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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
River Edge, N.J. :
World Scientific,
2003.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.