Effective nonlinear Schrodinger equations for cigar-shaped and disc-shaped Fermi superfluids at unitarity

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

Dynamical properties for the problem of a particle in an electric field of wave packet: Low velocity and relativistic approach

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

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]

Parameter space for a dissipative Fermi-Ulam model

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

Oscilador harmônico amortecido e séries infinitas

Neste trabalho discute-se um arranjo experimental bastante simples e de baixo custo, cujo objetivo consiste em se exemplificar de forma concreta a aplicação de técnicas matemáticas envolvendo solução por séries infinitas destinadas ao estudo de determinado fenômeno físico. Esta prática desenvolvida e direcionada aos alunos de um curso de Graduação em Matemática, consiste basicamente de um estudo quantitativo relacionado ao comportamento oscilatório amortecido de um sistema constituído por uma massa acoplada a uma mola. Os resultados experimentais corroboraram muito bem a teoria fenomenológica e possibilitam a determinação numérica de uma constante física normalmente considerada desprezível, mencionada de passagem nos livros textos. Um fato de destaque deste trabalho referente ao fenômeno ondulatório estudado, ilimitado no tempo, mas limitado no espaço, é o de permitir uma boa discussão com os estudantes sobre o conceito de limite matemático.

Salting kinetics and salt diffusivities in farmed Pantanal caiman muscle

A criação de jacaré do Pantanal (Caiman crocodilus yacare) em cativeiro tem sido estimulada, e entre as técnicas de processamento de sua carne, a salga é um processo de conservação relativamente simples e de baixo custo. O objetivo deste trabalho foi estudar a cinética de difusão de cloreto de sódio em carne de jacaré do Pantanal criado em cativeiro, durante a salga úmida. Foram utilizados volumes limitados de salmoura e os experimentos foram realizados com relações salmoura/músculo de 3, 4 e 5, com concentrações de salmoura de 15%, 20% e 25% em peso e temperaturas de 10, 15 e 20ºC. A solução analítica da segunda lei de Fick, considerando difusão unidimensional em uma placa infinita em contato com uma solução bem agitada de volume limitado, foi utilizada para calcular os coeficientes de difusão efetivos de sal e estimar o conteúdo de cloreto de sódio nos filés. Obteve-se boa concordância entre o modelo analítico considerado e os dados experimentais. As difusividades do sal nos filés ocorreram na faixa de 0,47x10-10 a 9,62x10-10 m²/s.

Genetic variability in natural populations of Zeyheria montana mart. from the Brazilian Cerrado

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

UNUSUALLY STRONG ATTRACTION IN THE PRESENCE OF CONTINUUM BOUND-STATE

The result of few-particle ground-state calculation employing a two-particle nonlocal potential supporting a continuum bound state in addition to a negative-energy bound state has occasionally revealed unusually strong attraction in producing a very strongly bound ground state. In the presence of the continuum bound state the difference of phase shift between zero and infinite energies has an extra jump of pi as in the presence of an additional bound state. The wave function of the continuum bound state is identical with that of a strongly bound negative-energy state, which leads us to postulate a pseudo bound state in the two-particle system in order to explain the unexpected attraction. The role of the Pauli forbidden states is expected to be similar to these pseudo states.

Surface effects on vortex dynamics in thin type-II superconducting stripes with random pinning

We analyze the dynamics of a driven vortex lattice moving in a thin Superconducting stripe. The two dimensional stripe is assumed to be finite in the longitudinal direction, where we take into account the Surface effects, and infinite in the transversal direction. The numerical simulations are performed using the Langevin dynamics, including the vortex-vortex interaction, interaction of vortices with the surface current, vortex images, transport current and randomly distributed pinning centers. We show results for the differential resistivity and the vortex trajectories as a function of the external force. (C) 2004 Elsevier B.V. All rights reserved.

On an optimal control design for Rossler system

In this Letter, an optimal control strategy that directs the chaotic motion of the Rossler system to any desired fixed point is proposed. The chaos control problem is then formulated as being an infinite horizon optimal control nonlinear problem that was reduced to a solution of the associated Hamilton-Jacobi-Bellman equation. We obtained its solution among the correspondent Lyapunov functions of the considered dynamical system. (C) 2004 Elsevier B.V All rights reserved.

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

A RELATIVE COHOMOLOGICAL INVARIANT FOR GROUP PAIRS

We define a cohomological invariant E(G, S, M) where G is a group, S is a non empty family of (not necessarily distinct) subgroups of infinite index in G and M is a F2G-module (F2 is the field of two elements). In this paper we are interested in the special case where the family of subgroups consists of just one subgroup, and M is the F2G-module F2(G/S). The invariant E(G, {S}, F2(G/S)) will be denoted by E(G, S). We study the relations of this invariant with other ends e(G) , e(G, S) and e(G, S), and some results are obtained in the case where G and S have certain properties of duality.

Quantization of (2+1)-spinning particles and bifermionic constraint problem

This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to the classical model of a spinless relativistic particle as well as to the Berezin-Marinov model of a 3 + 1 Dirac particle, it is possible to obtain a consistent relativistic quantum mechanics of such particles. In the present paper, we apply a similar approach to the problem of quantizing the massive 2 + 1 Dirac particle. However, we stress that such a problem differs in a nontrivial way from the one in 3 + 1 dimensions. The point is that in 2 + 1 dimensions each spin polarization describes different fermion species. Technically this fact manifests itself through the presence of a bifermionic constant and of a bifermionic first-class constraint. In particular, this constraint does not admit a conjugate gauge condition at the classical level. The quantization problem in 2 + 1 dimensions is also interesting from the physical viewpoint (e.g., anyons). In order to quantize the model, we first derive a classical formulation in an effective phase space, restricted by constraints and gauges. Then the condition of preservation of the classical symmetries allows us to realize the operator algebra in an unambiguous way and construct an appropriate Hilbert space. The physical sector of the constructed quantum mechanics contains spin-1/2 particles and antiparticles without an infinite number of negative-energy levels, and exactly reproduces the one-particle sector of the 2 + 1 quantum theory of a spinor field.

The generator coordinate Hartree-Fock method as strategy for building Gaussian basis sets to ab initio study of the process of adsorption of sulfur on platinum (200) surface

The scheme named generator coordinate Hartree-Fock method (GCHF) is used to build (22s14p) and (33s22p16d9f) gaussian basis sets to S ((3)P) and Pt ((3)D) atoms, respectively. Theses basis sets are contracted to [13s10p] and [19s13p9d5f] through of Dunning's segmented contraction scheme and are enriched with d and g polarization functions, [13s10p1d] and [19s13p9d5flg]. Finally, the [19s13p9d5f1g] basis Set to Pt ((3)D) was supplemented with s and d diffuse functions, [20s13p10d5flg], and used in combination with [13s10p1d] to study the effects of adsorption of S ((3)D) atom on a pt ((3)D) atom belonged to infinite Pt (200) surface. Atom-atom overlap population, bond order, and infrared spectrum of [pt(_)S](2 -) were calculated properties and were carried out at Hartree-Fock-Roothaan level. The results indicate that the process of adsorption of S ((3)P) on pt ((3)D) in the infinite Pt (200) surface is mainly caused by a strong contribution of sigma between the 3p(z) orbital of S ((3)P) and the 6s orbital of pt ((3)D). (c) 2004 Elsevier B.V. All rights reserved.

Vortices in superconductors with a columnar defect: Finite size effects

In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it is considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated. (c) 2005 Elsevier B.V. All rights reserved.