The use of electrostatic transduction has enabled high-Q miniaturized mechanical resonators made of non-piezoelectric material that vibrate at high and ultra high frequencies. However, this transduction technique suffers from large values of motional resistance associated with the technique, limiting its use for interfacing to standard 50 RF circuits. Piezoelectric transduction has advantages over the electrostatic method because of its comparable to 50 motional resistance. However, the technique requires use of thin film piezoelectric materials with the demonstrated Qs that are much lower than their corresponding non-piezoelectric resonators. This research proposes use of electrodynamic transduction, reports analytic and experimental studies on electrodynamic transduction for RF application, highlights the method’s advantages, and lists the contributions. The use of Lorentz-force transduction for RF micromechanical filters proposed in this work is pursued by experimentally evaluating the transduction technique implemented for microfabricated designs. By fabricating single and coupled microresonators in a few different fabrication technologies, including CMOS35, the performance of the Lorentz-force driven microresonators is studied. Using a laser vibrometer, the actual performance, including the displacement and velocity of the moving points of the microstructures’ surfaces, are measured. The mode shapes and resonance specifications of the microstructures in air and vacuum derived by laser vibrometer provide data for characterizing the employed Lorentz-force transduction technique. Furthermore, the results from the electrical measurements are compared to the micromechanical resonators’ frequency response obtained from the mechanical measurements by laser vibrometer. The significantly low values of motional resistance computed for the differently fabricated designs demonstrate the advantage of Lorentz-force transduction for RF filter applications. Should a device similar in size be driven electrostatically, the motional resistance would be multiple orders of magnitude higher. This research reports the experimental results obtained by examining a Lorentz- force transduction application for developing RF micromechanical filters. The results demonstrate the Lorentz-force transduction’s advantages over other transduction methods used for RF μ-mechanical filters. Compared to electrostatic transduction, the Lorentz-force method provides greater electromechanical coupling, multiple orders of magnitude lower motional resistance, the independence of the filter center frequency from the bias voltage, higher power handling, and no requirement for bias lines, which decreases the work in microfabrication. Unlike piezoelectric transduction, the electrodynamic technique requires no piezoelectric material. Use of non-piezoelectric materials provides more flexibility for resonator material in the IC-compatible fabrications. Power handling in electrodynamic transduction has fewer limitations than other transduction techniques because the higher power needed in electrostatic or piezoelectric methods requires a higher voltage, which is limited by the breakdown voltage. The higher power in Lorentz-force-based transduction demands a larger current. The larger current produces heat that is removable by applying an appropriate cooling technique.

This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. We study different structural, integrability, and smoothness properties of functions satisfying certain mixed norm conditions. Conditions of this type are determined by the behaviour of linear sections of functions. The work in this direction originates in a paper due to Gagliardo (1958), and was further developed by Fournier (1988), by Blei and Fournier (1989), and by Kolyada (2005). Here we continue these studies. We obtain some refinements of known embeddings for certain mixed norm spaces introduced by Gagliardo, and we study general properties of these spaces. In connection with these results, we consider a scale of intermediate mixed norm spaces, and prove intrinsic embeddings in this scale. We also consider more general, fully anisotropic, mixed norm spaces. Our main theorem states an embedding of these spaces to Lorentz spaces. Applying this result, we obtain sharp embedding theorems for anisotropic Sobolev-Besov spaces, and anisotropic fractional Sobolev spaces. The methods used are based on non-increasing rearrangements, and on estimates of sections of functions and sections of sets. We also study limiting relations between embeddings of spaces of different type. More exactly, mixed norm estimates enable us to get embedding constants with sharp asymptotic behaviour. This gives an extension of the results obtained for isotropic Besov spaces by Bourgain, Brezis, and Mironescu, and for anisotropic Besov spaces by Kolyada. We study also some basic properties (in particular the approximation properties) of special weak type spaces that play an important role in the construction of mixed norm spaces, and in the description of Sobolev type embeddings. In the last chapter, we study mixed norm spaces consisting of functions that have smooth sections. We prove embeddings of these spaces to Lorentz spaces. From this result, known properties of Sobolev-Liouville spaces follow.

