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The size and conformational complexity of proteins and other large systems represent major challenges for today's methods of quantum chemistry.This thesis is centered around the development of new computational tools to gain molecular-level insight into electronic transitions in such systems. To meet this challenge, we focus on the polarizable embedding (PE) model, which takes advantage of the fact that many electronic transitions are localized to a smaller part of the entire system.This motivates a partitioning of the large system into two regions that are treated at different levels of theory:The smaller part directly involved in the electronic process is described using accurate quantum-chemical methods, while the effects of the rest of the system, the environment, are incorporated into the Hamiltonian of the quantum region in an effective manner. This thesis presents extensions of the PE model with theaim of expanding its range of applicability to describe electronic transitions in large molecular systemsin the optical and X-ray regions. The developments cover both improvements with regardto the quantum region as well as the embedding potential representing the environment.Regarding the former, a damped linear response formulation has been implemented to allow for calculations of absorption spectra of large molecular systems acrossthe entire frequency range. A special feature of this development is its abilityto address core excitations that are otherwise not easily accessible.Another important development presented in this thesis is the coupling of the PE model to a multi-configuration self-consistent-field description of the quantum region and its further combination with response theory. In essence, this extends the PE model to the study of electronic transitions in large systems that are prone to static correlation --- a situation that is frequently encountered in biological systems. In addition to the direct environmental effects on the electronic structure of the quantum region, another important component of the description of electronic transitions in large molecular systems is an accurate account of the indirect effects of the environment, i.e., the geometrical distortions in the quantum region imposed by the environment. In thisthesis we have taken the first step toward the inclusion of geometry distortions in the PE frameworkby formulating and implementing molecular gradients for the quantum region. To identify critical points related to the environment description, we perform a theoretical analysis of the PE model starting from a full quantum-mechanicaltreatment of a composite system. Based on this, we present strategies for an accurate yet efficient construction of the embedding potentialcovering both the calculation of ground state and transition properties. The accurate representation of the environment makes it possible to reduce the size of the quantum region without compromising the overall accuracy of the final results. This further enables use of highly accurate quantum-chemical methods despite their unfavorable scaling with the size of the system. Finally, some examples of applications will be presented to demonstrate how the PE model may be applied as a tool to gain insight into and rationalize the factors influencing electronic transitions in large molecular systems of increasing complexity. / <p>The dissertation was awarded the best PhD thesis prize 2016 by the Danish Academy of Natural Sciences.</p><p></p><p>QC 20170209</p>

Dans cette thèse nous considérons l’équation des ondes amorties vectorielle sur une variété riemannienne compacte, lisse et sans bord. L’amortisseur est ici une fonction lisse allant de la variété dans l’espace des matrices hermitiennes de taille n. Les solutions de cette équation sont donc à valeurs vectorielles. Nous commençons dans un premier temps par calculer le meilleur taux de décroissance exponentiel de l’énergie en fonction du terme d’amortissement. Ceci nous permet d’obtenir une condition nécessaire et suffisante la stabilisation forte de l’équation des ondes amorties vectorielle. Nous mettons aussi en évidence l’apparition d’un phénomène de sur-amortissement haute fréquence qui n’existait pas dans le cas scalaire. Dans un second temps nous nous intéressons à la répartition asymptotique des fréquences propres de l’équation des ondes amorties vectorielle. Nous démontrons que, à un sous ensemble de densité nulle près, l’ensemble des fréquences propres est contenu dans une bande parallèle à l’axe imaginaire. La largeur de cette bande est déterminée par les exposants de Lyapunov d’un système dynamique défini à partir du coefficient d’amortissement. / In this thesis we are considering the vectorial damped wave equation on a compact and smooth Riemannian manifold without boundary. The damping term is a smooth function from the manifold to the space of Hermitian matrices of size n. The solutions of this équation are thus vectorial. We start by computing the best exponential energy decay rate of the solutions in terms of the damping term. This allows us to deduce a sufficient and necessary condition for strong stabilization of the vectorial damped wave equation. We also show the appearance of a new phenomenon of high-frequency overdamping that did not exists in the scalar case. In the second half of the thesis we look at the asymptotic distribution of eigenfrequencies of the vectorial damped wave equation. Were show that, up to a null density subset, all the eigenfrequencies are in a strip parallel to the imaginary axis. The width of this strip is determined by the Lyapunov exponents of a dynamical system defined from the damping term.

Il s'agit de déterminer l'influence d'une rotation solide sur la structure de la turbulence homogène incompressible. Les résultats du modèle spectral EDQNM étant probants en turbulence purement isotrope, la discrétisation spatiale devient un facteur limitant dans le cas anisotrope. Dans le cas où le nombre de Rossby est faible, un développement asymptotique en temps est possible. Le rôle joué par les surfaces résonantes étant dominant, le nouveau modèle conduit à une équation intégro-différentielle fermée pour l'énergie spectrale. Par un traitement numérique précis, un code parallélisé donne des résultats quantitatifs. Il apparaît que l'énergie se concentre avec le temps vers le plan perpendiculaire au vecteur rotation. De plus, le spectre intégré suit une loi de pente -3 dans la zone inertielle, sans que cela soit dû aux seuls vecteurs d'ondes horizontaux. Il n'y a donc pas de vraie bidimensionnalisation, mais les vecteurs proches du plan horizontal ont une dynamique spécifique.

