Diffusion processes provide a natural way of modelling a variety of physical and economic phenomena. It is often the case that one is unable to observe a diffusion process directly, and must instead rely on noisy observations that are discretely spaced in time. Given these discrete, noisy observations, one is faced with the task of inferring properties of the underlying diffusion process. For example, one might be interested in inferring the current state of the process given observations up to the present time (this is known as the filtering problem). Alternatively, one might wish to infer parameters governing the time evolution the diffusion process. In general, one cannot apply Bayes’ theorem directly, since the transition density of a general nonlinear diffusion is not computationally tractable. In this thesis, we investigate a novel method of simplifying the problem. The stochastic differential equation that describes the diffusion process is replaced with a simpler ordinary differential equation, which has a random driving noise that approximates Brownian motion. We show how one can exploit this approximation to improve on standard methods for inferring properties of nonlinear diffusion processes.

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Electronic Structure Theory has led to a variety of developments and applications. In the Nooijen group the focus is on the development and use of Coupled Cluster based approaches. Coupled Cluster is a very strong and accurate approach to the quantum mechanical problem. The research results presented in the thesis testify to the Similarity Transformed Equation of Motion Coupled Cluster (STEOM-CC) for being a very accurate and yet computationally inexpensive approach for excited states. This study reveals new features about STEOM and provides promise regarding future improvement in the methodology. STEOM can be used as the first step in the construction of the Vibronic model, which is a strong tool to move to paradigms beyond the Born-Oppenheimer approximation. Spin-Orbit Coupling (SOC) is a very important ingredient required to study relativistic phenomena and its quantum mechanical implementation for many body systems is not straightforward. The most widely used SOC operator in Chemical Physics is the Breit-Pauli operator, which requires employing non-trivial approximations to the Dirac equation to adapt the theory to many body systems. The integration of electronic structure approaches, Vibronic Coupling, and SOC is essential to study the phenomenon of intersystem crossing (transition between spin states) in fine detail. In this thesis a computational benchmark of STEOM is discussed, while the frameworks of Vibronic Coupling and Spin-Orbit Coupling (SOC) are considered on a theoretical level.

Ce travail répond à la question de l’identification de l'équation du mouvement à partir des mesures expérimentales. Les structures considérées ont soit une soit deux dimensions. La méthode présentée utilise les méthodes inverses locales qui se basent sur les mesures du champs vibratoire stationnaire. Ces méthodes sont indépendantes des conditions aux limites qui sont inconnues pour l'observateur. Deux méthodes de sélection des modèles sont utilisées pour choisir l'équation du mouvement la plus adaptée parmi un ensemble des modèles a priori. La méthode est appliquée a des nombreux cas expérimentaux. Trois problématiques sont traités: identification de la force axiale dans les poutres et membranes, identification de l'orthotropie de la plaque et identification d'un panel sandwich épais. / This works deals with a question of identification of the equation of motion based on experimental measurements. The considered structures are either one or two-dimensional plane structures. The developed methodology employs local inverse methods based on local steady-state vibration field and it is therefore independent of boundary conditions. Two different model selection techniques are used to select the most adapted equation of motion from a set of apriori candidate models. The method is applied to various experimental case studies as identification of axial force in beams and membranes, identification of plate orthotropy and identification of thick sandwich panel model.

Baseando-se em um sistema com um grau de liberdade, é apresentada neste trabalho a equação de movimento, bem como a sua resolução através das Transformadas de Fourier e da Transformada Rápida de Fourier (FFT). Através da análise da forma como são feitas as integrações nas transformadas, foram estudados e aplicados os ponderadores de Newton-Cotes na resolução da equação de movimento, de forma a aumentar substancialmente a precisão dos resultados em comparação com a forma convencional da Transformada de Fourier. / Based on a single degree of freedom model, this work shows the equation of motion, as well as its solution with the Fourier Transform and the Fast Fourier Transform (FFT). Through the analysis of the methods used in the Fourier Integral, the Newton-Cotes quadratures formulas were studied and applied for the solving of the equation of motion, in order to substantially increase the precision of the results in comparison to the usual Fourier Transform.

