TY - JOUR
T1 - A theoretical examination of diffusive molecular dynamics
AU - SIMPSON, G.
AU - LUSKIN, M.
AU - SROLOVITZ, D. J.
PY - 2016
Y1 - 2016
N2 - Diffusive molecular dynamics is a novel model for materials incorporating atomistic resolution and reaching diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy of the system with respect to the mean atomic coordinates (averaging over many vibrational periods), and to then perform a diffusive step where atoms and vacancies (or two species in a binary alloy) flow on a diffusive time scale via a master equation. We present a mathematical framework for studying this algorithm based on relative entropy, also known as the Kullback-Leibler divergence. This adds flexibility in how the algorithm is implemented and interpreted. We then compare our formulation, relying on relative entropy and absolute continuity of measures, to existing formulations and find agreement.
AB - Diffusive molecular dynamics is a novel model for materials incorporating atomistic resolution and reaching diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy of the system with respect to the mean atomic coordinates (averaging over many vibrational periods), and to then perform a diffusive step where atoms and vacancies (or two species in a binary alloy) flow on a diffusive time scale via a master equation. We present a mathematical framework for studying this algorithm based on relative entropy, also known as the Kullback-Leibler divergence. This adds flexibility in how the algorithm is implemented and interpreted. We then compare our formulation, relying on relative entropy and absolute continuity of measures, to existing formulations and find agreement.
KW - Diffusive
KW - Molecular dynamics
KW - Relative entropy
UR - http://www.scopus.com/inward/record.url?scp=85007140048&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85007140048&origin=recordpage
U2 - 10.1137/15M1024858
DO - 10.1137/15M1024858
M3 - RGC 21 - Publication in refereed journal
VL - 76
SP - 2175
EP - 2195
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 6
ER -