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)

Particle Competition and Cooperation in Networks for Semi-Supervised Learning

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

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.

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.

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.

CRITICAL EXPONENTS and SCALING PROPERTIES FOR THE CHAOTIC DYNAMICS of A PARTICLE IN A TIME-DEPENDENT POTENTIAL BARRIER

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)

Dynamical scaling in fractal structures in the aggregation of tetraethoxysilane-derived sonogels

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

Universal zero-bias conductance for the single-electron transistor

The thermal dependence of the zero-bias conductance for the single electron transistor is the target of two independent renormalization-group approaches, both based on the spin-degenerate Anderson impurity model. The first approach, an analytical derivation, maps the Kondo-regime conductance onto the universal conductance function for the particle-hole symmetric model. Linear, the mapping is parametrized by the Kondo temperature and the charge in the Kondo cloud. The second approach, a numerical renormalization-group computation of the conductance as a function the temperature and applied gate voltages offers a comprehensive view of zero-bias charge transport through the device. The first approach is exact in the Kondo regime; the second, essentially exact throughout the parametric space of the model. For illustrative purposes, conductance curves resulting from the two approaches are compared.

Ground state masses and binding energies of the nucleon, hyperon and heavy baryons in a light-front model

The ground state masses and binding energies of the nucleon, lambda0, lambdac+ , lambdab0 are studied within a constituent quark QCD-inspired light-front model. The light-front Faddeev equations for the Qqq composite spin 1/2 baryons, are derived and solved numerically. The experimental data for the masses are qualitatively described by a flavor independent effective interaction.

Spin-1 particle in the light-front approach

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

Fluid dynamics of air in a packed bed: velocity profiles and the continuum model assumption

Air flow through packed beds was analyzed experimentally under conditions ranging from those that reinforce the effect of the wall on the void fraction to those that minimize it. The packing was spherical particles, with a tube-to-particle diameter ratio (D/dp) between 3 and 60. Air flow rates were maintained between 1.3 and 4.44 m3/min, and gas velocity was measured with a Pitot tube positioned above the bed exit. Measurements were made at various radial and angular coordinate values, allowing the distribution of air flow across the bed to be described in detail. Comparison of the experimentally observed radial profiles with those derived from published equations revealed that at high D/dp ratios the measured and calculated velocity profiles behaved similarly. At low ratios, oscillations in the velocity profiles agreed with those in the voidage profiles, signifying that treating the porous medium as a continuum medium is questionable in these cases.

Effect of the levels of calcium and particle size of limestone on laying hens

O experimento foi realizado para avaliar o efeito dos níveis de cálcio (Ca) e da granulometria do calcário (GC) para poedeiras comerciais. Foram utilizadas 216 poedeiras da linhagem Dekalb White de 25 a 49 semanas de idade em um delineamento inteiramente casualizado, em esquema fatorial 3 × 2, composto de três níveis de cálcio (3,92; 4,02 e 4,12%) e duas granulometrias do calcário (fina - 0,60 mm; e grossa - 1,00 mm), que resultaram em seis tratamentos, com seis repetições de seis aves. Não houve efeito significativo dos níveis de cálcio e da granulometria do calcário nem da interação nível de cálcio × granulometria do calcário para o consumo de ração, o peso dos ovos, a gravidade específica, a espessura da casca, a porcentagem de casca, a unidade Haugh, a digestibilidade de cálcio e fósforo e a porcentagem do trato digestório. A produção, massa, conversão por massa e conversão por dúzia de ovos tiveram seus melhores resultados com 4,12% de cálcio na dieta. A porcentagem de moela e o consumo de ração observado às 15 h melhoraram com o aumento na granulometria do calcário de 0,60 para 1,00 mm. Houve efeito da interação entre nível de cálcio e granulometria do calcário para a resistência à quebra da tíbia, a densidade óssea, o comprimento do intestino delgado e o consumo de ração às 6, 9, 12, 18 e 21 h, respectivamente. Recomenda-se a adição de 4,12% de cálcio e calcário na granulometria grossa (1,00 mm) para melhor desempenho de poedeiras comerciais. Mais estudos são necessários para elucidar os mecanismos envolvidos na alteração do comportamento alimentar das poedeiras em resposta às mudanças nos níveis de cálcio e na granulometria do calcário das rações.

Competition between local potentials and attractive particle-particle interactions in superlattices

Naturally occuring or man-made systems displaying periodic spatial modulations of their properties on a nanoscale constitute superlattices. Such modulated structures are important both as prototypes of simple nanotechnological devices and as particular examples of emerging spatial inhomogeneity in interacting many-electron systems. Here we investigate the effect different types of modulation of the system parameters have on the ground-state energy and the charge-density distribution of the system. The superlattices are described by the inhomogeneous attractive Hubbard model, and the calculations are performed by density-functional and density-matrix renormalization group techniques. We find that modulations in local electric potentials are much more effective in shaping the system's properties than modulations in the attractive on-site interaction. This is the same conclusion we previously [M.F. Silva, N.A. Lima, A.L. Malvezzi, K. Capelle, Phys. Rev. B 71 (2005) 125130.] obtained for repulsive interactions, suggesting that it is not an artifact of a specific state, but a general property of modulated structures. (c) 2007 Elsevier Ltd. All rights reserved.