Thermodynamics of a bouncer model: a simplified one-dimensional gas

Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative dynamics with inelastic collisions: (i) for large initial energy; (ii) for low initial energy. For (i) we prove an exponential decay while for (ii) a power law marked by a changeover to the steady state is observed. A relation for collisions and time is obtained and allows us to write relevant observables as temperature and entropy as function of either number of collisions and time.Comment: 36 pages, 10 figures. To appear in: Communications in Nonlinear Science and Numerical Simulation, 201

Corrugated waveguide under scaling investigation

Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea is characterized using scaling arguments revealing critical exponents connected by an analytic relationship. The formalism is widely applicable to systems with mixed phase space, and especially in studies of the transition from integrability to non-integrability, including that in classical billiard problems.Comment: A complete list of my papers can be found in: http://www.rc.unesp.br/igce/demac/denis

Nuclear dimension and n-comparison

It is shown that if a C*-algebra has nuclear dimension n then its Cuntz semigroup has the property of n-comparison. It then follows from results by Ortega, Perera and Rørdam that σ-unital C*-algebras of finite nuclear dimension (and even of nuclear dimension at most ω) are stable if and only if they have no nonzero unital quotients and no nonzero bounded traces

Crises in a dissipative Bouncing ball model

The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the basins of the attracting fixed points is characterized, as we vary the control parameters. Crises between the attractors and their boundaries are observed. We found that the multiple attractors are intertwined, and when the boundary crisis between their stable and unstable manifolds occur, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, an impact physical crises is setup, and it may be useful as a mechanism to reduce the number of attractors in the system

Escape through a time-dependent hole in the doubling map

We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the sides of the hole are moving in or out of phase respectively. We find out that the escape rate is well described by the overlap of the hole with its images, for holes centred at periodic orbits.Comment: 9 pages, 7 figures. To appear in Physical Review E in 201

Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard

A competition between decay and growth of energy in a time-dependent stadium billiard is discussed giving emphasis in the decay of energy mechanism. A critical resonance velocity is identified for causing of separation between ensembles of high and low energy and a statistical investigation is made using ensembles of initial conditions both above and below the resonance velocity. For high initial velocity, Fermi acceleration is inherent in the system. However for low initial velocity, the resonance allies with stickiness hold the particles in a regular or quasi-regular regime near the fixed points, preventing them from exhibiting Fermi acceleration. Also, a transport analysis along the velocity axis is discussed to quantify the competition of growth and decay of energy and making use distributions of histograms of frequency, and we set that the causes of the decay of energy are due to the capture of the orbits by the resonant fixed points