711 citations · 2.4k across the 77 of their papers we have counts for
37 papers · 1 filter
Electronic Observables for Relaxed Bilayer 2D Heterostructures in Momentum Space
Daniel Massatt, Stephen Carr, Mitchell Luskin
Momentum space transformations for incommensurate 2D electronic structure calculations are fundamental for reducing computational cost and for representing the data in a more physi…
Modeling and Computation of Kubo Conductivity for 2D Incommensurate Bilayers
Simon Etter, Daniel Massatt, Mitchell Luskin +1
This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. Firstly, we derive…
Homogenization of plasmonic crystals: Seeking the epsilon-near-zero effect
Matthias Maier, Marios Mattheakis, Efthimios Kaxiras +2
By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodicall…
Stability and convergence of the string method for computing minimum energy paths
Brian Van Koten, Mitchell Luskin
We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy…
Analysis of rippling in incommensurate one-dimensional coupled chains
Paul Cazeaux, Mitchell Luskin, Ellad B. Tadmor
Graphene and other recently developed 2D materials exhibit exceptionally strong in-plane stiffness. Relaxation of few-layer structures, either free-standing or on slightly mismatch…
Analysis of a Predictor-Corrector Method for Computationally Efficient Modeling of Surface Effects in 1D
Andrew J. Binder, Mitchell Luskin, Christoph Ortner
The regular Cauchy--Born method is a useful and efficient tool for analyzing bulk properties of materials in the absence of defects. However, the method normally fails to capture s…
Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation
Matthias Maier, Dionisios Margetis, Mitchell Luskin
We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon-polariton, excited along a conducting sheet…
A Theoretical Examination of Diffusive Molecular Dynamics
Gideon Simpson, Mitchell Luskin, David J. Srolovitz
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to fi…
Analysis of an optimization-based atomistic-to-continuum coupling method for point defects
Derek Olson, Alexander V. Shapeev, Pavel Bochev +1
We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-bas…
Analysis of Transition State Theory Rates upon Spatial Coarse-Graining
Andrew Binder, Mitchell Luskin, Danny Perez +1
Spatial multiscale methods have established themselves as useful tools for extending the length scales accessible by conventional statics (i.e., zero temperature molecular dynamics…
Accuracy of computation of crystalline defects at finite temperature
Alexander V. Shapeev, Mitchell Luskin
The present paper aims at developing a theory of computation of crystalline defects at finite temperature. In a one-dimensional setting we introduce Gibbs distributions correspondi…
Development of an Optimization-Based Atomistic-to-Continuum Coupling Method
Derek Olson, Pavel Bochev, Mitchell Luskin +1
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accu…
An Optimization-Based Atomistic-to-Continuum Coupling Method
Derek Olson, Pavel Bochev, Mitchell Luskin +1
We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained o…
Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner +1
We formulate an atomistic-to-continuum coupling method based on blending atomistic and continuum forces. Our precise choice of blending mechanism is informed by theoretical predict…
Numerical Analysis of Parallel Replica Dynamics
Gideon Simpson, Mitchell Luskin
Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by th…
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…
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…
A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods
Brian Van Koten, Xingjie Helen Li, Mitchell Luskin +1
We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems - the stability of a Lomer dislocation pair under shear and the sta…
An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model
Xingjie Helen Li, Mitchell Luskin
The quasi-nonlocal quasicontinuum method (QNL) is a consistent hybrid coupling method for atomistic and continuum models. Embedded atom models are empirical many-body potentials th…
Analysis of the quasi-nonlocal approximation of linear and circular chains in the plane
Pavel Belik, Mitchell Luskin
We give an analysis of the stability and displacement error for linear and circular atomistic chains in the plane when the atomistic energy is approximated by the Cauchy-Born conti…
Analysis of Energy-Based Blended Quasicontinuum Approximations
Brian Van Koten, Mitchell Luskin
The development of patch test consistent quasicontinuum energies for multi-dimensional crystalline solids modeled by many-body potentials remains a challenge. The original quasicon…
A Generalized Quasi-Nonlocal Atomistic-to-Continuum Coupling Method with Finite Range Interaction
Xingjie Helen Li, Mitchell Luskin
The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks and dislocations with…