951 resultados para Non-Linear Elliptic Systems
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Single-walled carbon nanotubes (SWNTs) have been studied as a prominent class of high performance electronic materials for next generation electronics. Their geometry dependent electronic structure, ballistic transport and low power dissipation due to quasi one dimensional transport, and their capability of carrying high current densities are some of the main reasons for the optimistic expectations on SWNTs. However, device applications of individual SWNTs have been hindered by uncontrolled variations in characteristics and lack of scalable methods to integrate SWNTs into electronic devices. One relatively new direction in SWNT electronics, which avoids these issues, is using arrays of SWNTs, where the ensemble average may provide uniformity from device to device, and this new breed of electronic material can be integrated into electronic devices in a scalable fashion. This dissertation describes (1) methods for characterization of SWNT arrays, (2) how the electrical transport in these two-dimensional arrays depend on length scales and spatial anisotropy, (3) the interaction of aligned SWNTs with the underlying substrate, and (4) methods for scalable integration of SWNT arrays into electronic devices. The electrical characterization of SWNT arrays have been realized by polymer electrolyte-gated SWNT thin film transistors (TFTs). Polymer electrolyte-gating addresses many technical difficulties inherent to electrical characterization by gating through oxide-dielectrics. Having shown polymer electrolyte-gating can be successfully applied on SWNT arrays, we have studied the length scaling dependence of electrical transport in SWNT arrays. Ultrathin films formed by sub-monolayer surface coverage of SWNT arrays are very interesting systems in terms of the physics of two-dimensional electronic transport. We have observed that they behave qualitatively different than the classical conducting films, which obey the Ohm’s law. The resistance of an ultrathin film of SWNT arrays is indeed non-linear with the length of the film, across which the transport occurs. More interestingly, a transition between conducting and insulating states is observed at a critical surface coverage, which is called percolation limit. The surface coverage of conducting SWNTs can be manipulated by turning on and off the semiconductors in the SWNT array, leading to the operation principle of SWNT TFTs. The percolation limit depends also on the length and the spatial orientation of SWNTs. We have also observed that the percolation limit increases abruptly for aligned arrays of SWNTs, which are grown on single crystal quartz substrates. In this dissertation, we also compare our experimental results with a two-dimensional stick network model, which gives a good qualitative picture of the electrical transport in SWNT arrays in terms of surface coverage, length scaling, and spatial orientation, and briefly discuss the validity of this model. However, the electronic properties of SWNT arrays are not only determined by geometrical arguments. The contact resistances at the nanotube-nanotube and nanotube-electrode (bulk metal) interfaces, and interactions with the local chemical groups and the underlying substrates are among other issues related to the electronic transport in SWNT arrays. Different aspects of these factors have been studied in detail by many groups. In fact, I have also included a brief discussion about electron injection onto semiconducting SWNTs by polymer dopants. On the other hand, we have compared the substrate-SWNT interactions for isotropic (in two dimensions) arrays of SWNTs grown on Si/SiO2 substrates and horizontally (on substrate) aligned arrays of SWNTs grown on single crystal quartz substrates. The anisotropic interactions associated with the quartz lattice between quartz and SWNTs that allow near perfect horizontal alignment on substrate along a particular crystallographic direction is examined by Raman spectroscopy, and shown to lead to uniaxial compressive strain in as-grown SWNTs on single crystal quartz. This is the first experimental demonstration of the hard-to-achieve uniaxial compression of SWNTs. Temperature dependence of Raman G-band spectra along the length of individual nanotubes reveals that the compressive strain is non-uniform and can be larger than 1% locally at room temperature. Effects of device fabrication steps on the non-uniform strain are also examined and implications on electrical performance are discussed. Based on our findings, there are discussions about device performances and designs included in this dissertation. The channel length dependences of device mobilities and on/off ratios are included for SWNT TFTs. Time response of polymer-electrolyte gated SWNT TFTs has been measured to be ~300 Hz, and a proof-of-concept logic inverter has been fabricated by using polymer electrolyte gated SWNT TFTs for macroelectronic applications. Finally, I dedicated a chapter on scalable device designs based on aligned arrays of SWNTs, including a design for SWNT memory devices.
