Short-wave instabilities in the Benjamin-Bona-Mahoney-Peregrine equation: theory and numerics

In this paper we discuss the nonlinear propagation of waves of short wavelength in dispersive systems. We propose a family of equations that is likely to describe the asymptotic behaviour of a large class of systems. We then restrict our attention to the analysis of the simplest nonlinear short-wave dynamics given by U-0 xi tau, = U-0 - 3(U-0)(2). We integrate numerically this equation for periodic and non-periodic boundary conditions, and we find that short waves may exist only if the amplitude of the initial profile is not too large.

The application of interpolating MLS approximations to the analysis of MHD flows

The element-free Galerkin method (EFGM) is a very attractive technique for solutions of partial differential equations, since it makes use of nodal point configurations which do not require a mesh. Therefore, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. However, the imposition of boundary conditions is not straightforward, since the EFGM is based on moving-least-squares (MLS) approximations which are not necessarily interpolants. This feature requires, for instance, the introduction of modified functionals with additional unknown parameters such as Lagrange multipliers, a serious drawback which leads to poor conditionings of the matrix equations. In this paper, an interpolatory formulation for MLS approximants is presented: it allows the direct introduction of boundary conditions, reducing the processing time and improving the condition numbers. The formulation is applied to the study of two-dimensional magnetohydrodynamic flow problems, and the computed results confirm the accuracy and correctness of the proposed formulation. (C) 2002 Elsevier B.V. All rights reserved.

An application of the Adomian's decomposition method to the analysis of MHD duct flows

A new approach is proposed in this work for the treatment of boundary value problems through the Adomian's decomposition method. Although frequently claimed as accurate and having fast convergence rates, the original formulation of Adomian's method does not allow the treatment of homogeneous boundary conditions along closed boundaries. The technique here presented overcomes this difficulty, and is applied to the analysis of magnetohydrodynamic duct flows. Results are in good agreement with finite element method calculations and analytical solutions for square ducts. Therefore, new possibilities appear for the application of Adomian's method in electromagnetics.

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).

Magnetothermal instabilities in magnetized anisotropic plasmas

Using the 16-moment transport equations for an ideal anisotropic collisionless plasma we analyze the influence of pressure anisotropy on the magnetothermal (MTI) and heat-flux-driven buoyancy (HBI) instabilities. We calculate the dispersion relation and the growth rates for these instabilities in the presence of a background heat flux and for configurations with static pressure anisotropy, finding that when the frequency at which heat conduction acts is much larger than any other frequency in the system (i.e. weak magnetic field) the pressure anisotropy has no effect on the MTI/HBI, provided the degree of anisotropy is small. In contrast, when this ordering of timescales does not apply the instability criteria depend on pressure anisotropy.

Excitonic instabilities and spontaneous time-reversal symmetry breaking on the honeycomb lattice

We elucidate the close relationship between spontaneous time-reversal symmetry breaking and the physics of excitonic instabilities in strongly correlated multiband systems. The underlying mechanism responsible for the spontaneous breaking of time-reversal symmetry in a many-body system is closely related to the Cooper-like pairing instability of interband particle-hole pairs involving higher-order symmetries. Studies of such pairing instabilities have, however, mainly focused on the mean-field aspects of the virtual exciton condensate, which ignores the presence of the underlying collective Fermi-liquid excitations. We show that this relationship can be exploited to systematically derive the coupling of the condensate order parameter to the intraband Fermi-liquid particle-hole excitations. Surprisingly, we find that the static susceptibility is negative in the ordered phase when the coupling to the Fermi-liquid collective excitations are included, suggesting that a uniform condensate of virtual excitons, with or without time-reversal breaking, is an unstable phase at T = 0.

Control of instabilities in non-Newtonian free surface fluid flows

Free surface flows in inclined channels can develop periodic instabilities that are propagated downstream as shock waves with well-defined wavelengths and amplitudes. Such disturbances are called roll waves and are common in channels, torrential lava, landslides, and avalanches. The prediction and detection of such waves over certain types of structures and environments are useful for the prevention of natural risks. In this work, a mathematical model is established using a theoretical approach based on Cauchy's equations with the Herschel-Bulkley rheological model inserted into the viscous part of the stress tensor. This arrangement can adequately represent the behavior of muddy fluids, such as water-clay mixture. Then, taking into account the shallow water and the Rankine-Hugoniot's (shock wave) conditions, the equation of the roll wave and its properties, profile, and propagation velocity are determined. A linear stability analysis is performed with an emphasis on determining the condition that allows the generation of such instabilities, which depends on the minimum Froude number. A sensitivity analysis on the numerical parameters is performed, and numerical results including the influence of the Froude number, the index flow and dimensionless yield stress on the amplitude, the wavelength of roll waves and the propagation velocity of roll waves are shown. We show that our numerical results were in agreement with Coussot's experimental results (1994).

