxx, Gerry Myerson gives an answer to the question "If two numbers $a$ and $b$ are chosen uniformly and independently in $[0,10]$, what is the probability that the product $ab>4$". Both answers are nicely illustrated by Henry. Gilles Bonnet 17.05.14.
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Draw Cartesian axes labeled $A$ and $B$. You're asking about the fraction of the square $[0,10]\times[0,10]$ that is greater than $4$ units away (measured horizontally or vertically) from the diagonal $A=B$. Geometrically this region consists of two isosceles right triangles with side length $6$, so its total area is $36$. The desired probability is $0.36$.
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Can you please put a diagram.It will be easy to understand.Your ans is right. – Aizen Jun 27 '12 at 7:49
Also tell me why the other ans i.e area outside the curve AB=4 didn't work. – Aizen Jun 27 '12 at 7:54
To emphasize Gerry Myerson's answer
$$\int_{4/10}^{10} \left(10-\frac{4}{x}\right) \, dx \quad / \quad 10^2$$ $$= 0.96 - 0.04 \,\log_e 25 \approx 0.831\ldots$$
And for mjqxxxx's alternative interpretation of $AB \gt 4$
$$2 \times \frac{6 \times 6}{2}\quad / \quad 10^2 \quad = \quad 0.36$$
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This does not show the points where $AB > 4$. Note that this is a distance, not the product of the coordinates of $A$ and $B$. – mrf Jun 27 '12 at 9:31
+1 for supplying the diagram. – Gerry Myerson Jun 27 '12 at 11:33
I think where the original question says $AB$, it means the distance between points $A$ and $B$ on the segment, not the product of the distances of $A$ and $B$ from the left endpoint of the segment. – MJD Jun 27 '12 at 13:51
Draw Cartesian axes, labeled $A$ and $B$. You're asking about the part of $[0,10]\times[0,10]$ outside the curve $AB=4$.
-
A quick Monte Carlo simulation tallying proportion of pairs of uniform pseudoramdom points in [0,1] separated by more than 4/10 seems to converge to ~0.36, and this is approximately the numerical value of the integral of 4/(10x) from 4/10 to 1. (ie, 2 Log(5/2)/5). but is that the same as the "part outside" the curve AB=4? – alancalvitti Jun 27 '12 at 5:51
There's a square, there's a curve inside the square, and I want the proportion of the square above the curve. But why are you looking at numbers separated by more than 4/10, when the question is about products, not differences, of numbers? – Gerry Myerson Jun 27 '12 at 6:45
@GerryMyerson: Because the notation "$AB$" means the length of the segment from $A$ to $B$. Admittedly, the problem should ask for the probability that $AB > 4$ cm, not just "$4$". – mjqxxxx Jun 27 '12 at 7:31
@mjqxxxx, darn, looks like you're right. OK, everyone, ignore my answer and comment. – Gerry Myerson Jun 27 '12 at 11:32 | {"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": 0.8662999868392944, "perplexity": 427.7182664538431}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988308.23/warc/CC-MAIN-20150728002308-00271-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://crypto.stackexchange.com/questions/68075/how-can-i-exploit-the-structure-of-the-secp256k1-prime-for-fast-arithmetic | # How can I exploit the structure of the secp256k1 prime for fast arithmetic?
I'm implementing logic on an FPGA (programmable chip) that does the key verification part of ECDSA on the curve secpk256k1, in which all operations are mod p where $$p = 2^{256} - 2^{32} - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1$$ (a Mersenne prime).
I'm starting with building a circuit to do the modular reduction, I know about Barret's and Montgomery's algorithm, but I have been reading in several guides that because of the $$2^n - c$$ form, as well as it being a Mersenne prime that there are simpler ways to do the modulo reduction.
But I'm getting stuck on understanding the actual logic underneath this, I was wondering if any one have any good example or pointers to understand how to do this modulo operation a bit better?
There was a similar question here (except I'm doing this on FPGA not CPU, so the word size is irrelevant) but I don't totally understand the answers reply, so even just some helpful comments explaining the same thing would be a huge help. Fast modular reduction
This paper also has a fast implementation on page 7 (http://cse.iitkgp.ac.in/~debdeep/osscrypto/psec/downloads/PSEC-KEM_prime.pdf) which looks like it came from one of these optimizations above, but I would like to try understand how to get there myself.
• When I have a prime modulo, you are simply just running your XOR sums of registers and then adding them with a programmable overflow. You just MUX out some of the upper bits and add them to the lower bits. – b degnan Mar 17 at 18:59
• Note that $2^{256} - 2^{32} - 977$ is not a Mersenne prime, though to varying degrees it might be considered a generalized Mersenne prime. (Exactly where the boundary between generalized Mersenne primes and mere primes lies has never been clear to me.) – Squeamish Ossifrage Mar 17 at 19:04
Let $$p = 2^n - c$$. Then $$2^n - c \equiv 0 \pmod p$$, so $$2^n \equiv c \pmod p$$. Suppose you have an integer $$x = 2^n x_{\mathrm{hi}} + x_{\mathrm{lo}}.$$ Then $$x \equiv c\cdot x_{\mathrm{hi}} + x_{\mathrm{lo}} \pmod p.$$ In other words, you can compute a reduction step by shift/multiply/add: shift right by $$n$$, multiply by $$c$$, and add to the low $$n$$ bits.
The best case is when $$c = 1$$, so $$p$$ is a Mersenne prime: then you can skip the multiplication altogether. But you can generalize this further for $$p = 2^n - 2^m - d$$, since $$2^n \equiv 2^m + d \pmod p$$, so $$2^n x_{\mathrm{hi}} + x_{\mathrm{lo}} \equiv 2^m x_{\mathrm{hi}} + d \cdot x_{\mathrm{hi}} + x_{\mathrm{lo}} \pmod p.$$ That is, you can compute a reduction step by an $$n$$-bit shift, an $$m$$-bit shift, a multiply by $$d$$, and two adds.
Similarly, if $$p = 2^{2m} - 2^m - 1$$, like Ed448-Goldilocks uses, then you can compute a reduction step $$2^{2m} x_{\mathrm{hi}} + x_{\mathrm{lo}} \equiv 2^m x_{\mathrm{hi}} + x_{\mathrm{hi}} + x_{\mathrm{lo}}$$ with two $$n$$-bit shifts and two additions.
Obviously, you can always write any modulus as a sum of powers of two; the more terms there are, the more costly the reduction step is to write as a series of shifts and adds. In software implementations, at some point it may be faster to use the CPU's multiplier than your own shift-and-add steps. For instance, in secp256k1, I'd guess that it is fastest to write it as $$2^{256} - 2^{32} - 977$$ if you can take advantage of a CPU's 32x32->64-bit multiplier, but you should consult libsecp256k1 for the state of the art in arithmetic modulo this prime. | {"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": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9024008512496948, "perplexity": 460.31415043275473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670448.67/warc/CC-MAIN-20191120033221-20191120061221-00493.warc.gz"} |
http://mathhelpforum.com/differential-geometry/108229-uniform-continuity-print.html | Uniform Continuity
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• October 15th 2009, 08:25 AM
redsoxfan325
Uniform Continuity
A bounded derivative implies uniform continuity. However, there are certain instances of functions (most notably $\sqrt{x}$) that are uniformly continuous and have unbounded derivatives. I attempt to strengthen the theorem below:
Theorem: An everywhere continuous function $f$ is uniformly continuous on $\mathbb{R}$ if its derivative is bounded on $(-\infty,-m]$ and $[n,\infty)$ ( $m,n\in\mathbb{R}$).
Proof: On $[-m,n]$ we have a continuous function defined on a compact set, so it is uniformly continuous and $\exists~\delta_1$... On $(-\infty,-m]$ and $[n,\infty)$, $f$ has a bounded derivative so there exist $\delta_2$ and $\delta_3$ such that... Therefore taking $\delta=\min\{\delta_1,\delta_2,\delta_3\}$ proves that the entire function is uniformly continuous on $\mathbb{R}$.
So what's my question? My question is whether the above theorem is an if-and-only-if statement or whether the implication only goes in one direction. If not, what hypotheses can we add so that it does go both ways?
Thoughts? Counterexamples?
• October 15th 2009, 10:36 AM
Laurent
Quote:
Originally Posted by redsoxfan325
A bounded derivative implies uniform continuity. However, there are certain instances of functions (most notably $\sqrt{x}$) that are uniformly continuous and have unbounded derivatives. I attempt to strengthen the theorem below:
Theorem: An everywhere continuous function $f$ is uniformly continuous on $\mathbb{R}$ if its derivative is bounded on $(-\infty,-m]$ and $[n,\infty)$ ( $m,n\in\mathbb{R}$).
Proof: On $[-m,n]$ we have a continuous function defined on a compact set, so it is uniformly continuous and $\exists~\delta_1$... On $(-\infty,-m]$ and $[n,\infty)$, $f$ has a bounded derivative so there exist $\delta_2$ and $\delta_3$ such that... Therefore taking $\delta=\min\{\delta_1,\delta_2,\delta_3\}$ proves that the entire function is uniformly continuous on $\mathbb{R}$.
About this proof: perhaps you know that, but for a "full" proof you should take care of the case when the two points $x,y$ such that $|x-y|<\delta$ lie in different intervals (like $x). Either you say $|f(x)-f(y)|\leq |f(x)-f(n)|+|f(n)-f(y)|\leq 2\varepsilon$. Or you use the following trick: you define $\delta_1$ with uniform continuity on $[-m-1,n+1]$ and choose $\delta=\min(\delta_1,\delta_2,\delta_3,1)$ so that $|x-y|<\delta$ implies that $x,y$ are in the same interval (either $(-\infty,-m],$, $[-m-1,n+1]$ or $[n,+\infty)$).
Quote:
So what's my question? My question is whether the above theorem is an if-and-only-if statement or whether the implication only goes in one direction. If not, what hypotheses can we add so that it does go both ways?
Thoughts? Counterexamples?
Counterexample: you will be delighted to hear that the function $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=x^2\sin\frac{1}{|x|^{4/3}}$ ( $x\neq 0$), $f(0)=0$, is derivable on $\mathbb{R}$, yet its derivative is unbounded on any neighbourhood of 0.
In particular, $f$ is uniformly continuous and derivable on $[-1,1]$ while its derivative is unbounded (but finite, that's the difference with $\sqrt{x}$).
You can then define a derivable periodic function $g$ that looks like $f$ repeatedly. So that the derivative of $g$ is unbounded on any $[m,+\infty)$, while $g$ is uniformly continuous (it is continuous and periodic, so...).
• October 15th 2009, 12:17 PM
redsoxfan325
So what can we add to the theorem I proposed so that it is an iff statement? | {"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": 55, "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": 0.9929116368293762, "perplexity": 182.8134290305516}, "config": {"markdown_headings": false, "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-2014-41/segments/1410657138086.23/warc/CC-MAIN-20140914011218-00142-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://www.computer.org/csdl/trans/tc/1996/04/t0450-abs.html | Issue No. 04 - April (1996 vol. 45)
ISSN: 0018-9340
pp: 450-460
ABSTRACT
<p><b>Abstract</b>—In this paper we propose a probabilistic measure for self-checking (SC) circuits that is analogous to reliability of fault-tolerant systems. This measure is defined as the probability to achieve totally self-checking (TSC) goal at the <it>t</it>th cycle: <it>TSCG</it>(<it>t</it>). TSCG provides insight to the worst case dynamic behavior of SC circuits with respect to the application environment and component failure rates. TSCG surpasses the TSC definitions in determining the applicability of a circuit in a given application environment. An SC circuit achieves TSC goal when no erroneous information or data is propagated beyond the boundary of this circuit. TSCG is therefore the probability that this fault confinement mechanism is intact.</p><p>The SC properties are obtained through adding hardware redundancy to the original digital design. Which means that an SC circuit has a higher failure rate than the original circuit. Further, there are tradeoffs between the level of hardware redundancy, the reliability, and the TSCG. We give several examples in this paper to clearly demonstrate these tradeoffs for different design environments. The proposed probability measure allows designers to choose from cost-effective SC designs that are suitable for their specifications.</p><p>We emphasize that the TSCG is intended to provide a mean of dynamic error handling performance evaluation of SC designs. The TSC definitions and alike are still intact, since a cost-effective SC circuit must begin with a TSC circuit. The TSCG gives confidence in the use of cost-efficient error control codes and/or reduction in error handling capability. Analogous to reliability, the TSCG can be used in product specifications. This is a crucial step toward the practical applications of TSC or CED circuits.</p>
INDEX TERMS
Concurrent error detection, embedded circuits, error control coding, failure rate, fault modeling, probabilistic measure, physical layout for testability.
CITATION
Eiji Fujiwara, Jien-Chung Lo, "Probability to Achieve TSC Goal", IEEE Transactions on Computers, vol. 45, no. , pp. 450-460, April 1996, doi:10.1109/12.494102 | {"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": 0.9021387100219727, "perplexity": 2752.2338257270894}, "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-2017-13/segments/1490218189252.15/warc/CC-MAIN-20170322212949-00315-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=712380 | # Shear Failure of Adhered Polystyrene (to Aluminum)
by banfillb
Tags: adhered, aluminum, expansion, failure, foam, polystyrene, shear, thermal
P: 17 Hi All, So here's the problem. A project I am working on has a composite metal panel assembly, which a previous engineer designed. The metal panels are simply glued to the polystyrene (styrofoam sm). The problem is that the previous engineer did not consider the difference in thermal expansion between the foam and the aluminum, and the foam has begun to fail in shear, and detach from the metal panels. I'm putting together a report basically laying out the problem, and what I want to find is a temperature gradient which is "allowable" before the styrofoam will shear. Basically what I have done is set the thermal stress due to restricting thermal expansion (σ=EαdT) equal to the shear strength of the styrofoam (452kPa) and solved for the dT...which ended up coming out to 2.39degC.....which seems extremely low to me. Any suggestions on where I have gone wrong? The only thing I can think of is that I cant directly use the thermal stress due to restriction of thermal expansion directly as a shear force....not sure. Thanks,
P: 17 Thermal stress (σ) created by thermal expansion resistance will be calculated using the following formula: σ=E∙α∙dT Where: σ= Thermal Stress (kPa) E= Youngs Modulus (GPa) α= Thermal Expansion Coefficient (m/(m℃)) dT= Temperature Differential (℃) The thermal stress (σ) value will then be compared to the shear strength of the Styrofoam SM. If σ>F_v, then shear failure will occur. The thermal stress (σ) will then be set to the shear strength (F_v) of Styrofoam SM in order to find the minimum temperature differential which shearing in the Styrofoam SM will occur. CALCULATIONS: σ=E∙α∙dT σ=(3x10^6 kn/m^2 )(63x10^(-6) m/(m℃))(100℃) σ=18,900 kPa σ>F_v ∴, shearing WILL occur 452kPa=(3x10^6 kn/m^2 )(63x10^(-6) m/(m℃))∙dT dT=2.39℃ ∴, shearing will occur at any temperature differential greater than 2.39℃
Engineering Sci Advisor Thanks P: 6,066 You seem to have calculated the stress in the steel assuming it cannot expand, and then applied all that stress across the interface to the styrofoam. That is the wrong thing to do (and your temperature difference is obviously much too small). It would make more sense to find the difference in thermal strain between the metal and the foam (caused by the different expansion coefficients) and compare that with the elastic strain at which the foam will fail. But the measured data here http://ntrs.nasa.gov/archive/nasa/ca...2007006834.pdf seems to imply the thermal expansion of the foam is very nonlinear (and large, and irreversible) above about 100 C.
P: 17
## Shear Failure of Adhered Polystyrene (to Aluminum)
ahh this makes sense. Rather then calculating the shear stress in the foam, I calculated the force exerted to the aluminum layer BY the resistance of thermal expansion of the foam.
I have found an article which I am looking into:
http://www.ewp.rpi.edu/hartford/~ern...zalez/chen.pdf
Thanks for the reply and information!
Engineering Sci Advisor Thanks P: 6,066 You can probably simplify the analysis in that PDF, since I would guess Young's modulus for the foam is negligible compared with aluminum.
Related Discussions Mechanical Engineering 5 Engineering Systems & Design 3 Introductory Physics Homework 0 Engineering, Comp Sci, & Technology Homework 10 Mechanical Engineering 5 | {"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": 0.8510434627532959, "perplexity": 1821.226851986798}, "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-2014-10/segments/1394021429299/warc/CC-MAIN-20140305121029-00063-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://planetmath.org/hypoelliptic | # hypoelliptic
###### Definition.
Let $P$ be a partial differential operator defined in an open subset $U\subset{\mathbb{R}}^{n}$. If for every distribution (http://planetmath.org/Distribution4) $u$ defined in an open subset $V\subset U$ such that $Pu$ is $C^{\infty}$ (smooth), $u$ must also be $C^{\infty}$, then $P$ is called hypoelliptic.
Similarly, if the same assertion holds with $C^{\infty}$ replaced by real analytic, then $P$ is said to be analytically hypoelliptic.
Note that some authors use “hypoelliptic” to mean “analytically hypoelliptic.” Hence, if it is not clear from context, it is best to specify the regularity when using the term. For example, $C^{\infty}$-hypoelliptic instead of just hypoelliptic.
## References
• 1 J. Barros-Neto, Ralph A. Artino. , Lecture Notes in Pure and Applied Mathematics, 53. Marcel Dekker, Inc., New York, 1980. http://www.ams.org/mathscinet-getitem?mr=81k:35031MR 81k:35031
• 2 Bernard Helffer, Francis Nier. , Lecture Notes in Mathematics, 1862. Springer-Verlag, Berlin, 2005. http://www.ams.org/mathscinet-getitem?mr=2006a:58039MR 2006a:58039
• 3 Norio Shimakura. , Kinokuniya Company Ltd., Tokyo, Japan, 1978.
Title hypoelliptic Hypoelliptic 2013-03-22 16:01:13 2013-03-22 16:01:13 jirka (4157) jirka (4157) 7 jirka (4157) Definition msc 35H10 analytically hypoelliptic analytic hypoelliptic | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 12, "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": 0.9617583155632019, "perplexity": 1623.0500025525319}, "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/1568514572934.73/warc/CC-MAIN-20190916200355-20190916222355-00043.warc.gz"} |
https://brilliant.org/problems/exponential-prime-powers/ | # Exponential Prime Powers
Let $$N$$ be the sum of all prime powers that can be written as $$4^n+n^4$$ for some positive integer $$n$$.
What are the last 3 digits of $$N$$?
Details and assumptions
A prime power is a number of the form $$p^k$$, where $$p$$ is a prime and $$k$$ is a positive integer. Examples: 3,9,16.
× | {"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": 0.8790019154548645, "perplexity": 118.73248594079716}, "config": {"markdown_headings": true, "markdown_code": false, "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-2018-13/segments/1521257648205.76/warc/CC-MAIN-20180323083246-20180323103246-00738.warc.gz"} |
http://math.stackexchange.com/questions/159095/how-to-derive-ellipse-matrix-for-general-ellipse-in-homogenous-coordinates/198540 | # How to derive ellipse matrix for general ellipse in homogenous coordinates
So lets say we have an ellipse with axes a and b and the rotation angle $\phi$ and center at $(0,0)$. Now I apply the rotation to $x^2/a^2+y^2/b^2=1$ getting
$$x' = x\cos(\phi) + y\sin(\phi)$$ $$y' = y\cos(\phi) + x\sin(\phi)$$
$$x^2(b^2cos(\phi)^2 + a^2sin(\phi)^2) + y^2(b^2\sin(\phi)^2 + a^2\cos(\phi)^2) + (b^2-a^2)\sin(\phi)\cos(\phi)xy - a^2b^2$$
This is some kind of quadratic form but I need to derive the quadratic form which I'll be able to convert to ellipse matrix.
What are the next steps to do this?
Thanks
-
Thanks for editing formulas, Peter! – Michael Kupchick Jun 16 '12 at 19:59
In general, an ellipse in a general position $[h,k]$ (what I needed) is implicitly given as $$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$$ Rotating the $x$ and $y$ coords yields (you're missing a $-$ sign in the first line) $$x' = x\cos(\phi) - y\sin(\phi)$$ $$y' = x\sin(\phi) + y\cos(\phi)$$ Plugging this into ellipse equation, you get $$\frac{([x\cos(\phi) - y\sin(\phi)]-h)^2}{a^2} + \frac{([x\sin(\phi) + y\cos(\phi)]-k)^2}{b^2} = 1$$ Now, you will need this in a $Ax^2 + 2Bxy + Cy^2 + 2Dx + 2Ey + F = 0$ form, as the ellipse matrix constitutes of the coefficients $A,B,C,D,E,$ and $F$. So you rewrite the previous, getting $$-(a^2 b^2) + b^2 h^2 + a^2 k^2 - 2 b^2 h x \cos(\phi) + 2 a^2 k y \cos(\phi) + b^2 x^2 \cos(\phi)^2 + a^2 y^2 \cos(\phi)^2 - 2 a^2 k x \sin(\phi) - 2 b^2 h y \sin(\phi) - 2 a^2 x y \cos(\phi) \sin(\phi) + 2 b^2 x y \cos(\phi) \sin(\phi) + a^2 x^2 \sin(\phi)^2 + b^2 y^2 \sin(\phi)^2 = 0$$ The coefficients therefore are $$\begin{array} AA &=& b^2 \cos^2(\phi) + a^2 \sin^2(\phi) \\ B &=& -a^2 \cos(\phi) \sin(\phi) + b^2 \cos(\phi) \sin(\phi)\\ C &=& a^2 \cos^2(\phi) + b^2 \sin^2(\phi)\\ D &=& -b^2 h \cos(\phi) - a^2 k \sin(\phi)\\ E &=& a^2 k \cos(\phi) - b^2 h \sin(\phi)\\ F &=& -a^2 b^2 + b^2 h^2 + a^2 k^2\end{array}$$ and the final ellipse matrix $$M = \begin{bmatrix}A & B & D \\ B & C & E \\ D & E & F \end{bmatrix}$$ By multiplying $\begin{bmatrix}x&y&1\end{bmatrix}M\begin{bmatrix}x&y&1\end{bmatrix}^T$, you get the original $Ax^2 + 2Bxy + Cy^2 + 2Dx + 2Ey + F = 0$ equation, hence the matrix form. | {"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": 0.9410805702209473, "perplexity": 370.65651143832014}, "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/1432207931085.38/warc/CC-MAIN-20150521113211-00196-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://mathhelpforum.com/differential-equations/147813-laplace-first-second-derivatives.html | # Thread: Laplace of the first and second derivatives
1. ## Laplace of the first and second derivatives
It's been a long time since I last used Laplace so please forgive me if this is a dumb question.
Assuming I take the first and second derivatives of a function should the Laplace transforms of those derivatives be the same?
2. If you have a function $f(t)$, with corresponding Laplace transform $F(s)$, then the Laplace transform of $f'(t)$ is $s F(s)-f(0)$, where the upper- and lower-case letters are very carefully typed. Similarly, the second derivative of $f(t)$ would have the Laplace transform $s^{2}F(s)-sf(0)-f'(0)$. So you gain two things by Laplace transformation: differentiation becomes multiplication, and the initial conditions are automatically included in your answer! Of course, not all functions even have a Laplace transform, so this method can only get you so far. | {"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": 0.977001965045929, "perplexity": 175.0407291773885}, "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/1386164566315/warc/CC-MAIN-20131204134246-00052-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://chemistry.stackexchange.com/tags/heat/new | Tag Info
After some digging around on Google Scholar, I came across the following article: https://pubs.acs.org/doi/abs/10.1021/ja00499a052 which presents the following class of reactions: All of these reactions are endothermic in that they have positive molar enthalpies, and also produce near-infrared light at around 1000 nm. Reaction 1 (i.e. $\ce{R_1} = \ce{H}$) ... | {"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": 0.8306511044502258, "perplexity": 1017.1958061819306}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585916.29/warc/CC-MAIN-20211024081003-20211024111003-00236.warc.gz"} |
https://terrytao.wordpress.com/tag/inverse-conjecture/ | You are currently browsing the tag archive for the ‘inverse conjecture’ tag.
Note: this post is of a particularly technical nature, in particular presuming familiarity with nilsequences, nilsystems, characteristic factors, etc., and is primarily intended for experts.
As mentioned in the previous post, Ben Green, Tamar Ziegler, and myself proved the following inverse theorem for the Gowers norms:
Theorem 1 (Inverse theorem for Gowers norms) Let ${N \geq 1}$ and ${s \geq 1}$ be integers, and let ${\delta > 0}$. Suppose that ${f: {\bf Z} \rightarrow [-1,1]}$ is a function supported on ${[N] := \{1,\dots,N\}}$ such that
$\displaystyle \frac{1}{N^{s+2}} \sum_{n,h_1,\dots,h_{s+1}} \prod_{\omega \in \{0,1\}^{s+1}} f(n+\omega_1 h_1 + \dots + \omega_{s+1} h_{s+1}) \geq \delta.$
Then there exists a filtered nilmanifold ${G/\Gamma}$ of degree ${\leq s}$ and complexity ${O_{s,\delta}(1)}$, a polynomial sequence ${g: {\bf Z} \rightarrow G}$, and a Lipschitz function ${F: G/\Gamma \rightarrow {\bf R}}$ of Lipschitz constant ${O_{s,\delta}(1)}$ such that
$\displaystyle \frac{1}{N} \sum_n f(n) F(g(n) \Gamma) \gg_{s,\delta} 1.$
This result was conjectured earlier by Ben Green and myself; this conjecture was strongly motivated by an analogous inverse theorem in ergodic theory by Host and Kra, which we formulate here in a form designed to resemble Theorem 1 as closely as possible:
Theorem 2 (Inverse theorem for Gowers-Host-Kra seminorms) Let ${s \geq 1}$ be an integer, and let ${(X, T)}$ be an ergodic, countably generated measure-preserving system. Suppose that one has
$\displaystyle \lim_{N \rightarrow \infty} \frac{1}{N^{s+1}} \sum_{h_1,\dots,h_{s+1} \in [N]} \int_X \prod_{\omega \in \{0,1\}^{s+1}} f(T^{\omega_1 h_1 + \dots + \omega_{s+1} h_{s+1}}x)\ d\mu(x)$
$\displaystyle > 0$
for all non-zero ${f \in L^\infty(X)}$ (all ${L^p}$ spaces are real-valued in this post). Then ${(X,T)}$ is an inverse limit (in the category of measure-preserving systems, up to almost everywhere equivalence) of ergodic degree ${\leq s}$ nilsystems, that is to say systems of the form ${(G/\Gamma, x \mapsto gx)}$ for some degree ${\leq s}$ filtered nilmanifold ${G/\Gamma}$ and a group element ${g \in G}$ that acts ergodically on ${G/\Gamma}$.
It is a natural question to ask if there is any logical relationship between the two theorems. In the finite field category, one can deduce the combinatorial inverse theorem from the ergodic inverse theorem by a variant of the Furstenberg correspondence principle, as worked out by Tamar Ziegler and myself, however in the current context of ${{\bf Z}}$-actions, the connection is less clear.
One can split Theorem 2 into two components:
Theorem 3 (Weak inverse theorem for Gowers-Host-Kra seminorms) Let ${s \geq 1}$ be an integer, and let ${(X, T)}$ be an ergodic, countably generated measure-preserving system. Suppose that one has
$\displaystyle \lim_{N \rightarrow \infty} \frac{1}{N^{s+1}} \sum_{h_1,\dots,h_{s+1} \in [N]} \int_X \prod_{\omega \in \{0,1\}^{s+1}} T^{\omega_1 h_1 + \dots + \omega_{s+1} h_{s+1}} f\ d\mu$
$\displaystyle > 0$
for all non-zero ${f \in L^\infty(X)}$, where ${T^h f := f \circ T^h}$. Then ${(X,T)}$ is a factor of an inverse limit of ergodic degree ${\leq s}$ nilsystems.
Theorem 4 (Pro-nilsystems closed under factors) Let ${s \geq 1}$ be an integer. Then any factor of an inverse limit of ergodic degree ${\leq s}$ nilsystems, is again an inverse limit of ergodic degree ${\leq s}$ nilsystems.
Indeed, it is clear that Theorem 2 implies both Theorem 3 and Theorem 4, and conversely that the two latter theorems jointly imply the former. Theorem 4 is, in principle, purely a fact about nilsystems, and should have an independent proof, but this is not known; the only known proofs go through the full machinery needed to prove Theorem 2 (or the closely related theorem of Ziegler). (However, the fact that a factor of a nilsystem is again a nilsystem was established previously by Parry.)
The purpose of this post is to record a partial implication in reverse direction to the correspondence principle:
Proposition 5 Theorem 1 implies Theorem 3.
As mentioned at the start of the post, a fair amount of familiarity with the area is presumed here, and some routine steps will be presented with only a fairly brief explanation.
A few years ago, Ben Green, Tamar Ziegler, and myself proved the following (rather technical-looking) inverse theorem for the Gowers norms:
Theorem 1 (Discrete inverse theorem for Gowers norms) Let ${N \geq 1}$ and ${s \geq 1}$ be integers, and let ${\delta > 0}$. Suppose that ${f: {\bf Z} \rightarrow [-1,1]}$ is a function supported on ${[N] := \{1,\dots,N\}}$ such that
$\displaystyle \frac{1}{N^{s+2}} \sum_{n,h_1,\dots,h_{s+1}} \prod_{\omega \in \{0,1\}^{s+1}} f(n+\omega_1 h_1 + \dots + \omega_{s+1} h_{s+1}) \geq \delta.$
Then there exists a filtered nilmanifold ${G/\Gamma}$ of degree ${\leq s}$ and complexity ${O_{s,\delta}(1)}$, a polynomial sequence ${g: {\bf Z} \rightarrow G}$, and a Lipschitz function ${F: G/\Gamma \rightarrow {\bf R}}$ of Lipschitz constant ${O_{s,\delta}(1)}$ such that
$\displaystyle \frac{1}{N} \sum_n f(n) F(g(n) \Gamma) \gg_{s,\delta} 1.$
For the definitions of “filtered nilmanifold”, “degree”, “complexity”, and “polynomial sequence”, see the paper of Ben, Tammy, and myself. (I should caution the reader that this blog post will presume a fair amount of familiarity with this subfield of additive combinatorics.) This result has a number of applications, for instance to establishing asymptotics for linear equations in the primes, but this will not be the focus of discussion here.
The purpose of this post is to record the observation that this “discrete” inverse theorem, together with an equidistribution theorem for nilsequences that Ben and I worked out in a separate paper, implies a continuous version:
Theorem 2 (Continuous inverse theorem for Gowers norms) Let ${s \geq 1}$ be an integer, and let ${\delta>0}$. Suppose that ${f: {\bf R} \rightarrow [-1,1]}$ is a measurable function supported on ${[0,1]}$ such that
$\displaystyle \int_{{\bf R}^{s+1}} \prod_{\omega \in \{0,1\}^{s+1}} f(t+\omega_1 h_1 + \dots + \omega_{s+1} h_{s+1})\ dt dh_1 \dots dh_{s+1} \geq \delta. \ \ \ \ \ (1)$
Then there exists a filtered nilmanifold ${G/\Gamma}$ of degree ${\leq s}$ and complexity ${O_{s,\delta}(1)}$, a (smooth) polynomial sequence ${g: {\bf R} \rightarrow G}$, and a Lipschitz function ${F: G/\Gamma \rightarrow {\bf R}}$ of Lipschitz constant ${O_{s,\delta}(1)}$ such that
$\displaystyle \int_{\bf R} f(t) F(g(t) \Gamma)\ dt \gg_{s,\delta} 1.$
The interval ${[0,1]}$ can be easily replaced with any other fixed interval by a change of variables. A key point here is that the bounds are completely uniform in the choice of ${f}$. Note though that the coefficients of ${g}$ can be arbitrarily large (and this is necessary, as can be seen just by considering functions of the form ${f(t) = \cos( \xi t)}$ for some arbitrarily large frequency ${\xi}$).
