Related papers: Bootstrap percolation and kinetically constrained …
In this paper we study the Poisson stick model in two dimensional hyperbolic space $\mathbb{H}^2,$ where the sticks all have length $L.$ Typically, percolation models in hyperbolic space undergo two phase transitions as the intensity…
We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple…
Two coarse-grained models for polymer chains in dense glass-forming polymer melts are studied by computer simulation: the bond-fluctuation model on a simple cubic lattice, where a bond-length potential favors long bonds, is treated by…
The structural arrest of a polymeric suspension might be driven by an increase of the cross--linker concentration, that drives the gel transition, as well as by an increase of the polymer density, that induces a glass transition. These…
We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At mean-field level this approach is consistent with the…
Ultra-cold atoms in 1D bi-chromatic lattices constitute a surprisingly simple system for the study of topological insulators. We show that topological phase transitions constitute a general feature of bosons in 1D bi-chromatic lattices, and…
Upon intense femtosecond photo-excitation, a many-body system can undergo a phase transition through a non-equilibrium route, but understanding these pathways remains an outstanding challenge. Here, we use time-resolved second harmonic…
Majority bootstrap percolation is a monotone cellular automata that can be thought of as a model of infection spreading in networks. Starting with an initially infected set, new vertices become infected once more than half of their…
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…
Bootstrap percolation on an arbitrary graph has a random initial configuration, where each vertex is occupied with probability p, independently of each other, and a deterministic spreading rule with a fixed parameter k: if a vacant site has…
Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of…
We divide the circular boundary of a hyperbolic lattice into four equal intervals, and study the probability of a percolation crossing between an opposite pair, as a function of the bond occupation probability p. We consider the {7,3}…
We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be…
Majority bootstrap percolation is a model of infection spreading in networks. Starting with a set of initially infected vertices, new vertices become infected once half of their neighbours are infected. Balogh, Bollob\'{a}s and Morris…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
We consider the Constrained-degree percolation model on the hypercubic lattice, $\mathbb L^d=(\mathbb Z^d,\mathbb E^d)$ for $d\geq 3$. It is a continuous time percolation model defined by a sequence, $(U_e)_{e\in\mathbb E^d}$, of i.i.d.…
Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or…
Collective motion over increasing length scales is a signature of the vitrification process of liquids. We demonstrate the emergence of distinct static and dynamic length scales probed near the free surface in fully equilibrated…
Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…
We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive…