TEDE Communidade:
http://www.bdtd.uerj.br/handle/1/3685
Fri, 14 Jun 2024 17:59:37 GMT2024-06-14T17:59:37ZDeterminação de integrais primeiras para sistemas dinâmicos em duas e três dimensões com um algoritmo linear
http://www.bdtd.uerj.br/handle/1/22050
Título: Determinação de integrais primeiras para sistemas dinâmicos em duas e três dimensões com um algoritmo linear
Autor: Ferreira, Higor Silva
Primeiro orientador: Duarte, Luiz Guilherme Silva
Abstract: This work proposes, initially, a broad approach with regard to the non-classificatory or generalist methods to deal with first and second order ordinary differential equations. More specifically, we will be interested in rational ODE’s (which are directly related to autonomous polynomial differential systems) and, to this end, our starting point consists of the study of theoretical structures introduced by the end of 19th century, in a reference to the works of S. Lie and G. Darboux. In this sense, we present some details contained in each of these theories in order to establish a mixed procedure called the S - function method, which was recently implemented by the UERJ research group working in the topics. It is widely known that such methods present complications when applied to some specific cases, and it will become evident throughout this reading. Thus, implementing and refining algorithms to deal with these type of equations, when integrable, has been the main motivation of the group. Therefore, the development at the very end of this work presents, as a proposal, a highly efficient method that allows us to determine the Darboux polynomials with a linear procedure (the eigenpolynomials of the vector field associated with these equations have fundamental importance for the construction of an integrating factor). In this aspect, we reinforce some ideas which are discussed in the preceding chapters (introducing a notation in conformity with the most recent developments of the group) and definitively establish the algorithms for our purposes, in such a way that, one of them applies to rational first order ODE’s presenting a Darbouxian general solution, while the other two are useful to deal with problems involving second order ODE’s, in subcases that arise as follows: rational second order ODE’s presenting one elementary first integral and one non-Liouvillian first integral; rational second order ODE’s with two Liouvillian first integrals, one of them being elementary. We conclude
with a discussion on the performance of our method in computational terms, which we
can surely assert, beforehand, represents a routine of singular efficiency (due to the linearity of the equations involved in the procedure) in terms of consumed memory and execution time. Additionally, we present an example as an application of our method to an equation of a non-linear oscillator (Duffing van-der Pol) which is of great interest for various applications.
Instituição: Universidade do Estado do Rio de Janeiro
Tipo do documento: DissertaçãoThu, 29 Feb 2024 00:00:00 GMThttp://www.bdtd.uerj.br/handle/1/220502024-02-29T00:00:00ZObserváveis em modelos efetivos conﬁnantes: potencial quark–antiquark e momento magnético de núcleons
http://www.bdtd.uerj.br/handle/1/22039
Título: Observáveis em modelos efetivos conﬁnantes: potencial quark–antiquark e momento magnético de núcleons
Autor: Mena Correa, Carlos Stivens
Primeiro orientador: Palhares, Letícia Faria Domingues
Abstract: The understanding of hadronic physics, in terms of quarks and gluons, is still an open problem, since the color confinement mechanism still lacks a satisfactory analytical description from first principles. However, in order to address confinement, some approaches have been developed that explore or even manage to access information from the low-energy region of Quantum Chromodynamics (QCD), i.e. the nonperturbative part of QCD, where it is considered that the explanation for confinement may lie. Among the different methods, we focus on those that arise from the nonperturbative consequences of Gribov copies, which modify the infrared behavior of Yang-Mills propagators, especially that of the gluon propagator. At the same time, these approaches are motivated by the nonperturbative first-principle numerical results of lattice QCD. In this thesis, we will study the following models: Gribov–Zwanziger (GZ), refined Gribov–Zwanziger (RGZ), and Curci-Ferrari (CF, or massive gluon model). In the case of the gluon propagator, the nonperturbative information present in these approaches generates a structure of complex poles, which violates the positivity reflection axiom related to the physical interpretation of a particle, which could be considered as an indication of gluon confinement. The search for other signs of confinement in these formalisms is obviously of great importance to establish their role as consistent infrared realizations of QCD. With this in mind, and assuming