Calculating Sparse and Dense Correspondences for Near-Isometric Shapes

Comparing and analysing digital models are basic techniques of geometric shape processing. These techniques have a variety of applications, such as extracting the domain knowledge contained in the growing number of digital models to simplify shape modelling. Another example application is the analysis of real-world objects, which itself has a variety of applications, such as medical examinations, medical and agricultural research, and infrastructure maintenance. As methods to digitalize physical objects mature, any advances in the analysis of digital shapes lead to progress in the analysis of real-world objects. Global shape properties, like volume and surface area, are simple to compare but contain only very limited information. Much more information is contained in local shape differences, such as where and how a plant grew. Sadly the computation of local shape differences is hard as it requires knowledge of corresponding point pairs, i.e. points on both shapes that correspond to each other. The following article thesis (cumulative dissertation) discusses several recent publications for the computation of corresponding points: - Geodesic distances between points, i.e. distances along the surface, are fundamental for several shape processing tasks as well as several shape matching techniques. Chapter 3 introduces and analyses fast and accurate bounds on geodesic distances. - When building a shape space on a set of shapes, misaligned correspondences lead to points moving along the surfaces and finally to a larger shape space. Chapter 4 shows that this also works the other way around, that is good correspondences are obtain by optimizing them to generate a compact shape space. - Representing correspondences with a “functional map” has a variety of advantages. Chapter 5 shows that representing the correspondence map as an alignment of Green’s functions of the Laplace operator has similar advantages, but is much less dependent on the number of eigenvectors used for the computations. - Quadratic assignment problems were recently shown to reliably yield sparse correspondences. Chapter 6 compares state-of-the-art convex relaxations of graphics and vision with methods from discrete optimization on typical quadratic assignment problems emerging in shape matching

Hypercube matrix computation task

A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18)

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Frequency-dependent response of neurons to oscillating electric fields

Neuronal interactions with electric fields depend on the biophysical properties of the neuronal membrane as well as the geometry of the cell relative to the field vector. Biophysically detailed modeling of these spatial effects is central to understanding neuron-to-neuron electrical (ephaptic) interactions as well as how externally applied electrical fields, such as radio-frequency radiation from wireless devices or therapeutic Deep Brain Stimulation (DBS), interact with neurons. Here we examine in detail the shape-dependent response properties of cells in oscillating electrical fields by solving Maxwell's equations for geometrically extended neurons. Early modeling for compact (spherical) cells in alternating fields predicts a smaller effective membrane time constant for the field-cell system compared to direct current injection via whole-cell patch clamp. This result, predicting that cells should respond strongly to field oscillations in the kHz range, was verified later in vitro for murine myeloma cells. However, recent experiments on CA3 pyramidal cells (highly elongated neurons) in the hippocampus do not exhibit this high frequency response. In this thesis we examine the implications of modeling full two-way coupling between three-dimensional cylindrical neurons and the extracellular field utilizing three different methodologies, namely: cable equation, finite-difference and finite-element. Our modeling demonstrates that the electrotonic length and orientation of the cell to the field are key determinants of the neuronal response to oscillating fields. This explains the experimentally observed absence of the high frequency response for pyramidal neurons when the applied field direction is oriented along their dendritic axis. Additionally, we developed biophysically detailed models of neuronal membranes with quasi-active electrical properties stemming from voltage-gated currents. These are known to lead to resonances at characteristic frequencies in the case of current injection via whole-cell patch clamp. Interestingly, in the field-cell system, the resonance was masked in compact, spherical neurons but recovered in elongated neurons. Utilizing our cable and finite-element models, we investigate the effect of point-source stimulation on cylindrical neurons and find a novel type of "passive resonance" not reported before in the literature. We further extend our modeling by incorporating Hodgkin Huxley channels in to the membrane and construct a fully active, spiking model of a neuron, fully coupled to the applied electric fields. We then go on to embed the neuron in to an array of cells to validate our results at the tissue-level. These findings delineate the relationship between neuron shape, orientation and susceptibility to high frequency electric fields, with implications for DBS efficacy, ephaptic coupling in networks and the filtering properties of cortical tissue

Theoretical investigations prompted by experiments with baroclinic fluids

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Optimization of shell structure acoustics

