The Feigenbaum's delta for a high dissipative bouncing ball model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scaling Properties of a Hybrid Fermi-Ulam-Bouncer Model

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

THE EFFECT of WEAK DISSIPATION IN TWO-DIMENSIONAL MAPPING

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration

Some dynamical properties of a bouncing ball model under the presence of an external force modelled by two nonlinear terms are studied. The description of the model is made by the use of a two-dimensional nonlinear measure-preserving map on the variable's velocity of the particle and time. We show that raising the straight of a control parameter which controls one of the nonlinearities, the positive Lyapunov exponent decreases in the average and suffers abrupt changes. We also show that for a specific range of control parameters, the model exhibits the phenomenon of Fermi acceleration. The explanation of both behaviours is given in terms of the shape of the external force and due to a discontinuity of the moving wall's velocity.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

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.

Parameter space for a dissipative Fermi-Ulam model

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

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analysis of tectonic-controlled fluvial morphology and sedimentary processes of the western Amazon Basin: an approach using satellite images and digital elevation model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An introduction to numerical methods in low-dimensional quantum systems

This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms (DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. The important role played by the model symmetries is also examined. Special emphasis is given to the DMRG.

The energy landscape for solvent dynamics in electron transfer reactions: A minimalist model

Energy fluctuations of a solute molecule embedded in a polar solvent are investigated to depict the energy landscape for solvation dynamics. The system is modeled by a charged molecule surrounded by two layers of solvent dipolar molecules with simple rotational dynamics. Individual solvent molecules are treated as simple dipoles that can point toward or away from the central charge (Ising spins). Single-spin-flip Monte Carlo kinetics simulations are carried out in a two-dimensional lattice for different central charges, radii of outer shell, and temperatures. By analyzing the density of states as a function of energy and temperatures, we have determined the existence of multiple freezing transitions. Each of them can be associated with the freezing of a different layer of the solvent. (C) 2002 American Institute of Physics.

HIGHER-DERIVATIVE SCHWINGER MODEL

Using the operator formalism, we obtain the bosonic representation for the free fermion field satisfying an equation of motion with higher-order derivatives. Then, we consider the operator solution of a generalized Schwinger model with higher-derivative coupling. Since the increasing of the derivative order implies the introduction of an equivalent number of extra fermionic degrees of freedom, the mass acquired by the gauge field is bigger than the one for the standard two-dimensional QED. An analysis of the problem from the functional integration point of view corroborates the findings of canonical quantization, and corrects certain results previously announced in the literature on the basis of Fujikawa's technique.