SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

SAR imaging of buried objects from MoM modelled scattered field

Synthetic aperture radar (SAR) images of resonant buried objects are modelled in the presence of ground surface clutter. The method of moments (MoM) is used to model scattered fields from a resonant buried conductor and clutter is modelled as a bivariant Gaussian distribution. A diffraction stack SAR imaging technique is applied to the ultra-wideband waveforms to give a bipolar signal image. A number of examples have been computed to illustrate the combined effects of SAR processing with resonant targets and clutter. SAR images of different targets show differences which may facilitate target identification. To maximise the peak signal-to-clutter ratio, an image correlation technique is applied and the results are shown.

One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

Efeito da distribuição do tamanho das partículas abrasivas sobre as taxas e modos de desgaste para o ensaio de microabrasão

Neste trabalho, as distribuições de tamanhos das partículas de dois pós de Carboneto de Silício foram previamente avaliadas e os resultados indicaram uma distribuição Gaussiana para ambos, com tamanhos médios na ordem de 2 μm para o primeiro e 6 μm para o segundo. Posteriormente foram misturados os dois pós originais com diferentes frações mássicas, proporcionando uma nova série de pós de Carboneto de Silício (SiC), que seriam usados nos ensaios de microabrasão com configuração de esfera fixa. A caracterização desta nova série de pós mostrou larguras maiores para aqueles com alto porcentagem do abrasivo pequeno (2,11 μm), conservando a aparência Gaussiana dos originais. Por outro lado para os pós com uma quantidade maior do abrasivo grande (6,57 μm), foram obtidas curvas com uma leve tendência bimodal, mas também apresentaram maiores larguras. As provas foram conduzidas sobre aço carbono AISI 1020, para duas condições diferentes de carga normal e os resultados foram analisados em termos da taxa de desgaste, bem como dos micromecanismos de desgaste (abrasão por rolamento ou abrasão por riscamento). Os resultados indicaram que a fração mássica dos pós originais tem um efeito significante sobre os micromecanismos de desgaste observados e que as taxas de desgaste não segue uma relação linear com a fração mássica do pó com maior tamanho da partícula abrasiva. Além disso, a análise da severidade de contato determinou que esta diminui durante os ensaios conduzidos com carga constante. Este fenômeno está associado ao aumento da área da cratera de desgaste que produz uma diminuição da pressão de contato. Assim, um incremento para o número de eventos associado ao rolamento de partículas seria esperado, favorecendo a observação de múltiplas indentações ao longo dos sulcos formados previamente. Isto foi confirmado por meio de micrografias eletrônicas de varredura das amostras após ensaios de microabrasão.

A probabilistic methodology for distributed generation location in isolated electrical service area

Distributed generation unlike centralized electrical generation aims to generate electrical energy on small scale as near as possible to load centers, interchanging electric power with the network. This work presents a probabilistic methodology conceived to assist the electric system planning engineers in the selection of the distributed generation location, taking into account the hourly load changes or the daily load cycle. The hourly load centers, for each of the different hourly load scenarios, are calculated deterministically. These location points, properly weighted according to their load magnitude, are used to calculate the best fit probability distribution. This distribution is used to determine the maximum likelihood perimeter of the area where each source distributed generation point should preferably be located by the planning engineers. This takes into account, for example, the availability and the cost of the land lots, which are factors of special relevance in urban areas, as well as several obstacles important for the final selection of the candidates of the distributed generation points. The proposed methodology has been applied to a real case, assuming three different bivariate probability distributions: the Gaussian distribution, a bivariate version of Freund’s exponential distribution and the Weibull probability distribution. The methodology algorithm has been programmed in MATLAB. Results are presented and discussed for the application of the methodology to a realistic case and demonstrate the ability of the proposed methodology for efficiently handling the determination of the best location of the distributed generation and their corresponding distribution networks.

Generation of Nakagami correlated fading in GNSS signals affected by ionospheric scintillation

We propose a low complexity technique to generate amplitude correlated time-series with Nakagami-m distribution and phase correlated Gaussian-distributed time-series, which is useful for the simulation of ionospheric scintillation effects in GNSS signals. To generate a complex scintillation process, the technique requires solely the knowledge of parameters Sa (scintillation index) and σφ (phase standard deviation) besides the definition of models for the amplitude and phase power spectra. The concatenation of two nonlinear memoryless transformations is used to produce a Nakagami-distributed amplitude signal from a Gaussian autoregressive process.

Practical simulation of GNSS signals in the presence of ionospheric scintillaton

We propose a low complexity technique to generate amplitude correlated time-series with Nakagami-m distribution and phase correlated Gaussian-distributed time-series, which is useful in the simulation of ionospheric scintillation effects during the transmission of GNSS signals. The method requires only the knowledge of parameters S4 (scintillation index) and σΦ (phase standard deviation) besides the definition of models for the amplitude and phase power spectra. The Zhang algorithm is used to produce Nakagami-distributed signals from a set of Gaussian autoregressive processes.

