The orbit of Phobos exhibits an along-track acceleration, which suggests energy dissipation in the Mars-Phobos system. We hypothesize that the inferred dissipation occurs within Mars. We explore the response of a layered, incompressible Maxwell viscoelastic Mars to tidal forcing by Phobos using normal mode relaxation theory. Our results elucidate the general behavior of a tidally forced viscoelastic body, and have implications for the viscoelastic structure of Mars. We find the real and imaginary part of the degree-two tidal Love number for Mars to be 0.168 and -9.32x10^−4 respectively. Models which satisfy these and other constraints have either: a fluid core with radius 2040 km and density 5410 kg/m^3; or an elastic inner core with radius 1200 km and density 6700 kg/m^3, along with a fluid outer core with thickness 850 km and density 4850 kg/m^3. These findings support previous hypotheses that Mars has at least a fluid outer core.

The orbit of Phobos exhibits an along-track acceleration, which suggests energy dissipation in the Mars-Phobos system. We hypothesize that the inferred dissipation occurs within Mars. We explore the response of a layered, incompressible Maxwell viscoelastic Mars to tidal forcing by Phobos using normal mode relaxation theory. Our results elucidate the general behavior of a tidally forced viscoelastic body, and have implications for the viscoelastic structure of Mars. We find the real and imaginary part of the degree-two tidal Love number for Mars to be 0.168 and -9.32x10^−4 respectively. Models which satisfy these and other constraints have either: a fluid core with radius 2040 km and density 5410 kg/m^3; or an elastic inner core with radius 1200 km and density 6700 kg/m^3, along with a fluid outer core with thickness 850 km and density 4850 kg/m^3. These findings support previous hypotheses that Mars has at least a fluid outer core.

BEZERRA, Italo Pereira. Auto-organização de aglomerados finitos de dipolos magnéticos carregados. 2009. 65 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2009. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-05-04T18:22:34Z No. of bitstreams: 1 2009_dis_ipbezerra.pdf: 8023171 bytes, checksum: e47ba0b7e87905fb3b10ff887cc2f1f8 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-05-07T16:51:22Z (GMT) No. of bitstreams: 1 2009_dis_ipbezerra.pdf: 8023171 bytes, checksum: e47ba0b7e87905fb3b10ff887cc2f1f8 (MD5) / Made available in DSpace on 2015-05-07T16:51:22Z (GMT). No. of bitstreams: 1 2009_dis_ipbezerra.pdf: 8023171 bytes, checksum: e47ba0b7e87905fb3b10ff887cc2f1f8 (MD5) Previous issue date: 2009 / It is studied at this thesis a two-dimensional cluster of magnetic particles, with surface charge, confined by a circular parabolic potential. The particles have the same magnitude of magnetic dipole moment and the same amount and sign of surface charge. The goal of the present study is the characterization of the ground state configurations and the normal mode spectra of the cluster. The numerical study of the system is based on the Monte Carlo simulation technique, using the Metropolis Algorithm. It was also used the called Newton Method technique to reach the ground state configurations . The present study is divided in two parts: i) In the first one, the dependence of the equilibrium configurations and the normal modes is analyzed considering the presence or not of a external magnetic field. The magnetic dipole moment is taken as constant. ii) In the second one, the surface charge and the magnetic dipole moment are taken as constant, and the ground state configurations and the normal modes are studied as function the the external magnetic field intensity. At this part, it is also calculated the magnetization of the system as function of the external magnetic field. It was observed a great number of different ground state configurations, like concentric rings, and chains. The vibrational normal mode frequencies spectra was obtained by using the harmonic approximation. Due to the non-spatial symmetry of the magnetic dipole interaction, the normal modes must show an extra rotational component. It can be noted that due to surface charge of the particles the frequencies spectra can present elevated variation on the intensity. It can also be noted that some properties of the first case system also occurs on the second case system, and these properties are independent of the applied magnetic field, and in the second case system it can be noted that there are less different ground state configurations as compared with the first one. / Estuda-se, neste trabalho, aglomerados bidimensionais de partículas dipolares magnéticas, com carga elétrica superficial, confinadas em um potencial parabólico circular. As partículas possuem mesmo módulo de momento de dipolo magnético, assim como mesmos módulo e sinal de carga superficial. O objetivo do presente estudo é a caracterização das configurações do estado fundamental e do espectro dos modos normais do aglomerado. O sistema é estudado numericamente através de simulações Monte Carlo, utilizando o algoritmo de Metropolis. Utilizou-se ainda o chamado Método de Newton Modificado para auxiliar a obtenção das configurações de mínima energia. O estudo é dividido em duas partes: i) Na primeira, a dependência das configurações de equilíbrio e modos normais é analisada em função da carga superficial, na presença e ausência de campo magnético externo, considerando-se o momento de dipolo magnético constante. ii) Na segunda, a carga superficial e o momento de dipolo magnético são fixados e as configurações de equilíbrio e os modos normais são estudados em função da intensidade do campo magnético externo. Nesta parte, calcula-se ainda a magnetização do sistema em função do campo externo. O espectro de frequências dos modos normais de vibração foram obtidos através da técnica de aproximação harmônica. Devido à não-simetria espacial da interação magnética dipolar, os modos normais devem apresentar um componente extra de rotação. Observa-se que para um intervalo característico da carga superficial das partículas, o espectro de frequências sofre uma grande variação de intensidade. Observa-se que no caso dependente da carga, o sistema apresenta características que independem do campo magnético aplicado. Observa-se, no caso dependente do campo aplicado, uma menor variedade de configurações de equilíbrio deste tipo de sistema em relação ao dependente da carga.

