Related papers: Inhomogeneous bond percolation on square, triangul…
We study an intrinsic curvature model defined on fixed-connectivity triangulated lattices enclosing a spherical core by using the canonical Monte Carlo simulation technique. We find that the model undergoes a discontinuous transition of…
This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…
We study the direct and inverse spectral theory for a class of finite Hermitian banded matrices. Using the theory of matrix orthogonal polynomials, we provide an explicit procedure for reconstructing a banded matrix from a matrix-valued…
The purpose of this paper is to prove the equivalence$-$under rotations of distinct terms$-$of different forms of a determinantal equation that appears in the studies of wave propagation in Hookean solids, in the context of the Christoffel…
We revisit the phase transition for percolation on randomly stretched lattices. Starting with the usual square grid, keep all vertices untouched while erasing edges according as follows: for every integer $i$, the entire column of vertical…
In the standard cosmological framework, the Hubble diagram is interpreted by assuming that the light emitted by standard candles propagates in a spatially homogeneous and isotropic spacetime. However, the light from "point sources"--such as…
In recent years, there has been a proliferation of wide-field sky surveys to search for a variety of transient objects. Using relatively short focal lengths, the optics of these systems produce undersampled stellar images often marred by a…
We study pattern formation in a complex Swift Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems…
We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains using modeling for non-periodic domains with…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Let ${\mathbb{L}}$ be the $d$-dimensional hypercubic lattice and let ${\mathbb{L}}_0$ be an $s$-dimensional sublattice, with $2 \leq s < d$. We consider a model of inhomogeneous bond percolation on ${\mathbb{L}}$ at densities $p$ and…
The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents $\beta$. The…
We solve the weak percolation problem for multiplex networks with overlapping edges. In weak percolation, a vertex belongs to a connected component if at least one of its neighbors in each of the layers is in this component. This is a…
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six intersection points with neighboring circles is equal to -1.…
In three-dimensional critical percolation we study numerically the number of clusters, $N_{\Gamma}$, which intersect a given subset of bonds, $\Gamma$. If $\Gamma$ represents the interface between a subsystem and the environment, then…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing…
We consider bond percolation on $\Z^d\times \Z^s$ where edges of $\Z^d$ are open with probability $p<p_c(\Z^d)$ and edges of $\Z^s$ are open with probability $q$, independently of all others. We obtain bounds for the critical curve in $(p,…
A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…