Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Criação da matéria em cosmologias com velocidade da luz variável e eletrônico não-linear

In this work we obtain the cosmological solutions and investigate the thermodynamics of matter creation in two diferent contexts. In the first we propose a cosmological model with a time varying speed of light c. We consider two diferent time dependence of c for a at Friedmann-Robertson- Walker (FRW) universe. We write the energy conservation law arising from Einstein equations and study how particles are created as c decreases with cosmic epoch. The variation of c is coupled to a cosmological Λ term and both singular and non-singular solutions are possible. We calculate the "adiabatic" particle creation rate and the total number of particles as a function of time and find the constrains imposed by the second law of thermodynamics upon the models. In the second scenario, we study the nonlinearity of the electrodynamics as a source of matter creation in the cosmological models with at FRW geometry. We write the energy conservation law arising from Einstein field equations with cosmological term Λ, solve the field equations and study how particles are created as the magnetic field B changes with cosmic epoch. We obtain solutions for the adiabatic particle creation rate, the total number of particles and the scale factor as a function of time in three cases: Λ = 0, Λ = constant and Λ α H2 (cosmological term proportional to the Hubble parameter). In all cases, the second law of thermodynamics demands that the universe is not contracting (H ≥ 0). The first two solutions are non-singular and exhibit in ationary periods. The third case studied allows an always in ationary universe for a suficiently large cosmological term

Anisotropias da radiação cósmica de fundo e vínculos em modelos com decaimento do vácuo

Many astronomical observations in the last few years are strongly suggesting that the current Universe is spatially flat and dominated by an exotic form of energy. This unknown energy density accelerates the universe expansion and corresponds to around 70% of its total density being usually called Dark Energy or Quintessence. One of the candidates to dark energy is the so-called cosmological constant (Λ) which is usually interpreted as the vacuum energy density. However, in order to remove the discrepancy between the expected and observed values for the vacuum energy density some current models assume that the vacuum energy is continuously decaying due to its possible coupling with the others matter fields existing in the Cosmos. In this dissertation, starting from concepts and basis of General Relativity Theory, we study the Cosmic Microwave Background Radiation with emphasis on the anisotropies or temperature fluctuations which are one of the oldest relic of the observed Universe. The anisotropies are deduced by integrating the Boltzmann equation in order to explain qualitatively the generation and c1assification of the fluctuations. In the following we construct explicitly the angular power spectrum of anisotropies for cosmologies with cosmological constant (ΛCDM) and a decaying vacuum energy density (Λ(t)CDM). Finally, with basis on the quadrupole moment measured by the WMAP experiment, we estimate the decaying rates of the vacuum energy density in matter and in radiation for a smoothly and non-smoothly decaying vacuum

Teorias f(R) de gravidade na formulação de Palatini

In this dissertation, after a brief review on the Einstein s General Relativity Theory and its application to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models, we present and discuss the alternative theories of gravity dubbed f(R) gravity. These theories come about when one substitute in the Einstein-Hilbert action the Ricci curvature R by some well behaved nonlinear function f(R). They provide an alternative way to explain the current cosmic acceleration with no need of invoking neither a dark energy component, nor the existence of extra spatial dimensions. In dealing with f(R) gravity, two different variational approaches may be followed, namely the metric and the Palatini formalisms, which lead to very different equations of motion. We briefly describe the metric formalism and then concentrate on the Palatini variational approach to the gravity action. We make a systematic and detailed derivation of the field equations for Palatini f(R) gravity, which generalize the Einsteins equations of General Relativity, and obtain also the generalized Friedmann equations, which can be used for cosmological tests. As an example, using recent compilations of type Ia Supernovae observations, we show how the f(R) = R − fi/Rn class of gravity theories explain the recent observed acceleration of the universe by placing reasonable constraints on the free parameters fi and n. We also examine the question as to whether Palatini f(R) gravity theories permit space-times in which causality, a fundamental issue in any physical theory [22], is violated. As is well known, in General Relativity there are solutions to the viii field equations that have causal anomalies in the form of closed time-like curves, the renowned Gödel model being the best known example of such a solution. Here we show that every perfect-fluid Gödel-type solution of Palatini f(R) gravity with density and pressure p that satisfy the weak energy condition + p 0 is necessarily isometric to the Gödel geometry, demonstrating, therefore, that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on Gödel-type models to the framework of Palatini f(R) gravity theory. We derive an expression for a critical radius rc (beyond which causality is violated) for an arbitrary Palatini f(R) theory. The expression makes apparent that the violation of causality depends on the form of f(R) and on the matter content components. We concretely examine the Gödel-type perfect-fluid solutions in the f(R) = R−fi/Rn class of Palatini gravity theories, and show that for positive matter density and for fi and n in the range permitted by the observations, these theories do not admit the Gödel geometry as a perfect-fluid solution of its field equations. In this sense, f(R) gravity theory remedies the causal pathology in the form of closed timelike curves which is allowed in General Relativity. We also examine the violation of causality of Gödel-type by considering a single scalar field as the matter content. For this source, we show that Palatini f(R) gravity gives rise to a unique Gödeltype solution with no violation of causality. Finally, we show that by combining a perfect fluid plus a scalar field as sources of Gödel-type geometries, we obtain both solutions in the form of closed time-like curves, as well as solutions with no violation of causality

