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Title: Reaction–drift–diffusion models from master equations: application to material defects

Journal Article · · Modelling and Simulation in Materials Science and Engineering
ORCiD logo [1]; ORCiD logo [2]
  1. Centre National de la Recherche Scientifique (CNRS) (France); Aix-Marseille Univ., Marseille (France)
  2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations

We present a general method to produce well-conditioned continuum reaction–drift–diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e. continuous-time Markov chains) produced from atomic sampling of point defects in locally periodic environments, such as perfect lattices, ordered surface structures or dislocation cores, possibly under the influence of a slowly varying external field. Our approach also applies to any discrete, periodic Markov chain. Here, the analysis identifies a previously omitted non-equilibrium drift term, present even in the absence of external forces, which can compete in magnitude with the reaction rates, thus being essential to correctly capture the kinetics. To remove fast modes which hinder time integration, we use a generalized Bloch relation to efficiently calculate the eigenspectrum of the master equation. A well conditioned continuum equation then emerges by searching for spectral gaps in the long wavelength limit, using an established kinetic clustering algorithm to define a proper reduced, Markovian state space.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
89233218CNA000001
OSTI ID:
2282534
Report Number(s):
LA-UR--21-30179
Journal Information:
Modelling and Simulation in Materials Science and Engineering, Journal Name: Modelling and Simulation in Materials Science and Engineering Journal Issue: 3 Vol. 30; ISSN 0965-0393
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English

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36 MATERIALS SCIENCE
Markov models
coarse graining
defect diffusion
reaction–diffusion equations