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Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
The classical definitions of the Incipient Infinite Cluster (IIC) of percolation consist in conditioning the origin on being connected to radius $n$ and letting $n$ go to infinity. We provide a short proof of that convergence in the planar…
We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2.…
Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--$d$ Ising model. For geometrical clusters at the percolation temperature and Fortuin--Kasteleyn clusters at $T_c$, the number of surfaces of…
Diffusion Monte Carlo calculations on the possibility of having self-bound one-dimen\-sional droplets of SU(6) $\times$ SU(2) ultracold fermionic mixtures are presented. We found that, even though arrangements with attractive interactions…
We formulate and study a variational two-phase free boundary problem with Robin condition on the interface between the two phases, and we prove existence and regularity of solutions in dimension two
We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising…
A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. Assuming that the nodes of the wireless network are distributed as a…
A formalism is presented which allows covariant three-dimensional bound-state equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described…
Despite great progress in the study of critical percolation on $\mathbb{Z}^d$ for $d$ large, properties of critical clusters in high-dimensional fractional spaces and boxes remain poorly understood, unlike the situation in two dimensions.…
Here we prove critical exponents for Random Connections Models (RCMs) with random marks. The vertices are given by a marked Poisson point process on $\mathbb{R}^d$ and an edge exists between any pair of vertices independently with a…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
In the polluted bootstrap percolation model, the vertices of a graph are independently declared initially occupied with probability p or closed with probability q. At subsequent steps, a vertex becomes occupied if it is not closed and it…
The statistical properties of spectra of a three-dimensional quantum bond percolation system is studied in the vicinity of the metal insulator transition. In order to avoid the influence of small clusters, only regions of the spectra in…
We look at the properties of clusters of order parameter at critical points in thermal systems and consider their significance to statistical-mechanical ground rules. These properties have been previously obtained through the saddle-point…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…