LEADER 04920nam 2200589Ia 450 001 9910782116003321 005 20230617040906.0 010 $a1-281-93562-X 010 $a9786611935627 010 $a981-279-519-7 035 $a(CKB)1000000000537828 035 $a(DLC)2005277640 035 $a(StDuBDS)AH24685167 035 $a(SSID)ssj0000211823 035 $a(PQKBManifestationID)11175563 035 $a(PQKBTitleCode)TC0000211823 035 $a(PQKBWorkID)10136039 035 $a(PQKB)10051672 035 $a(MiAaPQ)EBC1681483 035 $a(WSP)00005282 035 $a(Au-PeEL)EBL1681483 035 $a(CaPaEBR)ebr10255570 035 $a(CaONFJC)MIL193562 035 $a(OCoLC)815752522 035 $a(EXLCZ)991000000000537828 100 $a20030925d2003 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA non-equilibrium statistical mechanics$b[electronic resource] $ewithout the assumption of molecular chaos /$fTian-Quan Chen 210 $aRiver Edge, N.J. $cWorld Scientific$dc2003 215 $a1 online resource (xvi, 420 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-238-378-6 320 $aIncludes bibliographical references (p. 407-414) and index. 327 $a1. 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. 330 $aThis book presents the construction of an asymptotic technique for solving the Liouville equation, which is to some degree an analogue of the Enskog-Chapman technique for solving the Boltzmann equation. Because the assumption of molecular chaos has been given up at the outset, the macroscopic variables at a point, defined as arithmetic means of the corresponding microscopic variables inside a small neighborhood of the point, are random in general. They are the best candidates for the macroscopic variables for turbulent flows. The outcome of the asymptotic technique for the Liouville equation reveals some new terms showing the intricate interactions between the velocities and the internal energies of the turbulent fluid flows, which have been lost in the classical theory of BBGKY hierarchy. 606 $aStatistical mechanics 606 $aSturm-Liouville equation 615 0$aStatistical mechanics. 615 0$aSturm-Liouville equation. 676 $a530.13 700 $aChen$b Tian-Quan$01477484 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782116003321 996 $aA non-equilibrium statistical mechanics$93692673 997 $aUNINA