279 research outputs found
Coarsening dynamics at unstable crystal surfaces
In this paper we focus on crystal surfaces led out of equilibrium by a growth
or erosion process. As a consequence of that the surface may undergo
morphological instabilities and develop a distinct structure: ondulations,
mounds or pyramids, bunches of steps, ripples. The typical size of the emergent
pattern may be fixed or it may increase in time through a coarsening process
which in turn may last forever or it may be interrupted at some relevant length
scale. We study dynamics in three different cases, stressing the main physical
ingredients and the main features of coarsening: a kinetic instability, an
energetic instability, and an athermal instability.Comment: 12 pages. Several minor changes. To appear in a Comptes Rendus
Physique special issue on "Coarsening Dynamics", see
https://sites.google.com/site/ppoliti/crp-special-issu
Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain
Peer reviewedPreprintPostprin
Random Deposition Model with a Constant Capture Length
We introduce a sequential model for the deposition and aggregation of
particles in the submonolayer regime. Once a particle has been randomly
deposited on the substrate, it sticks to the closest atom or island within a
distance \ell, otherwise it sticks to the deposition site. We study this model
both numerically and analytically in one dimension. A clear comprehension of
its statistical properties is provided, thanks to capture equations and to the
analysis of the island-island distance distribution.Comment: 14 pages, minor corrections. Accepted for publication in Progress of
Theoretical Physic
Coarsening process in one-dimensional surface growth models
Surface growth models may give rise to unstable growth with mound formation
whose tipical linear size L increases in time. In one dimensional systems
coarsening is generally driven by an attractive interaction between domain
walls or kinks. This picture applies to growth models for which the largest
surface slope remains constant in time (model B): coarsening is known to be
logarithmic in the absence of noise (L(t)=log t) and to follow a power law
(L(t)=t^{1/3}) when noise is present. If surface slope increases indefinitely,
the deterministic equation looks like a modified Cahn-Hilliard equation: here
we study the late stage of coarsening through a linear stability analysis of
the stationary periodic configurations and through a direct numerical
integration. Analytical and numerical results agree with regard to the
conclusion that steepening of mounds makes deterministic coarsening faster: if
alpha is the exponent describing the steepening of the maximal slope M of
mounds (M^alpha = L) we find that L(t)=t^n: n is equal to 1/4 for 1<alpha<2 and
it decreases from 1/4 to 1/5 for alpha>2, according to n=alpha/(5*alpha -2). On
the other side, the numerical solution of the corresponding stochastic equation
clearly shows that in the presence of shot noise steepening of mounds makes
coarsening slower than in model B: L(t)=t^{1/4}, irrespectively of alpha.
Finally, the presence of a symmetry breaking term is shown not to modify the
coarsening law of model alpha=1, both in the absence and in the presence of
noise.Comment: One figure and relative discussion changed. To be published in Eur.
Phys. J.
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