Electronic Structure Theory has led to a variety of developments and applications. In the Nooijen group the focus is on the development and use of Coupled Cluster based approaches. Coupled Cluster is a very strong and accurate approach to the quantum mechanical problem. The research results presented in the thesis testify to the Similarity Transformed Equation of Motion Coupled Cluster (STEOM-CC) for being a very accurate and yet computationally inexpensive approach for excited states. This study reveals new features about STEOM and provides promise regarding future improvement in the methodology. STEOM can be used as the first step in the construction of the Vibronic model, which is a strong tool to move to paradigms beyond the Born-Oppenheimer approximation. Spin-Orbit Coupling (SOC) is a very important ingredient required to study relativistic phenomena and its quantum mechanical implementation for many body systems is not straightforward. The most widely used SOC operator in Chemical Physics is the Breit-Pauli operator, which requires employing non-trivial approximations to the Dirac equation to adapt the theory to many body systems. The integration of electronic structure approaches, Vibronic Coupling, and SOC is essential to study the phenomenon of intersystem crossing (transition between spin states) in fine detail. In this thesis a computational benchmark of STEOM is discussed, while the frameworks of Vibronic Coupling and Spin-Orbit Coupling (SOC) are considered on a theoretical level.

In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space. / In der vorliegenden Arbeit wird eine diffentialgeometrische Formulierung der Elektroelastizitätstheorie entwickelt, die auch thermische und magnetische Einflüsse berücksichtigt. Hierbei wird die Bewegung von Körpern untersucht, die aus einem elastischen Material bestehen und sich durch mechanische Kräfte, Wärmezufuhr und den Einfluss eines äußeren elektromagnetischen Feldes verformen. Dazu werden physikalische Bilanzgleichungen (Massenerhaltung, Impuls-, Drehimpuls- und Energiebilanz) aufgestellt, um mit deren Hilfe eine Gleichung zu formulieren, die die Bewegung des Körpers während der Deformation beschreibt. Dabei werden sowohl der Körper als auch der umgebende Raum als Riemannsche Mannigfaltigkeiten modelliert, wobei zugelassen ist, dass der Körper eine geringere Dimension hat als der ihn umgebende Raum. Auf diese Weise kann man nicht nur - wie sonst üblich - die Deformation dreidimensionaler Körper im dreidimensionalen euklidischen Raum beschreiben, sondern auch die Deformation von Membranen und die Deformation innerhalb eines gekrümmten Raums. Weiterhin werden sogenannte konstitutive Gleichungen formuliert, die die Eigenschaften des verwendeten Materials kodieren. Die Energiebilanz ist eine skalare Gleichung und kann daher leicht auf Riemannschen Mannigfaltigkeiten formuliert werden. Es wird gezeigt, dass die Forderung der Invarianz der Energiebilanz unter der Wirkung von beliebigen Diffeomorphismen auf den umgebenden Raum bereits die restlichen Bilanzgleichungen impliziert. Das verallgemeinert ein Resultat von Marsden und Hughes, das nur für Körper anwendbar ist, die die selbe Dimension wie der umgebende Raum haben und keine elektromagnetischen Felder berücksichtigt. Üblicherweise wird in Arbeiten über Elektroelastizität die Entropieungleichung verwendet, um zu entscheiden, welche Deformationen physikalisch zulässig sind und welche nicht. Sie wird außerdem verwendet, um Einschränkungen für die möglichen Formen von konstitutiven Gleichungen, die das Material beschreiben, herzuleiten. Leider gehen die Meinungen über die physikalisch korrekte Formulierung der Entropieungleichung auseinander sobald elektromagnetische Felder beteiligt sind. Weiterhin ist unklar, wie die Entropieungleichung für den Fall einer Membran, die einem elektromagnetischen Feld ausgesetzt ist, formuliert werden muss. Daher zeigen wir, dass die Benutzung der Entropieungleichung ersetzt werden kann durch die Forderung, dass für einen gegebenen Prozess die Energiebilanz invariant ist unter der Wirkung eines beliebigen Diffeomorphimus' auf den umgebenden Raum und der linearen Reskalierung der Temperatur. Zum einen liefert diese Forderung die gewünschten Einschränkungen für die Form der konstitutiven Gleichungen, zum anderen benoetigt sie viel schwächere Annahmen als die übliche Argumentation mit der Entropieungleichung, die man in der Physikliteratur findet. Unser Resultat ist dabei wieder eine Verallgemeinerung eines Theorems von Marsden und Hughes, wobei es, so wie deren Resultat, nur für Körper gilt, die als offene Teilmengen des dreidimensionalen euklidischen Raums modelliert werden können.

