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The Self-Correlation Function of Real Gases; Fonction d'Autocorrelation des Gaz Reels; 0424 0423 041d 041a 0426 0418 042f 0421 0410 041c 041e 041a 041e 0420 0420 0415 041b 042f 0426 0418 0418 0420 0415 0410 041b 042c 041d 042b 0425 0413 0410 0417 041e 0412 ; La Funcion de Autocorrelacion de los Gases Reales

Conference:

Abstract

In the formal theory of inelastic scattering of neutrons, the self-correlation function has been worked out in terms of statistical averages of the derivatives of die N-body interaction-potential of the scatterer. In the present paper, these averages are evaluated for real gases by means of a cluster-expansion related to that of Mayer-Ursell. This leads to certain non-linear types of clusters, which are investigated with respect to the topology of the graphs, their multiplicity (by combinatorial analysis) and their quadrature. As one expects, in view of the many-body problem, some of the clusters are not separable and have to be machine-integrated. In this way, the self-correlation function {gamma}{sub s}(K, t) is calculated for short times, including also the first non-Gaussian term. The cluster-expansion breaks off after the first interaction term, so that the results are valid for low density only. This still gives rise to very many different types of clusters, containing up to seven points, for each coefficient. The assumed potential is a general two-particle, hard-core type. As Singwi et al. have shown, the long time behaviour of {gamma}s is determined by the time integral of the velocity auto-correlation: {integral}{sup {infinity}}{sub 0} {sub T}dt. To construct  More>>
Authors:
Sigmar, D. J. [1] 
  1. Institute for Theoretical Physics, Technical University of Vienna Vienna (Austria)
Publication Date:
Jun 15, 1965
Product Type:
Conference
Report Number:
IAEA-SM-58/1
Resource Relation:
Conference: Symposium on Inelastic Scattering of Neutrons, Bombay (India), 15-19 Dec 1964; Other Information: 8 refs.; Related Information: In: Inelastic Scattering of Neutrons. Vol. II. Proceedings of the Symposium on Inelastic Scattering of Neutrons| 590 p.
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CALCULATION METHODS; CLUSTER EXPANSION; CORRELATION FUNCTIONS; GASES; GRAPH THEORY; INELASTIC SCATTERING; MANY-BODY PROBLEM; MULTIPLICITY; NEUTRONS; PARTICLES; QUADRATURES; TOPOLOGY; VELOCITY
OSTI ID:
22184045
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA13M3389008580
Submitting Site:
INIS
Size:
page(s) 59-84
Announcement Date:
Jan 30, 2014

Conference:

