49 research outputs found
Persistence exponents for fluctuating interfaces
Numerical and analytic results for the exponent \theta describing the decay
of the first return probability of an interface to its initial height are
obtained for a large class of linear Langevin equations. The models are
parametrized by the dynamic roughness exponent \beta, with 0 < \beta < 1; for
\beta = 1/2 the time evolution is Markovian. Using simulations of
solid-on-solid models, of the discretized continuum equations as well as of the
associated zero-dimensional stationary Gaussian process, we address two
problems: The return of an initially flat interface, and the return to an
initial state with fully developed steady state roughness. The two problems are
shown to be governed by different exponents. For the steady state case we point
out the equivalence to fractional Brownian motion, which has a return exponent
\theta_S = 1 - \beta. The exponent \theta_0 for the flat initial condition
appears to be nontrivial. We prove that \theta_0 \to \infty for \beta \to 0,
\theta_0 \geq \theta_S for \beta
1/2, and calculate \theta_{0,S} perturbatively to first order in an expansion
around the Markovian case \beta = 1/2. Using the exact result \theta_S = 1 -
\beta, accurate upper and lower bounds on \theta_0 can be derived which show,
in particular, that \theta_0 \geq (1 - \beta)^2/\beta for small \beta.Comment: 12 pages, REVTEX, 6 Postscript figures, needs multicol.sty and
epsf.st
Evaporation and Step Edge Diffusion in MBE
Using kinetic Monte-Carlo simulations of a Solid-on-Solid model we
investigate the influence of step edge diffusion (SED) and evaporation on
Molecular Beam Epitaxy (MBE). Based on these investigations we propose two
strategies to optimize MBE-growth. The strategies are applicable in different
growth regimes: during layer-by-layer growth one can reduce the desorption rate
using a pulsed flux. In three-dimensional (3D) growth the SED can help to grow
large, smooth structures. For this purpose the flux has to be reduced with time
according to a power law.Comment: 5 pages, 2 figures, latex2e (packages: elsevier,psfig,latexsym
Spatial distribution of persistent sites
We study the distribution of persistent sites (sites unvisited by particles
) in one dimensional reaction-diffusion model. We define
the {\it empty intervals} as the separations between adjacent persistent sites,
and study their size distribution as a function of interval length
and time . The decay of persistence is the process of irreversible
coalescence of these empty intervals, which we study analytically under the
Independent Interval Approximation (IIA). Physical considerations suggest that
the asymptotic solution is given by the dynamic scaling form
with the average interval size . We show
under the IIA that the scaling function as and
decays exponentially at large . The exponent is related to the
persistence exponent through the scaling relation .
We compare these predictions with the results of numerical simulations. We
determine the two-point correlation function under the IIA. We find
that for , where , in agreement
with our earlier numerical results.Comment: 15 pages in RevTeX, 5 postscript figure
Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect
A flux line in a Type-II superconductor with a single nonuniform columnar
defect is studied by a perturbative diagrammatic expansion around an annealed
approximation. The system undergoes a finite temperature depinning transition
for the (rather unphysical) on-the-average repulsive columnar defect, provided
that the fluctuations along the axis are sufficiently large to cause some
portions of the column to become attractive. The perturbative expansion is
convergent throughout the weak pinning regime and becomes exact as the
depinning transition is approached, providing an exact determination of the
depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st
Stochastic growth equations on growing domains
The dynamics of linear stochastic growth equations on growing substrates is
studied. The substrate is assumed to grow in time following the power law
, where the growth index is an arbitrary positive number.
Two different regimes are clearly identified: for small the interface
becomes correlated, and the dynamics is dominated by diffusion; for large
the interface stays uncorrelated, and the dynamics is dominated by
dilution. In this second regime, for short time intervals and spatial scales
the critical exponents corresponding to the non-growing substrate situation are
recovered. For long time differences or large spatial scales the situation is
different. Large spatial scales show the uncorrelated character of the growing
interface. Long time intervals are studied by means of the auto-correlation and
persistence exponents. It becomes apparent that dilution is the mechanism by
which correlations are propagated in this second case.Comment: Published versio
Persistence and survival in equilibrium step fluctuations
Results of analytic and numerical investigations of first-passage properties
of equilibrium fluctuations of monatomic steps on a vicinal surface are
reviewed. Both temporal and spatial persistence and survival probabilities, as
well as the probability of persistent large deviations are considered. Results
of experiments in which dynamical scanning tunneling microscopy is used to
evaluate these first-passage properties for steps with different microscopic
mechanisms of mass transport are also presented and interpreted in terms of
theoretical predictions for appropriate models. Effects of discrete sampling,
finite system size and finite observation time, which are important in
understanding the results of experiments and simulations, are discussed.Comment: 30 pages, 12 figures, review paper for a special issue of JSTA
Unconventional MBE Strategies from Computer Simulations for Optimized Growth Conditions
We investigate the influence of step edge diffusion (SED) and desorption on
Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the
solid-on-solid (SOS) model. Based on these investigations we propose two
strategies to optimize MBE growth. The strategies are applicable in different
growth regimes: During layer-by-layer growth one can exploit the presence of
desorption in order to achieve smooth surfaces. By additional short high flux
pulses of particles one can increase the growth rate and assist layer-by-layer
growth. If, however, mounds are formed (non-layer-by-layer growth) the SED can
be used to control size and shape of the three-dimensional structures. By
controlled reduction of the flux with time we achieve a fast coarsening
together with smooth step edges.Comment: 19 pages, 7 figures, submitted to Phys. Rev.
Growth of Patterned Surfaces
During epitaxial crystal growth a pattern that has initially been imprinted
on a surface approximately reproduces itself after the deposition of an integer
number of monolayers. Computer simulations of the one-dimensional case show
that the quality of reproduction decays exponentially with a characteristic
time which is linear in the activation energy of surface diffusion. We argue
that this life time of a pattern is optimized, if the characteristic feature
size of the pattern is larger than , where is the surface
diffusion constant, the deposition rate and the surface dimension.Comment: 4 pages, 4 figures, uses psfig; to appear in Phys. Rev. Let
Spatial Persistence of Fluctuating Interfaces
We show that the probability, P_0(l), that the height of a fluctuating
(d+1)-dimensional interface in its steady state stays above its initial value
up to a distance l, along any linear cut in the d-dimensional space, decays as
P_0(l) \sim l^(-\theta). Here \theta is a `spatial' persistence exponent, and
takes different values, \theta_s or \theta_0, depending on how the point from
which l is measured is specified. While \theta_s is related to fractional
Brownian motion, and can be determined exactly, \theta_0 is non-trivial even
for Gaussian interfaces.Comment: 5 pages, new material adde
Denaturation of Heterogeneous DNA
The effect of heterogeneous sequence composition on the denaturation of
double stranded DNA is investigated. The resulting pair-binding energy
variation is found to have a negligible effect on the critical properties of
the smooth second order melting transition in the simplest (Peyrard-Bishop)
model. However, sequence heterogeneity is dramatically amplified upon adopting
a more realistic treatment of the backbone stiffness. The model yields features
of ``multi-step melting'' similar to those observed in experiments.Comment: 4 pages, LaTeX, text and figures also available at
http://matisse.ucsd.edu/~hw