abstract: ABSTRACT The unique structural features of deoxyribonucleic acid (DNA) that are of considerable biological interest also make it a valuable engineering material. Perhaps the most useful property of DNA for molecular engineering is its ability to self-assemble into predictable, double helical secondary structures. These interactions are exploited to design a variety of DNA nanostructures, which can be organized into both discrete and periodic structures. This dissertation focuses on studying the dynamic behavior of DNA nanostructure recognition processes. The thermodynamics and kinetics of nanostructure binding are evaluated, with the intention of improving our ability to understand and control their assembly. Presented here are a series of studies toward this goal. First, multi-helical DNA nanostructures were used to investigate how the valency and arrangement of the connections between DNA nanostructures affect super-structure formation. The study revealed that both the number and the relative position of connections play a significant role in the stability of the final assembly. Next, several DNA nanostructures were designed to gain insight into how small changes to the nanostructure scaffolds, intended to vary their conformational flexibility, would affect their association equilibrium. This approach yielded quantitative information about the roles of enthalpy and entropy in the affinity of polyvalent DNA nanostructure interactions, which exhibit an intriguing compensating effect. Finally, a multi-helical DNA nanostructure was used as a model `chip' for the detection of a single stranded DNA target. The results revealed that the rate constant of hybridization is strongly dominated by a rate-limiting nucleation step. / Dissertation/Thesis / Ph.D. Chemistry 2011

Este trabalho, realizado com o auxílio da termodinâmica computacional, dá continuação a um estudo sistemático, que trata dos fundamentos dos tratamentos termoquímicos metalúrgicos relacionados à nitretação e à nitrocarburação. O estudo concentrou-se nas ligas da família ABNT 10XX, do aço ABNT 4140 e do aço ferramenta AISI M2. A composição das ligas utilizadas na simulação, contudo, não correspondem exatamente à comercial. Uma simplificação foi necessária para que a simulação do processo fosse facilitada. O uso da termodinâmica computacional como ferramenta para determinação das fases presentes (ou que podem vir a se formar) em um sistema a certa temperatura e pressão simulando o processo de nitretação mostrou-se uma valiosa ferramenta de análise.Apesar de, na prática, estes prognósticos ainda dependerem de uma cinética micro ou macroscópica favorável para ser verdadeiros, a comparação dos resultados obtidos com a literatura mostrou uma boa concordância nos resultados, validando, assim, o emprego desta técnica de análise. Assim, além deste estudo ser um avanço na compreensão das fases que participam das microestruturas (nitretos e carbonitretos) que se formam nas ligas estudadas, também pode ser utilizado como um balizador na definição de parâmetros que permitam a seleção destas fases finais desejadas, economizando tempo e recursos na realização de ensaios experimentais. / This work, accomplished with the help of computational thermodynamics, provides the development of a systematic study concerning the basis of the thermochemical treatments related to nitriding and nitrocarburising. This study focused on the alloys of the ABNT 10XX family, on the ABNT 4140 steel and on the AISI M2 tool steel. However, the compositions used in the simulation do not correspond exactly to the commercial composition of the alloy, for they had their composition simplified in order to facilitate the simulation process. The use of computational thermodynamics as a tool to determine the phase present (or that can be formed) in a system under a specific temperature and pressure, simulating the nitriding process, proved to be a valuable analysis tool. Nevertheless, in practice, these prognostics still depend on a micro or macro kinetics in order to be true; the comparison of the results obtained with those found in the literature showed good agreement of results, validating, thus, the use of this analysis technique. So, besides this study being an advance when it comes to understanding phases (nitrides and carbonitrides) that are formed in the studied alloys, it can also be used as a mark in defining parameters that allow the selection of final desired structures, saving time and resources.

The project concerns the study of the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The goal of this research is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study the equilibrium properties of peculiar quantum systems, which are known to escape thermalization: the many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Then, I exploited the "Concentration of Measure" and the related "Typicality Arguments" to study the macroscopic properties of the basis states in a tentative theory of quantum gravity: Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. The ultimate goal of this line of research is to give a quantum description of a black hole which is consistent with the expected semiclassical behaviour. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why an horizon exhibits thermal properties.

