2,364 research outputs found
Fast kinetic Monte Carlo simulation of strained heteroepitaxy in three dimensions
Accelerated algorithms for simulating the morphological evolution of strained
heteroeptiaxy based on a ball and spring lattice model in three dimensions are
explained. We derive exact Green's function formalisms for boundary values in
the associated lattice elasticity problems. The computational efficiency is
further enhanced by using a superparticle surface coarsening approximation.
Atomic hoppings simulating surface diffusion are sampled using a multi-step
acceptance-rejection algorithm. It utilizes quick estimates of the atomic
elastic energies from extensively tabulated values modulated by the local
strain. A parameter controls the compromise between accuracy and efficiency of
the acceptance-rejection algorithm.Comment: 10 pages, 4 figures, submitted to Proceedings of Barrett Lectures
2007, Journal of Scientific Computin
A stochastic model for wound healing
We present a discrete stochastic model which represents many of the salient
features of the biological process of wound healing. The model describes fronts
of cells invading a wound. We have numerical results in one and two dimensions.
In one dimension we can give analytic results for the front speed as a power
series expansion in a parameter, p, that gives the relative size of
proliferation and diffusion processes for the invading cells. In two dimensions
the model becomes the Eden model for p near 1. In both one and two dimensions
for small p, front propagation for this model should approach that of the
Fisher-Kolmogorov equation. However, as in other cases, this discrete model
approaches Fisher-Kolmogorov behavior slowly.Comment: 16 pages, 7 figure
Alignment and Nonlinear Elasticity in Biopolymer Gels
We present a Landau type theory for the non-linear elasticity of biopolymer
gels with a part of the order parameter describing induced nematic order of
fibers in the gel. We attribute the non-linear elastic behavior of these
materials to fiber alignment induced by strain. We suggest an application to
contact guidance of cell motility in tissue. We compare our theory to
simulation of a disordered lattice model for biopolymers. We treat homogeneous
deformations such as simple shear, hydrostatic expansion, and simple extension,
and obtain good agreement between theory and simulation. We also consider a
localized perturbation which is a simple model for a contracting cell in a
medium.Comment: 5 pages, 4 Figure
Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study
We study the morphological evolution of strained heteroepitaxial films using
kinetic Monte Carlo simulations in two dimensions. A novel Green's function
approach, analogous to boundary integral methods, is used to calculate elastic
energies efficiently. We observe island formation at low lattice misfit and
high temperature that is consistent with the Asaro-Tiller-Grinfeld instability
theory. At high misfit and low temperature, islands or pits form according to
the nucleation theory of Tersoff and LeGoues.Comment: 4 pages, 4 figures, ReVTe
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