Cluster dynamics modelling of materials: A new hybrid deterministic/stochastic coupling approach

Terrier, Pierre; Athènes, Manuel; Jourdan, Thomas; Adjanor, Gilles; Stoltz, Gabriel

doi:10.1016/j.jcp.2017.08.015

Cited by 23 publications

(16 citation statements)

References 21 publications

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“…In this case, it is better to use a continuous approach. Terrier et al 133 combined these methods and came up with a hybrid deterministic/ stochastic coupling approach, which has already been successfully applied in a simple ''Fe-Vacancy-H-He'' system. If this hybrid method is extended to complex systems, the simulation scale of CD can be increased by several orders of magnitude.…”

Section: Comparative Discussionmentioning

confidence: 99%

An overview: multiscale simulation in understanding the radiation damage accumulation of reactor materials

Chen

Chu

et al. 2019

SIMULATION

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The reactor is an extreme environment of high temperature, high pressure, and high radiation dose. Damage accumulates in structural materials over service time. It will eventually lead to material failure, such as hardening, embrittlement, and swelling. The radiation damage accumulation is an inherent, complex, and multiscale process, which has been studied extensively with multiscale modeling and simulation methods. The rapid development of high-performance computing makes it possible to accurately operate multiscale simulation for the microstructure evolution of irradiated reactor materials. The European Union, the USA, and China have put great effort into this, and many related works have been carried out. This paper first outlines the basic application of multiscale modeling and simulation technology in understanding the effects of radiation on reactor structural materials. Then, some relevant projects carried out by the USA, the European Union, and China in recent years are summarized. Next, the paper focuses on three widely used simulation techniques at different scales: molecular dynamics, kinetic Monte Carlo, and cluster dynamics. For each method, some key developments in algorithms and computer implementations are reviewed. Finally, the comparison between them is discussed.

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Section: Comparative Discussionmentioning

confidence: 99%

An overview: multiscale simulation in understanding the radiation damage accumulation of reactor materials

Chen

Chu

et al. 2019

SIMULATION

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“…In other works [19,26,27,40], B is set to Diag(A) −1 . This setup arises in the standard KMC method based on (4). Noticeably, it entails that s i = 1/ √ A ii and A B ii = 1 for all i.…”

Section: F Conditional Reversibilitymentioning

confidence: 99%

“…Any KMC method consists of simulating a single kinetic trajectory among the many possible ones. In materials science, KMC methods may treat events [2][3][4], objects [5,6] or atoms [7].…”

Section: Introductionmentioning

confidence: 99%

Elastodiffusion and cluster mobilities using kinetic Monte Carlo simulations: Fast first-passage algorithms for reversible diffusion processes

Athènes

Kaur

Adjanor

et al. 2019

Phys. Rev. Materials

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The microstructural evolution of metals and alloys is governed by the diffusion of defects over complex energy landscapes. Whenever metastability occurs in atomistic simulations, well-separated time scales emerge making it necessary to implement event-based kinetic models at larger scales. The crucial task then involves characterizing the important events contributing to mass transport. We herein describe fast first-passage algorithms based on the theory of absorbing Markov chains assuming that defects undergo reversible diffusion. We show that the absorbing transition rate matrix can be transformed into a symmetric definite-positive matrix enabling us to implement direct and iterative sparse solvers. The efficiency of the approach is demonstrated with direct computations of elastodiffusion properties around a cavity in Aluminum and Monte Carlo computations of cluster diffusivity in low alloyed Manganese steels.

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“…This splitting allows us to work in a simpler framework and to prove rigorously the link between the Fokker-Planck approximation and BD for larger cluster sizes. Moreover, this splitting is also of interest for numerical simulations [42].…”

Section: Introductionmentioning

confidence: 99%

“…This regime is not well described by the Lifshitz-Slyozov equation, but rather by Fokker-Planck type equations, which can be seen as nonlinear transport equations supplemented by a diffusion term. Fokker-Planck equations related to BD were first presented in [16] and are still used and developed in more recent works in the materials science community [23,24,42]. They have also been considered in mathematical studies, where the diffusion is obtained as a higher order correction term in scaling limits [44,18,8].…”

Section: Introductionmentioning

confidence: 99%

A mathematical justification of the finite time approximation of Becker-Döring equations by a Fokker-Planck dynamics

Stoltz,

Terrier

2018

Preprint

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The Becker-Döring equations are an infinite dimensional system of ordinary differntial equations describing coagulation/fragmentation processes of species of integer sizes. Formal Taylor expansions motivate that its solution should be well described by a partial differential equation for large sizes, of advection-diffusion type, called Fokker-Planck equation. We rigorously prove the link between these two descriptions for evolutions on finite times rather than in some hydrodynamic limit, motivated by the results of numerical simulations and the construction of dedicated algorithms based on splitting strategies. In fact, the Becker-Döring equations and the Fokker-Planck equation are related through some pure diffusion with unbounded diffusion coefficient. The crucial point in the analysis is to obtain decay estimates for the solution of this pure diffusion and its derivates to control remainders in the Taylor expansions. The small parameter in this analysis is the inverse of the minimal size of the species.

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Cluster dynamics modelling of materials: A new hybrid deterministic/stochastic coupling approach

Cited by 23 publications

References 21 publications

An overview: multiscale simulation in understanding the radiation damage accumulation of reactor materials

An overview: multiscale simulation in understanding the radiation damage accumulation of reactor materials

Elastodiffusion and cluster mobilities using kinetic Monte Carlo simulations: Fast first-passage algorithms for reversible diffusion processes

A mathematical justification of the finite time approximation of Becker-Döring equations by a Fokker-Planck dynamics

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