OLIVEIRA, Paulo William Simão de. Estudo das propriedades estruturais e dinâmicas de um sistema binário quasi-unidimensional. 2007. 105 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2007. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-05-22T19:35:48Z No. of bitstreams: 1 2007_dis_pwsoliveira.pdf: 2259918 bytes, checksum: 48074a559be7bed99a345a92c3c2a969 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-05-22T20:06:53Z (GMT) No. of bitstreams: 1 2007_dis_pwsoliveira.pdf: 2259918 bytes, checksum: 48074a559be7bed99a345a92c3c2a969 (MD5) / Made available in DSpace on 2015-05-22T20:06:53Z (GMT). No. of bitstreams: 1 2007_dis_pwsoliveira.pdf: 2259918 bytes, checksum: 48074a559be7bed99a345a92c3c2a969 (MD5) Previous issue date: 2007 / The aim of this work is to study the structural and dynamical properties of a classical binary system of charged particles confined in a two dimensional channel. Such a system is described in the literature as quasi-unidimensional, and its relevance is supported by the possibility of technological applications, shown recently in the scientific literature, and also the interest and understanding of properties in condensed matter physics. Although the theoretical and numerical character of the present work, several experimental systems can be described by the present model. The summary of the contents of this work is presented in each chapter. In chapter 1, a general overview is given. The concept of Wigner crystallization is introduced, and examples of experimental systems, which exhibit such an ordered phase under proper conditions are given. We discuss the physics of complex plasmas, colloidal suspensions and applications in biological systems. A description of the simulation method is given in chapter 2. Scale transformations are introduced in order to construct a general model, i.e. no longer depending on particular features of the system, but only on relevant parameters of a general model. The Molecular Dynamics simulation technique (MD) is presented, focusing on the Langevin Dynamics. The competition between the inter-particle interaction, in the form of the electrostatic repulsion, and the external confinement, which is assumed to be parabolic and act only in one direction, generates a chain-like strutural pattern. A description of the model, the harmonic approach used in the analytical calculations of the normal modes spectrum, and the analytical calculation of the energy per particle of the different chain-configutations are given in chapter 3. The ground state configurations, the structural phase transitions and normal modes of the present chain-like binary system are presented in Chapter 4. In the low density regime particles crystallize in a single chain. When the density is increased a zig-zag transition occurs and the single chain splits into two chains. Such a transition is characterized by a spontaneous symmetry breaking. With the increase of the density the system changes to the four-chains configuration (case 1) (particles not aligned vertically), where the two -> four chains (case 1) transition occurs through a zig-zag transition accompanied by a shift along the chain direction. A further increase of the density will lead the system to a new ground state configuration with four chains (case 2) (particles aligned vertically). The dynamical properties are related to the phonon spectrum, in which the number of normal modes is two times the number particle in the unit cell. The conclusions and perspectives are presented in chapter 5. / O objetivo deste trabalho é estudar as propriedades estruturais e dinâmicas de um sistema binário clássico consistindo de partículas carregadas que estão confinadas em um canal bidimensional. Tal sistema é descrito na literatura como quasi-unidimensional, e esta relevância apoia-se na possibilidade de aplicações tecnológicas, como tem sido mostrado recentemente na literatura científica, bem como no interesse e entendimento em propriedades da Física da matéria condensada. Apesar do caráter teórico do presente estudo, diversos sistemas experimentais podem ser descritos pelo modelo aqui considerado. O resumo do conteúdo deste trabalho é apresentado em cada capítulo. No capítulo 1, é dada uma visão geral do presente trabalho. O conceito da cristalização de Wigner é introduzido e são dados exemplos de sistemas experimentais, que exibem uma fase ordenada sob circunstâncias apropriadas. Discute-se a Física dos plasmas complexos, das suspensões coloidais e aplicações em sistemas biológicos. Uma descrição do método de simulação é dada no capítulo 2. As transformações de escalas são introduzidas a fim de construir um modelo geral, isto é, não dependente das características particulares do sistema, mas somente das quantidades relevantes gerais. Apresenta-se a técnica de simulação por Dinâmica Molecular (DM), focalizando também a Dinâmica de Langevin. A competição entre a interação entre partícula, na forma de repulsão eletrostática, e o confinamento externo, que é suposto parabólico e age somente em uma direção, gera uma estrutura de cadeias no sistema. Uma descrição do modelo, bem como a aproximação harmônica utilizada para o cálculo dos modos normais e o cálculo da energia por partícula das várias estruturas de cadeias são dadas no capítulo 3. A configuração do estado fundamental, as transições estruturais de fase e modos normais para o sistema binário de cadeias são examinadas no capítulo 4. Para baixas densidades as partículas cristalizam-se em uma única cadeia; com o aumento da densidade uma transição zig − zag ocorre e a única cadeia se parte em duas. Observa-se que esta transição estrutural é caracterizada por uma quebra espontânea de simetria. Com o aumento da densidade, o sistema passa para quatro cadeias (caso 1) (partículas não alinhadas na vertical), onde a transição de duas para quatro cadeias (caso 1) ocorre com uma transição zig − zag, em cada uma das cadeias, acompanhadas por um deslocamento ao longo da direção da cadeia. Então com um aumento da densidade conduzirá a uma nova estrutura de quatro cadeias (caso 2) (partículas alinhadas na vertical). As propriedades dinâmicas aqui consideradas resumem-se ao espectro de fônons, no qual o número de modos normais é igual ao dobro do número de partículas na célula unitária. As conclusões e perspectivas são apresentadas no capítulo 5.

Made available in DSpace on 2016-02-05T18:29:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-05-15. Added 1 bitstream(s) on 2016-02-05T18:33:20Z : No. of bitstreams: 1 000856755.pdf: 11731796 bytes, checksum: c668f46b3261ebe0cc32124d8d290fad (MD5) / Neste trabalho investigamos algumas propriedades dinâmicas para um ensemble de partículas no modelo bouncer dissipativo. O modelo consiste de uma partícula clássica (ou um ensemble delas), sob ação de um campo gravitacional constante, colidindo contra uma parede que oscila no tempo. As equações que descrevem o modelo completo abrangem dois tipos de colisões: (i) diretas e; (ii) as indiretas. Existe ainda uma versão simplificada do modelo que é equivalente ao Mapa Padrão de Chirikov. Este por sua vez exibe uma transição de caos local para caos global quando o parâmetro ε atinge um valor crítico. O modelo conservativo preserva área no espaço de fases e pode exibir crescimento ilimitado de energia, fenômeno conhecido como Aceleração de Fermi. O fenômeno é suprimido através da introdução de dissipação via colisões inelásticas. A transição entre crescimento ilimitado e limitado de energia é descrita através de hipóteses de escala. Estas conduzem a uma função homogênea generalizada que fornece duas leis de escala, validadas através dos expoentes críticos. A expressão analítica da velocidade quadrática média das partículas nos leva ao cálculo dos mesmos expoentes da transição, obtidos de forma independente das simulações. Uma sobreposição de curvas Vrms vs. n valida os expoentes críticos obtidos. A conexão do modelo bouncer com a Termodinâmica é obtida através do desenvolvimento de uma expressão para a Entropia, em concordância com o 3o Postulado da Termodinâmica / In this work we investigate some dynamical properties for an ensemble of particles in a dissipative bouncer model. The model consists of a classical particle (or an ensemble of them) colliding against a wall that oscillates as function of the time, under the action of a constant gravitational field. The equations that describe the complete model include two types of collisions: (i) direct and; (ii) indirect. There is a simplified version of the model which is equivalent to Chirikov's standard map. The map shows a transition from local to global chaos when the parameter reaches a critical value. The conservative model preserves the phase space area and, depending on the initial conditions as well as control parameter, can show unlimited growth of energy, a phenomenon known as Fermi acceleration. The phenomenon is suppressed by introducing dissipation via inelastic collisions. The transition between unlimited and limited growth of energy is described by scaling hypothesis. Such scaling leads to a generalized homogeneous function that provides two scaling laws, validated by well defined critical exponents. The analytical expression of the mean square velocity of particles leads to the calculation of these exponents of the transition, obtained independently of the simulations. An overlap of the curves Vrms vs. n validates the critical exponents obtained. The connection of the bouncer model with Thermodynamics is obtained by developing an expression for the Entropy, in agreement with the 3rd Postulate of Thermodynamics

Este trabalho, realizado com o auxílio da termodinâmica computacional, dá continuação a um estudo sistemático, que trata dos fundamentos dos tratamentos termoquímicos metalúrgicos relacionados à nitretação e à nitrocarburação. O estudo concentrou-se nas ligas da família ABNT 10XX, do aço ABNT 4140 e do aço ferramenta AISI M2. A composição das ligas utilizadas na simulação, contudo, não correspondem exatamente à comercial. Uma simplificação foi necessária para que a simulação do processo fosse facilitada. O uso da termodinâmica computacional como ferramenta para determinação das fases presentes (ou que podem vir a se formar) em um sistema a certa temperatura e pressão simulando o processo de nitretação mostrou-se uma valiosa ferramenta de análise.Apesar de, na prática, estes prognósticos ainda dependerem de uma cinética micro ou macroscópica favorável para ser verdadeiros, a comparação dos resultados obtidos com a literatura mostrou uma boa concordância nos resultados, validando, assim, o emprego desta técnica de análise. Assim, além deste estudo ser um avanço na compreensão das fases que participam das microestruturas (nitretos e carbonitretos) que se formam nas ligas estudadas, também pode ser utilizado como um balizador na definição de parâmetros que permitam a seleção destas fases finais desejadas, economizando tempo e recursos na realização de ensaios experimentais. / This work, accomplished with the help of computational thermodynamics, provides the development of a systematic study concerning the basis of the thermochemical treatments related to nitriding and nitrocarburising. This study focused on the alloys of the ABNT 10XX family, on the ABNT 4140 steel and on the AISI M2 tool steel. However, the compositions used in the simulation do not correspond exactly to the commercial composition of the alloy, for they had their composition simplified in order to facilitate the simulation process. The use of computational thermodynamics as a tool to determine the phase present (or that can be formed) in a system under a specific temperature and pressure, simulating the nitriding process, proved to be a valuable analysis tool. Nevertheless, in practice, these prognostics still depend on a micro or macro kinetics in order to be true; the comparison of the results obtained with those found in the literature showed good agreement of results, validating, thus, the use of this analysis technique. So, besides this study being an advance when it comes to understanding phases (nitrides and carbonitrides) that are formed in the studied alloys, it can also be used as a mark in defining parameters that allow the selection of final desired structures, saving time and resources.

abstract: Many acidic hot springs in Yellowstone National Park support microbial iron oxidation, reduction, or microbial iron redox cycling (MIRC), as determined by microcosm rate experiments. Microbial dissimilatory iron reduction (DIR) was detected in numerous systems with a pH < 4. Rates of DIR are influenced by the availability of ferric minerals and organic carbon. Microbial iron oxidation (MIO) was detected from pH 2 – 5.5. In systems with abundant Fe (II), dissolved oxygen controls the presence of MIO. Rates generally increase with increased Fe(II) concentrations, but rate constants are not significantly altered by additions of Fe(II). MIRC was detected in systems with abundant ferric mineral deposition. The rates of microbial and abiological iron oxidation were determined in a variety of cold (T= 9-12°C), circumneutral (pH = 5.5-9) environments in the Swiss Alps. Rates of MIO were measured in systems up to a pH of 7.4; only abiotic processes were detected at higher pH values. Iron oxidizing bacteria (FeOB) were responsible for 39-89% of the net oxidation rate at locations where biological iron oxidation was detected. Members of putative iron oxidizing genera, especially Gallionella, are abundant in systems where MIO was measured. Speciation calculations reveal that ferrous iron typically exists as FeCO30, FeHCO3+, FeSO40 or Fe2+ in these systems. The presence of ferrous (bi)carbonate