Gas composition and analysis forms a large field of research whose requirements demand that measurement equipment be as affordable, uncomplicated and convenient as possible. The precise quantitative composition of an atmospheric, industrial or chemically synthesised sample of gas is of utmost importance when inferring the properties and nature of the environment from which the sample was taken, or for inferring how a prepared sample will react in its application. The most popular and widely used technique to achieve this is Gas Chromatography-Mass Spectrometry (GCMS) and, without a doubt, this technique has set the standard for gas analysis. Despite the accuracy of the GCMS technique, the equipment itself is bulky, expensive and cannot be applied readily to field work. Instead, most field work is conducted using a single gas detector, capable only of detecting one particular molecule or element at a time. Presented here is an interferometric technique that theoretically, has the ability to address all three issues of bulkiness, affordability and convenience, whilst not being limited to one particular element or molecule in its analysis. Identifying the unknown constituents of a gaseous mixture using the proposed method, employs the optical refractive properties of the mixture to determine its composition. A key aspect of this technique is that the refractive index of an arbitrary mixture of gases will vary depending on pressure and wavelength1. The Lorentz-Lorenz formula and the Sellmeier equations form the foundation of the theoretical background. The optical refractive properties of air and other atmospheric gases have been well established in the literature. The experimental investigations described here have been conducted based on this, insofar as no analysis has been conducted on gases that do not naturally occur in reasonable abundance in the atmosphere. However this does not in any way preclude the results and procedure developed from applying to a synthesised gas mixture. As mentioned, the platform of this technique relies on the pressure and wavelength dependence of the refractivity of the gas. The pressure dependence of the system is easily accounted for, in making this claim however it is still imperative the mixture be impervious to contamination from the wider atmosphere. Wavelength dependence however is perhaps slightly more difficult to accommodate. Multiple lasers, of differing wavelength form the radiative sources which underpin the method developed. Laser sources were chosen because of their coherence, making it easy to produce interference, when combined with the inherent stability of the Sagnac interferometer, provides for a very user friendly system that is able to quickly take results. The other key part of the experimental apparatus is the gas handling system, the gas(es) of interest need to be contained within an optical medium in the path of one of the beams of the interferometer. Precise manipulation of the pressure of the gas is critical in determining concentration, this has been achieved through the use of a gas syringe whose plunger is moved on a finely threaded screw, and measured on a digital manometer. The optical setup has also been explored, specifically in ruling out the use of such radiative sources as passing an incandescent source through a monochromator or the use of LED's to produce interference before settling on lasers to produce the required interference. Finally, a comprehensive theoretical background has been presented using classical electromagnetic theory as well as confirmation from a quantum perspective. The theoretical background for this study relies upon the Lorentz-Lorenz formula. It is commonly presented either from a classical or quantum perspective, in this work both classical and quantum mechanical treatments are given whilst also showing how each confirms the other. Furthermore, a thorough investigation into the dispersion functions of each of the major components of the atmosphere has been compiled from the study of refractivity on individual gases from other authors, in some cases, where no work has been done previously, this has been derived. The technique developed could be considered an ample addition to gas analysis techniques in certain circumstances in terms of expense, convenience and accuracy. The system can predict relative quantities of constituents of the atmosphere to at least 3%. The method described here would allow researchers more time to concentrate on actual results and more resources to allocate to broadening intellectual horizons. This would certainly justify further development.

