Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

Remarks on Parametric Surface Waves in a Nonlinear and Non-Ideally Excited Tank

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Statistical and dynamical properties of a dissipative kicked rotator

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

Consumo máximo de oxigênio e limiar anaeróbio de jogadores de futebol: comparação entre as diferentes posições

O grau de desenvolvimento das capacidades físicas no futebol é fator determinante do nível desportivo do jogador. O objetivo do presente estudo foi comparar valores de limiar anaeróbio e consumo máximo de oxigênio entre jogadores profissionais de futebol de diferentes posições. Para tanto, 25 atletas (idade = 22,08 ± 8,28 anos, peso = 76,12 ± 9,8kg, altura = 179,8 ± 7,1cm e relação corporal = 12,21 ± 3,67% de gordura corporal) foram divididos em cinco grupos, como se segue: goleiros (GO), zagueiros (ZA), laterais (LA), meio-campistas (MC) e atacantes (AT). O VO2max foi determinado em esteira ergométrica através de análise direta e a velocidade de corrida correspondente ao limiar anaeróbio fixo de 4mM (V4mM), em teste de campo (2 x 1.000m a 90 e 95% da velocidade máxima para a distância) através de interpolação linear. A V4mM foi menor (p < 0,05) para o grupo GO em relação aos demais grupos. Além disso, os grupos LA e MC apresentaram valores de V4mM significantemente maiores em relação aos grupos ZA e AT. O grupo GO mostrou VO2max significantemente menor em relação a todos os outros grupos, sendo que estes últimos não apresentaram diferença entre si. Uma vez que os atletas de diferentes posições não realizavam treinamento diferenciado, os autores creditam as diferenças encontradas à especificidade da movimentação durante partidas e coletivos.

Basins of attraction changes by amplitude constraining of oscillators with limited power supply

We investigate the dynamics of a Duffing oscillator driven by a limited power supply, such that the source of forcing is considered to be another oscillator, coupled to the first one. The resulting dynamics come from the interaction between both systems. Moreover, the Duffing oscillator is subjected to collisions with a rigid wall (amplitude constraint). Newtonian laws of impact are combined with the equations of motion of the two coupled oscillators. Their solutions in phase space display periodic (and chaotic) attractors, whose amplitudes, especially when they are too large, can be controlled by choosing the wall position in suitable ways. Moreover, their basins of attraction are significantly modified, with effects on the final state system sensitivity. (c) 2005 Elsevier Ltd. All rights reserved.

Shrimp-shape domains in a dissipative kicked rotator

Some dynamical properties for a dissipative kicked rotator are studied. Our results show that when dissipation is taken into account a drastic change happens in the structure of the phase space in the sense that the mixed structure is modified and attracting fixed points and chaotic attractors are observed. A detailed numerical investigation in a two-dimensional parameter space based on the behavior of the Lyapunov exponent is considered. Our results show the existence of infinite self-similar shrimp-shaped structures corresponding to periodic attractors, embedded in a large region corresponding to the chaotic regime. (C) 2011 American Institute of Physics. [doi:10.1063/1.3657917]

Analysis of the distances covered by first division Brazilian soccer players obtained with an automatic tracking method

Methods based on visual estimation still is the most widely used analysis of the distances that is covered by soccer players during matches, and most description available in the literature were obtained using such an approach. Recently, systems based on computer vision techniques have appeared and the very first results are available for comparisons. The aim of the present study was to analyse the distances covered by Brazilian soccer players and compare the results to the European players', both data measured by automatic tracking system. Four regular Brazilian First Division Championship matches between different teams were filmed. Applying a previously developed automatic tracking system (DVideo, Campinas, Brazil), the results of 55 outline players participated in the whole game (n = 55) are presented. The results of mean distances covered, standard deviations (s) and coefficient of variation (cv) after 90 minutes were 10,012 m, s = 1,024 m and cv = 10.2%, respectively. The results of three-way ANOVA according to playing positions, showed that the distances covered by external defender (10642 ± 663 m), central midfielders (10476 ± 702 m) and external midfielders (10598 ± 890 m) were greater than forwards (9612 ± 772 m) and forwards covered greater distances than central defenders (9029 ± 860 m). The greater distances were covered in standing, walking, or jogging, 5537 ± 263 m, followed by moderate-speed running, 1731 ± 399 m; low speed running, 1615 ± 351 m; high-speed running, 691 ± 190 m and sprinting, 437 ± 171 m. Mean distance covered in the first half was 5,173 m (s = 394 m, cv = 7.6%) highly significant greater (p < 0.001) than the mean value 4,808 m (s = 375 m, cv = 7.8%) in the second half. A minute-by-minute analysis revealed that after eight minutes of the second half, player performance has already decreased and this reduction is maintained throughout the second half. ©Journal of Sports Science and Medicine (2007).

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Educação e desenvolvimento de zero a três anos de idade: contribuições da psicologia histórico-cultural para a organização do ensino

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A dissipative Fermi-Ulam model under two different kinds of dissipation

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

PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving; the equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure. (C) 2004 Elsevier Ltd. All rights reserved.

Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations

For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary condition in L-2(Omega). For a dissipative nonlinearity f satisfying a suitable growth restrictions these equations define on the phase space H-0(1)(Omega) x L-2(Omega) semigroups {T-eta(t) : t >= 0} which have global attractors A(eta) eta >= 0. We show that the family {A(eta)}(eta >= 0), behaves upper and lower semi-continuously as the parameter eta tends to 0(+).

LOWER SEMICONTINUITY of PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

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

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.