It is likely that one could prove Theorem 2 by carefully going through the proof of Theorem 1 and replacing all instances of ${{\bf Z}}$ with ${{\bf R}}$ (and making appropriate modifications to the argument to accommodate this). However, the proof of Theorem 1 is quite lengthy. Here, we shall proceed by the usual limiting process of viewing the continuous interval ${[0,1]}$ as a limit of the discrete interval ${\frac{1}{N} \cdot [N]}$ as ${N \rightarrow \infty}$. However there will be some problems taking the limit due to a failure of compactness, and specifically with regards to the coefficients of the polynomial sequence ${g: {\bf N} \rightarrow G}$ produced by Theorem 1, after normalising these coefficients by ${N}$. Fortunately, a factorisation theorem from a paper of Ben Green and myself resolves this problem by splitting ${g}$ into a “smooth” part which does enjoy good compactness properties, as well as “totally equidistributed” and “periodic” parts which can be eliminated using the measurability (and thus, approximate smoothness), of ${f}$.
Ben Green, and I have just uploaded to the arXiv a short (six-page) paper “Yet another proof of Szemeredi’s theorem“, submitted to the 70th birthday conference proceedings for Endre Szemerédi. In this paper we put in print a folklore observation, namely that the inverse conjecture for the Gowers norm, together with the density increment argument, easily implies Szemerédi’s famous theorem on arithmetic progressions. This is unsurprising, given that Gowers’ proof of Szemerédi’s theorem proceeds through a weaker version of the inverse conjecture and a density increment argument, and also given that it is possible to derive Szemerédi’s theorem from knowledge of the characteristic factor for multiple recurrence (the ergodic theory analogue of the inverse conjecture, first established by Host and Kra), as was done by Bergelson, Leibman, and Lesigne (and also implicitly in the earlier paper of Bergelson, Host, and Kra); but to our knowledge the exact derivation of Szemerédi’s theorem from the inverse conjecture was not in the literature. Ordinarily this type of folklore might be considered too trifling (and too well known among experts in the field) to publish; but we felt that the venue of the Szemerédi birthday conference provided a natural venue for this particular observation.
The key point is that one can show (by an elementary argument relying primarily an induction on dimension argument and the Weyl recurrence theorem, i.e. that given any real ${\alpha}$ and any integer ${s \geq 1}$, that the expression ${\alpha n^s}$ gets arbitrarily close to an integer) that given a (polynomial) nilsequence ${n \mapsto F(g(n)\Gamma)}$, one can subdivide any long arithmetic progression (such as ${[N] = \{1,\ldots,N\}}$) into a number of medium-sized progressions, where the nilsequence is nearly constant on each progression. As a consequence of this and the inverse conjecture for the Gowers norm, if a set has no arithmetic progressions, then it must have an elevated density on a subprogression; iterating this observation as per the usual density-increment argument as introduced long ago by Roth, one obtains the claim. (This is very close to the scheme of Gowers’ proof.)
Technically, one might call this the shortest proof of Szemerédi’s theorem in the literature (and would be something like the sixteenth such genuinely distinct proof, by our count), but that would be cheating quite a bit, primarily due to the fact that it assumes the inverse conjecture for the Gowers norm, our current proof of which is checking in at about 100 pages…
Ben Green, Tamar Ziegler and I have just uploaded to the arXiv our paper “An inverse theorem for the Gowers $U^4$ norm“. This paper establishes the next case of the inverse conjecture for the Gowers norm for the integers (after the $U^3$ case, which was done by Ben and myself a few years ago). This conjecture has a number of combinatorial and number-theoretic consequences, for instance by combining this new inverse theorem with previous results, one can now get the correct asymptotic for the number of arithmetic progressions of primes of length five in any large interval $[N] = \{1,\ldots,N\}$.
To state the inverse conjecture properly requires a certain amount of notation. Given a function $f: {\Bbb Z} \to {\Bbb C}$ and a shift $h \in {\Bbb Z}$, define the multiplicative derivative
$\Delta_h f(x) := f(x+h) \overline{f(x)}$
and then define the Gowers $U^{s+1}[N]$ norm of a function $f: [N] \to {\Bbb C}$ to (essentially) be the quantity
$\| f\|_{U^{s+1}[N]} := ({\Bbb E}_{h_1,\ldots,h_{s+1} \in [-N,N]} {\Bbb E}_{x \in [N]} |\Delta_{h_1} \ldots \Delta_{h_{s+1}} f(x)|)^{1/2^{s+1}},$
where we extend f by zero outside of $[N]$. (Actually, we use a slightly different normalisation to ensure that the function 1 has a $U^{s+1}$ norm of 1, but never mind this for now.)
Informally, the Gowers norm $\|f\|_{U^{s+1}[N]}$ measures the amount of bias present in the $(s+1)^{st}$ multiplicative derivatives of $f$. In particular, if $f = e(P) := e^{2\pi i P}$ for some polynomial $P: {\Bbb Z} \to {\Bbb C}$, then the $(s+1)^{th}$ derivative of $f$ is identically 1, and so is the Gowers norm.
However, polynomial phases are not the only functions with large Gowers norm. For instance, consider the function $f(n) := e( \lfloor \sqrt{2} n \rfloor \sqrt{3} n )$, which is what we call a quadratic bracket polynomial phase. This function isn’t quite quadratic, but it is close enough to being quadratic (because one has the approximate linearity relationship $\lfloor x+y \rfloor = \lfloor x \rfloor + \lfloor y \rfloor$ holding a good fraction of the time) that it turns out that third derivative is trivial fairly often, and the Gowers norm $\|f\|_{U^3[N]}$ is comparable to 1. This bracket polynomial phase can be modeled as a nilsequence $n \mapsto F( g(n) \Gamma )$, where $n \mapsto g(n) \Gamma$ is a polynomial orbit on a nilmanifold $G/\Gamma$, which in this case has step 2. (The function F is only piecewise smooth, due to the discontinuity in the floor function $\lfloor \rfloor$, so strictly speaking we would classify this as an almost nilsequence rather than a nilsequence, but let us ignore this technical issue here.) In fact, there is a very close relationship between nilsequences and bracket polynomial phases, but I will detail this in a later post.
The inverse conjecture for the Gowers norm, GI(s), asserts that such nilsequences are the only obstruction to the Gowers norm being small. Roughly speaking, it goes like this:
Inverse conjecture, GI(s). (Informal statement) Suppose that $f: [N] \to {\Bbb C}$ is bounded but has large $U^{s+1}[N]$ norm. Then there is an s-step nilsequence $n \mapsto F( g(n) \Gamma )$ of “bounded complexity” that correlates with f.
This conjecture is trivial for s=0, is a short consequence of Fourier analysis when s=1, and was proven for s=2 by Ben and myself. In this paper we establish the s=3 case. An equivalent formulation in this case is that any bounded function $f$ of large $U^4$ norm must correlate with a “bracket cubic phase”, which is the product of a bounded number of phases from the following list
$e( \alpha n^3 + \beta n^2 + \gamma n), e( \lfloor \alpha n \rfloor \beta n^2 ), e( \lfloor \alpha n \rfloor \lfloor \beta n \rfloor \gamma n ), e( \lfloor \alpha n \rfloor \beta n )$ (*)
for various real numbers $\alpha,\beta,\gamma$.
It appears that our methods also work in higher step, though for technical reasons it is convenient to make a number of adjustments to our arguments to do so, most notably a switch from standard analysis to non-standard analysis, about which I hope to say more later. But there are a number of simplifications available on the s=3 case which make the argument significantly shorter, and so we will be writing the higher s argument in a separate paper.
The arguments largely follow those for the s=2 case (which in turn are based on this paper of Gowers). Two major new ingredients are a deployment of a normal form and equidistribution theory for bracket quadratic phases, and a combinatorial decomposition of frequency space which we call the sunflower decomposition. I will sketch these ideas below the fold.
For a number of reasons, including the start of the summer break for me and my coauthors, a number of papers that we have been working on are being released this week. For instance, Ben Green and I have just uploaded to the arXiv our paper “An equivalence between inverse sumset theorems and inverse conjectures for the $U^3$ norm“, submitted to Math. Proc. Camb. Phil. Soc.. The main result of this short paper (which was briefly announced in this earlier post) is a connection between two types of inverse theorems in additive combinatorics, namely the inverse sumset theorems of Freiman type, and inverse theorems for the Gowers uniformity norm, and more specifically, for the $U^3$ norm
$\|f\|_{U^3(G)}^8 := {\Bbb E}_{x,a,b,c \in G} f(x) \overline{f(x+a)} \overline{f(x+b)} \overline{f(x+c)} f(x+a+b) f(x+a+c) f(x+b+c) \overline{f(x+a+b+c)}$
on finite additive group G, where $f: G \to {\Bbb C}$ is a complex-valued function.
As usual, the connection is easiest to state in a finite field model such as $G = {\Bbb F}_2^n$. In this case, we have the following inverse sumset theorem of Ruzsa:
Theorem 1. If $A \subset {\Bbb F}_2^n$ is such that $|A+A| \leq K|A|$, then A can be covered by a translate of a subspace of ${\Bbb F}_2^n$ of cardinality at most $K^2 2^{K^4} |A|$.
The constant $K^2 2^{K^4}$ has been improved for large $K$ in a sequence of papers, from $K 2^{\lfloor K^3 \rfloor-1}$ by Ruzsa, $K^2 2^{K^2-2}$ by Green-Ruzsa, $2^{O(K^{3/2} \log(1+K)}$ by Sanders, $2^{2K+O(\sqrt{K} \log K})$ by Green and myself, and finally $2^{2K+O(\log K)}$ by Konyagin (private communication) which is sharp except for the precise value of the O() implied constant (as can be seen by considering the example when A consists of about 2K independent elements). However, it is conjectured that the polynomial loss can be removed entirely if one modifies the conclusion slightly:
Conjecture 1. (Polynomial Freiman-Ruzsa conjecture for ${\Bbb F}_2^n$.) If $A \subset {\Bbb F}_2^n$ is such that $|A+A| \leq K|A|$, then A can be covered by $O(K^{O(1)})$ translates of subspaces of ${\Bbb F}_2^n$ of cardinality at most |A|.
This conjecture was verified for downsets by Green and myself, but is open in general. This conjecture has a number of equivalent formulations; see this paper of Green for more discussion. In this previous post we show that a stronger version of this conjecture fails.
Meanwhile, for the Gowers norm, we have the following inverse theorem, due to Samorodnitsky:
Theorem 2. Let $f: {\Bbb F}_2^n \to [-1,1]$ be a function whose $U^3$ norm is at least 1/K. Then there exists a quadratic polynomial $Q: {\Bbb F}_2^n \to {\Bbb F}_2$ such that $|{\Bbb E}_{x \in {\Bbb F}_2^n} f(x) (-1)^{Q(x)}| \geq \exp( - O(K)^{O(1)} )$.
Note that the quadratic phases $(-1)^{Q(x)}$ are the only functions taking values in [-1,1] whose $U^3$ norm attains its maximal value of 1.
It is conjectured that the exponentially weak correlation here can be strengthened to a polynomial one:
Conjecture 2. (Polynomial inverse conjecture for the $U^3({\Bbb F}_2^n)$ norm). Let $f: {\Bbb F}_2^n \to [-1,1]$ be a function whose $U^3$ norm is at least 1/K. Then there exists a quadratic polynomial $Q: {\Bbb F}_2^n \to {\Bbb F}_2$ such that $|{\Bbb E}_{x \in {\Bbb F}_2^n} f(x) (-1)^{Q(x)}| \geq K^{-O(1)}$.
The first main result of this paper is
Theorem 3. Conjecture 1 and Conjecture 2 are equivalent.
This result was also independently observed by Shachar Lovett (private communication). We also establish an analogous result for the cyclic group ${\Bbb Z}/N{\Bbb Z}$, in which the notion of polynomial is replaced by that of a subexponential $\exp(K^{o(1)})$, and in which the notion of a quadratic polynomial is replaced by a 2-step nilsequence; the precise statement is a bit technical and will not be given here. We also observe a partial partial analogue of the correpsondence between inverse sumset theorems and Gowers norms in the higher order case, in particular observing that $U^4$ inverse theorems imply a certain rigidity result for “Freiman-quadratic polynomials” (a quadratic version of Conjecture 3 below).
Below the fold, we sketch the proof of Theorem 3.
Tamar Ziegler and I have just uploaded to the arXiv our paper, “The inverse conjecture for the Gowers norm over finite fields via the correspondence principle“, submitted to Analysis & PDE. As announced a few months ago in this blog post, this paper establishes (most of) the inverse conjecture for the Gowers norm from an ergodic theory analogue of this conjecture (in a forthcoming paper by Vitaly Bergelson, Tamar Ziegler, and myself, which should be ready shortly), using a variant of the Furstenberg correspondence principle. Our papers were held up for a while due to some unexpected technical difficulties arising in the low characteristic case; as a consequence, our paper only establishes the full inverse conjecture in the high characteristic case $p \geq k$, and gives a partial result in the low characteristic case $p < k$.
In the rest of this post, I would like to describe the inverse conjecture (in both combinatorial and ergodic forms), and sketch how one deduces one from the other via the correspondence principle (together with two additional ingredients, namely a statistical sampling lemma and a local testability result for polynomials).
Recently, I had tentatively announced a forthcoming result with Ben Green establishing the “Gowers inverse conjecture” (or more accurately, the “inverse conjecture for the Gowers uniformity norm”) for vector spaces ${\Bbb F}_p^n$ over a finite field ${\Bbb F}_p$, in the special case when p=2 and when the function $f: {\Bbb F}_p^n \to {\Bbb C}$ for which the inverse conjecture is to be applied is assumed to be a polynomial phase of bounded degree (thus $f= e^{2\pi i P/|{\Bbb F}|}$, where $P: {\Bbb F}_p^n \to {\Bbb F}_p$ is a polynomial of some degree $d=O(1)$). See my FOCS article for some further discussion of this conjecture, which has applications to both polynomiality testing and to various structural decompositions involving the Gowers norm.
This conjecture can be informally stated as follows. By iterating the obvious fact that the derivative of a polynomial of degree at most d is a polynomial of degree at most d-1, we see that a function $P: {\Bbb F}_p^n \to {\Bbb F}_p$ is a polynomial of degree at most d if and only if
$\sum_{\omega_1,\ldots,\omega_{d+1} \in \{0,1\}} (-1)^{\omega_1+\ldots+\omega_{d+1}} P(x +\omega_1 h_1 + \ldots + \omega_{d+1} h_{d+1}) = 0$
for all $x,h_1,\ldots,h_{d+1} \in {\Bbb F}_p^n$. From this one can deduce that a function $f: {\Bbb F}_p^n \to {\Bbb C}$ bounded in magnitude by 1 is a polynomial phase of degree at most d if and only if the Gowers norm
$\|f\|_{U^{d+1}({\Bbb F}_p^n)} := \bigl( {\Bbb E}_{x,h_1,\ldots,h_{d+1} \in {\Bbb F}_p^n} \prod_{\omega_1,\ldots,\omega_{d+1} \in \{0,1\}}$
${\mathcal C}^{\omega_1+\ldots+\omega_{d+1}} f(x + \omega_1 h_1 + \ldots + \omega_{d+1} h_{d+1}) \bigr)^{1/2^{d+1}}$
is equal to its maximal value of 1. The inverse conjecture for the Gowers norm, in its usual formulation, says that, more generally, if a function $f: {\Bbb F}_p^n \to {\Bbb C}$ bounded in magnitude by 1 has large Gowers norm (e.g. $\|f\|_{U^{d+1}} \geq \varepsilon$) then f has some non-trivial correlation with some polynomial phase g (e.g. $\langle f, g \rangle > c(\varepsilon)$ for some $c(\varepsilon) > 0$). Informally, this conjecture asserts that if a function has biased $(d+1)^{th}$ derivatives, then one should be able to “integrate” this bias and conclude that the function is biased relative to a polynomial of degree d. The conjecture has already been proven for $d \leq 2$. There are analogues of this conjecture for cyclic groups which are of relevance to Szemerédi’s theorem and to counting linear patterns in primes, but I will not discuss those here.
At the time of the announcement, our paper had not quite been fully written up. This turned out to be a little unfortunate, because soon afterwards we discovered that our arguments at one point had to go through a version of Newton’s interpolation formula, which involves a factor of d! in the denominator and so is only valid when the characteristic p of the field exceeds the degree. So our arguments in fact are only valid in the range $p > d$, and in particular are rather trivial in the important case $p=2$; my previous announcement should thus be amended accordingly. | {"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": 171, "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": 0.9502379894256592, "perplexity": 325.26537118954894}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646636.25/warc/CC-MAIN-20180319081701-20180319101701-00636.warc.gz"} |
http://cognet.mit.edu/journal/10.1162/08997660360581912 | Neural Computation
April 1, 2003, Vol. 15, No. 4, Pages 811-830
(doi: 10.1162/08997660360581912)
© 2003 Massachusetts Institute of Technology
Event-Driven Simulation of Spiking Neurons with Stochastic Dynamics
Article PDF (559.22 KB)
Abstract
We present a new technique, based on a proposed event-based strategy (Mattia & Del Giudice, 2000), for efficiently simulating large networks of simple model neurons. The strategy was based on the fact that interactions among neurons occur by means of events that are well localized in time (the action potentials) and relatively rare. In the interval between two of these events, the state variables associated with a model neuron or a synapse evolved deterministically and in a predictable way. Here, we extend the event-driven simulation strategy to the case in which the dynamics of the state variables in the inter-event intervals are stochastic. This extension captures both the situation in which the simulated neurons are inherently noisy and the case in which they are embedded in a very large network and receive a huge number of random synaptic inputs. We show how to effectively include the impact of large background populations into neuronal dynamics by means of the numerical evaluation of the statistical properties of single-model neurons under random current injection. The new simulation strategy allows the study of networks of interacting neurons with an arbitrary number of external afferents and inherent stochastic dynamics. | {"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": 0.8269285559654236, "perplexity": 626.6832287406841}, "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-2020-40/segments/1600402093104.90/warc/CC-MAIN-20200929221433-20200930011433-00434.warc.gz"} |
http://laneas.com/publication/joint-relay-selection-and-analog-network-coding-using-differential-modulation-two-way | # Joint Relay Selection and Analog Network Coding using Differential Modulation in Two-Way Relay Channels
Journal Article
### Authors:
Lingyang Song; Guo Hong; Bingli Jiao; Mérouane Debbah
### Source:
IEEE Transactions on Vehicular Technology, Volume 59, Number 56, p.2932-2939 (2010)
### Abstract:
In this paper, we consider a general bi-directional relay network with two sources and N relays when neither the source nodes nor the relays know the channel state information (CSI). A joint relay selection and analog network coding using differential modulation (RS-ANC-DM) is proposed. In the proposed scheme, the two sources employ differential modulations and transmit the differential modulated symbols to all relays at the same time. The signals received at the relay is a superposition of two transmitted symbols, which we call the analog network coded symbols. Then a single relay which has minimum sum SER is selected out of N relays to forward the ANC signals to both sources. To facilitate the selection process, in this paper we also propose a simple sub-optimal Min-Max criterion for relay selection, where a single relay which minimizes the maximum SER of two source nodes is selected. Simulation results show that the proposed Min-Max selection has almost the same performance as the optimal selection, but is much simpler. The performance of the proposed RS-ANC-DM scheme is analyzed, and a simple asymptotic SER expression is derived. The analytical results are verified through simulations.
Full Text: | {"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": 0.934434175491333, "perplexity": 760.847159830823}, "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/1558232256763.42/warc/CC-MAIN-20190522043027-20190522065027-00281.warc.gz"} |
https://itsvista.com/2011/01/kb2438651-2/ | # KB2438651
This article describes steps that you can follow to help troubleshoot problems that may occur when you install, uninstall, or upgrade a program on a Windows-based computer.
The Windows Installer Cleanup utility (MSICUU2.exe) that was previously referred to in this article resolved some installation problems but sometimes caused issues with other programs or components that are installed on the computer. Because of this, the tool has been removed from the Microsoft Download Center.
If you need to uninstall Office version 2003, 2007, or 2010, a new FixIT solution is available in the following Microsoft Knowledge Base article:
290301 How do I uninstall Office 2003, Office 2007, or Office 2010 suites if I cannot uninstall it from Control Panel?
If you need to uninstall Microsoft Security Essentials, see the following Microsoft Knowledge Base article:
2435760 How to manually uninstall Microsoft Security Essentials if you cannot uninstall it by using the Add or Remove Programs item | {"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": 0.8637900948524475, "perplexity": 4672.472050676585}, "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-2017-13/segments/1490218189462.47/warc/CC-MAIN-20170322212949-00547-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/214744 | Infoscience
Journal article
# Round-the-clock power supply and a sustainable economy via synergistic integration of solar thermal power and hydrogen processes
We introduce a paradigm-"hydricity"-that involves the coproduction of hydrogen and electricity from solar thermal energy and their judicious use to enable a sustainable economy. We identify and implement synergistic integrations while improving each of the two individual processes. When the proposed integrated process is operated in a standalone, solely power production mode, the resulting solar water power cycle can generate electricity with unprecedented efficiencies of 40-46%. Similarly, in standalone hydrogen mode, pressurized hydrogen is produced at efficiencies approaching similar to 50%. In the coproduction mode, the coproduced hydrogen is stored for uninterrupted solar power production. When sunlight is unavailable, we envision that the stored hydrogen is used in a "turbine"-based hydrogen water power (H2WP) cycle with the calculated hydrogen-to-electricity efficiency of 65-70%, which is comparable to the fuel cell efficiencies. The H2WP cycle uses much of the same equipment as the solar water power cycle, reducing capital outlays. The overall sun-to-electricity efficiency of the hydricity process, averaged over a 24-h cycle, is shown to approach similar to 35%, which is nearly the efficiency attained by using the best multijunction photovoltaic cells along with batteries. In comparison, our proposed process has the following advantages: (i) It stores energy thermochemically with a two-to threefold higher density, (ii) coproduced hydrogen has alternate uses in transportation/chemical/petrochemical industries, and (iii) unlike batteries, the stored energy does not discharge over time and the storage medium does not degrade with repeated uses. | {"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": 0.8331584930419922, "perplexity": 3863.390290658527}, "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-2017-30/segments/1500549448095.6/warc/CC-MAIN-20170728062501-20170728082501-00267.warc.gz"} |
http://www.pveducation.org/pvcdrom/characterisation/tandemcalc | # Tandem Calculations
## Description of Tandem Calc
TandemCalc is a Windows-standalone application for calculating maximum efficiency of tandem solar cells. The application was developed with MatLab as the code base and requires installation of a 'MatLab Compiler Runtime' to operate. The MCR installation file is part of the downloadable package. To run the application, after installing the MCR (which you should be taken through automatically when executing the package file), run the TandemCalcv1.exe program.
Overview of Application Usage:
Parameters:
- Spectrum Type (dropdown box). The options are Blackbody and 'AM 1.5'. When selecting 'AM 1.5', if 'Concentration' is 1 then AM1.5G is used, otherwise AM1.5D is used.
- Concentration
- Connection Type (dropdown box). The options are Independent and Series.
- Output Type. Currently hard-coded to download a text file (and display results on screen).
- Enter # of Bandgap Stacks: box that requires integer entry.
- Six columns of boxes for bandgap sweep by stack. Enter the bandgap sweeps in order from lowest bandgaps (Stack # 1) to highest bandgap (Stack # n, where n=the value entered under 'Enter # of Bandgap Stacks').
After entering your parameters, click 'Calculate Efficiencies'. You will then see a progress bar that includes an estimate of how much time is remaining for this calculation. When calculating for Independent, you may see a sequence of progress bars and the last progress bar may show a bogus % complete above 100%, however when that happens the program is nearly complete.
When the program is complete, you should see values under the fields at the bottom of the window.
Main Data File (data file that includes the efficiency % for each unique bandgap set calculated).
Help Data File (data file that includes the parameters you entered along with the max efficiency % and max efficiency bandgaps).
Max Efficiency % (maximum % efficiency based on the parameters you entered).
Max Efficiency Bandgaps (bandgaps related to the maximum-calculated efficiency %).
Reporting Defects and Enhancements
Please keep in mind that this software should be considered beta release and thus it is possible that despite the functional testing performed heretofore, you may enter parameters that result in an error I did not see/resolve. When this occurs, please log basic information related to the error at the following shared Google Doc in the 'Defects' tab.
Also if you have suggestions on how to improve this software application, please log it at the following shared Google Doc in the 'Enhancements' tab. | {"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": 0.8126317262649536, "perplexity": 4848.894337528579}, "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-2017-26/segments/1498128321025.86/warc/CC-MAIN-20170627064714-20170627084714-00696.warc.gz"} |
http://www.gradesaver.com/textbooks/math/trigonometry/trigonometry-10th-edition/chapter-1-trigonometric-functions-section-1-2-angle-relationships-and-similar-triangles-1-2-exercises-page-19/61 | ## Trigonometry (10th Edition)
1. Similar triangle problems. Ratio. You need to put shadow over shadow and set it equal to actual height over actual height of the building. $\frac{40}{300}=\frac{15}{b}$ 2. Then solve for b: $40b=4500$ $b=112.5$ 3. Don't forget the units 112.5 ft | {"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": 0.9568204879760742, "perplexity": 2075.2115597057323}, "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-2018-05/segments/1516084892892.86/warc/CC-MAIN-20180124010853-20180124030853-00567.warc.gz"} |
http://mathhelpforum.com/calculus/158088-f-0-1-0-1-f-injective.html | # Math Help - f: [0,1]-->]0,1[, f injective
1. ## f: [0,1]-->]0,1[, f injective
Hello,
I'm looking for a injective function defined as f: [0,1]-->]0,1[.
How should I start?
f:A--->B
A=[0,1]={x:0<=x<=1}
B=]0,1[={f(x):0<f(x)<1}
f(A)=B
x=y => f(x)=f(y) for all x,y in A.
It's not arctan(x) because im(arctan(x)) with x in[0,1] is not ]0,1[. So I rather think that f is only injective in [0,1].
I'm also thinking maybe I need to find f(x)^-1 first and then f(x), (since f is injective).
2. The easy way is to shift a countable set.
Let $T=\{0\}\cup\{\frac{1}{n}:n\in\mathbb{Z}^+\}$.
Then define $
f(x) = \left\{ {\begin{array}{r,l}
{\frac{1}{{x^{-1} + 2}},} & {x \in T\setminus\{0\}} \\
{x,} & {x \in [0,1]\backslash T} \\ \end{array} } \right.~\&~f(0)=\frac{1}{2}$
3. Originally Posted by Plato
The easy way is to shift a countable set.
Let $T=\{0\}\cup\{\frac{1}{n}:n\in\mathbb{Z}^+\}$.
Then define $
f(x) = \left\{ {\begin{array}{r,l}
{\frac{1}{{x^{-1} + 2}},} & {x \in T\setminus\{0\}} \\
{x,} & {x \in [0,1]\backslash T} \\ \end{array} } \right.~\&~f(0)=\frac{1}{2}$
Can you not just divide everything by 2 and add a quarter,
$f(x) = \frac{2x+1}{4}$? It's clearly injective, and maps to the interval $[\frac{1}{4}, \frac{3}{4}]\subset (0, 1)$...
4. $f(x) \colon [ 0,1 ] \longrightarrow ]0,1[$ not $f(x) \colon [ 0,1 ] \longrightarrow [\frac{1}{4},\frac{3}{4}]$...
5. Originally Posted by sunmalus
$f(x) \colon [ 0,1 ] \longrightarrow ]0,1[$ not $f(x) \colon [ 0,1 ] \longrightarrow [\frac{1}{4},\frac{3}{4}]$...
Well, if by $]0, 1[$ you mean the open set $(0, 1)$ ( $[0, 1]$ without the endpoints) then that is what that function does. It's just notation. There is no need for the function to be surjective.
6. I am very sorry but I meant f bijective and not f injective. So the example given by Plato still works because it is also surjective.
My apologies again. | {"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": 13, "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": 0.9409654140472412, "perplexity": 1604.8901630449636}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824624.99/warc/CC-MAIN-20160723071024-00039-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://mathematica.stackexchange.com/questions/56991/integrate-returns-unexpected-result | # Integrate returns unexpected result
Consider the following function $$g(x,y):= \frac{1}{( (1+y)^2+x^2 )( 1+ax^2y^2 )^2}$$, where I assume that $y\geq 0$ and $a\in (0,1]$ is a parameter. When I try to evaluate the integral $\int g(x,y)\,dx$ using Mathematica I get the following result:
$$\frac{\frac{axy^2(-1 + ay^2(1 + y)^2)}{(1 + ax^2y^2)} + \sqrt{a}y(-3 + ay^2(1 + y)^2)\arctan(\sqrt{a}xy) + \frac{2\arctan(\frac{x}{1 + y} )}{ 1 + y} }{2(-1 + ay^2(1 + y)^2)^2}$$ This result cannot be the correct primitive of $g(\cdot,y)$, since on the one hand the denominator is always has a positive root but the numerator is positive, and on the other hand we have that $$0\leq g(x,y)\leq \frac{1}{1+x^2 }$$ which implies that $g(\cdot,y)$ is Riemann integrable for all $y\geq 0$.
Could someone please tele me how to obtain a correct answer to the problem? This would be very much appreciated!
Code:
Integrate[1/(((1+y)^2+x^2)*(1+a*x^2*y^2)^2),x]
Output:
((a x y^2 (-1 + a y^2 (1 + y)^2))/(1 + a x^2 y^2) + Sqrt[a] y (-3 + a y^2 (1 + y)^2) ArcTan[Sqrt[a] x y] + ( 2 ArcTan[x/(1 + y)])/(1 + y))/(2 (-1 + a y^2 (1 + y)^2)^2)
-
Please post you expressions as Mathematica code, not in TeX. (Use backticks instead of dollar signs.) It makes it easier for those who would help you with your problem. – Michael E2 Aug 8 '14 at 20:49
please provide the mathematica command you used? – chris Aug 8 '14 at 20:50
Sure! Here's the code: Integrate[1/(((1+y)^2+x^2)*(1+a*x^2*y^2)^2),x] – user19057 Aug 8 '14 at 20:53
Please also post the output you get in Mathematica form so it's easy to compare. The output I get in v10 looks like what you posted, and D[%,x] gives the expected result. – Szabolcs Aug 8 '14 at 21:18
@Szabolcs same with v9 – chris Aug 8 '14 at 21:22
I said in a comment that one could "factor" out ((-1 + a y^2 (1 + y)^2)^2 from the numerator. What I meant was that numerator is $O(((-1 + a y^2 (1 + y)^2)^2)$. The integral is a complicated expression, so the easiest way to examine it, it seemed to me, is to look at the coefficients of the power series expansion about the real roots of the denominator.
integral = Integrate[1/(((1 + y)^2 + x^2)*(1 + a*x^2*y^2)^2), x];
There are two real roots, if 0 < a <= 1:
Solve[(-1 + a y^2 (1 + y)^2) == 0, y]
(*
{{y -> 1/2 (-1 - Sqrt[-4 Sqrt[a] + a]/Sqrt[a])},
{y -> 1/2 (-1 + Sqrt[-4 Sqrt[a] + a]/Sqrt[a])},
{y -> 1/2 (-1 - Sqrt[4 Sqrt[a] + a]/Sqrt[a])},
{y -> 1/2 (-1 + Sqrt[4 Sqrt[a] + a]/Sqrt[a])}}
*)
We see below that the first two coefficients of the series expansions about the two real roots are zero. Thus the integral is bounded for -b < y < b for any positive real b.
root = 1/2 (-1 - Sqrt[4 Sqrt[a] + a]/Sqrt[a]);
ParallelMap[
FullSimplify,
CoefficientList[
Normal@Series[Numerator[integral], {y, root, 2}] /. y -> u + root,
u]
]
(*
{0, 0, 1/2 (4 + Sqrt[a]) Sqrt[a] (<..>)}
*)
root = 1/2 (-1 + Sqrt[4 Sqrt[a] + a]/Sqrt[a]);
ParallelMap[
FullSimplify,
CoefficientList[
Normal@Series[Numerator[integral], {y, root, 2}] /. y -> u + root,
u]
]
(*
{0, 0, (1/(2 + Sqrt[a] + Sqrt[4 Sqrt[a] + a])) 4 (4 + Sqrt[a]) a (<..>)}
*)
Since as has been observed in the comments,
D[integral, x] // Simplify
(* 1/((1 + a x^2 y^2)^2 (x^2 + (1 + y)^2)) *)
it seems to me that the result integral is correct.
-
These singularities in $g(\cdot,y)$ are all removable. There are eight singular values of y, depending only on a, and you can take the limit as $y\rightarrow s$ for each singular value $s$ and obtain limit for all but finitely many values of $x$. Those are also removable by taking a limit. The function is still continuous, smooth, bounded, etc.