There is a need for a nonlinear flutter analysis method capable of predicting limit cycle oscillation in aeroelastic systems. A review is conducted of analysis methods and experiments that have attempted to better understand and model limit cycle oscillation (LCO). The recently developed method of nonlinear normal modes (NNM) is investigated for LCO calculation. Nonlinear normal modes were used to analyze a spring-mass-damper system with nonlinear damping and stiffness to demonstrate the ability and limitations of the method to identify limit cycle oscillation. The nonlinear normal modes method was then applied to an aeroelastic model of a pitch-plunge airfoil with nonlinear pitch stiffness and quasi-steady aerodynamics. The asymptotic coefficient solution method successfully captured LCO at a low relative velocity. LCO was also successfully modeled for the same airfoil with an unsteady aerodynamics model with the use of a first order formulation of NNM. A linear beam model of the Goland wing with a nonlinear aerodynamic model was also studied. LCO was successfully modeled using various numbers of assumed modes for the beam. The concept of modal truncation was shown to extend to NNM. The modal coefficients were shown to identify the importance of each mode to the solution and give insight into the physical nature of the motion. The quasi-steady airfoil model was used to conduct a study on the effect of the nonlinear normal mode's master coordinate. The pitch degree of freedom, plunge degree of freedom, both linear structural mode shapes with apparent mass, and the linear flutter mode were all used as master coordinates. The master coordinates were found to have a significant influence on the accuracy of the solution and the linear flutter mode was identified as the preferred option. Galerkin and collocation coefficient solution methods were used to improve the results of the asymptotic solution method. The Galerkin method reduced the error of the solution if the correct region of integration was selected, but had very high computational cost. The collocation method improved the accuracy of the solution significantly. The computational time was low and a simple convergent iteration method was found. Thus, the collocation method was found to be the preferred method of solving for the modal coefficients. / Ph. D.

In Chapter 2, we consider the hydrostatic equilibrium figure of a rotating earth model with arbitrary radial density profile. We derive an exact non-linear partial differential equation describing the equilibrium figure. Perturbation theory is used to obtain approximate forms of this equation, and we show that the first-order theory is equivalent to Clairaut's equation. In Chapter 3, a method for parametrizing the possible equilibrium stress fields of a laterally heterogeneous earth model is described. In this method a solution of the equilibrium equations is first found that satisfies some desirable physical property. All other solutions can be written as the sum of this equilibrium stress field and a divergence-free stress tensor field whose boundary tractions vanish. In Chapter 4, we consider the minor vector method for the stable numerical solution of systems of linear ordinary differential equations. Results are presented for the application of the method to the calculation of seismic displacement fields in spherically symmetric, self-gravitating earth models. In Chapter 5, we present a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. Numerical tests are presented to demonstrate the validity and effectiveness of this method for performing large mode coupling calculations. In Chapter 6, we consider the theoretical basis for the viscoelastic normal mode method which is used in studies of seismic wave propagation, post-glacial rebound, and post-seismic deformation. We show how the time-domain solution to the viscoelastodynamic equation can be written as a normal mode sum in a rigorous manner.