Gravitomagnetismo e o teste da sonda gravidade B

The so-called gravitomagnetic field arised as an old conjecture that currents of matter (no charges) would produce gravitational effects similar to those produced by electric currents in electromagnetism. Hans Thirring in 1918, using the weak field approximation to the Einsteins field equations, deduced that a slowly rotating massive shell drags the inertial frames in the direction of its rotation. In the same year, Joseph Lense applied to astronomy the calculations of Thirring. Later, that effect came to be known as the Lense- Thirring effect. Along with the de Sitter effect, those phenomena were recently tested by a gyroscope in orbit around the Earth, as proposed by George E. Pugh in 1959 and Leonard I. Schiff in 1960. In this dissertation, we study the gravitational effects associated with the rotation of massive bodies in the light of the Einsteins General Theory of Relativity. With that finality, we develop the weak field approximation to General Relativity and obtain the various associated gravitational effects: gravitomagnetic time-delay, de Sitter effect (geodesic precession) and the Lense-Thirring effect (drag of inertial frames). We discus the measures of the Lense-Thirring effect done by LAGEOS Satellite (Laser Geodynamics Satellite) and the Gravity Probe B - GPB - mission. The GPB satellite was launched into orbit around the Earth at an altitude of 642 km by NASA in 2004. Results presented in May 2011 clearly show the existence of the Lense-Thirring effect- a drag of inertial frames of 37:2 7:2 mas/year (mas = milliarcsec)- and de Sitter effect - a geodesic precession of 6; 601:8 18:3 mas/year- measured with an accuracy of 19 % and of 0.28 % respectively (1 mas = 4:84810��9 radian). These results are in a good agreement with the General Relativity predictions of 41 mas/year for the Lense-Thirring effect and 6,606.1 mas/year for the de Sitter effect.

Ondaletas e movimento browniano fracionário: aplicação à caracterização de poços de petróleo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Não-extensividade em percolação por ligações de longo - alcance

A linear chain do not present phase transition at any finite temperature in a one dimensional system considering only first neighbors interaction. An example is the Ising ferromagnet in which his critical temperature lies at zero degree. Analogously, in percolation like disordered geometrical systems, the critical point is given by the critical probability equals to one. However, this situation can be drastically changed if we consider long-range bonds, replacing the probability distribution by a function like . In this kind of distribution the limit α → ∞ corresponds to the usual first neighbor bond case. In the other hand α = 0 corresponds to the well know "molecular field" situation. In this thesis we studied the behavior of Pc as a function of a to the bond percolation specially in d = 1. Our goal was to check a conjecture proposed by Tsallis in the context of his Generalized Statistics (a generalization to the Boltzmann-Gibbs statistics). By this conjecture, the scaling laws that depend with the size of the system N, vary in fact with the quantitie

Efetividade da terapia fisica descongestiva na cicatrização de úlceras venosas

A venous ulcer is the most serious clinical manifestation of chronic venous failure, and the most frequent in lower limbs, accounting for 70% of all ulcers. Patients may suffer from this infirmity for several years without healing of the lesion if treatment is inadequate. The aim of this investigation was to verify the effectiveness of decongestive physical therapy in the healing of venous ulcers. This is a quasi-experimental, interventionist study, with paired, non-probabilistic sampling, composed of 50 patients divided into two groups: control and intervention, each composed of 25 patients. Both groups were identically treated for six months with daily dressings and the latter also underwent complex physical therapy consisting of a combination of the following techniques: manual lymphatic drainage, compression bandaging, lower limb elevation, myolymphokinetic exercises and skin care. The study was approved (Protocol no. 59/2007) by the Ethics Committee of the State University of Southeast Bahia. The Mann-Whitney and Chi-square tests were applied for data analysis. After statistical analysis the patients who underwent therapy showed a statistically significant difference with respect to wound contraction starting in the second month of treatment. Compared to the control, the intervention group showed a greater reduction in both pain and edema starting in the third and fourth month of therapy, respectively. To reinforce these findings, the mean percentage of tissue present at the base of the ulcer (granulation/fibrin ratio) was calculated. The intervention group showed greater granulation at the base of the ulcer compared to the control, significant from the second month of treatment on. It was observed in this study that lymphotherapy, when compared between the intervention and control groups, accelerated the healing process, and reduced pain and edema in the affected limbs. It is expected, therefore, that these results widen scientific knowledge and we suggest that this therapy be used 78 not only to reduce lymphedema, but also as a treatment option for venous ulcers, given its easy application and low cost. The data, therefore, demonstrated the importance of basic care on the part of a multiprofessional and transdisciplinary health team involved in the healing process of these infirmities, thereby contributing to better quality of life in these individuals

Comparação da incidência de câncer em infectados pelo HIV e em transplantados com a população geral

Introdução: Estudos demonstram uma relação entre a queda da imunidade e o aumento da incidência de câncer. Objetivo: Comparar a incidência de câncer em pacientes infectados pelo HIV e em transplantados com a da população geral. Métodos: Foi realizada revisão sistemática com metanálise, combinando descritores específicos nas bases de dados Pubmed, Scielo, Cancerlit e Google Scholar, buscando alta sensibilidade para responder o objetivo da pesquisa. Os artigos considerados de alta qualidade metodológica por apresentarem todos os critérios de inclusão foram avaliados por metanálise. Resultados: Foram incluídos 25 estudos envolvendo 866776 pessoas com HIV/AIDS e transplantados, em que foram diagnosticados 21260 novos casos de carcinoma. Observou-se que o risco para o surgimento de novos casos de câncer foi maior entre indivíduos com HIV/AIDS (SIR= 4, IC95% 3,78-4,24) e entre os transplantados (SIR= 3,28, IC95% 3,06-3,52) quando comparado com a população em geral. Conclusão: A incidência similar em ambas as populações pesquisadas sugere que o comprometimento do sistema imune, comum em ambas, é responsável pelo risco aumentado de novos casos de câncer. Investimentos em pesquisas que desenvolvam estratégias de prevenção mais eficazes para os dois grupos são necessários, pois podem contribuir para a redução da incidência e para a diminuição da mortalidade.

Estimativas de mortalidade para a região nordeste do Brasil em 2010: uma associação do método demográfico equação geral de balanceamento, com o estimador bayesiano empírico

One of the greatest challenges of demography, nowadays, is to obtain estimates of mortality, in a consistent manner, mainly in small areas. The lack of this information, hinders public health actions and leads to impairment of quality of classification of deaths, generating concern on the part of demographers and epidemiologists in obtaining reliable statistics of mortality in the country. In this context, the objective of this work is to obtain estimates of deaths adjustment factors for correction of adult mortality, by States, meso-regions and age groups in the northeastern region, in 2010. The proposal is based on two lines of observation: a demographic one and a statistical one, considering also two areas of coverage in the States of the Northeast region, the meso-regions, as larger areas and counties, as small areas. The methodological principle is to use the General Equation and Balancing demographic method or General Growth Balance to correct the observed deaths, in larger areas (meso-regions) of the states, since they are less prone to breakage of methodological assumptions. In the sequence, it will be applied the statistical empirical Bayesian estimator method, considering as sum of deaths in the meso-regions, the death value corrected by the demographic method, and as reference of observation of smaller area, the observed deaths in small areas (counties). As results of this combination, a smoothing effect on the degree of coverage of deaths is obtained, due to the association with the empirical Bayesian Estimator, and the possibility of evaluating the degree of coverage of deaths by age groups at counties, meso-regions and states levels, with the advantage of estimete adjustment factors, according to the desired level of aggregation. The results grouped by State, point to a significant improvement of the degree of coverage of deaths, according to the combination of the methods with values above 80%. Alagoas (0.88), Bahia (0.90), Ceará (0.90), Maranhão (0.84), Paraíba (0.88), Pernambuco (0.93), Piauí (0.85), Rio Grande do Norte (0.89) and Sergipe (0.92). Advances in the control of the registry information in the health system, linked to improvements in socioeconomic conditions and urbanization of the counties, in the last decade, provided a better quality of information registry of deaths in small areas

