Stochastic PDEs: domain formation in dynamic transitions
G.D. Lythe (CNLS, Los Alamos)
TL;DR
This paper investigates how stochastic partial differential equations model domain formation during dynamic phase transitions, providing analytical estimates that match numerical simulations.
Contribution
It introduces analytical estimates for domain sizes in stochastic PDEs during slow parameter sweeps, validated by numerical solutions.
Findings
Analytical estimates align with numerical results.
Domain size depends on noise and sweep rate.
Spatiotemporal evolution is characterized in the Ginzburg-Landau model.
Abstract
Spatiotemporal evolution in the real Ginzburg-Landau equation is studied with space-time noise and a slowly increasing critical parameter. Analytical estimates for the characteristic size of the domains formed in a slow sweep through the critical point agree with the results of finite difference solution of the stochastic PDEs.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Stochastic processes and financial applications · Nonlinear Dynamics and Pattern Formation