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 e caracterização da ferrita de MnZn obtida pelo método dos citratos precursores

It was synthesized MnZn ferrite with general formulae Mn1-xZnxFe2O4 (mol%), 0,3 ≤ x ≤ 0,7 by using the citrate precursor method. The precursors decomposition was studied by thermogravimetric analysis (TGA), differential thermogravimetric analysis (DTG), differential thermal analysis (DTA) and Fourier transform infrared (FTIR) of powder calcined at 350ºC/3,5h. X-ray diffraction pattern (XRD) of samples was done from 350 to 1200ºC/2h using various atmospheres. The power calcined at 350ºC/3,5h formed spinel phase. It is necessary atmosphere control to avoid secondary phase such as hematite. From 900 to 1200ºC was obtained 90,66 and 100% of MnZn spinel ferrite phase, respectively. Analysis by dispersive energy scanning (EDS) at 350ºC shows high Mn and Zn dispersion, indicating that the diffusion process was homogeneous. Semi-quantitative analysis by EDS verified that despite the atmosphere control during calcinations at high temperatures (< 800ºC) occurred ZnO evaporation causing stoichiometric deviation. Vibrating sample magnetometer (VSM) measures show soft ferrite material characteristics with Hc from 6,5 x 10-3 to 11,1 x 10-2 T. Saturation magnetization (Ms) and initial permeability (µi) of MnZn spinel phase obtained, respectively, from 14,3 to 83,8 Am2/kg and 14,1 to 62,7 (Am2/kg)T