This thesis analyzes a mathematical model for shell structure acoustics, and develops and implements the adjoint equations for this model. The adjoint equations allow the computation of derivatives with respect to large parameter sets in shape optimization problems where the thickness and mid-surface of the shell are computed so as to generate a radiated sound field subject to broad-band design requirements. The structure and acoustics are modeled, respectively, via the Naghdi shell equations, and thin boundary integral equations, with full coupling at the shell mid-surface. In this way, the three-dimensional structural-acoustic equations can be posed as a problem on the two-dimensional mid-surface of the shell. A wide variety of shapes can thus be explored without re-meshing, and the acoustic field can be computed anywhere in the exterior domain with little additional effort. The problem is discretized using triangular MITC shell elements and piecewise-linear Galerkin boundary elements, coupled with a simple one-to-one scheme. Prior optimization work on coupled shell-acoustics problems has been focused on applications with design requirements over a small range of frequencies. These problems are amenable to a number of simplifying assumptions. In particular, it is often assumed that the structure is dense enough that the air pressure loading can be neglected, or that the structural motions can be expanded in a basis of low-frequency eigenmodes. Optimization of this kind can be done with reasonable success using a small number of shape parameters because simple modal analysis permits a reasonable knowledge of the parts of the design that will require modification. None of these assumptions are made in this thesis. By using adjoint equations, derivatives of the radiated field can be efficiently computed with respect to large numbers of shape parameters, allowing a much richer space of shapes, and thus, a broader range of design problems to be considered. The adjoint equation approach developed in this thesis is applied to the computation of optimal mid-surfaces and shell thicknesses, using a large shape parameter set, proportional in size to the number of degrees of freedom in the underlying finite element discretization

Numerical methods for electromagnetic wave propagation and scattering in complex media

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Vita.Includes bibliographical references (p. 227-242).Numerical methods are developed to study various applications in electromagnetic wave propagation and scattering. Analytical methods are used where possible to enhance the efficiency, accuracy, and applicability of the numerical methods. Electromagnetic induction (EMI) sensing is a popular technique to detect and discriminate buried unexploded ordnance (UXO). Time domain EMI sensing uses a transient primary magnetic field to induce currents within the UXO. These currents induce a secondary field that is measured and used to determine characteristics of the UXO. It is shown that the EMI response is difficult to calculate in early time when the skin depth is small. A new numerical method is developed to obtain an accurate and fast solution of the early time EMI response. The method is combined with the finite element method to provide the entire time domain response. The results are compared with analytical solutions and experimental data, and excellent agreement is obtained. A fast Method of Moments is presented to calculate electromagnetic wave scattering from layered one dimensional rough surfaces. To facilitate the solution, the Forward Backward method with Spectral Acceleration is applied. As an example, a dielectric layer on a perfect electric conductor surface is studied. First, the numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation. Second, the accuracy, efficiency, and convergence of the method are studied for various rough surfaces and layer permittivities. The Finite Difference Time Domain (FDTD) method is used to study metamaterials exhibiting both negative permittivity and permeability in certain frequency bands.(cont.) The structure under study is the well-known periodic arrangement of rods and split-ring resonators, previously used in experimental setups. For the first time, the numerical results of this work show that fields propagating inside the metamaterial with a forward power direction exhibit a backward phase velocity and negative index of refraction. A new metamaterial design is presented that is less lossy than previous designs. The effects of numerical dispersion in the FDTD method are investigated for layered, anisotropic media. The numerical dispersion relation is derived for diagonally anisotropic media. The analysis is applied to minimize the numerical dispersion error of Huygens' plane wave sources in layered, uniaxial media. For usual discretization sizes, a typical reduction of the scattered field error on the order of 30 dB is demonstrated. The new FDTD method is then used to study the Angular Correlation Function (ACF) of the scattered fields from continuous random media with and without a target object present. The ACF is shown to be as much as 10 dB greater when a target object is present for situations where the target is undetectable by examination of the radar cross section only.by Christopher D. Moss.Ph.D

Theoretical and experimental study of light-nanoparticle interactions in high efficiency solar cells

