Related papers: Analogy and Difference between Gelation and Percol…
Within the framework of the random distribution assumption of cyclic bonds, the preceding theory of gelation is extended to mixing systems with various functionalities. To examine the validity of the assumption, the theory is applied to…
Within the framework of the random distribution assumption of cyclic bonds, the theory of gelation is extended to mixing systems of the R-Ag + R-Bf-g model, which is expected to have wider application such as micell formations in biological…
We study a two-component model for gelation consisting of $f$-functional monomers (the gel) and inert particles (the solvent). After equilibration as a simple liquid, the gel particles are gradually crosslinked to each other until the…
In the gelation theory it has been implicitly assumed that (I) a cyclic bond is a finite bond that returns to itself; (II) cyclic bonds distribute at random in network structures. In this paper these two assumptions are reexamined from a…
A discussion on the viscoelastic properties of weakly attractive colloids and the relation to a newly developed percolation theory is presented. The need for taking into account the particle-particle bond lifetime in order to compare…
A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of…
We study a model for the gel degradation by an enzyme, where the gel is schematized as a cubic lattice, and the enzyme as a random walker, that cuts the bonds over which it passes. The model undergoes a (reverse) percolation transition,…
We summarize ideas and methods that apply to rigidity and connectivity percolation. These include: constraint counting concepts, exact calculations on diluted trees and numerical results on diluted lattices using matching algorithms. The…
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 theory of gelation is tested by the recent experiments in poly(urethane) network. The result supports strongly the physical soundness of the theory.
Computer simulations were used to study the gel transition occurring in colloidal systems with short range attractions. A colloid-polymer mixture was modelled and the results were compared with mode coupling theory expectations and with the…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
Colloidal gels have unique mechanical and transport properties that stem from their bicontinous nature, in which a colloidal network is intertwined with a viscous solvent, and have found numerous applications in foods, cosmetics,…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
We study the evolution of percolation with freezing. Specifically, we consider cluster formation via two competing processes: irreversible aggregation and freezing. We find that when the freezing rate exceeds a certain threshold, the…
We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
We investigate the description of current transfer in polycrystalline superconductors by percolation theory and its limitations. Various computer models that have been proposed are reviewed and related to the experimental and theoretical…
One major goal in condensed matter physics is identifying the physical mechanisms that lead to arrested states of matter, especially gels and glasses. The complex nature and microscopic details of each particular system are relevant.…