87 research outputs found
Efficient kinetic Monte Carlo method for reaction-diffusion processes with spatially varying annihilation rates
We present an efficient Monte Carlo method to simulate reaction-diffusion
processes with spatially varying particle annihilation or transformation rates
as it occurs for instance in the context of motor-driven intracellular
transport. Like Green's function reaction dynamics and first-passage time
methods, our algorithm avoids small diffusive hops by propagating sufficiently
distant particles in large hops to the boundaries of protective domains. Since
for spatially varying annihilation or transformation rates the single particle
diffusion propagator is not known analytically, we present an algorithm that
generates efficiently either particle displacements or annihilations with the
correct statistics, as we prove rigorously. The numerical efficiency of the
algorithm is demonstrated with an illustrative example.Comment: 13 pages, 5 figure
Structures and transitions in bcc tungsten grain boundaries and their role in the absorption of point defects
We use atomistic simulations to investigate grain boundary (GB) phase
transitions in el- emental body-centered cubic (bcc) metal tungsten. Motivated
by recent modeling study of grain boundary phase transitions in [100] symmetric
tilt boundaries in face-centered cu- bic (fcc) copper, we perform a systematic
investigation of [100] and [110] symmetric tilt high-angle and low-angle
boundaries in bcc tungsten. The structures of these boundaries have been
investigated previously by atomistic simulations in several different bcc
metals including tungsten using the the {\gamma}-surface method, which has
limitations. In this work we use a recently developed computational tool based
on the USPEX structure prediction code to perform an evolutionary grand
canonical search of GB structure at 0 K. For high-angle [100] tilt boundaries
the ground states generated by the evolutionary algorithm agree with the
predictions of the {\gamma}-surface method. For the [110] tilt boundaries, the
search predicts novel high-density low-energy grain boundary structures and
multiple grain boundary phases within the entire misorientation range.
Molecular dynamics simulation demonstrate that the new structures are more
stable at high temperature. We observe first-order grain boundary phase
transitions and investigate how the structural multiplicity affects the
mechanisms of the point defect absorption. Specifically, we demonstrate a
two-step nucleation process, when initially the point defects are absorbed
through a formation of a metastable GB structure with higher density, followed
by a transformation of this structure into a GB interstitial loop or a
different GB phase.Comment: 40 pages, 19 figure
Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method
Computational tools for characterizing electromagnetic scattering from
objects with uncertain shapes are needed in various applications ranging from
remote sensing at microwave frequencies to Raman spectroscopy at optical
frequencies. Often, such computational tools use the Monte Carlo (MC) method to
sample a parametric space describing geometric uncertainties. For each sample,
which corresponds to a realization of the geometry, a deterministic
electromagnetic solver computes the scattered fields. However, for an accurate
statistical characterization the number of MC samples has to be large. In this
work, to address this challenge, the continuation multilevel Monte Carlo
(CMLMC) method is used together with a surface integral equation solver. The
CMLMC method optimally balances statistical errors due to sampling of the
parametric space, and numerical errors due to the discretization of the
geometry using a hierarchy of discretizations, from coarse to fine. The number
of realizations of finer discretizations can be kept low, with most samples
computed on coarser discretizations to minimize computational cost.
Consequently, the total execution time is significantly reduced, in comparison
to the standard MC scheme.Comment: 25 pages, 10 Figure
Efficient Reactive Brownian Dynamics
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle
simulations of reaction-diffusion systems based on the Doi or volume reactivity
model, in which pairs of particles react with a specified Poisson rate if they
are closer than a chosen reactive distance. In our Doi model, we ensure that
the microscopic reaction rules for various association and disassociation
reactions are consistent with detailed balance (time reversibility) at
thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to
separate reaction and diffusion, and solves both the diffusion-only and
reaction-only subproblems exactly, even at high packing densities. To
efficiently process reactions without uncontrolled approximations, SRBD employs
an event-driven algorithm that processes reactions in a time-ordered sequence
over the duration of the time step. A grid of cells with size larger than all
of the reactive distances is used to schedule and process the reactions, but
unlike traditional grid-based methods such as Reaction-Diffusion Master
Equation (RDME) algorithms, the results of SRBD are statistically independent
of the size of the grid used to accelerate the processing of reactions. We use
the SRBD algorithm to compute the effective macroscopic reaction rate for both
reaction- and diffusion-limited irreversible association in three dimensions.
We also study long-time tails in the time correlation functions for reversible
association at thermodynamic equilibrium. Finally, we compare different
particle and continuum methods on a model exhibiting a Turing-like instability
and pattern formation. We find that for models in which particles diffuse off
lattice, such as the Doi model, reactions lead to a spurious enhancement of the
effective diffusion coefficients.Comment: To appear in J. Chem. Phy
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