[EN] This thesis studies the optical properties of random arrays of metal nanoparticles in multilayered substrates such as a solar cell, as well as the electrooptic consequences for those substrates. This study difers from traditional models which assume independent spherical particles in an homogeneous medium. Moreover, the efects beyond the near field range are studied because substrates thicker than 150µm are used. The study in this thesis uses two main approaches: a) A theoretical approach based on simulations and analytical models. Starting with the traditional methods (Mie), alternatives are considered for considering the substrate efect, the shape of the nanoparticles as well as the efect of the surrounding nanoparticles. For this, the use of Green functions and the Sommerfeld identity are presented as interesting strategies against traditional numerical model that are not suitable due to the complexity of the system that leads to huge power, time and memory consumptions. Nevertheless, the analytical approach has its limits and dificulties, that are analysed in this thesis. The results obtained in the thesis are compared with experimental data and a critical analysis is performed to check the real suitability and the scope of this strategy for simulating these kinds of systems. b) An experimental approach, in which special attention has been paid to the self-aggregation method as a quick way of integrating the nanoparticles on the final device. Some issues have been detected and studied related with the degradation of the nanoparticles, and some strategies to minimise this efect are presented. Integrated samples have been prepared using diferent integration approaches. From the measurements and their analysis the infuence of the substrate and other factors on the nanoparticle behaviour is confrmed, and the enhancement potential of the solar cell is studied. This thesis has been carried out at Valencia Nanophotonics Technology Center (NTC, in Spain) partly in the context of the LIMA european project (FP7-ICT-2009.3.8) and has included a short term scientific mission at the Laboratory of Photonics and Nanostructures (CNRS-LPN) at Marcoussis (France).[ES] En esta tesis se realiza un estudio de las propiedades ópticas de agrupaciones aleatorias de nanopartículas metálicas cuando éstas se depositan en un sustrato multicapa como una célula solar, así como las consecuencias electroópticas sobre dicho sustrato. Este estudio supone una diferencia importante con respecto a las hipótesis de modelos tradicionales en los que se suponen partículas individuales, perfectamente esféricas y en medios homogéneos. Además, estudia los efectos más allá del campo cercano al utilizar sustratos de más de 150µm de grosor. El trabajo de esta tesis gira en torno a dos enfoques principales: a) Un enfoque más teórico basado en simulaciones y modelos analíticos. Partiendo de los métodos tradicionales (Mie), se estudian métodos para incluir el efecto del sustrato, de la forma de las partículas y el efecto de las partículas cercanas. Para este fin, el uso de funciones de Green y de la identidad matemática de Sommerfeld se presentan como alternativas de gran interés frente al uso de modelos numéricos, inviables dada la complejidad del sistema y los recursos de memoria y tiempo necesarios. Aún así, los modelos analíticos presentan sus propias limitaciones y difcultades que son analizadas en esta tesis. Las soluciones obtenidas con estos modelos se han comparado con datos experimentales y un análisis crítico se ha llevado a cabo para determinar el alcance y la fabilidad de estas estrategias de simulación. b) Un enfoque más experimental, en el que se ha hecho especial hincapié en la autoagregación de capas finas como vía rápida para integrar las partículas en el dispositivo fnal. También se han estudiado los problemas asociados a la estabilidad de las nanopartículas con el tiempo y a cómo minimizar la degradación. Por otro lado, se han preparado varios dispositivos integrados siguiendo distintas estrategias y de cuyas medidas y análisis se ha confrmado el efecto del sustrato y otros factores sobre el comportamiento de las nanopartículas, así como estudiado la potencial mejora de la eficiencia en células solares. Esta tesis se ha realizado en su mayoría en el Centro de Tecnología Nanofotónica de Valéncia (NTC, en España) enmarcada parcialmente en el proyecto europeo LIMA (FP7-ICT-2009.3.8) y ha incluido una estancia investigadora en el Laboratorio de Fotónica y Nanoestructuras (CNRS-LPN) en Marcoussis (Francia).[CA] En aquesta tesi es realitza un estudi de les propietats òptiques d'agrupacions aleatòries de nanopartícules metàl·liques quan aquestes es depositen sobre un substrat multicapa com una cel·lula solar, així com les consequències electroòptiques resultants en el substrat. Aquest estudi presenta una difèrencia important amb les hipotesis de models tradicionals en els quals es suposa una partícula tota sola, perfectament esfèrica i en un medi homogeni. A més a més, s'estudiaran els efectes més enlla del camp proper a l'utilitzar substrats de més de 150µm d'espessor. El treball d'aquesta tesi es fara mitjançant dues estratègies principalment: a) Un enfocament més teòric emprant simulacions i models analítics. Començant amb models tradicionals (Mie), s'estudiaran estratègies per a incloure l'efecte d'un substrat, de la forma de les partícules així com el de la presència de partícules al voltant. Amb aquesta fnalitat, les funcions de Green i la identitat matemàtica de Sommerfeld es presenten com unes eines de gran interés comparat amb l'ús de mètodes numèrics tradicionals, els quals tenen uns requeriments excessius de memòria i temps de càlcul. Amb tot, aquests models analítics també tenen les seues limitacions i dificultats que són estudiades en la tesi. Les solucions obteses amb aquests models s'han comparat amb dades experimentals i s'ha fet un anàlisi crític per determinar l'abast de la validesa i la fiabilitat d'aquestes estrategies de simulació. b) Un enfocament més experimental, en el qual s'ha posat l'accent en l'auto-agregació de pel·lícules fines com a estratègia per a l'integració de les partícules en el dispositiu fnal. També s'han estudiat els problemes associats a l'estabilitat de les partícules amb el temps així com vies per a minimitzar aquesta degradació. D'altra banda, s'han preparat diversos dispositius integrats mitjannant diferents estratègies i a partir de les mesures de les quals s'ha confirmat l'efecte del substrat i d'altres factors en el comportament de les nanopartícules i s'ha estudiat la potencial millora de l'eficiència de la cèl·lula solar. Aquesta tesi s'ha dut a terme majoritàriament en el Centre de Tecnologia Nanofotonica de Valéncia (NTC) parcialment enmarcada en el projecte europeu LIMA (FP7-ICT-2009.3.8), i inclou la realització d'una estància al Laboratori de Fotònica i Nanoestructures (CNRS-LPN) en Marcoussis (França).Cortés Juan, F. (2015). Theoretical and experimental study of light-nanoparticle interactions in high efficiency solar cells [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59404TESI