Abstract:
A new boundary condition for the Bogolyubov (BBGKY) hierarchy that takes into account
correlations associated with local conservation laws is formulated. The explicit form
of the boundary conditions is found for all reduced distribution functions. It is shown
that in the simplest approximation of “binary collisions” this boundary condition leads
to a kinetic equation for the single-particle distribution function in the form of the
modified Enskog equation.
Citation:
D. N. Zubarev, V. G. Morozov, “Formulation of boundary conditions for the BBGKY hierarchy with allowance for local conservation laws”, TMF, 60:2 (1984), 270–279; Theoret. and Math. Phys., 60:2 (1984), 814–820
\Bibitem{ZubMor84}
\by D.~N.~Zubarev, V.~G.~Morozov
\paper Formulation of boundary conditions for the BBGKY hierarchy with allowance for local conservation laws
\jour TMF
\yr 1984
\vol 60
\issue 2
\pages 270--279
\mathnet{http://mi.mathnet.ru/tmf5283}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=762268}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 60
\issue 2
\pages 814--820
\crossref{https://doi.org/10.1007/BF01018982}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984ACL9200010}
Linking options:
https://www.mathnet.ru/eng/tmf5283
https://www.mathnet.ru/eng/tmf/v60/i2/p270
This publication is cited in the following 22 articles:
M. V. Tokarchuk, “Unification of kinetic and hydrodynamic approaches in the theory of dense gases and liquids far from equilibrium”, Math. Model. Comput., 10:2 (2023), 272
I.R. Yukhnovskii, M.V. Tokarchuk, P.A. Hlushak, “Metod kolektivnikh zmіnnikh v teorіï nelіnіinikh fluktuatsіi z urakhuvannyam kіnetichnikh protsesіv”, Ukr. J. Phys., 67:8 (2022), 579
M. V. Tokarchuk, “To the kinetic theory of dense gases and liquids. Calculation of quasi-equilibrium particle distribution functions by the method of collective variables”, Math. Model. Comput., 9:2 (2022), 440
P. A. Glushak, B. B. Markiv, M. V. Tokarchuk, “Zubarev's nonequilibrium statistical operator method in the generalized statistics of multiparticle systems”, Theoret. and Math. Phys., 194:1 (2018), 57–73
Mykhailo Tokarchuk, Petro Hlushak, “Unification of Thermo Field Kinetic and Hydrodynamics Approaches in the Theory of Dense Quantum–Field Systems”, Particles, 2:1 (2018), 1
Hlushak P., Tokarchuk M., “Chain of Kinetic Equations For the Distribution Functions of Particles in Simple Liquid Taking Into Account Nonlinear Hydrodynamic Fluctuations”, Physica A, 443 (2016), 231–245
Yukhnovskii I.R. Hlushak P.A. Tokarchuk M.V., “BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids”, Condens. Matter Phys., 19:4 (2016), 43705
A. S. Trushechkin, “Microscopic solutions of kinetic equations and the irreversibility problem”, Proc. Steklov Inst. Math., 285 (2014), 251–274
B. Markiv, I. Omelyan, M. Tokarchuk, “Consistent Description of Kinetics and Hydrodynamics of Weakly Nonequilibrium Processes in Simple Liquids”, J Stat Phys, 155:5 (2014), 843
Markiv B.B., Tokarchuk R.M., Kostrobij P.P., Tokarchuk M.V., “Nonequilibrium statistical operator method in Renyi statistics”, Physica A-Statistical Mechanics and Its Applications, 390:5 (2011), 785–791
V. G. Morozov, “Kinetics of dense matter: Correlations and memory”, Phys. Part. Nuclei, 39:7 (2008), 1007
M. V. Tokarchuk, I. P. Omelyan, A. E. Kobryn, “Kinetic equation for liquids with a multistep potential of interaction: Calculation of transport coefficients”, Phys. Rev. E, 62:6 (2000), 8021
A.E. Kobryn, V.G. Morozov, I.P. Omelyan, M.V. Tokarchuk, “Enskog-Landau kinetic equation. Calculation of the transport coefficients for charged hard spheres”, Physica A: Statistical Mechanics and its Applications, 230:1-2 (1996), 189
A.E. Kobryn, I.P. Omelyan, M.V. Tokarchuk, “Normal solution to the Enskog-Landau kinetic equation: boundary conditions method”, Physics Letters A, 223:1-2 (1996), 37
I.P. Omelyan, M.V. Tokarchuk, “Kinetic equation for liquids with a multistep potential of interaction. H-theorem”, Physica A: Statistical Mechanics and its Applications, 234:1-2 (1996), 89
V.G. Morozov, G. Röpke, “Quantum kinetic equation for nonequilibrium dense systems”, Physica A: Statistical Mechanics and its Applications, 221:4 (1995), 511
D. N. Zubarev, V. G. Morozov, I. P. Omelyan, M. V. Tokarchuk, “Unification of the kinetic and hydrodynamic approaches in the theory of dense gases and liquids”, Theoret. and Math. Phys., 96:3 (1993), 997–1012
Yu. A. Tserkovnikov, “Kinetic equations in the method of two-time finite-temperature Green's functions. I. Renormalization of the collision integral”, Theoret. and Math. Phys., 96:3 (1993), 1013–1026
M. V. Tokarchuk, “On the statistical theory of a nonequilibrium plasma in its electromagnetic self-field”, Theoret. and Math. Phys., 97:1 (1993), 1126–1136
D. N. Zubarev, V. G. Morozov, I. P. Omelyan, M. V. Tokarchuk, “Kinetic equations for dense gases and liquids”, Theoret. and Math. Phys., 87:1 (1991), 412–424
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