Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.

Uma análise da dinâmica do pêndulo eletromecânico utilizando a teoria de pertubações

Pós-graduação em Matemática - IBILCE

Desenvolvimento de um método numérico para simular escoamentos viscoelásticos axissimétricos com superfícies livres: Modelo PTT

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Modelagem 1D e 2,5D de dados do método CSEM marinho em meios com anisotropia transversal inclinada

Neste trabalho apresentamos a solução do campo eletromagnético gerado por um dipolo elétrico horizontal em meios transversalmente isotrópicos com eixo de simetria vertical (TIV) e com eixo de simetria inclinado (TII). Para modelos unidimensionais, o campo eletromagnético foi obtido por duas metodologias distintas: (1) solução semi-analítica das equações de Maxwell com auxílio de potenciais vetores no caso TIV e (2) em modelos com anisotropia transversal inclinada o campo eletromagnético foi separado em primário e secundário, e então, o campo secundário foi calculado pelo método de elementos finitos no domínio (k_x, k_y, z) da transformada de Fourier. Para estruturas bidimensionais, foi aplicada a mesma metodologia usado nos modelos TII unidimensionais, onde o campo secundário foi calculado pelo método de elementos finitos no domínio (x, k_y, z), da transformada de Fourier, com a utilização de malhas não estruturadas para discretização dos modelos. Estas respostas foram usados para avaliar os efeitos da anisotropia elétrica nos dados CSEM marinho 1D e 2,5D.

Análise teórica do problema de Weaver da falha infinita, modo TE magnetotelúrico

É apresentada uma solução totalmente analítica do modelo da falha infinita para o modo TE magnetotelúrico, levando em conta a presença do ar, utilizando como base o trabalho de Sampaio apresentado em 1985, que apresenta uma solução parcialmente analítica e parcialmente numérica – solução híbrida. Naquela solução foram aplicadas oito condições de contorno, sendo que em quatro delas foram encontradas inconsistências matemáticas que foram dirimidas com alterações adequadas nas soluções propostas por Sampaio. Tais alterações propiciaram a chegarse à solução totalmente analítica aqui apresentada. A solução obtida foi comparada com a solução de Weaver, com a de Sampaio e com o resultado do método numérico dos elementos finitos para contrastes de resistividade iguais a 2, 10 e 50. A comparação da solução analítica, para o campo elétrico normalizado, com a solução de elementos finitos mostra que a solução analítica proporcionou resultados mais próximos, em comparação aos fornecidos por Weaver e por Sampaio. Este é um problema muito difícil, aberto para uma solução analítica definitiva. A solução apresentada aqui é, nesta direção, um grande passo.

Correspondence between the one-loop three-point vertex and the Y and Delta electric resistor networks

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F-4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F-4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F-4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Delta in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

Entanglement universality of two-qubit X-states

We demonstrate that for every two-qubit state there is a X-counterpart, i.e., a corresponding two-qubit X-state of same spectrum and entanglement, as measured by concurrence, negativity or relative entropy of entanglement. By parametrizing the set of two-qubit X-states and a family of unitary transformations that preserve the sparse structure of a two-qubit X-state density matrix, we obtain the parametric form of a unitary transformation that converts arbitrary two-qubit states into their X-counterparts. Moreover, we provide a semi-analytic prescription on how to set the parameters of this unitary transformation in order to preserve concurrence or negativity. We also explicitly construct a set of X-state density matrices, parametrized by their purity and concurrence, whose elements are in one-to-one correspondence with the points of the concurrence versus purity (CP) diagram for generic two-qubit states. (C) 2014 Elsevier Inc. All rights reserved.

Adsorção de polieletrólitos em superfícies opostamente carregadas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

Modeling the cosmological co-evolution of supermassive black holes and galaxies

In this Thesis, we investigate the cosmological co-evolution of supermassive black holes (BHs), Active Galactic Nuclei (AGN) and their hosting dark matter (DM) halos and galaxies, within the standard CDM scenario. We analyze both analytic, semi-analytic and hybrid techniques and use the most recent observational data available to constrain the assumptions underlying our models. First, we focus on very simple analytic models where the assembly of BHs is directly related to the merger history of DM haloes. For this purpose, we implement the two original analytic models of Wyithe & Loeb 2002 and Wyithe & Loeb 2003, compare their predictions to the AGN luminosity function and clustering data, and discuss possible modifications to the models that improve the match to the observation. Then we study more sophisticated semi-analytic models in which however the baryonic physics is neglected as well. Finally we improve the hybrid simulation of De Lucia & Blaizot 2007, adding new semi-analytical prescriptions to describe the BH mass accretion rate during each merger event and its conversion into radiation, and compare the derived BH scaling relations, fundamental plane and mass function, and the AGN luminosity function with observations. All our results support the following scenario: • The cosmological co-evolution of BHs, AGN and galaxies can be well described within the CDM model. • At redshifts z & 1, the evolution history of DM halo fully determines the overall properties of the BH and AGN populations. The AGN emission is triggered mainly by DM halo major mergers and, on average, AGN shine at their Eddington luminosity. • At redshifts z . 1, BH growth decouples from halo growth. Galaxy major mergers cannot constitute the only trigger to accretion episodes in this phase. • When a static hot halo has formed around a galaxy, a fraction of the hot gas continuously accretes onto the central BH, causing a low-energy “radio” activity at the galactic centre, which prevents significant gas cooling and thus limiting the mass of the central galaxies and quenching the star formation at late time. • The cold gas fraction accreted by BHs at high redshifts seems to be larger than at low redshifts.