Rubber like materials find wide applications in damping treatment of structures, vibration isolations and they appear prominently in the form of hoses in many structures such as aircraft engines. The study reported in this thesis addresses a few issues in computational modeling of vibration of structures with some of its components made up of rubber like materials. Specifically, the study explores the use of fractional derivatives in representing the constitutive laws of such material and focuses its attention on problems of parameter identification in linear time invariant systems with fractional order damping models. The thesis is divided into four chapters and two annexures. A review of literature related to mathematical modeling of damping with emphasis on fractional order derivative models is presented in chapter 1. The review covers lternatives available for modeling energy dissipation that include viscous, structural and hybrid damping models. The advantages of using fractional order derivative models in this context is pointed out and papers dealing with solution of differential equations with fractional order derivatives are reviewed. Issues related to finite element modeling and random vibration analysis of systems with fractional order damping models are also covered. The review recognizes the problems of system parameter identification based on inverse eigensensitivity and inverse FRF sensitivity as problems requiring further research. The problem of determination of derivatives of eigensolutions and FRF-s with respect to system parameters of linear time invariant systems with fractional order damping models is considered in chapter 2. The eigensolutions here are obtained as solutions of a generalized asymmetric eigenvalue problem. The order of system matrices here depends upon the mechanical degrees of freedom and also somewhat artificially on the fractional order of the derivative terms. The formulary for first and second order eigenderivatives are developed taking account of these features. This derivation also takes into account the various orthogonality relations satisfied by the complex valued eigenvectors. The system FRF-s are obtained by a straight forward inversion of the system dynamic stiffness matrix and also by using a series solution in terms of system eigensolutions. As might be expected, the two solutions lead to identical results. The first and the second order derivatives of FRF-s are obtained based on system dynamic matrix and without taking recourse to modal summation. Numerical examples that bring out various facets of eigensolutions, FRF-s and their sensitivities are presented with reference to single and multi degree freedom systems. The application sensitivity analysis developed in chapter 2 to problems of system parameter identification is considered in chapter 3. Methods based on inverse eigensensitivity and inverse FRF sensitivity are outlined. The scope of these methods cover first and second order analyses and applications to single and multi degree freedom systems. While most illustrations are based on synthetic measurement data, limited efforts are also made to implement the identification methods using laboratory measurement data. The experimental work has involved the measurement of FRF-s on a system consisting of two steel tubes connected by a rubber hose. The two system identification methods are shown to perform well especially when information on second order sensitivity are included in the analysis. The method based on inverse eigensolution is shown to become increasingly unwieldy to apply as the order of the system matrices increases while the FRF based method does not suffer from this drawback. The FRF based method also has the advantage that the prior knowledge of order of fractional order derivative terms is not needed in its implementation while such knowledge is assumed in the method based on eigensolutions. While the methods are shown to perform satisfactorily when synthetic measurement data is used, their success is not uniformly good when laboratory measurement data are employed. Chapter 4 presents a summary of contributions made in the thesis and also enlists a few suggestions for further research. Annexure I provides a précis of elementary notion of fractional order derivatives and integrals. A case study on finite element analysis of aircraft engine component made up of metallic and rubber materials is outlined in Annexure II and the study points towards possible advantages of using fractional order damping models in the study of such structures.

Spectroscopic techniques allow for studies of materials and organisms on the atomic and molecular level. Examples of such techniques are nuclear magnetic resonance (NMR) spectroscopy—one of the principal techniques to obtain physical, chemical, electronic and structural information about molecules—and magnetic resonance imaging (MRI)—an important medical imaging technique for, e.g., visualization of the internal structure of the human body. The less well-known spectroscopic technique of nuclear quadrupole resonance (NQR) is related to NMR and MRI but with the difference that no external magnetic field is needed. NQR has found applications in, e.g., detection of explosives and narcotics. The first part of this thesis is focused on detection and identification of solid and liquid explosives using both NQR and NMR data. Methods allowing for uncertainties in the assumed signal amplitudes are proposed, as well as methods for estimation of model parameters that allow for non-uniform sampling of the data. The second part treats two medical applications. Firstly, new, fast methods for parameter estimation in MRI data are presented. MRI can be used for, e.g., the diagnosis of anomalies in the skin or in the brain. The presented methods allow for a significant decrease in computational complexity without loss in performance. Secondly, the estimation of blood flow velo-city using medical ultrasound scanners is addressed. Information about anomalies in the blood flow dynamics is an important tool for the diagnosis of, for example, stenosis and atherosclerosis. The presented methods make no assumption on the sampling schemes, allowing for duplex mode transmissions where B-mode images are interleaved with the Doppler emissions.

L’identité de Ward est une relation qui permet d’identifier unmilieu de propagation linéaire dissipatif, c'est-à-dire d'estimer des paramètres qui le caractérisent. Dans les travaux exposés, cette identité est utilisée pour proposer de nouveaux modèles d’observation caractérisant un contexte d’estimation qualifié de passif : les sources qui excitent le système ne sont pas contrôlées par l’utilisateur. La théorie de l’estimation/détection dans ce contexte est étudiée et des analyses de performances sont menées sur divers estimateurs. La portée applicative des méthodes proposées concerne le domaine du Structural Health Monitoring (SHM), c’est-à-dire le suivi de l’état de santé desbâtiment, des ponts... L'approche est développée pour la modalité acoustique aux fréquences audibles, cette dernière s'avérant complémentaire des techniques de l’état de l’art du SHM et permettant entre autre, d’accéder à des paramètres structuraux et géométriques. Divers scénarios sont illustrés par la mise en oeuvre expérimentale des algorithmes développés et adaptés à des contraintes de calculs embarqués sur un réseau de capteurs autonome. / Ward identity is a relationship that enables damped linear system identification, ie the estimation its caracteristic properties. This identity is used to provide new observation models that are available in an estimation context where sources are uncontrolled by the user. An estimation and detection theory is derived from these models and various performances studies areconducted for several estimators. The reach of the proposed methods is extended to Structural Health Monitoring (SHM), that aims at measuring and tracking the health of buildings, such as a bridge or a sky-scraper for instance. The acoustic modality is chosen as it provides complementary parameters estimation to the state of the art in SHM, such as structural and geometrical parameters recovery. Some scenarios are experimentally illustrated by using the developed algorithms, adapted to fit the constrains set by embedded computation on anautonomous sensor network.

This thesis explores and expands upon theoretical means of quantifying a number of nonlinear spectroscopies, including two-photon absorption, resonant-inelastic x-ray scattering, Jones birefringence, and magnetic circular dichroism. On top of that, detailed information is given for the derivation and program implementation of damped cubic response functions. Complex-valued cubic response functions have been implemented in the quantum chemistry package DALTON, based on working equations formulated for an approximate-state wave function. An assessment of the implementation, such that for small frequencies the second-order hyperpolarizability should behave according to an analytic function that depends quadratically on the optical frequencies. It is demonstrated how two-photon absorption (TPA) can be described either through second-order transition moments or via the damped cubic response function. A few calculated TPA profiles are produced for a set of smaller molecules, in order to display the capability of the cubic response function in the x-ray frequency region. Resonance-inelastic x-ray scattering (RIXS) is explored in a similar manner as two-photon absorption. It is shown how the second-order hyperpolarizability can represent RIXS in the limit of intermediate-state and final-state resonances. Complications emerging from the complex dispersion of the hyperpolarizability are discussed. Moreover, linear birefringences, with focus on the Jones birefringence, are investigated for noble gases, monosubstituted benzenes, furan homologues, and a pure acetonitrile liquid. A linear relation between the Jones birefringence and the empirical para-Hammett constant as well as the permanent electric dipole moment is presented. Estimations of three linear birefringences --- Kerr, Cotton--Mouton, and Jones ---are obtained by averaging over a set of liquid snapshots. The Jones effect for acetonitrile turns out to be unusually large inmparison to the other two investigated linear birefringences. The final chapter of the thesis investigates magnetically induced circular dichroism (MCD). A question regarding relative stability of the first set of excited states for DNA-related molecular systems is resolved through MCD by exploiting the signed nature of circular dichroisms. Furthermore, to what extent solvent contributions affect MCD spectra is explored. The effect on uracil MCD spectrum due to thionation is studied, for which the degree of redshifting for systems 2-thiouracil and 4-thiouracil can be seen to be addative as compared to the 2,4-dithiouracil system. / <p>QC 20171129</p>

This thesis deals with mathematical modeling of multiphysics FSI (fluid-structure interaction) problem, describing mutual interaction of pressure pulsations and vibrations of indirect pipe in a 2D region. Firstly, physical partial differential equations are derived separately for both media, which are in turn coupled and solved analytically. Results of mentioned models include natural frequency values, amplitude-frequency characteristics and both natural and driven damped oscillations of pipe and liquid.

In this thesis, we are interested in damped wave models with time-dependent propagation speed and time-dependent damping term both having a time-dependent oscillation term. The main goal of this thesis is to understand the influence of strong time-dependent oscillations on Sobolev solutions to the linear models and consequently, to the semilinear models. Especially, due to the deteriorating influence of oscillations on solutions, a stabilization condition and higher-order regularity of the time-dependent coefficients may compensate 'bad behaviors' arising from oscillations.:1. Introduction 2. The influence of oscillations on linear damped wave equation with time-dependent coefficients 3. Global in time existence results for damped wave models with power nonlinearity 4. Global in time existence results for damped wave models with different power nonlinearities 5. Lp-Lq estimates for wave equations with strong time-dependent oscillations 6. Further research topics A. Basic tools B. List of symbols and abbreviations Bibliography