Data that is represented with high dimensionality presents a computational complexity challenge for many existing algorithms. Limiting dimensionality by discarding attributes is sometimes a poor solution to this problem because significant high-level concepts may be encoded in the data across many or all of the attributes. Non-linear dimensionality reduction (NLDR) techniques have been successful with many problems at minimizing dimensionality while preserving intrinsic high-level concepts that are encoded with varying combinations of attributes. Unfortunately, many challenges remain with existing NLDR techniques, including excessive computational requirements, an inability to benefit from prior knowledge, and an inability to handle certain difficult conditions that occur in data with many real-world problems. Further, certain practical factors have limited advancement in NLDR, such as a lack of clarity regarding suitable applications for NLDR, and a general inavailability of efficient implementations of complex algorithms. This dissertation presents a collection of papers that advance the state of NLDR in each of these areas. Contributions of this dissertation include: • An NLDR algorithm, called Manifold Sculpting, that optimizes its solution using graduated optimization. This approach enables it to obtain better results than methods that only optimize an approximate problem. Additionally, Manifold Sculpting can benefit from prior knowledge about the problem. • An intelligent neighbor-finding technique called SAFFRON that improves the breadth of problems that existing NLDR techniques can handle. • A neighborhood refinement technique called CycleCut that further increases the robustness of existing NLDR techniques, and that can work in conjunction with SAFFRON to solve difficult problems. • Demonstrations of specific applications for NLDR techniques, including the estimation of state within dynamical systems, training of recurrent neural networks, and imputing missing values in data. • An open source toolkit containing each of the techniques described in this dissertation, as well as several existing NLDR algorithms, and other useful machine learning methods.

The ability to effectively adapt a mesh is a very important feature of high fidelity finite element modeling. In a finite element analysis, a relatively high node density is desired in areas of the model where there are high error estimates from an initial analysis. Providing a higher node density in such areas improves the accuracy of the model and reduces the computational time compared to having a high node density over the entire model. Node densities can be determined for any model using the sizing functions based on the geometry of the model or the error estimates from the finite element analysis. Robust methods for mesh adaptation using sizing functions are available for refining triangular, tetrahedral, and quadrilateral elements. However, little work has been published for adaptively refining all hexahedral meshes using sizing functions. This thesis describes a new approach to drive hexahedral refinement based upon an error sizing function and a mechanism to compare the sizes of the node after refinement.

Mesh adaptation techniques are used to modify complex finite element meshes to reduce analysis time and improve accuracy. Modification of all-hexahedral meshes has proven difficult to the unique connectivity constraints they exhibit. This thesis presents an automated tool for local, conformal refinement of all-hexahedral meshes based on the insertion of multi-directional twist planes into the spatial twist continuum. The contributions of this thesis are (1) the ability to conformally refine all entities of an all-hexahedral element mesh, (2) the simplification of template insertion to multi-directional refinement. The refinement algorithm is divided into single hex sheet operations, where individual refinement steps are performed completely within a single hex sheet, and parallel sheet operation, where each refinement step occurs within two parallel hex sheets. Combining these two procedures facilitates the refinement of any mesh feature. Refinement is accomplished by replacing original mesh elements with one or more of six base templates selected by the number of nodes, flagged for refinement on the element. The refinement procedures are covered in detail with representative graphics and examples that illustrate the application of the techniques and the results of the refinement.

[pt] Malhas são amplamente usadas na discretização de domínios geométricos em aplicações na engenharia, como simulações de fluxo, transmissão de calor e deformação mecânica. O problema de geração de malhas é bem conhecido e estudado, mas a geração automática de malhas para um domínio físico com geometrias complexas, criando elementos que obedeçam a forma do objeto, e de tamanho e qualidade adequados, ainda é um desafio. Neste trabalho, foram estudados e implementados métodos para gerar malhas com restrições arbitrárias. O gerador implementado é do tipo de Delaunay, que constrói malhas Delaunay com restrições, e utiliza as propriedades da malha para inserir novos vértices e melhorar a qualidade dos elementos. / [en] Meshes are widely used in the discretization of geometric domains for engineering applications such as fluid flow simulator, heat transfer simulations and mechanical deformation. The mesh generation problem is well known and studied, nevertheless the automatic generation of meshes to domains with complex geometry, creating elements that conform to the forms, and of adequate size and quality, is still a challenge. In this work, mesh generation methods capable of generation mesh of arbitrary restrictions were studied and implemented. The implemented generator is a Delaunay generator, which constructs constrained Delaunay meshes, and utilizes the properties of the mesh to insert new vertices and improve the quality of the elements.

