Related papers: Analogy and Difference between Gelation and Percol…
We give the exact critical frontier of the Potts model on bowtie lattices. For the case of $q=1$, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff…
A novel theory for cell differentiation is proposed, based on simulations with interacting artificial cells which have metabolic networks within, and divide into two when the final product is accumulated. Results of simulations with coupled…
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…
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…
Using a unique home-made cell for four-contact impedance spectroscopy of conductive liquid samples, we establish the existence of two low frequency conductivity relaxations in aqueous solutions of gelatin, in both liquid and gel state. A…
Employing the lattice gas model, combined with the linear elasticity theory, a correlation between the equilibrium and transport properties of intercalated species is investigated. It is shown that the major features of the intercalation…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
We develop and validate a simulation framework for colloidal gelation. We first reproduce the benchmark results of Santos, Campanella, and Carignano for spherical, gel-forming particles, then extend the methodology to more complex systems…
It is shown that the percolation model of hydrogen-bonded crystals, which is a 6-vertex model with bond defects, is completely equivalent with an 8-vertex model in an external electric field. Using this equivalence we solve exactly a…
We show that a site percolation is a stronger model than a bond percolation. We use the van den Berg -- Kesten (vdBK) inequality to prove that site percolation on a neighborhood of a vertex of degree $4$ cannot be simulated even…
We consider generic finite range percolation models on $\mathbb{Z}^d$ under a high temperature assumption (exponential decay of connection probabilities and exponential ratio weak mixing). We prove that the rate of decay of point-to-point…
We obtain the exact solution of the bond-percolation thresholds with inhomogenous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in…
We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural…
Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium…
The mode-coupling theory (MCT) of the glass transition ranks among the most successful first-principles kinetic theories to describe glassy dynamics. However, MCT does not fully account for crucial aspects of the dynamics near the glass…
We represent a theory of polymer gelation as an analogue of liquid-glass transition in which elastic fields of stress and strain shear components appear spontaneously as a consequence of the cross-linking of macromolecules. This…
We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the $n^{\textrm{th}}$ copy is $\rho^{-n}$. We prove, under optimal…
We study the signal percolation through heart-like biological system. Starting from an initial distribution of waiting and inactive cells with probabilities $p$ and $(1-p)$ respectively, the signal propagation is observed in terms of active…
We show that a cut-and-paste model to mimic a trial-and-error process of adaptation displays two pairs of percolation and depinning transitions, one for persistence and the other for efficiency. The percolation transition signals the onset…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…