The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system

Kód výsledku v IS VaVaI

RIV/47813059:19240/14:#0005082 - isvavai.cz

Výsledek na webu

http://link.springer.com/article/10.1140%2Fepjp%2Fi2014-14157-4

DOI - Digital Object Identifier

10.1140/epjp/i2014-14157-4

Jazyk výsledku

angličtina

Název v původním jazyce

The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system

Popis výsledku v původním jazyce

In this investigation, exact particular realizations are sought for the microscopic statistical description which is associated with the classical dynamical system (CDS) formed by N identical smooth hard spheres subject to elastic collisions (S_N-CDS). The problem is posed in the framework of the ab initio statistical description of S_N-CDS recently developed. It is shown that the Liouville equation associated with S_N-CDS admits an exact particular solution for the N-body probability density function (PDF). This is factorized in terms of the i-th particle 1-body PDF (for all i = 1, N) via suitable weighting factors, which are denoted here as particle occupation coefficients. The latter are found to depend functionally only on the 1-body PDFs which areassociated with each of the remaining particles belonging to S_N-CDS. Furthermore, the 1-body PDF is proved to obey a well-defined statistical equation, referred to here as Master kinetic equation. This is an exact kinetic equation which

Název v anglickém jazyce

The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system

Popis výsledku anglicky

In this investigation, exact particular realizations are sought for the microscopic statistical description which is associated with the classical dynamical system (CDS) formed by N identical smooth hard spheres subject to elastic collisions (S_N-CDS). The problem is posed in the framework of the ab initio statistical description of S_N-CDS recently developed. It is shown that the Liouville equation associated with S_N-CDS admits an exact particular solution for the N-body probability density function (PDF). This is factorized in terms of the i-th particle 1-body PDF (for all i = 1, N) via suitable weighting factors, which are denoted here as particle occupation coefficients. The latter are found to depend functionally only on the 1-body PDFs which areassociated with each of the remaining particles belonging to S_N-CDS. Furthermore, the 1-body PDF is proved to obey a well-defined statistical equation, referred to here as Master kinetic equation. This is an exact kinetic equation which

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

European Physical Journal Plus

ISSN

2190-5444

e-ISSN

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Svazek periodika

129

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

33

Strana od-do

"157 - 1"-"157 - 33"

Kód UT WoS článku

000339959500001

EID výsledku v databázi Scopus

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