Logo image
Back
Spin-diffusions and diffusive molecular dynamics
Journal article   Open access   Peer reviewed

Spin-diffusions and diffusive molecular dynamics

Brittan Farmer, Mitchell Luskin, Petr Plechá, Gideon Simpson and Univ. of Minnesota, Minneapolis, MN (United States)
Modelling and simulation in materials science and engineering, v 25(8), p84003
24 Oct 2017
DOI: https://doi.org/10.1088/1361-651X/aa8e55
url
http://arxiv.org/abs/1702.01469View
SubmittedOpen Access (License Unspecified),  Open

Abstract

diffusive molecular dynamics kinetic Monte Carlo mean field approximation metastability quasistationary distributions
Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

Metrics

9 Record Views
2 citations in Web of Science
3 citations in Scopus

Details

InCites Highlights

Data related to this publication, from InCites Benchmarking & Analytics tool:

Collaboration types
Domestic collaboration
Web of Science research areas
Materials Science, Multidisciplinary
Physics, Applied
Logo image