Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Holographic dark energy and the universe expansion acceleration

By incorporating the holographic principle in a time-depending Lambda-term cosmology, new physical bounds on the arbitrary parameters of the model can be obtained. Considering then the dark energy as a purely geometric entity, for which no equation of state has to be introduced, it is shown that the resulting range of allowed values for the parameters may explain both the coincidence problem and the universe accelerated expansion, without resorting to any kind of additional structures. (C) 2006 Elsevier B.V. All rights reserved.

Theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of a sharp steplike initial discontinuity in a beam with one-dimensional striplike geometry. This approach is confirmed by numerical simulations, which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.

Cosmic acceleration from second order gauge gravity

We construct a phenomenological theory of gravitation based on a second order gauge formulation for the Lorentz group. The model presents a long-range modification for the gravitational field leading to a cosmological model provided with an accelerated expansion at recent times. We estimate the model parameters using observational data and verify that our estimative for the age of the Universe is of the same magnitude than the one predicted by the standard model. The transition from the decelerated expansion regime to the accelerated one occurs recently (at similar to 9.3 Gyr).

Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

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

Fermi acceleration on the annular billiard

We study the phenomenon of unlimited energy growth for a classical particle moving in the annular billiard. The model is considered under two different geometrical situations: static and breathing boundaries. We show that when the dynamics is chaotic for the static case, the introduction of a time-dependent perturbation allows that the particle experiences the phenomenon of Fermi acceleration even when the oscillations are periodic.

The presence and lack of Fermi acceleration in nonintegrable billiards

The unlimited energy growth ( Fermi acceleration) of a classical particle moving in a billiard with a parameter-dependent boundary oscillating in time is numerically studied. The shape of the boundary is controlled by a parameter and the billiard can change from a focusing one to a billiard with dispersing pieces of the boundary. The complete and simplified versions of the model are considered in the investigation of the conjecture that Fermi acceleration will appear in the time-dependent case when the dynamics is chaotic for the static boundary. Although this conjecture holds for the simplified version, we have not found evidence of Fermi acceleration for the complete model with a breathing boundary. When the breathing symmetry is broken, Fermi acceleration appears in the complete model.

Influences of the load centre of gravity on heavy vehicle acceleration

The aim of this paper is to analyse the influence of the load centre of gravity on heavy vehicle acceleration. This analysis is done through a method in which a vehicle centre of gravity map is used. A model for the driving force is presented for bus, truck and tractor-semi trailer combinations. The proposed model takes into consideration the resistance forces (drag, rolling resistance, translation and rotation acceleration, climbing resistance) and the 4 X 2 traction system. The positions of the vehicle centre of gravity as a function of the position of the load centre of gravity are determined. The vehicle acceleration is calculated based on the position of the load centre of gravity. This study analyses the acceleration of one of the Mercedes-Benz do Brasil tractor-semitrailer vehicle. A comparison of the acceleration for different maximum adhesion coefficients and ramps are presented, showing new results. An example showing the variations of the load centre of gravity position with the acceleration time and distance is provided. The load centre of gravity position is important for vehicle safety and the efficiency and economy in the transportation of the load.

Fermi acceleration on the annular billiard: a simplified version

A simplified version of a time-dependent annular billiard is studied. The dynamics is described using nonlinear maps and we consider two different configurations for the billiard, namely (i) concentric and (ii) eccentric cases. For the concentric case and for a null angular momentum, we confirm that the results for the Fermi-Ulam model are recovered and the particle does not experience the phenomenon of Fermi acceleration. However, on the eccentric case the particle demonstrates unlimited energy gain and Fermi acceleration is therefore observed.

Breaking down the Fermi acceleration with inelastic collisions

The phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving wall) is a sufficient condition to break down the process of Fermi acceleration. The phase transition from bounded to unbounded energy growth in the limit of vanishing dissipation is characterized.

Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions

Some dynamical properties of a classical particle confined inside a closed region with an oval-shaped boundary are studied. We have considered both the static and time-dependent boundaries. For the static case, the condition that destroys the invariant spanning curves in the phase space was obtained. For the time-dependent perturbation, two situations were considered: (i) non-dissipative and (ii) dissipative. For the non-dissipative case, our results show that Fermi acceleration is observed. When dissipation, via inelastic collisions, is introduced Fermi acceleration is suppressed. The behaviour of the average velocity for both the dissipative as well as the non-dissipative dynamics is described using the scaling approach. (C) 2009 Elsevier B.V. All rights reserved.

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Fermi acceleration and its suppression in a time-dependent Lorentz gas

Some dynamical properties for a Lorentz gas were studied considering both static and time-dependent boundaries. For the static case, it was confirmed that the system has a chaotic component characterized with a positive Lyapunov exponent. For the time-dependent perturbation, the model was described using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two different situations: (i) non-dissipative and (ii) dissipative dynamics. Our results confirm that unlimited energy growth is observed for the non-dissipative case. However, and totally new for this model, when dissipation via inelastic collisions is introduced, the scenario changes and the unlimited energy growth is suppressed, thus leading to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments. (C) 2010 Elsevier B.V. All rights reserved.

Fermi acceleration with memory-dependent excitation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)