Publications (25)
Strong Convergence of Integrators for Nonequilibrium Langevin Dynamics`
Matthew Dobson, Abdel Kader Geraldo
Several numerical schemes are proposed for the solution of Nonequilibrium Langevin Dynamics (NELD), and the rate of convergence is analyzed. Due to the special deforming boundary c…
SN 2019muj -- a well-observed Type Iax supernova that bridges the luminosity gap of the class
Barnabás Barna, Tamás Szalai, Saurabh W. Jha +38
We present early-time ( days) observations of SN 2019muj (= ASASSN-19tr), one of the best-observed members of the peculiar SN Iax class. Ultraviolet and optical photometri…
The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain
Matthew Dobson, Christoph Ortner, Alexander V. Shapeev
We show under general conditions that the linearized force-based quasicontinuum (QCF) operator has a positive spectrum, which is identical to the spectrum of the quasinonlocal quas…
An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the…
On assessing the accuracy of defect free energy computations
Matthew Dobson, Manh Hong Duong, Christoph Ortner
We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit o…
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…