EoR in alternative cosmological scenarios

The aim of this Thesis is to investigate the possibility that the observations related to the epoch of reionization can probe not only the evolution of the IGM state, but also the cosmological background in which this process occurs. In fact, the history of the IGM ionization is indeed affected by the evolution of the sources of ionizing photons that, under the assumption of a structure formation paradigm determined by the hierarchic growth of the matter uctuations, results strongly dependent on the characteristics of the background universe. For the purpose of our investigation, we have analysed the reionization history in innovative cosmological frameworks, still in agreement with the recent observational tests related to the SNIa and the CMB probes, comparing our results with the reionization scenario predicted by the commonly used LCDM cosmology. In particular, in this Thesis we have considered two different alternative universes. The first one is a at universe dominated at late epochs by a dynamic dark energy component, characterized by an equation of state evolving in time. The second cosmological framework we have assumed is a LCDM characterized by a primordial overdensity field having a non-Gaussian probability distribution. The reionization scenario have been investigated, in this Thesis, through semi-analytic approaches based on the hierarichic growth of the matter uctuations and on suitable assumptions concerning the ionization and the recombination of the IGM. We make predictions for the evolution and the distribution of the HII regions, and for the global features of reionization, that can be constrained by future observations. Finally, we brie y discuss the possible future prospects of this Thesis work.

Numerical studies of colloidal systems

The interplay of hydrodynamic and electrostatic forces is of great importance for the understanding of colloidal dispersions. Theoretical descriptions are often based on the so called standard electrokinetic model. This Mean Field approach combines the Stokes equation for the hydrodynamic flow field, the Poisson equation for electrostatics and a continuity equation describing the evolution of the ion concentration fields. In the first part of this thesis a new lattice method is presented in order to efficiently solve the set of non-linear equations for a charge-stabilized colloidal dispersion in the presence of an external electric field. Within this framework, the research is mainly focused on the calculation of the electrophoretic mobility. Since this transport coefficient is independent of the electric field only for small driving, the algorithm is based upon a linearization of the governing equations. The zeroth order is the well known Poisson-Boltzmann theory and the first order is a coupled set of linear equations. Furthermore, this set of equations is divided into several subproblems. A specialized solver for each subproblem is developed, and various tests and applications are discussed for every particular method. Finally, all solvers are combined in an iterative procedure and applied to several interesting questions, for example, the effect of the screening mechanism on the electrophoretic mobility or the charge dependence of the field-induced dipole moment and ion clouds surrounding a weakly charged sphere. In the second part a quantitative data analysis method is developed for a new experimental approach, known as "Total Internal Reflection Fluorescence Cross-Correlation Spectroscopy" (TIR-FCCS). The TIR-FCCS setup is an optical method using fluorescent colloidal particles to analyze the flow field close to a solid-fluid interface. The interpretation of the experimental results requires a theoretical model, which is usually the solution of a convection-diffusion equation. Since an analytic solution is not available due to the form of the flow field and the boundary conditions, an alternative numerical approach is presented. It is based on stochastic methods, i. e. a combination of a Brownian Dynamics algorithm and Monte Carlo techniques. Finally, experimental measurements for a hydrophilic surface are analyzed using this new numerical approach.

Biaxial extensional motion of an inertially driven radially expanding liquid sheet

We consider the inertially driven, time-dependent biaxial extensional motion of inviscid and viscous thinning liquid sheets. We present an analytic solution describing the base flow and examine its linear stability to varicose (symmetric) perturbations within the framework of a long-wave model where transient growth and long-time asymptotic stability are considered. The stability of the system is characterized in terms of the perturbation wavenumber, Weber number, and Reynolds number. We find that the isotropic nature of the base flow yields stability results that are identical for axisymmetric and general two-dimensional perturbations. Transient growth of short-wave perturbations at early to moderate times can have significant and lasting influence on the long-time sheet thickness. For finite Reynolds numbers, a radially expanding sheet is weakly unstable with bounded growth of all perturbations, whereas in the inviscid and Stokes flow limits sheets are unstable to perturbations in the short-wave limit.

Benefits of using a Wendland Kernel for free-surface flows

The aim of this paper Is lo discuss the influence of the selection of the interpolation kernel in the accuracy of the modeling of the internal viscous dissipation in Tree surface Hows, Simulations corresponding to a standing wave* for which an analytic solution available, are presented. Wendland and renormalized Gaussian kernels are considered. The differences in the flow pattern* and Internal dissipation mechanisms are documented for a range of Reynolds numbers. It is shown that the simulations with Wendland kernels replicate the dissipation mechanisms more accurately than those with a renormalized Gaussian kernel. Although some explanations are hinted we have Tailed to clarify which the core structural reasons for Mich differences are*

Frozen orbits for scientific missions using rotating tethers

We derive a semi-analytic formulation that permits to study the long-term dynamics of fast-rotating inert tethers around planetary satellites. Since space tethers are extensive bodies they generate non-keplerian gravitational forces which depend solely on their mass geometry and attitude, that can be exploited for controlling science orbits. We conclude that rotating tethers modify the geometry of frozen orbits, allowing for lower eccentricity frozen orbits for a wide range of orbital inclination, where the length of the tether becomes a new parameter that the mission analyst may use to shape frozen orbits to tighter operational constraints.