Random walks on cubic lattices with bond disorder
Abstract
The authors consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness the authors can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentration c. The method is applied to a hopping model on a d-dimensional cubic lattice having two types of bonds with conductivity sigma and sigma/sub 0/ = 1, with concentrations c and 1-c, respectively. For the square lattice the authors explicitly calculate the diffusion coefficient D(c,sigma) as a function of c, to O(c/sup 2/) terms included for different ratios of the bond conductivity sigma. The probability of return at long times is given by P/sub 0/(t) approx. (4..pi..D(c,sigma)t)/sup -d/2/, which is determined by the diffusion coefficient of the disordered system.
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Utrecht, Netherlands
- OSTI Identifier:
- 6312591
- Resource Type:
- Journal Article
- Journal Name:
- J. Stat. Phys.; (United States)
- Additional Journal Information:
- Journal Volume: 45:5/6
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CUBIC LATTICES; COMPUTERIZED SIMULATION; SUPERCONDUCTIVITY; TRANSPORT THEORY; CRYSTAL MODELS; DIFFUSION; GREEN FUNCTION; IMPURITIES; LAPLACE TRANSFORMATION; LORENTZ GAS; ORDER PARAMETERS; ORDER-DISORDER TRANSFORMATIONS; PROBABILITY; RANDOMNESS; SCATTERING; SYMMETRY; TWO-DIMENSIONAL CALCULATIONS; CRYSTAL LATTICES; CRYSTAL STRUCTURE; ELECTRIC CONDUCTIVITY; ELECTRICAL PROPERTIES; FLUIDS; FULLY IONIZED GASES; FUNCTIONS; GASES; INTEGRAL TRANSFORMATIONS; IONIZED GASES; MATHEMATICAL MODELS; PHASE TRANSFORMATIONS; PHYSICAL PROPERTIES; SIMULATION; TRANSFORMATIONS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
Citation Formats
Ernst, M H, and van Velthoven, P F.J. Random walks on cubic lattices with bond disorder. United States: N. p., 1986.
Web. doi:10.1007/BF01020586.
Ernst, M H, & van Velthoven, P F.J. Random walks on cubic lattices with bond disorder. United States. https://doi.org/10.1007/BF01020586
Ernst, M H, and van Velthoven, P F.J. 1986.
"Random walks on cubic lattices with bond disorder". United States. https://doi.org/10.1007/BF01020586.
@article{osti_6312591,
title = {Random walks on cubic lattices with bond disorder},
author = {Ernst, M H and van Velthoven, P F.J.},
abstractNote = {The authors consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness the authors can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentration c. The method is applied to a hopping model on a d-dimensional cubic lattice having two types of bonds with conductivity sigma and sigma/sub 0/ = 1, with concentrations c and 1-c, respectively. For the square lattice the authors explicitly calculate the diffusion coefficient D(c,sigma) as a function of c, to O(c/sup 2/) terms included for different ratios of the bond conductivity sigma. The probability of return at long times is given by P/sub 0/(t) approx. (4..pi..D(c,sigma)t)/sup -d/2/, which is determined by the diffusion coefficient of the disordered system.},
doi = {10.1007/BF01020586},
url = {https://www.osti.gov/biblio/6312591},
journal = {J. Stat. Phys.; (United States)},
number = ,
volume = 45:5/6,
place = {United States},
year = {Mon Dec 01 00:00:00 EST 1986},
month = {Mon Dec 01 00:00:00 EST 1986}
}