[EN] At present, different methods for magnetostatic force densities in a continuous medium are used. Some of them are based on models of interaction of matter with an external field and others are derived from Maxwell's tensors in matter. All of these densities are different. Current models of magnetomechanical interactions are conditioned by the choice of one of these densities. In this dissertation a new model of magnetomechanical interaction that is independent on force density adopted is proposed. The Cauchy stress tensor obtained is constituted by the addition of three components: elastic, magnetic and magnetoelastic tensors. The magnetic component is the only one dependent on force density adopted. It is found that the magnetoelastic Cauchy stress tensor is not in general symmetric and an extended magnetostatic force density that takes into account the effects of elastic interaction is defined. / [ES] En la actualidad, se emplean diferentes métodos para obtener las densidades de fuerza magnetostáticas en un medio continuo. Algunos de ellos se fundamentan en modelos de interacción de la materia con un campo externo y otros se derivan de tensores de Maxwell en la materia. Todas estas densidades son diferentes. Los modelos actuales de interacción magnetomecánica están condicionados por la elección de una de estas densidades. En esta Tesis se propone un nuevo modelo de interacción independiente de la densidad de fuerza adoptada. El tensor de Cauchy obtenido está constituido por un tensor elástico, otro magnético y otro magnetoelástico. La componente magnética es la única que depende del tensor de Maxwell o densidad de fuerza adoptada. Se constata que el tensor de Cauchy no es en general simétrico y se define una densidad de fuerza magnetostática extendida que tiene en cuenta los efectos de interacción elástica. / [CAT] En l'actualitat, s'utilitzen diferents mètods per a obtenir les densitats de forces magnetostàtiques en un medi continu. Alguns d'ells tenen els seus fonaments en models d'interacció de la matèria amb un camp extern y d'altres es deriven de tensors de Màxwell en la matèria. Totes les densitats son diferents. Els models actuals d'interacció magnetomecànica estan condicionats per l'elecció d'una d'aquestes densitats. En la present Tesi es propasa un nou model d'interacció independent de la densitat de força adoptada. El tensor de Cauchy obtingut està constituït per un tensor elàstic, un magnètic i un magnetoelàstic. La component magnètica és l'única que depend del tensor de Màxwell o densitat de força adoptada. Es constata que el tensor de Cauchy no és en general simètric i es defineix una densitat de força magnetostàtica estesa que té en compte els efectes d'interacció elàstica. / Usieto Galve, A. (2016). Modelización de la interacción magnetomecánica bajo un tensor de Cauchy de tensiones magnéticas obtenido por procedimientos energéticos [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/63240 / TESIS

This master thesis is devoted to the kinetic description in phase space of strongly magnetized plasmas. It addresses the problem of stability near equilibria for magnetically confined plasmas modeled by the relativistic Vlasov Maxwell system. A small physically pertinent parameter ε, with 0 < ε << 1, related to the inverse of a gyrofrequency, governs the strength of a spatially inhomogeneous applied magnetic field given by the function x→ε−1Be(x). Local C1-solutions do exist. But these solutions may blow up in finite time. This phenomenon can only happen at high velocities [14] and, since ε−1is large, standard results predict that this may occur at a time Tε shrinking to zero when ε goes to 0. It has been proved recently in [7] that, in the case of neutral, cold, and dilute plasmas (like in the Earth’s magnetosphere), smooth solutions corresponding to perturbations of equilibria exist on a uniform time interval [0,T], with 0< T independent of ε. We investigate here the hot situation, which is more suitable for the description of fusion devices. A condition is derived for which perturbed W1,∞-solutions with large initial momentum also exist on a uniform time interval, they remain bounded in the sup norm for well-prepared initial data, and moreover they inherit some kind of stability. / Graduate

Over the past several decades our understanding and meticulous characterization of the transient and spatial properties of materials evolved rapidly. The results present an exciting field for discovery, and craft materials to control and reshape light that we are just beginning to fathom. State-of-the-art nano-deposition processes, for example, can be utilized to build stratified waveguides made of thin dielectric layers, which put together result in a material with effective abnormal dispersion. Moreover, materials once deemed well known are revealing astonishing properties, v.gr. chalcogenide glasses undergo an atomic reconfiguration when illuminated with electrons or photons, this ensues in a temporal modification of its permittivity and permeability which could be used to build new Photonic Integrated Circuits.. This work revolves around the characterization and model of heterogeneous and time-varying materials and their applications, revisits Maxwell's equations in the context of nonlinear space- and time-varying media, and based on it introduces a numerical scheme that can be used to model waves in this kind of media. Finally some interesting applications for light confinement and beam transformations are shown.

