TEDE Coleção:http://www.bdtd.uerj.br/handle/1/36862024-06-14T08:10:04Z2024-06-14T08:10:04ZDeterminação de integrais primeiras para sistemas dinâmicos em duas e três dimensões com um algoritmo linearFerreira, Higor Silvahttp://www.bdtd.uerj.br/handle/1/220502024-05-27T17:18:57Z2024-02-29T00:00:00ZTítulo: 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: Dissertação2024-02-29T00:00:00ZEstrelas de nêutrons e propriedades microscópicas da matéria ultradensaSantos, Felippe Vieira Benicio doshttp://www.bdtd.uerj.br/handle/1/220012024-05-27T17:21:00Z2023-11-23T00:00:00ZTítulo: 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: Dissertação2023-11-23T00:00:00ZEstudo da fotoluminescência do Ga2O3 contendo a impureza Cr3+Freitas, Gabriel Alves dehttp://www.bdtd.uerj.br/handle/1/209982024-02-27T18:40:23Z2023-09-27T00:00:00ZTítulo: Estudo da fotoluminescência do Ga2O3 contendo a impureza Cr3+
Autor: Freitas, Gabriel Alves de
Primeiro orientador: Sosman, Lilian Pantoja
Abstract: In this work a study of the photoluminescence of β-Ga2O3 as a function of Cr3+ impurity
concentration was carried out. The samples were synthesized by solid state reaction with 0.1%, 1% and 5% of Cr3+. The optical properties were investigated by photoluminescence and excitation photoluminescence techniques at room temperature and atmospheric pressure. In the emission spectra were identified the R lines, which are characteristic of the 2E(2G) → 4A2(4F) transition of Cr3+ in octahedral site, superimposed on a broad and intense band in the near infrared region characteristic of the 4T2 (4F) → 4A2(4F) transition of Cr3+ in octahedral site. In photoluminescence excitation measurements the transitions 4A2(
4F) → 4T1(4F) and 4A2(4F) → 4T2(4F) were identified which are two bands in the visible region of the electromagnetic spectrum. The excitation and photoluminescence spectra were analyzed and interpreted according to the Crystal Field Theory and by the Tanabe-Sugano diagram for ion with d3 electronic configuration, and the crystal field parameters Dq and B were calculated from the solutions of the Tanabe-Sugano matrices. The decay time for the sample containing 0.1% Cr3+ was 0.22 ms and for the sample containing 1% Cr3+ was 0.11 ms, characteristics of the Cr3+ in octahedral sites.
Instituição: Universidade do Estado do Rio de Janeiro
Tipo do documento: Dissertação2023-09-27T00:00:00ZInflação quintessencial quenteAlmeida, Renato Silva dehttp://www.bdtd.uerj.br/handle/1/206832024-02-27T18:40:22Z2023-06-22T00:00:00ZTítulo: Inflação quintessencial quente
Autor: Almeida, Renato Silva de
Primeiro orientador: Ramos, Rudnei de Oliveira
Abstract: We study in this dissertation the possible unification of the regimes of inflation in the primordial universe and the accelerated expansion (dark energy) regimes in the later
universe by means of dissipative effects. In particular, we seek to analyze how such dissipative effects are able to produce a consistent dynamics unifying these two epochs of the universe. The topics covered aim to seek a general understanding of the dynamical nature of interactin fields and applications in cosmology, i.e., in the case of models involving a quintessence field. By doing so, we aim to describe quintessential inflation in the context
of warm inflation and characterized by different types of interactions between fields and
their consistency from the point of view of dynamical systems. Furthermore, we propose
interaction terms between the quintessence field and matter in a manner equivalent to the
interaction terms found in warm inflation, where the inflaton interacts with radiation. By
proposing the set of background equations together with parameterized dissipative terms
in a specific way, the dissipation term was radiation-related dominating during the inflationary period, thus leading to a warm inflation regime, while the matter-related dissipation
term dominating at late times. It was also possible to obtain the results related to the
evolution of the dissipation terms Qr, Qm,1 and Qm,2 together with the evolution equations. For the dynamics related to late times, we took into account the (x, y) plane. In
the (x, y) plane it was possible to have information about the behavior of the trajectories
that pass through the accelerated region, which is important to study the late dynamics
of the system, where it is possible to know the capacity of the system to reach a regime
dominated by DE. Another analysis made in this dissertation was the stability of the
slow-roll conditions. The analysis of the dynamical system took place in different regimes,
in order to study the stability of the system in them.
Instituição: Universidade do Estado do Rio de Janeiro
Tipo do documento: Dissertação2023-06-22T00:00:00Z