10,260 research outputs found
Growth instability due to lattice-induced topological currents in limited mobility epitaxial growth models
The energetically driven Ehrlich-Schwoebel (ES) barrier had been generally
accepted as the primary cause of the growth instability in the form of
quasi-regular mound-like structures observed on the surface of thin film grown
via molecular beam epitaxy (MBE) technique. Recently the second mechanism of
mound formation was proposed in terms of a topologically induced flux of
particles originating from the line tension of the step edges which form the
contour lines around a mound. Through large-scale simulations of MBE growth on
a variety of crystalline lattice planes using limited mobility, solid-on-solid
models introduced by Wolf-Villain and Das Sarma-Tamborenea in 2+1 dimensions,
we propose yet another type of topological uphill particle current which is
unique to some lattice, and has hitherto been overlooked in the literature.
Without ES barrier, our simulations produce spectacular mounds very similar, in
some cases, to what have been observed in many recent MBE experiments. On a
lattice where these currents cease to exist, the surface appears to be
scale-invariant, statistically rough as predicted by the conventional continuum
growth equation.Comment: 10 pages, 12 figure
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Morphological transitions in supercritical generalized percolation and moving interfaces in media with frozen randomness
We consider the growth of clusters in disordered media at zero temperature,
as exemplified by supercritical generalized percolation and by the random field
Ising model. We show that the morphology of such clusters and of their surfaces
can be of different types: They can be standard compact clusters with rough or
smooth surfaces, but there exists also a completely different "spongy" phase.
Clusters in the spongy phase are `compact' as far as the size-mass relation M ~
R^D is concerned (with D the space dimension), but have an outer surface (or
`hull') whose fractal dimension is also D and which is indeed dense in the
interior of the entire cluster. This behavior is found in all dimensions D >=
3. Slightly supercritical clusters can be of either type in , while they
are always spongy in D >= 4. Possible consequences for the applicability of KPZ
(Kardar-Parisi-Zhang) scaling to interfaces in media with frozen randomness are
studied in detail.Comment: 12 pages, including 10 figures; improved data & major changes
compared to v
Complete Wetting of Pits and Grooves
For one-component volatile fluids governed by dispersion forces an effective
interface Hamiltonian, derived from a microscopic density functional theory, is
used to study complete wetting of geometrically structured substrates. Also the
long range of substrate potentials is explicitly taken into account. Four types
of geometrical patterns are considered: (i) one-dimensional periodic arrays of
rectangular or parabolic grooves and (ii) two-dimensional lattices of
cylindrical or parabolic pits. We present numerical evidence that at the
centers of the cavity regions the thicknesses of the adsorbed films obey
precisely the same geometrical covariance relation, which has been recently
reported for complete cone and wedge filling. However, this covariance does not
hold for the laterally averaged wetting film thicknesses. For sufficiently deep
cavities with vertical walls and close to liquid-gas phase coexistence in the
bulk, the film thicknesses exhibit an effective planar scaling regime, which as
function of undersaturation is characterized by a power law with the common
critical exponent -1/3 as for a flat substrate, but with the amplitude
depending on the geometrical features.Comment: 12 page
A simple solid-on-solid model of epitaxial thin films growth: surface roughness and dynamics
The random deposition model must be enriched to reflect the variety of
surface roughness due to some material characteristics of the film growing by
vacuum deposition or sputtering. The essence of the computer simulation in this
case is to account for possible surface migration of atoms just after the
deposition, in connection with binding energy between atoms (as the mechanism
provoking the diffusion) and/or diffusion energy barrier. The interplay of
these two factors leads to different morphologies of the growing surfaces from
flat and smooth ones, to rough and spiky ones. In this paper we extended our
earlier calculation by applying some extra diffusion barrier at the edges of
terrace-like structures, known as Ehrlich-Schwoebel barrier. It is
experimentally observed that atoms avoid descending when the terrace edge is
approach and these barriers mimic this tendency. Results of our Monte Carlo
computer simulations are discussed in terms of surface roughness, and compared
with other model calculations and some experiments from literature. The power
law of the surface roughness against film thickness was confirmed.
The nonzero minimum value of the growth exponent near 0.2 was obtained
which is due to the limited range of the surface diffusion and the
Ehrlich-Schwoebel barrier. Observations for different diffusion range are also
discussed. The results are also confronted with some deterministic growth
models.Comment: 12 pages + 8 figures (to appear in Int. J. Mod. Phys. C, journal
style applied
Fast coarsening in unstable epitaxy with desorption
Homoepitaxial growth is unstable towards the formation of pyramidal mounds
when interlayer transport is reduced due to activation barriers to hopping at
step edges. Simulations of a lattice model and a continuum equation show that a
small amount of desorption dramatically speeds up the coarsening of the mound
array, leading to coarsening exponents between 1/3 and 1/2. The underlying
mechanism is the faster growth of larger mounds due to their lower evaporation
rate.Comment: 4 pages, 4 PostScript figure
Phase separation and critical percolation in bidimensional spin-exchange models
Binary mixtures prepared in an homogeneous phase and quenched into a
two-phase region phase-separate via a coarsening process whereby domains of the
two phases grow in time. With a numerical study of a spin-exchange model we
show that this dynamics first takes a system with equal density of the two
species to a critical percolation state. We prove this claim and we determine
the time-dependence of the growing length associated to this process with the
scaling analysis of the statistical and morphological properties of the
clusters of the two phases.Comment: 6 pages, 9 figure
Extreme mechanical resilience of self-assembled nanolabyrinthine materials
Low-density materials with tailorable properties have attracted attention for decades, yet stiff materials that can resiliently tolerate extreme forces and deformation while being manufactured at large scales have remained a rare find. Designs inspired by nature, such as hierarchical composites and atomic lattice-mimicking architectures, have achieved optimal combinations of mechanical properties but suffer from limited mechanical tunability, limited long-term stability, and low-throughput volumes that stem from limitations in additive manufacturing techniques. Based on natural self-assembly of polymeric emulsions via spinodal decomposition, here we demonstrate a concept for the scalable fabrication of nonperiodic, shell-based ceramic materials with ultralow densities, possessing features on the order of tens of nanometers and sample volumes on the order of cubic centimeters. Guided by simulations of separation processes, we numerically show that the curvature of self-assembled shells can produce close to optimal stiffness scaling with density, and we experimentally demonstrate that a carefully chosen combination of topology, geometry, and base material results in superior mechanical resilience in the architected product. Our approach provides a pathway to harnessing self-assembly methods in the design and scalable fabrication of beyond-periodic and nonbeam-based nano-architected materials with simultaneous directional tunability, high stiffness, and unsurpassed recoverability with marginal deterioration
Anisotropic diffusion limited aggregation in three dimensions : universality and nonuniversality
We explore the macroscopic consequences of lattice anisotropy for diffusion limited aggregation (DLA) in three dimensions. Simple cubic and bcc lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the approach is accelerated by the use of noise reduction. These states are strikingly anisotropic dendrites with a rich hierarchy of structure. For growth on an fcc lattice, our data suggest at least two stable fixed points of anisotropy, one matching the bcc case. Hexagonal growths, favoring six planar and two polar directions, appear to approach a line of asymptotic states with continuously tunable polar anisotropy. The more planar of these growths visually resembles real snowflake morphologies. Our simulations use a new and dimension-independent implementation of the DLA model. The algorithm maintains a hierarchy of sphere coverings of the growth, supporting efficient random walks onto the growth by spherical moves. Anisotropy was introduced by restricting growth to certain preferred directions
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