Systems such as the power grid, world wide web (WWW), and internet are categorized as complex systems because of the presence of a large number of interacting elements. For example, the WWW is estimated to have a billion webpages and understanding the dynamics of such a large number of individual agents (whose individual interactions might not be fully known) is a challenging task. Complex network representations of these systems have proved to be of great utility. Statistical physics is the study of emergence of macroscopic properties of systems from the characteristics of the interactions between individual molecules. Hence, statistical physics of complex networks has been an effective approach to study these systems. In this dissertation, I have used statistical physics to study two distinct phenomena in complex systems: i) Cascading failures and ii) Shortest paths in complex networks. Understanding cascading failures is considered to be one of the “holy grails“ in the study of complex systems such as the power grid, transportation networks, and economic systems. Studying failures of these systems as percolation on complex networks has proved to be insightful. Previously, cascading failures have been studied extensively using two different models: k-core percolation and interdependent networks. The first part of this work combines the two models into a general model, solves it analytically, and validates the theoretical predictions through extensive computer simulations. The phase diagram of the percolation transition has been systematically studied as one varies the average local k-core threshold and the coupling between networks. The phase diagram of the combined processes is very rich and includes novel features that do not appear in the models which study each of the processes separately. For example, the phase diagram consists of first- and second-order transition regions separated by two tricritical lines that merge together and enclose a two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a smaller occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition cycles from first-order to second-order to two-stage to first-order as the k-core threshold is increased. We setup the analytical equations describing the phase boundaries of the two-stage transition region and we derive the critical exponents for each type of transition. Understanding the shortest paths between individual elements in systems like communication networks and social media networks is important in the study of information cascades in these systems. Often, large heterogeneity can be present in the connections between nodes in these networks. Certain sets of nodes can be more highly connected among themselves than with the nodes from other sets. These sets of nodes are often referred to as ’communities’. The second part of this work studies the effect of the presence of communities on the distribution of shortest paths in a network using a modular Erdős-Rényi network model. In this model, the number of communities and the degree of modularity of the network can be tuned using the parameters of the model. We find that the model reaches a percolation threshold while tuning the degree of modularity of the network and the distribution of the shortest paths in the network can be used as an indicator of how the communities are connected.

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Collagen scaffolds are porous structures which are used in bioreactors and in a wide range of tissue engineering applications. In these contexts, the scaffolds may be subjected to conditions in which fluid is forced through the structure and the scaffold is simultaneously compressed. It is clear that fluid transport within collagen scaffolds, and the inter-relationships between permeability, scaffold structure, fluid pressure and scaffold deformation are of key importance. However, these relationships remain poorly understood. In this thesis, a series of isotropic collagen structures were produced using a freeze-drying technique from aqueous slurry concentrations 0.5, 0.75 and 1 wt%, and fully characterised using X-ray micro-tomography and compression testing. It was found that collagen wt% influenced structural parameters such as pore size, porosity, relative density and mechanical properties. Percolation theory was used to investigate the pore interconnectivity of each scaffold. Structures with lower collagen fraction resulted in larger percolation diameters, but lower mechanical stiffness. Aligned collagen scaffolds were also produced by altering the freeze-drying protocol and using different types of mould materials and designs. It was found that a polycarbonate mould with stainless base resulted in vertically aligned structures with low angular variation. When compared with isotropic scaffolds from slurry of the same concentration, aligned scaffolds had a larger percolation diameter. Tortuosity was used as a mathematical tool to characterise the interconnected pathways within each porous structure. The effect of the size of the region of interest (ROI) chosen and the size of the virtual probe particle used in the analysis on the values of tortuosity calculated were determined and an optimised calculation methodology developed. Increasing the collagen fraction within isotropic scaffolds increased the tortuosity, and aligned structures had smaller tortuosity values than their isotropic counterparts. Permeability studies were conducted using two complementary experimental rigs designed to cover a range of pressure regimes and the results were compared with predictions from mathematical models and computational simulations. At low pressures, it was found that the lower collagen fraction structures, which had more open morphologies, had higher permeabilities. Alignment of the structure also enhanced permeability. The scaffolds all experienced deformation at high pressures resulting in a restriction of fluid flow. The lower collagen fraction scaffolds experienced a sharper decrease in permeability with increased pressure and aligned structures were more responsive to deformation than their isotropic