Related papers: Percolation of randomly distributed growing cluste…
It has been proposed that during the early steps in the origin of life, small droplets could have formed via the segregation of molecules from complex mixtures by phase separation. These droplets could have provided chemical reaction…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
Crystallization represents the prime example of a disorder order transition. In realistic situations, however, container walls and impurities are frequently present and hence crystallization is heterogeneously seeded. Rarely the seeds are…
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with…
Assuming perfect collision efficiency, we demonstrate that turbulence can initiate and sustain the rapid growth of very small water droplets in air even when these droplets are too small to cluster, and even without having to take gravity…
We report numerical studies of the cluster development of two-phase flow in a steady-state environment of porous media. This is done by including biperiodic boundary conditions in a two-dimensional flow simulator. Initial transients of…
The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find…
We study numerically a model of nonequilibrium networks where nodes and links are added at each time step with aging of nodes and connectivity- and age-dependent attachment of links. By varying the effects of age in the attachment…
We study here the spontaneous clustering of a submonolayer of grains under horizontal circular shaking. The clustering of grains occurs when increasing the oscillation amplitude beyond a threshold. The dense area travels in a circular…
When dissipative particles are left alone, their fluctuation energy decays due to collisional interactions, clusters build up and grow with time until the system size is reached. When the effective dissipation is strong enough, this may…
We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as $p_{\downarrow}= p \cdot…
We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is…
Living cells use phase separation and concentration gradients to organize chemical compartments in space. Here, we present a theoretical study of droplet dynamics in gradient systems. We derive the corresponding growth law of droplets and…
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…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
This paper presents a comprehensive analysis of simple models useful to analyze the growth of nanostructures obtained by cluster deposition. After detailing the potential interest of nanostructures, I extensively study the first stages of…