Dans cette thèse, nous étudions les solutions de l'équation de Boltzmann. Nous nous intéressons au cadre homogène en espace où la solution f(t; x; v) dépend uniquement du temps t et de la vitesse v. Nous considérons des sections efficaces singulières (cas dit non cutoff) dans le cas Maxwellien. Pour l'étude du problème de Cauchy, nous considérons une fluctuation de la solution autour de la distribution Maxwellienne puis une décomposition de cette fluctuation dans la base spectrale associée à l'oscillateur harmonique quantique. Dans un premier temps, nous résolvons numériquement les solutions en utilisant des méthodes de calcul symbolique et la décomposition spectrale des fonctions de Hermite. Nous considérons des conditions initiales régulières et des conditions initiales de type distribution. Ensuite, nous prouvons qu'il n'y a plus de solution globale en temps pour une condition initiale grande et qui change de signe (ce qui ne contredit pas l'existence globale d'une solution faible pour une condition initiale positive - voir par exemple Villani Arch. Rational Mech. Anal 1998). / In this thesis, we study the solutions of the Boltzmann equation. We are interested in the homogeneous framework in which the solution f(t; x; v) depends only on the time t and the velocity v. We consider singular crosssections (non cuto_ case) in the Maxwellian case. For the study of the Cauchy problem, we consider a uctuation of the solution around the Maxwellian distribution then a decomposition of this uctuation in the spectral base associated to the quantum harmonic oscillator At first, we solve numerically the solutions using symbolic computation methods and spectral decomposition of Hermite functions. We consider regular initial data and initial conditions of distribution type. Next, we prove that there is no longer a global solution in time for a large initial condition that changes sign (which does not contradict the global existence of a weak solution for a positive initial condition - see for example Villani Arch. Rational Mech. Anal 1998).

<div>As high performance computing systems are advancing from petascale to exascale, scientific workflows to integrate simulation and visualization/analysis are a key factor to influence scientific campaigns. As one of the campaigns to study fluid behaviors, computational fluid dynamics (CFD) simulations have progressed rapidly in the past several decades, and revolutionized our lives in many fields. Lattice Boltzmann method (LBM) is an evolving CFD approach to significantly reducing the complexity of the conventional CFD methods, and can simulate complex fluid flow phenomena with cheaper computational cost. This research focuses on accelerating the workflow of LBM simulation and data analysis.</div><div><br></div><div>I start my research on how to effectively integrate each component of a workflow at extreme scales. Firstly, we design an in-situ workflow benchmark that integrates seven state-of-the-art in-situ workflow systems with three synthetic applications, two real-world CFD applications, and corresponding data analysis. Then detailed performance analysis using visualized tracing shows that even the fastest existing workflow system still has 42% overhead. Then, I develop a novel minimized end-to-end workflow system, Zipper, which combines the fine-grain task parallelism of full asynchrony and pipelining. Meanwhile, I design a novel concurrent data transfer optimization method, which employs a multi-threaded work-stealing algorithm to transfer data using both channels of network and parallel file system. It significantly reduces the data transfer time by up to 32%, especially when the simulation application is stalled. Then investigation on the speedup using OmniPath network tools shows that the network congestion has been alleviated by up to 80%. At last, the scalability of the Zipper system has been verified by a performance model and various largescale workflow experiments on two HPC systems using up to 13,056 cores. Zipper is the fastest workflow system and outperforms the second-fastest by up to 2.2 times.</div><div><br></div><div>After minimizing the end-to-end time of the LBM workflow, I began to accelerate the memory-bound LBM algorithms. We first design novel parallel 2D memory-aware LBM algorithms. Then I extend to design 3D memory-aware LBM that combine features of single-copy distribution, single sweep, swap algorithm, prism traversal, and merging multiple temporal time steps. Strong scalability experiments on three HPC systems show that 2D and 3D memory-aware LBM algorithms outperform the existing fastest LBM by up to 4 times and 1.9 times, respectively. The speedup reasons are illustrated by theoretical algorithm analysis. Experimental roofline charts on modern CPU architectures show that memory-aware LBM algorithms can improve the arithmetic intensity (AI) of the fastest existing LBM by up to 4.6 times.</div>

Mechanics of structure genome (MSG) is a unified homogenization theory that provides constitutive modeling of three-dimensional (3D) continua, beams and plates. In present work, the author extends the MSG to study the buckling of structures such as stiffened and sandwich panels. Such structures are usually slender or flat and easily buckle under compressive loads or bending moments which may result in catastrophic failure.<div><br><div>Buckling studies of stiffened and sandwich panels are found to be scattered. Most of the existed theories employ unnecessary assumptions or only apply to certain types of structures. There are few unified approaches that are capable of studying the buckling of different kinds of structures altogether. The main improvements of current approach compared with other methods in the literature are avoiding unnecessary assumptions, the capability of predicting all possible buckling modes including the global and local buckling modes, and the potential in studying the buckling of various types of structures.<br></div><div><br></div><div>For global buckling that features small local rotations, MSG mathematically decouples the 3D geometrical nonlinear problem into a linear constitutive modeling using structure genome (SG) and a geometrical nonlinear problem defined in a macroscopic structure. As a result, the original structures are simplified as macroscopic structures such as beams, plates or continua with effective properties, and the global buckling modes are predicted on macroscopic structures. For local buckling that features finite local rotations, Green strain is introduced into the MSG theory to achieve geometrically nonlinear constitutive modeling. Newton’s method is used to solve the nonlinear equilibrium equations for fluctuating functions. To find the bifurcated fluctuating functions, the fluctuating functions are then perturbed under the Bloch-periodic boundary conditions. The bifurcation is found when the tangent stiffness associated with the perturbed fluctuating functions becomes singular. Moreover, the arc-length method is introduced to solve the nonlinear equilibrium equations for post-local-buckling predictions because of its robustness. The imperfection is included in the form of geometrical imperfection by superimposing the scaled buckling modes in linear perturbation analysis on mesh.<br></div><div><br></div><div>Extensive validation case studies are carried out to assess the accuracy of the MSG theory in global buckling analysis and post-global-buckling analysis, and assess the accuracy of the extended MSG theory in local buckling and post-local-buckling analysis. Results using MSG theory and extended MSG theory in buckling analysis are compared with direct numerical solutions such as 3D FEA results and results in literature. Parametric studies are performed to reveal the relative influence of selective geometric parameters on buckling behaviors. The extended MSG theory is also compared with representative volume element (RVE) analysis with Bloch-periodic boundary conditions using commercial finite element packages such as Abaqus to assess the efficiency and accuracy of the present approach.<br></div></div>

Master thesis deals with design and construction of the most widely used engines currently. Overall, it is divided into five chapters, the first chapter deals with constructional features of various three-phase asynchronous motors, the second chapter briefly paid attention to single-phase motors. The next chapter focuses on the specific engine types, which differ from standard induction motors in its design implementation. This is an engine with full rotor, hysteresis, linear and with shaded field. Although asynchronous motors are considered the most reliable machines work in imperfect conditions, it leads to frequent breakdowns. This is covered in chapter four. Based on the findings from previous chapters the fifth chapter includes a preliminary draft of the asynchronous motor with a full rotor. The last chapter is devoted to the measurement on functional models.