counterparts. The inter-relationships between permeability, scaffold structure, fluid pressure and deformation of collagen scaffolds were explored. For isotropic samples, permeability followed a broad $(1- \epsilon)^2$ behaviour with strain as predicted by a tetrakaidecahedral structural model, with the constant of proportionality changing with collagen fraction. In contrast, the aligned structures did not follow this behaviour with the permeability dropping much more sharply in the early stages of compression. Open-cell polyurethane (PU) foams, sometimes used as dressings in wound healing applications, are often compared with collagen scaffolds in permeability models and were used in this thesis as a comparison structure. The foam had a higher permeability than the scaffolds due to its larger pore sizes and higher interconnectivity. In the light of the effects of compression on permeability, the changes in porous structure with compression were explored in isotropic and aligned 0.75 wt% scaffolds. Unlike the fluid flow experiments, these experiments were carried out in the dry state. Deformation in simple linear compression and in step-wise compression was studied, and the stress relaxation behaviour of the scaffolds characterised. A methodology was developed to characterise the structural changes accompanying compression using X-ray micro-tomography with an in situ compression stage. The methodology accounted for the need for samples to remain unchanged during the scan collection period for stable image reconstruction. The scaffolds were studied in uniaxial compression and biaxial compression and it was found that pore size and percolation diameter decreased with increasing compressive strain, while the tortuosity increased. The aligned structure was less affected than the isotropic at low compressions, in contrast to the results from the permeability study in which the aligned structure was more responsive to strain. This suggests that the degree of hydration may affect the structural changes observed. The insights gained in this study of the inter-relationships between microstructure, fluid dynamics and deformation in collagen scaffolds are of relevance to the informed design of porous structures for medical applications.

The major aim in search and rescue using mobile robots is to reach trapped survivors and to support rescue operations through the disaster environments. Our motivation is based on the fact that a search and rescue (SAR) robot can navigate within and penetrate a disaster area only if the area in question possesses connected voids Traversability or penetrability of a disaster area is a primary factor that guides the navigation of a search and rescue (SAR) robot, since it is highly desirable that the robot, without hitting a dead end or getting stuck, keeps its mobility for its primary task of reconnaissance and mapping when searching the highly unstructured environment We propose two novel guided prioritized exploration system: 1) percolation guided methodology where a percolator estimates the existence of connected voids in the upcoming yet unexplored region ahead of the robot so as to increase the efficiency of reconnaissance operation by the superior ability of the percolation guidance in speedy coverage of the area / 2) the hybrid exploration methodology that makes the percolation guided exploration collaborate with entropy based SLAM under a switching control dependent on either priority given to position accuracy or to map accuracy This second methodology has proven to combine the superiority of both methods so that the active SLAM becomes speedy, with high coverage rate of the area as well as accurate in localization.

This dissertation presents a novel multi-robot coordination control algorithm for search and rescue (SAR) operations. Continuous and rapid coverage of the unstructured and complex disaster areas in search of possible buried survivors is a time critical operation where prior information about the environment is either not available or very limited. Human navigation of such areas is definitely dangerous due to the nature of the debris. Hence, exploration of unknown disaster environments with a team of robots is gaining importance day by day to increase the efficiency of SAR operations. Localization of possible survivors necessitates uninterrupted navigation of robotic aiding devices within the rubbles without getting trapped into dead ends. In this work, a novel goal oriented prioritized exploration and map merging methodologies are proposed to generate efficient multi-robot coordination control strategy. These two methodologies are merged to make the proposed methodology more realistic for real world applications. Prioritized exploration of an environment is the first important task of the efficient coordination control algorithm for multi-robots. A goal oriented and prioritized exploration approach based on a percolation model for victim search operation in unknown environments is presented in this work. The percolation model is used to describe the behavior of liquid in random media. In our approach robots start prioritized exploration beginning from regions of the highest likelihood of finding victims using percolation model inspired controller. A novel map merging algorithm is presented to increase the performance of the SAR operation in the sense of time and energy. The problem of merging partial occupancy grid environment maps which are extracted independently by individual robot units during search and rescue (SAR) operations is solved for complex disaster environments. Moreover, these maps are combined using intensity and area based features without knowing the initial position and orientation of the robots. The proposed approach handles the limitation of existing works in the literature such as / limited overlapped area between partial maps of robots is sufficient for good merging performance and unstructured partial environment maps can be merged efficiently. These abilities allow multi-robot teams to efficiently generate the occupancy grid map of catastrophe areas and localize buried victim in the debris efficiently.

