Due to the requirements for high blade loading, modern turbo‐machine blades operate very close to the stall regime. This can lead to flow separation with periodic shedding of vortices, which could lead to self induced oscillations or stall flutter of the blades. Previous studies on stall flutter have focused on flows at high Reynolds number (Re ~ 106). The Reynolds numbers for fans/propellers of Micro Aerial Vehicles (MAVs), high altitude turbofans and small wind turbines are substantially lower (Re < 105). Aerodynamic characteristics of flows at such low Re is significantly different from those at high Re, due in part to the early separation of the flow and possible formation of laminar separation bubbles (LSB). The present study is targeted towards study of stall flutter in a cascade of blades at low Re. We experimentally study stall flutter of a cascade of symmetric NACA 0012 blades at low Reynolds number (Re ~ 30, 000) through forced sinusoidal pitching of the blades about mean angles of incidences close to stall. The experimental arrangement permits variations of the inter‐blade phase (σ) in addition to the oscillation frequency (f) and amplitude; the inter‐blade phase angle (σ) being the phase difference between the motions of adjacent blades in the cascade. The unsteady moments on the central blade in the cascade are directly measured, and used to calculate the energy transfer from the flow to the blade. This energy transfer is used to predict the propensity of the blades to undergo self‐induced oscillations or stall flutter. Experiments are also conducted on an isolated blade in addition to the cascade. A variety of parameters can influence stall flutter in a cascade, namely the oscillation frequency (f), the mean angle of incidence, and the inter‐blade phase angle (σ). The measurements show that there exists a range of reduced frequencies, k (=πfc/U, c being the chord length of the blade and U being the free stream velocity), where the energy transfer from the flow to the blade is positive, which indicates that the flow can excite the blade. Above and below this range, the energy transfer is negative indicating that blade excitations, if any, will get damped. This range of excitation is found to depend upon the mean angle of incidence, with shifts towards higher values of k as the mean angle of incidence increases. An important parameter for cascades, which is absent in the isolated blade case is the inter‐blade phase angle (σ). An excitation regime is observed only for σ values between ‐450 and 900, with the value of excitation being maximum for σ of 900. Time traces of the measured moment were found to be non‐sinusoidal in the excitation regime, whereas they appear to be sinusoidal in the damping regime. Stall flutter in a cascade has differences when compared with an isolated blade. For the cascade, the maximum value of excitation (positive energy transfer) is found to be an order of magnitude lower compared to the isolated blade case. Further, for similar values of mean incidence angle, the range of excitation is at lower reduced frequencies for a cascade when compared with an isolated blade. A comparison with un‐stalled or classical flutter in a cascade at high Re, shows that the inter‐blade phase angle is a major factor governing flutter in both cases. Some differences are observed as well, which appear to be due to stalled flow and low Re.

Microorganisms and drops are ubiquitous in nature: while drops can be found in sneezes, ink-jet printers, oceans etc, microorganisms are present in our stomach, intestine, soil, oceans etc. In most situations they are present in complex conditions: drop spreading on a rigid or soft substrate, drop covered with impurities that act as surfactants, marine microbe approaching a surfactant laden drop in density stratified oceanic waters in the event of an oil spill etc. In this thesis, we extract the physics underlying the influence of two such complicated effects (surfactant redistribution and density-stratification) on the motion of drops and swimming microorganisms when they are in isolation or in the vicinity of each other. This thesis is relevant in understanding the bioremediation of oil spill by marine microbes.<div><br></div><div>We divide this thesis into two themes. In the first theme, we analyze the motion of motile microorganisms near a surfactant-laden interface in homogeneous fluids. We begin by calculating the translational and angular velocities of a swimming microorganism outside a surfactant-laden drop by assuming the surfactant is insoluble, incompressible, and non-diffusing, as such system is relevant in the context of bioremediation of oil spill. We then study the motion of swimming microorganism lying inside a surfactant-laden drop by assuming the surfactant is insoluble, compressible, and has large surface diffusivity. This system is ideal for exploring the nonlinearities associated with the surfactant transport phenomena and is relevant in the context of targeted drug delivery systems wherein one uses synthetic swimmers to transport the drops containing drug. We then analyze the motion of a swimming organism in a liquid film covered with surfactant without making any assumptions about the surfactant and this system is relevant in the case of free-standing films containing swimming organisms as well as in the initial stages of the biofilm formation. In the second theme, we consider a density-stratified background fluid without any surfactants. In this theme, we examine separately a towed drop and a swimming microorganism, and find the drag acting on the drop, drop deformation, and the drift volume induced by the drop as well as the motility of the swimming microorganism.</div>

