Related papers: Selective Bootstrap Percolation
The Glauber dynamics of disordered spin models with multi-spin interactions on sparse random graphs (Bethe lattices) is investigated. Such models undergo a dynamical glass transition upon decreasing the temperature or increasing the degree…
Bootstrap percolation is a type of cellular automaton on graphs, introduced as a simple model of the dynamics of ferromagnetism. Vertices in a graph can be in one of two states: `healthy' or `infected' and from an initial configuration of…
We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the…
We consider a lattice polymer model (random walk), in which the walk is allowed to visit lattice bonds at most twice. Such a model might have some relevance to describe statistical properties of RNA molecules. In order to mimic base…
The glass transition of supercooled fluids is a particular challenge for computer simulation, because the (longest) relaxation times increase by about 15 decades upon approaching the transition temperature T_g. Brute-force molecular…
The simplest model of three coupled Bose-Einstein Condensates (BEC) is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean field approximation. This semiclassical…
A one-dimensional driven lattice gas with disorder in the particle hopping probabilities is considered. It has previously been shown that in the version of the model with random sequential updating, a phase transition occurs from a low…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
The theme of this paper is the analysis of bootstrap percolation processes on random graphs generated by preferential attachment. This is a class of infection processes where vertices have two states: they are either infected or…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
We study concentrated binary colloidal suspensions, a model system which has a glass transition as the volume fraction $\phi$ of particles is increased. We use confocal microscopy to directly observe particle motion within dense samples…
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having $N$ vertices, a dependent version of…
We consider cold polar molecules confined in a helical optical lattice similar to those used in holographic microfabrication. An external electric field polarizes molecules along the axis of the helix. The large-distance inter-molecular…
We study analytically and numerically a model metabolic cycle composed of an arbitrary number of species of catalytically active particles. Each species converts a substrate into a product, the latter being used as the substrate by the next…
Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions/contacts between particles in the…
We report an experimental investigation of the caging motion in a uniformly heated granular fluid, for a wide range of filling fractions, $\phi$. At low $\phi$ the classic diffusive behavior of a fluid is observed. However, as $\phi$ is…
The $r$-neighbour bootstrap process describes an infection process on a graph, where we start with a set of initially infected vertices and an uninfected vertex becomes infected as soon as it has $r$ infected neighbours. An inital set of…
A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution…
We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with…
We study the behavior of an assembly of $N$ granular particles contained in two compartments within a simple kinetic approach. The particles belonging to each compartment collide inelastically with each other and are driven by a stochastic…