Pecolação em uma rede multifractal

In this work we present the principal fractals, their caracteristics, properties abd their classification, comparing them to Euclidean Geometry Elements. We show the importance of the Fractal Geometry in the analysis of several elements of our society. We emphasize the importance of an appropriate definition of dimension to these objects, because the definition we presently know doesn t see a satisfactory one. As an instrument to obtain these dimentions we present the Method to count boxes, of Hausdorff- Besicovich and the Scale Method. We also study the Percolation Process in the square lattice, comparing it to percolation in the multifractal subject Qmf, where we observe som differences between these two process. We analize the histogram grafic of the percolating lattices versus the site occupation probability p, and other numerical simulations. And finaly, we show that we can estimate the fractal dimension of the percolation cluster and that the percolatin in a multifractal suport is in the same universality class as standard percolation. We observe that the area of the blocks of Qmf is variable, pc is a function of p which is related to the anisotropy of Qmf

Quantitative fractography under light microscopy: A digital image processing approach

This work is an example of the improvement on quantitative fractography by means of digital image processing and light microscopy. Two techniques are presented to investigate the quantitative fracture behavior of Ti-4Al-4V heat-treated alloy specimens, under Charpy impact testing. The first technique is the Minkowski method for fractal dimension measurement from surface profiles, revealing the multifractal character of Ti-4Al-4V fracture. It was not observed a clear positive correlation of fractal values against Charpy energies for Ti-4Al-4V alloy specimens, due to their ductility, microstructural heterogeneities and the dynamic loading characteristics at region near the V-notch. The second technique provides an entire elevation map of fracture surface by extracting in-focus regions for each picture from a stack of images acquired at successive focus positions, then computing the surface roughness. Extended-focus reconstruction has been used to explain the behavior along fracture surface. Since these techniques are based on light microscopy, their inherent low cost is very interesting for failure investigations.

Extended depth from focus reconstruction using NIH ImageJ plugins: Quality and resolution of elevation maps

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Simulação de Fluxo no Meio Poroso Utilizando o Fluent

The complexity of the Phenomenon of fluid flow in porous way causes a difficulty in its explicit description. Different in the cases where the flow is given through a pipe, where it is possible to measure the length and diameter of the pipe and to determine their ability to flow as a function of pressure, which is a complicated task in porous way. However, we try to approach clearly the equations used to conjecture the behavior of fluid flow in porous way. We made use of the Gambit to create a fractal geometry with the fluent we give the contour´s conditions we would want to analyze the data. The triangular mesh was created; it makes interactions with the discs of different rays, as barriers putted in the geometry. This work presents the results of a simulation with a flow of viscous fluids (oilliquid). The oil flows in a porous way constructed in 2D. The behavior evaluation of the fluid flow inside the porous way was realized with graphics, images and numerical results used for different datas analysis. The study was aimed in relation at the behavior of permeability (k) for different fractal dimensions. Taking into account the preservation of porosity and increasing the fractal distribution of the discs. The results showed that k decreases when we increase the numbers of discs, although the porosity is the same for all generations of the first simulation, in other words, the permeability decreases when we increase the fractality. Well, there are strong turbulence in the flow each time we increase the number of discs and this hinders the passage of the same to the exit. These results permitted to put in evidence how the permeability (k) is affected in a porous way with obstacles distributed in a diversified form. We also note that k decreases when we increase the pressure variation (P) within geometry. So, in front of the results and the absence of bibliographic subsidies about other theories, the work realized here can possibly by considered the unpublished form to explain and reflect on how the permeability is changed when increasing the fractal dimension in a porous way

