Nonlinear transport properties of non-ideal systems

Abstract

The theory of nonlinear transport is elaborated to determine the Burnett transport properties of non-ideal multi-element plasma and neutral systems. The procedure for the comparison of the phenomenological conservation equations of a continuous dense medium and the microscopic equations for dynamical variable operators is used for the definition of these properties. The Mori algorithm is developed to derive the equations of motion of dynamical value operators of a non-ideal system in the form of the generalized nonlinear Langevin equations. In consequence, the microscopic expressions of transport coefficients corresponding to second-order thermal disturbances (temperature, mass velocity, etc) have been found in the long wavelength and low frequency limits.

Nonlinear Transport Processes in Non‐Ideal Media

“…The problem of Burnett coefficients definition is discussed below according to the approach used in [6][7][8]. We write the corresponding expressions for the fluxes of heat, mass (charge), and momentum, which determine the linearized Burnett kinetic coefficients α qv , α av , β va , β vq for a continuous multicomponent charged medium.…”

“…We write the corresponding expressions for the fluxes of heat, mass (charge), and momentum, which determine the linearized Burnett kinetic coefficients α qv , α av , β va , β vq for a continuous multicomponent charged medium. The others coefficients in (1) are linear, while nonlinear Burnett kinetic coefficients are omitted (see, for example, [5][6][7][8]):…”

“…The conservation equations should be written for a certain selection of the expressions for the fluxes of heat, mass, charge, and momentum (see (1)). In this case, the system of conservation equations with the use of the local approximation for nonlinear kinetic coefficients after the Fourier-Laplace transformation is reduced to the following system of algebraic equations [6][7][8]:…”

“…The linearized and nonlinear Burnett kinetic coefficients for media with a weak interaction between particles (gas or plasma) are computed using kinetic equations (for example, the Boltzmann equation) and the well-known Chapman-Enskog method [5]. The Burnett kinetic coefficients for a non-ideal multicomponent charged medium (plasma) are determined according to the version of the theory of response to thermal perturbations proposed in [6][7][8]. These results can also be used for other continuous charged media: one and two component Coulomb systems, electrolytes, liquid metals, and nuclear matter, as well as for dense neutral media.…”

“…These results can also be used for other continuous charged media: one and two component Coulomb systems, electrolytes, liquid metals, and nuclear matter, as well as for dense neutral media. The approach proposed in [6][7][8] is based on comparison of phenomenological conservation equations for a charged continuous medium and equations of motion for the operators of the corresponding dynamic variables in the form of generalized Langevin equations (GLE). In deriving the equations of motion for the operators of dynamic variables, we used the algorithm proposed in [9,10].…”