Bose systems in spatially random or time-varying potentials

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.

One-dimensional trapped atoms: critical coupling parameter and critical number of particles

In this paper we consider the case of a Bose gas in low dimension in order to illustrate the applicability of a method that allows us to construct analytical relations, valid for a broad range of coupling parameters, for a function which asymptotic expansions are known. The method is well suitable to investigate the problem of stability of a collection of Bose particles trapped in one- dimensional configuration for the case where the scattering length presents a negative value. The eigenvalues for this interacting quantum one-dimensional many particle system become negative when the interactions overcome the trapping energy and, in this case, the system becomes unstable. Here we calculate the critical coupling parameter and apply for the case of Lithium atoms obtaining the critical number of particles for the limit of stability.

Modelos auto-similares para rádio fontes extragalácticas.

This work is a detailed study of self-similar models for the expansion of extragalactic radio sources. A review is made of the definitions of AGN, the unified model is discussed and the main characteristics of double radio sources are examined. Three classification schemes are outlined and the self-similar models found in the literature are studied in detail. A self-similar model is proposed that represents a generalization of the models found in the literature. In this model, the area of the head of the jet varies with the size of the jet with a power law with an exponent γ. The atmosphere has a variable density that may or may not be spherically symmetric and it is taken into account the time variation of the cinematic luminosity of the jet according to a power law with an exponent h. It is possible to show that models Type I, II and III are particular cases of the general model and one also discusses the evolution of the sources radio luminosity. One compares the evolutionary curves of the general model with the particular cases and with the observational data in a P-D diagram. The results show that the model allows a better agreement with the observations depending on the appropriate choice of the model parameters.

Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

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

A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity

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

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

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)

A thermoporometry and small-angle x-ray scattering study of wet silica sonogels as the pore volume fraction is varied

Silica sonogels with different porosities were prepared by acid sono-hydrolysis of tetraethoxysilane. Wet sonogels were studied using small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC shows a broad thermal peak below the normal water melting point associated with the melting of confined ice nanocrystals, or nanoporosity. The nanopore size distribution was determined from the Gibbs-Thomson equation. As the porosity is increased, a second sharp DSC thermal peak with onset temperature at the water melting point is apparent, which was associated with the melting of ice macrocrystals, or macroporosity. The DSC result could be causing misinterpretation of the macroporosity because water may not be exactly confined in very feeble silica network regions in sonogels with high porosity. The structure of the wet gels can be described fairly well as mutually self-similar mass fractal structures with characteristic length. increasing from similar to 1.8 to similar to 5.4 nm and mass fractal dimension D diminishing discretely from similar to 2.6 to similar to 2.3 as the porosity increases in the range studied. More specifically, such a structure could be described using a two-parameter correlation function gamma(r) similar to r(D-3) exp(-r/xi), which is limited at larger scale by the cut-off distance xi but without a well-defined small scale cut-off distance, at least up to the maximum angular domain probed using SAXS in the present study.

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.

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Soluções auto-similares das equações de Navier-Stokes em Lp-Fraco

Pós-graduação em Matemática - IBILCE

Modelo de propagação indoor multi-andar em 2.4 GHz com estimativa de parâmetros de QoS em chamadas VoIP

O advento de novas formas multimídia tem atraído uma clientela exigente, onde preocupação não é somente com o serviço, mas também, com a qualidade que esse serviço pode ser oferecido. As WLAN (Wireless Local Area Networks) tornaram-se a forma mais comum de roteamento de Internet, devido ao seu baixo custo e facilidade de implementação. Para realizar um bom roteamento é necessário um planejamento, utilizando-se modelos. Os modelos de propagação existentes na literatura fazem a predição da intensidade do sinal, mas algumas vezes não contemplam a previsão de um bom serviço. Nesse sentido a presente dissertação propõe-se a elaborar um modelo de propagação empírico indoor multi-andar que não só prediz a potência recebida, mas também faz uma previsão para algumas métricas de QoS (Quality of Service) de chamadas VoIP (Voice over Internet Protocol). Para a elaboração do modelo proposto foram feitas campanhas de medição, em um prédio de dois andares, em pisos distintos mantendo-se a posição do ponto de acesso (PA) fixa. Estudos de geometria analítica para a contagem e agregação de perdas em pisos e paredes. Os resultados do modelo proposto foram comparados com um modelo da literatura que tem um comportamento similar, onde é possível verificar o melhor desempenho do modelo proposto, e para efeito de estudo um andar completamente simulado foi introduzido para avaliação.