8 research outputs found
Analytical solution of generalized Burton--Cabrera--Frank equations for growth and post--growth equilibration on vicinal surfaces
We investigate growth on vicinal surfaces by molecular beam epitaxy making
use of a generalized Burton--Cabrera--Frank model. Our primary aim is to
propose and implement a novel analytical program based on a perturbative
solution of the non--linear equations describing the coupled adatom and dimer
kinetics. These equations are considered as originating from a fully
microscopic description that allows the step boundary conditions to be directly
formulated in terms of the sticking coefficients at each step. As an example,
we study the importance of diffusion barriers for adatoms hopping down
descending steps (Schwoebel effect) during growth and post-growth equilibration
of the surface.Comment: 16 pages, REVTeX 3.0, IC-DDV-94-00
Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution
In this work we incorporate, in a unified way, two anomalous behaviors, the
power law and stretched exponential ones, by considering the radial dependence
of the -dimensional nonlinear diffusion equation where , ,
, and are real parameters and is a time-dependent
source. This equation unifies the O'Shaugnessy-Procaccia anomalous diffusion
equation on fractals () and the spherical anomalous diffusion for
porous media (). An exact spherical symmetric solution of this
nonlinear Fokker-Planck equation is obtained, leading to a large class of
anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation
are also discussed by introducing an effective potential.Comment: Latex, 6 pages. To appear in Phys. Rev.
Superpositions of Probability Distributions
Probability distributions which can be obtained from superpositions of
Gaussian distributions of different variances v = \sigma ^2 play a favored role
in quantum theory and financial markets. Such superpositions need not
necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian
processes because they may introduce memory effects. We derive the general form
of the smearing distributions in v which do not destroy the semigroup property.
The smearing technique has two immediate applications. It permits simplifying
the system of Kramers-Moyal equations for smeared and unsmeared conditional
probabilities, and can be conveniently implemented in the path integral
calculus. In many cases, the superposition of path integrals can be evaluated
much easier than the initial path integral. Three simple examples are
presented, and it is shown how the technique is extended to quantum mechanics.Comment: 23 pages, RevTeX, minor changes, accepted to Phys. Rev.
A Simple Model for Anisotropic Step Growth
We consider a simple model for the growth of isolated steps on a vicinal
crystal surface. It incorporates diffusion and drift of adatoms on the terrace,
and strong step and kink edge barriers. Using a combination of analytic methods
and Monte Carlo simulations, we study the morphology of growing steps in
detail. In particular, under typical Molecular Beam Epitaxy conditions the step
morphology is linearly unstable in the model and develops fingers separated by
deep cracks. The vertical roughness of the step grows linearly in time, while
horizontally the fingers coarsen proportional to . We develop scaling
arguments to study the saturation of the ledge morphology for a finite width
and length of the terrace.Comment: 20 pages, 12 figures; [email protected]