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

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

Publication Type | Journal Article |

Year of Publication | 2011 |

Authors | Wang CJ, Guo XF, Liu DJ, Evans JW |

Journal Title | Journal of Statistical Physics |

Volume | 144 |

Pages | 1308-1328 |

Date Published | 09 |

Type of Article | Article |

ISBN Number | 0022-4715 |

Accession Number | WOS:000297133900011 |

Keywords | behavior, catalysis, Discrete, FAILURE, generic 2-phase coexistence, generic two-phase coexistence, interface, interface propagation, kinetic phase-transitions, propagation, reaction-diffusion equations, Schloegl's second model, systems, waves |

Abstract | 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. |

DOI | 10.1007/s10955-011-0288-6 |

Alternate Journal | J. Stat. Phys. |