Analysis on the formation of a FRC by flux measurements and MHD simulations

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

Morphoquantitative aspects of nitrergic myoenteric neurons from the stomach of diabetic rats supplemented with acetyl-L-carnitine

The NADPH-diaphorase (NADPH-d) positive myoenteric neurons from the body of the stomach of rats with streptozotocin-induced diabetes with or without supplementation with acetyl-L-carnitine (ALC) were evaluated. At the age of 105 days the animals were divided into four groups: normoglycaemic (C), normoglycaemic supplemented with ALC (CC), diabetic (D) and diabetic supplemented with ALC (DC). The supplementation with ALC (200 mg/kg body weight/day) to groups CC and DC was made during 105 days. After this period the animals were killed and the stomach removed and subjected to the histochemical technique of NADPH-d for the staining of the neurons of the myoenteric plexus. The area of 500 neurons of each group was investigated, as well as the neuronal density in an area of 23.84 mm(2) in each stomach. ALC promoted reduction (P < 0.05) of fasting glycaemia, water ingestion and areas of the profiles of the cell bodies of the NADPH-d neurons in the diabetic animals. The density of these neurons was not statistically different in the groups studied. It is suggested, therefore, a moderate neuroprotective effect of ALC, because the diminishment of the areas of the neuronal profiles in the supplemented diabetic animals, although being statistically significant relative to the non-supplemented diabetics, was not sufficient to equal the values from the non-diabetic controls.

Morphoquantitative aspects of NADH-diaphorase myenteric neurons in the ileum of diabetic rats treated with acetyl-L-carnitine

In this work, we investigated the effect of the acetyl-L-carnitine (ALC) supplementation (200 mg/kg/day) on the myenteric neurons of the ileum of rats made diabetic by streptozotocin (35 mg/kg, i.v.). Four groups were used: diabetic (D), diabetic supplemented with ALC (DC), control (C) and control supplemented with ALC (CC). After 15 weeks of diabetes induction the animals were killed and the ileum was collected and subjected to whole-mount preparation to evidence the myenteric neurons through the histochemical technique of the NADH-diaphorase. The density of neurons seen in 12.72 min(2) of ileum showed no difference among the groups, although in group D it was 22% smaller than in group C, while group DC was 9% smaller to group CC. The profiles of the cell bodies (PC) of 1000 neurons per group were analysed. The neurons PC in group D decreased (P < 0.0001) when compared with other groups and increased (P < 0.0001) when compared with group DC. The incidence of neurons with a PC inferior to 200 mu m(2) was larger in group D. The frequency of neurons with a PC higher than 200 mu m(2) in group DC was close to those seen in groups C and CC. We concluded that ALC eases the loss of neurons and makes the incidence of myenteric neurons with a PC higher than 200 mu m(2) similar to the control rats.

Influence of Heat Treatment on the Anelastic Properties of MgB(2)

The discovery of the superconductivity of MgB(2) was of great importance, because this material is one of the few known binary compounds and has one of the highest critical temperatures (39 degrees K). As MgB(2) is a granular compound, it is fundamentally important to understand the mechanisms of the interaction of the defects and the crystalline lattice, in addition to the eventual processes involving the grain boundaries that compose the material. In this sense, the mechanical spectroscopy measurements constitute a powerful tool for this study, because through them we can obtain important information about phase transitions, the behavior of interstitial or substitutional elements, dislocations, grain boundaries, diffusion, instabilities, and other imperfections of the lattice. For this paper, the samples were prepared using the PIT method and were characterized by density, X-ray diffraction, scanning electron microscopy, electric resistivity, magnetization, and mechanical spectroscopy. The samples were measured in their as-cast condition and after an ultra-high-vacuum heat treatment. The results showed complex spectra, in which were identified relaxation processes due to dislocation movement, interaction among interstitial elements and dislocations, auto-diffusion, and movement of grain boundaries. Some of these processes disappeared with the heat treatment.

Mean motion resonances and the stability of a circumbinary disk in a triple stellar system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Social support and infant malnutrition: a case-control study in an urban area of Southeastern Brazil

The relationship between malnutrition and social support was first suggested in the mid-1990s. Despite its plausibility, no empirical studies aimed at obtaining evidence of this association could be located. The goal of the present study was to investigate such evidence. A case-control study was carried out including 101 malnourished children (weight-for-age National Center for Health Statistics/WHO 5th percentile) aged 12-23 months, who were compared with 200 well-nourished children with regard to exposure to a series of factors related to their social support system. Univariate and multiple logistic regressions were carried out, odds ratios being adjusted for per capita family income, mother's schooling, and number of children. The presence of an interaction between income and social support variables was also tested. Absence of a partner living with the mother increased risk of malnutrition (odds ratio 2.4 (95 % CI 1.19, 4.89)), even after adjustment for per capita family income, mother's schooling, and number of children. The lack of economic support during adverse situations accounted for a very high risk of malnutrition (odds ratio 10.1 (95 % CI 3.48, 29.13)) among low-income children, but had no effect on children of higher-income families. Results indicate that receiving economic support is an efficient risk modulator for malnutrition among low-income children. In addition, it was shown that the absence of a partner living with the mother is an important risk factor for malnutrition, with an effect independent from per capita family income, mother's schooling, and number of children.