Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards. (C) 2010 Elsevier B.V. All rights reserved.

THE EFFECT of WEAK DISSIPATION IN TWO-DIMENSIONAL MAPPING

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dissipation and its consequences in the scaling exponents for a family of two-dimensional mappings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Suppressing Fermi acceleration in two-dimensional driven billiards

We consider a dissipative oval-like shaped billiard with a periodically moving boundary. The dissipation considered is proportional to a power of the velocity V of the particle. The three specific types of power laws used are: (i) F proportional to-V; (ii) F proportional to-V-2 and (iii) F proportional to-V-delta with 1 < delta < 2. In the course of the dynamics of the particle, if a large initial velocity is considered, case (i) shows that the decay of the particle's velocity is a linear function of the number of collisions with the boundary. For case (ii), an exponential decay is observed, and for 1 < delta < 2, an powerlike decay is observed. Scaling laws were used to characterize a phase transition from limited to unlimited energy gain for cases (ii) and (iii). The critical exponents obtained for the phase transition in the case (ii) are the same as those obtained for the dissipative bouncer model. Therefore near this phase transition, these two rather different models belong to the same class of universality. For all types of dissipation, the results obtained allow us to conclude that suppression of the unlimited energy growth is indeed observed.

Nonzero Gap Two-Dimensional Carbon Allotrope from Porous Graphene

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Magnetic field induced lattice effects in a quasi-two-dimensional organic conductor close to the Mott metal-insulator transition

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-dimensional induced gravity in reduced phase-space

We discuss the Dirac method analysis of two-dimensional induced gravity, coupled to bosonic matter fields, in reduced phase-space. After defining the extended Hamiltonian it is possible to fix the gauge completely. The Dirac brackets can all be obtained in closed form; nevertheless, the results are not particularly simple.

Loop scattering in two-dimensional QCD

Using the integrability conditions that we recently obtained in two-dimensional QCD with massless fermions we arrive at a sufficient number of conservation laws to fix the scattering amplitudes involving a local version of the Wilson loop operator.

The influence of internal surface treatments on tensile bond strength for two ceramic systems

Statement of the Problem: the ceramic composition and surface microstructure of all-ceramic restorations are important components of an effective bonding substrate. Hydrofluoric acid and sandblasting are well-known procedures for surface treatment; however, surface treatment for high alumina-containing and lithium disilicate ceramics have not been fully investigated.Purpose: This in vitro study evaluated the tensile bond strength of resin cement to two types of ceramic systems with different surface treatments.Methods and Materials: Thirty specimens of each ceramic system were made according to the manufacturer's instructions and embedded in polyester resin. Specimens of In-Ceram Alumina [1] and IPS Empress 2 [E] were distributed to three groups with differing surface treatments (n=10): sandblasting with 50 jam aluminum oxide (APA); sandblasting with 110 pm aluminum oxide modified with silica particles (ROCATEC System-RS); a combination of sandblasting with APA and 10% hydrofluoric acid etching (HA) for two minutes on In-Ceram and for 20 seconds for IPS Empress 2. After the respective surface treatments, all the specimens were silanated, and Rely-X resin cement was injected onto the ceramic surface and light polymerized. The specimens were stored in distilled water at 37 degrees C for 24 hours and thermally cycled 1,100 times (5 degrees C/55 degrees C). The tensile bond strength test was performed in a universal testing machine at a 0.5 mm/minute crosshead speed.Results: the mean bond strength values (AWa) for IPS Empress 2 were 12.01 +/- 5.93 (EAPA), 10.34 +/- 1.77 (ERS) and 14.49 +/- 3.04 (EHA). The mean bond strength values for In-Ceram Alumina were 9.87 +/- 2.40 JAPA) and 20.40 +/- 6.27 (IRS). All In-Ceram specimens treated with 10% hydrofluoric acid failed during thermal cycling.Conclusion: the Rocatec system was the most effective surface treatment for In-Ceram Alumina ceramics; whereas, the combination of aluminum oxide sandblasting and hydrofluoric acid etching for 20 seconds worked more effectively for Empress 2 ceramics.

Simulation of electron density maps for two-dimensional crystal structures using Mathematica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)