The values of $y$ of concern can be found to be:
SP = ReplaceAll[y, Solve[2 (-1 + a y^2 (1 + y)^2)^2 == 0, y]]
This will return a list of eight singular values of y. You can take the limit at each value:
Map[Limit[g[x, y, a], y -> #] &, SP]
and in each case, you obtain an expression that exists except for finitely many values of x. At those values of x, again, you can take limits as x approaches the singular value and obtain the value at this removable singularity.
The reason this limit exists, for reference, is because at any of these singular values, you will have 0 on the top of that big fraction too. You could even use L'Hôpital's rule to obtain the value -- but I'll let Mathematica take care of it (see above). You can verify this with:
G = Numerator[Integrate[1/(((1+y)^2+x^2)*(1+a*x^2*y^2)^2),x]];
Map[ReplaceAll[G,y->#]&,SP]
This gives you nothing but a list of 0s, confirming that these singularities might be removable. Taking limits (as above) proves that they are.
And, as many have stated, you can verify this integral by taking the derivative and everything works out. Mathematica generally treats removable singularities like they are irrelevant -- if it could eliminate them, it would, but here it's not easy to do that with elementary functions.
- | {"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": 0.8740332126617432, "perplexity": 811.5846934862026}, "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-2016-26/segments/1466783393518.22/warc/CC-MAIN-20160624154953-00174-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=619842 | # Boosting the angular momentum vector
by TriTertButoxy
Tags: angular, boosting, momentum, vector
P: 194 Since the angular momentum vector $\mathbf{J}$ is just a 3-vector, it transforms non-covariantly under Lorentz transformations -- more specifically, boosts generated by $\mathbf{K}$. Indeed, the commutator reads $[J_i,\,K_j]=i\epsilon_{ijk}J_k$. Under a finite boost, I find the angular momentum vector gets mixed up with the 'boost vector' $$\mathbf{J}\rightarrow\gamma\left[\mathbf{J}-\left(\frac{\gamma}{\gamma+1}(\mathbf{\beta}\cdot \mathbf{J})\mathbf{\beta}-\mathbf{\beta}\times\mathbf{K}\right)\right]$$ (c.f. the Lorentz transformation of the electric field). How do I interpret this result? In which direction does the new angular momentum vector point? It depends on the boost vector?
P: 834 The problem is that angular momentum is not a vector. It's a bivector. What precisely is this boost vector you speak of? Edit: you mean the vector along the 3-velocity of the frame we're boosting into? At any rate, it's much more elegant to consider angular momentum as a bivector. Then, you just get the result, $${J'}^{cd} = L_a^c L_b^d J^{ab}$$ where $J^{ab} = x^a p^b - p^a x^b$. | {"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": 0.9909021854400635, "perplexity": 496.1462820055426}, "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-2014-35/segments/1408500832155.37/warc/CC-MAIN-20140820021352-00200-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-connecting-concepts-through-application/chapter-6-logarithmic-functions-6-1-functions-and-their-inverses-6-1-exercises-page-493/23 | ## Intermediate Algebra: Connecting Concepts through Application
Place a horizontal line on any point of the graph. In order for the function to be a one-to-one function, the horizontal line must intersect the graph only once. Note: $l=$ the horizontal line | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9067456126213074, "perplexity": 388.39484114638805}, "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-2018-43/segments/1539583512015.74/warc/CC-MAIN-20181018214747-20181019000247-00526.warc.gz"} |
http://math.stackexchange.com/questions/376113/norm-product-inequality | # Norm product inequality
The following is about a proof in Bratteli Robinson vol 1. Let $\mathcal{A}$ be some C*-algebra. Show that $$\mathcal{B}=\{(A,\alpha)~|~A\in\mathcal{A}, \alpha\in\mathbb{C}\}$$ together with the norm $$\lVert(A,\alpha)\lVert=\sup_{B\in\mathcal{A}, \lVert B\lVert\leq 1} \lVert AB+\alpha B \lVert$$ and the operations $$(A,\alpha)(B,\beta)=(AB+\alpha B+\beta A, \alpha \beta)$$ $$\lambda(A,\alpha)=(\lambda A, \lambda\alpha)$$ $$(A,\alpha)+(B,\beta)=(A+B, \alpha+ \beta)$$ $$(A,\alpha)^*=(A^*,\bar{\alpha})$$ is again a C*-algebra. I understood the proof in general, but I don't see why the norm product inequality ($\lVert (A,\alpha)(B,\beta)\lVert\leq\lVert (A,\alpha)\lVert \lVert(B,\beta)\lVert$) holds. Any hints?
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Hint: Plug $\dfrac{BC + \beta C}{\Vert BC + \beta C\Vert}$ into the norm computation of $(A,\alpha)$ and compare to plugging in $C$ to the norm computation of $(A,\alpha)(B,\beta)$. | {"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": 0.9658297300338745, "perplexity": 296.8931441519817}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461861700326.64/warc/CC-MAIN-20160428164140-00084-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/3157/photon-absorption-probability-for-a-given-molecule-in-gas-phase | # Photon absorption probability for a given molecule in gas phase
So I'm pretty sure I'm approaching this problem in the wrong way and I need some guidance (my first hint is that I think I'm thinking about a quantum mechanical problem too classically)
Suppose there is an isolated molecule in the gas phase with an average cross-sectional area to be exposed to radiation of $A$. (For my specific problem, the molecule is trapped in a superfluid Helium droplet, but I think the calculation should be roughly the same). If the radiation source has a flux $f$ (in units of photons/second/square area/0.1% BW) at energy $E$, what is the probability of the molecule absorbing a photon within a given interaction time $t$ if the absorption probability at a given energy is $P(E)$?
This is pretty easy to calculate if I treat the whole problem classically, i.e. like a ball and a target model. For some reason, though, I get numbers that seem to be way too low if I do this. I know it has to be more complicated than that, since light is a wave also. What am I missing?
I understand that transition probabilities are related to wavefunction overlap, etc. Also, I should note that the radiation in my specific problem is in the hard x-ray region, though I don't think that should change the answer.
-
the set of quantities you offered us to calculate the result is strange, or at least unusual. In particular, there is nothing such as the (dimensionless) absorption probability $P(E)$ for a molecule to absorb a photon.
The absorption probability is given by the cross section which you called $A$. For every process, one has to determine the cross section again. Usually, the cross section is called $\sigma$ instead of $A$.
So the best thing I could do with your numbers and functions would be to imagine that the cross section in your case was given by $\sigma(E) = P(E)\cdot A$. But it is really misleading to factorize the cross section in such ways. In particular, a universal "cross section area $A$" doesn't mean anything. Molecules are not hard balls that have a universal well-defined cross-sectional areas. They're nuclei surrounded by soft wave functions of electrons that reach arbitrarily far but are getting weaker with the distance - in fact, the (one) wave function for $N$ electrons lives in an $3N$-dimensional space rather than the ordinary $3$-dimensional space.
The number of events, in your case absorption events, is simply the product of the integrated luminosity and the cross section $\sigma$. The integrated luminosity is the time integral of luminosity $L$. It is normally written as $L=\rho\times v$ where $\rho$ is the number density of the beam - in particles per unit volume - and $v$ is the velocity - for photons, it's the speed of light $c$. The quantity $L$ happens to be the same thing as your flux $f$. If there are some losses or extra percentages etc., you have to be careful about it.
The quantities such as the cross section are designed in such a way that you are allowed to imagine that the molecule is classical and literally has the cross-sectional area $\sigma$ - that's why they were designed - and you get the right probability. If you do think right, you will indeed find out that only a small percentage of the X-ray photons is absorbed. That's why X-rays are being used to see through human bodies at X-ray pictures.
Best wishes Lubos
-
I remember some "oscillator strength" in this context. There is a wikipedia entry for that.Georg – Georg Jan 17 '11 at 16:37
It is quite normal in spectroscopy to define absorption strength of a certain molecule in $cm^2$. Of course the value itself is defined by the transition probability and has no physical meaning but it is very handy for calculations. – gigacyan Jan 17 '11 at 20:03
Well my first guess that you shouldn't consider naive "cross-sectional area" of your molecule. It would be better If you calculated the cross section of absorption/scattering of photons on your molecule. It depends on different properties of your molecule and on the wavelength of the light.
But maybe your calculations are more or less correct. You said that you result "too low", but hard x-ray photons are indeed very good at passing through matter.
-
It is not unusual in spectroscopy to define an absorption cross-section of a molecule in $cm^2$. Although it has no real physical meaning (it can even be larger that the molecule itself) and can be derived from Einstein coefficients, it is what you can directly measure by experiment $$cross-section\;\;\alpha= \frac{total\;energy\;absorbed\;/s}{total\;incident\;intensity\;(energy/s/area)}$$ The relation to the Einstein coefficient if simply $\alpha=\frac{\hbar\omega}{c}B_{21}$
Basically, transition probability is Einstein coefficient times photon density. You problem could be to correctly define a fraction of photons that are resonant with the transition that you study. This would greatly depend on the kind of light source that you use.
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http://supercgis.com/relative-error/relative-error-with-absolute-value.html | Home > Relative Error > Relative Error With Absolute Value
# Relative Error With Absolute Value
## Contents
they could both be the smallest possible measure, or both the largest. Absolute Accuracy Error Example: 25.13 mL - 25.00 mL = +0.13 mL absolute error Relative Accuracy Error Example: (( 25.13 mL - 25.00 mL)/25.00 mL) x 100% = 0.52% This may apply to your measuring instruments as well. The relative error of the measurement is 2 mph / 60 mph = 0.033 or 3.3%More About Experimental Error Show Full Article Related This Is How To Calculate Percent Error What Check This Out
We will be working with relative error. Make the measurement with an instrument that has the highest level of precision. Ways to Improve Accuracy in Measurement 1. which is the absolute error? http://www.regentsprep.org/regents/math/algebra/am3/LError.htm
## Absolute Error Calculation
The accepted value for her experiment was 34 grams. To do so, simply subtract the measured value from the expected one. What are the absolute and relative errors of the approximation 22/7 of π? (0.0013 and 0.00040) 2. For example, if your experimental value is in inches but your real value is in feet, you must convert one of them to the other unit of measurement.
Well, we just want the size (the absolute value) of the difference. You can, however, say you had "10% relative error."[10] Community Q&A Unanswered Questions When a measured value is negative how do I determine the exact value and the relative value? Absolute Error and Relative Error: Error in measurement may be represented by the actual amount of error, or by a ratio comparing the error to the size of the measurement. What Is Absolute Error Absolute Error: Absolute error is simply the amount of physical error in a measurement.
An approximation error can occur because the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5cm but since What is the Formula for Relative Error? This tells you what percentage of the final measurement you messed up by. http://chemistry.about.com/od/workedchemistryproblems/fl/Absolute-Error-and-Relative-Error-Calculation.htm Example: For professional gravimetric chloride results we must have less than 0.2% relative error.
You report the absolute error in the measurement as 75 mm +/- 1 mm. Absolute Error Definition Note, however that this doesn't make sense when giving percentages, as your error is not 10% of 2 feet. No ... The temperature was measured as 38° C The temperature could be up to 1° either side of 38° (i.e.
## Absolute Error Formula
There are two problems with using the absolute error: Significance It gives you a feeling of the size of the error but how significant is the error? https://en.wikipedia.org/wiki/Approximation_error The width (w) could be from 5.5m to 6.5m: 5.5 ≤ w < 6.5 The length (l) could be from 7.5m to 8.5m: 7.5 ≤ l < 8.5 The area is Absolute Error Calculation Van Loan (1996). Relative Error Formula Eabs = |240 - 243.32753| ≈ 3.3 Ω Erel = |240 - 243.32753|/|243.32753| ≈ 0.014 Note: the label is the approximation of the actual value. 3.
But, if you are measuring a small machine part (< 3cm), an absolute error of 1 cm is very significant. his comment is here Relative error is expressed as fraction or is multiplied by 100 and expressed as a percent.Relative Error = Absolute Error / Known ValueFor example, a driver's speedometer says his car is going Back to Top The relative error formula is given byRelative error =$\frac{Absolute\ error}{Value\ of\ thing\ to\ be\ measured}$ = $\frac{\Delta\ x}{x}$.In terms of percentage it is expressed asRelative error = \$\frac{\Delta\ A resistor labeled as 240 Ω is actually 243.32753 Ω. Absolute Error And Relative Error In Numerical Analysis
But, if you tried to measure something that was 120 feet long and only missed by 6 inches, the relative error would be much smaller -- even though the value of The precision of a measuring instrument is determined by the smallest unit to which it can measure. Scalar Component of Vector Conceptual Physics Answers Relative Error Formula What is Relative Error? this contact form Incidental energy/material loss, such as the little fluid left in the beaker after pouring, changes in temperature due to the environment, etc.
Relative Precision Error Relative Standard Deviation (RSD) Coefficient of Variation (CV) Example: The CV of 53.15 %Cl, 53.56 %Cl, and 53.11 %Cl is (0.249 %Cl/53.27 %Cl)x100% = 0.47% relative uncertainty. Relative Error Chemistry But, if you are measuring a small machine part (< 3cm), an absolute error of 1 cm is very significant. Should the accepted or true measurement NOT be known, the relative error is found using the measured value, which is considered to be a measure of precision.
## If you are measuring a 200 foot boat, and miss the measurement by 2 feet, your percentage error will be much lower than missing the 20 foot tree measurement by 2
Calculate the absolute error and relative error. The precision is said to be the same as the smallest fractional or decimal division on the scale of the measuring instrument. Greatest Possible Error: Because no measurement is exact, measurements are always made to the "nearest something", whether it is stated or not. Relative Error Definition Note, the vertical bars are absolute value signs, meaning anything within them must be positive.
You pace from one tree to another and estimate that they're 18 feet apart. From 41.25 to 48 = 6.75 From 48 to 55.25 = 7.25 Answer: pick the biggest one! It is the difference between the result of the measurement and the true value of what you were measuring. http://supercgis.com/relative-error/relative-error-vs-absolute-error-matlab.html The error in measurement is a mathematical way to show the uncertainty in the measurement.
It is the difference between the result of the measurement and the true value of what you were measuring. If you measure the same object two different times, the two measurements may not be exactly the same. Please enter a valid email address. To determine the tolerance interval in a measurement, add and subtract one-half of the precision of the measuring instrument to the measurement.
Warnings If taking the regents exam, make sure you round correctly EditRelated wikiHows How to Compare and Order Fractions How to Find the Area of a Square Using the Length of between 37° and 39°) Temperature = 38 ±1° So: Absolute Error = 1° And: Relative Error = 1° = 0.0263... 38° And: Percentage Error = 2.63...% Example: You Examples: 1. HOWTO Calculating Absolute Error Given an approximation a of a value x, the absolute error Eabs is calculated using the formula: Calculating Relative Error Given an approximation a of
In this class, we will usually use the relative error, though if we are only trying to show that a sequence of errors is decreasing to zero, we may use the Updated August 13, 2015. Your absolute error is 20 - 18 = 2 feet (60.96 centimeters).[3] 2 Alternatively, when measuring something, assume the absolute error to be the smallest unit of measurement at your disposal. Relative error compares the absolute error against the size of the thing you were measuring.
So you know that your measurement is accurate to within + or - 1 mm; your absolute error is 1 mm. When the accepted or true measurement is known, the relative error is found using which is considered to be a measure of accuracy. Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts
Error in Measurement Topic Index | Algebra Index | | {"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": 0.9397916197776794, "perplexity": 805.0920700470332}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320174.58/warc/CC-MAIN-20170623202724-20170623222724-00505.warc.gz"} |
https://my-assignmentexpert.com/2021/01/22/simple-abstractalgebra-assignment-help/ | 19th Ave New York, NY 95822, USA
# abstract algebra代写|group thoery代写
Abstract algebra不算是一门简单的学科，这门学科在国内叫做抽象代数，经常有很多学生在学linear algebra或者analysis(advance calculus)的时候觉得并不困难，但是却觉得Abstract algebra很难，这是因为没有找到正确的方法学习Abstract algebra，UpriviateTA有一系列非常擅长Abstract algebra的老师，可以确保您在Abstract algebra取得满意的成绩。
identity The identity element is the function $$I: X \rightarrow G$$ which is identically equal to the identity element, $$e,$$ of $$G .$$ Indeed, for any $$f \in F$$ and any $$x \in X$$ we have $$(I * f)(x)=I(x) \cdot f(x)=e \cdot f(x)=f(x) .$$ Hence, $$I * f=f$$.
inverse Let $$f \in F$$ be any element of $$F .$$ Let $$g: X \rightarrow G$$ be defined by $$g(x):=$$ $$(f(x))^{-1}$$. Then for any $$x \in X$$ we have $$(g * f)(x)=g(x) \cdot f(x)=(f(x))^{-1}$$. $$f(x)=e=I(x) .$$ Hence, $$g * f=I$$ so that $$g$$ is a left-inverse of $$f$$.
associativity Let $$f, g,$$ and $$h$$ be elements of $$F$$. For any $$x \in X$$ we have $$f *(g * h)(x)=$$ $$f(x) \cdot(g * h)(x)=f(x) \cdot(g(x) \cdot h(x))=(f(x) \cdot g(x)) \cdot h(x)=(f * g)(x) \cdot h(x)=$$
$$(f * g) * h(x) .$$ Hence, $$f *(g * h)=(f * g) * h$$
$$a$$ must be the identity element.
to one. Thus, $$A$$ does not have an inverse in $$G$$.
$$x \mapsto\left\{\begin{array}{l} x+4 \text { if } x<12 \\ x-12 \text { if } x \geq 12 \end{array}\right.$$
Show that $$\sigma$$ is a permutation and describe its orbits.
abstract algebra代写请认准UpriviateTA. UpriviateTA为您的留学生涯保驾护航。 | {"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": 2, "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": 0.9965564608573914, "perplexity": 211.80843108373938}, "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-2022-49/segments/1669446710533.96/warc/CC-MAIN-20221128135348-20221128165348-00529.warc.gz"} |
http://lonelydeveloper.org/eprst/eprst_01_10 | # 1. Problem 1
## 1.1. Question
Random variable $$X$$ have uniform distribution on $$[0;3]$$. Let $$Z = \max(X,0)$$, $$W = \min (X,0)$$. Is it true:
1. $$P(Z>=0) > P(W>=0)$$
2. $$P(Z>0) = P(W>0)$$
3. $$P(Z>0) = P(W<0)$$
4. $$P(Z<0) = P(W<0)$$
4 is true; the rest is false
# 2. Problem 2
## 2.1. Question:
Random variable $$Y$$ has uniform distribution on the interval $$(-4,4)$$. Let $$Y' = sign(Y)$$ and $$S_1 = |Y|$$. $$P(0 < Y'S_1 < 1/2)$$ is equal:
1. $$\frac{1}{16}$$
2. $$1/3$$
3. $$3/4$$
4. $$3/16$$
1 is true; the rest is false
# 3. Problem 3
## 3.1. Question
Random variable $$X$$ has uniform distribution on the interval $$(0,4)$$ and $$Y$$ is independent with two point distribution $$P(Y= -1) = 1 - P(Y=1) = 1/3$$.
1. $$V(X-Y) \in (0.5; 2.1222]$$
2. $$V(X-Y) > V(X+Y)$$
3. $$V(X-Y) >= \frac{29}{9}$$
4. $$V(X-Y) <= \frac{20}{9}$$
5. $$V(X-Y) >= 3.7222$$
4 is true; the rest is false
The exact result: $$V(X-Y) = \frac{20}{9}$$.
The way to obtain it:
$$V(X-Y) = E((X-Y)^2) - (E(X-Y))^2 = E(X^2)-2E(XY)+E(Y^2)-(E(X)-E(Y))^2$$
$$E(X)=2; E(Y)=\frac{1}{3}; E(X^2)=\frac{16}{3}; E(Y^2)=1; E(XY)=\frac{2}{3}$$
We simply substitute values and get the exact result.
# 4. Problem 4
## 4.1. Question
Let $$E$$ and $$K$$ be independent events. Then:
1. $$E$$ and $$K$$ exclude themselves.
2. $$E^C$$ and $$K^C$$ exclude themselves.
3. $$E$$ and $$K^C$$ can be dependent.
4. $$E \cap K$$ is an impossible event.
5. $$E^C$$ and $$K^C$$ are independent.
5 is true; the rest is false
# 5. Problem 5
## 5.1. Question
Let $$E$$ and $$K$$ be any random events. Assume that $$0 < P(E),P(K)<1$$. Which of the statements is true:
1. $$P(E \cap K) < P(E|K)P(K)$$
2. $$P(E \cup K) > P(E)+P(K)$$
3. $$P(K \cap E) > min(P(E), P(K))$$
4. $$P(E \cup K) < max(P(E),P(K))$$
5. $$P(E^C)+P(K^C)+P(E \cup K) - P(E^C \cup K^C) = 1$$
5 is true; the rest is false
# 6. Problem 6
## 6.1. Question
Random variables $$X$$ and $$Y$$ are independent and have the same uniform distributions on the interval $$(0,3)$$.
1. $$P(X-Y>-1) > \frac{7}{9}$$
2. $$P(X-Y>-1) < \frac{2}{9}$$
3. $$P(X-Y>-1) \in (\frac{2}{9},\frac{1}{2}]$$
4. $$P(X-Y>-1) = \frac{23}{27}$$
5. $$P(X-Y>-1) \in (\frac{1}{2},\frac{7}{9}]$$
5 is true; the rest is false
The answer can be read from a simple drawing without any calculations.
# 7. Problem 7
## 7.1. Question
Density of a random variable X is equal to:
$$f_X(x) = \begin{cases} \frac{1}{8} & \text{for -1 <= x <0} \\ \frac{3}{8} & \text{for 0<=x<2} \\ \frac{1}{16} & \text{for 2 <= x <= 4} \end{cases}$$
1. $$P(-\frac{1}{2} < X < 3) = \frac{7}{8}$$
2. $$P(-\frac{1}{2} < X < 3) \leq \frac{1}{2}$$
3. $$P(-\frac{1}{2} < X < 3) = \frac{13}{16}$$
4. $$P(-\frac{1}{2} < X < 3) < \frac{3}{8}$$
5. $$P(-\frac{1}{2} < X < 3) \geq \frac{15}{16}$$
1 is correct; the rest is wrong
Moreover please note that by simple logic answer 4 cannot be true, because if it was, then answer 2 would be true too, and as it was written in the introduction to these problems, there's is only one true answer.
# 8. Problem 8
## 8.1. Question
In some technological process hree types of indicator are used to signal the failure. Probability [of] applying indicator of the first type is $$\frac{3}{10}$$, of the second type $$0.4$$, of the third time $$0.3$$. Indicators of particular types signal the failure respectively with probability equal to 0.6, 0.6, 0.4. The probability $$p$$ of the event that the failure would be signaled:
1. $$p \in [0.702;1]$$
2. $$p \in [0.594; 0.702)$$
3. $$[0.27;0.594)$$
4. $$[0;0.27)$$
3 is true; the rest is false
It is so, because: $$p = 0.6 \times 0.3 + 0.6 \times 0.4 + 0.4 \times 0.3 = 0.54$$
# 9. Problem 9
## 9.1. Question
Random variable U has uniform distribution on $$[-3,3]$$. Random variable $$Y = \lfloor U \rfloor$$ (where $$\lfloor x \rfloor$$ denotes the gretest integer not exceeding $$x$$) has c.d.f. with exactly:
1. 9 jumping points
2. 6 jumping points
3. 2 jumping points
4. 5 jumping points
5. 3 jumping points
2 is true; the rest is false
# 10. Problem 10
## 10.1. Question
On the probability space $$([-7,7], \mathcal{B}([-7,7]),P_L)$$ where $$P_L$$ is geometric probability, we define a random wariable $$X(\omega)$$.
$$X(\omega) = \begin{cases} 7 + \omega & \text{for \omega \in [-7; -\frac{1}{5}]} \\ 2 & \text{for \omega \in (-\frac{1}{5};\frac{1}{5})} \\ \frac{7}{2}-\omega & \text{for \omega \in [\frac{1}{5}; 7]}\end{cases}$$
The value of c.d.f. of random variable $$X$$ at the point $$2$$ (i.e. $$F_X(2)$$) is equal:
1. $$\frac{47}{140}$$
2. $$\frac{1}{7}$$
3. $$\frac{11}{28}$$
4. $$\frac{103}{140}$$
5. $$\frac{15}{28}$$
This one is tricky, as the result depends on what definition of c.d.f ( $$F_X(x)$$) we choose.
If we choose $$F_X(x) = P(X<x)$$ then we get $$F_X(2) = \frac{15}{28}$$.
If we choose $$F_X(x) = P(X \leq x)$$ then we obtain $$F_X(2) = \frac{79}{140}$$. | {"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": 0.921259343624115, "perplexity": 914.0762685877514}, "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/1558232261326.78/warc/CC-MAIN-20190527045622-20190527071622-00072.warc.gz"} |
http://unapologetic.wordpress.com/2009/04/21/inner-products-and-lengths/?like=1&source=post_flair&_wpnonce=e94a57fbb5 | # The Unapologetic Mathematician
## Inner Products and Lengths
We’re still looking at a real vector space $V$ with an inner product. We used the Cauchy-Schwarz inequality to define a notion of angle between two vectors.
$\displaystyle\cos(\theta)=\frac{\lvert\langle v,w\rangle\rvert}{\langle v,v\rangle^{1/2}\langle w,w\rangle^{1/2}}$
Let’s take a closer look at those terms in the diagonal. What happens when we compute $\langle v,v\rangle$? Well, if we’ve got an orthonormal basis around and components $v^ie_i$, we can write
$\displaystyle\langle v,v\rangle=\sum\limits_{i=1}^d\left(v^i\right)^2$
The $v^i$ are distances we travel in each of the mutually-orthogonal directions given by the vectors $e_i$. But then this formula looks a lot like the Pythagorean theorem about calculating the square of the resulting distance. It may make sense to define this as the square of the length of $v$, and so the quantities in the denominator above were the lengths of $v$ and $w$, respectively.
Let’s be a little more formal. We want to define something called a “norm”, which is a notion of length on a vector space. If we think of a vector $v$ as an arrow pointing from the origin (the zero vector) to the point at its tip, we should think of the norm $\lVert v\rVert$ as the distance between these two points. Similarly, the distance between the tips of $v$ and $w$ should be the length of the displacement vector $v-w$ which points from one to the other. But a notion of distance is captured in the idea of a metric! So whatever a norm is, it should give rise to a metric by defining the distance $d(v,w)$ as the norm of $v-w$.
Here are some axioms: A function from $V$ to $\mathbb{R}$ is a norm, written $\lVert v\rVert$, if
• For all vectors $v$ and scalars $c$, we have $\lVert cv\rVert=\lvert c\rvert\lVert v\rVert$.
• For all vectors $v$ and $w$, we have $\lVert v+w\rVert\leq\lVert v\rVert+\lVert w\rVert$.
• The norm $\lVert v\rVert$ is zero if and only if the vector $v$ is the zero vector.
The first of these is eminently sensible, stating that multiplying a vector by a scalar should multiply the length of the vector by the size (absolute value) of the scalar. The second is essentially the triangle inequality in a different guise, and the third says that nonzero vectors have nonzero lengths.
Putting these axioms together we can work out
$\displaystyle0=\lVert0\rVert=\lVert v-v\rVert\leq\lVert v\rVert+\lVert -v\rVert=\lVert v\rVert+\lvert-1\rvert\lVert v\rVert=2\lVert v\rVert$
And thus every vector’s norm is nonnegative. From here it’s straightforward to check the conditions in the definition of a metric.
All this is well and good, but does an inner product give rise to a norm? Well, the third condition is direct from the definiteness of the inner product. For the first condition, let’s check
$\displaystyle\sqrt{\langle cv,cv\rangle}=\sqrt{c^2\langle v,v\rangle}=\sqrt{c^2}\sqrt{\langle v,v\rangle}=\lvert c\rvert\sqrt{\langle v,v\rangle}$
as we’d hope. Finally, let’s check the triangle inequality. We’ll start with
\displaystyle\begin{aligned}\lVert v+w\rVert^2&=\langle v+w,v+w\rangle\\&=\langle v,v\rangle+2\langle v,w\rangle+\langle w,w\rangle\\&\leq\lVert v\rVert^2+2\lvert\langle v,w\rangle\rvert+\lVert w\rVert^2\\&\leq\lVert v\rVert^2+2\lVert v\rVert\lVert w\rVert+\lVert w\rVert^2\\&=\left(\lVert v\rVert+\lVert w\rVert\right)^2\end{aligned}
where the second inequality uses the Cauchy-Schwarz inequality. Taking square roots (which preserves order) gives us the triangle inequality, and thus verifies that we do indeed get a norm, and a notion of length.
April 21, 2009 - Posted by | Algebra, Geometry, Linear Algebra
1. So, what happens over a finite field of characteristic 2? You no longer have the same proof of non-negative norms!
….
Wait
….
What would I even mean by non-negative in characteristic 2?
….
Never mind me.
Comment by Mikael Vejdemo Johansson | April 21, 2009 | Reply
2. I don’t know, Mikael. What happens in a real vector space over a finite field at all?
Comment by John Armstrong | April 21, 2009 | Reply
3. [...] now we do get a notion of length, defined by setting as before. What about angle? That will depend directly on the Cauchy-Schwarz [...]
Pingback by Complex Inner Products « The Unapologetic Mathematician | April 22, 2009 | Reply
4. [...] If we have an inner product on a real or complex vector space, we get a notion of length called a “norm”. It turns out that the norm completely determines the inner [...]
Pingback by The Polarization Identities « The Unapologetic Mathematician | April 23, 2009 | Reply
5. [...] Parallelogram Law There’s an interesting little identity that holds for norms — translation-invariant metrics on vector spaces over or — that come from inner [...]
Pingback by The Parallelogram Law « The Unapologetic Mathematician | April 24, 2009 | Reply
6. [...] Gram-Schmidt Process Now that we have a real or complex inner product, we have notions of length and angle. This lets us define what it means for a collection of vectors to be [...]
Pingback by The Gram-Schmidt Process « The Unapologetic Mathematician | April 28, 2009 | Reply
7. [...] basis be orthonormal, we get a real inner product on complex numbers, which in turn gives us lengths and angles. In fact, this notion of length is exactly that which we used to define the absolute [...]
Pingback by Complex Numbers and the Unit Circle « The Unapologetic Mathematician | May 26, 2009 | Reply
8. [...] take a look at this last condition geometrically. We use the inner product to define a notion of (squared-)length and a notion of (the cosine of) angle . So let’s transform the space by and see what [...]
Pingback by Orthogonal transformations « The Unapologetic Mathematician | July 27, 2009 | Reply
9. [...] metric space, so all of the special things we know about metric spaces can come into play. Indeed, inner products define norms and norms on vector spaces define metrics. We can even write it down explicitly. If we write our [...]
Pingback by The Topology of Higher-Dimensional Real Spaces « The Unapologetic Mathematician | September 15, 2009 | Reply
10. [...] will come up when we talk about more general spaces. But we do want to be able to talk in terms of lengths and [...]
Pingback by Hard Choices « The Unapologetic Mathematician | September 22, 2009 | Reply
11. [...] functional . Thus we also find that . And we can interpret this inner product in terms of the length of and the angle between and [...]
Pingback by The Gradient Vector « The Unapologetic Mathematician | October 5, 2009 | Reply
12. [...] got an inner product on spaces of antisymmetric tensors, and that should give us a concept of length. Why can’t we just calculate the size of a parallelepiped by sticking it into this bilinear [...]
Pingback by Parallelepipeds and Volumes III « The Unapologetic Mathematician | November 4, 2009 | Reply
13. [...] to check our answer against later. For the base, we take the length of one vector, say . We use the inner product to calculate its length as . For the height we can’t just take the length of the other [...]
Pingback by An Example of a Parallelogram « The Unapologetic Mathematician | November 5, 2009 | Reply
14. [...] know a lot about the relation between the inner product and the lengths of vectors and the angle between them. Specifically, we can [...]
Pingback by Pairs of Roots « The Unapologetic Mathematician | January 28, 2010 | Reply
15. [...] a common way to come up with such a uniform structure is to define a norm on our vector space. That is, to define a function satisfying the three [...]