Shape memory alloys are incorporated as actuator elements due to their inherent ability to sense a change in temperature and actuate against external loads by undergoing a shape change as a result of a temperature-induced phase transformation. The cubic so-called austenite to the trigonal so-called R-phase transformation in NiTiFe shape memory alloys offers a practical temperature range for actuator operation at low temperatures, as it exhibits a narrow temperature-hysteresis with a desirable fatigue response. Overall, this work is an investigation of selected science and engineering aspects of low temperature NiTiFe shape memory alloys. The scientific study was performed using in situ neutron diffraction measurements at the newly developed low temperature loading capability on the Spectrometer for Materials Research at Temperature and Stress (SMARTS) at Los Alamos National Laboratory and encompasses three aspects of the behavior of Ni46.8Ti50Fe3.2 at 92 K (the lowest steady state temperature attainable with the capability). First, in order to study deformation mechanisms in the R-phase in NiTiFe, measurements were performed at a constant temperature of 92 K under external loading. Second, with the objective of examining NiTiFe in one-time, high-stroke, actuator applications (such as in safety valves), a NiTiFe sample was strained to approximately 5% (the R-phase was transformed to B19' phase in the process) at 92 K and subsequently heated to full strain recovery under a load. Third, with the objective of examining NiTiFe in cyclic, low-stroke, actuator applications (such as in cryogenic thermal switches), a NiTiFe sample was strained to 1% at 92 K and subsequently heated to full strain recovery under load. Neutron diffraction spectra were recorded at selected time and stress intervals during these experiments. The spectra were subsequently used to obtain quantitative information related to the phase-specific strain, texture and phase fraction evolution using the Rietveld technique. The mechanical characterization of NiTiFe alloys using the cryogenic capability at SMARTS provided considerable insight into the mechanisms of phase transformation and twinning at cryogenic temperatures. Both mechanisms contribute to shape memory and pseudoelasticity phenomena. Three phases (R, B19' and B33 phases) were found to coexist at 92 K in the unloaded condition (nominal holding stress of 8 MPa). For the first time the elastic modulus of R-phase was reported from neutron diffraction experiments. Furthermore, for the first time a base-centered orthorhombic (B33) martensitic phase was identified experimentally in a NiTi-based shape memory alloy. The orthorhombic B33 phase has been theoretically predicted in NiTi from density function theory (DFT) calculations but hitherto has never been observed experimentally. The orthorhombic B33 phase was observed while observing shifting of a peak (identified to be B33) between the R and B19' peaks in the diffraction spectra collected during loading. Given the existing ambiguity in the published literature as to whether the trigonal R-phase belongs to the P3 or P space groups, Rietveld analyses were separately carried out incorporating the symmetries associated with both space groups and the impact of this choice evaluated. The constrained recovery of the B19' phase to the R-phase recorded approximately 4% strain recovery between 150 K and 170 K, with half of that recovery occurring between 160 K and 162 K. Additionally, the aforementioned research methodology developed for Ni46.8Ti50Fe3.2 shape memory alloys was applied to experiments performed on a new high temperature Ni29.5Ti50.5Pd20 shape memory alloys. The engineering aspect focused on the development of (i) a NiTiFe based thermal conduction switch that minimized the heat gradient across the shape memory actuator element, (ii) a NiTiFe based thermal conduction switch that incorporated the actuator element in the form of helical springs, and (iii) a NiTi based release mechanism. Patents are being filed for all the three shape memory actuators developed as a part of this work. This work was supported by grants from SRI, NASA (NAG3-2751) and NSF (CAREER DMR-0239512) to UCF. Additionally, this work benefited from the use of the Lujan Center at the Los Alamos Neutron Science Center, funded by the United States Department of Energy, Office of Basic Energy Sciences, under Contract No. W-7405-ENG-36.

Simulations were performed to evaluate solution adaptive meshing strategies for flows with vortices whose axes of rotation are parallel to the bulk fluid motion. Two configurations were investigated: a wing in a wind tunnel and a missile spinning at 30Hz and 60Hz at 0◦ angle of attack with canards deflected 15◦. Feature-based descriptors were used to identify regions of the flow near vortices that are candidate regions for adaptive meshing. Several different adaptive meshing techniques were evaluated. These techniques include refinement around the vortex core, refinement near the vortex extent surface, refinement inside the extent surface, refinement inside and near the extent surface, and mesh regeneration using the vortex extent surface as an embedded surface. Results for the wing case, compared to experimental data, indicate that it is necessary to refine the region within and near the vortex extent surface to accurately recreate physical characteristics and achieve an acceptable solution.

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<p>The lateral superior olive (LSO) is a binaural nucleus that is critical for azimuthal sound localization. Bipolar principal cells of the LSO compute interaural level differences (ILDs) by comparing converging excitatory and inhibitory inputs driven by either ear. More specifically, this computation relies on integrating excitatory inputs from the ipsilateral cochlear nucleus with inhibitory, GABA/glycinergic inputs from the medial nucleus of the trapezoid body (MNTB), which are driven by sound originating at the contralateral ear. In order to reliably compute ILDs, the converging inputs must represent sounds of the same frequency. This specificity emerges during the first few weeks of postnatal life in rats as a result of functional and anatomical refinement. Interestingly, significant refinement of this auditory circuit occurs in the absence auditory experience. We focused on changes in the subcellular location of MNTB inputs and the expression of vesicular proteins before hearing onset.</p> <p>The subcellular distribution of inputs onto a neuron heavily influences synaptic integration and the mature distribution likely emerges during a period of circuit refinement. Little is known about how the inputs are distributed onto LSO principal cells and how the mature distribution is achieved. We studied the distribution of inhibitory inputs onto LSO neurons and found that significant re- distribution occurs before hearing onset. The mechanisms underlying the refinement of the inhibitory MNTB projection are not well understood but could be related to the transient co-transmission of the excitatory neurotransmitter glutamate. We studied the expression of vesicular proteins that may regulate the release of GABA/glycine and glutamate at the immature MNTB terminal. We found that MNTB terminals transiently express two Ca++ sensors, which may be associated with the different release properties for GABA/glycine and glutamate. Lastly, we asked one specific example of what controls the expression and sorting of vesicular proteins at the immature MNTB terminal.</p> / Doctor of Philosophy (PhD)