GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

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.

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

Phoretic mites (Acari: Chaetodactylidae) associated with the solitary bee Tetrapedia diversipes (Apidae: Tetrapediini)

Solitary bees of the genus Tetrapedia have a specific association with mites of the genus Roubikia (Chaetodactylidae). These mites are frequently found attached to active Tetrapedia bees. We quantified the number of mites on individuals of Tetrapedia diversipes Klug and examined the interaction between these species. Nests of T. diversipes were obtained from trap-nests placed in four localities in Sao Paulo, Brazil. The study lasted from March 2007 to February 2009. Out of a total of 650 nests with emergences, 118 were infested with mites (Roubikia sp.). From these nests, 176 individuals of T. diversipes emerged with mites on their bodies. Additionally, six individuals of Coelioxoides waltheriae, the specific kleptoparasitic bee to T. diversipes, emerged. Mites were attached mainly to the mesosoma. All nests infected with mites did not presented mortality of the immature. The mortality rate of nests was inversely related to the level of mite infestation, suggesting a mutualistic interaction in which mites may remove fungi from the nests, while the bees would provide the mites with transport, dispersal, and shelter.

Male sleeping aggregations of solitary oil-collecting bees in Brazil (Centridini, Tapinotaspidini, and Tetrapediini; Hymenoptera: Apidae)

Males of solitary bees usually spend the night in clusters on small branches of plants, cavities and flowers. The individuals usually return to the same location each evening during their life, exhibiting site fidelity to a particular plant. We report on the sleeping roosts of the males of some oil-collecting bees of the genera Centris, Paratetrapedia, Lanthanomelissa, Monoeca, and Tetrapedia, as well as the host plants. We discuss the role of the male clusters to the associated plants.

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Absorption of planar waves in a draining bathtub

We present an analysis of the absorption of acoustic waves by a black hole analogue in (2 + 1) dimensions generated by a fluid flow in a draining bathtub. We show that the low-frequency absorption length is equal to the acoustic hole circumference and that the high-frequency absorption length is 4 times the ergoregion radius. For intermediate values of the wave frequency, we compute the absorption length numerically and show that our results are in excellent agreement with the low-and high-frequency limits. We analyze the occurrence of superradiance, manifested as negative partial absorption lengths for corotating modes at low frequencies.

Scattering of massless scalar waves by Reissner-Nordstrom black holes

We present a study of scattering of massless planar scalar waves by a charged nonrotating black hole. Partial wave methods are applied to compute scattering and absorption cross sections, for a range of incident wavelengths. We compare our numerical results with semiclassical approximations from a geodesic analysis, and find excellent agreement. The glory in the backward direction is studied, and its properties are shown to be related to the properties of the photon orbit. The effects of the black hole charge upon scattering and absorption are examined in detail. As the charge of the black hole is increased, we find that the absorption cross section decreases, and the angular width of the interference fringes of the scattering cross section at large angles increases. In particular, the glory spot in the backward direction becomes wider. We interpret these effects under the light of our geodesic analysis.

Scattering of sound waves by a canonical acoustic hole

This is a study of a monochromatic planar perturbation impinging upon a canonical acoustic hole. We show that acoustic hole scattering shares key features with black hole scattering. The interference of wave fronts passing in opposite senses around the hole creates regular oscillations in the scattered intensity. We examine this effect by applying a partial wave method to compute the differential scattering cross section for a range of incident wavelengths. We demonstrate the existence of a scattering peak in the backward direction, known as the glory. We show that the glory created by the canonical acoustic hole is approximately 170 times less intense than the glory created by the Schwarzschild black hole, for equivalent horizon-to-wavelength ratios. We hope that direct experimental observations of such effects may be possible in the near future.

Nonlinear waves in a quark gluon plasma

We study the propagation of perturbations in the quark gluon plasma. This subject has been addressed in other works and in most of the theoretical descriptions of this phenomenon the hydrodynamic equations have been linearized for simplicity. We propose an alternative approach, also based on hydrodynamics but taking into account the nonlinear terms of the equations. We show that these terms may lead to localized waves or even solitons. We use a simple equation of state for the QGP and expand the hydrodynamic equations around equilibrium configurations. The resulting differential equations describe the propagation of perturbations in the energy density. We solve them numerically and find that localized perturbations can propagate for long distances in the plasma. Under certain conditions our solutions mimic the propagation of Korteweg-de Vries solitons.