Uma nova proposta de antena planar multibanda para comunicações móveis

The great interest observed in wireless communication systems has required the development of new configurations of microstrip antennas, because they are easily built and integrated to other microwave circuit components, which is suitable for the construction and development of planar antenna arrays and microwave integrated circuits. This work presents a new configuration of tapered microstrip antenna, which is obtained by impressing U-slots on the conducting patch combined with a transmission line matching circuit that uses an inset length. It is shown that the use of U-slots in the microstrip antenna conducting patch excites new resonating modes, that gives a multiband characteristic for the slotted microstrip antenna, that is suitable for applications in communication systems that operates several frequencies simultaneously. Up to this date, the works reported in the literature deals with the use of Uslotted microstrip rectangular antennas fed by a coaxial probe. The properties of a linear array of microstrip patch tapered antennas are also investigated. The main parameters of the U slotted tapered microstrip antennas are investigated for different sizes and locations of the slots impressed on the conducting patch. The analysis of the proposed antenna is performed by using the resonant cavity and equivalent transmission line methods, in combination with a parametric study, that is conducted by the use of the Ansoft Designer, a commercial computer aided microwave software well known by its accuracy and efficiency. The mentioned methods are used to evaluate the effect in the antennas parameters, like resonant frequency and return loss, produced by variations of the antenna structural parameters, accomplished separately or simultaneously. An experimental investigation is also developed, that consists of the design, construction and measurement of several U slotted microstrip antenna prototypes. Finally, theoretical and simulated results are presented that are in agreement with the measured ones. These results are related to the resonating modes identification and to the determination of the main characteristics of the investigated antennas, such as resonant frequency, return loss, and radiation pattern

Processo de difusão com agregação e reorganização espontânea em uma rede 2D

Difusive processes are extremely common in Nature. Many complex systems, such as microbial colonies, colloidal aggregates, difusion of fluids, and migration of populations, involve a large number of similar units that form fractal structures. A new model of difusive agregation was proposed recently by Filoche and Sapoval [68]. Based on their work, we develop a model called Difusion with Aggregation and Spontaneous Reorganization . This model consists of a set of particles with excluded volume interactions, which perform random walks on a square lattice. Initially, the lattice is occupied with a density p = N/L2 of particles occupying distinct, randomly chosen positions. One of the particles is selected at random as the active particle. This particle executes a random walk until it visits a site occupied by another particle, j. When this happens, the active particle is rejected back to its previous position (neighboring particle j), and a new active particle is selected at random from the set of N particles. Following an initial transient, the system attains a stationary regime. In this work we study the stationary regime, focusing on scaling properties of the particle distribution, as characterized by the pair correlation function ø(r). The latter is calculated by averaging over a long sequence of configurations generated in the stationary regime, using systems of size 50, 75, 100, 150, . . . , 700. The pair correlation function exhibits distinct behaviors in three diferent density ranges, which we term subcritical, critical, and supercritical. We show that in the subcritical regime, the particle distribution is characterized by a fractal dimension. We also analyze the decay of temporal correlations

Entropia de bloco no formalismo estatístico generalizado de Kaniadakis

A posição que a renomada estatí stica de Boltzmann-Gibbs (BG) ocupa no cenário cientifíco e incontestável, tendo um âmbito de aplicabilidade muito abrangente. Por em, muitos fenômenos físicos não podem ser descritos por esse formalismo. Isso se deve, em parte, ao fato de que a estatística de BG trata de fenômenos que se encontram no equilíbrio termodinâmico. Em regiões onde o equilíbrio térmico não prevalece, outros formalismos estatísticos devem ser utilizados. Dois desses formalismos emergiram nas duas ultimas décadas e são comumente denominados de q-estatística e k-estatística; o primeiro deles foi concebido por Constantino Tsallis no final da década de 80 e o ultimo por Giorgio Kaniadakis em 2001. Esses formalismos possuem caráter generalizador e, por isso, contem a estatística de BG como caso particular para uma escolha adequada de certos parâmetros. Esses dois formalismos, em particular o de Tsallis, nos conduzem também a refletir criticamente sobre conceitos tão fortemente enraizados na estat ística de BG como a aditividade e a extensividade de certas grandezas físicas. O escopo deste trabalho esta centrado no segundo desses formalismos. A k -estatstica constitui não só uma generalização da estatística de BG, mas, atraves da fundamentação do Princípio de Interação Cinético (KIP), engloba em seu âmago as celebradas estatísticas quânticas de Fermi- Dirac e Bose-Einstein; além da própria q-estatística. Neste trabalho, apresentamos alguns aspectos conceituais da q-estatística e, principalmente, da k-estatística. Utilizaremos esses conceitos junto com o conceito de informação de bloco para apresentar um funcional entrópico espelhado no formalismo de Kaniadakis que será utilizado posteriormente para descrever aspectos informacionais contidos em fractais tipo Cantor. Em particular, estamos interessados em conhecer as relações entre parâmetros fractais, como a dimensão fractal, e o parâmetro deformador. Apesar da simplicidade, isso nos proporcionará, em trabalho futuros, descrever estatisticamente estruturas mais complexas como o DNA, super-redes e sistema complexos

