相关论文: Analogy and Difference between Gelation and Percol…
Despite decades of intense study, the mechanisms underlying the extraordinary dynamics of supercooled liquids as they approach the glass transition remain, at best, mis-characterized, and at worst, misunderstood. A long standing endeavor is…
We have generalized the idea of backbend in a nearest-neighbor oriented bond percolation process by considering a backbend sequence $\beta : \mathbb{Z}_+ \to \mathbb{Z}_+ \cup \{\infty\}$, and defining a $\beta$-backbend path from the…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
Hyperbolic lattices interpolate between finite-dimensional lattices and Bethe lattices and are interesting in their own right with ordinary percolation exhibiting not one, but two, phase transitions. We study four constraint percolation…
Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to…
We numerically study the jamming transition in particulate systems with attraction by investigating their mechanical response at zero temperature. We find three regimes of mechanical behavior separated by two critical…
A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks…
We report on extensive molecular dynamics simulations on systems of soft spheres of functionality f, i.e. particles that are capable of bonding irreversibly with a maximum of f other particles. These bonds are randomly distributed…
We establish links between three different models for multifragmentation: the percolation model, the lattice gas model and the statistical multifragmentation model. There are remarkable similarities between the lattice gas model and the…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…
Message passing, also known as belief propagation, is a versatile framework for analyzing models defined on graphs. Its most prototypical application is percolation; yet, the interpretation of the message passing formulation of percolation…
We describe a percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Tissues are considered as structures made of regular healthy,…
The dynamical properties of the site frustrated percolation model are investigated and compared with those of glass forming liquids. When the density of the particles on the lattice becomes high enough, the dynamics of the model becomes…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…
Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel…
Determining the onset of rigidity in gels is a fundamental challenge with significant practical implications across different applications. Limited-valence, or patchy-particle systems have proven to be a valuable model to study the…
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…
We investigate site and bond percolation in triangular and square lattices subjected to linear distortion. In contrast to previously studied distortion schemes that preserve lattice geometry, linear distortion dislocates regular lattice…