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The transistor laser is a unique three-port device that operates simultaneously as a transistor and a laser. With quantum wells incorporated in the base regions of heterojunction bipolar transistors, the transistor laser possesses advantageous characteristics of fast base spontaneous carrier lifetime, high differential optical gain, and electrical-optical characteristics for direct “read-out” of its optical properties. These devices have demonstrated many useful features such as high-speed optical transmission without the limitations of resonance, non-linear mixing, frequency multiplication, negative resistance, and photon-assisted switching. To date, all of these devices operate as multi-mode lasers without any type of wavelength selection or stabilizing mechanisms. Stable single-mode distributed feedback diode laser sources are important in many applications including spectroscopy, as pump sources for amplifiers and solid-state lasers, for use in coherent communication systems, and now as TLs potentially for integrated optoelectronics. The subject of this work is to expand the future applications of the transistor laser by demonstrating the theoretical background, process development and device design necessary to achieve singlelongitudinal- mode operation in a three-port transistor laser. A third-order distributed feedback surface grating is fabricated in the top emitter AlGaAs confining layers using soft photocurable nanoimprint lithography. The device produces continuous wave laser operation with a peak wavelength of 959.75 nm and threshold current of 13 mA operating at -70 °C. For devices with cleaved ends a side-mode suppression ratio greater than 25 dB has been achieved.
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In this document we explore the issue of $L^1\to L^\infty$ estimates for the solution operator of the linear Schr\"{o}dinger equation, \begin{align*} iu_t-\Delta u+Vu&=0 &u(x,0)=f(x)\in \mathcal S(\R^n). \end{align*} We focus particularly on the five and seven dimensional cases. We prove that the solution operator precomposed with projection onto the absolutely continuous spectrum of $H=-\Delta+V$ satisfies the following estimate $\|e^{itH} P_{ac}(H)\|_{L^1\to L^\infty} \lesssim |t|^{-\frac{n}{2}}$ under certain conditions on the potential $V$. Specifically, we prove the dispersive estimate is satisfied with optimal assumptions on smoothness, that is $V\in C^{\frac{n-3}{2}}(\R^n)$ for $n=5,7$ assuming that zero is regular, $|V(x)|\lesssim \langle x\rangle^{-\beta}$ and $|\nabla^j V(x)|\lesssim \langle x\rangle^{-\alpha}$, $1\leq j\leq \frac{n-3}{2}$ for some $\beta>\frac{3n+5}{2}$ and $\alpha>3,8$ in dimensions five and seven respectively. We also show that for the five dimensional result one only needs that $|V(x)|\lesssim \langle x\rangle^{-4-}$ in addition to the assumptions on the derivative and regularity of the potential. This more than cuts in half the required decay rate in the first chapter. Finally we consider a problem involving the non-linear Schr\"{o}dinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, \begin{align*} iu_t+d(t) u_{xx}+|u|^2 u=0. \end{align*} We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in $x$ and in the Fourier transform of $x$.
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A detailed non-equilibrium state diagram of shape-anisotropic particle fluids is constructed. The effects of particle shape are explored using Naive Mode Coupling Theory (NMCT), and a single particle Non-linear Langevin Equation (NLE) theory. The dynamical behavior of non-ergodic fluids are discussed. We employ a rotationally frozen approach to NMCT in order to determine a transition to center of mass (translational) localization. Both ideal and kinetic glass transitions are found to be highly shape dependent, and uniformly increase with particle dimensionality. The glass transition volume fraction of quasi 1- and 2- dimensional particles fall monotonically with the number of sites (aspect ratio), while 3-dimensional particles display a non-monotonic dependence of glassy vitrification on the number of sites. Introducing interparticle attractions results in a far more complex state diagram. The ideal non-ergodic boundary shows a glass-fluid-gel re-entrance previously predicted for spherical particle fluids. The non-ergodic region of the state diagram presents qualitatively different dynamics in different regimes. They are qualified by the different behaviors of the NLE dynamic free energy. The caging dominated, repulsive glass regime is characterized by long localization lengths and barrier locations, dictated by repulsive hard core interactions, while the bonding dominated gel region has short localization lengths (commensurate with the attraction range), and barrier locations. There exists a small region of the state diagram which is qualified by both glassy and gel localization lengths in the dynamic free energy. A much larger (high volume fraction, and high attraction strength) region of phase space is characterized by short gel-like localization lengths, and long barrier locations. The region is called the attractive glass and represents a 2-step relaxation process whereby a particle first breaks attractive physical bonds, and then escapes its topological cage. The dynamic fragility of fluids are highly particle shape dependent. It increases with particle dimensionality and falls with aspect ratio for quasi 1- and 2- dimentional particles. An ultralocal limit analysis of the NLE theory predicts universalities in the behavior of relaxation times, and elastic moduli. The equlibrium phase diagram of chemically anisotropic Janus spheres and Janus rods are calculated employing a mean field Random Phase Approximation. The calculations for Janus rods are corroborated by the full liquid state Reference Interaction Site Model theory. The Janus particles consist of attractive and repulsive regions. Both rods and spheres display rich phase behavior. The phase diagrams of these systems display fluid, macrophase separated, attraction driven microphase separated, repulsion driven microphase separated and crystalline regimes. Macrophase separation is predicted in highly attractive low volume fraction systems. Attraction driven microphase separation is charaterized by long length scale divergences, where the ordering length scale determines the microphase ordered structures. The ordering length scale of repulsion driven microphase separation is determined by the repulsive range. At the high volume fractions, particles forgo the enthalpic considerations of attractions and repulsions to satisfy hard core constraints and maximize vibrational entropy. This results in site length scale ordering in rods, and the sphere length scale ordering in Janus spheres, i.e., crystallization. A change in the Janus balance of both rods and spheres results in quantitative changes in spinodal temperatures and the position of phase boundaries. However, a change in the block sequence of Janus rods causes qualitative changes in the type of microphase ordered state, and induces prominent features (such as the Lifshitz point) in the phase diagrams of these systems. A detailed study of the number of nearest neighbors in Janus rod systems reflect a deep connection between this local measure of structure, and the structure factor which represents the most global measure of order.
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This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.
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The Solar Intensity X-ray and particle Spectrometer (SIXS) on board BepiColombo's Mercury Planetary Orbiter (MPO) will study solar energetic particles moving towards Mercury and solar X-rays on the dayside of Mercury. The SIXS instrument consists of two detector sub-systems; X-ray detector SIXS-X and particle detector SIXS-P. The SIXS-P subdetector will detect solar energetic electrons and protons in a broad energy range using a particle telescope approach with five outer Si detectors around a central CsI(Tl) scintillator. The measurements made by the SIXS instrument are necessary for other instruments on board the spacecraft. SIXS data will be used to study the Solar X-ray corona, solar flares, solar energetic particles, the Hermean magnetosphere, and solar eruptions. The SIXS-P detector was calibrated by comparing experimental measurement data from the instrument with Geant4 simulation data. Calibration curves were produced for the different side detectors and the core scintillator for electrons and protons, respectively. The side detector energy response was found to be linear for both electrons and protons. The core scintillator energy response to protons was found to be non-linear. The core scintillator calibration for electrons was omitted due to insufficient experimental data. The electron and proton acceptance of the SIXS-P detector was determined with Geant4 simulations. Electron and proton energy channels are clean in the main energy range of the instrument. At higher energies, protons and electrons produce non-ideal response in the energy channels. Due to the limited bandwidth of the spacecraft's telemetry, the particle measurements made by SIXS-P have to be pre-processed in the data processing unit of the SIXS instrument. A lookup table was created for the pre-processing of data with Geant4 simulations, and the ability of the lookup table to provide spectral information from a simulated electron event was analysed. The lookup table produces clean electron and proton channels and is able to separate protons and electrons. Based on a simulated solar energetic electron event, the incident electron spectrum cannot be determined from channel particle counts with a standard analysis method.
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Este artículo presenta un nuevo método de identificación para sistemas de fase no mínima basado en la respuesta escalón. El enfoque propuesto provee un modelo aproximado de segundo orden evitando diseños experimentales complejos. El método propuesto es un algoritmo de identificación cerrado basado en puntos característicos de la respuesta escalón de sistemas de fase no mínima de segundo orden. Él es validado usando diferentes modelos lineales. Ellos tienen respuesta inversa entre 3,5% y 38% de la respuesta en régimen permanente. En simulaciones, ha sido demostrado que resultados satisfactorios pueden ser obtenidos usando el procedimiento de identificación propuesto, donde los parámetros identificados presentan errores relativos medios, menores que los obtenidos mediante el método de Balaguer.