We obtain first-order cover pebbling thresholds of the complete graph for Maxwell Boltzmann and Bose Einstein configurations.

En la fisica clasica, las ecuaciones de Maxwell unifica la teoria de la electricidad y el magnetismo en una sola teoria: Electromagnetismo. En este trabajo se presenta las ecuaciones de Maxwell desde el punto de vista del álgebra geométrica. Se desarrollan dos algebras asociativas: el álgebra geométrica euclideana tridimensional denotada con AG(3) y el álgebra geométrica pseudoeuclideana AG(3,1), las cuales van a servir como el modelo matemático a seguir para unificar las cuatro ecuaciones de Maxwell en una sola ecuacion. / --- In classical physics, Maxwell’s equations unified theory of electricity and magnetism into a single theory: electromagnetism. In this work the Maxwell equations is presented from the point of view of geometric algebra. Develop two associative algebras: the algebra dimensional Euclidean geometric denoted AG ( 3) and the geometric algebra pseudoeuclideana AG (3,1), which will serve as the mathematical model to unify the four Maxwell equations into a single equation / Tesis

Indiana University-Purdue University Indianapolis (IUPUI) / The two-part model (2PM) is the most widely applied modeling and estimation framework in empirical health economics. By design, the two-part model allows the process governing observation at zero to systematically differ from that which determines non-zero observations. The former is commonly referred to as the extensive margin (EM) and the latter is called the intensive margin (IM). The analytic focus of my dissertation is on the development of a general framework for specifying, estimating and drawing inference regarding causally interpretable (CI) effect parameters in the 2PM context. Our proposed fully parametric 2PM (FP2PM) framework comprises very flexible versions of the EM and IM for both continuous and count-valued outcome models and encompasses all implementations of the 2PM found in the literature. Because our modeling approach is potential outcomes (PO) based, it provides a context for clear definition of targeted counterfactual CI parameters of interest. This PO basis also provides a context for identifying the conditions under which such parameters can be consistently estimated using the observable data (via the appropriately specified data generating process). These conditions also ensure that the estimation results are CI. There is substantial literature on statistical testing for model selection in the 2PM context, yet there has been virtually no attention paid to testing the “one-part” null hypothesis. Within our general modeling and estimation framework, we devise a relatively simple test of that null for both continuous and count-valued outcomes. We illustrate our proposed model, method and testing protocol in the context of estimating price effects on the demand for alcohol.

To model dissipation of energy in vibrating civil structures, existence of viscous damping is commonly assumed primarily for mathematical convenience. In such a classical damper, the damping force is assumed to depend only on the velocity of deformation. Fluid viscous dampers that provide this type of damping have been manufactured to provide supplementary damping in civil and mechanical systems to enhance their performance. Some fluid dampers, however, exhibit stiffening characteristics at higher frequencies of deformation. The force deformation relationship of such dampers can be better represented by the Maxwell model of visco-elasticity. This model consists of a viscous dashpot in series with a spring, the latter element providing the stiffening characteristics. This study is concerned with the optimal utilization of such Maxwell dampers for seismic performance improvement of civil structures. The force deformation relationship of Maxwell dampers is described by a first order differential equation. Earlier studies dealing with these dampers, used an unsymmetric set of equations for combined structure and damper system. The solution of such equations for response analysis or for optimization calculation by a modal analysis approach would require the pair of the left and right eigenvectors. In this study, an auxiliary variable is introduced in the representation of a Maxwell damper to obtain symmetric equations of motion for combined structure and damper system. This eliminates the need for working with two sets of eigenvectors and their derivatives, required for optimal analysis. Since the main objective of installing these dampers is to reduce the structural response in an optimal manner, the optimization problem is defined in terms of the minimization of some response-based performance indices. To calculate the optimal parameters of dampers placed at different location in the structure, Rosen's gradient projection method is employed. For numerical illustration, a 24-story shear building is considered. Numerical results are obtained for seismic input defined by a spectral density function; however, the formulation permits direct utilization of response spectrum-based description of design earthquake. Three different performance indices -- inter story drift-based, floor acceleration-based, and base shear-based performance indices-- have been considered to calculate the numerical results. A computational scheme is presented to calculate the amount of total damping required to achieve a desired level of response reduction. The effect of ignoring the stiffening effect at higher frequencies in the Maxwell model on the optimal performance is evaluated by parametric variation of relaxation time coefficient. It is observed that the models with higher relaxation time parameter show a decreased response reducing damping effect. Thus ignoring the stiffening effect when it is, indeed, present would provide an unconservative estimation of the damping effect. The effect of brace flexibilities on different performance indices is also investigated. It is observed that flexibility in a brace reduces the effectiveness of the damper. / Master of Science

