Related papers: Percolation of randomly distributed growing cluste…
We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
In this article, we study the spreading of droplets of density-matched granular suspensions on the surface of a solid. Bidispersity of the particle size distribution enriches the conclusions drawn from monodisperse experiments by…
We study the cluster-size distribution of supercritical long-range percolation on $\mathbb{Z}^d$, where two vertices $x,y\in\mathbb{Z}^d$ are connected by an edge with probability $\mathrm{p}(\|x-y\|):=p\min(1,\beta\|x-y\|)^{-d\alpha}$ for…
We study the surface growth generated by the random deposition of particles of different sizes. A model is proposed where the particles are aggregated on an initially flat surface, giving rise to a rough interface and a porous bulk. By…
Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also…
We use experiments to study the evolution of bubble clusters in a swarm of freely rising, deformable bubbles. A new machine learning-aided algorithm allows us to identify and track bubbles in clusters and measure the cluster lifetimes. The…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…
The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease…
This paper investigates a clustering instability of a freely falling granular jet composed of 100 micron glass spheres. The granular flow out of a circular nozzle starts out spatially uniform and then, further downstream, breaks up into…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
Dynamical behavior of the clusters during relaxation is studied in two-dimensional Potts model using cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
An extended polymer collapses to form a globule when subjected to a quench below the collapse transition temperature. The process begins with the formation of clusters of monomers or ``pearls''. The nascent clusters merge, resulting in…
We study bond percolations on hierarchical scale-free networks with the open bond probability of the shortcuts $\tilde{p}$ and that of the ordinary bonds $p$. The system has a critical phase in which the percolating probability $P$ takes an…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…