La clairance mucociliaire est un processus physico-chimique qui sert à transporter et éliminer le mucus bronchique. Pour cela, des milliards d'appendices de taille micrométrique, que l'on nomme cils, recouvrent l'épithélium respiratoire. Ces cils propulsent le mucus en suivant un motif périodique comprenant une phase de poussée où leur pointe peut pénétrer dans le mucus, et une phase de récupération où ils sont totalement immergés dans le fluide périciliaire. Un dysfonctionnement de ce processus peut engendrer de nombreux problèmes de santé. Il a été observé expérimentalement que les cils ne battent pas aléatoirement, mais synchronisent leurs battements avec leurs voisins, formant ainsi des ondes métachronales. Toutefois, les observations in vivo sont extrêmement difficiles à réaliser, et les propriétés de ces ondes restent mal connues. Dans cette thèse, nous utilisons un solveur Lattice Boltzmann - Frontière Immergée afin de reproduire un épithélium bronchique et étudier l'émergence, ainsi que les capacités de transports et de mélanges, de ces ondes / The mucociliary clearance process is a physico-chemical process which aims is to transport and eliminate bronchial mucus. To do so, billions of micro-sized appendages, called cilia, cover the respiratory epithelium. These cilia propel the mucus by performing a periodical pattern composed of a stroke phase where their tips can enter the mucus layer, and a recovery phase where the cilia are completely immersed in the periciliary liquid layer. A failure of this process may induce numerous health problems. It has been experimentally observed that cilia do not beat randomly, but instead adapt their beatings accordingly to their neighbours, forming metachronal waves. However, in vivo observations are extremely difficult to perfom, and the properties of these waves remain poorly understood. In this thesis, we use a Lattice Boltzmann - Immersed Boundary solver to reproduce a bronchial epithelium and study the emergence, as well as the transport and mixing capacities, of these waves

Multiphase flows abound in nature and enterprises. Our daily interactions with fluids - washing, drinking, and cooking, for example - occur at a free surface and within the realm of multiphase flows. The applications of multiphase flows within the context of emulsions, which are caused by mixing two immiscible fluids, have been of interest since the nineteenth century: compartmentalizing one fluid in another is particularly of interest in applications in pharmaceutical, materials, microfluidics, chemical, and biological engineering. Even more control in compartmentalization and delivery can be obtained through the usage of double emulsions, which are emulsions of smaller drops (i.e., inner drop) within larger drops (i.e., outer drop). The goal of this work is to understand the dynamic behavior of compound drops in confined flow at low Reynolds numbers. These behaviors include the migration patterns, limit cycles, and equilibrium locations in confined flows such as channel flows.<br> <br>Firstly, we look at non-concentric compound drops that are subject to simple shear flows. The eccentricity in the inner drop is either within the place of shear, normal to the plane of shear, or mixed. We show unreported motions that persist throughout time regardless of the initial eccentricity, given that the deformations of the inner and outer drops are small. Understanding the temporal dynamics of compound drops within the simple shear flow, one of the simplest background flows that may be imposed, allows us to probe at the dynamics of more complicated background flows.<br> <br>Secondly, we look at the lateral migration of compound drops in a Poiseuille flow. Depending on the initial condition, we show that there are multiple equilibria. We also show that the majority of initial configurations results in the compound drop with symmetry about the short wall direction. We then show the time it takes for the interfaces to merge if a given initial configuration does not reach the aforementioned symmetry.<br> <br>Thirdly, while the different equilibria of compound drops offer some positional differences at different radii ratio, we show that the lift force profiles at non-equilibrium locations offer distinctly different results for compound drops with different radii ratio. We then look at how this effect is greater than changes that arise due to viscosity ratio changes, and offer insights on what may create such a change in the lift force profile.

This work is inspired by the peculiar behavior of the natural systems, namely the ability to produce self-sustained oscillations in the level of tens of Hertz in constant ambient conditions. This feature is one of the key signatures prescribed to living organisms. The firing rate of neuronal cells, a pulsating heart, or the beating of cilia and flagella are among many biological examples that possess amazing functionalities and unprecedented intelligence solely relying on bio-electro-chemical processes. Exploring shapeable polymeric technologies, new self-oscillating artificial microsystems were developed within this thesis. These microsystems rely on the novel nonlinear architecture that exhibits a negative differential resistance (NDR) within the parametric response that enables periodic oscillations. These systems are made of polymers and metals and were microfabricated in a planar fashion. The electrochemically deposited ionic electroactive polymers act as actuators of the system. Upon the self-assembly process, due to the interlayer strains, the planar device transforms into a three-dimensional soft nonlinear system that is able to perform self-sustained relaxation oscillations when subjected to a constant electric field while consuming extremely low powers (as low as several microwatts). The parameters of these systems were tuned for a high oscillation amplitude and frequency. This electro-mechanical parametric relaxation oscillator (EMPRO) can generate a rhythmic motion at stroke frequencies that are biologically relevant reaching up to ~95 Hz. The EMPRO oscillations at high frequencies generate a flow in the surrounding liquid, which was observed in the form of vortices around the micro actuators. This flow was further studied in ex-vivo conditions by measuring Doppler shifts of ultrasound waves. The EMPRO was made autonomous by integrating an electrochemical voltaic cell. Four different electrochemical batteries were tested to match the power consumption of the EMPRO system and electrochemical compatibility of the surrounding media. An Ag-Mg primary cell was then integrated with the EMPRO for autonomous operation without the need for external power sources, cables or controllers. This biomimicking self-powered self-sustaining oscillating microsystem is envisioned to be useful in novel application scenarios operating at low Reynolds numbers in biologically relevant conditions. Furthermore, as the system is electromechanical in nature, it could be integrated with electronic components such as sensors and communication devices in the next generation of autonomous microsystems.:  Table of contents Acronyms 7 1 Introduction 8 1.1 Motivation 9 1.2 Objectives 9 1.3 Thesis organization 10 2 Background 12 2.1 A brief review on nonlinear self-oscillation 12 2.2 Self-oscillating biological systems 13 2.3 Stimuli responsive materials 15 2.3.1 Electroactive polymers in electrochemical cells 16 2.3.2 Sources of electrical field for electroactive polymers 24 2.4 Self-oscillating synthetic systems 27 2.5 Movement in low Reynolds number regime 33 3 Materials and methods 38 3.1 Deposition methods 38 3.1.1 Photolithography 38 3.1.2 Plasma sputtering 41 3.1.3 Atomic layer deposition 42 3.1.4 Electrochemical polymerization 44 3.2 Shapeable polymeric platform technology 46 3.2.1 Sacrificial layer 46 3.2.2 Hydrogel swelling layer 47 3.2.3 Polyimide reinforcing layer 48 3.3 Characterization methods 49 3.3.1 Profilometry 49 3.3.2 Scanning electron and focused ion beam microscopy 50 3.3.3 Cyclic Voltammetry 52 3.3.4 Ultrasound and Doppler shift measurements 53 4 Electromechanical Parametric Relaxation Oscillators (EMPROs) 56 4.1 Relaxation oscillation in EMPROs 56 4.2 Theory of EMPRO relaxation oscillations 61 4.3 Realization of EMPROs 67 4.3.1 Design parameters of EMPROs 67 4.3.2 EMPRO on-chip battery integration 71 4.4 Fabrication of autonomous EMPROs 76 5 EMPRO performances 84 5.1 Externally biased EMPROs 84 5.2 Autonomous EMPROs 95 6 Conclusions and outlook 98 6.1 Outlook 99 Bibliography i List of Figures and Tables xi Versicherung xiii Acknowledgements xiv Scientific publications and contributions xvi Theses xvii Curriculum Vitae xix

