3 research outputs found
Rejection Enhanced Off-Lattice Kinetic Monte Carlo
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
Upscaling a model for the thermally-driven motion of screw dislocations
We formulate and study a stochastic model for the thermally-driven motion of
interacting straight screw dislocations in a cylindrical domain with a convex
polygonal cross-section. Motion is modelled as a Markov jump process, where
waiting times for transitions from state to state are assumed to be
exponentially distributed with rates expressed in terms of the potential energy
barrier between the states. Assuming the energy of the system is described by a
discrete lattice model, a precise asymptotic description of the energy barriers
between states is obtained. Through scaling of the various physical constants,
two dimensionless parameters are identified which govern the behaviour of the
resulting stochastic evolution. In an asymptotic regime where these parameters
remain fixed, the process is found to satisfy a Large Deviations Principle. A
sufficiently explicit description of the corresponding rate functional is
obtained such that the most probable path of the dislocation configuration may
be described as the solution of Discrete Dislocation Dynamics with an explicit
anisotropic mobility which depends on the underlying lattice structure.Comment: Major revision, including overhaul of notation, additions to Section
6 on Large Deviations, and resolution of conjecture in original version. 45
pages, 2 figures, 1 tabl