The first and most imperative step when designing a biologically inspired robot is to identify the underlying mechanics of the system or animal of interest. It is most common, perhaps, that this process generates a set of coupled nonlinear ordinary or partial differential equations. For this class of systems, the models derived from morphology of the skeleton are usually very high dimensional, nonlinear, and complex. This is particularly true if joint and link flexibility are included in the model. In addition to complexities that arise from morphology of the animal, some of the external forces that influence the dynamics of animal motion are very hard to model. A very well-established example of these forces is the unsteady aerodynamic forces applied to the wings and the body of insects, birds, and bats. These forces result from the interaction of the flapping motion of the wing and the surround- ing air. These forces generate lift and drag during flapping flight regime. As a result, they play a significant role in the description of the physics that underlies such systems. In this research we focus on dynamic and kinematic models that govern the motion of ground based robots that emulate flapping flight. The restriction to ground based biologically inspired robotic systems is predicated on two observations. First, it has become increasingly popular to design and fabricate bio-inspired robots for wind tunnel studies. Second, by restricting the robotic systems to be anchored in an inertial frame, the robotic equations of motion are well understood, and we can focus attention on flapping wing aerodynamics for such nonlinear systems. We study nonlinear modeling, identification, and control problems that feature the above complexities. This document summarizes research progress and plans that focuses on two key aspects of modeling, identification, and control of nonlinear dynamics associated with flapping flight. / Ph. D. / In this work we focus on modeling flapping flight mechanics by focusing our attention in two aspects of modeling. We first model the behavior of aerodynamic forces in charge of keeping the flying animal airborn. We present a mathematical model for history dependent profile of these forces. Also, we propose a novel adaptive controller to compensate these unknown forces in the dynamic model of the system. We also propose an algorithm to derive dynamic equations of the animal motion by using video data. We expect the model derived by this novel method to emulate the animal motion closely.

Cette thèse est consacrée à l'étude de deux systèmes, à la fois proches et différents par leur comportement : Co-Pt, système emblématique de l'ordre chimique, et Pt-Ag, système hybride présentant à la fois un ordre chimique et une tendance à la démixtion, ainsi qu'une forte tendance à la ségrégation. Afin de répondre à ces diverses questions, nous adoptons une approche semi-empirique à travers un potentiel à $N$-corps, permettant les relaxations atomiques, dans l'approximation du second moment de la densité d'états (SMA), couplé à des simulations Monte Carlo dans différents ensembles. Des agrégats de différentes tailles (allant de 1000 à 10000 atomes) et de différentes morphologies (octaèdre tronqué, décaèdre, ou icosaèdre) sont analysés en terme de composition chimique sur les différents sites inéquivalents (sommet, arête, facettes (100) et (111) et coeur) puis comparés aux systèmes de référence (surfaces, volume) sur toute la gamme de concentration. Pour le système Co-Pt, nous observons des structures ordonnées similaires à celles du volume pour le coeur et similaires à celles des surfaces pour les facettes. L'impact de la phase bidimensionnelle (√3×√3)R30◦ propre à la surface, est d'autant plus important sur l'ordre chimique au coeur que la nanoparticule est de petite taille. Pour le système Pt-Ag, nous observons une importante ségrégation de l'Ag en surface, ainsi qu'un enrichissement de Pt en sous-surface, et la stabilisation de la phase ordonnée L1$_{1}$ au coeur. Cette structure peut apparaître en un seul variant ou bien en adoptant tous les variants possibles, conduisant ainsi à une structure en pelures d'oignon. / Due to the correlation between atomic arrangement and physical properties, ordered nanoalloys are particularly interesting in the field of catalysis, magnetism, or optics. By reducing the system size, from alloy to nanoalloy, a lot of questions arise: Is chemical ordering conserved? What is the morphology of nanoalloys? What is the properties evolution as a size function? Is there a coupling between segregation and core ordering? This thesis is dedicated to two systems: Co-Pt, a typical example of ordering and Pt-Ag, hybrid system between ordering and demixion. To answer these questions, we performed Monte Carlo simulations in different ensembles with semi-empirical many-body potential within the Second Moment Approximation (SMA) of the density of states which allows atomic relaxations. Nanoparticles of different sizes (from 1000 to 10000 atoms) and shapes (truncated octahedra, decahedra, or icosahedra) are analyzed considering chemical composition on each site (vertex, edge, (111) and (100) facets and core) and compared to reference systems (surfaces and bulk) on the whole range of composition. For Co-Pt, we get ordered structures similar to the bulk ones and similar to surfaces for facets. The bidimensional phase (√3×√3)R30◦, purely due to surface effect, impacts core ordering, even more for small clusters. For Pt-Ag, we get a strong Ag segregation on surface coupled with a Pt sub-surface enrichment, and a stable L1$_{1}$ phase in the core. This ordered structure may appear with a single variant or with multiple variants, leading to an onion-like structure.

This doctoral study consists of three parts. In the first part, structural and electronic properties of Al_kTi_lNi_m (k+l+m=2,3) microclusters have been investigated by performing density functional theory (DFT) calculations within the B3LYP [which comprises the Becke-88 exchange functional and the correlation functional of Lee, Yang, and Parr] and the effective core potential (ECP) level. Dimers and trimers of the elements aluminum, titanium, and nickel, and their binary and ternary combinations have been studied in their ground states. The optimum geometries, possible dissociation channels, vibrational properties, and electronic structure of the clusters under study have been obtained. In the second part, after an empirical potential energy function (PEF) has been parametrized for the AlTiNi ternary system, stable (minimum-energy) structures of Al_kTi_lNi_m (k+l+m=4) microclusters have been determined by molecular dynamics (MD) simulations. The energetics of the microclusters in 1K and 300 K have been discussed. By performing, again, DFT calculations (within the B3LYP and ECP level), the possible dissociation channels and electronic properties of the obtained clusters have been calculated. In the last part, using the empirical PEF parametrized previously for the AlTiNi ternary system, minimum-energy structures of Al_nTi_nNi_n (n= 1-16) ternary alloy nanoparticles have been determined by performing MD simulations. The structural and energetic features of the obtained nanoparticles have been investigated.

Potential parameters that can handle multi-component oxide glass systems especially boron oxide are very limited in literature. One of the main goals of my dissertation is to develop empirical potentials to simulate multi-component oxide glass systems with boron oxide. Two approaches, both by introducing the composition dependent parameter feature, were taken and both led to successful potentials for boron containing glass systems after extensive testing and fitting. Both potential sets can produce reasonable glass structures of the multi-component oxide glass systems, with structure and properties in good agreement with experimental data. Furthermore, we have tested the simulation settings such as system size and cooling rate effects on the results of structures and properties of MD simulated borosilicate glasses. It was found that increase four-coordinated boron with decreasing cooling rate and system size above 1000 atoms is necessary to produce converged structure. Another application of the potentials is to simulate a six-component nuclear waste glass, international simple glass (ISG), which was for first time simulated using the newly developed parameters. Structural features obtained from simulations agree well with the experimental results. In addition, two series of sodium borosilicate and boroaluminosilicate glasses were simulated with the two sets of potentials to compare and evaluate their applicability and deficiency. Various analyses on the structures and properties such as pair distribution function, total correlation function, coordination number analysis, Qn distribution function, ring size distribution function, vibrational density of states and mechanical properties were performed. This work highlights the challenge of MD simulations of boron containing glasses and the capability of the new potential parameters that enable simulations of wide range of mixed former glasses to investigate new structure features and design of new glass compositions for various applications.

This thesis presents a study on two types of X-ray diffraction methodologies applied to the characterization of amorphous materials. The purpose of this study was to assess the feasibility of measuring the diffractive spectrum of amorphous materials by Energy-Dispersive X-ray Diffraction (EDXRD) utilizing Cadmium Zinc Telluride detectors. The total scattering intensity (coherent plus incoherent scatter) spectra precisely measured by high-energy Wide-Angle X-ray Scattering (WAXS) were compared to the EDXRD spectra to determine the level of agreement between the two techniques. The EDXRD spectra were constructed by applying a spectra fusing technique which combined the EDXRD spectra collected at different scattering angles rendering a continuous total scattering spectrum. The spectra fusing technique extended the momentum transfer range of the observed scattered spectrum beyond the limitations of the X-ray source and CZT detection efficiencies. Agreement between the WAXS and fused EDXRD spectra was achieved. In addition, this thesis presents the atomic pair correlation functions and coordination numbers of the first coordination shell for four hydrogen peroxide solutions of varying mass concentrations using Empirical Potential Structural Refinement (EPSR). The results are compared to the state-of-the art ad initio quantum mechanical charge field molecular dynamics (QMCF MD) model of the hydrogen peroxide in solution to support the model's predictions on why hydrogen peroxide is stable in water. The EPSR results using the coherent scattering intensity calculated from the WAXS data set predicts a hydration shell of 6.4 molecules of water surrounding hydrogen peroxide. The results also indicate that hydrogen peroxide is more likely to behave as a proton donor than acceptor. These findings are in agreement with QMCF MD model of aqueous hydrogen peroxide. / Physics

