Transport and conduction in random systems

doi:10.1016/0020-7225(84)90109-5

International Journal of Engineering Science

Volume 22, Issues 8–10, 1984, Pages 1083-1096

https://doi.org/10.1016/0020-7225(84)90109-5 Get rights and content

Abstract

We discuss the use of the effective medium approximation (EMA) for the calculation of the macroscopic properties of a microscopically disordered system. This technique has a long history for static problems, but has only recently been applied to time-dependent problems. Our discussion is restricted, for simplicity, to the case of a periodic lattice with disorder in transport properties at the level of individual bonds. We review recent applications of the EMA to disordered rate equations (master equations) and show how the basic formalism extends to a class of disordered integro-difference equations (generalized master equations) and to transport processes in which loss of the mobile species from the system is possible. In each case the macroscopic system properties, obtained by smoothing out spatial disorder, exhibit time-correlation or memory effects.

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Transport and conduction in random systems

Abstract

Int. J. Solids Structures

Int. J. Solids Structures

Solid St. Comm.

Phys. Rep.

Dispersion in flow through porous media

Electrical conductivity in inhomogeneous media

Models of Disorder

Theoretical approaches to inhomogeneous transport in disordered media

J. Phys. C

Macroscopic engineering properties of polycrystalline materials: elastic properties

J. Appl. Phys.

Percolation and conduction

Rev. Mod. Phys.

Coherent-medium approximation in the stochastic transport theory of random media

Phys. Rev. B

Effective-medium approximation for diffusion on a random lattice

Phys. Rev. Lett.

Frequency dependence of the hopping conductivity of a one-dimensional system calculated by the effective-medium method

Sov. Phys. Solid St.

Stochastic transport in disordered systems

J. Chem. Phys.

Stochastic Processes in Chemical Physics: The Master Equation

Random processes and random systems: an introduction

Percolation theory

Rep. Prog. Phys.

Percolation Theory for Mathematicians

Anomalous diffusion on percolating clusters

Phys. Rev. Lett.

A theory of conductivity in disordered resistor networks

J. Phys. C

On theories of transport in disordered media

J. Phys. C

On Pólya random walks, lattice Green functions and the bond percolation threshold

J. Phys. A