Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ""radiation"". Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. (C) 2009 Elseiver. B.V. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Fluctuations of the Stokes and anti-Stokes surface-enhanced resonance Raman scattering intensities in an electrochemical environment

Stokes and anti-Stokes SERRS intensity fluctuations were observed from a roughened silver electrode immersed in diluted solutions of Brilliant Green (BG), a behaviour linked to single-molecule events. The distributions of the anti-Stokes to Stokes ratios were obtained and their shape showed a strong dependence on the applied potential.

Reflection of matter waves in potential structures

In this paper the behavior of matter waves in suddenly terminated potential structures is investigated numerically. It is shown that there is no difference between a fully quantum mechanical treatment and a semiclassical one with regards to energy redistribution. For the quantum case it is demonstrated that there can be substantial reflection at the termination. The neglect of backscattering by the semiclassical method brings about major differences in the case of low kinetic energies. A simple phenomenological model is shown to partially explain the observed backscattering using dynamics of reduced dimensionality.

Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

Single-mode acceleration of matter waves in circular waveguides

Ultracold gases in ring geometries hold promise for significant improvements of gyroscopic sensitivity. Recent experiments have realized atomic and molecular storage rings with radii in the centimeter range, sizes whose practical use in inertial sensors requires velocities significantly in excess of typical recoil velocities. We use a combination of analytical and numerical techniques to study the coherent acceleration of matter waves in circular waveguides, with particular emphasis on its impact on single-mode propagation. In the simplest case we find that single-mode propagation is best maintained by the application of time-dependent acceleration force with the temporal profile of a Blackmann pulse. We also assess the impact of classical noise on the acceleration process.

Estimativas do erro nas aproximações de Galerkin para as equações de Navier-Stokes

Neste trabalho são provadas algumas estimativas de erro em espaços para as aproximações de Galerkin para a solução do sistema de equações de Navier-Stokes. Mostra-se que o erro decresce em proporção inversa aos autovalores do operador de Stokes.

Alguns aspectos numéricos e teóricos das equações de Navier-Stokes na modelagem do escoamento em torno de um vórtice

Neste trabalho desenvolvemos uma metodologia numérica para a solução do escoamento em torno de um vórtice. Como a análise completa deste tipo de fluxo não é uma tarefa fácil, simplificações quanto ao escoamento e ao método numérico são necessárias. Também investigamos o comportamento das soluções das equações governantes (Navier-Stokes) quando o tempo tende ao infinito. Nesse sentido, dividimos este trabalho em duas partes: uma numérica e outra analítica. Com o intuito de resolver numericamente o problema, adotamos o método de diferenças finitas baseado na formulação incompressível das equações governantes. O método numérico para integrar essas equações é baseado no esquema de Runge- Kutta com três estágios. Os resultados numéricos são obtidos para cinco planos bidimensionais de um vórtice com números de Reynolds variando entre 1000 e 10000. Na parte analítica estudamos taxas de decaimento das soluções das equações de Navier-Stokes quando os dados iniciais são conhecidos. Também estimamos as taxas de decaimento para algumas derivadas das soluções na norma L2 e comparamos com as taxas correspondentes da solução da equação do calor.

New challenges for international economic law teaching and research in México: Mexico’s outstanding waves of reforms

This position paper argues that at this time of Mexico’s ongoing big transformation, legal educators and researchers in Mexico need to pay greater attention to international economic law, and that a renewal and perhaps some re-orientation of the approach to teaching international economic law, could provide significant contributions to and shape and support both the objectives and outcomes of reform in Mexico. International Economic Law courses and research can be made more useful, not only for students themselves, but also for their contribution towards the role that academics, lawyers, and other epistemic communities need to play in the political, economic and social evolution that is accelerating in Mexico.

Characterization of heat waves affecting mortality rates of broilers between 29 days and market age

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

Damage Detection in Flexible Plate Using Lamb Waves

This paper presents an experimental technique for structural health monitoring (SHM) based on Lamb waves approach in an aluminum plate using piezoelectric material as actuators and sensors. Lamb waves are a form of elastic perturbation that remains guided between two parallel free surfaces, such as the upper and lower surfaces of a plate, beam or shelf. Lamb waves are formed when the actuator excites the surface of the structure with a pulse after receiving a signal. Two PZTs were placed in the plate surface and one of them was used to send a predefined wave through the structure. Thus, the other PZT (adjacent) becomes the sensor. Using this methodology, this paper presents one case of damage detection considering the aluminum plate in the free-free-free-free boundary condition. The damage was simulated by adding additional mass on the plate. It is proposed two damage detection indexes obtained from the experimental signal, involving the Fast Fourier Transform (FFT) and the power spectral density (PSD) that were computed using the output signal. The results show the viability of the presented methodology to damage detection in smart structures

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.