Pingback by Topological Vector Spaces, Normed Vector Spaces, and Banach Spaces « The Unapologetic Mathematician | May 12, 2010 | Reply
16. [...] inner product gives us a notion of length and angle. Invariance now tells us that these notions are unaffected by the action of . That is, [...]
Pingback by Invariant Forms « The Unapologetic Mathematician | September 27, 2010 | Reply
17. [...] it lets us measure things. Specifically, since is an inner product it gives us notions of the length and angle for tangent vectors at . We must be careful here; we do not yet have a way of measuring [...]
Pingback by (Pseudo-)Riemannian Metrics « The Unapologetic Mathematician | September 20, 2011 | Reply
18. [...] particular, if we stick the vector into the metric twice, like we do to calculate a squared-length when working with an inner product, we [...]
Pingback by Minkowski Space « The Unapologetic Mathematician | March 7, 2012 | Reply | {"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": 31, "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": 0.9918044209480286, "perplexity": 395.3294912321926}, "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-2013-20/segments/1368705543116/warc/CC-MAIN-20130516115903-00070-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.aimsciences.org/journal/1935-9179/2010/17/0 | # American Institute of Mathematical Sciences
ISSN:
1935-9179
eISSN:
1935-9179
All Issues
## Electronic Research Announcements
2010 , Volume 17
Select all articles
Export/Reference:
2010, 17: 1-11 doi: 10.3934/era.2010.17.1 +[Abstract](278) +[PDF](195.7KB)
Abstract:
We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T$: $\RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we consider, and obtain partial results for any continuous map $f$ on a compact metric space. In order to obtain complete results, the primary hypothesis we require is that the functions $T$ be continuously differentiable. This makes rigorous the general paradigm of reducing questions regarding the multifractal formalism to questions regarding the thermodynamic formalism. These results hold for a broad class of measurable potentials, which includes (but is not limited to) continuous functions. Applications include most previously known results, as well as some new ones.
2010, 17: 12-19 doi: 10.3934/era.2010.17.12 +[Abstract](203) +[PDF](160.5KB)
Abstract:
We give a new proof of the sharp weighted $L^p$ inequality
$|\|T\||_{L^p(w)} \leq C_{n,T}[w]_{A_p}^{\max(1,\frac{1}{p-1})},$
where $T$ is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift operators. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner [15] to estimate the oscillation of dyadic operators.
The method we use is flexible enough to obtain the sharp one-weight result for other important operators as well as a very sharp two-weight bump type result for $T$ as can be found in [5].
2010, 17: 20-33 doi: 10.3934/era.2010.17.20 +[Abstract](203) +[PDF](834.7KB)
Abstract:
We study a two-parameter family of one-dimensional maps and the related $(a,b)$-continued fractions suggested for consideration by Don Zagier and announce the following results and outline their proofs: (i) the associated natural extension maps have attractors with finite rectangular structure for the entire parameter set except for a Cantor-like set of one-dimensional zero measure that we completely describe; (ii) for a dense open set of parameters the Reduction theory conjecture holds, i.e. every point is mapped to the attractor after finitely many iterations. We also give an application of this theory to coding geodesics on the modular surface and outline the computation of the smooth invariant measures associated with these transformations.
2010, 17: 34-42 doi: 10.3934/era.2010.17.34 +[Abstract](225) +[PDF](173.1KB)
Abstract:
The main results announced in this note are an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and a limit theorem for such flows (Theorem 2). Given an abelian differential on a compact oriented surface, consider the space $\mathfrak B^+$ of Hölder cocycles over the corresponding vertical flow that are invariant under holonomy by the horizontal flow. Cocycles in $\mathfrak B^+$ are closely related to G.Forni's invariant distributions for translation flows [10]. Theorem 1 states that ergodic integrals of Lipschitz functions are approximated by cocycles in $\mathfrak B^+$ up to an error that grows more slowly than any power of time. Theorem 2 is obtained using the renormalizing action of the Teichmüller flow on the space $\mathfrak B^+$. A symbolic representation of translation flows as suspension flows over Vershik's automorphisms allows one to construct cocycles in $\mathfrak B^+$ explicitly. Proofs of Theorems 1, 2 are given in [5].
2010, 17: 43-56 doi: 10.3934/era.2010.17.43 +[Abstract](189) +[PDF](219.8KB)
Abstract:
We study Gauss curvature for random Riemannian metrics on a compact surface, lying in a fixed conformal class; our questions are motivated by comparison geometry. We next consider analogous questions for the scalar curvature in dimension $n>2$, and for the $Q$-curvature of random Riemannian metrics.
2010, 17: 57-67 doi: 10.3934/era.2010.17.57 +[Abstract](185) +[PDF](202.0KB)
Abstract:
This is an informal announcement of results to be described and proved in detail in [3]. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$. For example, generalizing a result of Helfgott (who handled the cases $n = 2$ and $3$), we show that any approximate subgroup of $\SL_n(\F_q)$ which generates the group must be either very small or else nearly all of $\SL_n(\F_q)$. The argument is valid for all Chevalley groups $G(\F_q)$. Extending work of Bourgain-Gamburd we also announce some applications to expanders, which will be proven in detail in [4].
2010, 17: 68-79 doi: 10.3934/era.2010.17.68 +[Abstract](139) +[PDF](192.4KB)
Abstract:
We prove the local differentiable rigidity of partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. The conclusions are based on geometric Katok-Damjanovic way and progress towards computations of the Schur multipliers of these non-split groups.
2010, 17: 80-89 doi: 10.3934/era.2010.17.80 +[Abstract](124) +[PDF](182.0KB)
Abstract:
In several contexts the defining invariant structures of a hyperbolic dynamical system are smooth only in systems of algebraic origin, and we prove new results of this smooth rigidity type for a class of flows.
For a transversely symplectic uniformly quasiconformal $C^2$ Anosov flow on a compact Riemannian manifold we define the longitudinal KAM-cocycle and use it to prove a rigidity result: The joint stable/unstable subbundle is Zygmund-regular, and higher regularity implies vanishing of the KAM-cocycle, which in turn implies that the subbundle is Lipschitz-continuous and indeed that the flow is smoothly conjugate to an algebraic one. To establish the latter, we prove results for algebraic Anosov systems that imply smoothness and a special structure for any Lipschitz-continuous invariant 1-form.
We obtain a pertinent geometric rigidity result: Uniformly quasiconformal magnetic flows are geodesic flows of hyperbolic metrics.
Several features of the reasoning are interesting: The use of exterior calculus for Lipschitz-continuous forms, that the arguments for geodesic flows and infranilmanifoldautomorphisms are quite different, and the need for mixing as opposed to ergodicity in the latter case.
2010, 17: 90-103 doi: 10.3934/era.2010.17.90 +[Abstract](116) +[PDF](241.7KB)
Abstract:
On reflexive spaces trigonometrically well-bounded operators (abbreviated "twbo's'') have an operator-ergodic-theory characterization as the invertible operators $U$ whose rotates "transfer'' the discrete Hilbert averages $(C,1)$-boundedly. Twbo's permeate many settings of modern analysis, and this note treats advances in their spectral theory, Fourier analysis, and operator ergodic theory made possible by applying classical analysis techniques pioneered by Hardy-Littlewood and L.C. Young to the R.C. James inequalities for super-reflexive spaces. When the James inequalities are combined with spectral integration methods and Young-Stieltjes integration for the spaces $V_{p}(\mathbb{T})$ of functions having bounded $p$-variation, it transpires that every twbo on a super-reflexive space $X$ has a norm-continuous $V_{p}(\mathbb{T})$-functional calculus for a range of values of $p>1$, and we investigate the ways this outcome logically simplifies and simultaneously advances the structure theory of twbo's on $X$. In particular, on a super-reflexive space $X$ (but not on the general reflexive space) Tauberian-type theorems emerge which improve to their $(C,0)$ counterparts the $(C,1)$ averaging and convergence associated with twbo's.
2010, 17: 104-121 doi: 10.3934/era.2010.17.104 +[Abstract](161) +[PDF](260.8KB)
Abstract:
We construct monotone Lagrangian tori in the standard symplectic vector space, in the complex projective space and in products of spheres. We explain how to classify these Lagrangian tori up to symplectomorphism and Hamiltonian isotopy, and how to show that they are not displaceable by Hamiltonian isotopies.
2010, 17: 122-124 doi: 10.3934/era.2010.17.122 +[Abstract](103) +[PDF](94.9KB)
Abstract:
We give a new characterization of spaces with nonnegative curvature in the sense of Alexandrov.
2010, 17: 125-137 doi: 10.3934/era.2010.17.125 +[Abstract](149) +[PDF](228.1KB)
Abstract:
This paper introduces a new Parseval frame, based on the 3-D shearlet representation, which is especially designed to capture geometric features such as discontinuous boundaries with very high efficiency. We show that this approach exhibits essentially optimal approximation properties for 3-D functions $f$ which are smooth away from discontinuities along $C^2$ surfaces. In fact, the $N$ term approximation $f_N^S$ obtained by selecting the $N$ largest coefficients from the shearlet expansion of $f$ satisfies the asymptotic estimate
||$f-f_N^S$||$_2^2$ ≍ $N^{-1} (\log N)^2, as N \to \infty.$
Up to the logarithmic factor, this is the optimal behavior for functions in this class and significantly outperforms wavelet approximations, which only yields a $N^{-1/2}$ rate. Indeed, the wavelet approximation rate was the best published nonadaptive result so far and the result presented in this paper is the first nonadaptive construction which is provably optimal (up to a loglike factor) for this class of 3-D data.
Our estimate is consistent with the corresponding 2-D (essentially) optimally sparse approximation results obtained by the authors using 2-D shearlets and by Candès and Donoho using curvelets.
2010, 17: 138-154 doi: 10.3934/era.2010.17.138 +[Abstract](180) +[PDF](418.2KB)
Abstract:
In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications is an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.
2010, 17: 155-160 doi: 10.3934/era.2010.17.155 +[Abstract](129) +[PDF](139.1KB)
Abstract:
Consider the following question: given two functions on a symplectic manifold whose Poisson bracket is small, is it possible to approximate them in the $C^0$ norm by commuting functions? We give a positive answer in dimension two, as a particular case of a more general statement which applies to functions on a manifold with a volume form. This result is based on a lemma in the spirit of geometric measure theory. We give some immediate applications to function theory and the theory of quasi-states on surfaces with area forms.
2016 Impact Factor: 0.483 | {"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": 0.9313402771949768, "perplexity": 487.11128421200374}, "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-2018-13/segments/1521257647299.37/warc/CC-MAIN-20180320052712-20180320072712-00130.warc.gz"} |
https://www.gradesaver.com/textbooks/math/statistics-probability/elementary-statistics-12th-edition/chapter-3-statistics-for-describing-exploring-and-comparing-data-3-4-measures-of-relative-standing-and-boxplots-basic-skills-and-concepts-page-124/9 | ## Elementary Statistics (12th Edition)
If a value is unusual, then it is more than two standard deviations far from the mean. $Minimum \ usual \ value=mean-2\cdot(standard \ deviation)=100-2\cdot15=70$ $Maximum \ usual \ value=mean+2\cdot(standard \ deviation)=100+2\cdot15=130$. Therefore the z scores are -2 and 2, the IQ scores are 70 and 130. | {"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": 0.8030902743339539, "perplexity": 510.42144009122575}, "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/1537267156613.38/warc/CC-MAIN-20180920195131-20180920215531-00340.warc.gz"} |
http://mathhelpforum.com/algebra/128514-logarithm-problems.html | # Thread: Logarithm Problems
1. ## Logarithm Problems
How would one solve for x in the following, using the laws of logarithms?
1) 5^x+3^2x=92
2) 4*5^x-3*0.4^2x=11
In 1), this is what I've done so far:
5^x+3^2x=92
log(5^x+3^2x)=log 92
log(5+3^2)^x=log 92
x log 14=log 92
but I don't think that it's correct, and things aren't any clearer for question 2).
2. Hello DemonX01
Originally Posted by DemonX01
How would one solve for x in the following, using the laws of logarithms?
1) 5^x+3^2x=92
2) 4*5^x-3*0.4^2x=11
In 1), this is what I've done so far:
5^x+3^2x=92
log(5^x+3^2x)=log 92
log(5+3^2)^x=log 92
x log 14=log 92
but I don't think that it's correct, and things aren't any clearer for question 2).
For number (1), you're right: your working is not correct.
However, I don't know what method you are supposed to use to solve these equations. The only way I can see is to use some sort of approximate numerical method. Doing this, I can tell you that the answers are: (1) 1.9311, and (2) 0.6758, correct to 4 d.p.
But I cheated a bit and used a spreadsheet.
3. Remember that $3^{2x}=(3^2)^x$
So you actually have:
$5^x+9^x=92$
I'll edit this post with an answer if I find it, but as Grandad couldn't, I doubt I'll be able to take it any further without using a spreadsheet, as I've next to no maths knowledge whatsoever by comparison. | {"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": 2, "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": 0.8026602864265442, "perplexity": 811.3717478221296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218191986.44/warc/CC-MAIN-20170322212951-00166-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00560449 | # Formalization of Hensel's lemma in Coq
* Corresponding author
2 ARENAIRE - Computer arithmetic
LIP - Laboratoire de l'Informatique du Parallélisme, Inria Grenoble - Rhône-Alpes
Abstract : Suppose we want to find the integral simple roots of a univariate polynomial with integer coefficients. We can use Hensel's lifting, which can be viewed as the $p$-adic variant of the Newton--Raphson's iteration. It enables us to compute the roots modulo increasing powers of a prime $p$. As soon as the considered power of $p$ becomes greater than a known bound on the roots, we easily obtain the sought integral roots. The bivariate version of this root-finding algorithm is extensively used by the Stehlé--Lefèvre--Zimmermann algorithm, designed to solve the so-called Table Maker's Dilemma in an exact way. Consequently, the formal verification of Hensel's lemma (i.e., the correctness lemma of Hensel's lifting method) will contribute to the validation of this kind of algorithm. In this talk, we describe the various steps we met during the formalization of Hensel's lemma with the Coq proof assistant along with the SSReflect extension.
Keywords :
Domain :
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00560449
Contributor : Érik Martin-Dorel <>
Submitted on : Friday, January 28, 2011 - 1:36:26 PM
Last modification on : Wednesday, November 20, 2019 - 2:57:50 AM
### Identifiers
• HAL Id : ensl-00560449, version 1
### Citation
Érik Martin-Dorel. Formalization of Hensel's lemma in Coq. TYPES 2010: The 17th Workshop on Types for Proofs and Programs, Oct 2010, Warsaw, Poland. ⟨ensl-00560449⟩
Record views | {"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": 0.918320894241333, "perplexity": 1560.1482737408076}, "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-2020-24/segments/1590347387219.0/warc/CC-MAIN-20200525032636-20200525062636-00092.warc.gz"} |
http://www.intechopen.com/books/micro-electronic-and-mechanical-systems/single-photon-eigen-problem-with-complex-internal-dynamics | Engineering » Electrical and Electronic Engineering » "Micro Electronic and Mechanical Systems", book edited by Kenichi Takahata, ISBN 978-953-307-027-8, Published: December 1, 2009 under CC BY-NC-SA 3.0 license. © The Author(s).
# Single Photon Eigen-Problem with Complex Internal Dynamics
By Nenad V. Delić, Jovan P. Šetrajčić, Dragoljub Lj. Mirjanić, Zdravko Ivanković, Dobrivoje Martinov, Snežana Jokić, Ivana Petrevska–Đukić, Dušanka Tešanović and Svetlana Pelemiš
DOI: 10.5772/7026
Article top
# Single Photon Eigen-Problemwith Complex Internal Dynamics
Nenad V. Delić1, Jovan P. Šetrajčić1, 8, Dragoljub Lj. Mirjanić2, 8, Zdravko Ivanković3, Dobrivoje Martinov4, Snežana Jokić4, Ivana Petrevska–Đukić5, Dušanka Tešanović6 and Svetlana Pelemiš
## 1. Introduction
Linearized single photon Hamiltonian is used for the analysis of its features in coordinate systems of various geometries. As it could have been expected, based on the general theory of relativity, it turned out that space geometry and physical features are closely interrelated. In Cartesian’s coordinates single photons are spatial plane waves, while in cylindrical coordinates they are one-dimensional plane waves the amplitudes of which falls in planes normal to the direction of propagation. The most general information on single photon characteristics has been obtained by the analysis in spherical coordinates. The analysis in this system has shown that single photon spin essentially influences its behavior and that the wave functions of single photon can be normalized for zero orbital momentum, only.
A free photon Hamiltonian is linearized in the second part of this paper using Pauli’s matrices. Based on the correspondence of Pauli’s matrices kinematics and the kinematics of spin operators, it has been proved that a free photon integral of motion is a sum of orbital momentum and spin momentum for a half one spin. Linearized Hamiltonian represents a bilinear form of products of spin and momentum operators. Unitary transformation of this form results in an equivalent Hamiltonian, which has been analyzed by the method of Green’s functions. The evaluated Green’s function has given possibility for interpretation of photon reflection as a transformation of photon to anti-photon with energy change equal to double energy of photon and for spin change equal to Dirac’s constant. Since photon is relativistic quantum object the exact determining of its characteristics is impossible. It is the reason for series of experimental works in which photon orbital momentum, which is not integral of motion, was investigated. The exposed theory was compared to the mentioned experiments and in some elements the satisfactory agreement was found.
## 2. Eigen-problem of single photon Hamiltonian
In the first part of this work the eigen-problem of single photon Hamiltonian was formulated and solutions were proposed. Based on the general theory of relativity, it turned out that space geometry and physical features are closely interrelated. Because of that the analyses was provided in Cartesian’s, cylindrical and spherical coordinate systems.
### 2.1. Introduction
E=cpx2+py2+pz2 (1)
where c is the light velocity in vacuum and px, py and pz are the components of photon momentum. If instead of classical momentum components we use quantum-mechanical operatorspνp^ν=ixν;ν= (x,y,z), where h2π= 1,05456×1034Js is Dirac's constant, we obtain quantum-mechanical single photon Hamiltonian:
H^=±cp^x2+p^y2+p^z2 (2)
This Hamiltonian is not a linear operator that contradicts the principle of superposition (Gottifried, 2003; Kadin, 2005). Klein and Gordon (Sapaznjikov, 1983) skirted this problem solving the eigen-problem of square of Hamiltonian (2):
H^2ϕ=E2ϕ (3)
since the square of Hamiltonian is a linear operator. This approach has given satisfactory description of single photon behaving. Up to now it is considered that this approach gives real picture of photon. Here will be demonstrated that Kline–Gordon picture of photon is incomplete.
Here we shall try to examine single photon behavior by means of linearized Hamiltonian (2). Linearization procedure is analogous to the procedure that was used by Dirac’s in the analysis of relativistic electron Hamiltonian (Dirac, 1958). We shall take that
p^x2+p^y2+p^z2=(α^ p^x+β^ p^y+χ^ p^z)2 (4)
i.e. we shall transform the sum of squares into the square of the sum using α^,β^ and χ^ matrices. In accordance with (4) these matrices fulfill the following relations:
α^2=β^2=χ^2=1;α^ β^+β^ α^=α^ χ^+χ^ α^=β^ χ^+χ^ β^=0. (5)
It is easy to show (Tošić, et al., 2008; Delić, et al., 2008) that (5) conditions are fulfilled by Pauli’s matrices
α^=(0110); β^=(0−ii0); χ^=(100−1) (6)
Combining (6), (4) and (2), we obtain linearized photon Hamiltonian which completely reproduces the quantum nature of light (Holbrow, et al., 2001; Torn, et al., 2004) in the form:
H^=±c(p^zp^x−ip^yp^x+ip^y−p^z)=±ℏci(∂∂z∂∂x−i∂∂y∂∂x+i∂∂y−∂∂z) (7)
.
Since linearized Hamiltonian is a 2×2 matrix, photon eigen-states must be columns and rows which two components. Operators of other physical quantities must be represented in the form of diagonal 2×2 matrices.
At the end of this presentation, it is important to underline the orbital momentum operator(L^00L^); L^=r^×p^does not commute with Hamiltonian (7). It means that it is not integral of motion as in Klein-Gordon theory (Davidov, 1963). It can be shown that integral of motion represents total momentum(J^00J^), where J^ is the sum of orbital momentum L^ and rotation momentum S^ which corresponds to 1/2 spin.
In further the eigen-problem of linearized single photon Hamiltonian will be analyzed in Cartesian’s, cylindrical and spherical coordinates.
### 2.2. Photons in Cartesian's picture
The eigen-problem of single photon Hamiltonian in Cartesian coordinates (we shall take it with plus sign) has the following form:
ℏci(∂∂z∂∂x−i∂∂y∂∂x+i∂∂y−∂∂z)(Ψ1Ψ2)=E(Ψ1Ψ2) (8)
wherefrom we obtain the following system of equations from:
(∂∂z−ik)Ψ1+(∂∂x−i∂∂y)Ψ2=0(∂∂x+i∂∂y)Ψ1−(∂∂z+ik)Ψ2=0 (9)
wherek=Ec. It follows from (9) that:
Ψ1=(∂∂z−ik)−1(∂∂x−i∂∂y)Ψ2 (10)
Since the operators z±ik and x±iy commute, through (11) we come to the following relation:
(∂∂z+ik)(∂∂z−ik)Ψ1+(∂∂x−i∂∂y)(∂∂x+i∂∂y)Ψ1=0 (11)
In the same manner, from (9) and (11), we come to the relation:
(∂∂z−ik)(∂∂z+ik)Ψ2+(∂∂x+i∂∂y)(∂∂x−i∂∂y)Ψ2=0 (12)
The two last relations are of identical form and can be substituted by one unique relation:
(∂2∂x2+∂2∂y2+∂2∂z2+k2)Ψ(x,y,z)=0 (13)
If we take in (14) that k2=kx2+ky2+kz2 andΨ(x,y,z)=A(x)B(y)C(z), we come to the following equation:
which is fulfilled if:
Equations (16) can be easily solved and each of them has two linearly independent particular integrals:
A1=a1eixkx; A2=a2e−ixkx;B1=b1eiyky; B2=b2e−iyky;C1=c1eizkz; C2=c2e−izkz. (16)
Based on these expressions, we conclude that eigen-vector of single photon (Ψ1Ψ2) has the following form:
(Ψ1Ψ2)=(Deik→r→De−ik→r→) (17)
Since k is a continuous variable, the normalization of (18) mast be done to δ–function, wherefrom follows:
D2∫d3r→(e−ik→′r→eik→′r→)(eik→r→e−ik→r→)=δ(k→−k′→) (18)
Solving these integrals, we come to: 2 D2 (2π)3 = 1, wherefrom we get the normalized single photon eigen-vector as:
(Ψ1Ψ2)=14π3(eik→r→e−ik→r→) (19)
As it can be seen from (20), the components of single photon eigen-vector are progressive plane wave ~eikr and the regressive one ~eikr. Since we consider a free single photon, the obtained conclusion is physically acceptable.
### 2.3. Photons in cylindrical picture
In this section of first part of the paper we are going to analyze the same problem in cylindrical coordinates. Since solving of partial equation of (Δ+k2)Ψ=0 type in cylindrical coordinates requires more general approach than that which was used in Cartesian's coordinates, it is necessary to examine single photon eigen-problem in cylindrical system.
In order to examine this problem, we shall start from the equation (14) in which Laplacian 2x2+2y2+2z2Δ will be given in cylindrical coordinates (ρ,φ,z) whereρэ [0,], φэ[0,2π]andzэ [,+]. The Laplacian in cylindrical coordinates has the following form:
Δ=2ρ2+1ρρ+1ρ22ϕ2+2z2
and therefore (14) withΨ(x,y,z) => Φ(ρ,φ,z), reduces to:
∂2Φ∂ρ2+1ρ∂Φ∂ρ+1ρ2∂2Φ∂ϕ2+∂2Φ∂z2+k2Φ=0 (20)
The square of wave vector k will be separated into two partskx2+ky2+kz2=q2+kz2. On the basis of this the equation (21) can be written as follows:
∂2Φ∂ρ2+1ρ∂Φ∂ρ+q2Φ+1ρ2∂2Φ∂ϕ2=−∂2Φ∂z2−kz2Φ (21)
By the substitution:
Φ(ρ,ϕ,z)=F(ρ,ϕ)G(z) (22)
the equation (22) reduces to:
1F(∂2F∂ρ2+1ρ∂F∂ρ+q2F+1ρ2∂2F∂ϕ2)=−1G(d2G∂z2+kz2G) (23)
This equation is fulfilled if:
∂2F∂ρ2+1ρ∂F∂ρ+q2F+1ρ2∂2F∂ϕ2=0d2G∂z2+kz2G=0 (24)
Now we separate the variables by substitution:
F(ρ,ϕ)=X(ρ)S(ϕ) (25)
after which, the (25) goes over to:
1X(ρ2∂2X∂ρ2+ρ∂X∂ρ+q2ρ2X)=−1Sd2S∂ϕ2≡m2 (26)
Introduction of the variables separation constant m2 represents generalization with respect to approach used in previous section. Since the function S(φ)must be single-sign S(φ) =S(φ+2π) we must that m is integer, i.e. m= 0,±1, ±2,...
Relation (27) is separated into two differential equations:
d2Sdϕ2+m2S=0;d2Xdρ2+1ρdXdρ+(q2−m2ρ2)X=0. (27)
The equation (25) has two particular integrals:
G1=g1eizkz; G2=g2e−izkz (28)
while the solution of the equation (28) is:
Sm(ϕ)=s0eim ϕ (29)
By the substitution of argumentρ=bξ, the equation (28) reduces to
d2Xdξ2+1ξdXdξ+(q2b2−m2ξ2)X=0 (30)
and taking thatb=1q, we translate (31) into Bessel's equation with integer index m:
d2Xdξ2+1ξdXdξ+(1−m2ξ2)X=0 (31)
It means that the solution of (28) is the m–order Bessel’s function: Jm, i.e.
X(ρ)=a0Jm(qρ) (32)
Taking into account (29), (30) and (33), we obtain the components of single photon eigen-vector:
Φ1(ρ,ϕ,z)=D1Jm(qρ)eizkzeimϕ; Φ2(ρ,ϕ,z)=D2Jm(qρ)e−izkzeimϕ (33)
Since q and kz are continuous variables, while m is a discrete one the normalization of eigen-vector must be done partially to δ–functions and partially to Kronecker’s symbol. It means that normalization condition is the following:
(|D1|2+|D2|2)∫02πdϕe±i(m−m′)ϕ∫−∞+∞dze±i(kz−k′z)zz∫0∞ρdρJm(q′ρ)Jm(qρ)=q−1δnmδ(kz−k′z)δ(q−q′) (34)
Using formula for normalization of Bessel functions with integer index (Korn & Korn, 1961):
∫0∞dxxJm(k′x)Jm(kx)=1kδ(k−k′) (35)
the normalization condition reduces into:|D1|2+|D2|2=14π2. It means that normalized single photon eigen-vector in cylindrical coordinates is given by:
(Φ1Φ2)=(D1Jm(qρ)eimρeizkzD2Jm(qρ)eimρe−izkz) (36)
The first component Φ1 corresponds to photon (velocity +c), while second component Φ2 corresponds to anti-photon (velocity –c). From this formula we conclude that single photon eigen-vector components are progressive and regressive plane waves along z-axis. In the (x,y) planes components change periodically with polar angle φ and decrease by the rule ρ-1/2 with distance between the axis and envelope of cylinder. The last is concluded on the basis of asymptotic behaving of Bessel’s functions (Korn & Korn, 1961):Jm(ρ)sinρρ, whenρ . We have seen during the analysis of a photon in Cartesian’s coordinates that only zero values of parameters of variables separation are physically imposed. In cylindrical coordinates, due to physical reasons again, one parameter of variable separation had zero value, while the other has to be a square of integer. The last is necessary since the solution must be single-sign function.
### 2.4. Photon in spherical picture
The analysis of single photon eigen-problem in spherical coordinates, as it well be shown later, requires introduction of two variable separation parameters. We start from the equation (14), where the Laplace’s operator will be written down in spherical coordinates (r,θ,φ), whererÎ[0,], θÎ[0,π]andφÎ[0,2π]. In these coordinates it is of the form:
Δ=1r2∂∂r(r2∂∂r)+1r2sinθ∂∂θ(sinθ∂∂θ)+1r2sin2θ∂2∂ϕ2 (37)
It means that (14), withΨ(x,y,z) Ω(r,θ,φ), becomes:
1r2∂∂r(r2∂Ω∂r)+1r2sinθ∂∂θ(sinθ∂Ω∂θ)+1r2sin2θ∂2Ω∂ϕ2+k2Ω=0 (38)
In the first stage of variables separation, we shall take that:
Ω(r,θ,ϕ)=R(r)Q(θ,ϕ) (39)
after which substitution into (37), it goes over to:
1R[∂∂r(r2∂R∂r)+k2r2R]=−1Q[1sinθ∂∂θ(sinθ∂Q∂θ)+1sin2θ∂2Q∂ϕ2]=Λ2 (40)
where Λ2 is the variable separation parameter. Double equality in (39) gives two equations:
d2Rdr2+2rdRdr+(k2−Λ2r2)R=01sinθ∂∂θ(sinθ∂Q∂θ)+1sin2θ∂2Q∂ϕ2+Λ2Q=0 (41)
It should be noted that equation (40) represents eigen-problem of L^22 operator. It means that Λ2 determines orbital quantum numbers. In this equation we shall take that:
Q(θ,ϕ)=T(θ)S(ϕ) (42)
after this substitution, which goes over to:
1B[sinθ∂∂θ(sinθ∂T∂θ)+TΛ2sin2θ]=−1S∂2S∂ϕ2=m2 (43)
In this double equality the variable separation parameter m must be integer since the solution S(φ)must be single-signed function. The same requirement appeared in the previous section where single photon vas analyzed in cylindrical coordinates. The equation (42) gives two second order differential equations:
d2Sdϕ2+m2S=0d2Tdθ2+cotθdTdθ+(Λ2−m2sin2θ)T=0 (44)
When the solution (43) is:
Sm(ϕ)=s0eimϕ; m= 0,±1,±2, …, (45)
the equation (43) is associated Legendre’s equation (Gottifried, 2003; Davidov, 1963). The complete procedure of solving of this equation cannot be found in literature. Instead of the general solving procedure of the equation (43) is solved for m = 0. Its solutions are Legendre’s polynomials (Korn & Korn, 1961; Janke, et al., 1960). Differentiating these polynomials m-th times it was possible to conclude that solution (43) can be expressed through m-th Legendre’s polynomials derivations.
