Arranjos Log-Periódicos Compactos em Microfita com Elementos Fractais de Koch

This work aims to present how the application of fractal geometry to the elements of a log-periodic array can become a good alternative when one wants to reduce the size of the array. Two types of log-periodic arrays were proposed: one with fed by microstrip line and other fed by electromagnetic coupling. To the elements of these arrays were applied fractal Koch contours, at two levels. In order to validate the results obtained some prototypes were built, which were measured on a vector network analyzer and simulated in a software, for comparison. The results presented reductions of 60% in the total area of the arrays, for both types. By analyzing the graphs of return loss, it was observed that the application of fractal contours made different resonant frequencies appear in the arrays. Furthermore, a good agreement was observed between simulated and measured results. The array with feeding by electromagnetic coupling presented, after application of fractal contours, radiation pattern with more smooth forms than the array with feeding by microstrip line

Processos aleatórios não-markovianos: perfis de memória

One of the mechanisms responsible for the anomalous diffusion is the existence of long-range temporal correlations, for example, Fractional Brownian Motion and walk models according to Elephant memory and Alzheimer profiles, whereas in the latter two cases the walker can always "remember" of his first steps. The question to be elucidated, and the was the main motivation of our work, is if memory of the historic initial is condition for observation anomalous diffusion (in this case, superdiffusion). We give a conclusive answer, by studying a non-Markovian model in which the walkers memory of the past, at time t, is given by a Gaussian centered at time t=2 and standard deviation t which grows linearly as the walker ages. For large widths of we find that the model behaves similarly to the Elephant model; In the opposite limit (! 0), although the walker forget the early days, we observed similar results to the Alzheimer walk model, in particular the presence of amnestically induced persistence, characterized by certain log-periodic oscillations. We conclude that the memory of earlier times is not a necessary condition for the generating of superdiffusion nor the amnestically induced persistence and can appear even in profiles of memory that forgets the initial steps, like the Gausssian memory profile investigated here.

Estudo sobre a detecção de invariância de escala discreta em sistemas com criticalidade auto-organizada

Recent studies have shown evidence of log-periodic behavior in non-hierarchical systems. An interesting fact is the emergence of such properties on rupture and breakdown of complex materials and financial failures. These may be examples of systems with self-organized criticality (SOC). In this work we study the detection of discrete scale invariance or log-periodicity. Theoretically showing the effectiveness of methods based on the Fourier Transform of the log-periodicity detection not only with prior knowledge of the critical point before this point as well. Specifically, we studied the Brazilian financial market with the objective of detecting discrete scale invariance in Bovespa (Bolsa de Valores de S˜ao Paulo) index. Some historical series were selected periods in 1999, 2001 and 2008. We report evidence for the detection of possible log-periodicity before breakage, shown its applicability to the study of systems with discrete scale invariance likely in the case of financial crashes, it shows an additional evidence of the possibility of forecasting breakage

Simetria de invariância de escala discreta, log-periodicidade e singularidades em tempo finito

Conselho Nacional de Desenvolvimento Científico e Tecnológico