DATE2018-12-06 16:10-17:00


SPEAKER王琪仁 助理教授(中正大學數學系

TITLECritical Droplet Solutions for Non-Equilibrium Phase Transitions in Crystal Lattice Systems

ABSTRACT Discontinuous phase transitions are common in the steady states of diverse non-equilibrium systems describing catalytic reaction-diffusion processes, biological transport, spatial epidemics, etc. These transitions are usually associated with equistability of two stable states, as can be determined by stationarity of a planar interface separating these states. For equilibrium systems, this criterion is equivalent to the Maxwell construction determining coexistence of two states at a unique equistability point. Analyses of nucleation phenomena near such transitions aims in part to characterize critical droplets of the more stable state embedded in the less stable metastable state, where these droplets correspond to stationary curved interfaces between the two states. There is a range of critical droplets and their critical sizes are expected to diverge when approaching the transition. The critical curvature which arrests propagation should vanish linearly approaching the transition. However, the analysis of discontinuous transitions in spatially discrete non-equilibrium systems also reveals an interface propagation failure. As a non-equilibrium counterpart to the classic Ising model, we consider stochastic lattice-versions of Schloegl’s 2nd model involving spontaneous annihilation X→ and autocatalytic creation +2X3X.