Publication Date
2-28-2020
Department
Ames Laboratory; Physics and Astronomy; Mathematics
Campus Units
Mathematics, Physics and Astronomy, Ames Laboratory
OSTI ID+
1602361
Report Number
IS-J 10048
DOI
https://doi.org/10.1103/PhysRevE.101.022803
Journal Title
Physical Review E
Volume Number
101
Issue Number
2
First Page
022803
Abstract
Bistable nonequilibrium systems are realized in catalytic reaction-diffusion processes, biological transport and regulation, spatial epidemics, etc. Behavior in spatially continuous formulations, described at the mean-field level by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, peq, of a control parameter, p, with metastability and hysteresis around peq. For each p, there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as p→peq. Spatially discrete analogs of these mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. We show that this feature, together with an orientation dependence of planar interface propagation also deriving from spatial discreteness, results in the occurrence of entire families of stationary droplets. The extent of these families increases approaching the transition and can be infinite if propagation failure is realized. In addition, there can exist a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems.
DOE Contract Number(s)
105-2115-M-194-011-MY2; AC02-07CH11358
Language
en
Department of Energy Subject Categories
97 MATHEMATICS AND COMPUTING
Publisher
Iowa State University Digital Repository, Ames IA (United States)
