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We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric…
We consider two-species random sequential adsorption (RSA) in which species A and B adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When the probability $x_A$ of choosing an A…
Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectednes percolation theory. In the 1980s the percolation threshold of slender…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Due to the much larger size of the colloidal particles with…
We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative…
Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. Since the system is strongly…
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…
In the polluted modified bootstrap percolation model, sites in the square lattice are independently initially occupied with probability $p$ or closed with probability $q$. A site becomes occupied at a subsequent step if it is not closed and…
A recent study of the rotation of the plane of polarization of light from 160 cosmological sources claims to find significant evidence for cosmological anisotropy. We point out methodological weaknesses of that study, and reanalyze the same…
We further study the interfaces arising in a situation of inhomogeneity. More precisely, we identify a characteristic length for the gradient percolation model, that enables us to tighten previous estimates established for it. This allows…
Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly…
The field theoretic renormalization group and operator product expansion are applied to the problem of a passive scalar advected by the Gaussian nonsolenoidal velocity field with finite correlation time, in the presence of large-scale…
Using Monte Carlo simulation, we have studied the percolation of discorectangles. Also known as stadiums or two-dimensional spherocylinders, a discorectangle is a rectangle with semicircles at a pair of opposite sides. Scaling analysis was…
The spectrum of the nonbacktracking matrix associated to a network is known to contain fundamental information regarding percolation properties of the network. Indeed, the inverse of its leading eigenvalue is often used as an estimate for…
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…
As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order…