Le dioxyde d’uranium UO2 est le combustible standard dans les réacteurs nucléaires à eau pressurisée (REP). Durant le fonctionnement du réacteur les pastilles combustibles subissent des contraintes thermiques et mécaniques. Pour cette raison il est très important de bien connaître les propriétés de ce système à la fois dans les conditions de fonctionnement normales et accidentelles (300 à 2000K). Lors des réactions de fission de l’uranium, des gaz rares comme le xénon sont produits à l’intérieur du combustible. En raison de leur faible solubilité, ces gaz vont former des bulles intra- et inter- granulaires dans l’UO2. La présence de ces bulles dans le combustible a un impact sur les propriétés macroscopiques de ce dernier. A l'échelle nanométrique, les bulles intragranulaires prennent la forme d’un octaèdre facetté, essentiellement suivant les directions (111) et (100). Devant la complexité de l’étude de la stabilité de cet octaèdre, nous avons décomposé le problème afin de pouvoir l’étudier de façon plus systématique et de découpler les différents effets. Dans un premier temps, nous avons déterminé la stabilité des surfaces planes (111) et (100) de l’UO2 et les modifications de microstructure engendrées par leur relaxation. Dans un deuxième temps, nous avons caractérisé les isothermes d’adsorption du xénon sur ces surfaces relaxées, en les comparant à ceux de l’incorporation dans une boîte vide pour identifier les effets de surface. Une attention particulière a été portée sur la microstructure du xénon dans ces systèmes. Finalement, nous avons effectué une analyse des propriétés mécaniques (profils de pression et de contrainte au voisinage des surfaces). / Uranium dioxide UO2 is the standard fuel in nuclear pressurized water reactors (PWR). During the operation of the reactor the fuel pellets undergo thermal and mechanical stresses. For this reason it is very important to understand these thermomechanical properties of this system both in normal operation conditions and accidental situations (300 to 2000K). During fission reactions of uranium, rare gases such as xenon are produced within the fuel. Due to their low solubility, these gases will either be released or form intra- and inter-granular bubbles inside the UO2. The presence of these bubbles in the fuel has an impact on the thermomechanical properties of the latter. We focus in this thesis on the study of intragranularbubbles and their impact on the thermomechanical properties of UO2 , through modeling at the atomic scale. At this scale, intragranular bubbles take the shape of an octahedron, presenting mainly (111) and (100) facets. Given the complexity of the study of the stability of this octahedron, we have simplified the problem in order to study it in a more systematic way and to decouple the various effects. First, the stability of (100) and (111) extended surfaces of UO2 and microscructural modifications generated by their relaxation were studied. In a second step, we dermined adsorption isotherms of xenon on these relaxed surfaces, and compared them to the incorporation ones inside an empty box in order to isolate surface effects. A specific attention has been given to the microstructure of xenon in these systems. Finally, an analysis of the mechanical properties (pressure and stress profiles near by the surface).

We employ the empirical potential function Airebo to computationally model free-standing Carbon-12 graphene in a classical setting. Our objective is to measure the mean square displacement (MSD) of atoms in the system for different average temperatures and Carbon-13 isotope concentrations. From results of the MSD we aim to develop a technique that employs Transmission Electron Microscopy (TEM), using high-angle annular dark filed (HAADF) detection, to obtain atomic-resolution images. From the thermally diffusive images, produced by the vibrations of atoms, we intent to resolve isotopes types in graphene. For this, we establish a relationship between the full width half maximum (FWHM) of real-space intensity images and MSD for temperature and isotope concentration changes. For the case of changes in the temperature of the system, simulation results show a linear relationship between the MSD as a function of increased temperature in the system, with a slope of 7.858×10-6 Å2/K. We also note a power dependency for the MSD in units of [Å2] with respect to the FWHM in units of [Å] given by FWHM(MSD)=0.20MSD0.53+0.67. For the case of increasing isotope concentration, no statistically significant changes to the MSD of 12C and 13C are noted for graphene systems with 2,000 atoms or more. We note that for the experimental replication of results, noticeable differences in the MSD for systems with approximately 320,000 atoms must be observable. For this, we conclude that isotopes in free-standing graphene cannot be distinguished using TEM.