%0 Journal Article
%J Journal of Statistical Physics
%D 2011
%T Schloegl's Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis
%A Wang, C. J.
%A Guo, X. F.
%A Liu, D. J.
%A Evans, J. W.
%K behavior
%K catalysis
%K Discrete
%K FAILURE
%K generic 2-phase coexistence
%K generic two-phase coexistence
%K interface
%K interface propagation
%K kinetic phase-transitions
%K propagation
%K reaction-diffusion equations
%K Schloegl's second model
%K systems
%K waves
%M WOS:000297133900011
%P 1308-1328
%R 10.1007/s10955-011-0288-6
%V 144
%X Schloegl's second model for autocatalysis on a hypercubic lattice of dimension d >= 2 involves: (i) spontaneous annihilation of particles at lattice sites with rate p; and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of diagonal pairs of particles on neighboring sites. Kinetic Monte Carlo simulations for a d = 3 cubic lattice reveal a discontinuous transition from a populated state to a vacuum state as p increases above p = p(e). However, stationary points, p = p(eq) (<= p(e)), for planar interfaces separating these states depend on interface orientation. Our focus is on analysis of interface dynamics via discrete reaction-diffusion equations (dRDE's) obtained from mean-field type approximations to the exact master equations for spatially inhomogeneous states. These dRDE can display propagation failure absent due to fluctuations in the stochastic model. However, accounting for this anomaly, dRDE analysis elucidates exact behavior with quantitative accuracy for higher-level approximations.
%Z Wang, Chi-Jen Guo, Xiaofang Liu, Da-Jiang Evans, J. W.Division of Chemical Sciences (Basic Energy Sciences), U.S. Department of Energy (USDOE) through the Ames Laboratory Chemical Physics; PCTC; USDOE by Iowa State University[DE-AC02-07CH11358]This work was supported by the Division of Chemical Sciences (Basic Energy Sciences), U.S. Department of Energy (USDOE) through the Ames Laboratory Chemical Physics and PCTC projects. Ames Laboratory is operated for the USDOE by Iowa State University under Contract No. DE-AC02-07CH11358.29SpringerNew york849oc
%8 09
%9 Article
%@ 0022-4715