800 research outputs found
Growing partially directed self-avoiding walks
A partially directed self-avoiding walk model with the 'kinetic growth' weighting is solved exactly, on the square lattice and for two restricted, strip geometries. Some finite-size effects are examined
Morphology of Fine-Particle Monolayers Deposited on Nanopatterned Substrates
We study the effect of the presence of a regular substrate pattern on the
irreversible adsorption of nanosized and colloid particles. Deposition of disks
of radius is considered, with the allowed regions for their center
attachment at the planar surface consisting of square cells arranged in a
square lattice pattern. We study the jammed state properties of a generalized
version of the random sequential adsorption model for different values of the
cell size, , and cell-cell separation, . The model shows a surprisingly
rich behavior in the space of the two dimensionless parameters
and . Extensive Monte Carlo simulations for system sizes of
square lattice unit cells were performed by utilizing an
efficient algorithm, to characterize the jammed state morphology.Comment: 11 pages, 10 figures, 3 table
Three-Species Diffusion-Limited Reaction with Continuous Density-Decay Exponents
We introduce a model of three-species two-particle diffusion-limited
reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three
persistence parameters (survival probabilities in reaction) of the hopping
particle. We consider isotropic and anisotropic diffusion (hopping with a
drift) in 1d. We find that the particle density decays as a power-law for
certain choices of the persistence parameter values. In the anisotropic case,
on one symmetric line in the parameter space, the decay exponent is
monotonically varying between the values close to 1/3 and 1/2. On another, less
symmetric line, the exponent is constant. For most parameter values, the
density does not follow a power-law. We also calculated various characteristic
exponents for the distance of nearest particles and domain structure. Our
results support the recently proposed possibility that 1d diffusion-limited
reactions with a drift do not fall within a limited number of distinct
universality classes.Comment: 12 pages in plain LaTeX and four Postscript files with figure
Size of rings in two dimensions
The authors report enumeration results for the radius of gyration and caliper size distribution of self-avoiding unrooted polygons of up to 28 steps, on the square lattice. The (second moment) radius of gyration series is sufficiently smooth to allow verification of the theoretical prediction v(rings)=v(walks) to 0.2% accuracy
Three-Dimensional Percolation Modeling of Self-Healing Composites
We study the self-healing process of materials with embedded "glue"-carrying
cells, in the regime of the onset of the initial fatigue. Three-dimensional
numerical simulations within the percolation-model approach are reported. The
main numerical challenge taken up in the present work, has been to extend the
calculation of the conductance to three-dimensional lattices. Our results
confirm the general features of the process: The onset of the material fatigue
is delayed, by developing a plateau-like time-dependence of the material
quality. We demonstrate that in this low-damage regime, the changes in the
conductance and thus, in similar transport/response properties of the material
can be used as measures of the material quality degradation. A new feature
found for three dimensions, where it is much more profound than in
earlier-studied two-dimensional systems, is the competition between the healing
cells. Even for low initial densities of the healing cells, they interfere with
each other and reduce each other's effective healing efficiency.Comment: 15 pages in PDF, with 6 figure
Coherence and Entanglement in Two-Qubit Dynamics: Interplay of the Induced Exchange Interaction and Quantum Noise due to Thermal Bosonic Environment
We present a review of our recent results for the comparative evaluation of
the induced exchange interaction and quantum noise mediated by the bosonic
environment in two-qubit systems. We report new calculations for
P-donor-electron spins in Si-Ge type materials. Challenges and open problems
are discussed.Comment: Invited Review, 17 pages in LaTeX, with 4 EPS figure
Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata
We review recent numerical studies and the phenomenology of spatially
synchronized collective states in many-body dynamical systems. These states
exhibit thermodynamic noise superimposed on the collective, quasiperiodic order
parameter evolution with typically one basic irrational frequency. We
concentrate on the description of the global temporal properties in terms of
second-order difference equations.Comment: 11 pages (plain TeX), 4 figures (PostScript), preprint OUTP-92-51
Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model
We reanalyze transfer matrix and Monte Carlo results for the critical Binder
cumulant U* of an anisotropic two-dimensional Ising model on a square lattice
in a square geometry with periodic boundary conditions. Spins are coupled
between nearest neighboring sites and between next-nearest neighboring sites
along one of the lattice diagonals. We find that U* depends only on the
asymptotic critical long-distance features of the anisotropy, irrespective of
its realization through ferromagnetic or antiferromagnetic next-nearest
neighbor couplings. We modify an earlier renormalization-group calculation to
obtain a quantitative description of the anisotropy dependence of U*. Our
results support our recent claim towards the validity of universality for
critical phenomena in the presence of a weak anisotropy.Comment: 4 pages, 2 figures; one reference and some clarifications adde
Fast-diffusion mean-field theory for k-body reactions in one dimension
We derive an improved mean-field approximation for k-body annihilation
reactions kA --> inert, for hard-core diffusing particles on a line,
annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping
and annihilation processes are correlated to mimic chemical reactions. Our new
mean-field theory accounts for hard-core particle properties and has a larger
region of applicability than the standard chemical rate equation especially for
large k values. Criteria for validity of the mean-field theory and its use in
phenomenological data fits are derived. Numerical tests are reported for
k=3,4,5,6.Comment: 16 pages, TeX (plain
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