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

Síntese, caracterização, propriedades e aplicação dos sistemas Mg- Al, Zn-Al e Mg-Fe

The Layered Double Hydroxides has become extremely promising materials due to its range of applications, easily obtained in the laboratory and reusability after calcination, so the knowledge regarding their properties is of utmost importance. In this study were synthesized layered double hydroxides of two systems, Mg-Al and Zn-Al, and such materials were analyzed with X-ray diffraction and, from these data, we determined the volume density, planar atomic density, size crystallite, lattice parameters, interplanar spacing and interlayer space available. Such materials were also subjected to thermogravimetric analysis reasons for heating 5, 10, 20 and 25 ° C / min to determine kinetic parameters for the formation of metaphases HTD and HTB based on theoretical models Ozawa, Flynn-Wall Starink and Model Free Kinetics. In addition, the layered double hydroxides synthesized in this working ratios were calcined heating 2.5 ° C / min and 20 ° C / min, and tested for adsorption of nitrate anion in aqueous solution batch system at time intervals 5 min, 15 min, 30 min, 1h, 2h and 4h. Such calcined materials were also subjected to exposure to the atmosphere and at intervals of 1 week, 2 weeks and 1 month were analyzed by infrared spectroscopy to study the kinetics of regeneration determining structural called "memory effect"