Pour un groupoïde de Lie, on construit un morphisme d'indice analytique à valeurs dans un certain quotient de la K-théorie de l'algèbre de convolution de fonctions lisses à support compact. La construction est aboutie grâce à l'introduction d'une algèbre de déformation de fonctions lisses sur le groupoïde tangent. Ceci permet en particulier de montrer une version plus primitive du théorème de l'indice longitudinal de Connes-Skandalis for Foliations, c'est à dire, un théorème de l'indice qui prend ses valeurs dans un groupe qui peut être accouplé avec des cocycles cycliques. Une autre application est la suivante: soit D un G-opérateur pseudodifférential eliiptique avec indice ind(D)€K_0(A) (où A est l'algèbre de convolution), alors l'accouplement de ind(D) avec un coycle cyclique borné ne dépend que de la classe du symbole principal de D. Ce résultat est général pour des goupoïdes étale.

The knowledge of the phase behaviour of heavy oils and bitumen is important in order to understand the phenomenon of coke formation. Computation of their phase behaviour, using an equation of state, faces problems due to their complex composition. Hence n-alkane binaries of polyaromatic hydrocarbons are used to approximate the phase behaviour of heavy oils and bitumen. Appropriate values of binary interaction parameters are required for an equation of state to predict the correct phase behaviour of these model binary fluids. This thesis deals with fitting of the binary interaction parameter for the Peng-Robinson equation of state using landmarks in the binary phase space such as K- and L-points. A K- or an L-point is a point in the phase space where two phases become critical in the presence of another phase in equilibrium. An algorithm to calculate K- and L-points using an equation of state was developed. The variation of calculated K- and L-points with respect to the binary interaction parameter was studied and the results were compared with the experimental data in the literature. The interaction parameter was then fitted using the best match of experimental results with the computed ones. The binary interaction parameter fitted using a K- or an L-point was then used to predict the P-T projection of the binary system in phase space. Also, the qualitative effect of the binary interaction parameter on the P-T projection was studied. A numerical and thermodynamic study of the algorithm was done. Numerical issues like the initial guesses, convergence criterion and numerical techniques were studied and the thermodynamic constraints in the generalization of the algorithm are discussed. It was observed that the binary interaction parameter not only affects the location of K- and L-points in the phase space but also affects the calculation procedure of K- and L-points. Along with the propane binaries of polyaromatic hydrocarbons, K- and L-points were also calculated for systems like methane binaries of higher n-alkanes and the ethane + ethanol binary. In the case of the ethane + ethanol system, K- and L-points, matching the experimental results were calculated with different values of the binary interaction parameter. But the Peng-Robinson equation of state was unable to predict the correct type of phase behaviour using any value of the binary interaction parameter. The Peng-Robinson equation of state was able to predict the correct type of phase behaviour with the binary interaction parameter, fitted using K- and/or L-points for methane + n-alkane systems. The systems studied were the methane binaries of n-pentane, n-hexane and n-heptane. For the propane binaries of polyaromatic hydrocarbons, no value of the binary interaction parameter was able to predict the K-point with a good accuracy. The binary interaction parameter which gave the best possible results for a K-point failed to predict the correct type of phase behaviour. The binary interaction parameter fitted using the P-T projection enabled the Peng-Robinson equation of state to give a qualitative match for the high pressure complex phase behaviour of these systems. Solid phase equilibria were not taken into consideration.

The knowledge of the phase behaviour of heavy oils and bitumen is important in order to understand the phenomenon of coke formation. Computation of their phase behaviour, using an equation of state, faces problems due to their complex composition. Hence n-alkane binaries of polyaromatic hydrocarbons are used to approximate the phase behaviour of heavy oils and bitumen. Appropriate values of binary interaction parameters are required for an equation of state to predict the correct phase behaviour of these model binary fluids. This thesis deals with fitting of the binary interaction parameter for the Peng-Robinson equation of state using landmarks in the binary phase space such as K- and L-points. A K- or an L-point is a point in the phase space where two phases become critical in the presence of another phase in equilibrium. An algorithm to calculate K- and L-points using an equation of state was developed. The variation of calculated K- and L-points with respect to the binary interaction parameter was studied and the results were compared with the experimental data in the literature. The interaction parameter was then fitted using the best match of experimental results with the computed ones. The binary interaction parameter fitted using a K- or an L-point was then used to predict the P-T projection of the binary system in phase space. Also, the qualitative effect of the binary interaction parameter on the P-T projection was studied. A numerical and thermodynamic study of the algorithm was done. Numerical issues like the initial guesses, convergence criterion and numerical techniques were studied and the thermodynamic constraints in the generalization of the algorithm are discussed. It was observed that the binary interaction parameter not only affects the location of K- and L-points in the phase space but also affects the calculation procedure of K- and L-points. Along with the propane binaries of polyaromatic hydrocarbons, K- and L-points were also calculated for systems like methane binaries of higher n-alkanes and the ethane + ethanol binary. In the case of the ethane + ethanol system, K- and L-points, matching the experimental results were calculated with different values of the binary interaction parameter. But the Peng-Robinson equation of state was unable to predict the correct type of phase behaviour using any value of the binary interaction parameter. The Peng-Robinson equation of state was able to predict the correct type of phase behaviour with the binary interaction parameter, fitted using K- and/or L-points for methane + n-alkane systems. The systems studied were the methane binaries of n-pentane, n-hexane and n-heptane. For the propane binaries of polyaromatic hydrocarbons, no value of the binary interaction parameter was able to predict the K-point with a good accuracy. The binary interaction parameter which gave the best possible results for a K-point failed to predict the correct type of phase behaviour. The binary interaction parameter fitted using the P-T projection enabled the Peng-Robinson equation of state to give a qualitative match for the high pressure complex phase behaviour of these systems. Solid phase equilibria were not taken into consideration.

The concepts of continuity for set-valued mappings were introduced by G. Bouligand and K. Kuratowski. There are two ways defining differentiability of set-valued mapping. One is defined by classical differentiability theorem and another is defined by normal cone which was introduced by B.S. Mordukhovich. In this thesis, we survey various definitions of continuity and differentiability for set-valued mapping.

The performance of modern high frequency components and electronic systems are often limited by the properties of the materials from which they are made. Over the past decade, there has been an increased emphasis on the development of new, high performance dielectrics for use in high frequency systems. The development of these materials requires novel broadband characterization, instrumentation, and extraction techniques, from which models can be formulated. For this project several types of dielectric sheets were characterized at terahertz (THz) frequencies using quasi-optical (free-space) techniques. These measurement systems included a Fourier Transform Spectrometer (FTS, scalar), a Time Domain Spectrometer (TDS, vector), a Scalar Network Analyzer (SNA), and a THz Vector Network Analyzer (VNA). Using these instruments the THz spectral characteristics of dielectric samples were obtained. Polarization based anisotropy was observed in many of the materials measured using vector systems. The TDS was the most informative and flexible instrument for dielectric characterization at THz frequencies. To our knowledge, this is the first such comprehensive study to be performed. Anisotropy effects within materials that do not come into play at microwave frequencies (e.g. ~10 GHz) were found, in many cases, to increase measured losses at THz frequencies by up to an order of magnitude. The frequency dependent properties obtained during the course of this study included loss tangent, permittivity (index of refraction), and dielectric constant. The results were largely consistent between all the different systems and correlated closely to manufacturer specifications over a wide frequency range (325 GHz-1.5 THz). Anisotropic behavior was observed for some of the materials. Non-destructive evaluation and testing (NDE/NDT) techniques were used throughout. A precision test fixture was developed to accomplish these measurements. Time delay, insertion loss, and S-parameters were measured directly, from which loss tangent, index of refraction, and permittivity was extracted. The test materials were low-loss dielectric slabs ranging in thickness from 1-60 mils. The substrate sheets were PTFE, fiberglass, and epoxy-ceramic composite substrates. The other group was polyethylene plastic sheets (LDPE/HDPE/UMHW) and 3D printer Photopolymers. The results were verified by using several online THz spectral databases and compared to manufacturer data sheets. Permittivity and loss of some of the test samples varied as a function of polarization angle. 0 - 90 degrees of rotation were tested (i.e., H-V, and 45 degrees polarization). Inter-molecular scattering in the composite materials raised the loss considerably. This effect was verified. Standard, well documented, material types were selected for the project for best comparison. These techniques can also be applied to analyze newer substances such as nanodielectrics.

Šis darbas pratęsia 2010 m. autorės atlikto bakalauro darbo „Elipsinio tipo B-erdvių beveik kontaktiniai metriniai hiperpaviršiai“ tyrinėjimus, apibendrina šio darbo rezultatus kitų tipų ir rūšių -struktūroms ir pritaiko juos liečiamųjų sluoksniuočių paviršių teorijoje. / In the work, the generalized (φ, ξ, η, g)-structures in normalized hypersurfaces M2n-1 T(En) are found and its properties are investigated. Geometric meaning in basis En of some interesting hypersurfaces (hypersphere, hyperplane, hypercone,…) is explained.

abstract: The mechanism of loss in high performance microwave dielectrics with complex perovskite structure, including Ba(Zn1/3Ta2/3)O3, Ba(Cd1/3Ta2/3)O3, ZrTiO4-ZnNb2O6, Ba(Zn1/3Nb2/3)O3, and BaTi4O9-BaZn2Ti4O11, has been investigated. We studied materials synthesized in our own lab and from commercial vendors. Then the measured loss tangent was correlated to the optical, structural, and electrical properties of the material. To accurately and quantitatively determine the microwave loss and Electron Paramagnetic Resonance (EPR) spectra as a function of temperature and magnetic field, we developed parallel plate resonator (PPR) and dielectric resonator (DR) techniques. Our studies found a marked increase in the loss at low temperatures is found in materials containing transition metal with unpaired d-electrons as a result of resonant spin excitations in isolated atoms (light doping) or exchange coupled clusters (moderate to high doping) ; a mechanism that differs from the usual suspects. The loss tangent can be drastically reduced by applying static magnetic fields. Our measurements also show that this mechanism significantly contributes to room temperature loss, but does not dominate. In order to study the electronic structure of these materials, we grew single crystal thin film dielectrics for spectroscopic studies, including angular resolved photoemission spectroscopy (ARPES) experiment. We have synthesized stoichiometric Ba(Cd1/3Ta2/3)O3 [BCT] (100) dielectric thin films on MgO (100) substrates using Pulsed Laser Deposition. Over 99% of the BCT film was found to be epitaxial when grown with an elevated substrate temperature of 635 C, an enhanced oxygen pressures of 53 Pa and a Cd-enriched BCT target with a 1 mol BCT: 1.5 mol CdO composition. Analysis of ultra violet optical absorption results indicate that BCT has a bandgap of 4.9 eV. / Dissertation/Thesis / Ph.D. Materials Science and Engineering 2013

Abstract This work presents a method for the fabrication of Li₂MoO₄ ceramics at room-temperature based on utilizing a small amount of water with Li₂MoO₄ powder. The densification of the ceramic takes place during pressing. Thus the shape and size of the final ceramic compact can easily be managed by controlling the mould dimensions and the amount of material. Post-processing at 120 °C is applied to remove residual water from the compact. This post-processing temperature can be chosen to be suitable to the other materials integrated, such as the substrate or electrodes, as long as the post-processing time is adequate to remove the residual water. The dielectric properties (relative permittivity of 5.1 and a loss tangent value of 0.00035 at 9.6 GHz) after optimization of the powder particle size, sample pressing pressure, and post-processing time were similar to those achieved for Li₂MoO₄ ceramics fabricated by sintering at 540 °C. The dielectric properties of Li₂MoO₄ ceramics were also modified using composite methods. For example, an addition of 10 volume-% of BaTiO₃ increased the relative permittivity from 6.4 to 9.7 and the loss tangent value from 0.0006 to 0.011 at 1 GHz. To investigate the thermal dependence of the permittivity, different amounts of rutile TiO₂ were incorporated into a Li₂MoO₄ ceramic matrix fabricated with the method described in this work. As the amount of TiO₂ increased from 10 to 30 volume-%, the thermal coefficient of permittivity decreased from 180 ppm/°C to -170 ppm/°C. The low processing temperature made the fabrication approach introduced here feasible for silver electrode integration without the formation of extra phases, which were observed in sintered samples with similar compositions in another study. A patch antenna was realized utilizing a Li₂MoO₄ ceramic disk fabricated by the room-temperature method. The antenna operating at ~4 GHz showed reasonably good performance. A relative humidity of 80% lowered the resonant frequency by 3.25% from the initial value, and reduced the total and radiation efficiencies of the antenna by ~2 dB. The changes were slowly reversible. Use of a silicone conformal coating reduced the shift of the resonant frequency to 1.26% from the initial value and also reduced the effect on efficiencies to ~1 dB. The use of the coating also speeded up the reversibility of the changes when the humidity was decreased. / Tiivistelmä Tässä työssä esitellään menetelmä, jolla Li₂MoO₄-keraameja voidaan valmistaa huoneenlämpötilassa. Menetelmä hyödyntää pientä määrää Li₂MoO₄-vesiliuosta ja sen kiteytymistä. Keraami tiivistyy kappaletta puristettaessa, joten sen koko ja muoto ovat sama kuin muotilla riippuen vain keraamin määrästä. Kappaleeseen jäänyt vesi poistetaan lämpökäsittelyllä yleensä 120 celsiusasteessa. Jälkikäsittelylämpötila voidaan valita muiden integroitavien materiaalien mukaan, kuten alusta- tai elektrodimateriaalin, kunhan jälkikäsittelyaikaa muokataan vastaavasti, jotta kaikki vesi poistuu. Optimoimalla Li₂MoO₄-jauheen partikkelikokoa, puristuspainetta ja jälkikäsittelyaikaa saavutettiin samankaltaiset dielektriset ominaisuudet taajuudella 9,6 GHz (suhteellinen permittiivisyys 5,1 ja häviötangentti 0,00035) kuin Li₂MoO₄-keraameilla, jotka on sintrattu 540 celsiusasteessa. Li₂MoO₄-keraamien dielektrisiä ominaisuuksia muokattiin myös lisäaineilla. Esimerkiksi 10 tilavuus-% BaTiO₃-jauhetta kasvatti suhteellista permittiivisyyttä taajuudella 1 GHz arvosta 6,4 arvoon 9,7 ja häviötangenttia arvosta 0,0006 arvoon 0,011. Myös eri määriä TiO₂-jauhetta (rutiili) lisättiin Li₂MoO₄-matriisiin permittiivisyyden lämpötilariippuvuuden tutkimiseksi. TiO₂-jauheen määrän kasvaessa 10 tilavuusprosentista 30 tilavuusprosenttiin laski permittiivisyyden lämpötilariippuvuus arvosta 180 ppm/°C arvoon -170 ppm/°C. Matalan käsittelylämpötilan ansiosta työssä esitelty valmistusmenetelmä soveltui käytettäväksi hopeaelektrodien kanssa. Aiemman tutkimuksen mukaan nämä komposiittimateriaalit muodostivat ei-toivottuja faaseja sintrattaessa hopean kanssa. Menetelmällä valmistettua Li₂MoO₄-keraamikiekkoa käytettiin mikroliuska-antennin valmistuksessa. Taajuudella 4 GHz toimivan antennin suorituskyky oli suunnitellun kaltainen. 80 prosentin suhteellinen ilmankosteus laski resonanssitaajuutta 3,25 % alkuperäisestä arvosta ja vähensi antennin kokonais- ja säteilytehokkuutta noin 2 dB. Muutokset palautuivat hitaasti. Silikonisuojalakan käyttö vähensi taajuuden laskua 1,26 prosenttiin alkuperäisestä arvosta ja tehokkuudet laskivat vain noin 1 dB. Suojalakan käyttö nopeutti muutosten palautuvuutta ilmankosteuden laskiessa.

