Related papers: Non-universality in clustered ballistic annihilati…
We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one…
Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas is studied in the framework of an exact analytic approach. For an initial symmetric three-velocity distribution, the problem can be solved exactly and it is…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…
We study, in the ensemble of constant particle number, processes in which a cluster of particles is annihilated and particles are created catalytically in active sites. In this ensemble, particles belonging to a cluster of $\ell$ particles…
In cluster tomography, we propose measuring the number of clusters $N$ intersected by a line segment of length $\ell$ across a finite sample. As expected, the leading order of $N(\ell)$ scales as $a\ell$, where $a$ depends on microscopic…
Clustering is one of the mayor collective phenomena observed in active matter. We study the overdamped motion of interacting active Brownian particles in two dimensions. An instability in the pair correlation function causes the onset of…
We show that the unsteadiness of turbulence has a drastic effect on turbulence parameters and in particle cluster formation. To this end we use direct numerical simulations of particle laden flows with a steady forcing that generates an…
I present a systematic analysis of formation of the universal annihilation catastrophe which develops in an open system, where species $A$ and $B$ diffuse from the bulk of restricted medium and die on its surface (desorb) by the reaction $A…
We consider a physical system comprising discrete massive particles on the real line whose trajectories interact via perfectly inelastic collision, also known as sticky particles. It turns out that polygons formed in a convex "cumulative…
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…
We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the…
We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader…
We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D_A>0 and D_B>0, and the interaction is given by mutual annihilation A+B->0. The initial condition…
Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…
We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…