711 citations · 2.4k across the 77 of their papers we have counts for
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Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation
Matthew Dobson, Mitchell Luskin
We give an analysis of a continuation algorithm for the numerical solution of the force-based quasicontinuum equations. The approximate solution of the force-based quasicontinuum e…
Non-ergodicity of Nose-Hoover dynamics
Frederic Legoll, Mitchell Luskin, Richard Moeckel
The numerical integration of the Nose-Hoover dynamics gives a deterministic method that is used to sample the canonical Gibbs measure. The Nose-Hoover dynamics extends the physical…
An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method
Mitchell Luskin, Christoph Ortner
We investigate two examples of node-based cluster summation rules that have been proposed for the quasicontinuum method: a force-based approach (Knap & Ortiz, J. Mech. Phys. Solids…
An Analysis of the Effect of Ghost Force Oscillation on Quasicontinuum Error
Matthew Dobson, Mitchell Luskin
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a line…