Made available in DSpace on 2016-12-08T17:19:34Z (GMT). No. of bitstreams: 1 Capa.pdf: 203956 bytes, checksum: 407d7f7b9ea4356c0eaa848e0eeb55d9 (MD5) Previous issue date: 2010-02-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Multi-walled carbon nanotubos dispersed in epoxy matrix (DGEBA) were aligned by a sinusoidal electric field with amplitude of 300 V / cm and frequency 1 kHz, during curing of the nanocomposites. Nanocomposites were subjected to the electric field (aligned nanotubes) and samples cured without the presence of the field (with nanotubes dispersed randomly) and NC concentration equal to 0.05, 0.1, 0.25 and 0.5% (m / m). The morphologies of aligned carbon nanotubes networks, in samples submitted to the electric field were characterized by means transmitted light optical microscopy analysis. It was observed that the geometry of the networks is strongly influenced by the concentration of nanotubes. The monitoring of electrical conductivity during the curing of the samples, allowed us to identify the three main stages of formation of networks. The first is related to the alignment and clustering of NCPM, the second is related to the stability of the network and the third to the cure of epoxy matrix. The Classical Percolation Theory has been used to relate the electrical conductivity (dc) to the content of NCPM, and allowed to determine the exponent of the electrical conductivity and percolation threshold of aligned samples and samples without alignment. The trend of increase in the electrical conductivity exponent in the aligned samples indicates the formation of an anisotropic network, since the conductivity is favored in the direction of alignment. The percolation threshold showed a decrease in the sample aligned, which may relate to the facilitation of the electric conduction process through the material. As for the dielectric properties, nanocomposites analyzed showed a behavior similar to the dielectric described by the first order Debye dielectric dispersion model. Both samples type showed a relaxation time of electric dipoles in the order of milliseconds, typical of interfacial polarization. The permittivity of aligned samples exhibited a magnitude increase in frequency of 200 Hz. This behavior may be related to the increased ability to trap electrical charges due to the formation of the network carbon nanotubes. The DMA and DIL analysis showed that Tg of the aligned samples decrease, indicating that the alignment affect the restriction on the movement of polymer chains. The micro-hardness analysis was not sensitive enough to characterize the hardness anisotropy, depending on the alignment of NCPM dispersed in the matrix. In the other hand, it was revealed that the incorporation of nanotubes creates free volume within the material, which reduces the hardness of the nanocomposites compared with pure epoxy. / Nanotubos de paredes múltiplas (NCPM) dispersos em matriz epóxi (DGEBA) foram alinhados com o auxilio de um campo elétrico senoidal, de amplitude de 300 V/cm e freqüência de 1 kHz, durante a cura dos nanocompósitos. Foram fabricados nanocompósitos submetidos ao campo elétrico (nanotubos alinhados) e amostras curadas sem a presença do campo (com nanotubos dispersos de modo aleatório), com teores de NCPM iguais a 0,05; 0,1; 0,25 e 0,5 % (m/m). As morfologias das redes alinhadas, nas amostras submetidas ao campo, foram caracterizadas por meio das analises de microscopia óptica de luz transmitida. Foi possível notar que a geometria das redes e fortemente influenciada pela concentração de nanotubos. O monitoramento da condutividade elétrica, durante a cura das amostras linhadas, permitiu identificar as três principais etapas de formação das redes. A primeira esta relacionada com o processo de alinhamento e aglomeração lateral dos NCPM, a segunda esta relacionada com a estabilidade da rede e a terceira com a cura da matriz epóxi. A Teoria da Percolação Clássica foi utilizada para descrever a condutividade elétrica (cc) em função do teor de NCPM, e permitiu determinar o expoente de condutividade elétrica e o limiar de percolação das amostras alinhadas e das amostras sem alinhamento. A tendência de acréscimo do expoente de condutividade elétrica nas amostras alinhadas indica a formação de uma rede anisotrópica, uma vez que o fluxo elétrico e favorecido na direção do alinhamento. O limiar de percolação apresentou uma diminuição nas amostras alinhadas, que pode estar relacionado com a facilitação do processo de condução através do material. Como relação as propriedades dielétricas, os nanocompósitos analisados (0,5 % m/m, alinhados e sem alinhamento) apresentaram um comportamento similar aos dielétricos descritos pelo modelo de dispersão dielétrica de primeira ordem de Debye. Ambas as amostras apresentaram um tempo de relaxação dos dipolos elétricos na ordem de milissegundos, característico de polarização interfacial. Na freqüência de 200 Hz a permissividade elétrica exibiu um aumento na ordem de grandeza, nas amostras alinhadas. Este comportamento pode estar relacionado com o aumento da capacidade de aprisionar cargas elétricas, devido a formação da rede. As analises de DMA e DIL mostraram que a Tg das amostras alinhadas diminuem, indicando que o alinhamento prejudica a restrição dos movimentos das cadeias poliméricas. Já a analise de microdureza Vickers nao se mostrou sensível o bastante para caracterizar a anisotropia de tal propriedade, em função do alinhamento dos NCPM dispersos na matriz. Em contra partida, foi possível perceber que a incorporação de nanotubos gera volumes livres no interior do material, que diminui a dureza dos nanocompósitos, quando comparado com o epóxi puro.

Made available in DSpace on 2015-03-03T15:16:22Z (GMT). No. of bitstreams: 1 EdemersonSBM.pdf: 812078 bytes, checksum: 167690407a20b9462083f00be2b0a159 (MD5) Previous issue date: 2007-12-28 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / 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 / Neste trabalho, o estudo de alguns sistemas complexos ? feito com a utiliza??o de dois procedimentos distintos. Na primeira parte, estudamos a utiliza??o da transformada Wavelet na an?lise e caracteriza??o (multi)fractal de s?ries temporais. Testamos a confiabilidade do M?todo do M?ximo do M?dulo da Transformada Wavelet (MMTW) com rela??o ao formalismo multifractal, por meio da obten??o do espectro de singularidade de s?ries temporais cuja fractalidade ? bem conhecida a priori. A seguir, usamos o m?todo do m?ximo do m?dulo da transformada wavelet para estudar a fractalidade dos ru?dos de crepita??o pulmonar, uma s?rie temporal biol?gica. Uma vez que a crepita??o pulmonar se d? no momento da abertura de uma via a?rea ? br?nquios, bronqu?olos e alv?olos ? que estava inicialmente fechada, podemos obter informa??es sobre o fen?meno de abertura em cascata das vias a?reas de todo o pulm?o. Como este fen?meno est? associado ? arquitetura da ?rvore pulmonar, a qual apresenta geometria fractal, a an?lise e caracteriza??o da fractalidade desse ru?do pode nos fornecer importantes par?metros de compara??o entre pulm?es sadios e aqueles acometidos por patologias que alteram a geometria da ?rvore pulmonar, tais como as doen?as obstrutivas e as de degenera??o parenquimatosa, que ocorre, por exemplo, no enfisema pulmonar. Na segunda parte, estudamos um modelo de percola??o por s?tios em rede quadrada, onde o aglomerado de percola??o cresce governado por uma regra de controle, correspondendo a um m?todo de busca autom?tica. Neste modelo de percola??o, que apresenta caracter?sticas de criticalidade auto-organizada, o m?todo de busca autom?tica n?o usa o algoritmo de Leath. Usa-se a seguinte regra de controle: pt+1 = pt +k(Rc ?Rt), onde p ? a probabilidade de percola??o, k ? um par?metro cin?tico onde 0 < k < 1 e R ? a fra??o de redes quadradas finitas de lado L, LxL, percolantes. Esta regra fornece uma s?rie temporal correspondente ? evolu??o din?mica do sistema, em especial da probabilidade de percola??o p. ? feita uma an?lise de escalas do sinal assim obtido. O modelo aqui utilizado permite que o m?todo de busca autom?tica para a percola??o por s?tios em rede quadrada seja, per si, estudado, avaliando-se a din?mica dos seus par?metros quando o sistema se aproxima do ponto cr?tico. Verifica-se que os escalonamentos de ?, o tempo decorrido at? que o sistema chegue ao ponto cr?tico, e de tcor, o tempo necess?rio para que o sistema perca suas correla??es, s?o, ambos, inversamente proporcionais a k, o par?metro cin?tico da regra de controle. Verifica-se ainda que o sistema apresenta duas escalas temporais distintas depois de ? : uma em que o sistema mostra ru?do do tipo 1 f? , indicando ser fortemente correlacionado; outra em que aparece um ru?do branco, indicando que se perdeu a correla??o. Para grandes intervalos de tempo a din?mica do sistema mostra que ele se comporta como um sistema erg?dico