Related papers: Self-Similarity in Random Collision Processes
In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
We consider a two-dimensional athermal binary mixture of Lennard-Jones particles with persistent random active forces. The liquid phase of this system for active forces exceeding a threshold value exhibits self-organization with long-range…
We determine the asymptotic behavior of the tails of the steady state velocity distribution of a homogeneously driven granular gas comprising of particles having a scalar velocity. A pair of particles undergo binary inelastic collisions at…
Model systems of self-propelled particles reproduce many phenomena observed in laboratory active matter systems that defy our thermal equilibrium-based intuition. In particular, in stationary states of self-propelled systems, it is…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…
An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a…
The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…
The velocity distribution of a fluidized dilute granular gas in the direction perpendicular to the gravitational field is investigated by means of Molecular Dynamics simulations. The results indicate that the velocity distribution can be…
Exploiting the idea that the fast partons of an energetic projectile can be treated as sources of color radiation interpreted as wee partons, it is shown that the recently observed property of extended limiting fragmentation implies a…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
In random tiling and dimer models we can get various limit shapes which gives the boundaries between different types of phases. The shape fluctuations at these boundaries give rise to universal limit laws, in particular the Airy process. We…
We consider ballistic aggregation equation for gases in which each particle is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For the constant aggregation rate we prove existence of self-similar solutions as well as…
Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with…
We study the statistics of flow events in the inherent dynamics in supercooled two- and three-dimensional binary Lennard-Jones liquids. Distributions of changes of the collective quantities energy, pressure and shear stress become…
We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions.…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…