In order to avoid such an artificial solving of the equation (43), we shall expose, briefly, its solving by means of potential series. This solving procedure may be comprehended as methodological contribution of this part of the paper. At the first stage, we translate the equation (43) into algebraic form by means of substitution of argumentcosθ=ζ:
(1−ζ2)d2Bdζ2−2ζdBdζ+(ζ2−m21−ζ2)B=0; ζ[–1,+1] (46)
The term m21ζ2 in (45) does not allow the solving of this equation by means of potential series. Consequently this term must be eliminated from the equation. The strategy of elimination is the following: by the substitution ofT=UּV, where U is an arbitrary function, the equation (45) reduces to the same form but with arbitrary constant in linear function with is multiplied by first derivative of V function. This arbitrary coefficient will be taken in the form 2(2s+1)where s is arbitrary. Arbitrary constant s will be determined in a way which eliminates the term m21ζ2 from equation for V function. By the described strategy the (45) becomes:
(1−ζ2)d2Vdζ2−2(2s+1)ζdVdζ+(Λ2−2s−4s2)V=0 (47)
This equation is suitable for solving by means of potential series. Arbitrary function U is given byU=(1ζ2)S, wheres= ±m/2. This means that function T has the form:
T=(1−ζ2)SV (48)
Since ζ[1,+1]the exponent s must not be negative since T would then have singularities in ζ= ±1 not allowing the normalization. Fortunate circumstance is that the exponent of the function ζ2has ± sign. This means that for m> 0can be takens= +m/2=|m|/2. Ifm< 0, we takes= m/=|m|/2. Based on this reasoning the equation (46) becomes:
(1−ζ2)d2Vdζ2−2(|m|+1)ζdVdζ+[Λ2−|m|(|m|+1)]V=0 (49)
The solution of this equation will looked for in the form of potential series:
V=∑n=0∞vnζn (50)
,
after which substitution in (48) we obtain recurrent formula for series coefficients:
vn+2=−Λ2−(n+|m|)(n+|m|+1)(n+1)(n+1)vn; n= 0,1,2, … (51)
Here arises a dilemma whether to leave the whole series or to cut it and retain a polynomial instead of series. In order to solve this dilemma, we shall analyze a special case of formula (50) whenm= Λ = 0. In this case formula (50) becomes:
vn+2=nn+2vn; n= 1,3,5, …, (52)
wherefrom it turns out thatvn=v12n+1, and this means that series solution (49) becomes:
V=ζ+ζ33+ζ55≡∫dζ1−ζ2=12lnζ−1ζ+1 (53)
From this formula is obvious that the series has singularities for ζ = ±1. This resolves above mentioned dilemma: the series must be cut and the polynomial obtained in this way must be taken as solution. From the formula (50) it is clear that the series will be cut if:
Λ2=l(l+1) ; l= 0,1,2, ... (54)
Now is clear that the series is cut whenl= |m|+n, wherefrom it follows that the degree of polynomial is l=|m|nand that quantum number m per module must not exceed l:|m|l. The obtained polynomials of l|m|degree are called the associated Legendre’s polynomials (Korn & Korn, 1961; Janke, et al., 1960) and by means of them T function is expressed as:
Tl,|m|(ζ)=(1−ζ2)|m|/2Ll−|m|(ζ) (55)
The product of functions (44) and (54) normalized per angles gives spherical harmonics (Gottifried, 2003; Davidov, 1963):
Yl,|m|=(−1)l+|m|2ll!eimϕ2π2l+12(l−|m|)!(l+|m|)!sin|m|θdl+|m|d(cosθ)l+|m|(sinθ)2l (56)
Finally we shall solve the equation (40) in which Λ2 is substituted byl(l+1). It means that it goes over to:
d2Rdr2+2rdRdr+(k2−l(l+1)r2)R=0; rÎ[0,∞) (57)
Substituting the function R with r1/2J(r)and substituting the argument r by ρ/k, we translate last equation into Bessel’s equation (Korn & Korn, 1961; Janke, et al., 1960) with l+1/2index having two linearly independent particular solution Jl+1/2(kr)andJl1/2(kr). Consequently the solutions of (40) are:
R1=w1(kr)−1/2Jl+1/2(kr)R2=w2(kr)−1/2J−l−1/2(kr) (58)
It is necessary for further to quote behaving of Bessel’s functions with half integer indices. It can be easily shown that:
J1/2(kr)=sinkrkrJ−1/2(kr)=coskrkr (59)
As well as using recurrent formula for Bessel’s functions (Janke, et al., 1960):
ddxJp=12Jp−1−12Jp+1 (60)
and taking that p= +1/2 andp= 1/2, we obtain respectively:
J3/2(x)=x−3/2sinx−x−1/2cosxJ−3/2(x)=−x−3/2cosx−x−1/2sinx (61)
Due to the factor x3/2functions J±3/2have strong singularities in zero so that they cannot be normalized in the interval0 r< . Due to the same reasons neitherJ±5/2,J±7/2, etc. cannot be normalized. It can be concluded that only solutions for A which are proportional to J±1/2have chances to be normalized. Those solutions are:
R1=WrsinkrkrR2=Wrcoskrkr (62)
The very important conclusion of this analysis is: only free photons with zero orbital momentum have chances to be normalized exist. For l> 0photon eigen-vector cannot be normalized.
We shall now examine whether the components of photon eigen-vector proportional to R1 and R2 can be normalized. Those components are:
Ω1=WrY00(θ,ϕ)sinkrkrΩ2=WrY00(θ,ϕ)coskrkr (63)
The normalization condition is the following:
W2∫02πdϕ∫0πdθsinθ|Y0,0(θ,ϕ)|2∫0∞drr2[J1/2(k′r)J1/2(kr)+J−1/2(k′r)J−1/2(kr)]==W2k′k∫0∞drcos(k−k′)r=1k2δ(k−k′). (64)
It is not difficult to show that:0drcos(kk)r=0, so that the condition (63) becomes meaningless. This means that even for l = 0 photon eigen-vector cannot be normalized.
The last possibility for normalization free photons eigen-vector is so called box quantization method. In this method the sphere is substituted by cube enveloping it and cyclic boundary conditions are required:eikr=eik(r+L), wherefrom it follows that wave vector is quantized:
k=2πLn; n= 1,2,3, ... (65)
Sincek=2π/λ, it gives that:
L = n λ; n= 1,2,3, ... (66)
It is seen that the first harmonic of electromagnetic waves has the wave length equal to the cube edge.
Photon energy is determined in the standard way:
E=ℏck=h2πc2πLn=hν0n; ν0=cL (67)
This expression for energy is in full accordance with Plank’s hypothesis (Planck, 1901).
In the normalization condition (63) the following translations has to be used:
δ(k−k′)→δnn→n=m1; ∫0∞dr→∫0Ldr=L; cos(k−k′)rkk′→cos2πL(n−m)r2πLnm→n=mL2πn. (68)
Combining this and (63) we obtain that the normalization constant isW=12πn. On the basis of this the normalized photon eigen-vector is given by:
(Ω1Ω2)=12πn(Y00(θ,ϕ)r−1/2J1/2(2πLnr)Y00(θ,ϕ)r−1/2J−1/2(2πLnr))=n21(2πn)3/2(sin2πLnr2πLnrcos2πLnr2πLnr); n=1,2,3,... (69)
As it can be seen the analysis of single photon eigen-problem in spherical coordinates has shown it orbital momentum of photon is equal to zero and that the spin S= 1/2is its unique rotational characteristics (Yao, et al., 2005). Physically it is fully understandable that orbital momentum of a free photon is equal to zero since it moves along the straight line. On straight line photon radius-vector r and its momentum p=mfr˙ are parallel and this gives thatl=r×p=0.
## 3. Free photon as a system with complex internal dynamics
In the second part of this work the free photon Hamiltonian will be linearized using Pauli’s matrices. Based on the correspondence of Pauli matrices kinematics and the kinematics of spin operators, the unitary transformation of this form (equivalent Hamiltonian), will be analyzed by the method of Green’s functions. Since photon is relativistic quantum object the exact determining of its characteristics is impossible. It is the reason for series of experimental works in which photon orbital momentum, which is not integral of motion, will be theoretically investigated.
### 3.1. Introduction
The fact that photon Hamiltonian is not a linear operator has a set of consequences that have not been studied sufficiently so far. The main reason is that photon characteristics have been mainly examined by means of Klein-Gordon’s equation (Gottifried, 2003; Davidov, 1963; Messiah, 1970; Davydov, 1976), which represents eigen-problem of photon Hamiltonian square. In this part of our paper we shall linearized photon Hamiltonian and examine some of photon characteristics witch follow from linearized Hamiltonian. The analogy with Dirac’s approach to the problem of electrons will be used (Gottifried, 2003; Dirac, 1958). Firstly will be examined integrals of motion of free photon and will be shown that the photon integral of motion is not orbital momentum. It will be shown that the integral of motion is total momentum being the sun of orbital one and spin momentum.
The evaluated Green’s function has given possibility for interpretation of photon reflection as a transformation of photon to anti-photon with energy change equal to double energy of photon and for spin change equal to Dirac’s constant (Dirac, 1958; Messiah, 1970). Since photon is relativistic quantum object the exact determining of its characteristics is impossible.
The discussion of obtained results and their comparison to the experimental data will be done at the last part.
### 3.2. Linearized photon Hamiltonian
We shall not deal with this eigen-problem in further of this paper. Instead of this we shall look for integrals of motion, i.e. those operators that commute with free-photon Hamiltonian (7). It is obvious that any function depending on momentum components represents an integral of motion, but this fact is not of physical interest.
It is of particular importance whether orbital momentum:
L→^=(L→^00L→^)L→^=r→×p→^ (70)
is photon integral of motion, since in non-relativistic quantum mechanics operator L^ is integral of motion of electron (Messiah, 1970; Davydov, 1976). The components of orbital momentum are given as follows:
L^x=yp^z−zp^y; L^y=zp^x−xp^z; L^z=xp^y−yp^x (71)
If we use commutation relations for components of radius vector and the components of momentum:[xi,pj]=iħδij, i,jÎ(x,y,z)and look for commutators of (69) with Hamiltonian (7), we come to the following relations:
[L^x,H^]=±iℏc(p^zβ^−p^yχ^);[L^y,H^]=±iℏc(p^xχ^−p^zα^);[L^z,H^]=±iℏc(p^yα^−p^xβ^) (72)
based on which it follows that orbital momentum is not a free photon integral of motion.
It should be pointed out that signs in (70) are obtained on the basis of obvious symmetry properties H^(r)=H^(r) andL(r)=L(r), where r is radius-vector.
In order to find some rotation characteristics that commute with a free photon Hamiltonian, we shall first show that commutation relations for matrices α^,β^ andχ^, given in section 2.1 by expression (6), are:
[α^,β^]=2iχ^;[χ^,α^]=2iβ^;[β^,χ^]=2iα^ (73)
while commutation relations for spin components (Dirac, 1958; Messiah, 1970):
[S^x,S^y]=iℏS^z;[S^z,S^x]=iℏS^y;[S^y,S^z]=iℏS^x (74)
are very similar to (71). Comparing (71) to (72) we can establish the correspondence between spin operator components and matrices α^,β^ andχ^:
S^x=ℏ2α^; S^y=ℏ2β^; S^z=ℏ2χ^ (75)
Commutators of matrices α^,β^ and χ^ with Hamiltonian are given by:
[α^,H^]=∓2ic(p^zβ^−p^yχ^);[β^,H^]=∓2ic(p^xχ^−p^zα^);[χ^,H^]=∓2ic(p^yα^−p^xβ^) (76)
We shall now look for a commutator of component J^x of total momentum, with photon Hamiltonian i.e. withH^(r). Using upper signs in formulas (70) and (74) we obtain:
[J^x,H^(r→)]=[(L^x+S^x),H^(r→)]=[(L^x+ℏ2α^),H^(r→)]=[L^x,H^(r→)]+ℏ2[α^,H^(r→)]= =iℏc(p^zβ^−p^yχ^)+ℏ2(−2ic)(p^zβ^−p^yχ^)=0. (77)
For lower signs in formulas (70) and (74)[1] - , we have:
[J^x,H^(−r→)]=[(L^x+S^x),H^(−r→)]=[(L^x+ℏ2α^),H^(−r→)]=[L^x,H^(−r→)]+ℏ2[α^,H^(−r→)]= =iℏc(p^zβ^−p^yχ^)+ℏ2(2ic)(p^zβ^−p^yχ^)=0. (78)
It can be proved, in the same manner, that both y and z components of total momentum J^=L^+S^ commute with photon Hamiltonian (the expression (7) with sign +, i.e. H^(r)will be called photon Hamiltonian). The expression (7) with sign –, i.e. H^(r)will be called anti-photon Hamiltonian. In the same manner can be proved that y and z components of total momentum J^=L^S^ commute with anti-photon Hamiltonian.
The final conclusion is the following: total momentum L^+S^ is integral of motion for photon, while total momentum L^S^ is integral of motion for anti-photon. Up to now we have the proof that total momentum L^+S^ is free photon integral of motion, but we do not know what magnitude of photon spin is.
If spin isS= 1/2, then the following relation is valid:
(S^x−iS^y)2=0 (79)
For spin S> 1/2the exponent in (77) is higher than 2, i.e. it must be 3,4,... etc. In (77) we shall go over to matrices α^ and β^ through relation (73). So we obtain:
(S^x−iS^y)2=ℏ24(α^−iβ^)2=ℏ24[α^−β^2+2i(α^β^+β^α^)]=0 (80)
(in the last stage of the upper proof the relations (72) from section 2.1 were used). Consequently, we can conclude that free photon integral of motion represents a total momentum which is the sum of orbital momentum and spin momentum which corresponds to the case whenS= 1/2.
In the same way can be concluded that anti-photon integral of motion is the sum of orbital momentum and spin momentum which corresponds to spinS= 1/2. It should be noticed that negative spin is rather senseless concept so that ±Sreally means±Sz, whereSz=ħ/2.
In nonrelativistic quantum mechanics (Gottifried, 2003; Davidov, 1963) the conclusion that J^ is integral of motion would mean that energy and total momentum of the quantum object can be measured simultaneously and exactly. Since photon is relativistic object (Berestetskii, et al., 1982) the maximal exactness of measuring of photon momentum is given byΔpΔt~ħ/c, and consequently energy and total momentum can be determined with an error of the orderΔEΔt~ħ. The orbital momentumL^, as it follows from (70), is not integral of motion, but for relativistic object this fact is not essential, since for relativistic objects absolutely exact determining of physical characteristics is in possible.
Considering the correspondence (73), photon Hamiltonian which is given by H^=c(α^p^x+β^p^y+χ^p^z) can be expressed by means of spin operators in the following form:
H^=2cℏ(S^xp^x+S^yp^y+S^zp^z) (81)
.
The obtained form of photon Hamiltonian, which includes operators of translation moment P^ and spin S^ suggest that a free photon has wealthy internal dynamics that consists of mutual action of its translation and spin characteristics. This “internal life” will be examined further in the paper.
### 3.3. Unitary transformation of photon Hamiltonian
Photon Hamiltonian (78) represents bilinear form in which photon momentum operators are multiplied by spin operators. Since momentum characterizes translation photon motion, and spin characterizes rotation, it is obvious that the internal dynamic structure of a photon is determined by both its translation and rotation characteristics, and that their interaction – considering the form of Hamiltonian (78), leads to hybridization of excitations (Agranovich, 2009). Spin operators in (78) correspond to spin S = 1/2 and its can then is represented by Pauli’s operators in the following manner (Tyablikov, 1967):
S^x−iS^y=ℏP+; S^x+iS^y=ℏP; 12−S^z=ℏP+P (82)
Pauli’s operators fulfill commutation relations:
[Pi,Pj+]=[1−2Pi+Pj]δij; [Pi,Pj]=[Pi+,Pj+]=0;Pi2=Pi+2=0; (P+P)e.v={0;1. (83)
After substitution of (79) in (78) (in this formula sign + is retained), we obtain the following form of Hamiltonian:
H^=cp^z+c[(p^x−ip^y)P+(p^x+ip^y)P+−2p^Pz+P] (84)
This conversion to Pauli operators has been made because the physical picture of processes is clearer through operator’s creation and annihilation of excitation.
Operators of moments are linear in operators of creation and annihilation of photon:P~A+A+, so it can easily be concluded that mean value of photon Hamiltonian over states 1n!(A+)nP+|0 is equal to zero. This means that the method of theory of perturbation would be inappropriate for Hamiltonian (81) analysis. This is why we would make unitary transformation of photon Hamiltonian with the goal to bring it into the form more suitable for calculation than the form (81), i.e. we shall go to equivalent Hamiltonian given by:
H^eq=eW^H^e−W^ (85)
where:
W^=ik→r→+ρ(P−P+)+iλP+P (86)
and ρ and λ are real parameters.
Equivalent Hamiltonian is found using Weil’s identity (Tošić, 1978):
eW^D^e−W^=∑n=0∞(1)nn![W^,[W^,...[W^,...[W^,D^]]...]︸n−times (87)
It has included the terms of the following type:P+P+, PP+andP+P. Undetermined parameter λ has been determined so that the member proportional to PP+ disappear from equivalent Hamiltonian. The final result of the described procedure is as follows:
H^eq=E0+H^+H^S (88)
where H^ is starting Hamiltonian, and
E0=ℏc(kxsin2ρ+kzcos2ρ)H^S=−g(P+P+)+2aP+P (89)
where are:
g=ℏcky2+kx2cos22ρ+kz2sin22ρ−kxkzsin4ρ; a=ℏc(kxsin2ρ+kzcos2ρ) (90)
We shall further analyze free photon behavior using method of Green’s functions (Tyablikov, 1967; Tošić, 1978; Rickayzen, 1980; Mahan, 1990; Šetrajčić, et al., 2008). Hamiltonian E0 is irrelevant in Green function techniques. Starting HamiltonianH^, as we have already concluded earlier, has zero mean value over states1n!(A+)nP+|0. This is why we shall exclude it from calculations. The analysis of photon internal processes will be made with HamiltonianH^S.
### 3.4. Green’s function of free photons
Since Pauli operators figure in H^S Hamiltonian without various configuration indices, the analysis of spin processes in a free photon will be made by means of anticommutator Pauli Green function:
Γ(t)=〈〈P(t)|P+(0)〉〉=Θ(t)〈P(t)P+(0)+P+(0)P(t)〉 (91)
where Θ(t)is Heaviside’s step function (Tyablikov, 1967; Tošić, 1978; Rickayzen, 1980). Correlator of anticommutator Pauli’s Green’s function contains mean value of anticommutator of Pauli’s operator of the same configuration index, and according to (80) it is equal to one. This fact simplifies evaluation of mean values by means of spectral intensity of Green function.
Differentiating Γ(t) per time and using equation of motion for operator P, we come to the following equation:
iℏdΓ(t)dt=iℏδ(t)+2aΓ(t)+2gΔ(t) (92)
The Green’s function of type: const|P+are equal to zero. The function Δtis given by:
Δ(t)=〈〈P+(t)P(t)|P+(0)〉〉 (93)
Using the same procedure, for defining function Δ(t)we obtain the following equation:
iℏdΔ(t)dt=gΓ(t)−gF(t) (94)
where:
F(t)=〈〈P+(t)|P+(0)〉〉 (95)
with defining following equation:
iℏdF(t)dt=−2gΔ(t)−2aF(t) (96)
In differential equations (88), (90) and (92), Furrier’s transformations time-frequency are then made:
f(t)=∫−∞+∞dte−iωtf(ω); f≡(Γ,Δ,F); δ(t)=12π∫−∞+∞dte−iωt (97)
so we obtain the system of algebraic equations:
(E−2a)Γ(ω)−2gΔ(ω)=iℏ2π; Δ(ω)=g[Γ(ω)−F(ω)];EF(ω)=−2[gΔ(ω)+aF(ω)]. (98)
Solving this system of equations, we find that:
Γ(ω)=iℏ2πE2+2aE−2g2(E2−E02)2 (99)
where:
E0=2a2+g2=2ℏck (100)
In order to determine spectral intensity of function Γ, it is necessary to break down the right side of the formula (87) into common fractions. So, we obtain the following:
Γ(ω)=i2π[2g2E021ω+(12−g2E02+aE0)1ω−ω0+(12−g2E02−aE0)1ω+ω0], (101)
where: ω = E/ħandω0= E0/ħ. Since function Γ is anticommutator function, its spectral intensity is given by the formula (Tyablikov, 1967; Tošić, 1978; Rickayzen, 1980):
ΙΓ(ω)=Γ(ω+iδ)+Γ(ω−iδ)eℏωkBT+1; δ→+0, (102)
and using Dirac’s formula:
1ω−ωk±iδ=P.V.{1ω−ωk}∓iπδ(ω−ωk) (103)
where P.V. denotes principal value of integral, we find the explicit expression for spectral intensity:
ΙΓ(ω)=2g2E02δ(ω)eℏωkBT+1+(12−g2E02+aE0)δ(ω−ω0)eℏωkBT+1+(12−g2E02−aE0)δ(ω+ω0)eℏωkBT+1 (104)
Now we can defined the expression for correlation function of a free photon as:
〈P+(0)P(t)〉≡∫−∞+∞dωe−iωtΙΓ(ω)=2g2E0212+(12−g2E02+aE0)e−iω0teℏω0kBT+1+(12−g2E02−aE0)eiω0teℏω0kBT+1 (105)
Next, we can calculate expression for concentration of spin excitations of a free photon. It is obtained from (101), if we take in it that t = 0, i.e.
〈P+P〉=12−aE0tanhℏckkBT (106)
Combining formulae for a over formula (86), and E0 from (96), and converting to sphere coordinate system, we find that:
xxxx
aE0=12(sin2ρsinθcosϕ+cos2ρcosθ) (107)
xxxx
In accordance with this and formula (102), we get the following expression for ordering parameter of spin subsystem in a free photon:
σ=1−2〈P+P〉=(sin2ρsinθcosϕ+cos2ρcosθ)tanhℏckkBT (108)
The set of results of this section requires some explanations. The most interesting results is that energy for spin translation from ħ/2to ħ/2is2ħck. This can be explained on the basis of measuring process in which incident photon bean is reflected by measuring devices. The momentum of incident phonon is ħkwhile the momentum reflected phonon is –ħk. So we obtain the change of photon momentumΔp= ħk(ħk) = 2ħk, and consequently the energy changeΔE= 2ħck. The energy ħckcorresponds to anti-photon, so that we can consider the described process as a transformation of photon to anti-photon. In this process the spin change takes place, also (the Greens function Γ(t)=P(t)|P+(0) was calculated). Since photon and anti-photon spins have opposite signs the change the spin isΔS=ħ/ (ħ/2) = =ħ. The value of ΔSis equal the value ħ and this is eigen-value of spin s = 1. This is the reason for behaving of photon as particle with spin s = 1.
The polar and azimuthally dependences of ordering parameter comes from the fact that incident bean must not be always orthogonal to the plane of measuring device.
## 4. Conclusions
1. The analysis of single photon behaving in coordinate systems of various geometries has shown the following:
2. The last result shows that linearization of photon Hamiltonian gives more complete picture of single photon than Kline-Gordon’s approach.
3. Concluding the exposed analysis we shall try to connect the results obtained in series of experimental investigation of photon orbital momentum (Beth, 1936; Leach, et al., 2002; Allen, et al., 1992; Allen, 1966; He, et al., 1995; Friese, et al., 1996; Markoski, et al., 2008; van Enk & Nienhuis, 2007; Santamato, et al., 1988; O’Neil, et al., 2002; Volke-Sepulveda, et al., 2002). We shall not describe all quoted experiments. Instead of it we shall describe the essential idea: the orbital momentum of photon was determines from the changes of torque of rotating particles. These changes where lied in some interval, so that the values of orbital momentum have had determined dispersion. As it vas said at the end of first section, such result is expectable for relativistic objects, in this case for photons. The azimuthally dependence of measured results is also predicted by the theory exposed in last Section.
Ending this analysis it should by noticed out that on the bases of given analysis the photon reflection can be considered as a transformation of photons to anti-photons.
## Notes
[1] - this corresponds to negative photon energies, i.e. corresponds to
## Acknowledgements
Investigations whose results are presented in this paper were partially supported by the Serbian Ministry of Sciences (Grant No 141044A) and by the Ministry of Sciences of Republic of Srpska.
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33 - K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, K. Dholakia, 2002 Orbital angular momentum of a high-order Bessel light beam J.Opt.B: Quantum Semiclass.Opt. 4 April 2002), 8289 | {"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": 0.9571391344070435, "perplexity": 2077.8190369244776}, "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-2015-14/segments/1427131297622.30/warc/CC-MAIN-20150323172137-00082-ip-10-168-14-71.ec2.internal.warc.gz"} |
http://eprint.iacr.org/2001/075 | ## Cryptology ePrint Archive: Report 2001/075
Pseudo-Random Functions and Factoring
Moni Naor and Omer Reingold and Alon Rosen
Abstract: Factoring integers is the most established problem on which cryptographic primitives are based. This work presents an efficient construction of {\em pseudorandom functions} whose security is based on the intractability of factoring. In particular, we are able to construct efficient length-preserving pseudorandom functions where each evaluation requires only a {\em constant} number of modular multiplications per output bit. This is substantially more efficient than any previous construction of pseudorandom functions based on factoring, and matches (up to a constant factor) the efficiency of the best known factoring-based {\em pseudorandom bit generators}.
Category / Keywords: pseudo-randomness, number theory
Publication Info: An extended abstract has appeared in STOC 2000. | {"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": 0.9002086520195007, "perplexity": 1952.4335991466971}, "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/1432207928423.12/warc/CC-MAIN-20150521113208-00279-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://link.springer.com/article/10.1007%2FBF02317423 | , Volume 37, Issue 3, pp 307-313
Measurement of deformations on concrete subjected to compression using image correlation
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Abstract
Because the nature of failure in concrete is complicated due to the material heterogeneity, a robust measuring method is essential to obtain reliable deformation data. A nondestructive displacement evaluation system using a digital image cross-correlation scheme, often called computer vision, is developed to make microscopic examinations of the fracture processes in concrete. This is a full-field measuring method that gives an accuracy within the micron range for a 100 mm × 75 mm viewing area. A feedback signal that combines the lateral and axial deformations provides a well-balanced imaging rate both before and after the peak load. Displacement vector diagrams or displacement contour maps of concrete reveal highly nonuniform deformations even in the elastic range. The processes of fracture in concrete are well defined at different deformation levels. | {"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": 0.8083981275558472, "perplexity": 2364.0490694184614}, "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-2013-48/segments/1386164023947/warc/CC-MAIN-20131204133343-00058-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://scoskey.org/presentation/martins-axiom-and-applications/ | Boise Set Theory Seminar, January 2018
Abstract: In this talk I presented the notation and machinery of forcing, the statement of Martin’s axiom, and some well-known applications in the area of Baire category and measure theory. | {"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": 0.94384765625, "perplexity": 941.9040251686896}, "config": {"markdown_headings": true, "markdown_code": false, "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/1537267163326.85/warc/CC-MAIN-20180926041849-20180926062249-00398.warc.gz"} |
https://socratic.org/questions/561beefb11ef6b52d4ce3e98 | Chemistry
Topics
# Question e3e98
Oct 12, 2015
Here's what I got.
#### Explanation:
The trick here is to use the given mole ratio to find a relationship between the ${\text{Fe}}^{2 +}$ and ${\text{Fe}}^{3 +}$ ions, on one side, and the ${\text{O}}^{2 -}$ ions on the other hand.
You know that the compound contains a mixture of ${\text{Fe}}^{3 +}$ and ${\text{Fe}}^{2 +}$ ions, but you don't know how many of each you have.
This is where the charge of the compound comes into play. The compound must be neutral, so the $\left(2 -\right)$ charge of the oxygen must be balanced by the overal charge of the iron cations.
To make the calculations as simple as possible, let's say that you have 100 moles of the compound, which will contain
• 93 iron(II) and iron(III) ions
• 100 ions of oxygen
Let's say that you have $x$ iron(II) ions and $y$ iron(III) ions. You can say that
$x + y = 93$
Now focus on the charge. You have 100 moles of ${\text{O}}^{2 -}$, which means that you must have
${\underbrace{x \cdot \left(2 +\right)}}_{\textcolor{b l u e}{\text{total charge of iron(II) ions")) + overbrace(y * (3+))^(color(red)("total charge of iron(III) ions}}} = | 100 \cdot \left(2 -\right) |$
Use the first equation to get $x = 93 - y$, then replace $x$ in the second equation
$2 \cdot \left(93 - y\right) + 3 y = 200$
$186 - 2 y + 3 y = 200$
$y = 200 - 186 \implies y = 14$
Therefore, you have $14$ iron(III) ions and
$93 - 14 = 79 \to$ iron(II) ions
Now, I don't know if you want to determine the percent composition of iron(III) ions in the total ions of iron or in the compound, so I'll show you both.
("14 Fe"^(3+)color(red)(cancel(color(black)("ions"))))/(93color(red)(cancel(color(black)("iron ions")))) xx 100 = 15.1% -> among iron ions
or
("14 Fe"^(3+)color(red)(cancel(color(black)("ions"))))/(193color(red)(cancel(color(black)("ions")))) xx 100 = 7.25% -># among total number of ions
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https://www.arxiv-vanity.com/papers/hep-th/9812239/ | PUPT-1828
MIT-CTP-2810
hep-th/9812239
Supergravity currents and linearized interactions
for Matrix Theory configurations
with fermionic backgrounds
Washington Taylor IV and Mark Van Raamsdonk
Center for Theoretical Physics
MIT, Bldg. 6-306
Cambridge, MA 02139, U.S.A.
Department of Physics
Joseph Henry Laboratories
Princeton University
Princeton, New Jersey 08544, U.S.A.
The leading terms in the long-range interaction potential between an arbitrary pair of matrix theory objects are calculated at one-loop order. This result generalizes previous calculations by including arbitrary fermionic background field configurations. The interaction potential at orders and is shown to correspond precisely with the leading terms expected from linearized supergravity interactions between arbitrary objects in M-theory. General expressions for the stress tensor, membrane current and 5-brane current of an arbitrary matrix configuration are derived, including fermionic contributions. Supergravity effects which are correctly reproduced include membrane/5-brane interactions, 0-brane/6-brane interactions, supercurrent/supercurrent interactions and the spin contributions to moments of the supergravity currents. The matrix theory description of the supergravity stress tensor, membrane current and 5-brane current are used to propose an explicit formulation of matrix theory in an arbitrary background metric and 3-form field.
December 1998
## 1 Introduction
Over a decade ago, a simple model of supersymmetric matrix quantum mechanics [1, 2, 3] was proposed as a regulated form of the quantum supermembrane theory in 11 dimensions [4, 5, 6]. Interest in this model declined when it was found to have a continuous spectrum [7], which seemed incompatible with a first-quantized interpretation of the theory in 11D. In 1996, interest in this “Matrix Theory” was rekindled when Banks, Fischler, Shenker and Susskind (BFSS) proposed that it gives a complete description of light-front M-theory in the large limit [8]. They pointed out that the continuous spectrum is natural since the theory should be understood as a second-quantized theory in 11 dimensions. BFSS argued that M-theory interactions, including those of classical supergravity, should arise as quantum effects in matrix theory. They gave as one piece of evidence for their conjecture the result that the leading long-range interaction between a pair of gravitons in 11D supergravity can be reproduced by a one-loop calculation in matrix theory [9].
In the two years following the BFSS conjecture, it has become clear that matrix theory encodes a remarkable amount of the structure of M-theory and 11D supergravity (for reviews, see [10, 11, 12, 13]). Matrix theory configurations corresponding to supergravitons [8, 14], membranes [6, 8] and fivebranes [15, 16] have been identified. The interactions between objects in Matrix theory have been found to agree with supergravity in a variety of situations. Two-graviton interactions have been shown to agree with supergravity up to terms of the form [17, 18, 19]. The spin-dependent interactions between two gravitons have been checked to leading order in for each power of the fermion fields encoding the graviton spin by performing one-loop matrix theory calculations [20, 21, 22, 23, 24]. It has been shown that the first nonlinear gravitational correction to 3-graviton scattering is correctly reproduced in a two-loop matrix theory calculation [25, 26, 27, 28, 29]. A subset of terms in the -graviton interaction potential have been reproduced by an -loop matrix theory calculation, although there is an indication that some 3-loop matrix theory terms may disagree with 4-graviton interactions in supergravity [29].
For more general matrix theory configurations, progress has been made towards identifying the structure responsible for the agreement between matrix theory and supergravity at leading orders. It was shown in [30] that the supergravity potential between an arbitrary pair of bosonic M-theory objects arising from the exchange of quanta with zero longitudinal momentum is exactly reproduced by terms in the one-loop matrix theory potential. This result was achieved through the identification of matrix theory quantities corresponding to the supergravity stress-energy tensor, membrane current and fivebrane current. Linearized interactions between multipole moments of the supergravity currents were shown to be reproduced correctly by an infinite series of terms in the effective matrix theory potential of the form .
In this work, we extend the results of [30] to a pair of completely general configurations, including non-vanishing fermionic fields in our matrix theory background. As in [30], we do not require that the matrix theory configurations preserve any supersymmetry. We demonstrate in complete generality that the on-shell matrix theory potential vanishes below and that at orders and the matrix theory calculation reproduces exactly the leading-order interactions expected from supergravity arising from the exchange of gravitons, gravitinos, and three form quanta with zero longitudinal momentum. In addition to the interactions considered in [30], these include a supercurrent-supercurrent interaction mediated by gravitino exchange, as well as membrane-fivebrane and zerobrane-sixbrane interactions (previously considered in [31, 32]). We give explicit matrix expressions for the integrated stress tensor, membrane current and 5-brane current of general matrix theory objects, including the fermionic contributions to these currents. We identify the fermionic contribution to the first moments of the currents, generalizing the previously known result for the spin contribution to graviton angular momentum [20]. We are also able to identify matrix expressions for the fermionic components of the supercurrent as well as a 6-brane current and its first moments.
