A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.

In this study, firstly, in order to achieve fine grains in solid solution strengthened AZ31 magnesium alloy by friction stir processing (FSP), various efforts have been made. It has found that with a newly designed cooling system, the microstructure of commercial AZ31 alloy can be refined dramatically by carefully controlling the FSP parameters. It is of scientific interest that nanometer grains have been observed in the resultant microstructure for the AZ alloy experienced by two-pass FSP. Besides, in order to modify the microstructure and mechanical properties, FSP is also applied to incorporate AZ31 Mg alloy with nano-ZrO2 particles, nano-SiO2 particles and different fractions of Al and Zn elements. The microstructure and mechanical properties of the modified alloy and composite samples are investigated and compared. By one-pass FSP coupled with rapid heat sink from liquid nitrogen cooling approach, the ultrafine grain size in AZ31 Mg alloy is successfully achieved. The grain boundaries are well defined and the mean grain size can be refined to 100~300 nm from the initial 75 £gm of commercial AZ31 Mg alloys sheets. The ultrafine grained structure can drastically increases the microhardness from the initial 50 up to 120 Hv, or an increment factor of 2.4 times. Furthermore, the nanometer grains can be even achieved by two passes FSP coupled with rapid heat sink. The resulting microstructure exhibits equiaxed grains ranging from 40 nm to 200 nm with an average grain size of less than 100 nm. The nanocrystalline grains can be characterized by the TEM observations and the diffraction rings in SAD patterns. The highest hardness point can reach ~150 Hv which is equal to triple of the AZ31 matrix, and the mean hardness also increases up to around 134 Hv. Bulk Mg-AZ31 based composites with 10~20 vol% of nano-ZrO2 particles and 5~10 vol% of nano-SiO2 particles are also successfully fabricated by FSP. The average grain size of the resultant composites could be effectively refined to 2~4 £gm, and it demonstrates much higher hardness values compared to commercial AZ31 billet. Moreover, for the Mg/ZrO2 composite fabricated by one pass and subsequent cooling pass FSP, the recrystallized grain size could be further refined to 0.4 £gm with the hardness value of 135 Hv. As for multi-element Mg base alloys fabricated by FSP, high fractions of Al and Zn elements can result in apparent grain refinement, this can be proved by the broadening of diffraction peaks. Multi-passes FSP can induce the appearance of intermetallic compounds, however, some of them are quasi-crystals with icosahedral point group symmetry. The average hardness of the resultant alloys reachs nearly 350 in Hv scale due to the generation of intermetallic compounds and grain refinement.

<p>This thesis deals with Computational Fluid Dynamics (CFD)simulations of the flow around delta wings at high angles ofattack. These triangular wings, mainly used in militaryaircraft designs, experience the formation of two vortices ontheir lee-side at large angles of attack. The simulation ofthis vortical flow by solving the Navier-Stokes equations isthe subject of this thesis. The purpose of the work is toimprove the understanding of this flow and contribute to thedesign of such a wing by developing methods that enable moreaccurate and efficient CFD simulations.</p><p>Simulations of the formation, burst and disappearance of thevortices while the angle of attack is changing are presented.The structured flow solver NSMB has been used to get thetime-dependent solutions of the flow. Both viscous and inviscidresults of a 70°-swept delta wing pitching in anoscillatory motion are reported. The creation of the dynamiclift and the hysteresis observed in the history of theaerodynamic forces are well reproduced.</p><p>The second part of the thesis is focusing on automatic meshrefinement and its influence on simulations of the delta wingleading-edge vortices. All the simulations to assess the gridquality are inviscid computations performed with theunstructured flow solver EDGE. A first study reports on theeffects of refining thewake of the delta wing. A70°-swept delta wing at a Mach number of 0.2 and an angleof attack of 27° where vortex breakdown is present abovethe wing, is used as testcase. The results show a strongdependence on the refinement, particularly the vortex breakdownposition, which leads to the conclusion that the wake should berefined at least partly. Using this information, a grid for thewing in the wind tunnel is created in order to assess theinfluence of the tunnel walls. Three sensors for automatic meshrefinement of vortical flows are presented. Two are based onflow variables (production of entropy and ratio of totalpressures) while the third one requires an eigenvalue analysisof the tensor of the velocity gradients in order to capture theposition of the vortices in the flow. These three vortexsensors are successfully used for the simulation of the same70° delta wing at an angle of attack of 20°. Acomparison of the sensors reveals the more local property ofthe third one based on the eigenvalue analysis. This lattertechnique is applied to the simulation of the wake of a deltawing at an angle of attack of 20°. The simulations on ahighly refined mesh show that the vortex sheet shed from thetrailing-edge rolls up into a vortex that interacts with theleading-edge vortex. Finally the vortex-detection technique isused to refine the grid around a Saab Aerosystems UnmannedCombat Air Vehicle (UCAV) configuration and its flight dynamicscharacteristics are investigated.</p><p><b>Key words:</b>delta wing, high angle of attack, vortex,pitching, mesh refinement, UCAV, vortex sensor, tensor ofvelocity gradients.</p>

We present an $hp$-adaptive strategy that is based on estimating the decay of the expansion coefficients when a function is expanded in $L^2$-orthogonal polynomails on a triangle or a tetrahedron. This method is justified by showing that the decay of the coefficients is exponential if and only if the function is analytic. Numerical examples illustrate the performance of this approach, and we compare it with two other $hp$-adaptive strategies.

Concurrent systems are getting more complex with the advent of multi-core processors and the support of concurrent programs. However, errors of concurrent systems are too subtle to detect with the traditional testing and simulation. Model checking is an effective method to verify concurrent systems by exhaustively searching the complete state space exhibited by a system. However, the main challenge for model checking is state explosion, that is the state space of a concurrent system grows exponentially in the number of components of the system. The state space explosion problem prevents model checking from being applied to systems in realistic size. After decades of intensive research, a large number of methods have been developed to attack this well-known problem. Compositional verification is one of the promising methods that can be scalable to large complex concurrent systems. In compositional verification, the task of verifying an entire system is divided into smaller tasks of verifying each component of the system individually. The correctness of the properties on the entire system can be derived from the results from the local verification on individual components. This method avoids building up the global state space for the entire system, and accordingly alleviates the state space explosion problem. In order to facilitate the application of compositional verification, several issues need to be addressed. The generation of over-approximate and yet accurate environments for components for local verification is a major focus of the automated compositional verification. This dissertation addresses such issue by proposing two abstraction refinement methods that refine the state space of each component with an over-approximate environment iteratively. The basic idea of these two abstraction refinement methods is to examine the interface interactions among different components and remove the behaviors that are not allowed on the components' interfaces from their corresponding state space. After the extra behaviors introduced by the over-approximate environment are removed by the abstraction refinement methods, the initial coarse environments become more accurate. The difference between these two methods lies in the identification and removal of illegal behaviors generated by the over-approximate environments. For local properties that can be verified on individual components, compositional reasoning can be scaled to large systems by leveraging the proposed abstraction refinement methods. However, for global properties that cannot be checked locally, the state space of the whole system needs to be constructed. To alleviate the state explosion problem when generating the global state space by composing the local state space of the individual components, this dissertation also proposes several state space reduction techniques to simplify the state space of each component to help the compositional minimization method to generate a much smaller global state space for the entire system. These state space reduction techniques are sound and complete in that they keep all the behaviors on the interface but do not introduce any extra behaviors, therefore, the same verification results derived from the reduced global state space are also valid on the original state space for the entire system. An automated compositional verification framework integrated with all the abstraction refinement methods and the state space reduction techniques presented in this dissertation has been implemented in an explicit model checker Platu. It has been applied to experiments on several non-trivial asynchronous circuit designs to demonstrate its scalability. The experimental results show that our automated compositional verification framework is effective on these examples that are too complex for the monolithic model checking methods to handle.