La perturbation d’un système peut donner lieu à de la propagation d’onde. Une façon classique d’appréhender ce phénomène est de rechercher les modes propres de vibration du milieu. Mathématiquement, trouver ces modes consiste à rechercher les valeurs et fonctions propres de l’opérateur de propagation. Cependant, d’un point de vue numérique, l’opération peut s’avérer coûteuse car les matrices peuvent avoir de très grandes tailles. En outre, dans la plupart des applications, des incertitudes sont inévitablement associées à notre modèle. La question se pose alors de savoir s’il faut attribuer d’importantes ressources de calcul pour une simulation dont la précision du résultat n’est pas assurée. Nous proposons dans cette thèse une démarche qui permet à la fois de mieux comprendre l’influence des incertitudes sur la propagation et de réduire considérablement les coûts de calcul pour la propagation des infrasons dans l’atmosphère. L’idée principale est que tous les modes n’ont pas la même importance et souvent, seule une poignée d’entre eux suffit à décrire le phénomène sans perte notable de précision. Ces modes s’avèrent être ceux qui sont les plus sensibles aux perturbations atmosphériques. Plus précisément, l’analyse de sensibilité permet d’identifier les structures de l’atmosphère les plus influentes, les groupes de modes qui leur sont associés et les parties du signal infrasonore qui leur correspondent. Ces groupes de modes peuvent être spécifiquement ciblés dans un calcul de spectre au moyen de techniques de projection sur des sous-espace de Krylov, ce qui implique un gain important en coût de calcul. Cette méthode de réduction de modèle peut être appliquée dans un cadre statistique et l’estimation de l’espérance et de la variance du résultat s’effectue là aussi sans perte notable de précision et avec un coût réduit. / The perturbation of a system can give rise to wave propagation. A classical approach to understand this phenomenon is to look for natural modes of vibration of the medium. Mathematically, finding these modes requires to seek the eigenvalues and eigenfunctions of the propagation operator. However, from a numerical point of view, the operation can be costly because the matrices can be of very large size. Furthermore, in most applications, uncertainties are inevitably associated with our model. The question then arises as to whether we should allocate significant computational resources for simulation while the accuracy of the result is not guaranteed. We propose in this thesis an approach that allows both a better understanding of the influence of uncertainties on the propagation and a significant decrease of computational costs for infrasound propagation in the atmosphere. The main idea is that all modes do not have the same importance and only a few of them is often sufficient to account for the phenomenon without a significant loss of accuracy. These modes appear to be those which are most sensitive to atmospheric disturbances. Specifically, a sensitivity analysis is used to identify the most influential structures of the atmosphere, the associated groups of modes and their associated parts of the infrasound signal. These groups of modes can be specifically targeted in a spectrum calculation with the projection of the operator onto Krylov subspaces, that allows a significant decrease of the computational cost. This method of model reduction can be applied in a statistical framework as well and estimations of the expectation and the variance of the results are carried out without a significant loss of accuracy and still with a low cost.

