Related papers: Analogy and Difference between Gelation and Percol…
The relationship between the conductivity and the polarization noise is measured in a gel as a function of frequency in the range $1Hz - 40Hz$. It is found that at the beginning of the transition from a fluid like sol to a solid like gel…
We consider a model for gelation of rigid rods, in which rods that are initially placed at random undergo diffusion, and form cross-links when they collide. In the limit of point-like cross-links, the number N of croslinks per rod…
We present some exact results on bond percolation. We derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice $\Lambda$ by $\ell$ bonds connecting the same adjacent vertices,…
We study a chemical gelation model in two dimensions which includes both monomer aggregations and bond fluctuations. Our numerical simulation shows that a sol-gel transition occurs when an initial monomer concentration is above a critical…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…
We present a theory of active, permeating, polar gels, based on a two-fluid model. An active relative force between the gel components creates a steady-state current. We analyze its stability, while considering two polar coupling terms to…
In chemical crosslinking of gelatin solutions, two different time scales affect the kinetics of the gel formation in the experiments. We complement the experimental study with Monte Carlo numerical simulations of a lattice model. This…
We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on…
We investigate the gel formation from the equilibrium sol phase in a simple model that has the characteristics of (colloidal) gel-forming systems at a finite temperature. At low volume fraction and low temperatures, particles are linked by…
We study the temperature dependence of the superconductor-insulator transition in granular superconductors. Empirically, these systems are characterized by very broad resistance tails, which depend exponentially on the temperature, and the…
We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al. [Nature 439, 828 (2006)], we consider a percolation process in which…
We study a microscopically realistic model of a physical gel and use computer simulations to investigate its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a…
In this paper, a partial integro-differential equation modeling of coagulation and multiple fragmentation events is studied. Our purpose is to investigate the global existence of gelling weak solutions to the continuous coagulation and…
We conjecture a new correlation-like inequality for percolation probabilities and support our conjecture with numerical evidence and a few special cases which we prove. This inequality, if true, implies that there is no percolation at…
We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a…
We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a…
Directed percolation is one of the most prominent universality classes of nonequilibrium phase transitions and can be found in a large variety of models. Despite its theoretical success, no experiment is known which clearly reproduces the…
We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap…