Дисертації з теми "Spherical coordinate"

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2007.
Title from electronic title page (viewed Mar. 27, 2008). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics and Astronomy." Discipline: Physics and Astronomy; Department/School: Physics and Astronomy.

A new angles-only initial relative orbit determination (IROD) algorithm is derived using three line-of-sight observations. This algorithm accomplishes this by taking a Singular Value Decomposition of a 6x6 matrix to arrive at an approximate initial relative orbit determination solution. This involves the approximate solution of 6 polynomial equations in 6 unknowns. An iterative improvement algorithm is also derived that provides the exact solution, to numerical precision, of the 6 polynomial equations in 6 unknowns. The initial relative orbit algorithm is also expanded for more than three line-of-sight observations with an iterative improvement algorithm for more than three line-of-sight observations. The algorithm is tested for a range of relative motion cases in low earth orbit and geosynchronous orbit, with and without the inclusion of J2 perturbations and with camera measurement errors. The performance of the IROD algorithm is evaluated for these cases and show that the tool is most accurate at low inclinations and eccentricities. Results are also presented that show the importance of including J2 perturbations when modelling the relative orbital motion for accurate IROD estimates. This research was funded in part by the Air Force Research Lab, Albuquerque, NM.

Orientador: Prof. Dr. Ricardo Luiz Viana
Dissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Física. Defesa: Curitiba, 24/05/2016
Inclui referências : f. 77-79
Resumo: Foi derivada uma equação de equilíbrio estacionário MHD de plasmas em rotação na direcção azimutal, no caso de um sistema de coordenadas esféricas, describindo o plasma como um fluido,e considerando a entropia como uma quantidade de superfície. A equação obtida é resolvida utilizando uma abordagem analítica e numérica para os perfis escolhidos das funções de corrente e de pressão em termos da função de fluxo. Gráficos foram feitos da solução obtida por este método. A rotação afecta apenas alguns componentes do campo magnético, da densidade decorrente, a corrente de fluxo poloidal, assim como a função de fluxo também é afectada pela rotação. palavras-chave: mhd. plasma. rotação. equilíbrio. estacionário
Abstract: An equation for MHD stationary equilibrium of rotating plasmas in the azimuthal direction is derived in the case of an spherical coordinate system, with a plasma description of a fluid, considered the entropy is a surface quantity. The equation obtained is solved using both an analytical and a semi-numerical approach for chosen profiles for the current and the pressure functions in terms of the flux function. Plots were made of the solution obtained by this method. The rotation affects only some components of the magnetic field and the current density, the flux function is also affected by the rotation. Keywords: mhd. plasma. rotation. equilibrium. stationary.

Isostatic equilibrium is commonly defined as the state achieved when there are no lateral gradients in hydrostatic pressure, and thus no lateral flow, at depth within the lower viscosity mantle that underlies a planetary body's outer crust. In a constant-gravity Cartesian framework, this definition is equivalent to the requirement that columns of equal width contain equal masses. Here we show, however, that this equivalence breaks down when the spherical geometry of the problem is taken into account. Imposing the "equal masses" requirement in a spherical geometry, as is commonly done in the literature, leads to significant lateral pressure gradients along internal equipotential surfaces and thus corresponds to a state of disequilibrium. Compared with the "equal pressures" model we present here, the equal masses model always overestimates the compensation depth-by similar to 27% in the case of the lunar highlands and by nearly a factor of 2 in the case of Enceladus. Plain Language Summary "Isostasy" is the principle that, just as an iceberg floats on the water, crustal rocks effectively float on the underlying higher density mantle, which behaves essentially like a fluid on geologic timescales. Although there are subtle inconsistencies among the various ways isostasy can be defined, they have not been historically problematic for bodies like the Earth, where the crust is thin compared with the overall radius. When the thickness of the crust is a nonnegligible fraction of a planetary body's radius, however, it becomes important to take the spherical geometry into account. In this case, the inconsistencies in the definitions can lead to significant discrepancies. Here we argue that one of the most commonly used approaches, which requires equal width columns to contain equal masses, always results in overestimating the crustal thickness. In particular, we suggest that the lunar and Martian highlands crustal thickness may have been overestimated by similar to 27% and similar to 10%, respectively, and that the ice shell thickness for Saturn's small icy moon Enceladus may have been overestimated by nearly a factor of 2.

The geometrical structure of a tree can consist of thousands, even millions, of branches, twigs and leaves in complex arrangements. The structure contains a lot of useful information and can be used for example to assess a tree's health or calculate parameters such as total wood volume or branch size distribution. Because of the complexity, capturing the structure of an entire tree used to be nearly impossible, but the increased availability and quality of particularly digital cameras and Light Detection and Ranging (LIDAR) instruments is making it increasingly possible. A set of digital images of a tree, or a point cloud of a tree from a LIDAR scan, contains a lot of data, but the information about the tree structure has to be extracted from this data through analysis. This work presents a method of reconstructing 3D models of trees from point clouds. The model is constructed from cylindrical segments which are added one by one. Bayesian inference is used to determine how to optimize the parameters of model segment candidates and whether or not to accept them as part of the model. A Hough transform for finding cylinders in point clouds is presented, and used as a heuristic to guide the proposals of model segment candidates. Previous related works have mainly focused on high density point clouds of sparse trees, whereas the objective of this work was to analyze low resolution point clouds of dense almond trees. The method is evaluated on artificial and real datasets and works rather well on high quality data, but performs poorly on low resolution data with gaps and occlusions.

This work serves to present the background, approach, and selected results for the initial master thesis and prototyping phase of Open Space, a joint visualization software development project by National Aeronautics and Space Administration (NASA), Linköping University (LiU) and the American Museum of Natural History (AMNH). The thesis report provides a theoretical introduction to heliophysics, modeling of space weather events, volumetric rendering, and an understanding of how these relate in the bigger scope of Open Space. A set of visualization tools that are currently used at NASA and AMNH are presented and discussed. These tools are used to visualize global heliosphere models, both for scientific studies and for public presentations, and are mainly making use of geometric rendering techniques. The paper will, in detail, describe a new approach to visualize the science models with volumetric rendering to better represent the volumetric structure of the data. Custom processors have been developed for the open source volumetric rendering engine Voreen, to load and visualize science models provided by the Community Coordinated Modeling Center (CCMC) at NASA Goddard Space Flight Center (GSFC). Selected parts of the code are presented by C++ code examples. To best represent models that are defined in non-Cartesian space, a new approach to volumetric rendering is presented and discussed. Compared to the traditional approach of transforming such models to Cartesian space, this new approach performs no such model transformations, and thus minimizes the amount of empty voxels and introduces less interpolation artifacts. Final results are presented as rendered images and are discussed from a scientific visualization perspective, taking into account the physics representation, potential rendering artifacts, and the rendering performance.

The basic problem with angle-only or bearings-only tracking is to estimate the trajectory of a target (i.e., position and velocity) by using noise corrupted sensor angle data. In this thesis, the tracking platform is an Aerial Vehicle and the target is simulated as another Aerial Vehicle. Therefore, the problem can be defined as a single-sensor bearings only tracking. The state consists of relative position and velocity between the target and the platform. In the case where both the target and the platform travel at constant velocity, the angle measurements do not provide any information about the range between the target and the platform. The platform has to maneuver to be able to estimate the range of the target. Two problems are investigated and tested on simulated data. The first problem is tracking non-maneuvering targets. Extended Kalman Filter (EKF), Range Parameterized Kalman Filter and particle filter are implemented in order to track non-maneuvering targets. As the second problem, tracking maneuvering targets are investigated. An interacting multiple model (IMM) filter and different particle filter solutions are designed for this purpose. Kalman filter covariance matrix initialization and regularization step of the regularized particle filter are discussed in detail.

碩士
國立中央大學
電機工程學系
101
The thesis develops a 3D spherical grid model, base on spherical coordinate and combined with impact-ionization model for the spherical P-N junction breakdown simulation. At theory aspect, we use poisson’s equation, electron and hole continuity equation to transfer the equivalent circuit into a model, and simulate the drift-diffusion current, generation and recombination current. At the structure, study the feature of spherical grid, and use trapezoid mesh to approximate the curvature, then build up the parameters. The breakdown voltage at spherical junction will be simulated with different radius and doping, and the result will be compared with Cartesian coordinate to verify this model. This model not only shows a good accuracy but also shows a less simulation time. Finally we investigate the application and feature of the 3D spherical grid model.

碩士
國立中興大學
資訊科學與工程學系所
99
Recently, due to the fast development of three dimensional (3D) models, watermarking three dimensional (3D) models for authentication and verification has become more and more important. In this paper, a new spherical coordinate based fragile watermarking scheme is proposed. At first, the three dimensional (3D) model is translated from the Cartesian coordinate system to the spherical coordinate system. Then the quantization index modulation technique is employed to embed and extract the watermark into the r coordinate for authentication and verification. By adapting the quantization index modulation technique together with some keys in the spherical coordinate system, the proposed method is robust against vertex reordering and similarity transformation attacks. Moreover, the distortion is controlled by the quantization step setting. Experimental results show that both the 100% embedding rate and low distortion can be achieved simultaneous in the proposed method. Moreover, the causality, convergence and synchronization problems can be overcome. Finally, the proposed scheme is robust against vertex reordering and similarity transformation attacks.

碩士
國立臺北科技大學
製造科技研究所
99
This paper describes fabricating technology to produce micro ball-ended spherical stylus tips for micro CMM’s tactile probing head. The study mainly used micro EDM method to glue and assemble micro glass spherical stylus tips. With combination of Wire Electro Discharge Grinding (WEDG) technology and position controlling function of CNC micro EDM, a micro ball-ended stylus could be assembled onto the front-top of micro electrode tool successfully. CCD in-process measurement was used to measure the profile and roundness of the styli tips. In order to investigate the fabrication characteristics, the study also used One Pulse Electric Discharge (OPED) technology to fabricate metal micro spherical stylus tips. The experimental results show that the roundness of the largest profile micro glass ball-ended stylus tips with diameter 0.07μm is as small as 2μm and adhesive force decreases rapidly at approximately 10.5mN. With the improvement of positional control technology and adhesive material, the gluing and assembling process of micro ball-ended stylus tips could be used on micro CMM’s tactile probing head for micro components metrology in the near future.

碩士
逢甲大學
資訊電機工程碩士在職學位學程
107
The purpose of the study is to design a zero-watermarking scheme for protecting copyright of 3D mesh objects. Owing to advance in technology, 3D models are commonly used in multiple fields such as healthcare, filmdom, interactive entertainment, and construction industry. In order to avoid the dangers of copying and using them without authentication, a novel zero-watermarking method based on the transformation of spherical coordinate and skewness of angle statistic is proposed. The main challenge is the robust feature selection and construction of the watermark. The skewness measure of the spherical angle is used to be the resilient feature. Experimental results display the robustness of the proposed scheme during common attacks such as translation, vertex reordering, uniform scaling, noise addition, smoothing, simplification, and cropping. This has demonstrated that the new method is suitable for the applications of the fields which need highly accurate 3D models.

A computational fluid dynamics model has been developed to examine the separation of an oil film from a spherical oil-coated particle falling through quiescent water due to gravity. Using this model, the separation process was studied as a function of the viscosity ratio of oil to water, R, and the ratio of viscous forces to surface tension, represented by the Capillary number Ca. The governing equations of this flow-induced motion are derived in a non-inertial spherical coordinate system, and discretized using a finite volume approach. The Volume-of-Fluid method is used to capture the oil/water interface. The model predicts two mechanisms for oil separation: at R less than 1, the shear difference between the particle/oil interface and the oil/water interface is not significant and Ca determines whether separation occurs or not; at R larger than 1, the shear difference is considerable, and the Ca effect becomes less dominant.

碩士
國立中央大學
電機工程研究所碩士在職專班
100
In this thesis, the breakdown phenomenon of a spherical PN junction is studied in 3D cylindrical coordinates. We analyze the shift of I-V curve, potential deviation and compare the deviation between 3D cylindrical coordinates and 3D Cartesian coordinates. We develop the trapezoid 3D cube in cylindrical coordinates. The simulation speed and accuracy in 3D cylindrical coordinates is better than that in Cartesian coordinates. We also verify the simulation result with the theory. Then, we change different parameters such as the radius of a p-n junction, doping concentration and grid points to see the dependence of breakdown voltage on these parameters. Finally, we study how to find a better grid design and get a better simulation result.

碩士
國立交通大學
應用數學系所
94
A simple and efficient compact fourth-order Poisson solver in cylindrical and spherical coordinates is presented. The solver relies on the truncated Fourier series expansion, where the differential equations of Fourier coefficients have been solved by fourth-order finite difference discretizations without pole conditions. And two kinds of efficient iterative method, GMRES and Bi-CGSTAB, with different preconditioners are applied to solve the resulted nonsymmetrical systems of Fourier coefficients.

A computational fluid dynamics model has been developed to study an oil-coated particle immersed in a uniform aqueous flow, to determine the conditions that favour oil separation. The governing flow equations are discretized using a finite volume approach, and the oil/water interface is captured using the Volume-of-Fluid (VOF) method in a 2D spherical coordinate system. The model predicts different mechanisms for oil separation. At a Reynolds number, Re, equal to 1, and at a low capillary number, Ca << 1, the high interfacial tension can induce rapid contact line motion, to the extent that the oil film can advance past its equilibrium position and separate from the particle. This mechanism requires that the contact angle measured through the oil phase is large. On the other hand, as Ca approaches 1, the shear exerted by the external flow stretches the oil into a thread that will eventually rupture and separate.

碩士
國立中央大學
電機工程研究所碩士在職專班
100
In this thesis, the major discussion is to improve the computer calculation time with the original simulation program in 3D rectangular coordinates. The small-angle method is used to divide the original silicon component into two parts. One is silicon region and the other is silicon-oxide region. The silicon region is inside the small-angle region, and we use the added silicon-oxide region to meet the simulation in 3D rectangular coordinates. Using this method, the simulation time is reduced to only one percent of the original. Further, the developed method is verified for its validity by the test with different parameters. So the small-angle method in 3D rectangular coordinates is workable and valuable.

Αντικείμενο της διατριβής είναι η επίλυση των προβλημάτων της σκέδασης επιπέδων ακουστικών κυμάτων χαμηλών συχνοτήτων από ένα διαπερατό σφαιρικό κέλυφος με έκκεντρο μαλακό, σκληρό ή διαπερατό πυρήνα και από μια μαλακή σφαίρα κάτω από ένα διαπερατό επίπεδο. Η λύση των προβλημάτων σκέδασης στην περιοχή χαμηλών συχνοτήτων επιδέχεται ανάπτυγμα Taylor σε δυνάμεις του κυματικού αριθμού k, όπου οι συντελεστές του αναπτύγματος (προσεγγίσεις χαμηλής συχνότητας) συνιστούν ακολουθία λύσεων στάσιμων προβλημάτων της θεωρίας δυναμικού. Ένα πρόβλημα σκέδασης μπορεί να δεχθεί προσέγγιση χαμηλών συχνοτήτων όταν το μήκος κύματος της κυματικής διαταραχής είναι πολύ μεγαλύτερο από την ακτίνα της ελάχιστης περιγεγραμμένης σφαίρας του σκεδαστή. Το δισφαιρικό σύστημα συντεταγμένων παρέχει κατάλληλο περιβάλλον για την επίλυση προβλημάτων πολλαπλής σκέδασης από δύο σφαίρες Αυτό ισχύει μόνο στη περιοχή των χαμηλών συχνοτήτων δεδομένου ότι η εξίσωση Laplace επιδέχεται διαμορφωμένο χωρισμό στις δισφαιρικές συντεταγμένες, ενώ δεν συμβαίνει το ίδιο στην εξίσωση Helmholtz. Προσαρμόζοντας το δισφαιρικό σύστημα συντεταγμένων στην δεδομένη γεωμετρία του κάθε προβλήματος απλουστεύεται η περιγραφή των χώρων που ορίζονται από το έκκεντρο σφαιρικό κέλυφος και οι σφαιρικές επιφάνειες του προβλήματός μας περιγράφονται από διαφορετικές τιμές της ίδιας συντεταγμένης μεταβλητής, ενώ ο απομακρυσμένος χώρος περιγράφεται από μια γειτονιά της αρχής των συντεταγμένων στο παραμετρικό χώρο των μεταβλητών η, θ. Επιλύοντας τα αντίστοιχα προβλήματα συνοριακών συνθηκών για μηδενική και πρώτης τάξεως προσεγγίσεις, καταλήγουμε σε αντίστοιχες αναγωγικές εξισώσεις ακολουθιών των συντελεστών ή αντίστοιχα συστήματα αναγωγικών εξισώσεων. Δεδομένου ότι οι ακολουθίες των συντελεστών συγκλείνουν ταχύτατα, περιοριζόμαστε στους πρώτους όρους συντελεστών και οι αναδρομικές εξισώσεις ή τα συστήματα αναγωγικών εξισώσεων ανάγονται σε εξισώσεις πινάκων ή γραμμικά συστήματα εξισώσεων με άγνωστους πίνακες στήλες και συντελεστές των αγνώστων τριδιαγώνιοι πίνακες. Με την πρωτότυπη αυτή μέθοδο προσδιορίζονται ακριβώς οι πρώτοι όροι χαμηλών συχνοτήτων των δύο προσεγγίσεων μηδενικής και οι πρώτης τάξεως, και στη συνέχεια οι προσεγγίσεις του πλάτους σκέδασης και των ενεργειακών διατομών σκέδασης. Μειώνοντας την απόσταση d των κέντρων συμπεραίνουμε ότι το πρόβλημα της σκέδασης ομόκεντρου σφαιρικού φλοιού δεν μπορεί να θεωρηθεί ειδική περίπτωση του προαναφερθέντος προβλήματος.
A plane wave is scattered by an acoustically soft, hard or penetrable sphere, covered by a penetrable non-concentric spherical lossless shell which disturbs the propagation of the incident plane wave field. There is exactly one bispherical coordinate system that fits the given two-sphere obstacle. If the wavelength of the incident field is much larger than the radius of the exterior sphere, Low Frequency Theory reduces the scattering problem to a sequence of potential problems which can be solved iteratively Applying the corresponding boundary value problem for each case, a set of two equations results as well as a recurrence equation with three unknown sequence of coefficients for zero-th order, and the first-order approximation is obtained, by solving two sets of two equations and a recurrence equation with three unknown sequence coefficients each for the soft core or the calculation of the zero–th order coefficients of the hard or penetrable core, leads to a solution of a linear system of two equations with two unknown columns and tri-diagonal square matrices are coefficients of the unknown columns, while the first-order approximation is obtained, by solving two linear systems of two equations with four unknown columns and eight tri-diagonal matrices as coefficients of the unknown columns. Applying the cut-off method for soft, hard and penetrable sphere, the low-frequency coefficients of the zero-th and first-order for the near field as well as the first and second-order coefficients are obtained for the normalized scattering amplitude and cross section. Decreasing the distance d of the centres we conclude that the problem of scattering concentric cell cannot be considered special case of mentioned before problem. A plane wave is scattered by an acoustical soft acoustic sphere embedded into an acoustically lossless half space, which disturbs the propagation of the incident wave field. In the first step, the problem of sound diffraction by only a penetrable plane is solved, were the amplitudes of reflective and diffractive acoustical waves are calculated. In the second step the diffractive as an incident wave is scattered by the embedded acoustical soft sphere. The low frequency zero-th and first order coefficients of the near field are calculated for the soft scatterer and finally the scattering amplitude and cross-section are determined.

This thesis contains solutions to chosen problems of applied mathematics. It comprises examples related to geometrical applications of the double and triple integrals´ theory, ie calculation methods of areas, volumes, mass and coordinates of gravity centres. Each problem´s solution is described in detail and supplemented with a picture. The problems are arranged according to complexity.

This thesis is devoted to creating a systematic way of determining all inequivalent orthogonal coordinate systems which separate the Hamilton-Jacobi equation for a given natural Hamiltonian defined on three-dimensional spaces of constant, non-zero curvature. To achieve this, we represent the problem with Killing tensors and employ the recently developed invariant theory of Killing tensors. Killing tensors on the model spaces of spherical and hyperbolic space enjoy a remarkably simple form; even more striking is the fact that their parameter tensors admit the same symmetries as the Riemann curvature tensor, and thus can be considered algebraic curvature tensors. Using this property to obtain invariants and covariants of Killing tensors, together with the web symmetries of the associated orthogonal coordinate webs, we establish an equivalence criterion for each space. In the case of three-dimensional spherical space, we demonstrate the surprising result that these webs can be distinguished purely by the symmetries of the web. In the case of three-dimensional hyperbolic space, we use a combination of web symmetries, invariants and covariants to achieve an equivalence criterion. To completely solve the equivalence problem in each case, we develop a method for determining the moving frame map for an arbitrary Killing tensor of the space. This is achieved by defining an algebraic Ricci tensor. Solutions to equivalence problems of Killing tensors are particularly useful in the areas of multiseparability and superintegrability. This is evidenced by our analysis of symmetric potentials defined on three-dimensional spherical and hyperbolic space. Using the most general Killing tensor of a symmetry subspace, we derive the most general potential “compatible” with this Killing tensor. As a further example, we introduce the notion of a joint invariant in the vector space of Killing tensors and use them to characterize a well-known superintegrable potential in the plane. xiii