Related papers: Non-universality in clustered ballistic annihilati…
We study a system of branching Brownian motions on $\mathbb R$ with annihilation: at each branching time a new particle is created and the leftmost one is deleted. In [7] it has been studied the case of strictly local creations (the new…
The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the problem…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
We consider inertial particles suspended in an incompressible turbulent flow. Due to inertia of particles, their velocity field acquires small compressible component. Its presence leads to a new qualitative effect --- possibility of…
The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a…
The persistent motion of bacteria produces clusters with a stationary cluster size distribution (CSD). Here we develop a minimal model for bacteria in a narrow channel to assess the relative importance of motility diversity (i.e.…
The physical cluster originally conceived by Hill (J. Chem. Phys, 23, 617) is generalized for the case $N > 2$ in a novel way. Contrary to Hill's pairwise generalization, this definition assures that all constituent molecules of the cluster…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We consider mixtures of oppositely driven particles, showing that their non-equilibrium steady states form lanes parallel to the drive, which coexist with transient jammed clusters where particles are temporarily immobilised. We analyse the…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
To first order, the initial cluster luminosity function appears to be universal. This means that the brightest young cluster in a galaxy can be predicted from the total number of young clusters based purely on statistics. This suggests that…
We investigate the kinetics of systems in which particles of one species undergo binary fragmentation and pair annihilation. In the latter, nonlinear process, fragments react at collision to produce an inert species, causing loss of mass.…
We consider a system of annihilating particles where particles start from the points of a Poisson process on either the full-line or positive half-line and move at constant i.i.d. speeds until collision. When two particles collide, they…
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
In this paper, we recall various features of non equilibrium granular systems. Clusters with specific properties are found depending on the packing density, going from loose (a granular gas) to sintered (though brittle) polycrystalline…
When particles on a line collide, they may coalesce into one. Such systems arise in the voter model, where boundaries between opinion clusters perform coalescing random walks, and in reaction-diffusion theory, where diffusing particles…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
Clustering is a central approach for unsupervised learning. After clustering is applied, the most fundamental analysis is to quantitatively compare clusterings. Such comparisons are crucial for the evaluation of clustering methods as well…
This model describes cluster aggregation in a stirred colloidal solution Interacting clusters compete for growth in this 'winner-takes-all' model; for finite assemblies, the largest cluster always wins, i.e. there is a uniform sediment. In…