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The accurate prediction of stress histories for the fatigue analysis is of utmost importance for the design process of wind turbine rotor blades. As detailed, transient, and geometrically non-linear three-dimensional finite element analyses are computationally weigh too expensive, it is commonly regarded sufficient to calculate the stresses with a geometrically linear analysis and superimpose different stress states in order to obtain the complete stress histories. In order to quantify the error from geometrically linear simulations for the calculation of stress histories and to verify the practical applicability of the superposition principal in fatigue analyses, this paper studies the influence of geometric non-linearity in the example of a trailing edge bond line, as this subcomponent suffers from high strains in span-wise direction. The blade under consideration is that of the IWES IWT-7.5-164 reference wind turbine. From turbine simulations the highest edgewise loading scenario from the fatigue load cases is used as the reference. A 3D finite element model of the blade is created and the bond line fatigue assessment is performed according to the GL certification guidelines in its 2010 edition, and in comparison to the latest DNV GL standard from end of 2015. The results show a significant difference between the geometrically linear and non-linear stress analyses when the bending moments are approximated via a corresponding external loading, especially in case of the 2010 GL certification guidelines. This finding emphasizes the demand to reconsider the application of the superposition principal in fatigue analyses of modern flexible rotor blades, where geometrical nonlinearities become significant. In addition, a new load application methodology is introduced that reduces the geometrically non-linear behaviour of the blade in the finite element analysis.
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We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.
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Dissertação de mest. em Engenharia de Sistemas e Computação - Área de Sistemas de Controlo, Faculdade de Ciências e Tecnologia, Univ.do Algarve, 2001
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Dissertação de mest. em Engenharia de Sistemas e Computação, Faculdade de Ciências e Tecnologia, Univ. do Algarve, 2002
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Resumo: Registros de sobrevivência do nascimento ao desmame de 3846 crias de ovinos da raça Santa Inês foram analisados por modelos de reprodutor linear e não linear (modelo de limiar), para estimar componentes de variância e herdabilidade. Os modelos usados para sobrevivência, analisada como característica da cria, incluíram os efeitos fixos de sexo, da combinação tipo de nascimento-criação da cria e da idade da ovelha ao parto, efeito da covariável peso da cria ao nascer e efeitos aleatórios de reprodutor, da classe rebanho-ano-estação e do resíduo. Componentes de variância para o modelo linear foram estimados pelo método da máxima verossimilhança restrita (REML) e para o modelo não linear por uma aproximação da máxima verossimilhança marginal (MML), pelo programa CMMAT2. O coeficiente de herdabilidade (h2) estimado pelo modelo de limiar foi de 0,29, e pelo modelo linear, 0,14. A correlação de ordem de Spearman entre as capacidades de transmissão dos reprodutores, com base nos dois modelos foi de 0,96. As estimativas de h2 obtidas indicam a possibilidade de se obter, por seleção, ganho genético para sobrevivência. [Linear and nonlinear models in genetic analyses of lamb survival in the Santa Inês hair sheep breed]. Abstract: Records of 3,846 lambs survival from birth to weaning of Santa Inês hair sheep breed, were analyzed by linear and non linear sire models (threshold model) to estimate variance components and heritability (h2). The models that were used to analyze survival, considered in this study as a lamb trait, included the fixed effects of sex of the lamb, combination of type of birth-rearing of lamb, and age of ewe, birth weight of lamb as covariate, and random effects of sire, herd-year-season and residual. Variance components were obtained using restricted maximum likelihood (REML), in linear model and marginal maximum likelihood in threshold model through CMMAT2 program. Estimate of heritability (h2) obtained by threshold model was 0.29 and by linear model was 0.14. Rank correlation of Spearman, between sire solutions based on the two models was 0.96. The obtained estimates in this study indicate that it is possible to acquire genetic gain to survival by selection.
