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)

Aplicabilidade das equações isotermas de Freundlich e Langmuir na interação biossortiva de corantes têxteis com Saccharomyces cerevisiae liofilizada

This paper presents a study of the applicability of adsorption isotherms, known as Langmuir and Freundlich isotherm, between the biosorptive interaction of yeast lyophilized Saccharomyces cerevisiae and textile dyes. To that end, we prepared stock solutions of the textile dyes Direct Red 23 and Direct Red 75 in the concentration of 1.000μg/mL and a yeast suspension at 2,5%. We did experiments for two cases, firstly for the case that we have a fix concentration of yeast at 0,500mg/mL and an variable concentration of dye range from40, 50, 60, 80 and 100μg/mL, then for the case that we fixed the concentration of dye at 100μg/mL and the yeast concentration was variable range from 0,250, 0,500, 0,750, 1,000, 1,250mg/mL. For the dye Direct Red 23 we did analysis in the pH 2,5, 4,5 and 6,5; for the Direct Red 75, we just did for the pH 2,5. We leave the dye solution in contact with the yeast for 2 hours at a constant temperature of 30°C and then centrifuged and analyzed the sample in a spectrophotometer and finally made and analysis of parameters for the removal and study of the isotherms. After the biosorption, was observed that for the Direct Red 23 in the pH 2,5 was needed 1,407mg/mL of yeast for total removal, while for the pH 4,5 was needed 8,806mg/mL and in pH 6,5 was 9,286mg/mL; for the Direct Red 75 in pH 2,5 was needed 1,337mg/mL. This difference can be explain by the adsorption isotherms, was observed that in the case when the yeast was fix when we had in a acid pH the behavior of the system was compatible with the Langmuir isotherm, and thus, an monolayer pattern. And that when we decrease the acidity of the medium the system became more compatible with a Freundlich isotherm, and thus, a multilayer pattern; for the case that the yeast was variable this is not much evident, however for the pH 2,5 she became compatible with a Langmuir isotherm... (Complete abstract click electronic access below)

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)

Synergy between polyaniline and OMt clay mineral in Langmuir-Blodgett films for the simultaneous detection of traces of metal ions

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

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.

Poly(3-octylthiophene)/stearic acid langmuir and langmuir-blodgett films: preparation and characterization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Co-deposition of gold nanoparticles and metalloporphyrin using the langmuir-blodgett (LB) technique for Surface-Enhanced Raman Scattering (SERS)

The synergistic effect produced by metallic nanoparticles when incorporated into different systems empowers a research field that is growing rapidly. In addition, organometallic materials are at the center of intensive research with diverse applications such as light-emitting devices, transistors, solar cells, and sensors. The Langmuir-Blodgett (LB) technique has proven to be suitable to address challenges inherent to organic devices, since the film properties can be tuned at the molecular level. Here we report a strategy to incorporate gold nanoparticles (AuNPs) into the LB film by co-deposition in order to achieve surface-enhanced Raman scattering (SERS) of the zinc(II)-protoporphyrin (IX) dimethyl ester (ZnPPIX-DME). Prior to the LB co-deposition, the properties of the Langmuir monolayer of ZnPPIX-DME at the air-water interface, containing AuNPs in the subphase, are studied through the surface-pressure versus mean molecular area (π-A) isotherms. The ZnPPIX-DME+AuNPs π-A isotherm presented a significant shift to higher molecular area, suggesting an interaction between both ZnPPIX-DME molecules and AuNPs. Those interactions are a key factor allowing the co-deposition of both AuNPs and ZnPPIX-DME molecules onto a solid substrate, thus forming the LB film. SERS of ZnPPIX-DME was successfully attained, ensuring the spatial distribution of the AuNPs. Higher enhancement factors were found at AuNP aggregates, as a result of the intense local electromagnetic field found in the metal nanoparticle aggregates. The main vibrational bands observed in the SERS spectra suggest a physical adsorption of the ZnPPIX-DME onto the surface of AuNPs. The latter is not only in agreement with the interactions pointed out by the π-A isotherms but also suggests that this interaction is kept upon LB film co-deposition.

Filmes de Langmuir-Blodgett de nanopartículas de prata

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Propriedades luminescentes de polioxometalato contendo európio(III) correlacionadas à sua conformação em sólido estendido e em filmes auto-organizados de Langmuir e Langmuir-Blodgett

Pós-graduação em Química - IQ