Repercussão geral e súmula vinculante: os efeitos no controle difuso

Brazil since its first republican constitution has adopted systems of laws control. The review activity was given to three state powers or functions state, Executive, Legislative and Judiciary. However, it appears that in the country along the constitutional history, has stood considerably the jurisdictional control of the most important control. Initially, back in 1891, Brazil adopted the jurisdictional control of diffuse from U.S, whose role in monitoring of standards is delivered to all organs of the judiciary, which may face a case, put on trial, ascertain whether or not the possibility of applying a law, removing its impact in case of unconstitutionality. In 1969, entered in the second legal model of judicial review, the concentrated control of constitutionality, whose inspiration comes from the positivist theory of Hans Kelsen, and was adopted by the Austrian Constitution of 1920. According to the abstract control the supervision of law is given to a Court or Constitutional Court, responsible for the analysis of the legal constitutionality independent of its application to a specific case. In Brazil the role of concentrated control was handed over exclusively to the Supreme Court, which serves as the Constitutional Court, which accumulates that function with other constitutionally provided jurisdiction. Throughout this period, from 1891 until today, Brazil has maintained a dual system of judicial control of legal constitutionality, where they coexist and harmonize the diffuse control exercised by any organ of the Judiciary, and concentrated control of competence the Supreme Court. However, one must recognize that with the advent of the Federal Constitution of 1988, the concentrated control has emerged on the national stage due to two important factors: the expansion of the legal capacity to sue and the inclusion of other ways control, besides the already known Direct Claim of Unconstitutionality. This concentrated control and projection of the Supreme Court s attempt to become a true constitutional court, led to a relative weakening of diffuse control even when performed by the Brazilian Constitutional Court. In order to become a true constitutional court, all decisions handed down by the Supreme in the exercise of constitutional jurisdiction should have the same weight and the same measure, or at least bring improvement to similar effects, once is the responsible for the final word when it comes to constitutional interpretation. Thus, the writs of certiorari and stare decisis were responsible for profound changes in the diffuse control, allowing the Supreme Court can strengthen its decisions even in the diffuse control. These two institutions have substantially changed the legal status of diffuse control, allowing an extension of the effects of decisions handed down by the Supreme Court, so that you can no longer be said that the effects of this control to restrict the disputing parties in the process

Construtivismo de marco teórico-pedagógico a grife: um estudo a partir das mensagens veiculadas na internet

