Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Experience-dependent upregulation of multiple plasticity factors in the hippocampus during early REM sleep

Sleep is beneficial to learning, but the underlying mechanisms remain controversial. The synaptic homeostasis hypothesis (SHY) proposes that the cognitive function of sleep is related to a generalized rescaling of synaptic weights to intermediate levels, due to a passive downregulation of plasticity mechanisms. A competing hypothesis proposes that the active upscaling and downscaling of synaptic weights during sleep embosses memories in circuits respectively activated or deactivated during prior waking experience, leading to memory changes beyond rescaling. Both theories have empirical support but the experimental designs underlying the conflicting studies are not congruent, therefore a consensus is yet to be reached. To advance this issue, we used real-time PCR and electrophysiological recordings to assess gene expression related to synaptic plasticity in the hippocampus and primary somatosensory cortex of rats exposed to novel objects, then kept awake (WK) for 60 min and finally killed after a 30 min period rich in WK, slow-wave sleep (SWS) or rapid-eye-movement sleep (REM). Animals similarly treated but not exposed to novel objects were used as controls. We found that the mRNA levels of Arc, Egr1, Fos, Ppp2ca and Ppp2r2d were significantly increased in the hippocampus of exposed animals allowed to enter REM, in comparison with control animals. Experience-dependent changes during sleep were not significant in the hippocampus for Bdnf, Camk4, Creb1, and Nr4a1, and no differences were detected between exposed and control SWS groups for any of the genes tested. No significant changes in gene expression were detected in the primary somatosensory cortex during sleep, in contrast with previous studies using longer post-stimulation intervals (>180 min). The experience-dependent induction of multiple plasticity-related genes in the hippocampus during early REM adds experimental support to the synaptic embossing theory.

Effect of Passive Fit Absence in the Prosthesis/Implant/Retaining Screw System: A Two-Dimensional Finite Element Analysis

The misfit between prostheses and implants is a clinical reality, but the level that can be accepted without causing mechanical or biologic problem is not well defined. This study investigates the effect of different levels of unilateral angular misfit prostheses in the prosthesis/implant/retaining screw system and in the surrounding bone using finite element analysis. Four models of a two-dimensional finite element were constructed: group I (control), prosthesis that fit the implant; groups 2 to 4, prostheses with unilateral angular misfit of 50, 100, and 200 mu m, respectively. A load of 133 N was applied with a 30-degree angulation and off-axis at 2 mm from the long axis of the implant at the opposite direction of misfit on the models. Taking into account the increase of the angular misfit, the stress maps showed a gradual increase of prosthesis stress and uniform stress in the implant and trabecular bone. Concerning the displacement, an inclination of the system due to loading and misfit was observed. The decrease of the unilateral contact between prosthesis and implant leads to the displacement of the entire system, and distribution and magnitude alterations of the stress also occurred.

A Decomposition and Noise Removal Method Combining Diffusion Equation and Wave Atoms for Textured Images

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

On exact boundary controllability for linearly coupled wave equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Mixing of superconducting d(x2-y2) state with s-wave states for different filling and temperature

We study the order parameter for mixed-symmetry states involving a major d(x2-y2) state and various minor s-wave states (s, s(xy), and Sx2+y2) for different filling and temperature for mixing angles 0 and pi /2. We employ a two-dimensional tight-binding model incorporating second-neighbor hopping for tetragonal and orthorhombic lattice. There is mixing for the symmetric s state both on tetragonal and orthorhombic lattice. The s(xy) state mixes with the d(x2-y2) state only on orthorhombic lattice. The s(x2+y2) state never mixes with the d(x2-y2) state. The temperature dependence of the order parameters is also studied. (C) 2001 Elsevier B.V. B.V. All rights reserved.

On asymptotic solutions of integrable wave equations

Asymptotic 'soliton train' solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker-Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Dynamics of bright matter-wave solitons in a Bose-Einstein condensate with inhomogeneous scattering length

We investigate dynamical effects of a bright soliton in Bose-Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross-Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.