Related papers: The structure of typical clusters in large sparse …
Stellar clusters are critical constituents within galaxies: they are the result of highest-density star formation, and through their spatially and temporally correlated feedback they regulate their host galaxy evolution. We present a novel…
We study the cluster size distribution of particles for a two-species exclusion process which involves totally asymmetric transport process of two oppositely directed species with stochastic directional switching of the species on a 1D…
We establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion, covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum…
We present a numerical study of settling and clustering of small inertial particles in homogeneous and isotropic turbulence. Particles are denser than the fluid, but not in the limit of being much heavier than the displaced fluid. At fixed…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
We establish that if a sequence of spaces equipped with resistance metrics and measures converge with respect to the Gromov-Hausdorff-vague topology, and a certain non-explosion condition is satisfied, then the associated stochastic…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
We investigate a class of stochastic aggregation processes involving two types of clusters: active and passive. The mass distribution is obtained analytically for several aggregation rates. When the aggregation rate is constant, we find…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
We study a ballistic agglomeration process in the reaction-controlled limit. Cluster densities obey an infinite set of Smoluchowski rate equations, with rates dependent on the average particle energy. The latter is the same for all cluster…
We consider a family of discrete coagulation-fragmentation equations closely related to the one-dimensional forest-fire model of statistical mechanics: each pair of particles with masses $i,j \in \nn$ merge together at rate 2 to produce a…
We investigate the large-scale distribution of galaxy clusters taken from several X-ray catalogs. Different statistics of clustering like the conditional correlation function (CCF) and the minimal spanning tree (MST) as well as void…
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These…
We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size $N$ onto stochastic networks, computing transition probabilities…
We propose an efficient and fast numerical algorithm of finding a \emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable…
Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a…
The Smoluchowski equation for irreversible aggregation in suspensions of equally charged particles is studied. Accumulation of charges during the aggregation process leads to a crossover from power law to sub-logarithmic cluster growth at a…
A microscopic statistical model of a quantum solid is developed, where inside a crystalline lattice there can exist regions of disorder, such as dislocation networks or grain boundaries. The cores of these regions of disorder are allowed…
We consider the doubly infinite Sierpinski gasket graph $SG_0$, rescale it by factor $2^{-n}$, and on the rescaled graphs $SG_n=2^{-n}SG_0$, for every $n\in \mathbb{N}$, we investigate the limit shape of three aggregation models with…