5,051 research outputs found
Rate theory for correlated processes: Double-jumps in adatom diffusion
We study the rate of activated motion over multiple barriers, in particular
the correlated double-jump of an adatom diffusing on a missing-row
reconstructed Platinum (110) surface. We develop a Transition Path Theory,
showing that the activation energy is given by the minimum-energy trajectory
which succeeds in the double-jump. We explicitly calculate this trajectory
within an effective-medium molecular dynamics simulation. A cusp in the
acceptance region leads to a sqrt{T} prefactor for the activated rate of
double-jumps. Theory and numerical results agree
Lattice Effects in Crystal Evaporation
We study the dynamics of a stepped crystal surface during evaporation, using
the classical model of Burton, Cabrera and Frank, in which the dynamics of the
surface is represented as a motion of parallel, monoatomic steps. The validity
of the continuum approximation treated by Frank is checked against numerical
calculations and simple, qualitative arguments. The continuum approximation is
found to suffer from limitations related, in particular, to the existence of
angular points. These limitations are often related to an adatom detachment
rate of adatoms which is higher on the lower side of each step than on the
upper side ("Schwoebel effect").Comment: DRFMC/SPSMS/MDN, Centre d'Etudes Nucleaires de Grenoble, 25 pages,
LaTex, revtex style. 8 Figures, available upon request, report# UBFF30119
Numerical test of the damping time of layer-by-layer growth on stochastic models
We perform Monte Carlo simulations on stochastic models such as the
Wolf-Villain (WV) model and the Family model in a modified version to measure
mean separation between islands in submonolayer regime and damping time
of layer-by-layer growth oscillations on one dimension. The
stochastic models are modified, allowing diffusion within interval upon
deposited. It is found numerically that the mean separation and the damping
time depend on the diffusion interval , leading to that the damping time is
related to the mean separation as for the WV model
and for the Family model. The numerical results are in
excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure
What is in a pebble shape?
We propose to characterize the shapes of flat pebbles in terms of the
statistical distribution of curvatures measured along the pebble contour. This
is demonstrated for the erosion of clay pebbles in a controlled laboratory
apparatus. Photographs at various stages of erosion are analyzed, and compared
with two models. We find that the curvature distribution complements the usual
measurement of aspect ratio, and connects naturally to erosion processes that
are typically faster at protruding regions of high curvature.Comment: Phys. Rev. Lett. (to appear
Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold
Given a Riemannian manifold M and a hypersurface H in M, it is well known
that infinitesimal convexity on a neighborhood of a point in H implies local
convexity. We show in this note that the same result holds in a semi-Riemannian
manifold. We make some remarks for the case when only timelike, null or
spacelike geodesics are involved. The notion of geometric convexity is also
reviewed and some applications to geodesic connectedness of an open subset of a
Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference
and several comments, statement of last proposition correcte
Spiral surface growth without desorption
Spiral surface growth is well understood in the limit where the step motion
is controlled by the local supersaturation of adatoms near the spiral ridge. In
epitaxial thin-film growth, however, spirals can form in a step-flow regime
where desorption of adatoms is negligible and the ridge dynamics is governed by
the non-local diffusion field of adatoms on the whole surface. We investigate
this limit numerically using a phase-field formulation of the
Burton-Cabrera-Frank model, as well as analytically. Quantitative predictions,
which differ strikingly from those of the local limit, are made for the
selected step spacing as a function of the deposition flux, as well as for the
dependence of the relaxation time to steady-state growth on the screw
dislocation density.Comment: 9 pages, 3 figures, RevTe
Nanoscale Observation of Alkane Delayering
Noncontact Atomic Force Microscopy and synchrotron x-ray scattering
measurements on dotriacontane (n-C32H66 or C32) films adsorbed on SiO2-coated
Si(100) wafers reveal a narrow temperature range near the bulk C32 melting
point Tb in which a monolayer phase of C32 molecules oriented perpendicular to
surface is stable. This monolayer phase undergoes a delayering transition to a
three-dimensional (3D) fluid phase on heating to just above Tb and to a solid
3D phase on cooling below Tb. An equilibrium phase diagram provides a useful
framework for interpreting the unusual spreading and receding of the monolayer
observed in transitions to and from the respective 3D phases.Comment: 13 pages, 3 figure
Random Walks for Spike-Timing Dependent Plasticity
Random walk methods are used to calculate the moments of negative image
equilibrium distributions in synaptic weight dynamics governed by spike-timing
dependent plasticity (STDP). The neural architecture of the model is based on
the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which
forms a negative image of the reafferent signal from the fish's own electric
discharge to optimize detection of sensory electric fields. Of particular
behavioral importance to the fish is the variance of the equilibrium
postsynaptic potential in the presence of noise, which is determined by the
variance of the equilibrium weight distribution. Recurrence relations are
derived for the moments of the equilibrium weight distribution, for arbitrary
postsynaptic potential functions and arbitrary learning rules. For the case of
homogeneous network parameters, explicit closed form solutions are developed
for the covariances of the synaptic weight and postsynaptic potential
distributions.Comment: 18 pages, 8 figures, 15 subfigures; uses revtex4, subfigure, amsmat
Hopping motion of lattice gases through nonsymmetric potentials under strong bias conditions
The hopping motion of lattice gases through potentials without
mirror-reflection symmetry is investigated under various bias conditions. The
model of 2 particles on a ring with 4 sites is solved explicitly; the resulting
current in a sawtooth potential is discussed. The current of lattice gases in
extended systems consisting of periodic repetitions of segments with sawtooth
potentials is studied for different concentrations and values of the bias.
Rectification effects are observed, similar to the single-particle case. A
mean-field approximation for the current in the case of strong bias acting
against the highest barriers in the system is made and compared with numerical
simulations. The particle-vacancy symmetry of the model is discussed.Comment: 8 pages (incl. 6 eps figures); RevTeX 3.
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