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)

On the dynamical properties of an elliptical-oval billiard with static boundary

Some dynamical properties for a classical particle confined inside a closed region with an elliptical-oval-like shape are studied. The dynamics of the model is made by using a two-dimensional nonlinear mapping. The phase space of the system is of mixed kind and we have found the condition that breaks the invariant spanning curves in the phase space. We have discussed also some statistical properties of the phase space and obtained the behaviour of the positive Lyapunov exponent. (C) 2009 Elsevier B.V. All rights reserved.

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.

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)

Effect of robust torus on the dynamical transport

In the present work, we quantify the fraction of trajectories that reach a specific region of the phase space when we vary a control parameter using two symplectic maps: one non-twist and another one twist. The two maps were studied with and without a robust torus. We compare the obtained patterns and we identify the effect of the robust torus on the dynamical transport. We show that the effect of meandering-like barriers loses importance in blocking the radial transport when the robust torus is present.

Introduction to Focus Issue: Statistical mechanics and billiard-type dynamical systems

Dynamical systems of the billiard type are of fundamental importance for the description of numerous phenomena observed in many different fields of research, including statistical mechanics, Hamiltonian dynamics, nonlinear physics, and many others. This Focus Issue presents the recent progress in this area with contributions from the mathematical as well as physical stand point. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730155]

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

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

Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl's ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.

Comparative genomic hybridization analysis detects frequent over-representation of DNA sequences at 3q, 7p, and 8q in head and neck carcinomas

Comparative genomic hybridization (CGH) was used to identify chromosomal imbalances in 19 samples of squamous cell carcinoma of the head and neck (HNSCC). The chromosome arms most often or er-represented were 3q (48%), 8q (42%), and 7p (32%); in many cases, these changes were observed at high copy number. Other commonly over-represented sites were 1q, 2q, 6p, 6q, and 18q. The most frequently under-represented segments were 3p and 22q. Loss of heterozygosity of two polymorphic microsatellite loci from chromosome 22 was observed in two tongue tumors, in agreement with the CGH analysis. Gains of 1q and 2q material were detected in patients exhibiting a clinical history of recurrence and/or metastasis followed by terminal disease. This association suggests that gain of 1q and 2q map be a new marker of head and neck tumors with a refractory clinical response. (C) 2000 Elsevier B.V. All rights reserved.

Representation and analysis of soccer players' actions using principal components

This paper proposes the use of the Principal Components Analysis (PCA) method to represent and to analyse soccer players' actions distribution in the pitch. The seven games of the Brazilian National Team during the 2002 World Cup were analysed. The player's position actions were measured from videotapes in a computer interface. The results were: a) the graphical representation, given by two orthogonal segments in the two directions of maximal variability and centred at the mean of each player's actions position; b) the eccentricity measurement, given by the variability ratio and c) the actions zone area, given by variability product. The results showed that the individual characteristics of acting were well represented by the PCA, allowing comparisons among games and providing insights related to the tactical organisation of the team.

Dynamical scaling properties of nanoporous undoped and Sb-doped SnO2 supported thin films during tri- and bidimensional structure coarsening

The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped SnO2 sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering (SAXS) during in situ isothermal treatments at 450 and 650 degrees C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped SnO2 and 3% Sb-doped SnO2 films are similar (alpha approximate to 0.09), this value being invariant with respect to the firing temperature. In the case of undoped SnO2 films, another kinetic exponent, alpha('), corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent alpha, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped SnO2 films fired at 650 degrees C, we have determined that alpha(')approximate to 2 alpha, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamical scaling functions and their asymptotic behavior at high q (q being the modulus of the scattering vector) provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped SnO2 films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems.

On the coupling of the self-dual field to dynamical U(1) matter and its dual theory

We consider arbitrary U (1) charged matter non-minimally coupled to the self-dual field in d = 2 + 1. The coupling includes a linear and a rather general quadratic term in the self-dual field. By using both Lagragian gauge embedding and master action approaches we derive the dual Maxwell Chern-Simons-type model and show the classical equivalence between the two theories. At the quantum level the master action approach in general requires the addition of an awkward extra term to the Maxwell Chern-Simons-type theory. Only in the case of a linear coupling in the self-dual field can the extra term be dropped and we are able to establish the quantum equivalence of gauge invariant correlation functions in both theories.

RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .2. APPLICATION TO THE TRINUCLEON SYSTEM

We calculate the contribution of relativistic dynamics on the neutron-deutron scattering length and triton binding energy employing five sets trinucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off- and on-shell variations of two- and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (C) 1994 Academic Press, Inc.

Electronic correlations for a two-level dimer: dynamical susceptibilities

The exact solution for the full electronic Hamiltonian for a two-level dimer is obtained. The parameter constellation (20) is reparametrized via orthogonal Slater atomic orbitals, yielding a three-parameter model. With the dimer embedded in a thermal bath, several temperature-dependent dynamical susceptibilities are computed. (C) 2002 Elsevier B.V. B.V. All rights reserved.