Aluminium alloys, including both foundry and wrought alloys, have been extensively used for light-weight structural and functional applications. A grain refined as-cast microstructure is generally highly desirable for either subsequent processing ability or mechanical properties of the finished components. In this thesis, the grain refined microstructures in Al alloys have been achieved by intensive melt shearing using the melt conditioning by advanced shearing technology (MCAST) without deliberate grain refiner additions. Such grain refinement has been attributed to the enhanced heterogeneous nucleation on the dispersed oxide particles. It has been established that the naturally occurring oxides in molten Al alloys normally have a good crystallographic match with the a-Al phase, indicating the high potency of oxide particles as the nucleation sites of the a-Al phase. The governing factors for these oxide particles to be effective grain refiners in Al alloys have been proposed, including the achievement of good wetting between oxide particles and liquid aluminium, a sufficient number density and uniform spatial distribution of the dispersed oxide particles, and near equilibrium kinetic conditions in liquid alloys. In the present study, near equilibrium kinetic conditions can be achieved by intensive melt shearing using a twin screw mechanism, which has been confirmed by the observed equilibrium a-AlFeSi phase in a cast Al alloy and the transformation from g- to a-Al2O3 at 740±20oC under intensive shearing. For different alloy systems, depending on the alloy system, and melting conditions, due to the particular types of oxide formed and its crystallographic and chemical characteristics, the nucleation site of the nucleated phase is different. Specifically, MgAl2O4 relative to MgO, and a-Al2O3 relative to g-Al2O3, have higher potency as heterogeneous nucleation sites of a-Al phase in Al alloys. In future, the modification of the crystallographic match, and of the other surface characteristics related to the interfacial energy between the specific oxides and nucleated phase by trace alloying addition through segregation to the interface between oxides and nucleated phases combined with physical melt processing (such as intensive shearing in the present study) should be investigated in more detail.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第18987号 / 工博第4029号 / 新制||工||1620 / 31938 / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 辻 伸泰, 教授 白井 泰治, 教授 松原 英一郎 / 学位規則第4条第1項該当

The ability of a neuron to alter its synaptic connections during development is essential to circuit assembly. Synapse remodeling or refinement has been observed in many species and many neuronal circuits, yet the mechanisms defining which neurons undergo remodeling are unclear. Moreover, the molecules that execute the process of remodeling are also obscure. To address this issue, we sought to identify targets of the transcription factor unc-55 COUP-TF, which acts as a cell-specific repressor of synapse remodeling in C. elegans. unc-55 COUP-TF is expressed in VD neurons, where it prevents synapse remodeling. DD neurons can remodel synapses because they do not express unc-55 COUP-TF. Ectopic expression of unc-55 COUP-TF in DD neurons prevents remodeling. We identified the transcription factor Hunchback-like hbl-1 as a target of UNC-55 COUP-TF repression. Differential expression of hbl-1 explains the cell-type specificity of remodeling. hbl-1 is expressed in the DD neurons that are capable of remodeling, and is not expressed in the VD neurons that do not remodel. In unc-55 mutants, hbl-1 expression increases in VD neurons where it promotes ectopic remodeling. Moreover, hbl-1 expression levels bidirectionally regulate the timing of DD remodeling, as increases in hbl-1 cause precocious remodeling while decreases in hbl-1 cause remodeling delays. Finally, hbl-1 coordinates heterochronic microRNA and neuronal activity pathways to regulate the timing of remodeling. Increases or decreases in circuit activity cause increases or decreases in hbl-1 expression, and consequently early or delayed remodeling. Thus, convergent regulation of hbl-1 expression defines a genetic mechanism that patterns activity-dependent synaptic remodeling across cell types and across developmental time. We identified other targets of UNC-55 COUP-TF regulation using gene expression profiling, and implicate some of these factors in the regulation of remodeling using functional genomic screens. Our work suggests roles for conserved networks of transcription factors in the regulation of remodeling. We propose a model in which hbl-1 and other targets of unc-55 COUP-TF transcriptional repression are responsible for regulating synapse remodeling in C. elegans.

