Generic two-phase coexistence in a type-2 Schloegl model for autocatalysis on a square lattice: Analysis via heterogeneous master equations
Date
2023-03-03
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Iowa State University Digital Repository, Ames IA (United States)
Abstract
Schloegl’s second model (also known as the quadratic contact process) on a square lattice involves spontaneous
annihilation of particles at lattice sites at rate p, and their autocatalytic creation at unoccupied sites
with n 2 occupied neighbors at rate kn. Kinetic Monte Carlo (KMC) simulation reveals that these models
exhibit a nonequilibrium discontinuous phase transition with generic two-phase coexistence: the p value for
equistability of coexisting populated and vacuum states, peq (S), depends on the orientation or slope, S, of a planar
interface separating those phases. The vacuum state displaces the populated state for p > peq (S), and the opposite
applies for p < peq (S) for 0 < S < ∞. The special “combinatorial” rate choice kn = n(n−1)/12 facilitates
an appealing simplification of the exact master equations for the evolution of spatially heterogeneous states
in the model, which aids analytic investigation of these equations via hierarchical truncation approximations.
Truncation produces coupled sets of lattice differential equations which can describe orientation-dependent
interface propagation and equistability. The pair approximation predicts that peq(max) = peq (S = 1) = 0.096 45
and peq (min) = peq (S→∞) = 0.088 27, values deviating less than 15% from KMC predictions. In the pair
approximation, a perfect vertical interface is stationary for all p < peq (S =∞) = 0.089 07, a value exceeding
peq (S→∞). One can regard an interface for large S→∞as a vertical interface decorated with isolated kinks.
For p < peq (S =∞), the kink can move in either direction along this otherwise stationary interface depending
upon p, but for p = peq (min) the kink is also stationary.
Series Number
Journal Issue
Is Version Of
Versions
Series
IS-J 11008
Academic or Administrative Unit
Type
article
Comments
This article is published as Shen, Zheren, Da-Jiang Liu, and James W. Evans. "Generic two-phase coexistence in a type-2 Schloegl model for autocatalysis on a square lattice: Analysis via heterogeneous master equations." Physical Review E 107, no. 3 (2023): 034104.
DOI: 10.1103/PhysRevE.107.034104.
Copyright 2023 American Physical Society.
Posted with permission.
DOE Contract Number(s): AC02-07CH11358.