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.

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

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

Fermi acceleration with memory-dependent excitation

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.

Numerical exploration of resonant dynamics in the system of Saturnian major satellites

We numerically investigate the long-term dynamics of the Saturnian system by analyzing the Fourier spectra of ensembles of orbits taken around the current orbits of Mimas, Enceladus, Tethys, Rhea and Hyperion. We construct dynamical maps around the current position of these satellites in their respective phase spaces. The maps are the result of a great deal of numerical simulations where we adopt dense sets of initial conditions and different satellite configurations. Several structures associated to the current two-body mean-motion resonances, unstable regions associated to close approaches between the satellites, and three-body mean-motion resonances in the system, are identified in the map. (C) 2010 Elsevier Ltd. All rights reserved.

Competition between suppression and production of Fermi acceleration

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.

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

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)

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.

Numerical chromosome polymorphism in Mikania cordifolia Willd. (Asteraceae)

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

Numerical study about natural escape and capture routes by the Moon via Lagrangian points L1 and L2

The lunar sphere of influence, whose radius is some 66,300 km, has regions of stable orbits around the Moon and also regions that contain trajectories which, after spending some time around the Moon, escape and are later recaptured by lunar gravity. Both the escape and the capture occur along the Lagrangian equilibrium points L1 and L2. In this study, we mapped out the region of lunar influence considering the restricted three-body Earth-Moon-particle problem and the four-body Sun-Earth-Moon-particle (probe) problem. We identified the stable trajectories, and the escape and capture trajectories through the L I and L2 in plots of the eccentricity versus the semi-major axis as a function of the time that the energy of the osculating lunar trajectory in the two-body Moon-particle problem remains negative. We also investigated the properties of these routes, giving special attention to the fact that they supply a natural mechanism for performing low-energy transfers between the Earth and the Moon, and can thus be useful on a great number of future missions. (C) 2007 Published by Elsevier Ltd on behalf of COSPAR.

PHYLOGENETIC STUDIES OF SOME SPECIES OF THE GENUS COFFEA .1. NUMERICAL-ANALYSIS OF FLAVONOID COMPOUNDS

Flavonoid compounds were analyzed in ripe fruit pulp of ten species of Coffea, including two cultivars of C. arabica and two of C. canephora. Three coefficients of similarity: Simple-Matching, Jaccard and Ochiai and three different clustering methods, Single Linkage, Complete Linkage and Unweighted Pair Group, Using Arithmetic Averages (UPGMA), were used to analyze the data.Jaccard and Ochiai's coefficients of association showed a more coherent result, when compared with taxonomic and hybridization studies. Inclusion of Psilanthopsis kapakata in the genus Coffea, as C. kapakata, is justified by the similarity of this species with other studied species, and clusters clearly approximate the species C. arabica and C. eugenioides. The latter is one of the possible parents of the allotetraploid species C. arabica, C. congensis is the only species whose position remains ambiguous, probably due to the fact that the plants of this species that were introduced into the Campinas collections, were hybrids and not typical of C. congensis.