منابع مشابه
Chaotic time-dependent billiards
A billiard in the form of a stadium with periodically perturbed boundary is considered. Two types of such billiards are studied: stadium with strong chaotic properties and a near-rectangle billiard. Phase portraits of such billiards are investigated. In the phase plane areas corresponding to decrease and increase of the velocity of billiard particles are found. Average velocities of the particl...
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Dynamical systems of a billiard type are a fundamental notion relevant for the understanding of numerous phenomena observed in statistical mechanics, Hamiltonian dynamics, nonlinear physics, and others. By means of billiard models, the principal ideas as Boltzmann ergodic hypothesis, related to the foundation of statistical physics, and deterministic diffusion gained more deep insight. However,...
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A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growt...
متن کاملThermodynamics of dispersing Billiards with Time-Dependent Boundaries
By means of a thermodynamic approach we analyze billiards in the form of the Lorentz gas with the open horizon. For periodic and stochastic oscillations of the scatterers, the average velocity of the particle ensemble as a function of time is analytically obtained. It is shown that the consequence of such oscillations is Fermi acceleration which is larger for periodic oscillations. The describe...
متن کاملTime irreversible billiards with piecewise-straight trajectories.
We introduce a new family of billiards which break time reversal symmetry in spite of having piece-wise straight trajectories. We show that our billiards preserve the ergodic and mixing properties of conventional billiards while they may turn into exponential the power law decay of correlations characteristic of Sinai type billiards. Such billiards can be implemented by squeezing the transverse...
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ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2009
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2009/848619