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)

Análise do tempo de ação de medicações intracanais sobre candida albicans, enterococcus faecalis, escherichia cole em canais radiculares

The purpose of this study was to evaluate in vitro the antimicrobial activity of intracanal medications against Candida albicans, Enterococcus faecalis, Escherichia coli present in root canals. It was used 24 single root human teeths, contaminated for 28 days and prepared with physiological saline solution as irrigation solution. The teeth were divided into 2 groups according to the intracanal medication used: 1) 2% gel chlorhexidine, 2) sterile and pyrogen free physiological saline solution. Samples were taken of the root canals immediately after instrumentation, 7 days after intracanal medication and 7 days after removal of intracanal medication. For all samples the antimicrobial activity was performed by plating method. All results were submitted to Mann-Whitney and Dunn's test with significance of 5%. There was significant reduction of microorganisms after instrumentation and the intracanal medication of 2% gel chlorhexidine completely eliminated C. albicans and E. coli, and significantly reduced E. faecalis. It was concluded that 2% gel chlorhexidine as intracanal medication for 7 days was effective on microorganisms

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.