Made available in DSpace on 2015-03-03T11:52:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-07-03Bitstream added on 2015-03-03T12:06:59Z : No. of bitstreams: 1 000798812.pdf: 406540 bytes, checksum: 7793d5a1f9bfbe358b5dde7a7418b448 (MD5) / O século passado é considerado como a era das Teorias Quânticas de Campos. Desta forma, neste trabalho, forneceremos todos os detalhes de uma descoberta teórica inesperada de uma partícula de matéria de spin 1/2 com dimensão de massa 1. Esses espinores recebem o nome de ELKO, o qual vem do acrônimo alemão Eigenspinores des Ladungskonjugationsoperators, e são fundamentados em um conjunto completo de autoespinores de helicidade dual do operador conjugação de carga. O ELKO pertence a um subgrupo do grupo completo de Lorentz. Portanto, a lei de transformação entre suas componentes não é dada pela simetria de paridade, e desta maneira não satisfaz a equação de Dirac. Intrinsicamente nas somas de spin para o ELKO aparece um termo que quebra a simetria de Lorentz, levando então à apreciação da Very Special Relativity, que nada mais é do que um subgrupo do grupo de Lorentz, cuja álgebra deixa as somas de spin invariantes ou covariantes. Pela razão do propagador do ELKO ser o mesmo de Klein-Gordon a menos de um fator, a lagrangiana associada é a do campo escalar, por esta razão o ELKO é dotado de dimensão de massa 1 / The last century is considered as the era of Quantum Field Theories. Thus, in this work, we provide all the details of an unexpected theoretical discovery of a matter particle spin 1/2 endowed with mass dimension 1. These spinors are the so called ELKO, which comes from the German acronym Eigenspinores des Ladungskonjugationsoperators, based on a complete set of a dual helicity eigenspinors of the charge conjugation operator. ELKO belongs to a subgroup of the full Lorentz group. Therefore, the law of transformation between its components is not given by the parity symmetry, and thus it does not satisfies the Dirac equation. It appears, intrinsically in the spin sums a Lorentz symmetry breaking term, then it will be better analysed within the Very Special Relativity, which is a subgroup of the Lorentz group, whose algebra leaves the spin sums invariant or covariant under transformations. Since the ELKO propagator is the same of Klein-Gordon propagator apart from a term, than the associated lagrangian is the scalar field one, for this reason ELKO is endowed with mass dimension 1

abstract: The research of this dissertation has involved the nanoscale quantitative characterization of patterned magnetic nanostructures and devices using off-axis electron holography and Lorentz microscopy. The investigation focused on different materials of interest, including monolayer Co nanorings, multilayer Co/Cu/Py (Permalloy, Ni81Fe19) spin-valve nanorings, and notched Py nanowires, which were fabricated via a standard electron-beam lithography (EBL) and lift-off process. Magnetization configurations and reversal processes of Co nanorings, with and without slots, were observed. Vortex-controlled switching behavior with stepped hysteresis loops was identified, with clearly defined onion states, vortex states, flux-closure (FC) states, and Omega states. Two distinct switching mechanisms for the slotted nanorings, depending on applied field directions relative to the slot orientations, were attributed to the vortex chirality and shape anisotropy. Micromagnetic simulations were in good agreement with electron holography observations of the Co nanorings, also confirming the switching field of 700-800 Oe. Co/Cu/Py spin-valve slotted nanorings exhibited different remanent states and switching behavior as a function of the different directions of the applied field relative to the slots. At remanent state, the magnetizations of Co and Py layers were preferentially aligned in antiparallel coupled configuration, with predominant configurations in FC or onion states. Two-step and three-step hysteresis loops were quantitatively determined for nanorings with slots perpendicular, or parallel to the applied field direction, respectively, due to the intrinsic coercivity difference and interlayer magnetic coupling between Co and Py layers. The field to reverse both layers was on the order of ~800 Oe. Domain-wall (DW) motion within Py nanowires (NWs) driven by an in situ magnetic field was visualized and quantified. Different aspects of DW behavior, including nucleation, injection, pinning, depinning, relaxation, and annihilation, occurred depending on applied field strength. A unique asymmetrical DW pinning behavior was recognized, depending on DW chirality relative to the sense of rotation around the notch. The transverse DWs relaxed into vortex DWs, followed by annihilation in a reversed field, which was in agreement with micromagnetic simulations. Overall, the success of these studies demonstrated the capability of off-axis electron holography to provide valuable insights for understanding magnetic behavior on the nanoscale. / Dissertation/Thesis / Ph.D. Materials Science and Engineering 2010