Citation Formats

Sigmar, D. J. The Self-Correlation Function of Real Gases; Fonction d'Autocorrelation des Gaz Reels; 0424 0423 041d 041a 0426 0418 042f 0421 0410 041c 041e 041a 041e 0420 0420 0415 041b 042f 0426 0418 0418 0420 0415 0410 041b 042c 041d 042b 0425 0413 0410 0417 041e 0412 ; La Funcion de Autocorrelacion de los Gases Reales. IAEA: N. p., 1965. Web.
Sigmar, D. J. The Self-Correlation Function of Real Gases; Fonction d'Autocorrelation des Gaz Reels; 0424 0423 041d 041a 0426 0418 042f 0421 0410 041c 041e 041a 041e 0420 0420 0415 041b 042f 0426 0418 0418 0420 0415 0410 041b 042c 041d 042b 0425 0413 0410 0417 041e 0412 ; La Funcion de Autocorrelacion de los Gases Reales. IAEA.
Sigmar, D. J. 1965. "The Self-Correlation Function of Real Gases; Fonction d'Autocorrelation des Gaz Reels; 0424 0423 041d 041a 0426 0418 042f 0421 0410 041c 041e 041a 041e 0420 0420 0415 041b 042f 0426 0418 0418 0420 0415 0410 041b 042c 041d 042b 0425 0413 0410 0417 041e 0412 ; La Funcion de Autocorrelacion de los Gases Reales." IAEA.
@misc{etde_22184045,
title = {The Self-Correlation Function of Real Gases; Fonction d'Autocorrelation des Gaz Reels; 0424 0423 041d 041a 0426 0418 042f 0421 0410 041c 041e 041a 041e 0420 0420 0415 041b 042f 0426 0418 0418 0420 0415 0410 041b 042c 041d 042b 0425 0413 0410 0417 041e 0412 ; La Funcion de Autocorrelacion de los Gases Reales}
author = {Sigmar, D. J.}
abstractNote = {In the formal theory of inelastic scattering of neutrons, the self-correlation function has been worked out in terms of statistical averages of the derivatives of die N-body interaction-potential of the scatterer. In the present paper, these averages are evaluated for real gases by means of a cluster-expansion related to that of Mayer-Ursell. This leads to certain non-linear types of clusters, which are investigated with respect to the topology of the graphs, their multiplicity (by combinatorial analysis) and their quadrature. As one expects, in view of the many-body problem, some of the clusters are not separable and have to be machine-integrated. In this way, the self-correlation function {gamma}{sub s}(K, t) is calculated for short times, including also the first non-Gaussian term. The cluster-expansion breaks off after the first interaction term, so that the results are valid for low density only. This still gives rise to very many different types of clusters, containing up to seven points, for each coefficient. The assumed potential is a general two-particle, hard-core type. As Singwi et al. have shown, the long time behaviour of {gamma}s is determined by the time integral of the velocity auto-correlation: {integral}{sup {infinity}}{sub 0} {sub T}dt. To construct the integrand for all times, we can make use of our cluster-expansion for small t and adopt Langevin's diffusion theory for large t. Numerical computations are under way. (author) [French] Dans la theorie formelle de la diffusion inelastique des neutrons, on a etabli la fonction d'autocorrelation en se fondant sur les moyennes statistiques des derivees du potentiel d'interaction a N corps du diffuseur. L'auteur a evalue ces moyennes pour des gaz reels a l'aide d'un developpement par amas en rapport avec celui de Mayer-Ursell. U obtient ainsi des types d'amas non lineaires qu'il etudie du point de vue de la topo- logie des diagrammes, de leur multiplicite (par analyse combinatoire) et de leur quadrature. Comme on peut s'y attendre pour ce probleme a plusieurs corps, certains amas ne sont pas separables et doivent etre integres au moyen d'un ordinateur. De cette facon, la fonction d'autocorrelation {gamma}{sub s}(K, t) est calculee pour des temps courts, {gamma} compris le premier terme non gaussien. Le developpement par amas cesse de s'appliquer apres le premier terme d'interaction, de sorte que les resultats ne sont valables que pour les faibles densites. On obtient encore de tres nombreux types differents d'amas qui contiennent jusqu'a sept points, pour chaque coefficient. Le potentiel admis est du type general a deux particules et a coeur dur. Comme Singwi et son equipe l'ont montre, le comportement a long terme de {gamma}{sub s} est determine par l'integrale de temps de l'autocorrelation de vitesse: {integral}{sup {infinity}}{sub 0} {sub T}dt. En vue de determiner l'expression a integrer pour toutes les valeurs temps, on peut utiliser le developpement par amas propose par l'auteur lorsque t est petit et adopter la theorie de la diffusion de Langevin lorsque t est grand. On est en train de faire des calculs numeriques. (author) [Spanish] En la teoria formalista de la dispersion inelastica de neutrones, la funcion de autocorrelacion se ha elaborado sobre la base de los promedios estadisticos de las derivadas del potencial de interaccion (N cuerpos) del dispersor. En la memoria, estos promedios se calculan para los gases reales segun el procedimiento de un desarrollo en racimo, que guarda relacion con la de Mayer-Ursell. Ello da origen a ciertos tipos no lineales de racimos, que se estudian en lo que respecta a la topologia de los graficos, a su multiplicidad (por analisis combinatorio) y a su cuadratura. Como es de esperar, dado el problema de la multiplicidad de cuerpos, algunos de los racimos no son separables y han de ser integrados con una calculadora electronica. De esta manera se calcula la funcion de autocorrelacion {gamma}{sub s}(K, t) para tiempos breves, incluido el primer termino no gaussiano. El desarrollo en racimo cesa despues del primer termino de interaccion, de forma que los resultados solo son validos para densidades bajas. Pero aun asi aparecen en cada coeficiente muchos tipos diferentes de racimos que contienen hasta siete puntos. En cuanto al potencial, se admite la hipotesis de un nucleo rigido formado por dos particulas. Como han demostrado Singwi y sus col., el comportamiento a largo plazo de {gamma}{sub s} viene determinado por la integral, respecto del tiempo, de la autocorrelacion de la velocidad; {integral}{sup {infinity}}{sub 0} {sub T}dt. Con el fin de determinar el integrando correspondiente a cualquier tiempo, se puede recurrir al desarrollo en racimo cuando t es pequefio, y aceptar la teoria de la difusion de Langevin en los casos en que t es grande. Se estan realizando calculos numericos. (author) [Russian] V formal'noj teorii neuprugogo rassejanija nejtronov funkcija samokorreljacii vyvedena v sredne-statisticheskih proizvodnyh vzaimodejstvie-potencial N-tela rasseivatelja. V dannom doklade jeti srednie znachenija opredeljajutsja dlja real'nyh gazov razlozheniem na gruppy, svjazannym s metodom Majera-Ursellja. Jeto privodit k polucheniju nekotoryh nelinejnyh tipov grupp, kotorye izuchajutsja v otnoshenii topologii graf, ih mnogokratnosti (metodami kombinatornogo analiza) i ih kvadratury. Kak predpolagaetsja v svjazi s problemoj mnogih tel, nekotorye iz grupp nerazdelimy, i ih neobhodimo integrirovat' s pomosh'ju schetno-reshajushhih mashin. Takim putem rasschityvaetsja funkcija samokorreljacii {gamma}{sub s}(K, t) dlja korotkih promezhutkov vremeni, v tom chisle i pervyj negaussovskij chlen. Razlozhenie na gruppy preryvaetsja posle pervogo chlena, vyrazhajushhego vzaimodejstvie, tak chto rezul'taty spravedlivy tol'ko dlja nizkoj plotnosti. Jeto tem ne menee privodit k samym razlichnym tipam grupp, v kotoryh soderzhitsja do 7 tochek dlja kazhdogo kojefficienta. V kachestve potenciala predpolagaetsja obychnaja tverdaja serdcevina s dvumja chasticami. Kak pokazali Singvi i dr., harakteristika {gamma}{sub s} dlja prodolzhitel'nogo vremeni opredeljaetsja vremennym integralom po skorosti-avtokorreljacii: {integral}{sup {infinity}}{sub 0} {sub T}dt. Dlja sostavlenija podintegral'nogo vyrazhenija dlja vseh sluchaev my mozhem ispol'zovat' nashe razlozhenie na gruppy dlja nebol'shih znachenij t i prinjat' teoriju diffuzii Lanzhevena dlja bol'shih znachenij t. Chislovye podschety gotovjatsja. (author)}
place = {IAEA}
year = {1965}
month = {Jun}
}