Related papers: Self-Similarity in Random Collision Processes
Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in…
A kinetic equation for the collisional evolution of stable, bound, self gravitating and slowly relaxing systems is established, which is valid when the number of constituents is very large. It accounts for the detailed dynamics and self…
We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability $p$, or undergo an elastic shock with probability $1-p$. Restricting to homogeneous systems, we provide in…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three…
Self-similarity in tornadic and some non-tornadic supercell flows is studied and power laws relating various quantities in such flows are demonstrated. Magnitudes of the exponents in these power laws are related to the intensity of the…
The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…
We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous…
We study the number of collisions $X_n$ of an exchangeable coalescent with multiple collisions ($\Lambda$-coalescent) which starts with $n$ particles and is driven by rates determined by a finite characteristic measure $\nu({\rm…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
Many systems in nature have arborescent and bifurcated structures such as trees, fern, snails, lungs, the blood vessel system, etc. and look self-similar over a wide range of scales. Which are the mechanical and dynamic properties that…
We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…
We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis, first put forward by [FM]: they do…
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
We study a simple aggregation model that mimics the clustering of traffic on a one-lane roadway. In this model, each ``car'' moves ballistically at its initial velocity until it overtakes the preceding car or cluster. After this encounter,…
Rayleigh-Taylor (RT) mixing has critical importance for a broad range of process in nature and technology, from supernovae and plasma fusion to oil recovery and nano-fabrication. In most instances, RT flows are driven by variable…
We compute the joint distribution of relative velocities and separations of identical inertial particles suspended in randomly mixing and turbulent flows. Our results are obtained by matching asymptotic forms of the distribution. The method…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
We study relaxation properties of two-body collisions in infinite spatial dimension. We show that this process exhibits multiscaling asymptotic behavior as the underlying distribution is characterized by an infinite set of nontrivial…