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

Avaliação de um método de cromatografia em fase gasosa head space e estudo da estabilidade do etanol em amostras de sangue

The ethanol is the most overused psychoactive drug over the world; this fact makes it one of the main substances required in toxicological exams nowadays. The development of an analytical method, adaptation or implementation of a method known, involves a process of validation that estimates its efficiency in the laboratory routine and credibility of the method. The stability is defined as the ability of the sample of material to keep the initial value of a quantitative measure for a defined period within specific limits when stored under defined conditions. This study aimed to evaluate the method of Gas chromatography and study the stability of ethanol in blood samples, considering the variables time and temperature of storage, and the presence of preservative and, with that check if the conditions of conservation and storage used in this study maintain the quality of the sample and preserve the originally amount of analyte present. Blood samples were collected from 10 volunteers to evaluate the method and to study the stability of ethanol. For the evaluation of the method, part of the samples was added to known concentrations of ethanol. In the study of stability, the other side of the pool of blood was placed in two containers: one containing the preservative sodium fluoride 1% and the anticoagulant heparin and the other only heparin, was added ethanol at a concentration of 0.6 g/L, fractionated in two bottles, one being stored at 4ºC (refrigerator) and another at -20ºC (freezer), the tests were performed on the same day (time zero) and after 1, 3, 7, 14, 30 and 60 days of storage. The assessment found the difference in results during storage in relation to time zero. It used the technique of headspace associated with gas chromatography with the FID and capillary column with stationary phase of polyethylene. The best analysis of chromatographic conditions were: temperature of 50ºC (column), 150ºC (jet) and 250ºC (detector), with retention time for ethanol from 9.107 ± 0.026 and the tercbutanol (internal standard) of 8.170 ± 0.081 minutes, the ethanol being separated properly from acetaldehyde, acetone, methanol and 2-propanol, which are potential interfering in the determination of ethanol. The technique showed linearity in the concentration range of 0.01 and 3.2 g/L (0.8051 x + y = 0.6196; r2 = 0.999). The calibration curve showed the following equation of the line: y = x 0.7542 + 0.6545, with a linear correlation coefficient equal to 0.996. The average recovery was 100.2%, the coefficients of variation of accuracy and inter intra test showed values of up to 7.3%, the limit of detection and quantification was 0.01 g/L and showed coefficient of variation within the allowed. The analytical method evaluated in this study proved to be fast, efficient and practical, given the objective of this work satisfactorily. The study of stability has less than 20% difference in the response obtained under the conditions of storage and stipulated period, compared with the response obtained at time zero and at the significance level of 5%, no statistical difference in the concentration of ethanol was observed between analysis. The results reinforce the reliability of the method of gas chromatography and blood samples in search of ethanol, either in the toxicological, forensic, social or clinic

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.