A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated, and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences and a complex-variable approach. Several simplifying approximations to the complete linearization of the residual are also presented. A first-order approximation to the dependent variables is implemented in the adjoint and design equations, and the effect of a "frozen" eddy viscosity and neglecting mesh sensitivity terms is also examined. The resulting derivatives from these approximations are all shown to be inaccurate and often of incorrect sign. However, a partially-converged adjoint solution is shown to be sufficient for computing accurate sensitivity derivatives, yielding a potentially large cost savings in the design process. The convergence rate of the adjoint solver is compared to that of the flow solver. For inviscid adjoint solutions, the cost is roughly one to four times that of a flow solution, whereas for turbulent computations, this ratio can reach as high as ten. Sample optimizations are performed for inviscid and turbulent transonic flows over an ONERA M6 wing, and drag reductions are demonstrated. / Ph. D.

BACKGROUND: Mice have millions of olfactory sensory neurons that express one out of about 1,200 odorant receptor genes, giving them the ability to detect over 100,000 odorants. The activation of the sensory neurons is based on the different structural features of odor stimuli that each type of receptor has been genetically programmed to respond to. The activation at the level of the receptors corresponds to specific combinatorial codes for each odorant. Information from the receptors is sent to the olfactory bulb - where there is also a specific glomerular activation pattern for each odorant - and then to the olfactory tubercle, which plays a role in goal-directed behaviors and receives input from other parts of the brain that are essential for motivated behaviors. As a result of chronic social isolation, mice have been found to have impaired neurogenesis in their olfactory bulb, increased Tac2 expression, and decreased prefrontal cortex and hippocampal volumes. Since these neurological deficits alter the processing of olfactory information, using social isolation as a way to induce depression-like phenotypes in mice may provide insight into how changes in mental states are reflected in mouse behavior. OBJECTIVE: To determine the relationship between odor concentration and olfactory sensitivity in mice, and how the relationship is impacted by social isolation. METHODS: A total of 7 mice of either the C57BL/6J or tac1-cre strain aged 3-4 months were used. They underwent headplate surgery before going through habituation, after which they went through go/no-go task training. A custom 8-slot olfactometer and a behavioral box were used to run behavioral experiments, where up to 8 odorant tubes were placed in the olfactometer and mice were head-fixed in the behavioral box. Odorants were either blank odors made of only deionized water or different concentrations of n-butanol diluted in deionized water. With the blank odors as the “go” stimulus, the n-butanol odors as the “no-go” stimulus, and another blank odor as the “cheat” stimulus, mice went through go/no-go/cheat sessions over decreasing n-butanol concentrations. Python scripts were used to run experiments and collect data regarding the responses of the mice during each trial. RESULTS: By the end of the training period, mice were able to achieve an accuracy of at least 85% during go/no-go tasks. There is an overall downward trend in the performances of mice over decreasing n-butanol concentrations, but there were also large and unexpected improvements in performance at lower concentrations before and after isolation. There were many fluctuations in the average latencies to odor on incorrect no-go trials over decreasing n-butanol concentrations before and after the isolation period. Although sample sizes for each sex were too low for statistical analyses, preliminary data suggests that at low odor concentrations, social isolation might lead to enhanced performance in males and decreased performance in females. CONCLUSIONS: Mice can learn to associate novel odors with a water reward. Using social isolation as a way to induce depression in mice does not hinder mice from performing odor discrimination tasks. Conclusions cannot be made regarding the effect of social isolation on mouse olfactory sensitivity. Although there appears to be an improvement in performance as a result of isolation in male mice and a dampening of performance in female mice, further research will need to be conducted using larger sample sizes across both sexes.

A finite element solver has been developed for performing analysis and sensitivity analysis with Poisson's equation. An application of Poisson's equation in fluid dynamics is that of poential flow, in which case Posson's equaiton reduces to Laplace's equation. The stiffness matrix and sensitivity of the stiffness matrix are evaluated by direct integrations, as opposed to numerical integration. This allows less computational effort and minimizes the sources of computational errors. The capability of evaluating sensitivity derivatives has been added in orde to perform design sensitivity analysis of non-lifting airfoils. The discrete-direct approach to sensitivity analysis is utilized in the current work. The potential flow equations and the sensitivity equations are computed by using a preconditionaed conjugate gradient method. This method greatly reduces the time required to perfomr analysis, and the subsequent design optimization. Airfoil shape is updated at each design iteratioan by using a Bezier-Berstein surface parameterization. The unstrucured grid is adapted considering the mesh as a system of inteconnected springs. Numerical solutions from the flow solver are compared with analytical results obtained for a Joukowsky airfoil. Sensitivity derivaatives are validated using carefully determined central finite difference values. The developed software is then used to perform inverse design of a NACA 0012 and a multi-element airfoil.

The ultrastructural mechanism for strain rate sensitivity of collagenous tissue has not been well studied at the collagen fibril level. The objective is to reveal the mechanistic contribution of the collagen fibril to strain rate sensitivity. Collagen fibrils underwent significantly greater fibril strain relative to global tissue strain at higher strain rates. A better understanding of tendon mechanisms at lower hierarchical levels would help establish a basis for future development of constitutive models and assist in tissue replacement design. High rate mechanical property of tendon was also studied. Tendon was compressed under high strain rate (550 /s) using a polycarbonate split Hopkinson pressure bar (PSHPB). The objectives are to investigate the tissue behavior of porcine tendon at high rates. Tendon’s high rate behavior was compared with brain and liver at both hydrated and dehydrated states to investigate how water content and ultrastructural affect high rate responses of soft tissues.

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