# Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence

Title | Schloegl's second model for autocatalysis on hypercubic lattices: Dimension dependence of generic two-phase coexistence |

Publication Type | Journal Article |

Year of Publication | 2012 |

Authors | Wang CJ, Liu DJ, Evans JW |

Journal Title | Physical Review E |

Volume | 85 |

Pages | 041109 |

Date Published | 04 |

Type of Article | Article |

ISBN Number | 1539-3755 |

Accession Number | WOS:000302699300004 |

Keywords | catalysis, dynamics, FAILURE, interface propagation, kinetic phase-transitions, systems, waves |

Abstract | Schloegl's second model on a (d >= 2)-dimensional hypercubic lattice involves: (i) spontaneous annihilation of particles with rate p and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of suitable pairs of neighboring particles. This model provides a prototype for nonequilibrium discontinuous phase transitions. However, it also exhibits nontrivial generic two-phase coexistence: Stable populated and vacuum states coexist for a finite range, p(f)(d) < p < p(e)(d), spanned by the orientation-dependent stationary points for planar interfaces separating these states. Analysis of interface dynamics from kinetic Monte Carlo simulation and from discrete reaction-diffusion equations (dRDEs) obtained from truncation of the exact master equation, reveals that p(e(f)) similar to 0.211 3765 + c(e(f))/d as d -> infinity, where Delta c = c(e) - c(f) approximate to 0.014. A metastable populated state persists above p(e)(d) up to a spinodal p = p(s)(d), which has a well-defined limit p(s)(d -> infinity) = 1/4. The dRDEs display artificial propagation failure, absent in the stochastic model due to fluctuations. This feature is amplified for increasing d, thus complicating our analysis. |

URL | <Go to ISI>://WOS:000302699300004 |

DOI | 10.1103/PhysRevE.85.041109 |

Alternate Journal | Phys. Rev. E |