Numerical methods and tangible interfaces for pollutant dispersion simulation

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia do Ambiente, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Extended truncated Tweedie-Poisson model

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

Identification of potential rockfall source areas at a regional scale using a DEM-based geomorphometric analysis

The availability of high resolution Digital Elevation Models (DEM) at a regional scale enables the analysis of topography with high levels of detail. Hence, a DEM-based geomorphometric approach becomes more accurate for detecting potential rockfall sources. Potential rockfall source areas are identified according to the slope angle distribution deduced from high resolution DEM crossed with other information extracted from geological and topographic maps in GIS format. The slope angle distribution can be decomposed in several Gaussian distributions that can be considered as characteristic of morphological units: rock cliffs, steep slopes, footslopes and plains. A terrain is considered as potential rockfall sources when their slope angles lie over an angle threshold, which is defined where the Gaussian distribution of the morphological unit "Rock cliffs" become dominant over the one of "Steep slopes". In addition to this analysis, the cliff outcrops indicated by the topographic maps were added. They contain however "flat areas", so that only the slope angles values above the mode of the Gaussian distribution of the morphological unit "Steep slopes" were considered. An application of this method is presented over the entire Canton of Vaud (3200 km2), Switzerland. The results were compared with rockfall sources observed on the field and orthophotos analysis in order to validate the method. Finally, the influence of the cell size of the DEM is inspected by applying the methodology over six different DEM resolutions.

BME-based uncertainty assessment of the Chernobyl fallout

The vast territories that have been radioactively contaminated during the 1986 Chernobyl accident provide a substantial data set of radioactive monitoring data, which can be used for the verification and testing of the different spatial estimation (prediction) methods involved in risk assessment studies. Using the Chernobyl data set for such a purpose is motivated by its heterogeneous spatial structure (the data are characterized by large-scale correlations, short-scale variability, spotty features, etc.). The present work is concerned with the application of the Bayesian Maximum Entropy (BME) method to estimate the extent and the magnitude of the radioactive soil contamination by 137Cs due to the Chernobyl fallout. The powerful BME method allows rigorous incorporation of a wide variety of knowledge bases into the spatial estimation procedure leading to informative contamination maps. Exact measurements (?hard? data) are combined with secondary information on local uncertainties (treated as ?soft? data) to generate science-based uncertainty assessment of soil contamination estimates at unsampled locations. BME describes uncertainty in terms of the posterior probability distributions generated across space, whereas no assumption about the underlying distribution is made and non-linear estimators are automatically incorporated. Traditional estimation variances based on the assumption of an underlying Gaussian distribution (analogous, e.g., to the kriging variance) can be derived as a special case of the BME uncertainty analysis. The BME estimates obtained using hard and soft data are compared with the BME estimates obtained using only hard data. The comparison involves both the accuracy of the estimation maps using the exact data and the assessment of the associated uncertainty using repeated measurements. Furthermore, a comparison of the spatial estimation accuracy obtained by the two methods was carried out using a validation data set of hard data. Finally, a separate uncertainty analysis was conducted that evaluated the ability of the posterior probabilities to reproduce the distribution of the raw repeated measurements available in certain populated sites. The analysis provides an illustration of the improvement in mapping accuracy obtained by adding soft data to the existing hard data and, in general, demonstrates that the BME method performs well both in terms of estimation accuracy as well as in terms estimation error assessment, which are both useful features for the Chernobyl fallout study.

Dispersal probability distributions and the wave-front speed problem

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models

Numerical signs fos a transition in the 2d Random Field Ising Model at T=0

Intensive numerical studies of exact ground states of the two-dimensional ferromagnetic random field Ising model at T=0, with a Gaussian distribution of fields, are presented. Standard finite size scaling analysis of the data suggests the existence of a transition at ¿c=0.64±0.08. Results are compared with existing theories and with the study of metastable avalanches in the same model.

Antireflection coatings from analogy between electron scattering and spin precession

We use the analogy between scattering of a wave from a potential, and the precession of a spin-half particle in a magnetic field, to gain insight into the design of an antireflection coating for electrons in a semiconductor superlattice. It is shown that the classic recipes derived for optics are generally not applicable due to the different dispersion law for electrons. Using the stability conditions we show that a Poisson distribution of impedance steps is a better approximation than is a Gaussian distribution. Examples are given of filters with average transmissivity exceeding 95% over an allowed band.

Ectopic development of skeletal muscle induced by subcutaneous transplant of rat satellite cells

The present study analyzes the ectopic development of the rat skeletal muscle originated from transplanted satellite cells. Satellite cells (10(6) cells) obtained from hindlimb muscles of newborn female 2BAW Wistar rats were injected subcutaneously into the dorsal area of adult male rats. After 3, 7, and 14 days, the transplanted tissues (N = 4-5) were processed for histochemical analysis of peripheral nerves, inactive X-chromosome and acetylcholinesterase. Nicotinic acetylcholine receptors (nAChRs) were also labeled with tetramethylrhodamine-labeled alpha-bungarotoxin. The development of ectopic muscles was successful in 86% of the implantation sites. By day 3, the transplanted cells were organized as multinucleated fibers containing multiple clusters of nAChRs (N = 2-4), resembling those from non-innervated cultured skeletal muscle fibers. After 7 days, the transplanted cells appeared as a highly vascularized tissue formed by bundles of fibers containing peripheral nuclei. The presence of X chromatin body indicated that subcutaneously developed fibers originated from female donor satellite cells. Differently from the extensor digitorum longus muscle of adult male rat (87.9 ± 1.0 µm; N = 213), the diameter of ectopic fibers (59.1 µm; N = 213) did not obey a Gaussian distribution and had a higher coefficient of variation. After 7 and 14 days, the organization of the nAChR clusters was similar to that of clusters from adult innervated extensor digitorum longus muscle. These findings indicate the histocompatibility of rats from 2BAW colony and that satellite cells transplanted into the subcutaneous space of adult animals are able to develop and fuse to form differentiated skeletal muscle fibers.