This thesis is resulted of a research on propagated the social representations of constructivism in the Internet, which as had estimated basic the idea of Moscovici (1961) of that the media it has determinative paper in the popularization of the scientific theories, in formation e propagation of the social representations and in the construction of behaviors human beings. Understanding the Internet as latest space of circulation of social communications, therefore, privileged field (and still not explored) for studies of social representations, we choose this half midiático as investigative field of our research, it if it constitutes in the "great ocean of the new informational planet" (LEVY, 2000, p. 126), besides making possible the interaction with different forms of images, different individuals, different ' world ', configuring itself as important space of symbolic production e of analysis of the representational process in the world contemporary. Based in these questions, we trace as objective to analyze the circulating speech propagated on-line on the constructivism, searching to apprehend the social representations shared the respect. This objective was constructed in face of the insertion of the theory constructivist in the educational way has two decades more than, as well as of its consolidation as reference in different social contexts, mainly in midiático. The question that directed the research was: as this theory obtains to penetrate in some layers of our society, to influence the world readings e the behaviors of different people? That modifications it suffers in this trajectory and which the paper of the Internet in this process? The corpus of the research was constituted of the substances on the theory found in the Internet, in pages in Portuguese of Google, in the period of 27 of July of 2004 the 17 of August of 2004. The data they had been analyzed on the basis of the project of analysis of content elaborated for Moscovici (1961) and in the estimated theoreticians of the social communication, in special of the hypermedia. The results had disclosed that the Internet participates of determinative form in the process of popularization of the constructivism theory, not only spreading out its estimated theoretician- methodological for the domain public (diffusion), but propagating positive beliefs and images of its postulates (propagation) and using them it service of interests politicians e financiers (propaganda). The popularization of the constructivism in the Internet and social representations of this theory propagated configure one process in which the theory passes of pedagogical theoretical landmark for grief, assuming a commercial character extremely and the status of solution for problems of the education and the society, stirring up attitudes and behaviors in public, most general possible, that comes to take care of to the interests politicians e marketing. Recognizing the diversity, the permanent renewal of information and the negotiation of directions gifts in the Internet, as well as the innumerable ones forms of access to the information found by it, we consider results of the research as fruits of the inherent characteristics to this way midiático, to the time where we call the attention for relativity these results, for the plasticity of knowing them and sensible propagated on-line e for the great challenge that the hypermedia imposes to the study of communication phenomena, of the social representations and in educational quarrels and for the necessity of new research that they investigate the forms of socialization of the information and communication propitiated by hypermedia and its implications in the construction of the symbolic universes and in practical social

Trajetória profissional e rupturas epistemológicas na educação física e na atuação do professor

This dissertation is the result of concerns with the theoretical-methodological and pedagogical learning processes occurred in the practice of physical education in school, which accompany me since the initial training, when I experienced learning in a piecemeal fashion, focused on technicality and sportivization. In order to better qualify the pedagogical interventions of physical education in school, I have always been worried on applying what I received at the University, but the routine of classes was always demanding others doings. In this sense, there were many moments of epistemological ruptures occurred in my training, in which I always sought new investment in training to account for the provision of a more humanistic and grounded in real educational precepts physical education. To that end I had to reflect on the pedagogical interventions throughout my training, in order not to carry out the activities as heavy doings, but as metamorphoses of knowledge and thus generating learning for students. Thus, this dissertation fits into this context with the overall goal of discussing my professional career, considering the epistemological ruptures of Physical Education, occurred in my training and expertise. The objective is also to identify the contributions of these formations in professional activities, centered on storytelling and reflection of significant experiences in the teaching of sports and Physical Education. We highlight the paradigm shifts, leaving the gymnastic methods, through dance-physical education method, psychomotor, reaching the contemporary critical theories experienced from the culture of movement as well as its implications for professional practice. We chose a qualitative research, using the autobiographical method, using as sources or techniques, narratives, photographic recording and video samples. In the studies within the area of education, for the most part, qualitative research came to oppose the positivist view of the quantification on analysis of social phenomena. New ideas were appearing in order to present innovative perspectives to understand the real. The survey data will be presented in narrated form (descriptive), analyzed based on the theoretical framework that guides the study, especially authors who discuss school physical education, vocational training and body conception. We believe our study may be of relevance for training in Physical Education that as from pedagogical reflections in certain historical realities, envisions being able to open new perspectives for the performance of other physical education teachers

Atividades experimentais no ensino de biologia em escolas públicas do estado do Rio Grande do Norte, Brasil: caracterização geral e concepção de professores