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In day to day life we encounter many different materials which are intermediate between crystalline solids and simple liquids that include paints , glues , suspensions, polymers, surfactants, food and cosmetic products and so on. ‘Soft condensed matter’ is an emerging field of science that aims to generalize the flow and various deformation mechanisms in this apparent diverse class of materials from a ‘mesoscopic’ point of view (important length scales for these systems is usually 10nm-1μm) where the actual atomic and molecular details governed by various quantum mechanical laws are not very important. These soft systems are held together by weaken tropic forces and therefore can be perturbed easily (the typical elastic modulus of these materials is many orders of magnitude lower compared to metallic solids). Moreover, very long relaxation times in these systems(∼10−3 to 1 s) have made them ideal candidates to study non-equilibrium physics. The present Thesis is an endeavor to understand linear and non-linear flow behavior and low Reynolds number instabilities in various soft matter systems like suspensions of flocculated carbon nanotubes and carbon black, surfactant gels, colloidal glasses, Langmuir monolayers etc probed mainly by bulk and interfacial rheology, in-situ light scattering, particle image velocimetry(PIV) techniques and Fourier transform rheology. We also use dynamic light scattering techniques for particle sizing and characterization of Brownian systems. Chapter 1 gives a general introduction to soft condensed matter, particularly, the important length and time scales, various interactions and the rich phase behavior emerged from the delicate balance between energy and entropy in these systems. In this context, We describe the detailed phase behavior of two such systems studied in this thesis. We next describe briefly a few important concepts which motivate the main problems studied in the present thesis like the shear-thickening in suspensions of Brownian and non-Brownian particles, non-equilibrium steady state fluctuation relations in driven systems, elasticity driven instabilities in complex fluids, jamming transitions and aging behavior. This is followed by a discussion of the experimental techniques like linear and nonlinear rheology, including the Fourier transform rheology. Chapter 2 discusses the experimental techniques used by us in detail. We first describe the different components and mode of operations of the MCR-300 stress-controlled rheometer (Paar Physica, Germany) and various experimental geometries. Next we discuss the set up for two dimensional rheological measurements. The homebuilt imaging set up for in-situ polarized light scattering and direct imaging studies is described along with the in-situ particle image velocimetry (PIV) to map out the exact spatially resolved velocity profiles in 2D systems. We give a brief account of the techniques of Fourier transform rheology. At the end of this chapter, we briefly describe the angle resolved dynamic light scattering (DLS) set up (Brookhaven Instruments, USA). In Chapter 3, we study colossal discontinuous shear-thickening transition in confined suspensions of fractal clusters formed by multi-wall carbon nanotubes (MWNT) by rheology and in-situ imaging experiments. Monotonic decrease in viscosity with increasing shear stress, known as shear thinning, is a known rheological response to shear flow in complex fluids in general and for flocculated suspensions in particular. In the present experiments we demonstrate a discontinuous shear thickening transition where the viscosity jumps sharply above a critical shear stress by four to six orders of magnitude in flocculated suspensions of MWNT even at very low weight fractions(∼0.5%). Rheo-optical observations reveal the shear-thickened state as a percolated structure of MWNT flocs spanning the system size. We present a dynamic phase diagram of the non-Brownian MWNT dispersions revealing a starting jammed state followed by shear-thinning and shear-thickened states. The present study further suggests that the shear-thickened state obtained as a function of shear stress is likely to be a generic feature of fractal clusters under flow, albeit under confinement. An understanding of the shear thickening phenomena in confined geometries is pertinent for flow controlled fabrication techniques in enhancing the mechanical strength and transport properties of thin films and wires of nanostructured composites as well as in lubrication issues. We try to understand the flow of jammed and shear-thickened states under constant applied strain rate by studying the building up and relaxation of individual stress fluctuation events similar to the flow in dense granular materials. We also characterize the metastable shear thickened states by superposing a small sinusoidal stress component on a steady applied stress as well as by studying the a thermal entropy consuming fluctuations which are also observed for other jammed systems under an applied steady shear stress as described in the next chapter. Chapter 4 reports the study of non-equilibrium fluctuations in concentrated gels and glassy systems(in jammed state), the nature of fluctuations and their systemsize dependence in the framework of fluctuation relation and Generalized Gumbel distribution. In the first part, we show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions (PDFs) of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress and in all cases show similar symmetry properties as predicted by Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear rate fluctuations increase with the decrease of the systemsize. In the second part of this chapter, we report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the Generalized Gumbel (GG) distribution like many other equilibrium and non-equilibrium systems with high degree of correlations but do not obey Gallavotti-Cohen Steady State Fluctuation Relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution. We also establish the universality of the observations reported in this chapter in the light of other jammed systems under shear. We examine in the first part of Chapter 5, the shear-thinning behavior of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve (stress vs shear rate) consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs showing coexistence of fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile which is linear at low shear rates becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behavior like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation. In the second part of this chapter, we study in detail the non-linear viscoelastic behavior of Langmuir monolayers. Under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes(γ), the storage modulus (G”) decreases monotonically whereas the loss modulus (G”) exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G” and G” are in the ratio 2:1. The peak in G” is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence of the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is very general and exhibits many of the features observed in 3D complex fluids. We report in the first part of Chapter 6 scattering dichroism experiments to quantify the spatio-temporal nematodynamics of shear-thinning worm like micellar gels of surfactant Cetyltrimethylammonium Tosylate (CTAT) in the presence of salt sodium chloride (NaCl) enroute to rheochaos. For shear rates past the plateau onset, we observe a presence of alternating bright and dark‘ intertwined’ birefringent structures along the vorticity direction. The orientational order corresponding to these structures are predominantly oriented at +45deg and−45deg to the flow (v) in the (v,∇v) plane. The orientational dynamics of the nematics especially at the interface between the structures, has a one-to-one correspondence with the temporal behavior of the stress. Experiments show that the spatial motion of the vorticity structures depend on the gap thickness of the Couette cell. We next discuss the random temporal flow behavior of this system at high values of applied shear rate/stress in the framework of elastic turbulence in the second part of this chapter. Here, we study the statistical properties of spatially averaged global injected power fluctuations for the worm-like micellar system described above. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdf scan be well described by an universal large deviation functional form given by the Generalized Gumbel (GG) distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in-situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence. In Chapter 7, we study the vorticity banding under large amplitude oscillatory shear (LAOS) in a dilute worm-like micellar gel formed by surfactant CTAT by Fourier transform rheology and in-situ polarized light scattering. Under LAOS we found the signature of a non-trivial order-disorder transition of Taylor vortices. In the non-linear regime, higher harmonicde composition of the resulting stress signal reveals that the third harmonic I3 shows a very prominent maximum at the strain value where the number density (nv) of the Taylor vortices is maximum for a wide range of angular frequencies both above and below the linear crossover point. Subsequent increase in applied strain results in distortions of the vortices and a concomitant decrease in nv when I3 also drops very sharply and acts like an order parameter for this order-disorder transition. We further quantify the transition by defining an independent order parameter like quantity from the spatial correlation function of the scattered intensity and equivalently its Fourier transform which essentially captures the non monotonous third harmonic behavior. Lissajous plots indicate an intra-cycle strain hardening for the values of γ corresponding to the peak of I3 similar to that observed for hard-sphere glasses. Our study is an important step forward to correlating the structures developed in the system under LAOS to the appearances of the higher harmonics in the non-linear regime. The Thesis concludes with a summary of the main results and a brief account on the scope of future work as described in Chapter 8.

