Supondo que o núcleo possa ser tratado como um fluido perfeito, nós estudamos as condições para a formação de solitons de Korteweg-de Vries (KdV) na matéria nuclear. A existência de solitons de KdV depende da equação de estado nuclear que, por sua vez, depende da teoria microcóspica subjacente da interação núcleon-núcleon e das aproximações feitas durante os cálculos. No nosso trabalho, nós retomamos estudos sobre solitons no núcleo feitos no passado e substituímos a equação de estado usada anteriormente por outra mais moderna e mais realista, baseada no modelo de Walecka e suas variantes. Nossa análise mostra que solitons de KdV podem ser formados no interior do núcleo com largura em torno de um a dois fermis. / Assuming that the nucleus can be treated as a perfect fluid we study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. The existence of these solitons depends on the nuclear equation of state, which, in its turn, depends on the underlying microscopic theory of the nucleon-nucleon interaction and also on the approximations used in the calculations. In this work we reexamine early works on nuclear solitons, replacing the old equations of state by others, more modern and more realistic, base on QHD and on its variants. Our analysis shows that KdV solitons may indeed be formed in the nucleus with a width around one and two fermis.

Assumindo que a matéria nuclear seja um fluido perfeito, estudamos a propagação de perturbações na densidade bariônica. A equação de estado é obtida através de um modelo relativístico em campo médio, o qual é uma variante do modelo não-linear de Walecka. A expansão das equações de Euler e da continuidade na hidrodinâmica relativística em torno das configurações de equilíbrio nos levam a equações diferenciais para a perturbação na densidade. Resolvemos tais equações numericamente para perturbações lineares e esféricas mediante pulsos iniciais. Para perturbações lineares econtramos soluções solitônicas de pulsos isolados e soluções com vários solitons seguidas de ``radiação\'\'. Dependendo da equação de estado um forte amortecimento pode ocorrer. Consideramos também a evolução de perturbações em um meio sem efeitos dissipativos. Nesse caso observamos a formação e quebra de ondas de choque. Depois estudamos todo o formalismo na matéria nuclear em temperatura finita. Nossos resultados podem ser relevantes para análise de dados do RHIC. Eles sugerem que ondas de choque formadas na fase de plasma de quarks e gluons podem sobreviver e se propagar na fase hadrônica. Também estudamos a equação de onda não-linear para perturbações na densidade bariônica e densidade de energia no plasma de quarks e gluons (QGP). Sob certas condições solitons podem existir no QGP. Finalmente discutimos métodos alternativos de soluções de equações di-ferenciais não-lineares. / Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ``radiation\'\'. Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. We also study the non-linear wave equation for pertubations in baryon density and energy density in quark-gluon-plasma (QGP). Under certains conditions solitons may exist in QGP. Finally we discuss alternatives methods for solving non-linear differential equations.

Supondo que o núcleo possa ser tratado como um fluido perfeito, nós estudamos as condições para a formação de solitons de Korteweg-de Vries (KdV) na matéria nuclear. A existência de solitons de KdV depende da equação de estado nuclear que, por sua vez, depende da teoria microcóspica subjacente da interação núcleon-núcleon e das aproximações feitas durante os cálculos. No nosso trabalho, nós retomamos estudos sobre solitons no núcleo feitos no passado e substituímos a equação de estado usada anteriormente por outra mais moderna e mais realista, baseada no modelo de Walecka e suas variantes. Nossa análise mostra que solitons de KdV podem ser formados no interior do núcleo com largura em torno de um a dois fermis. / Assuming that the nucleus can be treated as a perfect fluid we study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. The existence of these solitons depends on the nuclear equation of state, which, in its turn, depends on the underlying microscopic theory of the nucleon-nucleon interaction and also on the approximations used in the calculations. In this work we reexamine early works on nuclear solitons, replacing the old equations of state by others, more modern and more realistic, base on QHD and on its variants. Our analysis shows that KdV solitons may indeed be formed in the nucleus with a width around one and two fermis.