Buracos negros têm as suas oscilações próprias, que são chamadas modos quase-normais. As oscilações próprias de buracos negros astrofísicos podem ser observadas no futuro mais próximo com a ajuda de detectores de ondas gravitacionais. Os modos quase-normais são também muito importantes no contexto de teste da estabilidade de objetos negros, da correspondência anti-deSitter/ Teoria Campos Conformes (AdS/CFT) e nas teorias em dimensões mais altas, como os cenários de mundo-brana e teoria das cordas. Esta tese revê um numero de trabalhos, que fornecem um estudo completo do espectro quase normal de grande classe de buracos negros em quatro e mais altas dimensões para campos de vários spins e perturbações gravitacionais. Foi estudada numericamente a dependência dos modos quase-normais sobre um numero de fatores, como a presença da constante cosmológica, o parâmetro de Gauss-Bonnet ou o a éter no espaco-tempo, a dependência do espectro sobre os parâmetros do buraco negro e os campos em consideração. Pela analise do espectro quase-normal, foi estudada a estabilidade de buracos negros Reissner-Nordstrom-de Sitter em dimensões mais altas, buracos negros de Kaluza-Klein com horizontes esmagados, buracos negros de Gauss-Bonnet e cordas negras. Uma atenção especial foi prestada à evolução de campos massivos no contexto de vários buracos negros. Foram considerados os seus toques quase-normais e as caudas de tempo tardio. Alem disso, foram apresentadas duas novas técnicas numéricas: uma generalização da melhora de Nollert para do método de Frobenius para problemas em dimensões mais altas e um método qualitativamente novo, que permite calcular freqüências quase-normais de buracos negros, cujas métricas não são conhecidas analiticamente. Também foi considerada uma possibilidade da construção do análogo acústico do buraco negro de Schwarzschild. / Black holes have their proper oscillations, which are called the quasi-normal modes. The proper oscillations of astrophysical black holes can be observed in the nearest future with the help of gravitational wave detectors. Quasi-normal modes are also very important in the context of testing of the stability of black objects, the anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence and in higher dimensional theories, such as the brane-world scenarios and string theory. This dissertation reviews a number of works, which provide a thorough study of the quasi-normal spectrum of a wide class of black holes in four and higher dimensions for fields of various spin and gravitational perturbations. We have studied numerically the dependance of the quasi-normal modes on a number of factors, such as the presence of the cosmological constant, the Gauss-Bonnet parameter or the aether in the space-time, the dependance of the spectrum on parameters of the black hole and fields under consideration. By the analysis of the quasi-normal spectrum, we have studied the stability of higher dimensional Reissner-Nordstr¨om-de Sitter black holes, Kaluza-Klein black holes with squashed horizons, Gauss-Bonnet black holes and black strings. Special attention is paid to the evolution of massive fields in the background of various black holes. We have considered their quasi-normal ringing and the late-time tails. In addition, we present two new numerical techniques: a generalisation of the Nollert improvement of the Frobenius method for higher dimensional problems and a qualitatively new method, which allows to calculate quasi-normal frequencies for black holes, which metrics are not known analytically. Also we considered a possibility of construction of the acoustic analogue of the Schwarzschild black hole.

Estudamos a evolução temporal de perturbações escalares na vizinhança de uma estrela com densidade uniforme que colapsa em um buraco negro. O trabalho começa com um estudo básico de gravitação e modos quasi-normais. O objetivo principal é resolver a equação de Klein-Gordon sem massa para a perturbação escalar, cuja solução depende de métodos numéricos. Com este objetivo, tratamos os aspectos teóricos de buracos negros e estrelas a partir da solução prevista pela Relatividade Geral para um buraco negro, estrelas com densidade uniforme e estrelas em colapso. Estudamos também uma maneira de reduzirmos a Equação de Klein-Gordon para uma forma conveniente de ser integrada, assim como os métodos numéricos necessários para resolver essa equação. Encontramos soluções para os modos variando a massa M, o raio inicial R e o rótulo do momento angular l. Essas soluções são irregulares em muitas situações, mas em geral elas são crescentes, de acordo com o comportamente observado de explosões de Supernovas. / This work is a study on the time evolution of scalar perturbations around a star collapsing to a black hole. It starts with a basic study of gravitation and quasi-normal modes. The aim is to derive the solution of the massless Klein-Gordon equation, that depends on numerical methods. Aiming at this goal, we studied theoretical aspects of stars, black holes and gravitational collapse. The methods include coordinate substitutions to modify the Klein-Gordon equation to a simple form. We also studied numerical methods for partial differential equations. Solutions of the quasi-normal modes were found with different values of M, R and l. The solutions are irregular in several situations, but some of them display increasing modes, that could be explained by the explosive behavior of Supernovas.

