Stochastic Dynamics of Crystal Defects

Swinburne, Thomas D.

doi:10.1007/978-3-319-20019-4

“…Using the Einstein relation D = kT/(LB), where L = k121ka, the drag parameter B was extracted at each temperature. This di↵usion-based, zero- stress simulation method to measure dislocation drag has been shown to be in very good agreement with drift-based, stressdriven simulations (Swinburne, 2015), a demonstration of the fluctuation-dissipation relation as applied to dislocations. Simulation results are shown in fig.…”

Section: Fitting Procedures For H111i{110} Edge Dislocationssupporting

confidence: 64%

A phenomenological dislocation mobility law for bcc metals

Po

¹

,

Cui

²

,

Rivera

³

et al. 2016

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a b s t r a c tDislocation motion in body centered cubic (bcc) metals displays a number of specific features that result in a strong temperature dependence of the flow stress, and in shear deformation asymmetries relative to the loading direction as well as crystal orientation. Here we develop a generalized dislocation mobility law in bcc metals, and demonstrate its use in discrete Dislocation Dynamics (DD) simulations of plastic flow in tungsten (W) micro pillars. We present the theoretical background for dislocation mobility as a motivating basis for the developed law. Analytical theory, molecular dynamics (MD) simulations, and experimental data are used to construct a general phenomenological description. The usefulness of the mobility law is demonstrated through its application to modeling the plastic deformation of W micro pillars. The model is consistent with experimental observations of temperature and orientation dependence of the flow stress and the corresponding dislocation microstructure.

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“…If the objectives of a simulation are 'static' macroscopic equilibrium properties such as free energy or reaction rates, then a wide variety of choices of proxy dynamics which appropriately sample the relevant measures are available. However, if the objective is to capture a dynamical property of the physical system such as kinematic viscosity or a diffusion rate, then it is important to capture the correct effective dynamics of the reaction coordinates arising due to the relevant dynamics of the full system over moderate timescales [9,19,25,47,51,64].…”

Section: Introductionmentioning

confidence: 99%

Coarse-Graining of Overdamped Langevin Dynamics via the Mori--Zwanzig Formalism

Hudson¹,

Li²

2020

Multiscale Model. Simul.

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The Mori-Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and its use in deriving approximate models, a particular benchmark example is studied both numerically and via a formal asymptotic expansion. The example considered demonstrates the importance of memory effects in determining the correct temporal behaviour of such systems.

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“…If the objectives of a simulation are 'static' macroscopic equilibrium properties such as free energy or reaction rates, then a wide variety of choices of proxy dynamics which appropriately sample the relevant measures are available. However, if the objective is to capture a dynamical property of the physical system such as kinematic viscosity or a diffusion rate, then it is important to capture the correct effective dynamics of the reaction coordinates arising due to the relevant dynamics of the full system over moderate timescales [8,18,24,44,48,57].…”

Section: Introductionmentioning

confidence: 99%

Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism

Hudson¹,

Li²

2018

Preprint

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The Mori-Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and its use in deriving approximate models, a particular benchmark example is studied both numerically and via a formal asymptotic expansion. The example considered demonstrates the importance of memory effects in determining the correct temporal behaviour of such systems.

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Stochastic Dynamics of Crystal Defects

Abstract: The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 6 publications

References 72 publications

A phenomenological dislocation mobility law for bcc metals

A phenomenological dislocation mobility law for bcc metals

Coarse-Graining of Overdamped Langevin Dynamics via the Mori--Zwanzig Formalism

Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism

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