On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

About the Use of the HdHr Algorithm Group in Integrating the Movement Equation with Nonlinear Terms

This work summarizes the HdHr group of Hermitian integration algorithms for dynamic structural analysis applications. It proposes a procedure for their use when nonlinear terms are present in the equilibrium equation. The simple pendulum problem is solved as a first example and the numerical results are discussed. Directions to be pursued in future research are also mentioned. Copyright (C) 2009 H.M. Bottura and A. C. Rigitano.

Some exact solutions of the Dirac equation

Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions.

Exact closed-form solutions of the Dirac equation for a class of effective Morse potentials

Exact bounded solutions for a fermion subject to exponential scalar potential in 1 + 1 dimensions are found in closed form. We discuss the existence of zero modes which are related to the ultrarelativistic limit of the Dirac equation and are responsible for the induction of a fractional fermion number on the vacuum.

Dirac equation exact solutions for generalized asymmetrical Hartmann potentials

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar potential. The cases of some quasi-exactly solvable and Morse-like potentials are briefly commented. (c) 2006 Elsevier B.V. All rights reserved.

Exact closed-form solutions of the Dirac equation with a scalar exponential potential

The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an exponential potential, we have an effective Morse potential which reveals itself as an essentially relativistic problem. Exact bound solutions are found in closed form for this problem. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail, particularly the existence of zero modes. (c) 2005 Elsevier B.v. All rights reserved.

On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bound states of the Duffin-Kemmer-Petiau equation with a mixed minimal-nonminimal vector cusp potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comment on Solutions of the Duffin-Kemmer-Petiau equation for a pseudoscalar potential step in (1+1) dimensions

It is shown that the paper Solutions of the Duffin-Kemmer-Petiau equation for a pseudoscalar potential step in (1+1) dimensions by Abdelmalek Boumali has a number of misconceptions

Real spectra for the non-Hermitian Dirac equation in 1+1 dimensions with the most general coupling

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Adsorção de Mn (II) e Zn (II) em soluções aquosas usando perlita expandida revestida com quitosana

In this work, chitosan was used as a coating of pure perlite in order to increase the accessibility of the groups OH- e NH2+the adsorptionof ions Mn2+ e Zn2+.The characterization results of the expanded perlite classified as microporous and whose surface area 3,176 m2 g-1after the change resulted in 4,664 m2g-1.From the thermogravimetry(TG) it was found that the percentage of coating was34,3%.The infrared analysis can prove the presence of groups Si-OH, Si-O e Al-O-Siresulting from the perlite and C=O, NH2and OH characterization of chitosan. The experiments on experiments on the adsorption of Mn and Zn were performed in the concentration range of10 a 50 mgL-1and the adsorption capacity inpH 5,8 e 5,2 was 19,49 and 23,09 mgg-1to 25 oC,respectively.The adsorption data were best fitted to Langmuir adsorption model to Langmuir adsorption model for both metalionsisindicative of monolayer adsorption. The kinetics of adsorption were calculated from the equation of Lagergren fitting the model pseudo-second-order for all initial concentrations, suggesting that adsorption of ions Mn2+ and Zn2+ follows the kinetics of pseudo-second-order and whose constant Speedk2(g/mg.min) are 0,105 e 3,98 and capacity and maximum removal qe 4,326 e 3,348,respectively.In this study we used a square wave voltammetry cathodic stripping voltammetry to quantify the adsorbed ions, and the working electrode glassy carbon, reference electrode silver / silver chloride and a platinum auxiliary electrode. The attainment of the peaks corresponding to ions Mn2+ and Zn2+ was evaluated in and electrochemical cell with a capacity of 30 mL using a buffer system (Na2HPO4/NaH2PO4)at pH 4 and was adjusted with solutionsH3PO4 0,1molL-1and NaOH 0,1 molL-1and addition of the analyte has been a cathodic peak in- 0,873 Vand detection limit of2,55x10-6molL-1para Zn.The dough used for obtaining the adsorption isotherm was 150 mg and reached in 120 min time of equilibrium for both metal ions.The maximum adsorption for 120 min with Mn concentration 20 mgL-1 and Zn 10 mgL-1,was91, 09 e 94, 34%, respectively

