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A non-equilibrium statistical mechanics : without the assumption of molecular chaos /

This work presents the construction of an asymptotic technique for solving the Liouville equation, which is an analogue of the Enskog-Chapman technique for the Boltzmann equation. Because the assumption of molecular chaos has not been introduced, the macroscopic variables defined by the arithmetic m...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Chen, Tian-Quan
Formato: Electrónico eBook
Idioma:Inglés
Publicado: River Edge, N.J. : World Scientific, 2003.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Chen, Tian-Quan. 
245 1 2 |a A non-equilibrium statistical mechanics :  |b without the assumption of molecular chaos /  |c Tian-Quan Chen. 
260 |a River Edge, N.J. :  |b World Scientific,  |c 2003. 
300 |a 1 online resource (xvi, 420 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
504 |a Includes bibliographical references (pages 407-414) and index. 
588 0 |a Print version record. 
505 0 |a 1. Introduction. 1.1. Historical background. 1.2. Outline of the book -- 2. H-functional. 2.1. Hydrodynamic random fields. 2.2. H-Functional -- 3. H-functional equation. 3.1. Derivation of H-functional equation. 3.2. H-functional equation. 3.3. Balance equations. 3.4. Reformulation -- 4. K-Functional. 4.1. Definition of K-functional -- 5. Some useful formulas. 5.1. Some useful formulas. 5.2. A remark on H-functional equation -- 6. Turbulent Gibbs distributions. 6.1. Asymptotic analysis for Liouville equation. 6.2. Turbulent Gibbs distributions. 6.3. Gibbs mean -- 7. Euler K-functional equation. 7.1. Expressions of B[symbol] and B[symbol]. 7.2. Euler K-functional equation. 7.3. Reformulation. 7.4. Special cases. 7.5. Case of deterministic flows -- 8. Functionals and distributions. 8.1. K-functionals and turbulent Gibbs distributions. 8.2. Turbulent Gibbs measures. 8.3. Asymptotic analysis -- 9. Local stationary Liouville equation. 9.1. Gross determinism. 9.2. Temporal part of material derivative of T[symbol]. 9.3 Spatial part of material derivative of T[symbol]. 9.4. Stationary local Liouville equation -- 10. Second order approximate solutions. 10.1. Case of Reynolds-Gibbs distributions. 10.2. A poly-spherical coordinate system. 10.3. A solution to the equation (10.24)[symbol]. 10.4. A solution to the equation (10.24)[symbol]. 10.5. A solution to the equation (10.24)[symbol]. 10.6. A solution to the equation (10.24)[symbol]. 10.7. A solution to the equation (10.24)[symbol]. 10.8. A solution to the equation (10.24)[symbol]. 10.9. Equipartition of energy -- 11. A finer K-functional equation. 11.1. The expression of B[symbol]. 11.2. The contribution of G[symbol] to B[symbol]. 11.3. The contribution of G[symbol] to B[symbol]. 11.4. The contribution of G[symbol] to B[symbol]. 11.5. The expression of B[symbol]. 11.6. The contribution of G[symbol] to B[symbol]. 11.7. The contribution of G[symbol] to B[symbol]. 11.8. The contribution of G[symbol] to B[symbol]. 11.9. The contribution of G[symbol] to B[symbol]. 11.10. The contribution of G[symbol] to B[symbol]. 11.11. The contribution of G[symbol] to B[symbol]. 11.12. A finer K-functional equation -- 12. Conclusions. 12.1. A view on turbulence. 12.2. Features of the finer K-functional equation. 12.3. Justification of the finer K-functional equation. 12.4. Open problems. 
520 |a This work presents the construction of an asymptotic technique for solving the Liouville equation, which is an analogue of the Enskog-Chapman technique for the Boltzmann equation. Because the assumption of molecular chaos has not been introduced, the macroscopic variables defined by the arithmetic means of the corresponding microscopic variables are random in general. Therefore, it is convenient for describing the turbulence phenomena. The asymptotic technique for the Liouville equation reveals a term showing the interaction between the temperature and the velocity of the fluid flows, which will be lost under the assumption of molecular chaos. 
546 |a English. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
650 0 |a Statistical mechanics. 
650 0 |a Sturm-Liouville equation. 
650 6 |a Mécanique statistique. 
650 6 |a Équation de Sturm-Liouville. 
650 7 |a SCIENCE  |x Physics  |x General.  |2 bisacsh 
650 7 |a Statistical mechanics  |2 fast 
650 7 |a Sturm-Liouville equation  |2 fast 
776 0 8 |i Print version:  |a Chen, Tian-Quan.  |t Non-equilibrium statistical mechanics.  |d River Edge, N.J. : World Scientific, 2003  |z 9812383786  |z 9789812383785  |w (DLC) 2005277640  |w (OCoLC)53089822 
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