species appear to increase abiotic iron oxidation rates relative to locations without significant concentrations. This approach, integrating geochemistry, rates, and community composition, reveals biogeochemical conditions that permit MIO, and locations where the abiotic rate is too fast for the biotic process to compete. For a reaction to provide habitability for microbes in a given environment, it must energy yield and this energy must dissipate slowly enough to remain bioavailable. Thermodynamic boundaries exist at conditions where reactions do not yield energy, and can be quantified by calculations of chemical energy. Likewise, kinetic boundaries exist at conditions where the abiotic reaction rate is so fast that reactants are not bioavailable; this boundary can be quantified by measurements biological and abiological rates. The first habitability maps were drawn, using iron oxidation as an example, by quantifying these boundaries in geochemical space. / Dissertation/Thesis / Doctoral Dissertation Geological Sciences 2017

abstract: Cooperativity can be used to manipulate binding affinities of DNA biosensors – improving specificity without sacrificing sensitivity; examples include tentacle probes (TPs) and cooperative primers (CPs). This thesis body of work: (1) used TPs to develop a rapid, low-cost diagnostic for detecting the point mutation leading to Navajo Neurohepatopathy (NNH) and (2) used CPs to amplify a symmetric bowtie-barcoded origami with captured t-cell receptor (TCR) α and β mRNA of a single cell. NNH (affecting 1-in-1600 Navajo babies) is a fatal genetic disorder often caused by 149G>A mutation and is characterized by brain damage and liver disease/failure. Phoenix Children’s Hospital currently uses gene sequencing to identify the 149G>A mutation. While this process is conclusive, there are limitations, as it requires both time (3-4 weeks) and money (>$700). Ultimately, these factors create barriers that can directly impact a patient’s quality of life. Assessment of the developed TP diagnostic, using genomic DNA derived from FFPE patient liver samples, suggests nearly 100% specificity and sensitivity while reducing cost to ~$250 (including cost of labor) and providing a diagnosis within 48 hours. TCR specificity is dependent on V(D)J recombination as well as pairing of the αβ chains. Drs. Schoettle and Blattman have developed a solution in which a bowtie-barcoded origami strand nanostructure is transfected into individual cells of a heterogeneous cell population to capture and protect αβ mRNA. When PCR of the origami template is performed with Vα, X, Vβ, and Y primers, the α and β gene segments cannot be tied back to a barcode – and paired. Assessment of the developed CPs for PCR suggests correct individual amplification using (1) Va + Xcp and (2) Vβ + Ycp primers, whereas combination of all the primers (Va, Xcp, Vb, and Ycp) suggests hybridization of the Vα + Xcp and Vβ + Ycp products due to the origami target symmetry. / Dissertation/Thesis / Third Iteration for Cooperative Primers / Masters Thesis Biomedical Engineering 2018

A finalidade deste trabalho é estabelecer as conexões entre física de buracos negros e termodinâmica, atentando para eventuais semelhanças e diferenças entre ramos aparentemente bem diversos da física moderna. Tais conexões foram inicialmente buscadas e estabelecidas na década de 1970, graças ao trabalho de S. Hawking e Jacob D. Bekenstein, entre outros, e sucessivamente aprofundadas nos anos subseqüentes, notadamente na última década. O mérito maior do primeiro foi estabelecer a emissão de radiação com espectro térmico por buracos negros em geral, mesmo aqueles desprovidos de rotação e carga (buracos negros de Schwarzschild). O segundo encarregou-se de correlacionar leis termodinâmicas clássicas com processos envolvendo buracos negros. Neste trabalho, procuramos inicialmente estudar os buracos negros de Schwarzschild e Kerr-Newman no tocante às suas propriedades gerais, bem como o problema do movimento de partículas nos espaços-tempos em questão, para discutir-se brevemente o problema de extração de energia de buracos negros, como apontado por Penrose e outros. Estabelecidas as propriedades gerais, pode-se enfim derivar a Termodinâmica destes buracos, correlacionando-se entropia e área, e obter expressões para a temperatura de corpo negro dos mesmos - em perfeita consonância com a derivação de Hawking, não abordada aqui, feita através da Teoria Quântica de Campos. Com a temperatura, pode-se estudar as capacidades térmicas, reveladores de propriedades típicas de buracos