This thesis focuses on the design and development of a fixed wing micro air vehicle (MAV) and on the development of randomized sampling based motion planning and control algorithms for path planning and stabilization of the MAV. In addition, the thesis also contains probabilis-tic analyses of the algorithmic properties of randomized sampling based algorithms, such as completeness and asymptotic optimality. The thesis begins with a detailed discussion on aerodynamic design, computational fluid dy-namic simulations of propeller wake, wind tunnel tests of a 150mm fixed wing micro air ve-hicle. The vehicle is designed in such a way that in spite of the various adverse effects of low Reynolds number aerodynamics and the complex propeller wake interactions with the airframe, the vehicle shows a balance of external forces and moments at most of the operating conditions. This is supported by various CFD analysis and wind tunnel tests and is shown in this thesis. The thesis also contains a reasonably accurate longitudinal and lateral dynamical model of the MAV, which are verified by numerous flight trials. However, there still exists a considerable amount of model uncertainties in the system descrip-tion of the MAV. A robust feedback stabilized close loop flight control law, is designed to attenuate the effects of modelling uncertainties, discrete vertical and head-on wind gusts, and to maintain flight stability and performance requirements at all allowable operating conditions. The controller is implemented in the MAV autopilot hardware with successful close loop flight trials. The flight controller is designed based on the probabilistic robust control approach. The approach is based on statistical average case analysis and synthesis techniques. It removes the conservatism present in the classical robust feedback design (which is based the worst case de-sign techniques) and associated sluggish system response characteristics. Instead of minimizing the effect of the worst case disturbance, a randomized techniques synthesizes a controller for which some performance index is minimized in an empirical average sense. In this thesis it is shown that the degree of conservatism in the design and the number of samples used to by the randomized sampling based techniques has a direct relationship. In particular, it is shown that, as the lower bound on the number of samples reduces, the degree of conservatism increases in the design. Classical motion planning and obstacle avoidance methodologies are computationally expen-sive with the number of degrees of freedom of the vehicle, and therefore, these methodologies are largely inapplicable for MAVs with 6 degrees of freedom. The problem of computational complexity can be avoided using randomized sampling based motion planning algorithms such as probabilistic roadmap method or PRM. However, as a pay-off these algorithms lack algorith-mic completeness properties. In this thesis, it is established that the algorithmic completeness properties are dependent on the choice of the sampling sequences. The thesis contains analy-sis of algorithmic features such as probabilistic completeness and asymptotic optimality of the PRM algorithm and its many variants, under the incremental and independent problem model framework. It is shown in this thesis that the structure of the random sample sequence affects the solution of the sampling based algorithms. The problem of capturing the connectivity of the configuration space in the presence of ob-stacles, which is a central problem in randomized motion planning, is also discussed in this thesis. In particular, the success probability of one such randomized algorithm, named Obsta-cle based Probabilistic Roadmap Method or OBPRM is estimated using geometric probability theory. A direct relationship between the weak upper bound of the success probability and the obstacle geometric features is established. The thesis also contains a new sampling based algorithm which is based on geometric random walk theory, which addresses the problem of capturing the connectivity of the configuration space. The algorithm shows better performance when compared with other similar algorithm such as the Randomized Bridge Builder method for identical benchmark problems. Numerical simulation shows that the algorithm shows en-hanced performance as the dimension of the motion planning problem increases. As one of the central objectives, the thesis proposes a pre-processing technique of the state space of the system to enhance the performance of sampling based kino-dynamic motion plan-ner such as rapidly exploring random tree or RRT. This pre-processing technique can not only be applied for the motion planning of the MAV, but can also be applied for a wide class of vehicle and complex systems with large number of degrees of freedom. The pre-processing techniques identifies the sequence of regions, to be searched for a solution, in order to do mo-tion planning and obstacle avoidance for an MAV, by an RRT planner. Numerical simulation shows significant improvement over the basic RRT planner with a small additional computa-tional overhead. The probabilistic analysis of RRT algorithm and an approximate asymptotic optimality analysis of the solution returned by the algorithm, is also presented in this thesis. In particular, it is shown that the RRT algorithm is not asymptotically optimal. An integral part of the motion planning algorithm is the capability of fast collision detection between various geometric objects. Image space based methods, which uses Graphics Pro-cessing Unit or GPU hardware, and do not use object geometry explicitly, are found to be fast and accurate for this purpose. In this thesis, a new collision detection method between two convex/non-convex objects using GPU, is provided. The performance of the algorithm, which is an extension of an existing algorithm, is verified with numerous collision detection scenarios.