Les séismes de grande magnitude (MW > 7) et les tsunamis associés induisent des perturbations qui peuvent être détectées dans l’atmosphère et l’ionosphère à partir des mesures TEC (contenu total en électron). Dans cette thèse, J’étudie la possibilité d’utiliser ce signal ionosphérique afin de compléter le système de surveillance et d’alerte aux tsunamis. Ainsi, j’étudie le couplage entre la Terre solide, l’océan, l’atmosphère. Je démontre en particulier que seule la fréquence à 1.5 mHz entre les modes de tsunami et les modes de gravité atmosphériques peut être détectée via l’ionosphère et met en évidence que l’efficacité du couplage océan/atmosphère est sensible à la profondeur de l’océan et l’heure locale. Ces développements ont permis de réaliser la modélisation complète de la signature ionosphérique de 3 tsunamis d’amplitude 2, 3 et 60 cm en plein océan : respectivement le tsunami d’Haida Gwaii en 2012 et le tsunami des Kouriles en 2006 en champ lointain et le tsunami de Tohoku 2011 en champ plus proche. Enfin, nous avons démontré que l’amplitude crête à crête de la hauteur du tsunami inversée reconstruit avec moins de 20 % d’erreur l’amplitude mesurée par une bouée DART dans ces trois cas / Large earthquake (MW > 7) and tsunamis are known to induce perturbations which can be detected in the atmosphere and ionosphere using total electron content (TEC) measurements. In this thesis, I first investigated on the possibility of using these ionospheric signals in order to complete the tsunami monitoring and warning system. Thus, I study the coupling between the solid Earth, the ocean, the atmosphere. I demonstrate that only the resonance at 1.5 mHz between the tsunami modes and the atmospheric gravity modes can be detected through ionosphere and highlight the fact that the efficiency of the coupling ocean/atmosphere is sensitive to ocean depth and local time. These developments enables the complete modelling of the ionospheric signature of 3 tsunami with an amplitude of 2, 3 and 60cm in deep ocean: the 2012 Haida Gwaii and the 2006 Kuril tsunami in far field and the 2011 Tohoku tsunami in closer field respectively. Finally, we demonstrated that the peak-to- peak amplitude of the height of the inverted tsunami reconstructs with less than 20% error the amplitude measured by a DART buoy in these three cases

Orientador: Marcos Roberto de Mattos Fontes / Resumo: Acidentes ofídicos são considerados um problema de saúde pública global, dada sua alta ocorrência de mortes, onde alguns casos resultam em sequelas irreparáveis, deixando o indivíduo desabilitado por toda a vida. Somente no Brasil, em média 20 mil mortes ao ano são registradas. Desta forma, alguns pesquisadores têm buscado estudar a estrutura-função de componentes dos venenos de serpentes peçonhentas à fim de desenvolver alternativas terapêuticas para esse problema de grande interesse médico. Um dos componentes que tem recebido atenção nas últimas décadas é a BthTX-I, uma proteína PLA2s-homóloga não catalítica, devido seu efeitos farmacológico notadamente miotóxico. Embora diversas técnicas tenham sido empregadas na compreensão do mecanismo de ação dessas proteínas, o conhecimento nessa área permanece controverso, tornando-se necessário a continuidade de estudos. O estudo estrutural e computacional de proteínas constitui uma alternativa viável para identificar as várias conformações de uma dada proteína, bem como seu comportamento dinâmico. Sendo assim, o presente trabalho buscou aplicar métodos computacionais, como simulação de MD, análise de Modos Normais (NM) e Dinâmica Molecular excitada por Modos Normais (MDeNM) à BthTX-I em pH ácido ou básico e nativa ou em complexo com o α-tocoferol – molécula tida como ativadora alostérica – na descrição do seu espaço conformacional, buscando compreender os aspectos estruturais do seu mecanismo de ação. Além disso, foram empregadas té... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Ophidian accidents constitute a global public health problem due its high mortality, with some cases leading to permanent sequels. In Brazil, around 20 thousand deaths are registered. Therefore, researchers have been studying the snake venom composition in order to develop therapeutic alternatives to this medical problem. Some components from snake venom are highlighted in the past decades, as BthTX-I, a non-catalytic PLA2s-homologous protein, due its many pharmacological effects, notably myotoxic. Although many techniques have been employed to better understand the molecular mechanism of action for these proteins, this knowledge remains controversial, emphasizing the need to progress this field. The structural and computational study of proteins is a valuable tool to access the various conformations of a given protein, as well its dynamical behavior. Thus, the present work applied computational methods as MD, Normal Modes (NM) analysis and Molecular Dynamics with excited Normal Modes (MDeNM) to BthTX-I in acidic or basic pH and unbound or bound to α-tocopherol – a molecule identified as an allosteric activator – in order to describe the conformational space of this protein and determine the structural aspects of its mechanism of action. Further, biophysical experiments as Dynamic Light Scattering (DLS) were employed in order to comprehend the oligomeric form of BthTX-I with or without α-tocopherol. MD simulations showed that dimeric form of BthTX-I is stable when in neutral/... (Complete abstract click electronic access below) / Doutor