Estudo de Fractalidade e Evolução Dinâmica de Sistemas Complexos

In this work, the study of some complex systems is done with use of two distinct procedures. In the first part, we have studied the usage of Wavelet transform on analysis and characterization of (multi)fractal time series. We have test the reliability of Wavelet Transform Modulus Maxima method (WTMM) in respect to the multifractal formalism, trough the calculation of the singularity spectrum of time series whose fractality is well known a priori. Next, we have use the Wavelet Transform Modulus Maxima method to study the fractality of lungs crackles sounds, a biological time series. Since the crackles sounds are due to the opening of a pulmonary airway bronchi, bronchioles and alveoli which was initially closed, we can get information on the phenomenon of the airway opening cascade of the whole lung. Once this phenomenon is associated with the pulmonar tree architecture, which displays fractal geometry, the analysis and fractal characterization of this noise may provide us with important parameters for comparison between healthy lungs and those affected by disorders that affect the geometry of the tree lung, such as the obstructive and parenchymal degenerative diseases, which occurs, for example, in pulmonary emphysema. In the second part, we study a site percolation model for square lattices, where the percolating cluster grows governed by a control rule, corresponding to a method of automatic search. In this model of percolation, which have characteristics of self-organized criticality, the method does not use the automated search on Leaths algorithm. It uses the following control rule: pt+1 = pt + k(Rc − Rt), where p is the probability of percolation, k is a kinetic parameter where 0 < k < 1 and R is the fraction of percolating finite square lattices with side L, LxL. This rule provides a time series corresponding to the dynamical evolution of the system, in particular the likelihood of percolation p. We proceed an analysis of scaling of the signal obtained in this way. The model used here enables the study of the automatic search method used for site percolation in square lattices, evaluating the dynamics of their parameters when the system goes to the critical point. It shows that the scaling of , the time elapsed until the system reaches the critical point, and tcor, the time required for the system loses its correlations, are both inversely proportional to k, the kinetic parameter of the control rule. We verify yet that the system has two different time scales after: one in which the system shows noise of type 1 f , indicating to be strongly correlated. Another in which it shows white noise, indicating that the correlation is lost. For large intervals of time the dynamics of the system shows ergodicity

Espectros fractais em sistemas nanoestruturados e cristais fotônicos

The study of the elementary excitations such as photons, phonons, plasmons, polaritons, polarons, excitons and magnons, in crystalline solids and nanostructures systems are nowdays important active field for research works in solid state physics as well as in statistical physics. With this aim in mind, this work has two distinct parts. In the first one, we investigate the propagation of excitons polaritons in nanostructured periodic and quasiperiodic multilayers, from the description of the behavior for bulk and surface modes in their individual constituents. Through analytical, as well as computational numerical calculation, we obtain the spectra for both surface and bulk exciton-polaritons modes in the superstructures. Besides, we investigate also how the quasiperiodicity modifies the band structure related to the periodic case, stressing their amazing self-similar behavior leaving to their fractal/multifractal aspects. Afterwards, we present our results related to the so-called photonic crystals, the eletromagnetic analogue of the electronic crystalline structure. We consider periodic and quasiperiodic structures, in which one of their component presents a negative refractive index. This unusual optic characteristic is obtained when the electric permissivity and the magnetic permeability µ are both negatives for the same range of angular frequency ω of the incident wave. The given curves show how the transmission of the photon waves is modified, with a striking self-similar profile. Moreover, we analyze the modification of the usual Planck´s thermal spectrum when we use a quasiperiodic fotonic superlattice as a filter.

