3,619 research outputs found
Persistence of Kardar-Parisi-Zhang Interfaces
The probabilities that a growing Kardar-Parisi-Zhang interface
remains above or below the mean height in the time interval are
shown numerically to decay as with and . Bounds on are
derived from the height autocorrelation function under the assumption of
Gaussian statistics. The autocorrelation exponent for a
--dimensional interface with roughness and dynamic exponents and
is conjectured to be . For a recently proposed
discretization of the KPZ equation we find oscillatory persistence
probabilities, indicating hidden temporal correlations.Comment: 4 pages, 3 figures, uses revtex and psfi
Anti-Coarsening and Complex Dynamics of Step Bunches on Vicinal Surfaces during Sublimation
A sublimating vicinal crystal surface can undergo a step bunching instability
when the attachment-detachment kinetics is asymmetric, in the sense of a normal
Ehrlich-Schwoebel effect. Here we investigate this instability in a model that
takes into account the subtle interplay between sublimation and step-step
interactions, which breaks the volume-conserving character of the dynamics
assumed in previous work. On the basis of a systematically derived continuum
equation for the surface profile, we argue that the non-conservative terms pose
a limitation on the size of emerging step bunches. This conclusion is supported
by extensive simulations of the discrete step dynamics, which show breakup of
large bunches into smaller ones as well as arrested coarsening and periodic
oscillations between states with different numbers of bunches.Comment: 26 pages, 11 figure
Damping of Oscillations in Layer-by-Layer Growth
We present a theory for the damping of layer-by-layer growth oscillations in
molecular beam epitaxy. The surface becomes rough on distances larger than a
layer coherence length which is substantially larger than the diffusion length.
The damping time can be calculated by a comparison of the competing roughening
and smoothening mechanisms. The dependence on the growth conditions,
temperature and deposition rate, is characterized by a power law. The
theoretical results are confirmed by computer simulations.Comment: 19 pages, RevTex, 5 Postscript figures, needs psfig.st
Linear theory of unstable growth on rough surfaces
Unstable homoepitaxy on rough substrates is treated within a linear continuum
theory. The time dependence of the surface width is governed by three
length scales: The characteristic scale of the substrate roughness, the
terrace size and the Ehrlich-Schwoebel length . If (weak step edge barriers) and ,
then displays a minimum at a coverage , where the initial surface width is reduced by a factor
. The r\^{o}le of deposition and diffusion noise is analyzed. The
results are applied to recent experiments on the growth of InAs buffer layers
[M.F. Gyure {\em et al.}, Phys. Rev. Lett. {\bf 81}, 4931 (1998)]. The overall
features of the observed roughness evolution are captured by the linear theory,
but the detailed time dependence shows distinct deviations which suggest a
significant influence of nonlinearities
Variational Formulation for the KPZ and Related Kinetic Equations
We present a variational formulation for the Kardar-Parisi-Zhang (KPZ)
equation that leads to a thermodynamic-like potential for the KPZ as well as
for other related kinetic equations. For the KPZ case, with the knowledge of
such a potential we prove some global shift invariance properties previously
conjectured by other authors. We also show a few results about the form of the
stationary probability distribution function for arbitrary dimensions. The
procedure used for KPZ was extended in order to derive more general forms of
such a functional leading to other nonlinear kinetic equations, as well as
cases with density dependent surface tension.Comment: RevTex, 8pgs, double colum
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
An Exactly Solved Model of Three Dimensional Surface Growth in the Anisotropic KPZ Regime
We generalize the surface growth model of Gates and Westcott to arbitrary
inclination. The exact steady growth velocity is of saddle type with principal
curvatures of opposite sign. According to Wolf this implies logarithmic height
correlations, which we prove by mapping the steady state of the surface to
world lines of free fermions with chiral boundary conditions.Comment: 9 pages, REVTEX, epsf, 3 postscript figures, submitted to J. Stat.
Phys, a wrong character is corrected in eqs. (31) and (32
Interfaces with a single growth inhomogeneity and anchored boundaries
The dynamics of a one dimensional growth model involving attachment and
detachment of particles is studied in the presence of a localized growth
inhomogeneity along with anchored boundary conditions. At large times, the
latter enforce an equilibrium stationary regime which allows for an exact
calculation of roughening exponents. The stochastic evolution is related to a
spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of
late stages. For vanishing gaps the interface can exhibit a slow morphological
transition followed by a change of scaling regimes which are studied
numerically. Instead, a faceting dynamics arises for gapful situations.Comment: REVTeX, 11 pages, 9 Postscript figure
Pattern Dynamics of Vortex Ripples in Sand: Nonlinear Modeling and Experimental Validation
Vortex ripples in sand are studied experimentally in a one-dimensional setup
with periodic boundary conditions. The nonlinear evolution, far from the onset
of instability, is analyzed in the framework of a simple model developed for
homogeneous patterns. The interaction function describing the mass transport
between neighboring ripples is extracted from experimental runs using a
recently proposed method for data analysis, and the predictions of the model
are compared to the experiment. An analytic explanation of the wavelength
selection mechanism in the model is provided, and the width of the stable band
of ripples is measured.Comment: 4 page
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