The numerical solutions of Maxwell’s equations have been the cornerstone of photonic design for over a century. In recent years, the field of photonics has witnessed a surge in interest in inverse design, driven by the potential to engineer nonintuitive photonic structures with remarkable properties. However, the conventional approach to inverse design, which relies on fully discretized numerical simulations, faces significant challenges in terms of computational efficiency and scalability. This thesis delves into an alternative paradigm for inverse design, leveraging the power of semi-analytical methods. Unlike their fully discretized counterparts, semi-analytical methods hold the promise of enabling simulations that are independent of the computational grid size, potentially revolutionizing the design and optimization of photonic structures. To achieve this goal, we put forth a more generalized formalism for semi-analytical methods and have developed a comprehensive differential theory to underpin their operation. This theoretical foundation not only enhances our understanding of these methods but also paves the way for their broader application in the field of photonics. In the final stages of our investigation, we illustrate how the semi-analytical simulation framework can be effectively employed in practical photonic design scenarios. We demonstrate the synergy of semi-analytical methods with ray tracing techniques, showcasing their combined potential in the creation of large-scale optical lens systems and other complex optical devices.

<p>The goal of this thesis is to perform a simple theoretical analysis of the problem of two optical cavities coupled by a common mirror which is movable. The mirror position controls the electromagnetic mode structure of the double cavity. Modes can be transferred from one side to the other by moving the mirror, thereby allowing deterministic and on-demand transfer of photons between two cavities. By mapping the Maxwell wave equation onto the Schr\"{o}dinger wave equation, we are able to make use of the Landau-Zener result for the transition probability at an avoided crossing to obtain the conditions for adiabatic transfer.</p> / Master of Science (MS)

We developed a quantitative measurement technique using atomic force microscopy (AFM) to study the effects of both DC and AC external electric fields on the forces between two dielectric microspheres. In this work we measured the DC and AC electric field-induced forces and adhesion force between two barium titanate (BaTiO?) glass microspheres in a low humidity environment by this technique. The objective here is to find out the correlation between these measured forces and applied field strength, frequency, and the separation distance between the two spheres was studied. Since the spheres would oscillate under an AC field, the AC field-induced force was divided into dynamic component (i.e., time-varying term) and static component (i.e., time-averaged term) to investigate. The oscillatory response occurs at a frequency that is twice the drive frequency since the field-induced force is theoretically proportional to the square of the applied field. This behavior can be observed in the fast Fourier transformation (FFT) spectra of the time series of the deflection signal. The magnitude of the vibration response increases when the frequency of the drive force is near resonant frequency of the particle-cantilever probe. The amplitude of this vibration increases with proximity of the two particles, and ultimately causes the particles to repeatedly hit each other as in tapping mode AFM. The effect of the Maxwell-Wagner interfacial relaxation on the DC electric field-induced force was discovered by monitoring the variation of the field-induced force with time. The static component of the AC electric field-induced force does not vary with the applied frequency in the range from 1 to 100 kHz, suggesting that the crossover frequency may equal to or less than 1 kHz and the permittivities of the BaTiO? glass microspheres and medium dominate the field-3 induced force. The AC field-induced force is proportional to the square of the applied electric field strength. This relationship persists even when the separation between the spheres is much smaller than the diameter of the microspheres. The large magnitude of the force at small separations suggests that the local field is distorted by the presence of a second particle, and the continued dependence on the square of the field but the measured force is much larger than the theoretical results, suggesting that the local electric field around the closely spaced spheres is distorted and enhanced but the effects of the local field distortion may have not much to with the applied electric field. Compared with the calculated results from different models, our results demonstrate that the field-induced force is much more long-range than expected in theory. In addition, the DC field-induced adhesion force is larger than the AC field-induced one due to the interfacial charge accumulation, agreeing with the discovery of the Maxwell-Wagner interfacial relaxation effect on the DC field-induced force. No obvious correlation between the field-induced adhesion and the applied frequency is found. However, both the DC and AC field-induced adhesion forces display the linearity with the square of the applied electric field strength as well. / Master of Science