711 citations · 2.4k across the 77 of their papers we have counts for
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Positive-Definiteness of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner
The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasi…
Formulation and optimization of the energy-based blended quasicontinuum method
M. Luskin, C. Ortner, B. Van Koten
We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical result…
Lattice Stability for Atomistic Chains Modeled by Local Approximations of the Embedded Atom Method
Xingjie Helen Li, Mitchell Luskin
The accurate approximation of critical strains for lattice instability is a key criterion for predictive computational modeling of materials. In this paper, we present a comparison…
A mathematical formalization of the parallel replica dynamics
C. Le Bris, T. Lelièvre, M. Luskin +1
The purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics and molecular dynamics, namely the parall…
Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation
Mitchell Luskin, Christoph Ortner
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementin…