An expansion method for the stationary Schrodinger equation of a particle moving freely in an arbitrary axisymmeric three dimensional region defined by an analytic function is introduced. The region is transformed into the unit ball by means of coordinate substitution. As a result the Schrodinger equation is considerably changed. The wavefunction is expanded into a series of spherical harmonics, thus, reducing the transformed partial differential equation to an infinite system of coupled ordinary differential equations. A Fourier-Bessel expansion of the solution vector in terms of Bessel functions with real orders is employed, resulting in a generalized matrix eigenvalue problem. The method is applied to two particular examples. The first example is a prolate spheroidal billiard which is also treated by using an alternative method. The numerical results obtained by using both the methods are compared. The second exampleis a billiard family depending on a parameter. Numerical results concerning the second example include the statistical analysis of the eigenvalues.

We establish a strong connection between buildings and Hecke algebras through the study of two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. In the affine case, it is shown how the building gives rise to a combinatorial and geometric description of the Macdonald spherical functions, and of the centers of affine Hecke algebras. The algebra homomorphisms from A into the complex numbers are studied, and some associated spherical harmonic analysis is conducted. This generalises known results concerning spherical functions on groups of p-adic type. As an application of this spherical harmonic analysis we prove a local limit theorem for radial random walks on affine buildings.

Thesis (M.S.)--Nuclear and Radiological Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Stacey, Weston M.; Committee Co-Chair: de Oliveira, Cassiano R.E.; Committee Member: Hertel, Nolan; Committee Member: van Rooijen, Wilfred F.G.

Animals are often able to solve complex navigational tasks in very challenging terrain, despite using low resolution sensors and minimal computational power, providing inspiration for robots. In particular, many species of insect are known to solve complex navigation problems, often combining an array of different behaviours (Wehner et al., 1996; Collett, 1996). Their nervous system is also comparatively simple, relative to that of mammals and other vertebrates. In the first part of this thesis, the visual input of a navigating desert ant, Cataglyphis velox, was mimicked by capturing images in ultraviolet (UV) at similar wavelengths to the ant’s compound eye. The natural segmentation of ground and sky lead to the hypothesis that skyline contours could be used by ants as features for navigation. As proof of concept, sky-segmented binary images were used as input for an established localisation algorithm SeqSLAM (Milford and Wyeth, 2012), validating the plausibility of this claim (Stone et al., 2014). A follow-up investigation sought to determine whether using the sky as a feature would help overcome image matching problems that the ant often faced, such as variance in tilt and yaw rotation. A robotic localisation study showed that using spherical harmonics (SH), a representation in the frequency domain, combined with extracted sky can greatly help robots localise on uneven terrain. Results showed improved performance to state of the art point feature localisation methods on fast bumpy tracks (Stone et al., 2016a). In the second part, an approach to understand how insects perform a navigational task called path integration was attempted by modelling part of the brain of the sweat bee Megalopta genalis. A recent discovery that two populations of cells act as a celestial compass and visual odometer, respectively, led to the hypothesis that circuitry at their point of convergence in the central complex (CX) could give rise to path integration. A firing rate-based model was developed with connectivity derived from the overlap of observed neural arborisations of individual cells and successfully used to build up a home vector and steer an agent back to the nest (Stone et al., 2016b). This approach has the appeal that neural circuitry is highly conserved across insects, so findings here could have wide implications for insect navigation in general. The developed model is the first functioning path integrator that is based on individual cellular connections.

[pt] Utilizam-se métodos de energia para a análise das resultantes de tensões que surgem em cascas esféricas de pequena espessura, submetidas a pressão interna. A análise é conduzida, aplicando o princípio da Energia Potencial Mínima, primeiramente através do método de Ritz e, logo após, através da descretização do vaso em elementos finitos, aproveitando a simetria da casca e utilizando um elemento curvilíneo. São obtidos resultados numéricos, estudando-se o comportamento dos esforços e distribuições dos mesmos, para calotas esféricas com engaste circunferêncial na base. Admitem-se variações na posição do vínculo assim como a presença ou não de um apoio elástico com espessura constante ou variável. / [en] The stress analysis of spherical shells subjected to internal pressures, using energy methods is presented in this paper. The performance of the Ritz method was compared with a finite element method using a curvilinear element, for axisymmetric loads. It is shown that the F.B.M gives superiors results, particularly when the shell is supported elastically. The analysis was performed for different support conditions and shells with non-uniform thickness. Several numerical results were collected in order to compare the relative advantages of the flexibility of the elastic foundation, the flexibility of the shell and the location of the clamped edge along the meridian.

Halo nuclei are formed when the last protons or neutrons are weakly bound to a tightly bound core. This allows the halo nucleons to tunnel far away from the core, resulting in a large r.m.s radius and therefore a large reaction cross section. Usually, halo nuclei possess only one bound state, the ground state, with all excited states being more or less unbound. When a nuclear potential is too weak to form a bound ground or excited state, the state can nevertheless be manifest physically as a positive energy resonance. Experimentally, low energy resonance like structures have been observed in the three-body continuum of certain halo nuclei eg. 6He → alpha + n + n. However, from a strict theoretical point of view, a resonance corresponds to a pole in the scattering amplitude at a complex energy. Halo nuclei have been successfully modelled as three-body systems in the hyper-spherical harmonic calculation scheme. Here the R-matrix method is used in solving the coupled hyperradial equations. It is critical that the long-range nature of the couplings in this system are incorporated correctly when evaluating the S-matrix. This is achieved through the use of coupled asymptotic solutions to the radial equation. These procedures have enabled a number of resonance-like S-matrix poles to be located for the 2+, 0+ and 1- spin-parity states in the low energy continuum of 6He.

This thesis presents Bayesian geoacoustic inversion of seabed reflection-coefficient data as part of the U.S. Office of Naval Research Seabed Characterization Experiment 2017 at the New England Mud Patch. First, a linearized, ray-based Bayesian inversion of acoustic arrival times is carried out for high-precision estimation of experiment geometry and uncertainties, representing an important first step to inferring seabed properties using geoacoustic inversion methods such as reflection inversion. The high-precision estimates for source-receiver ranges, source depths, receiver depths, and water depths at reflection points along the survey track are used to calculate grazing angles, with angle uncertainties computed using Monte Carlo methods. The experiment geometry uncertainties are obtained using analytic linearized estimates, and verified with nonlinear analysis. Second, a trans-dimensional (trans-D) Bayesian inversion of reflection-coefficient data is carried out for geoacoustic parameters and uncertainties of fine-grained/cohesive sediments. The trans-D inversion samples probabilistically over an unknown number of seabed interfaces and the parameters of a zeroth- or first-order autoregressive error model. The numerical method of parallel tempering reversible jump Markov-chain Monte Carlo sampling is employed. Spherical-wave reflection coefficient modelling is applied using plane-wave decomposition in the Sommerfeld integral. The inversion provides marginal posterior probability profiles for Buckingham's viscous grain-shearing parameters: porosity, grain-to-grain compressional modulus, material exponent, and compressional viscoelastic time constant as a function of depth in the sediment. These parameters are used to compute dispersion relationships for each layer in the model, providing marginal posterior probability profiles for compressional-wave velocity and attenuation at different frequencies, as well as density. The geoacoustic inversion results are compared to independent measurements of sediment properties. / Graduate

O presente trabalho enfoca o estudo de transdutores indutivos de deslocamento linear. Dentre os diversos dispositivos dessa natureza, procurou-se desenvolver um estudo mais aprofundado do transdutor indutivo diferencial com núcleo de esferas. O desenvolvimento experimental, com a construção de quatro protótipos, levou ao projeto de um transdutor com características adequadas ao uso industrial. / The present work focuses on the study of inductive transducers of linear displacement. Among the several devices of that nature, a more detailed study of the inductive differential transducer was attempted with core of spherical balls. The experimental development of four prototypes resulted in a transducer with characteristics adequate for industrial use to be designed.

abstract: In-situ exploration of planetary bodies such as Mars or the Moon have provided geologists and planetary scientists a detailed understanding of how these bodies formed and evolved. In-situ exploration has aided in the quest for water and life-supporting chemicals. In-situ exploration of Mars carried out by large SUV-sized rovers that travel long distance, carry sophisticated onboard laboratories to perform soil analysis and sample collection. But their large size and mobility method prevents them from accessing or exploring extreme environments, particularly caves, canyons, cliffs and craters. This work presents sub- 2 kg ball robots that can roll and hop in low gravity environments. These robots are low-cost enabling for one or more to be deployed in the field. These small robots can be deployed from a larger rover or lander and complement their capabilities by performing scouting and identifying potential targets of interest. Their small size and ball shape allow them to tumble freely, preventing them from getting stuck. Hopping enables the robot to overcome obstacles larger than the size of the robot. The proposed ball-robot design consists of a spherical core with two hemispherical shells with grouser which act as wheels for small movements. These robots have two cameras for stereovision which can be used for localization. Inertial Measurement Unit (IMU) and wheel encoder are used for dead reckoning. Communication is performed using Zigbee radio. This enables communication between a robot and a lander/rover or for inter-robot communication. The robots have been designed to have a payload with a 300 gram capacity. These may include chemical analysis sensors, spectrometers and other small sensors. The performance of the robot has been evaluated in a laboratory environment using Low-gravity Offset and Motion Assistance Simulation System (LOMASS). An evaluation was done to understand the effect of grouser height and grouser separation angle on the performance of the robot in different terrains. The experiments show with higher grouser height and optimal separation angle the power requirement increases but an increase in average robot speed and traction is also observed. The robot was observed to perform hops of approximately 20 cm in simulated lunar condition. Based on theoretical calculations, the robot would be able to perform 208 hops with single charge and will operate for 35 minutes. The study will be extended to operate multiple robots in a network to perform exploration. Their small size and cost makes it possible to deploy dozens in a region of interest. Multiple ball robots can cooperatively perform unique in-situ science measurements and analyze a larger surface area than a single robot alone on a planet surface. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2016

Made available in DSpace on 2014-06-11T19:22:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-07-29Bitstream added on 2014-06-13T20:10:04Z : No. of bitstreams: 1 basso_gg_me_sjrp_parcial.pdf: 127718 bytes, checksum: 3bfde1c4f9ff597bf78cc0fd338d9fe8 (MD5) Bitstreams deleted on 2015-08-28T16:08:53Z: basso_gg_me_sjrp_parcial.pdf,. Added 1 bitstream(s) on 2015-08-28T16:09:58Z : No. of bitstreams: 1 000670722.pdf: 6039395 bytes, checksum: a8326c9658e562fa0ebe828de242a31a (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Financiadora de Estudos e Projetos (FINEP) / Partículas poliméricas com tamanho e morfologia controlados e propriedades físico-químicas adequadas são amplamente utilizadas em aplicações médicas, como na embolização, uma técnica cirúrgica utilizada para tratar malformações arteriovenosas (MAVs), conter hemorragias, tratar localmente tumores hipervascularizados (THVs) e outras doenças vasculares. Este procedimento é realizado com materiais de diferentes formas e composições, sendo as partículas de poli(álcool vinílico) (PVA) freqüentemente utilizadas por apresentarem um alto grau de desempenho. Elas estão disponíveis no mercado nas morfologias esférica e não-esférica, sendo que as esféricas apresentam uma maior eficácia no tratamento. O presente trabalho objetivou desenvolver e aprimorar partículas esféricas de PVA e poli(acetato vinílico) (PVAc) para serem utilizadas em embolização. Suas sínteses foram realizadas em duas etapas: a polimerização em suspensão do monômero acetato vinílico (VAc) em PVAc e a saponificação do polímero PVAc em PVA, com variações na velocidade de agitação e na concentração da solução de hidróxido de sódio (NaOH), na etapa da saponificação. As partículas foram caracterizadas por microscopia eletrônica de varredura (MEV), difração de raios-X (DRX), calorimetria diferencial de varredura (DSC) e ressonância magnética nuclear de 13 C - cross polarization / magic angle spinning (13 C RMN CP/MAS). Foram analisadas a distribuição de tamanhos, a dimensão fractal, a determinação da biocarga, que determinou os parâmetros de esterilização por radiação gama, e a citotoxicidade, pelo teste de “Reatividade Biológica in vitro”. Os resultados indicaram que a morfologia esférica foi obtida durante a primeira etapa da síntese e que essa morfologia não foi afetada pelo segundo processo. A velocidade de agitação e a concentração de NaOH influenciaram... / Polymeric particles with controlled size and morphology and appropriated physicochemical properties are widely used in medical applications, such as embolization, a surgical technique used to treat arteriovenous malformations (AVMs), stop bleedings, treat locally hypervascular tumors (HVTs) and other vascular diseases. This procedure is performed with materials of different shapes and compositions, and the poly(vinyl alcohol) (PVA) particles are often used for presenting a high degree of performance. They are commercially available in spherical and non-spherical morphologies, and the spherical particles have a greater efficacy in the treatment. This study aimed to develop and improve spherical PVA and poly(vinyl acetate) (PVAc) particles for use in embolization. Their syntheses were performed in two stages: the suspension polymerization of vinyl acetate (VAc) monomer in PVAc and the saponification of PVAc polymer in PVA, with variations in the stirring speed and the concentration of sodium hydroxide (NaOH) solution, at the saponification step. The particles were characterized by scanning electronic microscopy (SEM), X-ray diffraction (XRD), differential scanning calorimetry (DSC) and 13 C nuclear magnetic resonance - cross polarization / magic angle spinning (13 C NMR CP/MAS). We analyzed the size distribution, the fractal dimension, the determining of the bioburden, which determined the parameters of sterilization by gamma irradiation, and the cytotoxicity, by the “Biological Reactivity in vitro”. The results indicated that the spherical morphology was obtained during the first stage of the synthesis and that this morphology was not affected by the second process. The stirring speed and the NaOH concentration influenced the size of the particles. The commercial particles have a fractal dimension greater than the synthesized particles... (Complete abstract click electronic access below)