confinement as something intrinsic to QCD, in this thesis we investigate in some observables the consequences and phenomenological impact of the non-perturbative characteristics of the different approaches mentioned. First, related to the observable of the energy spectrum, we focus on the calculation and analysis of the static potential between a heavy quark–antiquark pair, whose linear behavior, corroborated by lattice QCD, is considered a sign of confinement. Our objective is also to verify the validity of the mentioned approaches and their compatibility with perturbative predictions, and also whether such models can produce quark confinement through a linear potential. Our results indicate that the calculated potentials are in agreement with the high-energy perturbative result and also that these potentials present interesting non-perturbative corrections. In the case of Curci-Ferrari (massive gluon), due to the systematic introduction of more interaction effects that include corrections at one and two loops, these become very significant due to the emergence of a semilinear behavior of its potential in the region of intermediate distances. The other observable studied in this thesis is the magnetic moment, in particular that of the proton. Due to the difficulty that the calculation presents, we adopted the constituent quark model (CQM), which within its own limitations allows us to calculate the magnetic moment of hadrons as a function of the magnetic moments of their constituent quarks. In order to extract the magnetic moment of the quarks and with the aim of studying the phenomenological impact of the different types of propagators of the GZ, RGZ, and CF approaches, we analyzed the quark-photon vertex (QPV) (up to the order of one it loop) focusing on the contribution coming from QCD, which depends on the gluon propagator. Our results indicate that the contributions of the different approaches to the magnetic moment of the quarks are smaller in relation to the perturbative result (massless gluon) since these are suppressed due to the mass terms present in the gluon propagators, which in the GZ and CF cases present a very similar behavior even if the GZ case has imaginary poles and the CF case does not (at tree level). In the RGZ case, due to the more elaborate structure and complex poles of its propagator, more contributions to the magnetic moment of the quarks appear, which may even exceed the value of the perturbative result for certain values of the RGZ parameters. Regarding the magnetic moment of the proton, calculated in CQM, the most interesting result arises when the mass of the constituent quark is adjusted to reproduce the mass of the proton. In this case, by adjusting the mass parameters of the mentioned approaches, we can reproduce the moment of the proton. The values obtained are even comparable to other mass values obtained for the gluon mass.
Instituição: Universidade do Estado do Rio de Janeiro
Tipo do documento: TeseTue, 19 Dec 2023 00:00:00 GMThttp://www.bdtd.uerj.br/handle/1/220392023-12-19T00:00:00ZEstrelas de nêutrons e propriedades microscópicas da matéria ultradensa
http://www.bdtd.uerj.br/handle/1/22001
Título: Estrelas de nêutrons e propriedades microscópicas da matéria ultradensa
Autor: Santos, Felippe Vieira Benicio dos
Primeiro orientador: Palhares, Letícia Faria Domingues
Abstract: The present work addresses the subject of the modeling of neutron stars. Neutron
stars are extremely dense and compact astronomical objects that arise after a supernova
explosion. These stars are composed mostly of neutrons and have unique and complex
characteristics that challenge our current understanding of physics. The dissertation aims
to provide a comprehensive and detailed introduction to the modeling of these stars, exploring the theories and methods used to understand their internal structure, their physical
properties and their dynamic behavior. Understanding these aspects is fundamental to
astrophysics, as neutron stars play a crucial role in a wide range of astrophysical phenomena such as pulsars, X-ray emission and neutron star mergers. The work begins by
providing a thorough review of the existing literature, ranging from the fundamentals
of nuclear and particle physics to astrophysical theories related to neutron stars. The
most recent theoretical models are discussed, such as the approval of the state of matter
of neutrons and the numerical simulations used to study the structure and evolution
of these stars. Then, observational methods and available data are presented that help
us to restrict and validate the theoretical models. Observation techniques such as the
analysis of X-ray spectra and the detection of gravitational waves, which provide crucial
information about the properties of neutron stars, are covered. Finally, the dissertation
discusses the challenges and gaps in current knowledge, targeting areas of future research.
