相关论文: Knudsen's law and random billiards in irrational t…
We report on density waves in granular material, investigated both experimentally and numerically. When granular material falls through a long narrow pipe one observes recurrent clogging. The kinetic energy of the falling particles…
In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules, composing an ideal gas. In such a gas, the motion of each individual molecule can be considered…
Explicit density expansions of non-equilibrium probability distribution functions for molecular Brownian particle in ideal gas are obtained in original form what visually implies (is exact solution to) the previously established dynamical…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
It is argued that two-particle collisions of relativistic particles "at a distance", irrespective of their position in the configuration space, generate uniform distribution of particles in Lorentz invariant phase space.
Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or "draw" these…
We study a one-dimensional system of spatially extended particles, which are fixated to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by a Gaussian noise and to have dissipative,…
We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…
We study limit theorems in the context of random perturbations of dispersing billiards in finite and infinite measure. In the context of a planar periodic Lorentz gas with finite horizon, we consider random perturbations in the form of…
It is shown that electromagnetic vortices can act as beam guides for charged particles. The confinement in the transverse directions is due to the rotation of the electric and magnetic fields around the vortex line. Large class of exact…
We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…
Polygonal billiards are an example of pseudo-chaotic dynamics, a combination of integrable evolution and sudden jumps due to conical singular points that arise from the corners of the polygons. Such pseudo-chaotic behaviour, often…
We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which…
As three particles are advected by a turbulent flow, they separate from each other and develop non trivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of…
We show numerically that large amplitude, \textit{shape deformations}, imposed on a spherical-cap, incompressible, sessile gas bubble pinned on a rigid wall can produce a sharp, wall-directed jet. For such a bubble filled with a permanent…
The geometry of a billiard boundary fundamentally governs its dynamics, ranging from integrable to mixed and fully chaotic regimes. Bean- and peanut-shaped billiards have varying curvature with both focusing and defocusing walls without a…
It is often asserted or implicitly assumed, without justification, that the results of two-dimensional investigations of plasma turbulence are applicable to the three-dimensional plasma environments of interest. A projection method is…
The analysis and boundary optimal control of the nonlinear transport of gas on a network of pipelines is considered. The evolution of the gas distribution on a given pipe is modeled by an isothermal semilinear compressible Euler system in…