One motivation for the work described in this paper is the goal of developing a systematic formalism for describing general -body interactions in matrix theory in terms of structures such as the stress tensor and membrane current which have natural interpretations in supergravity. The nonlinear structure of gravity can be probed by studying 3-body processes in matrix theory. As was mentioned in [27], however, knowledge of the full two-body interaction between objects with nonzero fermionic degrees of freedom is a key step towards carrying out a general calculation of 3-body interactions even between three purely bosonic configurations.
Another application of the results in this paper is to the formulation of matrix theory in a general metric and 3-form background. If the matrix theory conjecture is correct, then the effective action for matrix theory in a wide class of backgrounds can be determined by including extra background blocks in the matrices and integrating out the off-diagonal fields connecting to the background. Armed with a precise knowledge of the form of the matrix theory stress current, membrane and 5-brane currents, we propose a concrete algorithm for constructing the matrix theory action in a general background, and we explicitly give the leading terms for this action in the presence of a weak background field.
It has been proposed that the full set of matrix theory interaction terms which correspond to classical 2-body interactions in gravity should take the form of a nonabelian Born-Infeld theory [33, 34, 35]. Assuming this to be true, our result for the term in the effective 2-body potential should be related to a supersymmetric nonabelian Born-Infeld action. We compare our results to previous results on supersymmetric Born-Infeld theory [36, 37] and find that this correspondence seems to hold.
In Section 2 we calculate to order the complete one-loop matrix theory effective potential for a background corresponding to general widely separated systems. We also calculate the potential to order including all terms which are at most quadratic in the fermion backgrounds. As the calculations are somewhat involved, we present only a summary of some salient features in Section 2, leaving a more detailed account to Appendix A. The results for the effective potential are summarized in Section 2.4.
In Section 3 we describe the supergravity interactions at orders and which arise from the exchange of gravitons, gravitinos and 3-form quanta. We show that these interactions correspond precisely with the matrix theory potential computed in Section 2 when the proper identification is made of the matrix theory stress tensor, membrane current, 5-brane current, 6-brane current and fermionic components of the supercurrent. The expressions we find for the supergravity currents are summarized in subsection 3.6.
Section 4 contains a discussion of our results, a comparison to other related results in the literature, and some suggestions for how the results of this paper might be applied. In particular, we discuss the connection to higher-order terms in the nonabelian Born-Infeld theory, we briefly discuss the application to the general 3-body problem, we mention possible generalizations to higher-dimensional theories, and we give a concrete suggestion for a formulation of matrix theory in a general background using the matrix forms we have found for the supergravity currents.
## 2 Calculation of the effective action
We wish to study the Matrix Theory interaction between an arbitrary pair of isolated systems, whose centers of mass are separated at time by a distance which is large compared to the sizes of the two individual systems. In particular, we wish to calculate the matrix theory effective action around a background which is block-diagonal in both bosonic and fermionic matrices.
There are a number of approaches which can be used to perform such a calculation. The simplest approach is to use the quasi-static approximation to calculate the ground state energy of the harmonic oscillator modes corresponding to the off-diagonal degrees of freedom in the theory. This approach was used in [38] to compute the leading term in the interaction potential between a pair of purely bosonic matrix theory systems. Unfortunately, in the presence of fermionic backgrounds this approach cannot be applied in a straightforward fashion. The terms in the tree-level action which are quadratic in the off-diagonal fluctuations include products of bosonic and fermionic fluctuations, complicating the problem significantly. Furthermore, as we shall discuss in more detail, unlike the case of a purely bosonic background, in the case of a completely general background there are non-vanishing terms involving fermions which appear in the effective action below order . These terms vanish when we enforce the matrix theory equations of motion to calculate the effective potential between two physical systems; the fact that such terms appear already at order , however, makes the validity of the quasi-static approximation in the general case rather questionable.
Another approach one might consider using to calculate the effective potential for general backgrounds would be to find a supersymmetric completion of the bosonic potential of the form computed in [38]. Unfortunately, however, the supersymmetry transformations under which the tree level action is invariant are corrected by subleading terms [18]. Determining precisely how the supersymmetry transformations are modified seems to be just as difficult a problem as doing the full calculation of the effective action.
In this paper we chose to do the calculation using the most conceptually straightforward approach: an explicit summation over all one-loop diagrams in the chosen background. This approach leads to a rather lengthy but finite calculation. In this section we describe the tools used to do the calculation and give brief descriptions of each of the pieces of the calculations. More details are included in Appendix A for the reader interested in following the calculations in detail or carrying out analogous calculations themselves. The reader primarily interested in the results may wish to skip from Section 2.1 directly to the summary of results for the effective action in section 2.4
### 2.1 Action and propagators
We begin with the matrix theory action 111We use Euclidian conventions, taking , . Throughout the work, indices run from 1 to 9 while indices run from 0 to 9.
S = −12R∫dτTr{−DτXiDτXi+12[Xi,Xj][Xi,Xj]−(DclaXqua)2 +ΘαDτΘα−Θαγiαβ[Xi,Θβ]}
with a covariant background-field gauge fixing term
DclaXqua≡DτX0+i[Bi,Xi]
plus the corresponding ghost action not written here. We expand the bosonic and fermionic matrices in terms of background and fluctuation degrees of freedom
(1)
where and describe background fields and and are the fluctuating fields. The two systems are described respectively by hatted matrices of size and tilded matrices of size . We take , , while and are constants, interpreted as the centers of mass of the two systems at ( is taken to vanish at for both systems).
We would like to compute the effective action obtained by integrating out the off-diagonal fields and to one loop. For this purpose, we need only keep the terms quadratic in these fields, and we find that the relevant terms in the action (including the term quadratic in off-diagonal ghost fields) are:
Squad = −1R∫dτ[Y†a((∂2τ−r2−2r⋅K−K2+i˙K0+2iK0∂τ)δab+2iFab)Yb (2) +χ†(∂τ−to0.0pt$r$/−to0.0pt$K$/)χ+χ†γaLYa+Y†aLγaχ +C∗(∂2τ−r2−2r⋅K−K2+i˙K0+2iK0∂τ)C]
Here, we are treating and as -component vectors acted on by matrices
Ki≡^Xi⊗to0.0pt11~N×~N−to0.0pt11^N×^N⊗~XTi, (3)
Li≡^θi⊗to0.0pt11~N×~N−to0.0pt11^N×^N⊗~θTi
and
F0i = ∂τKi+i[K0,Ki] Fij = i[Ki,Kj]
We have defined
γ0=−i
(though this does not satisfy the usual anticommutation relations with the other gamma matrices). The only contribution from the quadratic ghost term here will be a set of terms containing purely bosonic fields which will cancel terms from the boson and fermion loops.
For our calculation, we shall treat all terms involving the matrices and as vertices, using only the terms
Sprop=−1R∫dτ(Y†a(∂2τ−r2)Ya+χ†(∂τ−to0.0pt$r$/)χ)
to determine the propagators. These are given simply by:
=δabδlmδkn∫dk2πeik(τ−σ)k2+r2≡δabδlmδknΔ(τ−σ)
for the bosonic propagator, and
<χklα(τ)χ†mnβ(σ)>=δlmδkn∫dk2πeik(τ−σ)(to0.0pt$r$/+ik)αβk2+r2≡δlmδkn(to0.0pt$r$/+∂τ)αβΔ(τ−σ)
for the fermionic propagator. We thus have a fermion-fermion vertex,
−χ†to0.0pt$K$/χ (4)
two mixed vertices,
χ†γaLYa, (5)
Y†aLγaχ. (6)
and boson-boson vertices given by
iY†a˙K0Yb, (7)
2iY†aK0∂τYa, (8)
and
−Y†aMabYb (9)
where we define:
Mab=2r⋅K+K2−2iFab
### 2.2 Tools
Before proceeding with the calculation, we make a few observations which help to simplify the calculation considerably.
#### 2.2.1 Gauge invariance
First, we may take advantage of the 0+1 dimensional gauge symmetry, noting that by our choice of background field gauge, the effective action we calculate should be invariant under a dimensional gauge transformation. In particular, the result must contain only covariant derivatives, with and appearing in the combination . Thus, we could set = 0, calculating terms with all numbers of derivatives and restoring ’s in the end by replacing derivatives with covariant derivatives. Alternatively, we may restrict the calculation to non-derivative terms, keeping a non-zero , and deduce the derivative terms from the terms. We will use both approaches, depending on which part of the calculation we are interested in. One approach may also be used as a check of the other.
#### 2.2.2 0+0 dimensional calculation
At this point, we note that the action (2) above is closely related to the dimensional action
S0+0 = −1R(Y†a(−r2)δab−Mab)Yb (10) −χ†(to0.0pt$r$/+to0.0pt$K$/)χ+χ†γaLYa+Y†aLγaχ)
which arises from the dimensional reduction of the theory to 0 dimensions. This is the quadratic part in fluctuations of the (0+0)-dimensional action which was used by Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT) to conjecture a matrix formulation of IIB string theory [39]. If we restrict to considering terms involving no derivatives or factors of , we find that the - and -dimensional calculations are exactly analogous, except that the -dimensional propagators are simply
=δabδlmδkn1r2,
and
<χklα(τ)χ†mnβ(σ)>=δlmδknto0.0pt$r$/αβr2
The form of the leading term in the bosonic 2-body potential in the -dimensional theory was computed by IKKT in [39] and is the same up to a constant as the 2-body term calculated for matrix theory in [38]. As we shall see below, the answer from the simpler dimensional calculation will often aid us in computing the full dimensional result.
#### 2.2.3 r⋅K and to0.0pt$r$/ terms
A further simplification arises from the fact that in the action (2), and appear only in the combination (a trivial consequence of their definitions). Thus, a transformation
ri→ri+Λi (11)
is exactly equivalent to a transformation
Ki→Ki+Λi. (12)
As described in detail in the body of the calculation, this property will allow us to ignore all terms containing and certain terms with an coupled to a gamma matrix during the calculation, and to deduce these at the end using a transformation (12) on the remaining terms.
#### 2.2.4 D=10 Notation
It turns out that a certain subset of terms in the effective action at each order are the dimensional reduction of Lorentz and gauge invariant terms, while many of the remaining terms are simply related to these by insertions of operators such as , and which are not invariant under the symmetries but which do have the dimensional gauge invariance and rotational invariance of the Matrix Theory action.
Thus, we will find that the fermionic terms in the effective action may often be written most naturally and concisely using gamma matrices defined by
Γi=[0γiγi0],Γ0=[0γ0−γ00] (13)
and a 32 component spinor whose first sixteen components are taken to vanish and whose remaining components are the 16 component spinor considered previously. Note that these gamma matrices correctly satisfy the relations defining the Clifford algebra,
{Γa,Γb}=2δab.
Given that the original action has a covariant form, one might wonder why not all terms in the one loop effective action may be written in this way. However, in computing the one loop potential, we integrate over only a single momentum rather than a ten-component momentum vector. Further, in writing our result, we make an expansion in the transverse seperation . Neither of these respect the ten dimensional structure that we started with, so we should not expect the full one loop effective action to be the dimensional reduction of the result.
### 2.3 Summary of the calculation
We divide the calculation up by the number of fermionic fields appearing in the result. The leading term with fermions comes from choosing each of the vertices (5) and (6). Such a term will have bosonic and fermionic propagators, and thus appear at order . Thus, up to order , where we expect the leading-order interactions, we will have terms with zero, two, and four fermions.
#### 2.3.1 bosonic terms
The purely bosonic terms at one loop were previously calculated for a general background in [38], using the quasistatic approximation in which the background fields (and their derivatives) appearing in the action (2) were assumed to be time-independent. Since we are no longer restricting to this approximation, it is interesting to check whether any higher derivative terms appear up to . In our calculation, these extra derivative terms come from keeping higher order terms in the Taylor expansions of the background fields about a particular time, rather than assuming that the background fields are time independent.
Calculating with , the non-vanishing vertices containing only bosonic background fields are (4), (9), and the ghost vertex. The only diagrams we may build with these are loops with a single one of these vertex types repeated arbitrarily many times. These three types of contributions are calculated explicitly in Section A.1 of the appendix, and it is found that all terms with explicit derivatives cancel up to and including order , leaving exactly the action
Γbos1/r7=∫dτ1516r7STr(FabFbcFcdFda−14FabFabFcdFcd) (14)
calculated in [38]. Here, denotes a symmetrized trace in which we average over all possible orderings of the matrices in the trace (treating any commutators such as as a unit).
Thus, to this order the result of our full calculation agrees with the quasistatic calculation. However, as we shall see below, we expect the appearance of higher-derivative terms at order which would not appear in a quasistatic approximation. These are proportional to the average of all possible insertions of (covariant derivative squared) into the terms (14) of the action. Interestingly, the cancellation up to order is off shell, that is, it does not require use of the equations of motion. We will see that this is not the case for terms with fermionic fields.
We will also be interested in terms of order . At this order, we find two purely bosonic contributions. The first, studied in [40, 30], is proportional to an insertion of into the action,
−10516STr(FabFbcFcdFda(r⋅K)−14FabFabFcdFcd(r⋅K))
The second contribution contains a nine index totally antisymmetric tensor coming from the trace of nine gamma matrices, and is given by
35rs256r9STr(FijFklFmn˙KpKq)ϵijklmnpqs
We will discuss the physical interpretation of these two terms below.
#### 2.3.2 two-fermion terms
We now move on to terms in the effective action with two factors of the background fermion fields . These terms arise from loops with a single insertion of each of the two boson-fermion vertices (5) and (6) to give two factors of . In addition, we may have an arbitrary number of boson-boson vertices and fermion-fermion vertices.
The details of the calculation, performed using a non-vanishing and ignoring derivative terms, are found in Section A.2 of the appendix. In contrast to the case of the purely bosonic terms, we find that the off-shell action does not vanish below , and in fact there are non-vanishing contributions to the effective action starting at . However, if we are interested in the effective potential between two physical systems, we must require that the background fields satisfy the Matrix Theory equations of motion, and in this case, the non-vanishing contributions begin at order , in agreement with supergravity.
We now give our result for the two-fermion terms in the one loop matrix theory effective action to order . As mentioned above, we have a subset of terms which are the dimensional reduction of a Lorentz and gauge invariant action. These are given in notation (omitting the leading ) by
Γcov1/r3 = Tr(¯Lto0.0pt$D$/L) Γcov1/r5 = 38iTr(¯LΓbDaFabL) +316iTr(¯LΓ[ab]Fabto0.0pt$D$/L)−316iTr(¯LΓ[ab]to0.0pt$D$/LFab) Γcov1/r7 = −564Tr(¯LΓeΓaΓbΓdFabto0.0pt$D$/LFde) −516Tr(¯LΓaΓcFabFbcto0.0pt$D$/L)−516Tr(¯LΓcΓato0.0pt$D$/LFabFbc) +532Tr(¯LΓdΓbΓcDaFabLFcd) −516Tr(¯LΓcDaFabLFcd)−516Tr(¯LΓcFcbDaFabL) +1516STr(¯LΓbΓcΓdFabFcdDaL)
All other terms up to order come from insertions of , , or into the covariant terms. To write these, we define an operation to be the average of all possible different insertions of the operators between elements of the trace. For example,
Sym(Tr(¯Lto0.0pt$D$/L);→K2,D20)= 16[Tr(D20¯L→K2to0.0pt$D$/L)+Tr(¯LD20→K2to0.0pt$D$/L)+Tr(¯L→K2D20to0.0pt$D$/L) +Tr(D20¯Lto0.0pt$D$/L→K2)+Tr(¯LD20to0.0pt$D$/L→K2)+Tr(¯Lto0.0pt$D$/LD20→K2)]
Note that any commutators in the trace are treated as single element. We can now write the full set of two-fermion terms in the off-shell action up to order as (again omitting factors of )
Γ1/r3 = Γcov1/r3 Γ1/r4 = −3Sym(Γcov1/r3;r⋅K) Γ1/r5 = Γcov1/r5+14Sym(Γcov1/r3;D20)−32Sym(Γcov1/r3;→K2)+152Sym(Γcov1/r3;r⋅K,r⋅K) Γ1/r6 = −5Sym(Γcov1/r5;r⋅K)−158Sym(Γcov1/r3;D20,r⋅K) (16) +152Sym(Γcov1/r3;→K2,r⋅K)−352Sym(Γcov1/r3;r⋅K,r⋅K,r⋅K) Γ1/r7 = Γcov1/r7+58Sym(Γcov1/r5;D20)−52Sym(Γcov1/r5;→K2)+352Sym(Γcov1/r5;r⋅K,r⋅K) +158Sym(Γcov1/r3;→K2,→K2)−1516Sym(Γcov1/r3;D20,→K2)+116Sym(Γcov1/r3;D20,D20) −1054Sym(Γcov1/r3;→K2,r⋅K,r⋅K)+10548Sym(Γcov1/r3;D20,r⋅K,r⋅K) +3158Sym(Γcov1/r3;r⋅K,r⋅K,r⋅K,r⋅K)
We will see that things simplify greatly when we restrict to a background that satisfies the matrix theory equations of motion. In our notation, these equations of motion read
to0.0pt$D$/L=0 (17)
and
DaFab=i¯LΓbL (18)
Examining the covariant terms above, we see that apart from the final term in the action, all terms listed contain either or , and so these terms either cancel directly or may be canceled by the four-fermion terms which we will soon calculate.
In the applications below, we will also be interested in certain terms at . We find that apart from terms containing , the two fermion terms at are given by the gauge invariant expression
Again, we’ll see the physical interpretation of these terms below.
#### 2.3.3 four-fermion terms
The remaining terms in the one-loop Matrix theory effective action up to order contain four fermions. These arise from a loop with two each of the vertices (5) and (6) plus insertions of the boson-boson vertices and the fermion-fermion vertex.
The calculation of four-fermion terms, performed setting to 0 and calculating derivative terms explicitly, appears in Section A.3 of the appendix. The calculation relies heavily on the use of Fierz identities for symmetric gamma matrices, and a discussion of these as they apply to non-abelian four-fermion terms is given in Appendix B.
We find first a set of terms (77), (84), (108) listed in the appendix which are obtained simply by replacing with each time it appears in the two-fermion terms. These terms serve to cancel all two-fermion terms containing in the on-shell effective action.
The remaining four-fermion terms which do not contain all appear at , so we indeed have complete cancellation of all terms below in the on-shell effective potential, in agreement with supergravity. These remaining four-fermion terms are given by
Γ4L1/r7 = 532(Tr(¯LΓaDbL¯LΓaDbL)+Tr(Db¯LΓaLDb¯LΓaL)+2Tr(¯LΓaLDb¯LΓaDbL)) +5i32(Tr(¯LΓcFabL¯LΓ[cab]L)+Tr(¯LΓ[cab]LFab¯LΓcL)+Tr(¯LΓc¯LFabLΓ[cab]L)) +5128(Tr(Lγ[ki][˙Ki,L]LγkL)+Tr(Lγ[ki]L[˙Ki,L]γkL)) −5128(Tr(Lγ[kl]˙L˙Lγ[lk]L)+2Tr(Lγk˙L˙LγkL)+6Tr(L˙L˙LL)) +5256(Tr(Lγ[kli]Ki˙LLγ[lk]L)+6Tr(Lto0.0pt$K$/˙LLL)+2Tr(LKi˙LLγiL) −Tr(˙Lγ[kli]KiLLγ[lk]L)−6Tr(˙Lto0.0pt$K$/LLL)−2Tr(˙LKiLLγiL)) +15256(Tr(Lγ[kli]KiL˙Lγ[lk]L)+6Tr(Lto0.0pt$K$/L˙LL)+2Tr(LKiL˙LγiL) −Tr(Lγ[kli]KiLLγ[lk]˙L)−6Tr(Lto0.0pt$K$/LL˙L)−2Tr(LKiLLγi˙L)) +564(Tr(Lγ[kli]KiLLγ[lkj]KjL)+2Tr(Lγ[ki]KiLLγ[kj]KjL) +6Tr(LγiKiLLγjKjL)+2Tr(LγjKiLLγiKjL) −2Tr(LγiKjLLγiKjL)+2Tr(LKiLLKiL))
Here, we note that some of the terms have a form, while others do not seem to combine into covariant expressions. In particular, it appears that there is no way to rewrite the above expression in a form with all ’s appearing in commutators, even taking into account all possible Fierz identities.
### 2.4 Summary of results for effective potential
We have now calculated the complete one-loop matrix theory effective action to order for a background corresponding to two widely separated systems. The off-shell action is given by expressions (2.3.2), (16), (2.3.3), (77), (84) and (108) and has non-vanishing contributions beginning at order . However, as we saw above, enforcing the Matrix theory equations of motion (17) and (18) we find complete cancellation of all terms at orders less than , in agreement with supergravity. The on-shell effective action (which we may interpret as the negative of an effective potential for the system) is given by
Γ1/r7 = 1516r7STr(FabFbcFcdFda−14FabFabFcdFcd) +1516r7STr(¯LΓbΓcΓdFabFcdDaL)+Γ4L
where is given in (2.3.3) (replacing, if we like, factors of by ). At , we have terms proportional to the insertion of into the symmetrized trace of the terms plus additional terms. The full expression to quadratic order in in the fermion backgrounds is given by
There are also four-fermion and six-fermion terms which contribute to which we have not calculated. In the next section, we will compare the terms in (2.4) and (2.4) to leading-order supergravity interactions, and will find a complete interpretation for all of these terms in terms of physical quantities familiar from supergravity.
## 3 Comparison to supergravity
In order to compare our Matrix theory result with supergravity, we would like to understand from a supergravity point of view the interactions that exist between two arbitrary widely separated systems at leading orders in the inverse separation distance. The leading terms in the long-range effective potential between two separated systems are described in supergravity by the linearized theory. The terms in the linearized theory arising from graviton and 3-form exchange between arbitrary bosonic systems were analyzed in [30] and shown to agree with matrix theory for processes with no longitudinal momentum transfer. In this section we generalize that discussion to include fermionic backgrounds. This gives rise to additional contributions from the fermion backgrounds to the gravitational, “electric” and “magnetic” interactions mediated by the graviton and 3-form quantum, as well as new interactions arising from gravitino exchange. Extending the analysis out to order we also find new interactions in the bosonic sector describing “dyonic” membrane-5-brane and 0-brane-6-brane interactions.
All the interactions in the linearized theory can be written in a current-current form corresponding to an instantaneous potential in light-front time between the two separated systems proportional to the product of moments of the stress tensor, membrane current, 5-brane current, 6-brane current and fermionic components of a supercurrent. To identify the matrix theory and supergravity interaction potentials the only structure needed is the detailed form of these currents in matrix theory language, expressed as traces of products of the backgrounds for the two systems. A synopsis of our results for these currents is given in section 3.6.
### 3.1 Linearized supergravity interactions
In this subsection we discuss the general structure of the linearized supergravity interactions we expect to reproduce in matrix theory. The detailed forms of the specific interactions are discussed and compared to matrix theory in the following subsections. The propagating fields of eleven dimensional supergravity are a graviton, a three form gauge field, and a gravitino. The classical linearized supergravity theory arises from considering all tree-level processes in which a single quantum is exchanged between two classical sources. For an eleven-dimensional spacetime with one compact direction, the propagators for all the fields go like , so at orders below all classical supergravity interactions can be described by the linearized theory.
Arbitrary sources can be coupled linearly to the supergravity fields by adding extra terms to the action of the form
where and are the stress-energy tensor, membrane current, 5-brane current and fermionic supercurrent components of the source. The field has a 7-form field strength dual222The true duality relation is somewhat more complicated, however we ignore the additional terms in the linearized theory since they are products of more than one field. to that of the 3-form field
It is difficult to formulate a consistent quantum theory which contains both and and which couples both to membranes and 5-branes since (24) is difficult to impose at the quantum level. We are only interested in the classical theory here, however, so we may impose (24) as a classical condition. This still leads to some complications since there is not always a single-valued solution for of (24) for a given field . We discuss this issue further in 3.4.
The classical interactions in the linearized theory can be determined by simply taking the quadratic part of the supergravity action and solving explicitly for the propagating fields in the presence of the given background. If we have a background containing two well-separated objects, we may treat one object as a source, solve for the fields produced by this source, and use (23) to find the effective action of the second object which is treated as a probe in the fields produced by the first object.
Another approach to explicitly describing the linearized theory, which is slightly more transparent in the light-front formalism, is to follow the standard field theory prescription for writing the interactions in terms of the propagators of the gravity fields. Keeping only the quadratic terms in the supergravity action, we have interactions arising from graviton, 3-form and gravitino exchange. To study interactions between two isolated systems, we assume that each of the sources in (23) may be decomposed into the sum of two terms whose supports are separated by some large distance, for example = . The leading-order interactions are then given by all diagrams of the form
ˆ×−−−−−−˜× (25)
coupling a hatted source to a tilded source. The following non-vanishing terms appear in the effective potential (up to overall coefficients):
Vgravity = ∫d11x∫d11y^TIJ(x)⟨hIJ(x)hKL(y)⟩~TKL(y) (26) Velectric = ∫d11x∫d11y^JIJK(x)⟨AIJK(x)ALMN(y)⟩~JLMN(y) (27) Vmagnetic = ∫d11x∫d11y^MIJKLMN(x)⟨ADIJKLMN(x)ADPQRSTU(y)⟩~MPQRSTU(y) (28) Vsuper = ∫d11x∫d11y¯^SIα(x)⟨ψαI(x)¯ψβJ(y)⟩~SJβ(y) +∫d11x∫d11y¯~SIα(x)⟨ψαI(x)¯ψβJ(y)⟩^SJβ(y)
In addition, there are membrane-fivebrane interactions of the form and proportional to a propagator . These terms, however, cannot be completely described by a potential. These terms are discussed separately in section (3.4) below.
To compare with matrix theory, we must take supergravity on a spacetime with a lightlike direction compactified, and also consider only processes involving the exchange of quanta with zero longitudinal momentum. The appropriate Green’s function and propagators for the bosonic fields are discussed and calculated in [30]. Denoting the light-front time coordinate by , the compact direction by , and the remaining spatial directions by , the appropriate propagators are all proportional to
δ(x+−y+)1|→x−→y|7
Note that this is independent of , a consequence of the fact that we have restricted to the exchange of quanta with zero momentum in , which therefore have wavefunctions spread evenly over this direction. Also notable is the fact that such a propagator gives rise to interactions which are instantaneous with respect to light-front time (see, for example [41]).
We now show schematically how we can relate these supergravity interactions to the matrix theory potential we have calculated. Examining the interactions (26-3.1) above, we see that all have the form
∫d11x∫d11y^C(x)⟨ϕ(x)ϕ(y)⟩~C(y) (30)
where is a general source and is a propagating field. Note that in general, a gauge-fixing choice may be necessary to explicitly calculate the propagator and to determine how the components of the tensor currents are contracted. Since the propagator is independent of and , the integrals over these variables act only on the background currents. We may rewrite the interaction as an explicit series in by replacing the currents by equivalent distributions
∫dx−C(x+,x−,→x)=C(x+)δ(→x−→x0)−C(i)(x+)∂iδ(→x−→x0)+12C(ij)(x+)∂i∂jδ(→x−→x0)+⋯ (31)
where we define the spatial moments of the current about the point by
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http://mathhelpforum.com/advanced-statistics/121852-sampling-replacement-standard-deviation.html | # Math Help - Sampling with replacement - standard deviation
1. ## Sampling with replacement - standard deviation
Can anyone help me with this problem?
Suppose there are N balls in total. At each sampling, a ball is randomly taken out, marked with a mark, and put back to the samples. If a ball is taken out for a second time during a sampling, just put back without doing anything. Let X denote the number of balls being marked after n repeated samplings. The expectation of X can be calculated as: N*(1 - (1 - 1/N)^n) . But how to calculate the standard deviation of X?
2. Originally Posted by southliguang
Can anyone help me with this problem?
Suppose there are N balls in total. At each sampling, a ball is randomly taken out, marked with a mark, and put back to the samples. If a ball is taken out for a second time during a sampling, just put back without doing anything. Let X denote the number of balls being marked after n repeated samplings. The expectation of X can be calculated as: N*(1 - (1 - 1/N)^n) . But how to calculate the standard deviation of X?
The probability that a given ball is not marked is $p=N^{-n}$. So the distribution of the number of unmarked balls is $B(N,p)$. The standard deviation of the number of marked balls is equal to that of the number of unmarked balls.
CB | {"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": 2, "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": 0.8905024528503418, "perplexity": 309.65287254254076}, "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-2014-35/segments/1409535921318.10/warc/CC-MAIN-20140909050505-00261-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://www.ipp.cas.cn/xueshujiaoliu/xueshubaogao/201707/t20170721_378685.html | 学术报告 HT-7/EAST系列学术报告
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7月25日 Accelerator Base Fusion Reactor
五室第八十八期研讨会
2017-07-21|点击： | 【大 中 小】【打印】【关闭】
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Copyright@2010 中国科学院等离子体物理研究所 版权所有地址：中国安徽合肥蜀山湖路350号 邮编：230031 电话：+86-0551-65591307 传真:+86-0551-65591310 | {"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": 0.9861921072006226, "perplexity": 2011.8700190862755}, "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-2017-34/segments/1502886105927.27/warc/CC-MAIN-20170819220657-20170820000657-00429.warc.gz"} |
http://mathoverflow.net/feeds/question/76235 | Hitting set problem variant - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T02:10:42Z http://mathoverflow.net/feeds/question/76235 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/76235/hitting-set-problem-variant Hitting set problem variant Postamar 2011-09-23T20:46:18Z 2011-09-24T19:05:52Z <p>Given any collection $\mathcal{C} = \{E_1, E_2, ..., E_m\}$ of finite and nonempty discrete sets, is there a set $I$ such that $$\forall E_k \in \mathcal{C}, \; E_k \cap I \neq \emptyset,$$ and $$\forall i \in I, \; \exists E_k \in \mathcal{C}, E_{k} \cap I = \{i\}$$ ? </p> <p>For example, for $E_1 = \{1,2\}$, $E_2 = \{2,3\}$ and $E_3 = \{1,3\}$ with $m = 3$, a possible $I$ is $\{1,2\}$.</p> <p>I've been trying to answer this question ever since stumbling upon it in my research, under a different form. I'm hardly a real mathematician so I submitted this problem to some nearby theoretical computer scientists hoping they'd tell me it was trivial, but no such luck.</p> <p>All I've found until now are a few of rather trivial observations. To begin with, the second property to be verified by $I$ is equivalent to there being an injection $g$ from $I$ to $\{1, ..., m\}$ such that $E_{g(i)} \cap I = \{i\}$ for all $i \in I$. Also, the problem can be formulated as a graph problem using a bipartite graph with $m$ vertices on one side representing the sets in the collection and vertices on the other side for each element in the union set $\bigcup_{i=1}^m E_k$, but graph theory isn't my forte either. Finally, notice that we only really need to consider the collections where $E_1, ..., E_m$ also verify the following properties:</p> <ul> <li>any one set $E_j$ is not included in any other $E_k$;</li> <li>there exists no element $e$ in exactly one set $E_k$, in other words $e$ is either in none or in at least two sets of $\mathcal{C}$.</li> </ul> http://mathoverflow.net/questions/76235/hitting-set-problem-variant/76267#76267 Answer by Brendan McKay for Hitting set problem variant Brendan McKay 2011-09-24T11:27:44Z 2011-09-24T11:27:44Z <p>Let $I$ be a minimal set that intersects each $E_j$, where minimal means that no point can be removed from $I$ without it no longer intersecting each $E_j$. Take any $i\in I$. We know $i$ lies in some $E_j$, otherwise $I$ was not minimal. If every $E_j$ that contains $i$ also contains another element of $I$, then we can remove $i$ from $I$ and it still intersects each $E_j$, so again $I$ would not be minimal. So some $E_j$ that includes $i$ contains no other element of $I$.</p> http://mathoverflow.net/questions/76235/hitting-set-problem-variant/76281#76281 Answer by Max Alekseyev for Hitting set problem variant Max Alekseyev 2011-09-24T18:59:55Z 2011-09-24T19:05:52Z <p>Let $\mathcal{E} = \bigcup_{k=1}^m E_k.$</p> <p>For each $j\in\mathcal{E}$, let $A_j = \{ k\in [1,m] : j\in E_k \}$. Then the anticipated subset $I\subset\mathcal{E}$ should satisfy the following requirements: $$\bigcup_{i\in I} A_i = \{ 1, 2, \dots, m \}$$ and $$\forall i\in I\quad A_i\not\subset \bigcup_{j\in I\atop j\ne i} A_j.$$ (the latter means that there exists $k\in A_i$ such that $k\not\in A_j$ for all $j\in I\setminus\{i\}$, that is, $E_k\cap I=\{i\}$)</p> <p>That is, the collection $\{ A_i : i\in I\}$ forms a minimal cover of the set $\{ 1, 2, \dots, m\}$. Such cover always exists -- one can start with the collection $\{ A_j : j\in\mathcal{E} \}$ and iteratively remove $A_i$ that is a subset of the union of the remaining sets until no such sets left.</p> <p>In the example with $E_1=\{1,2\}$, $E_2=\{2,3\}$ and $E_3=\{1,3\}$ we have $A_1 = \{1,3\}$, $A_2 = \{ 1,2\}$, $A_3=\{2,3\}$. Clearly, removing any set from the collection $\{ A_1, A_2, A_3 \}$ leaves us with a solution.</p> | {"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": 0.9089556932449341, "perplexity": 281.4472831914013}, "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-2013-20/segments/1368710006682/warc/CC-MAIN-20130516131326-00067-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/huffman-tree.39673/ | # Huffman tree
1. Aug 17, 2004
### david90
The question ask me to compute the expected code length of
5 nodes A B C D E each of frequency .1 .1 .2 .2 .4 respectively.
