Schloegl’s Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis

摘要: Schloegl’s second model for autocatalysis on a hypercubic lattice of dimension d≥2 involves: (i) spontaneous annihilation particles at sites with rate p; and (ii) autocatalytic creation vacant proportional to the number diagonal pairs neighboring sites. Kinetic Monte Carlo simulations d=3 cubic reveal discontinuous transition from populated state vacuum as p increases above p=p e . However, stationary points, eq (≤p ), planar interfaces separating these states depend interface orientation. Our focus is analysis dynamics via discrete reaction-diffusion equations (dRDE’s) obtained mean-field type approximations exact master spatially inhomogeneous states. These dRDE can display propagation failure absent due fluctuations in stochastic model. accounting this anomaly, elucidates behavior quantitative accuracy higher-level approximations.