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Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
Lattices with a basis can host crystallographic defects which share the same topological charge (e.g.~the Burgers vector $\vec b$ of a dislocation) but differ in their microscopic structure of the core. We demonstrate that in insulators…
Self-gravitating systems have acquired growing interest in statistical mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual approach of statistical mechanics cannot be applied to a system of many point particles…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…
Random sets with long-range dependence can be generated using a Boolean model with power-law grain sizes. We study thinnings of such Boolean models which have the hard-core property that no grains overlap in the resulting germ-grain model.…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…
To insight the relationships between the self-organizing structures of cells, such as the cell clusters, and the properties of biotissues is helpful in revealing the function and designing biomaterial. Traditional random foam model neglects…
The exchange-driven growth model describes the mean field kinetics of a population of composite particles (clusters) subject to pairwise exchange interactions. Exchange in this context means that upon interaction of two clusters, one loses…
Variations of transport efficiency in structured environments between distinct individuals in actively self-propelled systems is both hard to study and poorly understood. Here, we study the transport of a non-tumbling {\ecoli} strain, an…
We investigate the effect of dust on the scaling properties of galaxy clusters based on hydrodynamic N-body simulations of structure formation. We have simulated five dust models plus a radiative cooling and adiabatic models using the same…
We study the effective behavior of random, heterogeneous, anisotropic, second order phase transitions energies that arise in the study of pattern formations in physical-chemical systems. Specifically, we study the asymptotic behavior, as…
We present a stochastic model of dynamically interacting grains in one dimension, in the presence of a low vibrational intensity, to investigate the effect of shape on the statics and dynamics of the compaction process. Regularity and…
The flow behavior of granular matter is significantly influenced by the shape of constituent particles. This effect is particularly pronounced for very concave particles, which exhibit unique flow characteristics such as higher porosity and…
The interaction between transitivity and sparsity, two common features in empirical networks, implies that there are local regions of large sparse networks that are dense. We call this the blessing of transitivity and it has consequences…
We explore the effect of shape -- jagged vs. regular -- in the jamming limit of very gently shaken packings. Our measure of shape $\eps$ is the void space occupied by a disordered grain; we show that depending on its number-theoretic…
We study numerically the influence of confinement on the solid fraction and on the structure of three-dimensional random close packed (RCP) granular materials subject to gravity. The effects of grain shape (spherical or polyhedral),…
We investigate the effect of fragmentation on the homogeneous free cooling of inelastic hard spheres, using Boltzmann kinetic theory and Direct Monte Carlo simulations. We analyze in detail a model where dissipative collisions may…
We investigate random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and…
The dynamics of a hollow cylinder containing granules and rolling down an inclined plane was investigated. A theoretical approach for investigating the behaviour of such a cylinder was proposed. The critical angle of the plane that allows…
We study number density distribution and the behavior of time correlation functions in the density of grains for a quasi-two dimensional system of vibrated grains. We study the system at various packing fractions, from low to high. At low…