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Irreversible thermodynamics of nonlinear transport processes
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HOMOGENEOUS ALGORITHM FOR THERMAL CONDUCTIVITY: APPLICATION OF NONCANONICAL LINEAR RESPONSE THEORY, Denis J. Evans, Research School of Chemistry, Australian National Unioersity, P.O. Box 4, Canberra, A.C.T., 2600, Australia We develop an extension of linear response theory for non-canonical, classical systems. This theory allows the design of a translationally invariant nonequilibrium simulation algorithm for calculating the thermal conductivity of dense fluids. When applied to the Lennard-Jones representation of argon, excellent agreement with experiment is obtained. HYDRODYNAMIC EQUATIONS IN EXTENDED (GENERALIZED) IRREVERSIBLE THER09340 Mexico, MODYNAMICS, L.S. Garcia-Colin *, Physics Department, U.A.M.-lztapafapa, D.F., Mexico, and M. Lbpez de Harot, Physics Department, The Rockefeller University, New York, New York 10021, USA For a simple isotropic fluid it is shown that the nonlinear stationary state solutions of the time evolution equations for the fast (non-conserved) variables appearing in the generalized Gibbs relation of extended irreversible thermodynamics correspond, to all orders in the’gradients of the slow (conserved) variables, to the constitutive equations of hydrodynamics. The case of the Burnett equations is explicitly illustrated. *Also at Facultad de Ciencias de la U.N.A.M. and miembro de1 Colegio National. ton leave from Facultad de Ciencias de la U.N.A.M. GENERALIZED HYDRODYNAMICS FOR INHOMOGENEOUS FLUIDS: NONLINEAR EQUATIONS VIA GENERALIZED LANGEVIN THEORY, Martin Grant and Rashmi C. Desai, Department of Physics, University of Toronto, Toronto, Ontario, Canada MSS lA7 We use the generalized Langevin approach to derive nonlinear hydrodynamic equations for inhomogeneous fluids. This work is an extension of our recent paper* in which the equations (linear) of motion were obtained for the number density, momentum density, energy density, stress tensor and heat flux. It constitutes a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels and is analogous to the 13 moment equations of Grad for low density fluids. In the present extension, to deduce nonlinear hydrodynamic equations, we include the appropriate bilinear variables and use the projection operator technique of Zwanzig and Mori. The effect of inhomogeneity is to introduce a number of essential nonlocal features in the hydrodynamic equations. These equations are applied to study the behavior of transverse current-current correlation in a liquid-vapor system with a diffuse planar interface. We analyze the asymptotic, long-time, behavior of the “stretch” and “squeeze” viscositiest associated with the transverse current-current correlation function. The long-time power-law behavior, in the interface region, is t-‘, akin to that of a two dimensional fluid. *M. Grant and R.C. Desai, Phys. Rev. A25 (1982) 2727. tM. Grant and R.C. Desai, J. Chem. Phys. 76 (1982) 5160. ONEDIMENSIONAL HARMONIC LIQUID: A FOKKER-PLANCK DESCRIPTION OF FLUCTUATIONS FROM THE NONEQUILIBRIUM STEADY STATE, R.A. Guyer, Laboratory for Low Temperature Physics, Department of Physics and Astronomy, Hasbrouck Laboratory, University of Massachusetts, Amherst, Massachusetts 01003, USA The one-dimensional harmonic liquid, subject to a temperature gradient, is studied using the Fokker-Planck (Fp) equation. A formalism is set up for the solution of the FP equation and calculation of (1) the phase-space distribution function for the nonequilibrium steady state (NESS), (2) the conditional probability for evolution through phase space in the NESS, (3) phase-function averages in the NESS, (4) the correlation of phase-functions in the NESS, etc.
HOMOGENEOUS ALGORITHM FOR THERMAL CONDUCTIVITY: APPLICATION OF NONCANONICAL LINEAR RESPONSE THEORY, Denis J. Evans, Research School of Chemistry, Australian National Unioersity, P.O. Box 4, Canberra, A.C.T., 2600, Australia We develop an extension of linear response theory for non-canonical, classical systems. This theory allows the design of a translationally invariant nonequilibrium simulation algorithm for calculating the thermal conductivity of dense fluids. When applied to the Lennard-Jones representation of argon, excellent agreement with experiment is obtained. HYDRODYNAMIC EQUATIONS IN EXTENDED (GENERALIZED) IRREVERSIBLE THER09340 Mexico, MODYNAMICS, L.S. Garcia-Colin *, Physics Department, U.A.M.-lztapafapa, D.F., Mexico, and M. Lbpez de Harot, Physics Department, The Rockefeller University, New York, New York 10021, USA For a simple isotropic fluid it is shown that the nonlinear stationary state solutions of the time evolution equations for the fast (non-conserved) variables appearing in the generalized Gibbs relation of extended irreversible thermodynamics correspond, to all orders in the’gradients of the slow (conserved) variables, to the constitutive equations of hydrodynamics. The case of the Burnett equations is explicitly illustrated. *Also at Facultad de Ciencias de la U.N.A.M. and miembro de1 Colegio National. ton leave from Facultad de Ciencias de la U.N.A.M. GENERALIZED HYDRODYNAMICS FOR INHOMOGENEOUS FLUIDS: NONLINEAR EQUATIONS VIA GENERALIZED LANGEVIN THEORY, Martin Grant and Rashmi C. Desai, Department of Physics, University of Toronto, Toronto, Ontario, Canada MSS lA7 We use the generalized Langevin approach to derive nonlinear hydrodynamic equations for inhomogeneous fluids. This work is an extension of our recent paper* in which the equations (linear) of motion were obtained for the number density, momentum density, energy density, stress tensor and heat flux. It constitutes a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels and is analogous to the 13 moment equations of Grad for low density fluids. In the present extension, to deduce nonlinear hydrodynamic equations, we include the appropriate bilinear variables and use the projection operator technique of Zwanzig and Mori. The effect of inhomogeneity is to introduce a number of essential nonlocal features in the hydrodynamic equations. These equations are applied to study the behavior of transverse current-current correlation in a liquid-vapor system with a diffuse planar interface. We analyze the asymptotic, long-time, behavior of the “stretch” and “squeeze” viscositiest associated with the transverse current-current correlation function. The long-time power-law behavior, in the interface region, is t-‘, akin to that of a two dimensional fluid. *M. Grant and R.C. Desai, Phys. Rev. A25 (1982) 2727. tM. Grant and R.C. Desai, J. Chem. Phys. 76 (1982) 5160. ONEDIMENSIONAL HARMONIC LIQUID: A FOKKER-PLANCK DESCRIPTION OF FLUCTUATIONS FROM THE NONEQUILIBRIUM STEADY STATE, R.A. Guyer, Laboratory for Low Temperature Physics, Department of Physics and Astronomy, Hasbrouck Laboratory, University of Massachusetts, Amherst, Massachusetts 01003, USA The one-dimensional harmonic liquid, subject to a temperature gradient, is studied using the Fokker-Planck (Fp) equation. A formalism is set up for the solution of the FP equation and calculation of (1) the phase-space distribution function for the nonequilibrium steady state (NESS), (2) the conditional probability for evolution through phase space in the NESS, (3) phase-function averages in the NESS, (4) the correlation of phase-functions in the NESS, etc.