Publications (45)
Conservative Integrators for a Toy Model of Weak Turbulence
Aquil D. Jones, Gideon Simpson, William Wilson
Weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers, while persisting for all finite time. It has been conjectured by Bourg…
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…
A splitting method to reduce MCMC variance
Robert J. Webber, David Aristoff, Gideon Simpson
We explore whether splitting and killing methods can improve the accuracy of Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions.…
Focusing Singularity in a Derivative Nonlinear Schrödinger Equation
Xiao Liu, Gideon Simpson, Catherine Sulem
We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, . In the -supercritical regime, , our sim…
Petviashvilli's Method for the Dirichlet Problem
Derek Olson, Soumitra Shukla, Gideon Simpson +1
We examine the Petviashvilli method for solving the equation on a bounded domain with Dirichlet boundary conditions. We prove a…
Asymptotic Stability of Ascending Solitary Magma Waves
Gideon Simpson, Michael I. Weinstein
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is fou…