Assumindo que a matéria nuclear seja um fluido perfeito, estudamos a propagação de perturbações na densidade bariônica. A equação de estado é obtida através de um modelo relativístico em campo médio, o qual é uma variante do modelo não-linear de Walecka. A expansão das equações de Euler e da continuidade na hidrodinâmica relativística em torno das configurações de equilíbrio nos levam a equações diferenciais para a perturbação na densidade. Resolvemos tais equações numericamente para perturbações lineares e esféricas mediante pulsos iniciais. Para perturbações lineares econtramos soluções solitônicas de pulsos isolados e soluções com vários solitons seguidas de ``radiação\'\'. Dependendo da equação de estado um forte amortecimento pode ocorrer. Consideramos também a evolução de perturbações em um meio sem efeitos dissipativos. Nesse caso observamos a formação e quebra de ondas de choque. Depois estudamos todo o formalismo na matéria nuclear em temperatura finita. Nossos resultados podem ser relevantes para análise de dados do RHIC. Eles sugerem que ondas de choque formadas na fase de plasma de quarks e gluons podem sobreviver e se propagar na fase hadrônica. Também estudamos a equação de onda não-linear para perturbações na densidade bariônica e densidade de energia no plasma de quarks e gluons (QGP). Sob certas condições solitons podem existir no QGP. Finalmente discutimos métodos alternativos de soluções de equações di-ferenciais não-lineares. / Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ``radiation\'\'. Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. We also study the non-linear wave equation for pertubations in baryon density and energy density in quark-gluon-plasma (QGP). Under certains conditions solitons may exist in QGP. Finally we discuss alternatives methods for solving non-linear differential equations.

The study of matter at extreme densities has been a major focus in theoretical physics in the last half-century. The wide spectrum of information that the field produces provides an invaluable contribution to our knowledge of the world in which we live. Most fascinatingly, the insight into the world around us is provided from knowledge of the intangible, at both the smallest and largest scales in existence. Through the study of nuclear physics we are able to investigate the fundamental construction of individual particles forming nuclei, and with further physics we can extrapolate to neutron stars. The models and concepts put forward by the study of nuclear matter help to solve the mystery of the most powerful interaction in the universe; the strong force. In this study we have investigated a particular state-of-the-art model which is currently used to refine our knowledge of the workings of the strong interaction and the way that it is manifested in both neutron stars and heavy nuclei, although we have placed emphasis on the former for reasons of personal interest. The main body of this work has surrounded an effective field theory known as Quantum Hadrodynamics (QHD) and its variations, as well as an extension to this known as the Quark-Meson Coupling (QMC) model, and variations thereof. We further extend these frameworks to include the possibility of a phase transition from hadronic matter to deconfined quark matter to produce hybrid stars, using various models. We have investigated these pre-existing models to deeply understand how they are justified, and given this information, we have expanded them to incorporate a modern understanding of how the strong interaction is manifest. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1458960 / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2010

We analyze a number of systems of evolution equations that arise in the study of physical chemistry. First we discuss the well-posedness of a system of mixing compressible barotropic multicomponent flows. We discuss the regularity of these variational solutions, their existence and uniqueness, and we analyze the emergence of a novel type of entropy that is derived for the system of equations. Next we present a numerical scheme, in the form of a discontinuous Galerkin (DG) finite element method, to model this compressible barotropic multifluid. We find that the DG method provides stable and accurate solutions to our system, and that further, these solutions are energy consistent; which is to say that they satisfy the classical entropy of the system in addition to an additional integral inequality. We discuss the initial-boundary problem and the existence of weak entropy at the boundaries. Next we extend these results to include more complicated transport properties (i.e. mass diffusion), where exotic acoustic and chemical inlets are explicitly shown. We continue by developing a mixed method discontinuous Galerkin finite element method to model quantum hydrodynamic fluids, which emerge in the study of chemical and molecular dynamics. These solutions are solved in the conservation form, or Eulerian frame, and show a notable scale invariance which makes them particularly attractive for high dimensional calculations. Finally we implement a wide class of chemical reactors using an adapted discontinuous Galerkin finite element scheme, where reaction terms are analytically integrated locally in time. We show that these solutions, both in stationary and in flow reactors, show remarkable stability, accuracy and consistency. / text