This work has its motivation in the study of the ergodic properties of the Lorenz geometric model, constructed to approximate the behavior of solutions of the Lorenz equations. Simultaneously, Afraimovich in [17] and Guckenheimer and Williams [18], constructed a geometric model that mimics the dynamics of the original Lorenz equations. Here, we build ergodic physical measures for two types of applications that arise from the Lorenz geometric model. The first one is a piecewise expanding one-dimensional map and the second is a two-dimensional application wich contracts the leaves of an invariant foliation. To construct the ergodic physical measure for the one dimensional Lorenz map, we make use of an operator (transfer operator) acting in the space of bounded variation functions, while the second uses the Riesz representation theorem and some other topological properties. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Este trabalho tem sua motivação no modelo geométrico construído para aproximar o comportamento das soluções das equações de Lorenz. Simultaneamente Afraimovich em [17] e Guckenheimer e Williams [18] construíram um modelo geométrico. Essencialmente ele consiste na construção de medidas físicas e ergódicas para dois tipos de aplicações, uma unidimensional que é seccionalmente expansora (piecewise expanding) e outra bidimensional que contrai as folhas de uma folheação invariante. A primeira faz uso de um operador (operador de transferência) agindo no espaço das funções de variação limitada, enquanto que a segunda utiliza o teorema de representação Riesz bem como algumas outras propriedades topológicas.

The measure of non-compactness is defined for any continuous mapping T : X Y between two Banach spaces X and Y as β(T) := inf { r > 0: T(BX) can be covered by finitely many open balls with radius r } . It can easily be shown that 0 ≤ β(T) ≤ ∥T∥ and that β(T) = 0, if and only if the mapping T is compact. My supervisor prof. Stanislav Hencl has proved in his paper that the measure of non-compactness of the known embedding W k,p 0 (Ω) → Lp∗ (Ω), where kp is smaller than the dimension, is equal to its norm. In this thesis we prove that the measure of non-compactness of the embedding between function spaces is under certain general assumptions equal to the norm of that embedding. We apply this theorem to the case of Lorentz spaces to obtain that the measure of non-compactness of the embedding Wk 0 Lp,q (Ω) → Lp∗,q (Ω) is for suitable p and q equal to its norm. 1

PINHEIRO, Hudson Pacheco. Oscilador de Dirac: cenário para um estudo de um sistema de dois níveis. 2009. 58 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 2015-05-04T18:27:36Z No. of bitstreams: 1 2009_dis_hppinheiro.pdf: 441836 bytes, checksum: c589381b3cd54d223a335b8a2d021c67 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-05-07T16:57:51Z (GMT) No. of bitstreams: 1 2009_dis_hppinheiro.pdf: 441836 bytes, checksum: c589381b3cd54d223a335b8a2d021c67 (MD5) / Made available in DSpace on 2015-05-07T16:57:51Z (GMT). No. of bitstreams: 1 2009_dis_hppinheiro.pdf: 441836 bytes, checksum: c589381b3cd54d223a335b8a2d021c67 (MD5) Previous issue date: 2009 / Nesta dissertação, estudamos como se comporta o modelo do oscilador de Dirac, inserido em um sistema de dois níveis, ao interagir com o campo eletromagnético externo, desconsiderando a quantização do campo (teoria semiclássica). Para tal, obtemos as funções de inversão de população de energia e de spin em três situações gerais: sem termos que violam a simetria de Lorentz; com a introdução de um termo CPT-ímpar que quebra a simetria vetorial de Lorentz; com a introdução de um termo CPT-ímpar que quebra a simetria de Lorentz por meio de um acoplamento axial. Em seguida, analisamos o caso especial da ressonância entre o sistema e o campo incidente. Nesse caso, toda a influência do oscilador de Dirac foi perdida e as funções de inversão de população de energia e de spin reduziram-se aos resultados encontrados na literatura científica.

