Doctoral Dissertations

Orcid ID

https://orcid.org/0000-0002-6394-0695

Date of Award

5-2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Tim Schulze

Committee Members

Ohannes Karakashian, Steven Wise, Haixuan Xu

Abstract

We introduce a new kinetic Monte Carlo (KMC) algorithm for off-lattice simulation. In off-lattice KMC one needs to calculate the rates for all possible moves from the current state by searching the energy landscape for index-1 saddle points surrounding the current basin of attraction. We introduce a rejection scheme where the true rates are replaced by rate estimates. This is done by first associating each saddle point with a key atom defined to be the atom that moves the most or that corresponds to the largest energy change if the transition were to take a place, then constructing an estimate for the total rate associated with each atom by using a nearest-neighbor bond count. These estimates allow one to select a set of possible transitions, one of which is accepted or rejected based on a localized saddle point search focused on a particular atom. In principle, this allows a performance boost that scales with the number of particles in the system. We test the method on a growing two-species nanocluster with an emerging core-shell structure bound by Lennard-Jones potential. In addition to that, we give a detailed review for the dimer method used in this study to locate index-1 saddle points on the potential energy surface.

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