Waves of Change Within Civil Society in Latin America: Mexico City and Sao Paulo

For the past half a century, Latin American scholars have been pointing toward the emergence of new social actors as agents of social and political democratization. The first wave of actors was characterized by the emergence of novel agents-mainly, new popular movements-of social transformation. At first, the second wave, epitomized by nongovernmental organizations (NGOs), was celebrated as the upsurge of a new civil society, but later on, it was the target of harsh criticism. The literature often portrays this development in Latin American civil society as a displacement trend of actors of the first wave by the second wave-""NGOization""-""and even denounces new civil society as rootless, depoliticized, and functional to retrenchment. Thus, supposedly, NGOization encumbers social change. The authors argue that NGOization diagnosis is a flawed depiction of change within civil society. Rather than NGOization related to the depoliticization and neoliberalization of civil society, in Mexico City and Sao Paulo, there has been modernization of organizational ecologies, changes in the functional status of civil society, and interestingly, specialization aimed at shaping public agenda. The authors argue that such specialization, instead of encumbering social change, brings about different repertoires of strategies and skills purposively developed for influencing policy and politics. Their argument relies on comparative systematic evidence. Through network analysis, they examine the organizational ecology of civil society in Mexico City and Sao Paulo.

Effects of bilateral adrenalectomy on systemic kainate-induced activation of the nucleus of the solitary tract. Regulation of blood pressure and local neurotransmitters

Glutamatergic transmission through metabotropic and ionotropic receptors, including kainate receptors, plays an important role in the nucleus of the solitary tract (NTS) functions. Glutamate system may interact with several other neurotransmitter systems which might also be influenced by steroid hormones. In the present study we analyzed the ability of systemic kainate to stimulate rat NTS neurons, which was evaluated by c-Fos as a marker of neuronal activation, and also to change the levels of NTS neurotransmitters such as GABA, NPY, CGRP, GAL, NT and NO by means of quantitative immunohistichemistry combined with image analysis. The analysis was also performed in adrenalectomized and kainate stimulated rats in order to evaluate a possible role of adrenal hormones on NTS neurotransmission. Male Wistar rats (3 month-old) were used in the present study. A group of 15 rats was submitted either to bilateral adrenalectomy or sham operation. Forty-eight hours after the surgeries, adrenalectomized rats received a single intraperitoneal injection of kainate (12 mg/kg) and the sham-operated rats were injected either with saline or kainate and sacrificed 8 hours later. The same experimental design was applied in a group of rats in order to register the arterial blood pressure. Systemic kainate decreased the basal values of mean arterial blood pressure (35%) and heart rate (22%) of sham-operated rats, reduction that were maintained in adrenalectomized rats. Kainate triggered a marked elevation of c-Fos positive neurons in the NTS which was 54% counteracted by adrenalectomy. The kainate activated NTS showed changes in the immunoreactive levels of GABA (143% of elevation) and NPY (36% of decrease), which were not modified by previous ablation of adrenal glands. Modulation in the levels of CGRP, GAL and NT immunoreactivities were only observed after kainate in the adrenalectomized rats. Treatments did not alter NOS labeling. It is possible that modulatory function among neurotransmitter systems in the NTS might be influenced by steroid hormones and the implications for central regulation of blood pressure or other visceral regulatory mechanisms control should be further investigated.

Preliminary findings from a new animal model for Peyronie`s disease involving extracorporeal shock waves

To develop an experimental model in rabbits to analyse the efficiency of extracorporeal shock wave therapy (ESWT) for Peyronie`s disease. We used 15 adult male rabbits divided into three equal groups. In group 1 (no penile ESWT) rabbits had three sessions of ESWT with 2000 shocks each (15 kV), but a rubber mat was placed between the shock head and rabbit to protect the penis; the rabbits were killed at 7 days after the last session of ESWT. In group 2 the rabbits had three sessions of ESWT using the same parameters, and were killed immediately after the last session to analyse the penis. In group 3 the rabbits had three sessions of ESWT as before but were killed at 7 days after the last session, and the penile tissue analysed macroscopically and histologically. The results showed clearly that the model was efficient, creating a similar situation to that when applying ESWT in the human penis. All of the rabbits in groups 2 and 3 had haematomas and diffuse petechiae after ESWT, and only four had urethral and penile bleeding. Almost all macroscopic changes disappeared after 48 h and only one rabbit in group 3 after 7 days had a haematoma on the dorsal penile surface. The histology (assessed using haematoxylin and eosin staining) of the cavernous body of the penis showed: unchanged histology in group 1; in group 2 there was a dilated and congested vascular space in the cavernous body, with interstitial extensive bleeding in the dermis; and in group 3 there was an increase in interstitial fibrous tissue in the cavernous septum, with deposition of collagen fibres and thickening of the tunica albuginea. The present model was efficient in producing tissue injury in the normal penis when treated with ESWT, suggesting that this promising model should be considered for use future studies of Peyronie`s disease.