Submitted by Edileide Reis (leyde-landy@hotmail.com) on 2014-09-09T13:42:27Z No. of bitstreams: 1 Helcimar Moura de Jesus.pdf: 483976 bytes, checksum: 8c832780cd99f08a109b59d2c25fcb5c (MD5) / Approved for entry into archive by Fatima Cleômenis Botelho Maria (botelho@ufba.br) on 2014-09-09T13:49:23Z (GMT) No. of bitstreams: 1 Helcimar Moura de Jesus.pdf: 483976 bytes, checksum: 8c832780cd99f08a109b59d2c25fcb5c (MD5) / Made available in DSpace on 2014-09-09T13:49:23Z (GMT). No. of bitstreams: 1 Helcimar Moura de Jesus.pdf: 483976 bytes, checksum: 8c832780cd99f08a109b59d2c25fcb5c (MD5) / Muitos físicos e filósofos da ciência aceitam a afirmação de que as teorias eletrodinâmicas de Lorentz e de Einstein são empiricamente equivalentes [Dorlig, 1968], isto é, que não existem experimentos para os quais as referidas teorias prevêem resultados distintos. Assumida a mencionada equivalência, os critérios a serem adotados para a escolha entre as duas teorias passam a ser de natureza extra científica, tais como: simplicidade,“força heurística”, menor quantidade de pressupostos, etc. A referida equivalência empírica é corroborada com o experimento de Michelson-Morley (EMM) [Michelson 1881, 1887] [Shankland 1963] que pode ser explicado mediante ambas as teorias. Particularmente, na teoria de Lorentz, adota-se a contração de Lorentz-Fitzgerald [Shankland 1963]. No entanto, Miranda Filho [Miranda Filho 2004] revela que a citada hipótese de contração falha ao explicar o resultado negativo do experimento quando se modifica a configuração original do aparato (EMM generalizado ou EMMG) para formar a figura de interferência num plano distinto das superfícies dos espelhos. Em contrapartida, a teoria de Einstein continua a explicá-lo. Mas, na eletrodinâmica de Lorentz de 1904, a referida contração constitui apenas parte de sua teoria. Logo, embora a contração de Lorentz-Fitzgerald não seja suficiente para cobrir a explicação do EMMG apresentada por Miranda Filho, não podemos dizer que a teoria completa não o faça. Este é, portanto, o nosso terreno de investigação para analisar a referida equivalência ou não das duas teorias eletrodinâmicas.

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2004-09Bitstream added on 2014-06-13T18:06:49Z : No. of bitstreams: 1 costa_lc_dr_ift.pdf: 1010600 bytes, checksum: bc05c2dfbdfafca45a21ea8884cb5c3f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Na presente tese, investiga-se uma versão estendida da eletrodinâmica quântica, onde se introduz um termo de acoplamento axial renormalizável não invariante, dando ênfase à quebra dinâmica das simetrias de Lorentz e CPT no setor de gauge e à ambigüidade no coeficiente do termo do tipo Chern-Simons, induzido através de correções radiativas e outros métodos não perturbativos. Aspectos da teoria efetiva de Euler-Kockel-Heisenberg a tempertura finita também são investigados à luz do formalismo conhecido como Thermo Field Dynamics. / In the present thesis it is investigated an extended version of quantum electrodynamic where a renormalized non-invariant axial coupling term introduced, emphasizing the dynamic violation of the Lorentz and CPT symmetries in the gauge sector of the theory as well as the ambiguity of the coeficient of the Chern-Simon-like term, induced through radiative corrections and other non-perturbative methods. Some aspects of the Euler-Kockel-Heisenber effective theory at finite temperature have also been addressed in the context of the Thermo Field Dynamics formalism.