Irreversible random and cooperative processes on lattices: Spatial correlations

Journal Article · Mon Oct 01 00:00:00 EDT 1984 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526021· OSTI ID:6536724

Evans, J W; Burgess, D R; Hoffman, D K

For processes where ''filling'' events occur irreversibly and, in general, cooperatively at the sites of a lattice, the minimal closed hierarchy of rate equations involves only probabilities for (effectively) connected subconfigurations of empty sites. Extended hierarchies of equations for (effectively) disconnected empty subconfigurations couple back to these. Here we consider a solution to the latter via previously developed exact and approximate truncation schemes based on a shielding property of empty sites. Numerical results for several processes are presented for correlation behavior in both autocatalytic and autoinhibitory rate regimes. The asymptotic large separation behavior of the spatial correlations is analyzed most easily by z-transforming the equations with respect to separations and is fundamentally different from that of equilibrium distributions.

• Research Organization: Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 6536724
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 25:10; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

656000 -- Condensed Matter Physics
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CORRELATIONS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
DATA
DISTRIBUTION
EQUILIBRIUM
INFORMATION
IRREVERSIBLE PROCESSES
NUMERICAL DATA
PROBABILITY
RANDOMNESS