The importance of advancing neutron star modeling is highlighted, considering the
continuous evolution of observational technology and the need to improve our theoretical
models to explain phenomena not yet understood. In short, this Master’s thesis provides
a comprehensive and up-to-date overview of neutron star modeling, highlighting the importance of these fascinating astrophysical objects and outlining future research changes
in this ever-evolving field.
Instituição: Universidade do Estado do Rio de Janeiro
Tipo do documento: DissertaçãoThu, 23 Nov 2023 00:00:00 GMThttp://www.bdtd.uerj.br/handle/1/220012023-11-23T00:00:00ZWorking towards a gauge-invariant description of the Higgs model: from local composite operators to spectral density functions
http://www.bdtd.uerj.br/handle/1/21977
Título: Working towards a gauge-invariant description of the Higgs model: from local composite operators to spectral density functions
Autor: Egmond, Duive Maria Van
Primeiro orientador: Guimarães, Marcelo Santos
Abstract: Analisamos diferentes soluções invariantes do BRST para a introdução de um termo de massa nas teorias de Yang-Mills (YM). Primeiro, analisamos o campo invariante de calibre composto não local Ahµ(x), que pode ser localizado pelo campo tipo Stueckelbergξa(x). Isto nos permite introduzir um termo de massa no modelo SU(N) YM, uma característica que foi indicada em um nível não perturbativo por estudos analíticos e numéricos. A conﬁguração de Ah(x) , obtida através da minimização de Rd4xA2ao longo da órbita de calibre, da origem a uma ação renormalizável de todas as ordens, uma característica que será ilustrada por meio de uma classe de ﬁxações de calibre covariantes que, como tanto quanto o Rξ-gauge de ’t Hooft de teorias de calibre quebradas espontaneamente, fornecem uma massa para o campo do tipo Stueckelberg. Em seguida, consideramos o modelo unitário de Abelian Higgs e investigamos suas funções espectrais na ordem de um loop. Esta análise permite desembaraçar o que é físico e o que não é ao nível dos propagadores de partículas elementares, em conjunto com as identidades Nielsen. Destacamos o papel dos gráﬁcos de girinos e das escolhas de medidores para obter resultados sensatos. Também introduzimos uma ação Abeliana de Curci-Ferrari acoplada a um campo escalar para modelar um fóton massivo que, como o modelo não-Abeliano de Curci-Ferrari, é deixado invariante por uma simetria BRST não-nilpotente modiﬁcada. Ilustramos claramente sua natureza não unitária diretamente do ponto de vista da função espectral. Isso fornece um análogo funcional da observação de Ojima no formalismo canônico: existem estados fantasmas com norma diferente de zero nos estados invariantes do BRST do modelo Curci-Ferrari. Finalmente, as propriedades espectrais de um conjunto de operadores compostos invariantes de calibre locais são investigadas no modelo U(1) e SU(2) de Higgs quantizado no medidor ’t Hooft Rξ. Esses operadores nos permitem fornecer uma descrição invariante de calibre do espectro da teoria, superando assim certas comodidade são usar os campos elementares padrão. É mostrado que as funções espectrais dos campos elementares sofrem de uma forte dependência não física do parâmetro de calibre ξ, e podem até exibir comportamento de violação de positividade. Em contraste, os operadores locais invariantes do BRST exibem uma densidade espectral positiva bem deﬁnida.
Instituição: Universidade do Estado do Rio de Janeiro
Tipo do documento: TeseFri, 11 Sep 2020 00:00:00 GMThttp://www.bdtd.uerj.br/handle/1/219772020-09-11T00:00:00Z