Aplicação de sabões de ácidos graxos epoxidados como inibidores de corrosão em oleoduto

Corrosion usually occurs in pipelines, so that it is necessary to develop new surface treatments to control it. Surfactants have played an outstanding role in this field due to its capacity of adsorbing on metal surfaces, resulting in interfaces with structures that protect the metal at low surfactant concentrations. The appearance of new surfactants is a contribution to the area, as they increase the possibility of corrosion control at specific conditions that a particular oil field presents. The aim of this work is to synthesize the surfactants sodium 12 hydroxyocadecenoate (SAR), sodium 9,10-epoxy-12 hydroxyocadecanoate (SEAR), and sodium 9,10:12,13-diepoxy-octadecanoate (SEAL) and apply them as corrosion inhibitors, studying their action in environments with different salinities and at different temperatures. The conditions used in this work were chosen in order to reproduce oil field reality. The study of the micellization of these surfactants in the liquid-gas interface was carried out using surface tensiometry. It was observed that cmc increased as salt concentration was increased, and temperature and pH were decreased, while cmc decreased with the addition of two epoxy groups in the molecule. Using the values of cmc and the Gibbs equation, the values of Gibbs free energy of adsorption, area per adsorbed molecule, and surface excess were calculated. The surface excess increases as salt concentration and temperature decreases, increasing as pH is increased. The area per adsorbed molecule and the free energy of adsorption decrease with salt concentration, temperature, and pH increase. SAXS results showed that the addition of epoxy group in surfactant structure results in a decrease in the repulsion between the micelles, favoring the formation of more oblong micellar structures, ensuring a better efficiency of metal coverage. The increase in salt and surfactant concentrations provides an increase in micellar diameter. It was shown that the increase in temperature does not influence micellar structure, indicating thermal stability that is advantageous for use as corrosion inhibitor. The results of inhibition efficiency for the surfactants SEAR and SEAL were considered the best ones. Above cmc, adsorption occurred by the migration of micelles from the bulk of the solution to the metal surface, while at concentrations below cmc film formation must be due to the adsorption of semi-micellar and monomeric structures, certainly due to the presence of the epoxy group, which allows side interactions of the molecule with the metal surface. The metal resistance to corrosion presented values of 90% of efficiency. The application of Langmuir and Frumkin isotherms showed that the later gives a better description of adsorption because the model takes into account side interactions from the adsorbing molecules. Wettability results showed that micelle formation on the solid surface occurs at concentrations in the magnitude of 10-3 M, which isthe value found in the cmc study. This value also justifies the maximum efficiencies obtained for the measurements of corrosion resistance at this concentration. The values of contact angle as a function of time suggest that adsorption increases with time, due to the formation of micellar structures on metal surface

Estudos de sorção de um corante aniônico modelo em partículas de quitosana reticulada

Textile activity results in effluents with a variety of dyes. Among the several processes for dye-uptaking from these wastewaters, sorption is one of the most effective methods, chitosan being a very promising alternative for this end. The sorption of Methyl Orange by chitosan crosslinked particles was approached using equilibrium and kinetic analyses at different pH s. Besides the standard pseudo-order analysis normally effectuated (i.e. pseudo-first-order and pseudo-second-order), a novel approach involving a pseudo-nth-order kinetics was used, nbeing determined via non-linear regression, using the Levenberg-Marquardt method. Zeta potential measurements indicated that electrostatic interactions were important for the sorption process. Regarding equilibrium experiments, data were well fitted to a hybrid Langmuir-Freundlich isotherm, and estimated Gibbs free energy of adsorption as a function of mass of dye per area of chitosan showed that the process of adsorption becomes more homogeneous as the pH of the continuous phase decreased. Considering the kinetics of sorption, although a pseudo-nth-order description yielded good fits, a kinetic equation involving diffusion adsorption phenomena was found to be more consistent in terms of a physicochemical description of the sorption process