Microglia, the brain's resident immune cells and phagocytes, are emerging as critical regulators of developing synaptic circuits in the healthy brain after having long been thought to function primarily during central nervous system (CNS) injury or disease. Recent work indicates that microglia engulf synapses in the developing brain; however, how microglia know which synapses to target for removal remains a major open question. For my dissertation research, I studied microglia-mediated pruning in the retinogeniculate system and sought to identify the molecules regulating microglial engulfment of synaptic inputs. I discovered that "eat me" and "don't eat me" signals, immune molecules known for either promoting or inhibiting macrophage phagocytosis of cells or debris, localize to the dorsal lateral geniculate nucleus of the thalamus (dLGN) and direct retinogeniculate refinement. We found that "eat me" signal C3 and its microglial receptor, CR3, are required for normal engulfment, and that loss of either of these molecules leads to a reduction in phagocytosis and sustained deficits in refinement. These data suggest that microglia-mediated pruning may be analogous to the removal of non-self material by phagocytes in the immune system. To test this hypothesis, I examined whether protective signals are required to prevent excess microglial engulfment, as they prevent phagocytosis of self cells in the immune system. I found that protective "don't eat me" signal CD47 is required to prevent excess microglial engulfment and retinogeniculate pruning during development. Moreover, another "don't eat me signal", CD200, also prevents overpruning. Together, these findings indicate that immune molecules instruct microglia as to which synapses to engulf and present a model in which a balance of stimulatory and inhibitory cues is necessary to guide remodeling of immature synaptic circuits. These data shed new light on mechanisms regulating synaptic refinement and microglial function in the healthy, developing CNS, and may have implications for disorders characterized by immune dysregulation and circuit disconnectivity, such as autism spectrum disorder (ASD) and schizophrenia.

To simulate increasingly complex physical phenomena and systems, tightly integrated design-through-analysis (DTA) tools are essential. In this dissertation, the complementary strengths of isogeometric analysis and T-splines are coupled and enhanced to create a seamless DTA framework. In all cases, the technology de- veloped meets the demands of both design and analysis. In isogeometric analysis, the smooth geometric basis is used as the basis for analysis. It has been demonstrated that smoothness offers important computational advantages over standard finite elements. T-splines are a superior alternative to NURBS, the current geometry standard in computer-aided design systems. T-splines can be locally refined and can represent complicated designs as a single watertight geometry. These properties make T-splines an ideal discretization technology for isogeometric analysis and, on a higher level, a foundation upon which unified DTA technologies can be built. We characterize analysis-suitable T-splines and develop corresponding finite element technology, including the appropriate treatment of extraordinary points (i.e., unstructured meshing). Analysis-suitable T-splines form a practically useful subset of T-splines. They maintain the design flexibility of T-splines, including an efficient and highly localized refinement capability, while preserving the important analysis-suitable mathematical properties of the NURBS basis. We identify Bézier extraction as a unifying paradigm underlying all isogeometric element technology. Bézier extraction provides a finite element representation of NURBS or T-splines, and facilitates the incorporation of T-splines into existing finite element programs. Only the shape function subroutine needs to be modified. Additionally, Bézier extraction is automatic and can be applied to any T-spline regardless of topological complexity or polynomial degree. In particular, it represents an elegant treatment of T-junctions, referred to as "hanging nodes" in finite element analysis We then detail a highly localized analysis-suitable h-refinement algorithm. This algorithm introduces a minimal number of superfluous control points and preserves the properties of an analysis-suitable space. Importantly, our local refinement algorithm does not introduce a complex hierarchy of meshes. In other words, all local refinement is done on one control mesh on a single hierarchical “level” and all control points have similar influence on the shape of the surface. This feature is critical for its adoption and usefulness as a design tool. Finally, we explore the behavior of T-splines in finite element analysis. It is demonstrated that T-splines possess similar convergence properties to NURBS with far fewer degrees of freedom. We develop an adaptive isogeometric analysis framework which couples analysis-suitable T-splines, local refinement, and Bézier extraction and apply it to the modeling of damage and fracture processes. These examples demonstrate the feasibility of applying T-spline element technology to very large problems in two and three dimensions and parallel implementations. / text