applied math seminar
Stephen D Bond, Sandia National Laboratories
Monday, October 30, 2017 -
3:30pm to 4:30pm
Numerical methods for simulating diffusion modeled by Generalized Langevin dynamics Abstract:
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. We have derived a family of extended variable integrators for the Generalized Langevin equation (GLE) with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity or position distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel. Connections with physical experiments are presented (including diffusing-wave spectroscopy experiments performed at Sandia). This is joint work with Andrew D. Baczewski (Sandia National Laboratories). Bio: Stephen Bond is a senior research scientist in the Computational Mathematics department at Sandia National Laboratories. He earned a Ph.D. in Mathematics from the University of Kansas in 2000. He was a postdoctoral researcher in the Mathematics and Biochemistry departments at the University of California, San Diego, and an assistant professor in the Computer Science department at the University of Illinois, before moving to Sandia in 2011. His research focuses on the development and analysis of numerical methods for problems arising in biochemistry, chemistry, plasma physics and material science.
Contact Name: Pavel Lushnikov