相关论文: The Simplest Piston Problem I: Elastic Collisions

We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy ``piston'', with elastic collisions between particles but inelastic collisions between the light particles and the interval…

The effects of purely elastic collisions on the dynamics of heavy inertial particles is investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of inter-particle separations and relative…

A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic barrier…

We study a heavy piston of mass $M$ that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system's averaged equation and showed…

We consider the motion of two massive particles along a straight line. A lighter particle bounces back and forth between a heavier particle and a stationary wall, with all collisions being ideally elastic. It is known that if the lighter…

We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged…

We study a dynamical system consisting of a massive piston in a cubical container of large size $L$ filled with an ideal gas. The piston has mass $M\sim L^2$ and undergoes elastic collisions with $N\sim L^3$ non-interacting gas particles of…

A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on…

We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…

Elastic singularities such as crack tips, when in motion through a medium that is itself vibrating, are subject to forces orthogonal to the direction of motion and thus impossible to determine by energy considerations alone. This fact is…

We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it…

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…

An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…

The dynamics of three soft interacting particles on a ring is shown to correspond to the motion of one particle inside a soft triangular billiard. The dynamics inside the soft billiard depends only on the {\it masses ratio} between…

Electrostatic forces between small groups of colloidal particles are measured using blinking optical tweezers. When the electrostatic screening length is significantly larger than the particle radius, forces are found to be non-pairwise…

The probability distribution for multiple collisions observed in the chaotic low energy domain in the bouncing ball model is shown to be scaling invariant concerning the control parameters. The model considers the dynamics of a bouncing…

In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance…

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a…

We consider a heavy piston in an infinite cylinder surrounded by ideal gases on both sides. The piston moves under elastic collisions with gas atoms. We assume here that the gases always exert equal pressures on the piston, hence the piston…

A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…