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

As praças públicas de Natal/RN no âmbito dos problemas socioambientais urbanos

This paper presents the public square as a subsystem of the city for the potential integration of elements 'natural' and built environment. But sometimes the suitability of projects and the social processes involved are not compatible and favorable to their real functions in urban space. The city of Natal, with a population of 803,739 inhabitants has 253 public parks not uniformly distributed in the urban area, but mostly in central areas and their absence in some peripheral neighborhoods. In this sense, the objective of this paper is to analyze the quality and spatiality of the city's public squares within the urban socio-environmental problems. For this, use of simple random sampling to define the sample and the proportional allocation of districts, totaling 168 squares to be raised. We prepared a form to collect data on the field that includes aspects of leisure, infrastructure and environment. For each square sampled was calculated Square Quality Index (PQI), then calculating the average per IQP neighborhood. The rates found were crossed with census data and Municipal Public Administration by neighborhood, using multivariate analysis. We generated maps, charts and tables, considered appropriate to each question format, focused comparison. The public square appears as an indicator of environmental challenges present in intra-urban spaces of the city. Their spatial distribution is not consistent demand population, both by disposition and by how much. In terms of quality are characterized by different levels of inadequacy and degradation aspects of leisure, environmental and infrastructure, often causing disfigurement, abandonment and improper occupation in such spaces. Multivariate analysis point to a central concentration and their problems in certain administrative units, not only as regards the public squares, but also to aspects of education, income, and other violence, perpetuating the problem. The various levels of inadequacy and degradation of public squares have been more blatant in the poorest neighborhoods of the city, pointing to a structural pattern associated with the intrinsic characteristics of the neighborhood and the socioeconomic profile of the local population. These are problems of social and environmental dimensions, threaded in and influenced the political, economic and broader social process of transformation of the city and the urban. Based on an uneven process in which space necessarily reflect the contradictions inherent in the active forces and interests. Thus evidencing the importance of managing the necessary public effectively engaged with the problems that are present there, in order to equate them, without being prioritized certain areas of the city at the expense of others