Estimativa de expoentes críticos em Percolação

In Percolation Theory, functions like the probability that a given site belongs to the infinite cluster, average size of clusters, etc. are described through power laws and critical exponents. This dissertation uses a method called Finite Size Scaling to provide a estimative of those exponents. The dissertation is divided in four parts. The first one briefly presents the main results for Site Percolation Theory for d = 2 dimension. Besides, some important quantities for the determination of the critical exponents and for the phase transistions understanding are defined. The second shows an introduction to the fractal concept, dimension and classification. Concluded the base of our study, in the third part the Scale Theory is mentioned, wich relates critical exponents and the quantities described in Chapter 2. In the last part, through the Finite Size Scaling method, we determine the critical exponents fi and. Based on them, we used the previous Chapter scale relations in order to determine the remaining critical exponents

Unidade e multiplicidade do tempo: uma abordagem transdisciplinar

Procurou-se, neste trabalho, pensar o tempo no contexto das ciências da saúde, no qual se entrelaçam aspectos físicos, biológicos, psicológicos e sociológicos. Enquanto em nossa percepção do mundo e de nós mesmos o tempo se apresenta sob muitas facetas, na física clássica, conforme o modelo newtoniano, assumia-se a existência de um tempo absoluto, unilinear, homogêneo e independente do observador. Com a teoria da relatividade e o estudo dos sistemas complexos, um novo conceito de tempo apresenta-se na física: o tempo fractal, o qual possibilita maior compatibilidade com as abordagens psicológicas e sociológicas. Nesta perspectiva, a experiência de vida de uma pessoa, e seus respectivos processos de construção da saúde, envolveria uma multiplicidade de tempos, que coexistem e se organizam segundo um padrão coerente de auto-similaridade. Uma quebra desse padrão estaria correlacionada com a ocorrência da doença. Sugere-se que uma abordagem mais adequada do adoecimento deveria levar em conta, como referência para o profissional de saúde, o conceito de tempo fractal, possibilitando maior sintonia do paciente com a complexidade da natureza e, por conseguinte, consigo mesmo.

Comments about some species abundance patterns: classic, neutral, and niche partitioning models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A simplified Fermi Accelerator Model under quadratic frictional force

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Transition to turbulence in the Reynolds' experiment

In this study we simulate numerically the Reynolds' experiment for the transition from laminar to turbulent flow in a pipe. We present a discussion of the results from a dynamical systems perspective when a control parameter, the Reynolds number, is increased. The Landau scenario, where the transition is described by the excitation of infinite oscillatory modes within the fluid, is not observed. Instead what happens is best explained by the Ruelle-Takens scenario in terms of strange attractors. The Lyapunov exponent and fractal dimension for the attractor are calculated together with a measure of complex behaviour called the Lempel-Ziv complexity. (C) 2001 Elsevier B.V. B.V. All rights reserved.

The upgraded DO detector

The DO experiment enjoyed a very successful data-collection run at the Fermilab Tevatron collider between 1992 and 1996. Since then, the detector has been upgraded to take advantage of improvements to the Tevatron and to enhance its physics capabilities. We describe the new elements of the detector, including the silicon microstrip tracker, central fiber tracker, solenoidal magnet, preshower detectors, forward muon detector, and forward proton detector. The uranium/liquid -argon calorimeters and central muon detector, remaining from Run 1, are discussed briefly. We also present the associated electronics, triggering, and data acquisition systems, along with the design and implementation of software specific to DO. (c) 2006 Elsevier B.V. All rights reserved.