I already did the tree and derive the huffman code.
What does it mean by " compute the expected code length ?"
2. Aug 17, 2004
### suffian
i guess it means the avg size of the encoded data in bits per symbol.
Last edited by a moderator: Aug 17, 2004
3. Aug 18, 2004
### TenaliRaman
expected code length is also called the average code length (L)
= $$\sum_{i=0}^{n} p_i * l_i$$
where p_i is the probability of the symbol and l_i is the length of the symbol
-- AI | {"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": 0.9785763025283813, "perplexity": 2527.959712307156}, "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/1480698541910.39/warc/CC-MAIN-20161202170901-00035-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://www.math.gatech.edu/seminars-colloquia/series/aco-student-seminar/aurko-roy-20160226 | ## Strong reductions for extended formulations
Series:
ACO Student Seminar
Friday, February 26, 2016 - 13:05
1 hour (actually 50 minutes)
Location:
Skiles 005
,
Georgia Tech
Organizer:
We generalize the existing reduction mechanism due to Braun, Pokutta and Zink (2014)for linear programming problems and semidefinite programming problems in two ways 1) relaxing the requirement of affineness2) extending to fractional optimization problems As applications we prove several new LP-hardness and SDP-hardnessresults, e.g., for the (non-uniform) Sparsest Cut problem with bounded treewidth on the supply graph, the Balanced Separator problem with bounded treewidth onthe demand graph, the Max Cut problem and the Matching problem on 3-regular graphs.We also provide a new, very strong Lasserre integrality gapfor the Independent Set problem, which is strictly greater than thebest known LP approximation, showing that the Lasserre hierarchydoes not always provide the tightest SDP relaxation.Joint work with Gabor Braun and Sebastian Pokutta. | {"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": 0.8992646932601929, "perplexity": 3752.444800264367}, "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-2018-09/segments/1518891813818.15/warc/CC-MAIN-20180221222354-20180222002354-00266.warc.gz"} |
http://mathoverflow.net/questions/54467/average-compared-with-discrete-average-for-some-lbrace-1-1-rbrace-polynomia | # Average compared with discrete average for some $\lbrace -1,1 \rbrace$ polynomials
Let $k>0$ be a positive integer. Set $n=4k.$ Let $R(t)$ be a polynomial of degree $n-1$ with coefficients in $\lbrace -1,1 \rbrace$.
Consider the discrete average
$$D(n,R) = \frac{\sum_{j=0}^{n-1} \vert R(exp(2\pi i j/n)) \vert}{n}$$
and the average
$$A(n,R) = \frac{\int_{0}^{2\pi} \vert R(exp(it) \vert dt}{2\pi}.$$
When $k=1$ so that $n=4$ we have that for one half of the possible polynomials $R(t)$ $$D(n,R) \leq A(n,R).$$
Question: What happens when $k>1.$
-
I don't know. Your $A(n,R)$ (which doesn't actually depend on $n$) is essentially the Mahler measure of $R$, q.v. – Gerry Myerson Feb 6 '11 at 1:00
Thanks to Gerry and to Or. In order to have a feeling of what happens when $n$ is big (so that computations may become more complicated). Can be useful to observe (besides nice gerry's observation) that $$A(n,R) = \int_{0}^{1} \vert R(exp(2\pi i t) \vert dt$$ so that seems that some kind of Riemann sums are involved ? – Luis H Gallardo Feb 6 '11 at 19:42
You can interpret $D(n,R)$ as a Riemann sum for $A(R)$. There are estimates for the difference between the two in terms of properties of $R$ and of the set $\lbrace0,1/n,\dots,(n-1)/n\rbrace$ - see Koksma's inequality, also the Erdos-Turan inequality. Those inequalities won't tell you anything about the sign of the difference. For that, you'd have to walk through the proofs of the inequalities. One reference is the Kuipers-Niederreiter book on Uniform Distribution of Sequences. – Gerry Myerson Feb 7 '11 at 0:04
Warn to myself: Since the polynomial $R(t)$ has degree $n-1$ (that depends on $n$) seems that we cannot let $n$ go to infinity to recover the integral from the Riemann Sum. – Luis H Gallardo Feb 7 '11 at 18:24
I just discover that these polynomials $R(t)$ are called Littlewood polynomials See the nice paper of Peter Borwein and Michael Mossinghoff (available on the net): The $L_1$ norm of polynomials. – Luis H Gallardo Feb 7 '11 at 19:15
The claims seems to be false. Numerical integration for $k=2, (n=8)$ gives that for $152$ out of the $256=2^8$ polynomials ($59.3\%$) you have $D(n,R) \leq A(n,R)$.
I do not see why having n a multiple of 4 should matter. The fact that for half of polynomials the inequality holds at $n=4$ seems like a coincident. You get the following numbers for different values of $n$: ($m$ is the number of polynomials for which $D \leq A$)
## $n$, $2^n$, $m$, $fraction$
1 2 2 1.000
2 4 4 1.000
3 8 6 0.750
4 16 8 0.500
5 32 16 0.500
6 64 36 0.562
7 128 66 0.515
8 256 152 0.593
-
@Or: Thanks again for calculations. I would know if the inequalities that hold depends or not on the corresponding circulant matrix being singular or not. More precisely we can attach to each such polynomial $R(t)= r_0 + \ldots + r_{n-1}t^{n-1}$ a circulant matrix $C(R)$ that has first row precisely $r_0, \ldots, r_{n-1}.$ Take the inequality $A(n,R) \leq D(n,R)$ for example. Is this inequality satisfied by about the same number of $R$'s with $det(C(R))=0$ as well as about the same number of $R$'s with $\det(C(R)) \neq 0$ ??? – Luis H Gallardo Feb 7 '11 at 18:35
That's interesting. Why is the relation to the circulant matrix? For $n=4$ indeed $A \geq D$ iff $det(C)=0$. In general this doesn't hold but statistically it might be more likely to get $A \geq D$ when $det(C)=0$. For example, for $n=8$ you have $56 (A\geq D,det\neq 0)$, $96 (A\geq D,det=0)$, $72 (A < D,det \neq 0)$, $32 (A < D,det=0)$, – Or Zuk Feb 11 '11 at 6:38 | {"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": 0.9690178632736206, "perplexity": 242.16782623929106}, "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/1424936462099.15/warc/CC-MAIN-20150226074102-00290-ip-10-28-5-156.ec2.internal.warc.gz"} |
http://www.jos.ac.cn/app/article/app/doi/10.1088/1674-4926/36/2/023003?pageType=en | ## Electronic structures and phase transition characters of β-, P61-, P62- and δ-Si3N4 under extreme conditions: a density functional theory study
###### Corresponding author: Dong Chen, [email protected]
• College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China
Abstract: This paper describes the results of structural, electronic and elastic properties of silicon nitride (in its high-pressure P61 and P62 phases) through the first-principles calculation combined with an ultra-soft pseudo-potential. The computed equilibrium lattice constants agree well with the experimental data and the theoretical results. The strongest chemical bond (N--Si bond) shows a covalent nature with a little weaker ionic character. P61-Si3N4 is more stable than P62-Si3N4 due mainly to the fact that the shorter N--Si bond in the P61 phase allows stronger electron hybridizations. We have also predicted the phase stability of Si3N4 using the quasi-harmonic approximation, in which the lattice vibration and phonon effect are both considered. The results show that the β → P61 phase transition is very likely to occur at 42.9 GPa and 300 K. The reason why the β → P61 → δ phase transitions had never been observed is also discussed.
### HTML
Figure (3) Table (2) Reference (37) Relative (20) | {"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": 0.9222038388252258, "perplexity": 3614.1699244772603}, "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-2021-17/segments/1618038060603.10/warc/CC-MAIN-20210411000036-20210411030036-00199.warc.gz"} |
https://www.physicsforums.com/threads/torsion-problem-for-strenght-of-materials-help.300311/ | Torsion problem for strenght of materials help
1. Mar 16, 2009
duffman1278
1. The problem statement, all variables and given/known data
2. Relevant equations
tao=Tc/J
theta=TL/JG
3. The attempt at a solution
I got the torque of the motor as 210,085lb-in
Then I converted the 4* to .698 rad
From there I plugged it into the equations. I solved for T from tao=Tc/J then plugged that T into the theta=TLJG and put everything else in there.
When I did that I got a diameter of 3.44" or 1.72" radius. I don't get what I'm doing wrong?
2. Mar 17, 2009
nvn
duffman1278: Conversion mistake; 4 deg is not 0.698 rad. Also, generally always maintain four (or
five) significant digits throughout all your intermediate calculations, then round only the final answer
to three significant digits, unless the final answer begins with 1, in which case round the final answer
to four significant digits.
Initially compute T from the given data, at which point T is known, not an unknown. Do not solve for
T in the stress nor deflection equation; solve for d. The unknown is d. Try it again.
3. Mar 17, 2009
duffman1278
The 4 degree's I put on here was just a type-o this is what I got when I redid it.
$$\phi$$= .069813
T(shaft)= 52,521.1312 lb-in
G= 12x106
$$\tau$$= 12,000psi
L= 120"
I solved for T as you said in which I got
T=$$\stackrel{\tau*J}{c}$$
I then plugged that T into the $$\phi$$=$$\stackrel{TL}{JG}$$
That then gave me $$\phi$$=$$\stackrel{L\tau}{Gc}$$
I solved for "c" which would be the radius and it gave me 1.72 or 3.43in still.
4. Mar 17, 2009
nvn
The answer for T is already given in the third line of post 3. Don't solve
for T again after that; just use it in your other equations thereafter to
solve for d (or c).
5. Mar 17, 2009
duffman1278
I love you!! omfg this stupid problem was so easy the entire time.
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http://mathonline.wikidot.com/the-arzela-ascoli-theorem-part-1 | The Arzelà–Ascoli Theorem Part 1
# The Arzelà–Ascoli Theorem Part 1
We are now going to look at a very famous theorem known as The Arzelà–Ascoli Theorem. We will prove the theorem in three parts on The Arzelà–Ascoli Theorem Part 1, The Arzelà–Ascoli Theorem Part 2, and The Arzelà–Ascoli Theorem Part 3 pages.
First we review some important definitions.
• On the Boundedness of a Subset of C(X) page we saw that a collection of functions $\Gamma \subseteq C(X)$ is said to be bounded if there exists an $M \in \mathbb{R}$, $M > 0$ such that for all $f \in \Gamma$ and for all $x \in X$ we have that:
(1)
\begin{align} \quad \mid f(x) \mid \leq M \end{align}
• On the Equicontinuity of a Subset of C(X) page we saw that a collection of functions $\Gamma \subseteq C(X)$ is said to be equicontinuous on $X$ if for all $\epsilon > 0$ there exists a $\delta > 0$ such that for all $f \in \Gamma$ and for all $x, y \in X$, if $d(x, y) < \delta$ then:
(2)
\begin{align} \quad \mid f(x) - f(y) \mid < \epsilon \end{align}
Theorem 1 (The Arzelà–Ascoli Theorem): Let $(X, d)$ be a compact metric space, and for each $n \in \mathbb{N}$ let $f_n : X \to \mathbb{R}$ be a continuous function. Then if the sequence of functions $(f_n(x))_{n=1}^{\infty}$ in $C(X)$ is bounded and equicontinuous then there exists a uniformly convergent subsequence.
• Proof: We begin the proof by showing that there exists a subset $S \subseteq X$ that is countable and dense.
• Let $n \in \mathbb{N}$ and for each $x \in X$, consider the open ball centered at $x$ with radius $\frac{1}{n}$:
(3)
\begin{align} \quad B \left ( x, \frac{1}{n} \right ) = \left \{ y \in X : d(x, y) < \frac{1}{n} \right \} \end{align}
• Clearly we have that the union of these balls is an open covering of $X$ since each $x \in X$ is the center of one of these open balls, so, $\displaystyle{X \subseteq \bigcup_{x \in X} B \left ( x, \frac{1}{n} \right )}$.
• Since $(X, d)$ is a compact metric space there exists a finite subcollection of $\left \{ B \left (x, \frac{1}{n} \right ) : x \in X \right \}$ that also covers $X$. In other words, there exists $\left \{ B\left ( x_1, \frac{1}{n} \right ), B \left ( x_2, \frac{1}{n} \right ), ..., B\left (x_k , \frac{1}{n} \right ) : x_1, x_2, ..., x_k \in X \right \} \subseteq \left \{ B \left (x, \frac{1}{n} \right ) : x \in X \right \}$ such that:
(4)
\begin{align} \quad X \subseteq \bigcup_{i=1}^{k} B \left ( x_k, \frac{1}{n} \right ) \end{align}
• Let $S_n = \{ x_1, x_2, ..., x_k \}$. Then for each $n \in \mathbb{N}$, $S_n$ is countable, and furthermore, if we let $S = \bigcup_{n=1}^{\infty} S_n$ then $S$ is also countable (as it is a countable union of (finitely) countable sets). We claim that $S$ is also dense.
• Let $x \in X$ and $r > 0$ and consider the intersection of $S$ with the open ball $B(x, r)$:
(5)
\begin{align} \quad S \cap B(x, r) = \left ( \bigcup_{n=1}^{\infty} S_n \right ) \cap \left \{ y \in X : d(x, y) < \frac{1}{r} \right \} \end{align}
• For each $r > 0$, there exists an $n_r \in \mathbb{N}$ such that $\frac{1}{n_r} < \frac{1}{r}$. For each point $y \in B(x, r)$ we have that $d(x, y) < \frac{1}{r}$, and since every point $y \in X$ is of a distance of less than $\frac{1}{n_r}$ of a point in $S_{n_r} \subset S$. So $S \cap B(x, r) \neq \emptyset$, so $S$ is a countable dense subset of $X$. | {"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": 5, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9994896054267883, "perplexity": 85.83020349439909}, "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-2017-51/segments/1512948581033.57/warc/CC-MAIN-20171216010725-20171216032725-00607.warc.gz"} |
https://www.physicsforums.com/threads/magnetic-field-energy-density-confusion.692708/ | # Magnetic Field Energy Density Confusion
1. May 20, 2013
### dgreenheck
I am trying to find the approximate force imparted on a piece of iron on the axis of a finite length solenoid. One website said a good approximation was to take the difference of the magnetic field energy from when the piece of iron was directly outside the solenoid and when the piece of iron was inside the solenoid.
The formula for the magnetic field energy density is:
$\frac{1}{2}\frac{B^{2}}{μ}$
So here's the point where I am confused on: The piece of iron is attracted to the solenoid, so the energy has to go down. But I thought that putting a piece of iron in the center of a solenoid made it a stronger electromagnetic, a.k.a. the magnetic field lines are more concentrated with a high permeability core. Wouldn't this imply that the magnetic field energy density goes up, contradicting my first point? I know my fundamentals are messed up somewhere, but I can't quite figure out where.
Can you offer guidance or do you also need help?
Draft saved Draft deleted
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http://mathoverflow.net/questions/16310/why-does-one-invert-g-m-in-the-construction-of-the-motivic-stable-homotopy-cat | Why does one invert $G_m$ in the construction of the motivic stable homotopy category?
Morel and Voevodsky construct the motivic stable homotopy category, a category through which all cohomology theories factor and where they are representable, by starting with a category of schemes, Yoneda-embedding it into simplicial presheaves, endowing those with the $\mathbb{A}^1$-local model structure, and then passing to $S^1 \wedge \mathbb{G}_m$-spectra. The last step ensures that smashing with $S^1$ or with $\mathbb{G}_m$ induce functors with a quasi-inverse on the homotopy category.
Inverting $S^1$ leads to a triangulated structure on the homotopy category, which is very welcome, but I would like a motivation for inverting $\mathbb{G}_m$. Since $\mathbb{P}^1$ is $\mathbb{A}^1$-equivalent to $S^1 \wedge \mathbb{G}_m$ I would also be content with a motivation to invert $\mathbb{P}^1$.
I must admit I already know some answers which certainly are reason enough to invert $\mathbb{G}_m$, e.g. (from slides by Marc Levine, start at page 64):
1. Inverting $\mathbb{G}_m$ is necessary to produce a Gysin sequence
2. The algebraic K-theory spectrum appears naturally as a $\mathbb{P}^1$-spectrum
However, I am greedy and would like to hear a motivation like the one for inverting the Lefschetz motive in the construction of pure motives: There one could say that for all envisaged realization functors which should factor through the category of pure motives, the effect of tensoring with the Lefschetz motive can be undone (e.g. is just a change of Galois representation leaving the cohomology groups unchanged).
Or, related to this, as Emerton explained in his nice answer here one has to invert the Lefschetz motive in order to make the Pure Motives a rigid tensor category. Ideally one would like the triangulated category of motives to arise as derived category of some rigid tensor category - if this was true, would it be reflected in the fact that $\mathbb{P}^1$ or $\mathbb{G}_m$ are invertible? (in this case of course one should ensure iinvertibility when constructing a candidate for this derived category)
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I guess there are "internal" and "external" motivations. External for instance -- most natural examples of functors we have from the stable motivic homotopy category to some other category invert G_m (e.g. any of the usual realizations, or K-theory). Internal for instance -- we want the suspension spectra of varieties to be dualizable under the smash product.
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BTW the phenomenon of wanting to invert extra spheres in nonstandard stable settings is not special to motivic theory. For example in equivariant stable homotopy theory, you gotta invert those representation spheres, and if you want to do stable homotopy theory over a space it's probably handy to invert sphere bundles... – Dustin Clausen Feb 24 '10 at 23:07
wait was i right about K-theory? is it monoidal for smash product? i dunno. – Dustin Clausen Feb 24 '10 at 23:15
.. and these two motivations are exactly the same as those mentioned (for the Lefschetz motive) in the last two paragraphs of the question! – Anatoly Preygel Feb 24 '10 at 23:45
toly: true!! just in the stable instead of abelian context, but the motivation is the same. – Dustin Clausen Feb 24 '10 at 23:51
Remember how duality works for suspension spectra of compact manifolds in the ordinary stable homotopy category: X is dual to X^(-T_X), i.e. you need Thom spectra of virtual bundles. Here the duality comes from the purity map X x X --> X^(T_x). Now, in the motivic case, there a notion of Thom space for which purity works, namely take your vector bundle mod the complement of its zero section. These are the things you need to invert, and they look like smash products of P^1's. (p.s. I learned this stuff form a lecture of Jacob Lurie at Harvard...) – Dustin Clausen Feb 25 '10 at 16:46
$H^1({\mathbb G}_m)$ is the same motive as $H^2(\mathbb P^1)$, so I believe that inverting $\mathbb G_m$ is the same as inverting the Lefschetz motive. (Topologically, fundamental classes all ultimately arise from the $H^1$ of the circle, so we must invert this if fundamental classes are to be invertible.) In the pure context, one is not allowed to talk about ${\mathbb G}_m$, and so talks of $H^2(\mathbb P^1)$ instead; but I do think it is the same process.
Note that this is compatible with Dustin Clausen's and Marty's answers: in all realizations (Galois representations, computing periods, ... ) of motives, we can and do invert the Lefschetz motive (since it just becomes the inverse cyclotomic character, or $2 \pi i$, or ... ). Incidentally, related to David Roberts's answer, smashing with $\mathbb G_m$ is what number theorists call a Tate twist, I believe, and on the level of Galois representations it it is just tensoring with the cyclotomic character (here I am thinking of $H_1(\mathbb G_m)$). So asking for $\mathbb G_m$ to be invertible is the same as asking that one can perform Tate twists (of arbitrary integer power) on the level of motives.
Now if $M$ is a motive over a number field, with $L$-function $L(M,s)$, and $M(n)$ is its $n$th Tate twist, then the $L$-function of $M(n)$ is simply $L(M,s + n)$. So the Tate twisting parameter is the same as the parameter $s$ in the $L$-function (restricted to integer values, of course). Thus the desire to have this parameter really be an integer (and not just a natural number) also has deep roots in the conjectured relations between special values of $L$-functions and the arithmetic geometry of motives. (If one looks at the simplest $L$-function, namely the Riemann zeta function, it has special values at positive and negative integers, and one certainly wants to consider all of these and relate all of them to motivic considerations.)
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Though I'm not an expert on motives, by any measure, I think that an answer to your question can be given by considering periods. As Kontsevich and Zagier recall in their paper "Periods", publ. IHES, Section 4.2, one can form a square matrix of periods from a pair consisting of a smooth algebraic variety $X$ over $Q$ and a divisor with normal crossings $D \subset X$, also defined over $Q$. One simply pairs a basis for the relative singular homology of $(X,D)$ with coefficients in $Q$ with a basis of the relative de Rham cohomology of $(X,D)$ of appropriate degrees. This entries of this pairing matrix are the so-called "periods".
This matrix -- in general -- is almost invertible as a matrix over the ring of periods. However, to invert the matrix, one must also adjoin $1/2 \pi i$ to the ring of periods -- this corresponds precisely to inverting (the period of) $G_m$ as you mention.
So, as I understand it, one can not achieve comparison isomorphisms of Betti and de Rham realizations of motives (or at least not write down the isomorphism in both directions) without inverting the period of $G_m$.
Or, it also follows from Kontsevich-Zagier that one cannot define the triple-product on the ring of periods, without having $1/2 \pi i$. Defining this triple-product is necessary, if one wishes to endow $Spec$ of the ring of periods with the structure of a pro-algebraic torsor for the motivic Galois group.
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As for the triangulated category perspective (and I'm not an expert) it comes down to having the shift functor invertible, and from what I understand, this is formally like suspension, i.e. smashing with $\mathbb{G}_m$ (the analogy is closest for $\mathbb{G}_m(\mathbb{C}) = \mathbb{C}^\times$ which is homotopic to the circle). There is a bit of abstract perspective on this at motivic cohomology at the nLab
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The triangulated category structure comes only from inverting the simplicial circle, not G_m. As for the nLab page: I had a look and found it horribly misleading (there are just plainly wrong statements)!! I inserted two warnings there but have no time right now to edit it nicely... – Peter Arndt Feb 25 '10 at 16:33
Thanks, Peter, for these two warnings. The first of them I incorporated into the text. What else is "horribly misleading"? The first part at half is supposed to be pretty literally a summary of the lecture by Jardine linked to there. My apologies for that mistake I made which you pointed out. Good that you caught it. – Urs Schreiber Feb 25 '10 at 20:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9099036455154419, "perplexity": 392.525031869265}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988860.88/warc/CC-MAIN-20150728002308-00165-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://yonsei.pure.elsevier.com/en/publications/higgs-inflation-from-standard-model-criticality | # Higgs inflation from standard model criticality
Yuta Hamada, Hikaru Kawai, Kin Ya Oda, Seong Chan Park
Research output: Contribution to journalArticlepeer-review
72 Citations (Scopus)
## Abstract
The observed Higgs mass MH=125.9±0.4GeV leads to the criticality of the standard model, that is, the Higgs potential becomes flat around the scale 1017-18GeV for the top mass 171.3 GeV. Earlier we proposed a Higgs inflation scenario in which this criticality plays a crucial role. In this paper, we investigate the detailed cosmological predictions of this scenario in light of the latest Planck and BICEP2 results. We also consider the Higgs portal scalar dark matter model, and compute the Higgs one-loop effective potential with the two-loop renormalization group improvement. We find a constraint on the coupling between the Higgs boson and dark matter which depends on the inflationary parameters.
Original language English 053008 Physical Review D - Particles, Fields, Gravitation and Cosmology 91 5 https://doi.org/10.1103/PhysRevD.91.053008 Published - 2015 Mar 26
## All Science Journal Classification (ASJC) codes
• Nuclear and High Energy Physics
• Physics and Astronomy (miscellaneous) | {"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": 0.9858385324478149, "perplexity": 3174.4073532726893}, "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/1614178359624.36/warc/CC-MAIN-20210227234501-20210228024501-00402.warc.gz"} |
https://www.physicsforums.com/threads/force-3.186256/ | Force (3)
1. Sep 22, 2007
aligass2004
1. The problem statement, all variables and given/known data
Bob, who has a mass of 85 kg, can throw a 450g rock with a speed of 30m/s. The distance through which his hand moves as he accelerates the rock forward from rest until he releases it is 1.8m. a.) What constant force must Bob exert on the rock to throw it with this speed? b.) If Bob is standing on frictionless ice, what is his recoil speed after releasing the rock?
2. Relevant equations
F=ma
3. The attempt at a solution
I have no idea how to start this problem. There are way too many elements of the problem for me to know how to start.
2. Sep 22, 2007
learningphysics
Think of it like a kinematics problem... find the acceleration, then you can find the force.
3. Sep 23, 2007
aligass2004
Ok. I tried using Vxf^2 = Vxi^2 + 2ax(delta x) to find the acceleration, but that didn't work.
4. Sep 23, 2007
learningphysics
What number did you get for acceleration?
5. Sep 23, 2007
aligass2004
-250 m/s^2
6. Sep 23, 2007
learningphysics
You shouldn't have the minus sign...
7. Sep 23, 2007
aligass2004
Ok, I got that one, 112.5N. Now how do I start part b?
8. Sep 23, 2007
learningphysics
Use conservation of momentum.
9. Sep 23, 2007
aligass2004
We haven't gone over momentum yet.
10. Sep 23, 2007
learningphysics
Oh... you can also do it this way. What is the force acting on Bob (use newton's third law). Then you can find Bob's acceleration... Also find the time over which Bob has contact with the rock (you can get this now easily, because you have acceleration of the rock)
Using bob's acceleration and time, you can get bob's velocity at the end of the time period...
11. Sep 23, 2007
aligass2004
Using Newton's third law would make the force acting on Bob -112.5N. So using that I found the acceleration to be -1.324m/s^2. Then I used Vxf = Vxi + ax (delta time). The answer I got was 30.079, which was wrong.
12. Sep 23, 2007
learningphysics
How are you getting 30.079? Vxi = 0. ax = -1.324. delta t = 30/250=0.12s.
13. Sep 23, 2007
aligass2004
I was using the wrong time. I didn't think to use acceleration = change in velocity/time. I got -0.159, which is still wrong.
14. Sep 23, 2007
learningphysics
Did you try 0.159?
15. Sep 23, 2007
aligass2004
The positive answer was right, which is good because that was my last guess at the problem.
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http://math.stackexchange.com/questions/107635/factoring-polynomial-with-complex-coefficients | # Factoring polynomial with complex coefficients
Given the equation $z^2+4iz-13=0$, solve for $z$ without the quadratic formula.
In real numbers set, when I find this kind of equations I usually complete the perfect square trinomial.In this case:
$(z^2+4iz-4)-13+4=0$
$(z+2i)^2-9=0$
I chosen $-4$ because the number whose double is $4i$, is $2i$. And the square of $2i$ is $-4$.
$z+2i= \pm \sqrt{9}$
$z=3-2i \vee z=-3-2i$
Is this correct?Thanks
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Yes. This is correct, and this method demonstrates that you can factor any quadratic polynomial in $z$ by completing the square (the closed form of which is called the quadratic equation). We are using the fact that $AB = 0 \implies A = 0$ or $B = 0$. Such rings where this fact is true are called Integral domains. The set of real numbers and the set of complex numbers are two examples of such integral domains. – JavaMan Feb 9 '12 at 22:26
For fun, let's do it in silly high school style. We want to find two numbers whose product is $13$ and whose sum is $-4i$, It is clear that $3-2i$ and $-3-2i$ work. – André Nicolas Feb 9 '12 at 23:13
Yes it is correct.
You could also have 'simplified' it by setting $w = iz$, and getting a quadratic in $w$ with only real coefficients.
On a side note: Questions which have ill defined things like 'without using quadratic formula', 'without using secant' etc are ridiculous and ought to be banned from classrooms.
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I gave a +1 for the last sentiment, which I strongly agree with... – Ｊ. Ｍ. Feb 9 '12 at 23:03
@Aryabhata : One should not use the quadratic formula if the quadratic formula is what one is trying to prove. – Michael Hardy Feb 10 '12 at 1:11
What you did is correct.
You can check by substitution: If $z=3-2i$ then
$$(z+2i)^2-9= ((3-2i)+2i)^2-9 = 3^2-9=0.$$
If $z=-3-2i$ then $$(z+2i)^2 - 9 = ((-3-2i) + 2i)^2 - 9 = (-3)^2 - 9 = 0.$$
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8988195061683655, "perplexity": 386.6713234727771}, "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-2014-49/segments/1416931009777.87/warc/CC-MAIN-20141125155649-00170-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://nwalsh.com/tex/texhelp/ltx-37.html | # \raggedright
This declaration corresponds to the flushleft environment. This declaration can be used inside an environment such as quote or in a parbox.
Unlike the flushleft environment, the \raggedright command does not start a new paragraph; it simply changes how LaTeX formats paragraph units. To affect a paragraph unit's format, the scope of the declaration must contain the blank line or \end command (of an environment like quote) that ends the paragraph unit. | {"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": 0.9980433583259583, "perplexity": 4541.700685503872}, "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/1512948563629.48/warc/CC-MAIN-20171215040629-20171215060629-00487.warc.gz"} |
https://www.physicsforums.com/threads/stamps-word-problem.645763/ | # Homework Help: Stamps word problem
1. Oct 21, 2012
### Taylor_1989
I got the word problem off the internet, just for a bit of practice, and get slightly lost towards the end. It tells me becky had 216 stamps, the thing is I am not to sure how to set up the equation I will show my working below.
Ada, Becky and Cathy had some stamps. Cathy had 20%more stamps than Ada. Cathy had 75% as many stamps as Becky. Becky gave 45 stamps to Ada and Cathy in the ratio of 4:1 so that all three girls will have the same number of stamps.
a) How many stamps did Becky have at first?
1. $C=A*120\%$ $C=B*75\%$
2. ratio $\frac{45}{5}=9$ $9*4=36$$9*1=9$
3. $B-45=C+9=A+36$
This is the point of confusion, I am not quite sure how to solve for B. I know I should some how sub 1 into 3 to make the equation, but not to sure how? could someone point me in the right direction, to how to solve this.
I did convert the percentages to fraction: $\frac{6}{5}$ and $\frac{3}{4}$ but still did not help.
Would really apprecaite the guidence
2. Oct 21, 2012
### bossman27
From this point, all you need to do is substitute $.75B$ for $C$ and solve for $B$, forgetting about $A$, though you can check to make sure you got it right by solving for all of the final stamp counts.
3. Oct 21, 2012
### Taylor_1989
If I solve for $B$ I get $207$, I should be getting $216$
Here is how I did it, I personally cant see where I am going wrong, but obviously I am somewhere: $B-45=\frac{3}{4}B+9$ $\rightarrow$ $4(B-45)=3(B+9)$ $\rightarrow$ $4B-180=3B+27$ $\rightarrow$ $B=207$
4. Oct 21, 2012
### bossman27
$B - 45 = .75B + 9$
$.25B = 54 \Rightarrow B = 216$
Your problem was that you solved it as though it was:
$B - 45 = \frac{3}{4}(B+9)$
and $\frac{3}{4}(B+9) \neq \frac{3}{4} B + 9$
5. Oct 21, 2012
### Taylor_1989
Got it, thanks for that fella; been bugging me all day. | {"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": 0.8604428172111511, "perplexity": 3688.2475989449545}, "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-2018-26/segments/1529267863259.12/warc/CC-MAIN-20180619232009-20180620012009-00621.warc.gz"} |
http://math.stackexchange.com/questions/90301/does-robinson-arithmetic-satisfy-modal-logics-axiom-4?answertab=oldest | # Does robinson arithmetic satisfy modal logic's “axiom 4”?
