Related papers: Self-Similarity in Random Collision Processes
An exponentially decaying system looks as if its decay was a generalized power or double-exponential law, provided one takes into account the relativistic time dilation in a detector, the delay of the emitted signal, and the accelerations…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in $\mathbb{R}^3$. We obtain in both cases the explicit conditional distributions of the position of the moving particle when the number of…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
Spatially extended chaotic systems with power-law decaying interactions are considered. Two coupled replicas of such systems synchronize to a common spatio-temporal chaotic state above a certain coupling strength. The synchronization…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the distance from the surface, there…
In this report, the explicit probability density functions of the random Euclidean distances associated with equilateral triangles are given, when the two endpoints of a link are randomly distributed in 1) the same triangle, 2) two adjacent…
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…
We study the propagation of regularity of solutions to a three dimensional system of linear parabolic PDE known as the kinematic dynamo equations. The divergence free drift velocity is assumed to be at the critical regularity level with…
The aim of this paper is to investigate the distribution of a continuous homopolymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously vary two parameters: the…
Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is…
We introduce and analyze a class of interacting particle systems on the real line that combine features of the stochastic rat race and (deterministic) follow-the-leader models. The particle system evolves as a continuous-time pure jump…
We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We…
We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the…
Self-similar dynamical processes are characterized by a growing length scale $\xi$ which increases with time as $\xi \sim t^{1/z}$, where z is the dynamical exponent. The best known example is a simple random walk with z=2. Usually such…
Several general trends have been identified for equilibrated, self-gravitating collisionless systems, such as density or anisotropy profiles. These are integrated quantities which naturally depend on the underlying velocity distribution…
We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution on a space of trees is said to be self-similar if it is invariant with respect to the operation of pruning, which cuts…