Publications (84)
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…
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…
Spin-Diffusions and Diffusive Molecular Dynamics
Brittan A Farmer, Mitchell Luskin, Petr PlechÃ¡Ä +1
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds…
Moiré of Moiré: Modeling Mechanical Relaxation in Incommensurate Trilayer van der Waals Heterostructures
Ziyan Zhu, Paul Cazeaux, Mitchell Luskin +1
The incommensurate stacking of multi-layered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physi…
Existence of the first magic angle for the chiral model of bilayer graphene
Alexander B. Watson, Mitchell Luskin
We consider the chiral model of twisted bilayer graphene introduced by Tarnopolsky-Kruchkov-Vishwanath (TKV). TKV have proved that for inverse twist angles such that the effec…
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…