Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Energy decay for the linear Klein-Gordon equation and boundary control

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An integrable evolution equation for surface waves in deep water

In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite depth. From it, and using a multiscale perturbative method, an asymptotic model for small wave steepness ratio is derived. The model is shown to be completely integrable. The Lax pair, the first conserved quantities as well as the symmetries are exhibited. Theoretical and numerical studies reveal that it supports periodic progressive Stokes waves which peak and break in finite time. Comparison between the limiting wave solution of the asymptotic model and classical results is performed.

Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Fokker-Planck equation for a bistable potential

The Fokker-Planck equation is studied through its relation to a Schrodinger-type equation. The advantage of this combination is that we can construct the probability distribution of the Fokker-Planck equation by using well-known solutions of the Schrodinger equation. By making use of such a combination, we present the solution of the Fokker-Planck equation for a bistable potential related to a double oscillator. Thus, we can observe the temporal evolution of the system describing its dynamic properties such as the time tau to overcome the barrier. By calculating the rates k = 1/tau as a function of the inverse scaled temperature 1/D, where D is the diffusion coefficient, we compare the aspect of the curve k x 1/D, with the ones obtained from other studies related to four different kinds of activated process. We notice that there are similarities in some ranges of the scaled temperatures, where the different processes follow the Arrhenius behavior. We propose that the type of bistable potential used in this study may be used, qualitatively, as a simple model, whose rates share common features with the rates of some single rate-limited thermally activated processes. (C) 2014 Elsevier B.V. All rights reserved.

Solution to bilharmonic equation with vanishing potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influência da atividade de forragem, números de adultos e de larvas, na diferenciação de castas de Mischocyttarus cerberus styx Richards, 1940 (Hymenoptera, Vespidae, Mischocyttarini)

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Morphology of Richards' gland in the swarm-founding wasp (Hymenoptera, Vespidae)

Richards' gland is known for the majority of Epiponini wasps, and despite few experimental evidences, the taxonomic distribution in swarm-founder species and the function of this gland remain rather unclear. This work presents a morphological description of Richards' gland in Protonectarina sylveirae. The gland is formed by a cluster of class 3 cells underneath the anterior margin of the fifth metasomal sternite, and a reservoir formed by the intersegmental membrane between the fourth and fifth metasomal sternites where the secretion can be stored. The secretory cells contain a branched end apparatus that carries the secretory products towards the duct cell. Externally, the cuticle of the sternite, where the duct cells penetrate, is characterized by modifications as scales with very numerous pores. The presence of Richards' gland according to the model proposed by Samacá et al. 2013 in Protonectarina corroborates the single origin of this gland in Epiponini. The occurrence of a Golgi apparatus and smooth endoplasmic reticulum suggests pheromone production.

On the periodic orbits of the third-order differential equation x ′′′ − µx ′′ + x ′ − µx = εF (x, x ′ , x ′′)

In this paper we study the periodic orbits of the third-order differential equation x ′′′−µx ′′+ x ′ − µx = εF (x, x ′ , x ′′), where ε is a small parameter and the function F is of class C 2 .

Multivacuum states in a fermionic gap equation with massive gluons and confinement

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrodinger equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

About the minimum time transference in a fractional differential equation

The use of fractional calculus when modeling phenomena allows new queries concerning the deepest parts of the physical laws involved in. Here we will be dealing with an apparent paradox in which the time of transference from zero in a system with fractional derivatives can be strictly shortened relatively to the minimal time transference done in an equivalent system in the frame of the entire derivatives.

Shallow viscous fluid heated from below and the Kadomtsev-Petviashvili equation

The non-linear evolution of nearly one-dimensional undamped waves in a viscous fluid adequately heated from below is shown to be governed by the Kadomtsev-Petviashvili equation. Its solitary-wave solution is explicitly shown. © 1990.

General method for reducing the two-body Dirac equation

A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed. © 1992 American Institute of Physics.

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.