A bounded upwinding scheme for computing convection-dominated transport problems

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

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time

Controlling dispersal dynamics of Aedes aegypti

The dengue virus is transmitted in regions previously infested with the mosquito Aedes aegypti. To assess the spreading and establishment of the dengue disease vector, a mathematical model is developed that takes into account the diffusion and advection phenomena. A discrete model based on the cellular automata approach, which is a good framework to deal with small populations, is also developed to be compared with the continuous modeling.

Modal analysis of anisotropic diffused-channel waveguide by a scalar finite element method

A procedure to model optical diffused-channel waveguides is presented in this work. The dielectric waveguides present anisotropic refractive indexes which are calculated from the proton concentration. The proton concentration inside the channel is calculated by the anisotropic 2D-linear diffusion equation and converted to the refractive indexes using mathematical relations obtained from experimental data, the arbitrary refractive index profile is modeled by a. nodal expansion in the base functions. The TE and TM-like propagation properties (effective index) and the electromagnetic fields for well-annealed proton-exchanged (APE) LiNbO3 waveguides are computed by the finite element method.

Drying of persimmon: Mathematical model for diffusivity as a simultaneous function of moisture content and shrinkage

Fresh persimmon has a high moisture content (about 85% wet basis) making it highly perishable and requiring adequate drying conditions to obtain an acceptable dehydrated product. Drying kinetics of persimmon cv. Rama Forte was studied in a fixed bed dryer at temperatures ranging from 50 to 80 degreesC and air velocity of 0.8 m/s. Shrinkage during drying was described by a linear correlation with respect to water content. Evaluation of effective diffusivity as a function of moisture content, with undergoing shrinkage during drying was based on Fourier series solution of Fick's diffusion equation. Effective diffusivity values at moisture contents between 0.09 - 4.23 kg water/kg dry matter were found to be in the range of 2.6 x 10(-10) m(2)/s to 5.4 x 10(-10) m(2)/s, and its dependence on air drying temperature was represented by an Arrhenius type equation. Activation energy increased with decreasing water content in persimmons.

Pressure field along the axis of a high-power klystron amplifier

The pressure field in a high-power klystron amplifier is investigated to scale the ionic vacuum pump used to maintain the ultra high-vacuum in the device in order to increase its life-time. The investigation is conducted using an 1.3 GHz, 100 A - 240 keV high-power klystron with five reentrant coaxial cavities, assembled in a cylindrical drift tube 1.2 m long. The diffusion equation is solved to the regime molecular flow to obtain the pressure profile along the axis of the klystron drift tube. The model, solved by both analytical and numerical procedures, is able to determine the pressure values in steady-state case. This work considers the specific conductance and all important gas sources, as in the degassing of the drift tube and cavities walls, cathode, and collector. For the drift tube degassing rate equals to q(deg) = 2x10(-12) (-)mbar.L.s(-1) cm(-2) (degassing rate per unit area), to cavities q(cavity) = 3x10(-13) mbar.L.s(-1)cm(-2), to the cathode q(cathode) = 6x10(-9)_mbar.L.s(-1) and to the collector q(collector) = 6x10(-9) mbar.L.s(-1), it was found that a 10 L.s(-1) ionic vacuum pump connected in the output waveguide wall is suitable. In this case, the pressure obtained in the cathode is p(cathode) = 6.3x10(-9) mbar, in the collector p(collector) = 2.7x10(-9) mbar, and in the output waveguide p = 2.1x10(-9) mbar. Although only the steady-state case is analyzed, some aspects that may be relevant in a transient situation, for instance, when the beam hits the drift tube walls, producing a gas burst, is also commented.

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pressure field in the cathode-anode region of a high-power klystron amplifier

The pressure field of a high-power klystron amplifier in the cathode and anode region was investigated. The investigation was performed using a 1.3 GHz, 100 A and 240 kV high-power klystron with five reentrant coaxial cavities, assembled in cylindrical drift tube 1.2 m long. The diffusion equation in mathematical model was also solved by using a 3-D finite element method code, in order to obtain pressure profile in region of interest. The results show that density profile of molecules between cathode-anode region was determined, where cathode pressure is approximately 10% higher than anode pressure.

Estudo do coeficiente de difusão no enovelamento de proteínas na rede

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estudo dos métodos de solução da equação de Fokker-Planck linear e não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelagem de perfis de indução no domínio do tempo por diferenças finitas

Apresentamos aqui uma metodologia alternativa para modelagem de ferramentas de indução diretamente no domínio do tempo. Este trabalho consiste na solução da equação de difusão do campo eletromagnético através do método de diferenças finitas. O nosso modelo consiste de um meio estratificado horizontalmente, através do qual simulamos um deslocamento da ferramenta na direção perpendicular às interfaces. A fonte consiste de uma bobina excitada por uma função degrau de corrente e o registro do campo induzido no meio é feito através de uma bobina receptora localizada acima da bobina transmissora. Na solução da equação de difusão determinamos o campo primário e o campo secundário separadamente. O campo primário é obtido analiticamente e o campo secundário é determinado utilizando-se o método de Direção Alternada Implícita, resultando num sistema tri-diagonal que é resolvido através do método recursivo proposto por Claerbout. Finalmente, determina-se o valor máximo do campo elétrico secundário em cada posição da ferramenta ao longo da formação, obtendo-se assim uma perfilagem no domínio do tempo. Os resultados obtidos mostram que este método é bastante eficiente na determinação do contato entre camadas, inclusive para camadas de pequena espessura.

Transferência de calor inversa do método convencional e do otimizado de lubri-refrigeração na retificação plana tangencial

Pós-graduação em Ciência e Tecnologia de Materiais - FC

Processamento do alho negro

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

How population loss through habitat boundaries determines the dynamics of a predator-prey system

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