Drag polars for three Micro Air Vehicles (MAVs) were measured at Reynolds numbers of 70,000, 50,000, 30,000, and 10,000 and compared to predictions generated using the classical approach. The MAVs tested had different configurations and aspect ratios varying from 1.2 to 1.6 and ratios of wetted surface area to planform area from 2.6 to 3.9. A force balance was used to measure the lift and drag on the MAVs at angles of attack ranging from -5 degrees (or -10 degrees) to 10 degrees. The force balance allowed the MAVs to rotate in the pitching axis. The MAV angle of attack was set using an elevator installed on the MAV and controlled using a standard radio control used by RC plane enthusiasts. Uncertainty analysis performed on the data showed the uncertainty for high Reynolds numbers was dominated by velocity uncertainty, and uncertainty for the lower Reynolds numbers was dominated by uncertainty in the force measurements. Agreement between measured and predicted drag polars was good with the measured drag never being more than two times the predicted drag. For the majority of the tests, the drag coefficients followed the expected Reynolds number trend: increasing with decreasing Reynolds number.

Turbulent boundary layers approximating those found on the NASA Orion Multi-Purpose Crew Vehicle (MPCV) thermal protection system during atmospheric reentry from the International Space Station have been studied by direct numerical simulation, with the ultimate goal of reducing aerothermodynamic heating prediction uncertainty. Simulations were performed using a new, well-verified, openly available Fourier/B-spline pseudospectral code called Suzerain equipped with a ``slow growth'' spatiotemporal homogenization approximation recently developed by Topalian et al. A first study aimed to reduce turbulence-driven heating prediction uncertainty by providing high-quality data suitable for calibrating Reynolds-averaged Navier--Stokes turbulence models to address the atypical boundary layer characteristics found in such reentry problems. The two data sets generated were Ma[approximate symbol] 0.9 and 1.15 homogenized boundary layers possessing Re[subscript theta, approximate symbol] 382 and 531, respectively. Edge-to-wall temperature ratios, T[subscript e]/T[subscript w], were close to 4.15 and wall blowing velocities, v[subscript w, superscript plus symbol]= v[subscript w]/u[subscript tau], were about 8 x 10-3 . The favorable pressure gradients had Pohlhausen parameters between 25 and 42. Skin frictions coefficients around 6 x10-3 and Nusselt numbers under 22 were observed. Near-wall vorticity fluctuations show qualitatively different profiles than observed by Spalart (J. Fluid Mech. 187 (1988)) or Guarini et al. (J. Fluid Mech. 414 (2000)). Small or negative displacement effects are evident. Uncertainty estimates and Favre-averaged equation budgets are provided. A second study aimed to reduce transition-driven uncertainty by determining where on the thermal protection system surface the boundary layer could sustain turbulence. Local boundary layer conditions were extracted from a laminar flow solution over the MPCV which included the bow shock, aerothermochemistry, heat shield surface curvature, and ablation. That information, as a function of leeward distance from the stagnation point, was approximated by Re[subscript theta], Ma[subscript e], [mathematical equation], v[subscript w, superscript plus sign], and T[subscript e]/T[subscript w] along with perfect gas assumptions. Homogenized turbulent boundary layers were initialized at those local conditions and evolved until either stationarity, implying the conditions could sustain turbulence, or relaminarization, implying the conditions could not. Fully turbulent fields relaminarized subject to conditions 4.134 m and 3.199 m leeward of the stagnation point. However, different initial conditions produced long-lived fluctuations at leeward position 2.299 m. Locations more than 1.389 m leeward of the stagnation point are predicted to sustain turbulence in this scenario. / text