abstract: In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrödinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrödinger equation in R^n with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrödinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application. / Dissertation/Thesis / Ph.D. Applied Mathematics for the Life and Social Sciences 2011

The thesis consists of two parts, a theoretical part and an applied part, and in addition an Appendix. Except for a very short chapter in the applied part and the appendix we only present previously unknown results leading to a very concise style. In the theoretical part we study rates of decay for vector-valued functions and semigroups of operators depending on a real and positive variable. Under boundedness assumptions on the function/semigroup itself and under analytic extendability assumptions of its Laplace transform/resolvent across the imaginary axis we provide (almost) sharp rates of decay. Our results improve known results in this very active area of research. In the second part of the thesis we apply our results to specific examples (from the field of PDEs): local energy decay for wave equations on exterior domains, energy decay for damped wave equations on bounded domains and decay for a viscoelastic boundary damping model for sound waves. Many more examples can be found in the vast literature.

Accurate hydraulic conductivity values are necessary for understanding groundwater flow. Methods for estimating hydraulic conductivity show limitations because measured values vary several orders of magnitude in high permeability aquifers. Slug tests, while cost and time efficient, result in values lower than expected. It is proposed that underdamped behavior of water in a well is similar to mass on a damped spring; hence, models constructed to simulate behavior independent of aquifer effects might replicate some tests. The Poiseuille and Darcy-Weisbach models, and extensions of these models considering entry/exit effects, are applied to an aquifer-free laboratory test, and real wells. Aquifer-free laboratory tests are modeled well using both Poiseuille and Darcy-Weisbach models with entry/exit effects. The Poiseuille model for wells does not agree with observed data, possibly because of high Reynolds numbers. The Darcy-Weisbach model does agree with well data significantly better, although the friction factor relies on a single Reynolds number.

This work is aimed to creating a system for presentation of oscilations. The main part consist of electromagnetic damper, which properties are suitable for use in this system. In the first part are some conditions for design of damper body . In he second part are selected next parameters for electromagnetic damper and of the whole system by MATLAB / Simulink with iterative method. In last part is whole system analyzed and the results indicate next changes in the structure of the system.

Les actionneurs multi-axes sont de plus en plus prisés par les concepteurs de systèmes de nanopositionnement car ils permettent une réduction de l'espace occupé et de l'énergie consommée, une dextérité plus grande et une modularité avec peu de contraintes pour les applications. Certains de ces actionneurs et systèmes multi-axes sont cependant caractérisés par des oscillations mal-amorties qui compromettent de manière drastique leurs performances générales. Cette thèse concerne l'exploitation des techniques de commande en boucle-ouverte input-shaping classiquement utilisées pour amortir de manière sans capteurs les oscillations dans les systèmes mono-axes et les étendent pour qu'ils soient utilisables pour les systèmes multi-axes. Les résultats proposés dans la thèse qui sont des techniques input-shaping multivariables sont ensuite appliquées sur des actionneurs piézoélectriques classiquement dédiés pour les applications de nanopositionnement. / Multi-axes actuators are becoming more and more tempting to nanopositioning system designers as they enable them to save space, reduce energy consumption, increase dexterity and offer more modularity and freedom with fewer constraints to their applications. Some of these multi-axes actuators and systems exhibit however badly damped vibrations which strongly compromise their global performances. This thesis work exploits the advantages of the well-known feedforward input shaping techniques usually used to damp vibrations in monovariable (SISO) systems to present a new multivariable (MIMO) input shaping technique that can be used to damp vibrations in multi-axes systems. The approach that was used in this study is to extend a previous work that was done on multiple-input single-output (MISO) systems and generalize it for MIMO systems. The study demonstrates also the application of this newly developed technique on different piezoelectric actuators commonly used in nanopositioning systems.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21412号 / 理博第4432号 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 堤 誉志雄, 教授 泉 正己, 教授 上 正明 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The electrochemical behavior of nickel (Ni) in different concentrations of sulfuric acid (H2SO4) was studied via cyclic voltammetry (CV) over a range of potentials (0.0 V– 3.0 V) at room temperature. The presented work displays novel experiments where external forcing by a platinum (Pt) electrode changed the proton concentration at a Ni electrode surface in order to control the frequency and magnitude of periodic oscillations produced. When studying unique phenomena such as the Ni phenomena in this thesis, efficient, durable, and inexpensive technology is always beneficial. A coupled microelectrode array sensor or CMAS which has been used for over four decades to study pitting corrosion, crevice corrosion, intergranular corrosion, galvanic corrosion, and other heterogeneous electrochemical processes were fabricated in a novel, systematic, inexpensive, and time efficient process. The presented work shows how to make the CMAS and proved that they functioned properly.

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In the first part of this thesis, suitable function spaces for analysis of partial differ- ential equations in unbounded domains are introduced and studied. The results are then applied in the second part on semilinear wave equation in Rd with non- linear source term and nonlinear damping. The source term is supposed to be bounded by a polynomial function with a subcritical growth. The damping term is strictly monotone and satisfying a polynomial-like growth condition. Global existence is proved using finite speed of propagation. Dissipativity in locally uni- form spaces and the existence of a locally compact attractor are then obtained after additional conditions imposed on the damping term.