88 research outputs found
Multiscale Kinetic Monte-Carlo for Simulating Epitaxial Growth
We present a fast Monte-Carlo algorithm for simulating epitaxial surface
growth, based on the continuous-time Monte-Carlo algorithm of Bortz, Kalos and
Lebowitz. When simulating realistic growth regimes, much computational time is
consumed by the relatively fast dynamics of the adatoms. Continuum and
continuum-discrete hybrid methods have been developed to approach this issue;
however in many situations, the density of adatoms is too low to efficiently
and accurately simulate as a continuum. To solve the problem of fast adatom
dynamics, we allow adatoms to take larger steps, effectively reducing the
number of transitions required. We achieve nearly a factor of ten speed up, for
growth at moderate temperatures and large D/F.Comment: 7 pages, 6 figures; revised text, accepted by PR
A Hybrid Monte Carlo Method for Surface Growth Simulations
We introduce an algorithm for treating growth on surfaces which combines
important features of continuum methods (such as the level-set method) and
Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in
continuum theory, but attach them to islands one atom at a time. The technique
is borrowed from the Dielectric Breakdown Model. Our method allows us to give a
realistic account of fluctuations in island shape, which is lacking in
deterministic continuum treatments and which is an important physical effect.
Our method should be most important for problems close to equilibrium where KMC
becomes impractically slow.Comment: 4 pages, 5 figure
Matter-Wave Solitons in the Presence of Collisional Inhomogeneities: Perturbation theory and the impact of derivative terms
We study the dynamics of bright and dark matter-wave solitons in the presence
of a spatially varying nonlinearity. When the spatial variation does not
involve zero crossings, a transformation is used to bring the problem to a
standard nonlinear Schrodinger form, but with two additional terms: an
effective potential one and a non-potential term. We illustrate how to apply
perturbation theory of dark and bright solitons to the transformed equations.
We develop the general case, but primarily focus on the non-standard special
case whereby the potential term vanishes, for an inverse square spatial
dependence of the nonlinearity. In both cases of repulsive and attractive
interactions, appropriate versions of the soliton perturbation theory are shown
to accurately describe the soliton dynamics.Comment: 12 pages, 5 fugure
ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation
An Alternative Method to Deduce Bubble Dynamics in Single Bubble Sonoluminescence Experiments
In this paper we present an experimental approach that allows to deduce the
important dynamical parameters of single sonoluminescing bubbles (pressure
amplitude, ambient radius, radius-time curve) The technique is based on a few
previously confirmed theoretical assumptions and requires the knowledge of
quantities such as the amplitude of the electric excitation and the phase of
the flashes in the acoustic period. These quantities are easily measurable by a
digital oscilloscope, avoiding the cost of expensive lasers, or ultrafast
cameras of previous methods. We show the technique on a particular example and
compare the results with conventional Mie scattering. We find that within the
experimental uncertainties these two techniques provide similar results.Comment: 8 pages, 5 figures, submitted to Phys. Rev.
Kinetic Monte Carlo Simulation of Strained Heteroepitaxial Growth with Intermixing
An efficient method for the simulation of strained heteroepitaxial growth
with intermixing using kinetic Monte Carlo is presented. The model used is
based on a solid-on-solid bond counting formulation in which elastic effects
are incorporated using a ball and spring model. While idealized, this model
nevertheless captures many aspects of heteroepitaxial growth, including
nucleation, surface diffusion, and long range effects due elastic interaction.
The algorithm combines a fast evaluation of the elastic displacement field with
an efficient implementation of a rejection-reduced kinetic Monte Carlo based on
using upper bounds for the rates. The former is achieved by using a multigrid
method for global updates of the displacement field and an expanding box method
for local updates. The simulations show the importance of intermixing on the
growth of a strained film. Further the method is used to simulate the growth of
self-assembled stacked quantum dots
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