negros não compartilhadas por sistemas clássicos. A reboque destas, entra a discussão sobre a estabilidade termodinâmica de buracos negros em ensembles canônicos e microcanônicos, através do método das séries lineares, de Poincaré, fechando o presente trabalho. Assim, os capítulos 1 e 2 tratam das soluções de Schwarzschild e Kerr-Newman, respectivamente, abordando-lhes as propriedades gerais e o problema do movimento de partículas, materiais ou não, nessas geometrias. O capítulo 3 estabelece as pontes entre Termodinâmica e buracos negros, sendo crucial para o restante do trabalho. No capítulo 4 estudamos temperaturas e capacidades térmicas de diversos buracos negros, e finalmente no capítulo 5 vem o problema da estabilidade termodinâmica dos buracos negros. / In the present work, we have established the connections between black-hole physics and thermodynamics, searching for similarities and differences between these two branches of physicxs, which might look quite far apart. Such links were first sought for and established during the 1970s, thanks to the pioneering work of S. Hawking and Jacob D. Bekenstein, among others, and continuously developed in the following years, notably in the last decade. Hawking's major achievement was the prediction, from arguments based on Quantum Field Theory, that black holes radiate with a thermal spectrum, even the uncharged and nonrotating ones (the Schwarzschild black holes). Bekenstein's biggest merit was to find the link between classical thermodynamical laws and processes involving black holes. In this work, we started with Schwarzschild and Kerr-Newman black holes, working out their general properties, as well as the problem of particle motion in such spacetimes, so that we could briefly discuss the issue of energy extraction from black holes, as established by Penrose and others. Once the general features of these black holes were known, it was possible to derive the black-hole thermodynamics, due to a simple relation between black-hole entropy and area. Expressions for the black-hole temperature were then easily obtained, in perfect agreement with Hawking's own derivation, not considered here. With temperatures at hand, heat capacities could be thoroughly examined, showing intrinsic properties of black holes, not shared by classical systems. The question of thermodynamic stability of black holes arose naturally from heat capacity analysis, and we have analysed black holes in both the microcanonical and canonical ensembles, in the light of Poincaré's linear series method, completing the current work. Chapters 1 and 2 deal with the Schwarzschild and Kerr-Newman solutions, respectively, deriving their general features and working out particle motion in these geometries. Chapter 3 establishes the links between black-hole physics and thermodynamics, being of crucial importance for the subsequent chapters. Chapter 4 provides an extensive study of black-hole temperatures and heat capacities, paving the way for the last chapter, Chapter 5, concerning to thermodynamic stability of black holes.

A introdução de uma nova expressão matemática para a entropia permite construir novos ensembles na Teoria das Matrizes Aleatórias. Neste trabalho, apresenta-se uma estrutura geral para construção de todos os possíveis ensemble. Portanto, os elementos das matrizes podem ser números reais, complexos ou mesmo quaternions. O principio da entropia (não-extensiva) máxima e o Cálculo Variacional são usados para realizar essa façanha. Esta tese está comprometida com a construção do Ensemble Ortogonal Generalizado, cujas matrizes aleatórias são simétricas e seus elementos são os números reais, especificamente. As distribuições das matrizes, as distribuições de um elemento da matriz e as estatísticas espectrais são obtidas, estudadas e os resultados apresentados. / The introduction of a new mathematical expression for the entropy allows the construction of new ensembles in Random Matrices Theory. A general structure is presented to the construction of all possible ensembles. Therefore the matrix\'s elements can be real numbers, complex numbers or even quaternions. The generalized of the maximum entropy (nonextensive) principle and the variational calculus are to use to realize this achievement. This thesis concerned with the construction of the Generalized Orthogonal Ensemble, whose random matrices are symetric and its elements are real numbers. The matrix distribuit ion, the distribuition of an element of the matrix and the spectrum statistical were to obtained, studied and the results presented.