Recent research has revealed that the majority of Biology teachers believe the practice of experimental activities as a didactical means would be the solution for the improvement of the Biology teaching-learning process. There are, however, studies which signal the lack of efficiency in such practice lessons as far as building scientific knowledge is concerned. It is also said that despite the enthusiasm on the teachers‟ part, such classes are rarely taught in high school. Several studies point pedagogical difficulties as well as nonexistence of a minimal infrastructure needed in laboratories as cause of low frequency in experimental activities. The poor teacher performance in terms of planning and development of classes; the large number of students per class; lack of financial stimulus for teachers are other reasons to be taken into account among others, in which can also be included difficulties of epistemological nature. That means an unfavorable eye of the teacher towards experimental activities. Our study aimed to clarify if such scenario is generalized in high schools throughout the state of Rio Grande do Norte Brazil. During our investigation a sample of twenty teaching institutions were used. They were divided in two groups: in the first group, five IFRN- Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte schools. Two of those in Natal, and the other three from the country side. The second group is represented by fifteen state schools belonging to the Natal metropolitan area. The objectives of the research were to label schools concerning laboratory facilities; to identify difficulties pointed by teachers when performing experiment classes, and to become familiar with the conceptions of the teachers in regarding biology experiment classes. To perform such task, a questionnaire was used as instrument of data collecting. It contained multiple choice, essay questions and a semi-structured interview with the assistance of a voice recorder. The data analysis and the in loco observation allowed the conclusion that the federal schools do present better facilities for the practice of experimental activities when compared to state schools. Another aspect pointed is the fact that teachers of federal schools have more time available for planning the experiments; they are also better paid and are given access a career development, which leads to better salaries. All those advantages however, do not show a significantly higher frequency regarding the development of experiments when compared to state school teachers. Both teachers of federal and state schools pointed infra-structure problems such as the availability of reactants, equipments and consumption supplies as main obstacle to the practice of experiments in biology classes. Such fact leads us to conclude that maybe there are other problems not covered by the questionnaire such as poor ability to plan and execute experimental activities. As far as conceptions about experimental activities, it was verified in the majority of the interviewees a inductive-empiric point of view of science possibly inherited during their academic formation and such point of view reflected on the way they plan and execute experiments with students

Os Polímeros como Sistemas Complexos

Neste trabalho, através de simulações computacionais, identificamos os fenômenos físicos associados ao crescimento e a dinâmica de polímeros como sistemas complexos exibindo comportamentos não linearidades, caos, criticalidade auto-organizada, entre outros. No primeiro capítulo, iniciamos com uma breve introdução onde descrevemos alguns conceitos básicos importantes ao entendimento do nosso trabalho. O capítulo 2 consiste na descrição do nosso estudo da distribuição de segmentos num polímero ramificado. Baseado em cálculos semelhantes aos usados em cadeias poliméricas lineares, utilizamos o modelo de crescimento para polímeros ramificados (Branched Polymer Growth Model - BPGM) proposto por Lucena et al., e analisamos a distribuição de probabilidade dos monômeros num polímero ramificado em 2 dimensões, até então desconhecida. No capítulo seguinte estudamos a classe de universalidade dos polímeros ramificados gerados pelo BPGM. Utilizando simulações computacionais em 3 dimensões do modelo proposto por Lucena et al., calculamos algumas dimensões críticas (dimensões fractal, mínima e química) para tentar elucidar a questão da classe de universalidade. Ainda neste Capítulo, descrevemos um novo modelo para a simulação de polímeros ramificados que foi por nós desenvolvido de modo a poupar esforço computacional. Em seguida, no capítulo 4 estudamos o comportamento caótico do crescimento de polímeros gerados pelo BPGM. Partimos de polímeros criticamente organizados e utilizamos uma técnica muito semelhante aquela usada em transições de fase em Modelos de Ising para estudar propagação de danos chamada de Distância de Hamming. Vimos que a distância de Hamming para o caso dos polímeros ramificados se comporta como uma lei de potência, indicando um caráter não-extensivo na dinâmica de crescimento. No Capítulo 5 analisamos o movimento molecular de cadeias poliméricas na presença de obstáculos e de gradientes de potenciais. Usamos um modelo generalizado de reptação para estudar a difusão de polímeros lineares em meios desordenados. Investigamos a evolução temporal destas cadeias em redes quadradas e medimos os tempos característicos de transporte t. Finalizamos esta dissertação com um capítulo contendo a conclusão geral denoss o trabalho (Capítulo 6), mais dois apêndices (Apêndices A e B) contendo a fenomenologia básica para alguns conceitos que utilizaremos ao longo desta tese (Fractais e Percolação respectivamente) e um terceiro e ´ultimo apêndice (Apêndice C) contendo uma descrição de um programa de computador para simular o crescimentos de polímeros ramificados em uma rede quadrada