Baseando-se em um sistema com um grau de liberdade, é apresentada neste trabalho a equação de movimento, bem como a sua resolução através das Transformadas de Fourier e da Transformada Rápida de Fourier (FFT). Através da análise da forma como são feitas as integrações nas transformadas, foram estudados e aplicados os ponderadores de Newton-Cotes na resolução da equação de movimento, de forma a aumentar substancialmente a precisão dos resultados em comparação com a forma convencional da Transformada de Fourier. / Based on a single degree of freedom model, this work shows the equation of motion, as well as its solution with the Fourier Transform and the Fast Fourier Transform (FFT). Through the analysis of the methods used in the Fourier Integral, the Newton-Cotes quadratures formulas were studied and applied for the solving of the equation of motion, in order to substantially increase the precision of the results in comparison to the usual Fourier Transform.

Thesis (Ph.D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains ix, 176 p.; also includes graphics. Includes bibliographical references (p. 172-176). Available online via OhioLINK's ETD Center

The current methodologies in body scanning diagnostic uses different simultaneous imaging modalities like Ultrasound (US), magnetic resonance imaging (MRI), single photon emission tomography (SPECT) and positron emission tomography (PET). The field requires combination of different modalities for effective use in clinical diagnostics. Such incorporation of different modalities has already been achieved. For example, PET-CT hybrid scanner is designed to acquire align functional and anatomical images and recently US-MRI scanner has successfully shown to improve diagnosis of prostate cancer. The non ionizing radiation hybrid US-MRI is of great interest in health care industry. Further these US and MRI modalities uses different contrast agents like micro-sized gas bubbles (MBs) encapsulated by surfactant for US and superparamagnetic nanoparticles for MRI imaging modalities to further enables new diagnostic opportunities and therapeutic applications. Recently in our 3MiCRON project, we have developed the multimodal contrast agent that could be supported for both US and MRI. This was achieved by coating the magnetic nanoparticles to the poly vinyl alcohol (PVA) surfactant shelled MBs. The nanoparticles in the shell effect the structure can alter the MBs performance as an ultrasound contrast agent. The present thesis is conducted to examine the acoustic and mechanical properties of such multimodal contrast agents. These multimodal contrast agents were prepared by coating the surface of PVA-shelled MBs by two following strategies: (1) The superparamagnetic iron oxide (Fe3O4) nano-particles (SPIONs) were chemically anchored to the surface of poly vinyl alcohol (PVA) shelled MBs namely MBs-chem and (2) in the second strategy the SPIONs were physical entrapped into the PVA shell while formation of PVA surface on the gas bubble were named as MBs-phys. To understand the scattering efficiency and viscoelastic properties of these modified agents, we investigated the backscattering power, attenuation coefficient and phase velocity measurements. Our acoustic experimental results indicate that both the modified MBs and non-modified plain PVA-shelled ultrasound contrast agents have the same echogenic response. The investigation of mechanical properties of modified MBs revealed that the attached SPIONs on the PVA shell has reduced the stiffness of MBs-chem shell, while, the SPIONs inside the shell has increased MBs-phys stiffness. As a result, MBs-chem exhibits soft shell behavior under ultrasound exposure than both MBs-phys. Finally, the images were obtained through the MRI investigations at the department of Radiology, Karolinksa Institute, has demonstrated that both MB types have enough magnetic susceptibility that further provides good detectability in vitro and in vivo. As an outlook, the modified magnetic gas bubbles, i.e. both MBs-chem and MBs-phys can be proposed as a potential contrast agent for both US and MR imaging and can be further utilized in potential therapeutic applications. / <p>QC 20131126</p>