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 $r_0$ 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, $a$, and cell-cell separation, $b$. The model shows a surprisingly rich behavior in the space of the two dimensionless parameters $\alpha=a/2r_0$ and $\beta=b/2r_0$. Extensive Monte Carlo simulations for system sizes of $500\times500$ 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