Does Robinson arithmetic prove the theorem "if sigma is provable then 'sigma is provable' is provable' for a fixed sentence sigma?
It's clear to me that you can get a primitive recursive function f from (proofs of sigma) to (proofs of "there is a proof of sigma"). Q can represent f, but can it actually prove that f has this property?
If not, then how do you get Godel's second incompleteness theorem for Q?
-
This is the third Hilbert-Bernays-Löb derivability condition.
My source (Mendelson, Introduction to Mathematical Logic) just asserts it and notes that it "requires a careful and difficult proof". The impression I get is that this careful and difficult proof is indeed claimed to be doable in System Q, but that is not stated in so many words.
Mendelson refers to Boolos, The Logic of Provability (1993), ch. 2, and Shoenfield, Mathematical Logic (1967), pp. 211-213 -- neither of which I have.
Edit: This answer to an earlier question claims that Q itself cannot verify the HBL conditions.
-
It's would seem amazing for $Q$ to be able to prove something like this, since $Q$ does not have induction, and one would seem to want to prove such a thing by induction on the size of the assumed proof. – JDH Dec 11 '11 at 2:20
@JDH: Good point. – Henning Makholm Dec 11 '11 at 2:22
I was interested in this a few months ago and looked into it some. As far as I can tell, the common belief is that $Q$ is not able to prove the derivability conditions, but at the same time I was not able to find an actual proof in print that $Q$ does not prove them. However, there are published proofs that the conclusion of the second incompleteness theorem holds for $Q$, and these proofs simply avoid the derivability conditions altogether. – Carl Mummert Dec 11 '11 at 2:50
Oh I see. Q can't prove Con(Q) for the same reason it can't prove the derivability condition: because it's so weak that it can't prove much of anything. It probably can't even prove that the various ways of saying Con(Q) are equivalent. – Larry D'Anna Dec 12 '11 at 1:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.9247413873672485, "perplexity": 449.25014684727915}, "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-2016-18/segments/1461860110805.57/warc/CC-MAIN-20160428161510-00117-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/questions-involving-differentials-again.633381/ | # Questions involving differentials (again)
• Start date
• #1
333
0
What is the change of variables using differentials trick K&K are referring to here?
Are there any formalities behind this?
---
Also, when people derive the kinematic equations using calculus? I notice they rely on differentials
e.g.
http://physics.info/kinematics-calculus/
The first one, they had a=dv/dt then multiplied both sides by dt and integrated with respect to that variable...perhaps it's cause I'm still not all that comfortable with playing around with differentials like that yet but it doesn't seem 'proper' to do that. Are there alternate methods that DON'T involve treating differentials like that?
Another method that cancelled the differentials is shown here at the end:
I'm not sure about that either
Last edited by a moderator:
• #3
333
0
Oh yes, just found it. It looks like the substitution rule for integration...
For the second part (kinematic equations link), when they integrate the differential, don't integral signs already come with the differential, the variable that you're integrating with respect to?
• #4
haruspex
Homework Helper
Gold Member
2020 Award
35,136
6,271
For the second part (kinematic equations link), when they integrate the differential, don't integral signs already come with the differential, the variable that you're integrating with respect to?
Are you referring to the dv = a.dt line? That is just saying that in a small interval of time, dt, the velocity increase, dv, will be a.dt. This is the logical first step whether you're integrating or differentiating. From there, you can either divide both sides by dt, then take the limit as dt tends to zero, to get the derivative; or perform a sum of dt's over a range, then take the limit to obtain an integral.
Does that help?
• #5
333
0
^ Yes! Thanks a lot!
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1K | {"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": 0.9446461796760559, "perplexity": 2303.0028718436747}, "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-2021-04/segments/1610703518201.29/warc/CC-MAIN-20210119072933-20210119102933-00659.warc.gz"} |
https://mysqlpreacher.com/how-do-you-create-a-report-in-latex/ | Categories :
## How do you create a report in LaTeX?
11:15Suggested clip 58 secondsLatex Tutorial 1 of 11: Starting a Report and Title Page – YouTubeYouTubeStart of suggested clipEnd of suggested clip
### What is LaTeX formatting of a document?
Put simply, LaTeX is a typesetting and document preparation system that “includes features designed for the production of technical and scientific documentation.” For most people, it means that you can use LaTeX to create documents with text and formatting that would be difficult in a standard word processor.
#### Is LaTeX better than Word?
Here LaTeX is faster because you write down only the contents and software wastes no time thinking about layout. The separate type setting steps are only done at the end, which saves you time. Basic Word features are very easy to use and everybody can produce a simple document with reasonable layout.
How do I write an overleaf report?
You can use Overleaf to create, edit and publish your report with nothing to install and no sign up required – simply click the ‘Open as Template’ button to create your project report instantly.
How do I use LaTeX overleaf templates?
To create a document from a template, in the Project Management page click New Project, a drop-down menu will display, below Templates click on the document type you are about to write. You will be redirected to a list of templates where you can select one that is suitable.
## What is a LaTeX template?
LaTeX, pronounced lay-tech, is a document preparation system commonly used by scientists, engineers, mathematicians and other professionals. This results in professional-looking documents that are of a different class to the output from a word processor.
### Why is LaTeX used?
Quality and Aesthetics. Simply, documents produced using LaTeX just look better. This means that LaTeX can create everything from business cards to books to presentations. Advanced built-in referencing also allows LaTeX to easily handle very large and complex documents with many cross-references, such as theses.
#### Is LaTeX considered a programming language?
LaTeX, computer programming language used for typesetting technical documents. LaTeX is a free software package created in 1985 by the American computer scientist Leslie Lamport as an addition to the TeX typesetting system. LaTeX was created to make it easier to produce general-purpose books and articles within TeX.
How do I use LaTeX in Word?
On Office 365 version 1707 or laterPut the Equation Editor into LaTeX mode. In the Equation Editor Design ribbon, go to the Conversions group and click LaTeX.Type the LaTeX.Open the Convert dropdown menu and click Current – Professional.The LaTeX will be processed into the Equation Editor’s native format.
Can I convert LaTeX to Word?
There are several ways to convert. directly type or paste LaTeX code into Word. use a Word import filter. use a Word macro: load LaTeX file as plain text, then search for LaTeX markup and replace the markup by formatting, special characters and equations.
## Can LaTeX create word?
GrindEQ LaTeX-to-Word converts LaTeX, AMS-LaTeX, Plain TeX, or AMS-TeX documents to Microsoft Word format. Works with Microsoft Word for Windows, 32-bit and 64-bit compatible.
### How do you write an equation in LaTeX?
Using inline math – embed formulas in your text To make use of the inline math feature, simply write your text and if you need to typeset a single math symbol or formula, surround it with dollar signs: This formula $f(x) = x^2$ is an example. Output equation: This formula f(x)=x2 is an example.
#### How do I install LaTeX?
Installing LaTeX on WindowsGo to your desktop and then double-click on the protext folder to open it. Double-click on Setup.exe to begin the installation.In the proTeXt pop-up window, click the Install button next to MiKTeX. In the proTeXt pop-up window, click the Install button next to TeXstudio. You have now installed both LaTeX and the editor.
How do you write limits in LaTeX?
3:34Suggested clip · 49 secondsHow to insert Limits, Summation and Integral Equations in LaTeX …YouTubeStart of suggested clipEnd of suggested clip
How do you write divided in LaTeX?
To write a fraction, you use the code \frac{expression in the numerator}{expression in the denominator} . Formulas that appear in text are called inline. Inline formulas are sometimes squashed to avoid altering the height of the lines….Arithmetics.FormulaLaTeX-coden×mn\times m±2\pm 22÷32\div 323\frac{2}{3}6
## How do you write square root in LaTeX?
The \sqrt command produces the square root (radical) symbol with the argument as radicand. The optional argument, root, determines what root to produce, i.e. the cube root of x+y would be typed as $\sqrt[3]{x+y}$.
### What is Dfrac LaTeX?
\dfrac means that the fraction is set in displaystyle. \tfrac means that the fraction is set in textstyle. with \frac : the actual context implies the decision above.
#### What is LaTeX word processing?
LaTeX (/ˈlɑːtɛx/ LAH-tekh or /ˈleɪtɛx/ LAY-tekh, often stylized as LaTeX) is a software system for document preparation. When writing, the writer uses plain text as opposed to the formatted text found in “What You See Is What You Get” word processors like Microsoft Word, LibreOffice Writer and Apple Pages.
Is LaTeX difficult to learn?
Is LaTeX hard to learn, and what is a good source to learn how to use it? Latex has somewhat of a sharp learning curve, but once you get past how it works you’ll be able to create your documents very quickly.
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LaTeX is not dead at all, it is the most used tool to write scientific article in many fields, such as physics and computer science. | {"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": 0.9173871278762817, "perplexity": 3687.441068775254}, "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-2023-06/segments/1674764500058.1/warc/CC-MAIN-20230203154140-20230203184140-00032.warc.gz"} |
http://tex.stackexchange.com/questions/96831/using-liberation-font-with-pdflatex-no-xelatex-lualatex?answertab=votes | # Using Liberation font with pdflatex (no XeLaTeX/LuaLaTeX)
I am looking for a substitute for the Times font we are using throughout our documents. This is how we load our fonts:
``````\usepackage{txfonts}
\renewcommand{\ttdefault}{cmtt}
\DeclareMathAlphabet{\mathtt}{OT1}{cmtt}{m}{n}
\SetMathAlphabet{\mathtt}{bold}{OT1}{cmtt}{b}{n}
``````
(I know there's `newtxfonts` out by now, but that's not the issue here.)
The Linux Libertine font is an alternative which I could simply load using `\usepackage{libertine}`, but it's looking quite different from Times, and I'm not sure if this will be appreciated. Actually, I would prefer using the Liberation family, but so far I only found instructions that require the `fontspec` package, and hence the use of XeLaTeX/LuaLaTeX. At the current stage, I would prefer not to add this additional requirement so that all documents still can be compiled with `pdflatex`.
So: Is there a way to use the Liberation font family in a `pdflatex` environment? (EDIT: In other words, has anyone packaged this font already for `pdflatex`, and I missed that in my search?)
If not: I have found The Installation and Use of OpenType Fonts in LaTeX -- would this be the way to go to convert an OTF representation of Liberation for use with `pdflatex`? Which extra steps would be required to create an easy-to-use LaTeX package?
Also important for me, perhaps not worth a separate question: Can Liberation also be used as math font, or is there a math font that looks good in a Liberation document?
-
You cannot use OpenType fonts natively unless you use XeTeX or LuaTeX (it's one of the main features of these systems actually) so yes, converting the font like in the link you found is actually the only possibility. – Christian Feb 5 '13 at 10:19
The Liberation font has not been packaged for pdflatex, yet. So your options are either XeTeX/LuaTeX with the `fontspec` package, or to convert the font to Type 1 fonts yourself. The TUGboat article you linked to is a good description, but maybe you prefer Stephan Lehmkes's answer. This particularly uses True Type fonts, which is the format the Liberation fonts come in.
Concerning a fitting math font, I suggest to look at the `newtxmath` package, or `mtpro2`, whose `lite` version is free to use. | {"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": 0.9499791264533997, "perplexity": 1219.0519767035537}, "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/1432207929012.53/warc/CC-MAIN-20150521113209-00105-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.meteoswiss.admin.ch/services-and-publications/publications/reports-and-bulletins/en/1987/precipitation-measurement-and-hydrology.html | # Precipitation Measurement and Hydrology
Good agreement between radar and raingauges is found close to radar sites (13 % error for 6 hours of integration in a well defined catchment area) but strong variability and underestimation by radar occurs at longer ranges. The better of the two Swiss radars sees on the average only 25 % of the rain - in spite of the fact, that i t measures 100 % close to the radar (Sec. 4.6) - because of earth curvature or shielding by topography (See. 3.1). Similar, but not quite so dramatic results are found in flat country. In other words, the main problem of using radar för precipitation measurements and hydrology in operational applications comes from the inability to measure precipitation close enough to the ground. Because of the fact that this problem is hardly detectable in well defined experiments, i t did not reeeive the attention in the past which i t deserved as a dominant problem in operational applications at longer ranges.
Authors Joss J, Waldvogel A 145 1987 Reports & Bulletins
• Measurement & forecasting systems | {"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": 0.8336285352706909, "perplexity": 1903.5481257842348}, "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-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00816.warc.gz"} |
http://tex.tips/category/layout/ | # Order of float placement parameters
Did you know that the order of the float placement specifiers h, t, b and p, like in
has absolutely no effect? Thus [hb] is exactly the same as [bh]: both allow the float only to be placed “here” or at the bottom but not the top of a page nor on a float page.
The order of possible positions is hard-coded in the algorithm: 1. here, 2. top of this page, 3. bottom of this page, 4. float page, 5. top of next page and finally 6. bottom of next page.
# Point vs. Big Point
In TeX 1pt (TeX point) is defined as 1/72.27 inch. Many other applications like Word and Adobe InDesign etc. however use a slightly bigger point – defined as 1/72 inch – the DTP or PostScript Point. In TeX this unit is named Big Point: 1bp.
# Paragraphs – the right way
in LaTeX the only two regular ways to end a paragraph are an empty line or the \par macro. Thus
and
is basically the same.
Please do not use \\, \newline or anything else to “end” a paragraph; it is considered to be bad style and actually wrong: From LaTeX’s point of view this only ends the line but belongs to the same paragraph. Therefore the indention or skip between paragraphs can’t work properly. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9569640159606934, "perplexity": 3005.252142011829}, "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/1568514574765.55/warc/CC-MAIN-20190922012344-20190922034344-00403.warc.gz"} |
https://class12chemistry.com/tag/significance-of-kc-chemistry-notes/ | ## Significance of Kc Chemistry Notes
Significance of Kc :
We write above equation at 298 K as follows:
So, the value of K determines the limit of cell reaction. Example For Zn-Cu cell, K = 2 × 109 at 298 K. | {"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": 0.9307329654693604, "perplexity": 3852.6909770470343}, "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-2021-49/segments/1637964362230.18/warc/CC-MAIN-20211202145130-20211202175130-00202.warc.gz"} |
http://www.songtextemania.com/need_a_way_out_songtext_fairline.html | # Need A Way Out Songtext
## Fairline
### von Mehr Songtexte
Need A Way Out Songtext
(Check, check)
My brittle bones are breaking and I could barely breathe
And every little thing, oh every little thing has been killing me
Don't play me now, I got a say
I'm drowning out, I need a change
I just need a way out, I'm telling you
Well I just need a way out, I'm telling you
'cause I don't really wanna be here now
I don't really wanna be here now
I sit alone, I'm shaking and I could hardly see
Will I ever leave, will I ever be free from what's taking me
I'm spinning 'round to find a way
I'm breaking out, I need a change
I just need a way out, I'm telling you
Well I just need a way out, I'm telling you
'cause I don't really wanna be here now
I don't really wanna be here
And I don't really wanna be here now
I don't really wanna be here now
I finally see why I have to leave
And I don't really wanna be here now
I don't really wanna be here
And I don't really wanna be here now
I don't really wanna be here
I just need a way out
I'm telling you
I just need a way out
Break me out baby, I need a way out now
Break me out girl, I need a way out
Break me out baby, I need a way out now
Break me out girl, I need a way
I just need a way out, I'm telling you
Well I just need a way out, I'm telling you now | {"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": 0.8817588090896606, "perplexity": 4548.081781374581}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316549.78/warc/CC-MAIN-20190821220456-20190822002456-00487.warc.gz"} |
http://mathhelpforum.com/calculus/77788-stuck-help.html | # Math Help - Stuck ? help
1. ## Stuck ? help
The acceleration in ms-2 ofa body starting from restis given by
f(t)= 1/10te^0.1t
Determine the velocity of the body after 20 seconds
Do not know where to start
2. Remember:
$\ddot {x(t)} = \dot {v(t)} = a(t)$
Then:
$v = \int_{ }^{ } a(t)dt$
So we have:
$a(t) = \frac {t}{10}e^{\frac {t}{10}}$
We also know that $v(0) = 0$ since the body starts from rest.
Then:
$v(t) = \int_{ }^{ } \frac {t}{10}e^{\frac {t}{10}}$
This can be done by parts if you want. You get:
$v(t) = e^{t/10} (t-10) + c$.
$0 = (0 - 10) + c$.
Then,
$c = 10$.
Then,
$v(t) = e^{t/10} (t-10) + 10$.
If you want the velocity at t = 20, you have:
$v(20) = e^{20/10} (20-10) + 10 = (10e^{2}+10) \frac {m}{s}$
3. thanks for your help,I am slowly getting to grips with it. | {"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": 10, "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": 0.9339944124221802, "perplexity": 2577.6318450487256}, "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/1432207928817.29/warc/CC-MAIN-20150521113208-00062-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://www.ck12.org/book/CK-12-Algebra-I-Concepts/section/12.7/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 12.7: Excluded Values for Rational Expressions
Difficulty Level: At Grade Created by: CK-12
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Practice Excluded Values for Rational Expressions
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What if you had a rational expression like \begin{align*}\frac{x + 2}{x^2 + 3x + 2}\end{align*}? How could you simplify it? After completing this Concept, you'll be able to reduce rational expressions like this one to their simplest terms and find their excluded values.
### Watch This
CK-12 Foundation: 1207S Rational Expressions
Watch this video for more examples of how to simplify rational expressions.
YourTeacher: Simplifying Rational Expressions
### Guidance
A simplified rational expression is one where the numerator and denominator have no common factors. In order to simplify an expression to lowest terms, we factor the numerator and denominator as much as we can and cancel common factors from the numerator and the denominator.
Simplify Rational Expressions
#### Example A
Reduce each rational expression to simplest terms.
a) \begin{align*}\frac{4x-2}{2x^2+x-1}\end{align*}
b) \begin{align*}\frac{x^2-2x+1}{8x-8}\end{align*}
c) \begin{align*}\frac{x^2-4}{x^2-5x+6}\end{align*}
Solution
a) \begin{align*}\text{Factor the numerator and denominator completely:} \qquad \frac{2(2x-1)}{(2x-1)(x+1)}\!\\ \\ \text{Cancel the common factor} \ (2x - 1): \qquad \qquad \qquad \qquad \qquad \frac{2}{x+1}\end{align*}
b) \begin{align*}\text{Factor the numerator and denominator completely:} \qquad \frac{(x-1)(x-1)}{8(x-1)}\!\\ \\ \text{Cancel the common factor}\ (x - 1): \qquad \qquad \qquad \qquad \qquad \ \ \frac{x-1}{8}\end{align*}
c) \begin{align*}\text{Factor the numerator and denominator completely:} \qquad \frac{(x-2)(x+2)}{(x-2)(x-3)}\!\\ \\ \text{Cancel the common factor} (x - 2): \qquad \qquad \qquad \qquad \qquad \quad \frac{x+2}{x-3}\end{align*}
When reducing fractions, you are only allowed to cancel common factors from the denominator but NOT common terms. For example, in the expression \begin{align*}\frac{(x+1) \cdot (x-3)}{(x+2) \cdot (x-3)}\end{align*}, we can cross out the \begin{align*}(x - 3)\end{align*} factor because \begin{align*}\frac{(x-3)}{(x-3)}=1\end{align*}. But in the expression \begin{align*}\frac{x^2+1}{x^2-5}\end{align*} we can’t just cross out the \begin{align*}x^2\end{align*} terms.
Why can’t we do that? When we cross out terms that are part of a sum or a difference, we’re violating the order of operations (PEMDAS). Remember, the fraction bar means division. When we perform the operation \begin{align*}\frac{x^2+1}{x^2-5}\end{align*}, we’re really performing the division \begin{align*}(x^2+1) \div (x^2-5)\end{align*} — and the order of operations says that we must perform the operations inside the parentheses before we can perform the division.
Using numbers instead of variables makes it more obvious that canceling individual terms doesn’t work. You can see that \begin{align*}\frac{9+1}{9-5}=\frac{10}{4}=2.5\end{align*} — but if we canceled out the 9’s first, we’d get \begin{align*}\frac{1}{-5}\end{align*}, or -0.2, instead.
Find Excluded Values of Rational Expressions
Whenever there’s a variable expression in the denominator of a fraction, we must remember that the denominator could be zero when the independent variable takes on certain values. Those values, corresponding to the vertical asymptotes of the function, are called excluded values. To find the excluded values, we simply set the denominator equal to zero and solve the resulting equation.
#### Example B
Find the excluded values of the following expressions.
a) \begin{align*}\frac{x}{x+4}\end{align*}
b) \begin{align*}\frac{2x+1}{x^2-x-6}\end{align*}
Solution
a) \begin{align*}\text{When we set the denominator equal to zero we obtain:} \quad \ \ x+4=0 \Rightarrow x=-4\!\\ \\ \text{So} \ \mathbf{-4} \ \text{is the excluded value.}\end{align*}
b) \begin{align*}\text{When we set the denominator equal to zero we obtain:} \qquad x^2-x-6=0\!\\ \\ \text{Solve by factoring:} \qquad \qquad \qquad \qquad \qquad \qquad \ \qquad \qquad \qquad (x-3)(x+2)=0\!\\ \\ {\;} \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \qquad \qquad \Rightarrow x=3 \ \text{and}\ x = -2\!\\ \\ \text{So}\ \mathbf{3}\ \mathbf{and}\ \mathbf{-2} \ \text{are the excluded values.}\end{align*}
Removable Zeros
Removable zeros are those zeros from the original expression, but is not a zero for the simplified version of the expression. However, we have to keep track of them, because they were zeros in the original expression. This is illustrated in the following examples.
#### Example C
Determine the removable values of \begin{align*}\frac{4x-2}{2x^2+x-1}\end{align*}.
Solution:
Notice that in the expressions in Example A, we removed a division by zero when we simplified the problem. For instance, we rewrote \begin{align*}\frac{4x-2}{2x^2+x-1}\end{align*} as \begin{align*}\frac{2(2x-1)}{(2x-1)(x+1)}\end{align*}. The denominator of this expression is zero when \begin{align*}x = \frac{1}{2}\end{align*} or when \begin{align*}x = -1\end{align*}.
However, when we cancel common factors, we simplify the expression to \begin{align*}\frac{2}{x+1}\end{align*}. This reduced form allows the value \begin{align*}x = \frac{1}{2}\end{align*}, so \begin{align*}x = -1\end{align*} is its only excluded value.
Technically the original expression and the simplified expression are not the same. When we reduce a radical expression to its simplest form, we should specify the removed excluded value. In other words, we should write our final answer as \begin{align*}\frac{4x-2}{2x^2+x-1}=\frac{2}{x+1}, x \neq \frac{1}{2}\end{align*}.
#### Example D
Determine the removable values of the expressions from Example A parts b and c.
Solution:
We should write the answer from Example A, part b as \begin{align*}\frac{x^2-2x+1}{8x-8}=\frac{x-1}{8}, x \neq 1\end{align*}.
The answer from Example A, part c as \begin{align*}\frac{x^2-4}{x^2-5x+6}=\frac{x+2}{x-3}, x \neq 2\end{align*}.
Watch this video for help with the Examples above.
CK-12 Foundation: Rational Expressions
### Guided Practice
Find the excluded values of \begin{align*}\frac{4}{x^2-5x}\end{align*}.
Solution
\begin{align*}\text{When we set the denominator equal to zero we obtain:} \quad \ \ x^2-5x=0\!\\ \\ \text{Solve by factoring:} \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ x(x-5)=0\!\\ \\ {\;} \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ \Rightarrow x=0 \ \text{and} \ x = 5\!\\ \\ \text{So} \ \mathbf{0 \ and \ 5}\ \text{are the excluded values.}\end{align*}
### Explore More
Reduce each fraction to lowest terms.
1. \begin{align*}\frac{4}{2x-8}\end{align*}
2. \begin{align*}\frac{x^2+2x}{x}\end{align*}
3. \begin{align*}\frac{9x+3}{12x+4}\end{align*}
4. \begin{align*}\frac{6x^2+2x}{4x}\end{align*}
5. \begin{align*}\frac{x-2}{x^2-4x+4}\end{align*}
6. \begin{align*}\frac{x^2-9}{5x+15}\end{align*}
7. \begin{align*}\frac{x^2+6x+8}{x^2+4x}\end{align*}
8. \begin{align*}\frac{2x^2+10x}{x^2+10x+25}\end{align*}
9. \begin{align*}\frac{x^2+6x+5}{x^2-x-2}\end{align*}
10. \begin{align*}\frac{x^2-16}{x^2+2x-8}\end{align*}
11. \begin{align*}\frac{3x^2+3x-18}{2x^2+5x-3}\end{align*}
12. \begin{align*}\frac{x^3+x^2-20x}{6x^2+6x-120}\end{align*}
Find the excluded values for each rational expression.
1. \begin{align*}\frac{2}{x}\end{align*}
2. \begin{align*}\frac{4}{x+2}\end{align*}
3. \begin{align*}\frac{2x-1}{(x-1)^2}\end{align*}
4. \begin{align*}\frac{3x+1}{x^2-4}\end{align*}
5. \begin{align*}\frac{x^2}{x^2+9}\end{align*}
6. \begin{align*}\frac{2x^2+3x-1}{x^2-3x-28}\end{align*}
7. \begin{align*}\frac{5x^3-4}{x^2+3x}\end{align*}
8. \begin{align*}\frac{9}{x^3+11x^2+30x}\end{align*}
9. \begin{align*}\frac{4x-1}{x^2+3x-5}\end{align*}
10. \begin{align*}\frac{5x+11}{3x^2-2x-4}\end{align*}
11. \begin{align*}\frac{x^2-1}{2x^2+x+3}\end{align*}
12. \begin{align*}\frac{12}{x^2+6x+1}\end{align*}
13. In an electrical circuit with resistors placed in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of each resistance. \begin{align*}\frac{1}{R_c}=\frac{1}{R_1}+\frac{1}{R_2}\end{align*}. If \begin{align*}R_1 = 25 \ \Omega\end{align*} and the total resistance is \begin{align*}R_c = 10 \ \Omega\end{align*}, what is the resistance \begin{align*}R_2\end{align*}?
14. Suppose that two objects attract each other with a gravitational force of 20 Newtons. If the distance between the two objects is doubled, what is the new force of attraction between the two objects?
15. Suppose that two objects attract each other with a gravitational force of 36 Newtons. If the mass of both objects was doubled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?
16. A sphere with radius \begin{align*}R\end{align*} has a volume of \begin{align*}\frac{4}{3} \pi R^3\end{align*} and a surface area of \begin{align*}4 \pi R^2\end{align*}. Find the ratio of the surface area to the volume of a sphere.
17. The side of a cube is increased by a factor of 2. Find the ratio of the old volume to the new volume.
18. The radius of a sphere is decreased by 4 units. Find the ratio of the old volume to the new volume.
### Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 12.7.
### Vocabulary Language: English
Oblique Asymptote
Oblique Asymptote
An oblique asymptote is a diagonal line marking a specific range of values toward which the graph of a function may approach, but generally never reach. An oblique asymptote exists when the numerator of the function is exactly one degree greater than the denominator. An oblique asymptote may be found through long division.
Rational Expression
Rational Expression
A rational expression is a fraction with polynomials in the numerator and the denominator.
Vertical Asymptote
Vertical Asymptote
A vertical asymptote is a vertical line marking a specific value toward which the graph of a function may approach, but will never reach.
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Oct 01, 2012 | {"extraction_info": {"found_math": true, "script_math_tex": 64, "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": 0.9991232752799988, "perplexity": 1205.9452383698458}, "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-2016-26/segments/1466783392099.27/warc/CC-MAIN-20160624154952-00191-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://mathspace.co/textbooks/syllabuses/Syllabus-411/topics/Topic-7314/subtopics/Subtopic-97548/?activeTab=theory | New Zealand
Level 8 - NCEA Level 3
# Write Equations of Parabolas
Lesson
Given certain identifying information, it is possible to construct the equation of a parabola. It becomes fairly straightforward when the axes of the parabola are parallel to the coordinate axes.
In such cases, there are four basic orientations to consider as shown in this diagram. In each of the parabolas, the focus $S$S is positioned on the axis of symmetry of the parabola and on the same side that the parabola is opening to.
Consider the following examples where we can use this diagram to construct the equation.
##### Example 1
A parabola has its vertex at the origin. It's focus lies on the y-axis, $5$5 units directly below the vertex.
Diagram (b) above shows a focus directly below the vertex. By putting $\left(h,k\right)=\left(0,0\right)$(h,k)=(0,0), we see that the basic form of the equation becomes $x^2=-4ay$x2=4ay. We also know that the focal length $a=5$a=5, and because the vertex is at the origin, it must mean that the coordinates of the focus are $\left(0,-5\right)$(0,5).
The equation becomes $x^2=-20y$x2=20y., and the directrix is the line $y=-5$y=5.
##### Example 2
A particular parabola with a vertex at the origin opens upward and passes through the point $\left(-12,3\right)$(12,3)
From the diagram, this parabola is clearly given by $x^2=4ay$x2=4ay. Points on the curve satisfy the equation, so we know that $\left(-12\right)^2=4a\left(3\right)$(12)2=4a(3), and when solved we establish that the focal length is $12$12.
The equation becomes $x^2=48y$x2=48y, the directrix is the line $y=-12$y=12, and the focus is at $\left(0,12\right)$(0,12)
##### Example 3
Find the equation of a parabola with its vertex at $\left(-4,3\right)$(4,3) and its directrix at $x=-9$x=9
Since the directrix is the line $x=-9$x=9 and the vertex is at $\left(-4,3\right)$(4,3), then the focal length must be $5$5 (in other words the gap between $x=-9$x=9 and $x=-4$x=4 is clearly $5$5).
The directrix is on the opposite side of the curve to the focus, so the focus must have the coordinates $\left(1,3\right)$(1,3)
Clearly the curve opens outward to the right, and this means (referring to the diagram) that the equation has the form $\left(y-h\right)^2=4a\left(x-k\right)$(yh)2=4a(xk)
The equation is therefore $\left(y-3\right)^2=20\left(x+4\right)$(y3)2=20(x+4).
##### example 4
A certain parabola has a horizontal axis of symmetry, a vertex at $\left(2,6\right)$(2,6) and passes through the point $\left(-30,-10\right)$(30,10). Find the equation of the parabola.
If the parabola passes through the point $\left(-30,-10\right)$(30,10), and the vertex is at $\left(2,6\right)$(2,6), then quite clearly, the parabola is opening up to the left. Hence the correct form to choose is form (d) above given by $\left(y-h\right)^2=-4a\left(x-k\right)$(yh)2=4a(xk)
Hence the equation becomes $\left(y-6\right)^2=-4a\left(x-2\right)$(y6)2=4a(x2). Again, the point $\left(-30,-10\right)$(30,10) satisfies the equation, so we need to solve $\left(-10-6\right)^2=-4a\left(-30-2\right)$(106)2=4a(302) for $a$a.
Thus:
$\left(-16\right)^2$(−16)2 $=$= $-4a\left(-32\right)$−4a(−32) $\left(-16\right)^2$(−16)2 $=$= $128a$128a $256$256 $=$= $128a$128a $\therefore$∴ $a$a $=$= $2$2
The equation of the parabola is therefore $\left(y-6\right)^2=-8\left(x-2\right)$(y6)2=8(x2). Its directrix is the vertical line $x=4$x=4 and the focus has the coordinates $\left(0,6\right)$(0,6).
#### More Examples
##### Question 1
A particular parabola with a vertex at the origin opens left and passes through the point $\left(-1,-6\right)$(1,6). By determining the focal length $a$a or otherwise, find the equation of the parabola.
##### Question 2
A certain parabola has a horizontal axis of symmetry, a vertex at $\left(-1,-2\right)$(1,2) and passes through the point $\left(-3,-10\right)$(3,10). By determining the focal length $a$a, find the equation of the parabola.
##### Question 3
A parabola has its vertex at the origin. It has a focal length measuring $a=4$a=4 units, and its focus lies on the $x$x-axis.
State both possible equations of the parabola.
### Outcomes
#### M8-1
Apply the geometry of conic sections
#### 91573
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