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Efficient and reliable techniques for power delivery and utilization are needed to account for the increased penetration of renewable energy sources in electric power systems. Such methods are also required for current and future demands of plug-in electric vehicles and high-power electronic loads. Distributed control and optimal power network architectures will lead to viable solutions to the energy management issue with high level of reliability and security. This dissertation is aimed at developing and verifying new techniques for distributed control by deploying DC microgrids, involving distributed renewable generation and energy storage, through the operating AC power system. To achieve the findings of this dissertation, an energy system architecture was developed involving AC and DC networks, both with distributed generations and demands. The various components of the DC microgrid were designed and built including DC-DC converters, voltage source inverters (VSI) and AC-DC rectifiers featuring novel designs developed by the candidate. New control techniques were developed and implemented to maximize the operating range of the power conditioning units used for integrating renewable energy into the DC bus. The control and operation of the DC microgrids in the hybrid AC/DC system involve intelligent energy management. Real-time energy management algorithms were developed and experimentally verified. These algorithms are based on intelligent decision-making elements along with an optimization process. This was aimed at enhancing the overall performance of the power system and mitigating the effect of heavy non-linear loads with variable intensity and duration. The developed algorithms were also used for managing the charging/discharging process of plug-in electric vehicle emulators. The protection of the proposed hybrid AC/DC power system was studied. Fault analysis and protection scheme and coordination, in addition to ideas on how to retrofit currently available protection concepts and devices for AC systems in a DC network, were presented. A study was also conducted on the effect of changing the distribution architecture and distributing the storage assets on the various zones of the network on the system’s dynamic security and stability. A practical shipboard power system was studied as an example of a hybrid AC/DC power system involving pulsed loads. Generally, the proposed hybrid AC/DC power system, besides most of the ideas, controls and algorithms presented in this dissertation, were experimentally verified at the Smart Grid Testbed, Energy Systems Research Laboratory. All the developments in this dissertation were experimentally verified at the Smart Grid Testbed.
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Fully articulated hand tracking promises to enable fundamentally new interactions with virtual and augmented worlds, but the limited accuracy and efficiency of current systems has prevented widespread adoption. Today's dominant paradigm uses machine learning for initialization and recovery followed by iterative model-fitting optimization to achieve a detailed pose fit. We follow this paradigm, but make several changes to the model-fitting, namely using: (1) a more discriminative objective function; (2) a smooth-surface model that provides gradients for non-linear optimization; and (3) joint optimization over both the model pose and the correspondences between observed data points and the model surface. While each of these changes may actually increase the cost per fitting iteration, we find a compensating decrease in the number of iterations. Further, the wide basin of convergence means that fewer starting points are needed for successful model fitting. Our system runs in real-time on CPU only, which frees up the commonly over-burdened GPU for experience designers. The hand tracker is efficient enough to run on low-power devices such as tablets. We can track up to several meters from the camera to provide a large working volume for interaction, even using the noisy data from current-generation depth cameras. Quantitative assessments on standard datasets show that the new approach exceeds the state of the art in accuracy. Qualitative results take the form of live recordings of a range of interactive experiences enabled by this new approach.
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Il progetto di tesi è incentrato sull’ottimizzazione del procedimento di taratura dei regolatori lineari degli anelli di controllo di posizione e velocità presenti negli azionamenti usati industrialmente su macchine automatiche, specialmente quando il carico è ad inerzia variabile in dipendenza dalla posizione, dunque non lineare, come ad esempio un quadrilatero articolato. Il lavoro è stato svolto in collaborazione con l’azienda G.D S.p.A. ed il meccanismo di prova è realmente utilizzato nelle macchine automatiche per il packaging di sigarette. L’ottimizzazione si basa sulla simulazione in ambiente Matlab/Simulink dell’intero sistema di controllo, cioè comprensivo del modello Simulink degli anelli di controllo del drive, inclusa la dinamica elettrica del motore, e del modello Simscape del meccanismo, perciò una prima necessaria fase del lavoro è stata la validazione di tali modelli affinché fossero sufficientemente fedeli al comportamento reale. Il secondo passo è stato fornire una prima taratura di tentativo che fungesse da punto di partenza per l’algoritmo di ottimizzazione, abbiamo fatto ciò linearizzando il modello meccanico con l’inerzia minima e utilizzando il metodo delle formule di inversione per determinare i parametri di controllo. Già questa taratura, seppur conservativa, ha portato ad un miglioramento delle performance del sistema rispetto alla taratura empirica comunemente fatta in ambito industriale. Infine, abbiamo lanciato l’algoritmo di ottimizzazione definendo opportunamente la funzione di costo, ed il risultato è stato decisamente positivo, portando ad un miglioramento medio del massimo errore di inseguimento di circa il 25%, ma anche oltre il 30% in alcuni casi.