144 resultados para discontinuous vector fields

em Queensland University of Technology - ePrints Archive


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Texture based techniques for visualisation of unsteady vector fields have been applied for the visualisation of a Finite volume model for variably saturated groundwater flow through porous media. This model has been developed by staff in the School of Mathematical Sciences QUT for the study of salt water intrusion into coastal aquifers. This presentation discusses the implementation and effectiveness of the IBFV algorithm in the context of visualisation of the groundwater simulation outputs.

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This paper studies the practical but challenging problem of motion planning for a deeply submerged rigid body. Here, we formulate the dynamic equations of motion of a submerged rigid body under the architecture of differential geometric mechanics and include external dissipative and potential forces. The mechanical system is represented as a forced affine-connection control system on the configuration space SE(3). Solutions to the motion planning problem are computed by concatenating and reparameterizing the integral curves of decoupling vector fields. We provide an extension to this inverse kinematic method to compensate for external potential forces caused by buoyancy and gravity. We present a mission scenario and implement the theoretically computed control strategy onto a test-bed autonomous underwater vehicle. This scenario emphasizes the use of this motion planning technique in the under-actuated situation; the vehicle loses direct control on one or more degrees of freedom. We include experimental results to illustrate our technique and validate our method.

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In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector fields. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces.

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In this paper, we develop and validate a new Statistically Assisted Fluid Registration Algorithm (SAFIRA) for brain images. A non-statistical version of this algorithm was first implemented in [2] and re-formulated using Lagrangian mechanics in [3]. Here we extend this algorithm to 3D: given 3D brain images from a population, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the non-statistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the regularizing (i.e., the non-conservative Lagrangian) terms, creating four versions of the algorithm. We evaluated the accuracy of each algorithm variant using the manually labeled LPBA40 dataset, which provides us with ground truth anatomical segmentations. We also compared the power of the different algorithms using tensor-based morphometry -a technique to analyze local volumetric differences in brain structure- applied to 46 3D brain scans from healthy monozygotic twins.

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We defined a new statistical fluid registration method with Lagrangian mechanics. Although several authors have suggested that empirical statistics on brain variation should be incorporated into the registration problem, few algorithms have included this information and instead use regularizers that guarantee diffeomorphic mappings. Here we combine the advantages of a large-deformation fluid matching approach with empirical statistics on population variability in anatomy. We reformulated the Riemannian fluid algorithmdeveloped in [4], and used a Lagrangian framework to incorporate 0 th and 1st order statistics in the regularization process. 92 2D midline corpus callosum traces from a twin MRI database were fluidly registered using the non-statistical version of the algorithm (algorithm 0), giving initial vector fields and deformation tensors. Covariance matrices were computed for both distributions and incorporated either separately (algorithm 1 and algorithm 2) or together (algorithm 3) in the registration. We computed heritability maps and two vector and tensorbased distances to compare the power and the robustness of the algorithms.

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In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented, where the deformation was regularized by penalizing deviations from a zero rate of strain. In, the terms regularizing the deformation included the covariance of the deformation matrices Σ and the vector fields (q). Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.

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Genetic and environmental factors influence brain structure and function profoundly. The search for heritable anatomical features and their influencing genes would be accelerated with detailed 3D maps showing the degree to which brain morphometry is genetically determined. As part of an MRI study that will scan 1150 twins, we applied Tensor-Based Morphometry to compute morphometric differences in 23 pairs of identical twins and 23 pairs of same-sex fraternal twins (mean age: 23.8 ± 1.8 SD years). All 92 twins' 3D brain MRI scans were nonlinearly registered to a common space using a Riemannian fluid-based warping approach to compute volumetric differences across subjects. A multi-template method was used to improve volume quantification. Vector fields driving each subject's anatomy onto the common template were analyzed to create maps of local volumetric excesses and deficits relative to the standard template. Using a new structural equation modeling method, we computed the voxelwise proportion of variance in volumes attributable to additive (A) or dominant (D) genetic factors versus shared environmental (C) or unique environmental factors (E). The method was also applied to various anatomical regions of interest (ROIs). As hypothesized, the overall volumes of the brain, basal ganglia, thalamus, and each lobe were under strong genetic control; local white matter volumes were mostly controlled by common environment. After adjusting for individual differences in overall brain scale, genetic influences were still relatively high in the corpus callosum and in early-maturing brain regions such as the occipital lobes, while environmental influences were greater in frontal brain regions that have a more protracted maturational time-course.

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Vector field visualisation is one of the classic sub-fields of scientific data visualisation. The need for effective visualisation of flow data arises in many scientific domains ranging from medical sciences to aerodynamics. Though there has been much research on the topic, the question of how to communicate flow information effectively in real, practical situations is still largely an unsolved problem. This is particularly true for complex 3D flows. In this presentation we give a brief introduction and background to vector field visualisation and comment on the effectiveness of the most common solutions. We will then give some examples of current development on texture-based techniques, and given practical examples of their use in CFD research and hydrodynamic applications.

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The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses. © 2000 American Institute of Physics.

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A complete change of career forces a seismic shift in every aspect of your life. From day one, you have to face the loss of long held beliefs, behaviours, the known world of self, and security. We came from professions that themselves are poles apart, and many of the challenges we faced entering the profession were the same: juggling full-time work, part time study, and family commitmemts, taking a pay cut, and loss of social life. But over a short period of time we both transitioned to our new profession successfully. so what make our successful transition possible?