This thesis examines the advantages to nonlinear least-squares (NLS) fitting of diffusion-weighted MRI data over the commonly used linear least-squares (LLS) approach. A modified fitting algorithm is proposed which accounts for the positive bias experienced in magnitude images at low SNR. For b-values in the clinical range (~1000 s/mm2), the increase in precision of FA and fibre orientation estimates is almost negligible, except at very high anisotropy. The optimal b-value for estimating tensor parameters was slightly higher for NLS. The primary advantage to NLS was improved performance at high b-values, for which complex fibre architectures were more easily resolved. This was demonstrated using a model-selection classifier based on higher-order diffusion models. Using a b-value of 3000 s/mm2 and magnitude-corrected NLS fitting, at least 10% of voxels in the brain exhibited diffusion profiles which could not be represented by the tensor model.

Multiple-Input Multiple-Output (MIMO) systems are a pivotal solution for the significant enhancement of the band-limited wireless channels’ communication capacity. MIMO system is essentially a wireless system with multiple antennas at both the transmitter and receiver ends. Compared to the conventional wireless systems, the main advantages of the MIMO systems are the higher system capacity, more bit rates, more link reliability, and wider coverage area. All of these features are currently considered as crucial performance requirements in wireless communications. Additionally, the emerging new services in wireless applications have created a great motivation to utilize the MIMO systems to fulfil the demands these applications create. The MIMO systems can be combined with other intelligent techniques to achieve these benefits by employing a higher spectral efficiency. The MIMO system design is a multifaceted problem which needs both antenna considerations and baseband signal processing. The performance of the MIMO systems depends on the cross-correlation coefficients between the transmitted/received signals by different antenna elements. Therefore, the Electromagnetic (EM) characteristics of the antenna elements and wireless environment can significantly affect the MIMO system performance. Hence, it is important to include the EM properties of the antenna elements and the physical environment in the MIMO system design and optimizations. In this research, the MIMO system model and system performance are introduced, and the optimum MIMO antenna system is investigated and developed by considering the electromagnetic aspects within three inter-related topics: 1) Fast Numerical Analysis and Optimization of the MIMO Antenna Structures: An efficient and fast optimization method is proposed based on the reciprocity theorem along with the method of moment analysis to minimize the correlation among the received/transmitted signals in MIMO systems. In this method, the effects of the radio package (enclosure) on the MIMO system performance are also included. The proposed optimization method is used in a few practical examples to find the optimal positions and orientations of the antenna elements on the system enclosure in order to minimize the cross-correlation coefficients, leading to an efficient MIMO operation. 2) Analytical Electromagnetic-Theoretic Model for the MIMO Antenna Design: The first requirement for the MIMO antennas is to obtain orthogonal radiation modes in order to achieve uncorrelated signals. Since the Spherical Vector Waves (SVW) form a complete set of orthogonal Eigen-vector functions for the radiated electromagnetic fields, an analytical method based on the SVW approach is developed to excite the orthogonal SVWs to be used as the various orthogonal modes of the MIMO antenna systems. The analytic SVW approach is used to design spherical antennas and to investigate the orthogonality of the radiation modes in the planar antenna structures. 3) Systematic SVW Methodology for the MIMO Antenna Design: Based on the spherical vector waves, a generalized systematic method is proposed for the MIMO antenna design and analysis. The newly developed methodology not only leads to a systematic approach for designing MIMO antennas, but can also be used to determine the fundamental limits and degrees of freedom for designing the optimal antenna elements in terms of the given practical restrictions. The proposed method includes the EM aspects of the antenna elements and the physical environment in the MIMO antenna system, which will provide a general guideline for obtaining the optimal current sources to achieve the orthogonal MIMO modes. The proposed methodology can be employed for any arbitrary physical environment and multi-antenna structures. Without the loss of generality, the SVW approach is employed to design and analyze a few practical examples to show how effective it can be used for MIMO applications. In conclusion, this research addresses the electromagnetic aspects of the antenna analysis, design, and optimization for MIMO applications in a rigorous and systematic manner. Developing such a design and analysis tool significantly contributes to the advancement of high-data-rate wireless communication and to the realistic evaluation of the MIMO antenna system performance by a robust scientifically-based design methodology.

Machine learning methods have been promising tools in science and engineering fields. The use of these methods in chemistry and drug design has advanced after 1990s. In this study, molecular electrostatic potential (MEP) surfaces of PCP-like compounds are modelled and visualized in order to extract features which will be used in predicting binding affinity. In modelling, Cartesian coordinates of MEP surface points are mapped onto a spherical self-organizing map. Resulting maps are visualized by using values of electrostatic potential. These values also provide features for prediction system. Support vector machines and partial least squares method are used for predicting binding affinity of compounds, and results are compared.

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.

The mechanical properties of materials are usually evaluated by performing a tensile or hardness test on the sample. Tensile tests are often time consuming, destructive and need specially prepared specimens. On the other hand, there is no direct theoretical correlation between the hardness number and the mechanical properties of a material although phenomenological relationships do exist. The advantages of indentation techniques are that they are non-destructive, quick, and can be applied to small material samples and localized in fashion. Mechanical properties are typically determined from spherical indentation load-depth curves. This process is again a time consuming one and not suitable for situations where a quick assessment is required such as in the sheet metal rolling industry. In the present study, a novel method of measuring mechanical properties of the material by multiple spherical indentations is developed. A series of indentations are made on the substrate with a spherical indenter with different loads. The diameter of the indentation is related to the load applied to determine the mechanical properties of the material, namely the yield strength and the work hardening parameters. To determine the diameter of the indentation quickly, a fiber optic sensing technique is developed. An incident light beam from a semiconductor laser is coupled back into an optical fiber upon reflection from the metal surface. By measuring the diffused light power reflected from the metal surface, the diameter of the indentation is measured. The spherical indentation technique is difficult for real time mechanical property measurement of sheet metal in a processing line. Problems arise as the strip is traveling at 2,000 to 4,000 ft/min (10,000 to 20,000 mm/sec) in the processing line. As a first step in developing a process that could be implemented in a real time processing line, a preliminary study has been conducted for the prediction of yield strength by laser shock processing.

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.

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.

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

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.

Bakalauro darbą „Įstrižojo astigmatizmo kompiuterinis modeliavimas sferiniuose ir asferiniuose lęšiuose“ sudaro įvadas, 5 dėstymo skyriai, išvados ir priedai. Darbe pateikiami 50 paveikslai ir 2 lentelės, cituojami 16 literatūros šaltinių. Darbo apimtis 66 lapai. Darbe apibendrinta literatūra apie lęšių aberacijas, jų įtaką regėjimo kokybei, bei minimalizavimą asferiniais lęšiais. Taip pat pateikiami matematiniai sferinių ir asferinių lęšių modeliai, bei įstrižojo astigmatizmo analizė šiuose lęšiuose. Įvade iškeliami darbo tikslai ir uždaviniai. Pirmajame skyriuje pateikta teorinė medžiaga apie lęšių aberacijas, antrajame – apie sferinius ir asferinius lęšius. Išanalizuoti galimi asferinių lęšių paviršiai ir jų pranašumas prieš sferinius paviršius. Trečiajame skyriuje pateikiamas matematinis spindulių eigos modelis sferiniame paviršiuje. Ketvirtajame – matematinis spindulių eigos modelis asferiniame paviršiuje. Penktajame skyriuje lyginami kompiuterinių modelių pagalba gauti įstrižojo astigmatizmo apibūdinti rezultatai, tangentinėmis paklaidomis. / The bachelor’s thesis „The computer modeling of oblique astigmatism in spherical and aspherical lenses” consists of introduction, 5 chapters, conclusions and attachments. The thesis introduces 50 figures, 2 tables and refers to 16 literary sources. The volume of the work is 66 pages. The work summarizes the literature which describes the lens aberrations, its influence to quality of vision and reduction by using aspheric lenses. There is also included mathematical models of spherical and aspheric lenses, and analysis of oblique astigmatism in them. The introduction sets the aims and the goals of the study. The first chapter contains theoretic material about lens aberrations, the second – about spherical and aspheric lenses, the analysis about available surfaces of aspheric lenses and advantages of them. The third chapter contains mathematical model of light rays pathway in spherical lenses. The fourth chapter contains mathematical model of light rays pathway in aspheric lenses. The fifth chapter contains comparison of oblique astigmatism described as tangential errors in those two models.