This work focuses on the construction of functional representations in high-dimensional spaces.Attention is focused on the modeling of ignition phenomena using detailed kinetics, and on the ignition delay time as the primary quantity of interest (QoI). An iso-octane air mixture is first considered, using a detailed chemical mechanism with 3,811 elementary reactions. Uncertainty in all reaction rates is directly accounted for using associated uncertainty factors, assuming independent log-uniform priors. A Latin hypercube sample (LHS) of the ignition delay times was first generated, and the resulting database was then exploited to assess the possibility of constructing polynomial chaos (PC) representations in terms of the canonical random variables parametrizing the uncertain rates. We explored two avenues, namely sparse regression (SR) using LASSO, and a coordinate transform (CT) approach. Preconditioned variants of both approaches were also considered, namely using the logarithm of the ignition delay time as QoI. A global sensitivity analysis is performed using the representations constructed by SR and CT. Next, the tangent linear approximation is developed to estimate the sensitivity of the ignition delay time with respect to individual rate parameters in a detailed chemical mechanism. Attention is focused on a gas mixture reacting under adiabatic, constant-volume conditions. The approach is based on integrating the linearized system of equations governing the evolution of the partial derivatives of the state vector with respect to individual random variables, and a linearized approximation is developed to relate the ignition delay sensitivity to the scaled partial derivatives of temperature. In particular, the computations indicate that for detailed reaction mechanisms the TLA leads to robust local sensitivity predictions at a computational cost that is order-of-magnitude smaller than that incurred by finite-difference approaches based on one-at-a-time rate parameters perturbations. In the last part, we explore the potential of utilizing TLA-based sensitivities to identify active subspace and to construct suitable representations. Performance is assessed based contrasting experiences with CT-based machinery developed earlier.

The diploma thesis deals with the problem of speed determination during tangent collisions of two vehicles. The theoretical part describes the available literature and the preparation of an expert experiment. The practical part describes the experiment itself. Its results are processed and compared with the literature in the theoretical part. The aim of work is to extend knowledge about tangent collisions and reduce the error rate in determining crash in the expert analysis or claims in insurance companies.