Cette thèse a été réalisée dans le cadre du programme de Partenariat Hubert Curien (PHC Toubkal). L’objectif du projet consiste à élaborer des revêtements organosilicés par plasma froid d’azote pour la protection d’un acier contre la corrosion en milieu NaCl 3%. Dans ce contexte, un procédé permettant d’obtenir, à partir du 1,1,3,3-tétraméthyldisiloxane (TMDSO), un revêtement amorphe assisté par plasma froid micro-onde basse pression (PECVD) a été développé. Ce procédé permet le dépôt de films minces sans l’utilisation de solvant. Dans un premier temps, la mise en œuvre d’un plan d’expérience a permis l’optimisation de plusieurs paramètres expérimentaux tels que, le temps de dépôt, le débit d’azote, le débit d’oxygène, le débit du monomère (TMDSO) et la puissance du générateur micro-onde. La microstructure, l’adhérence, l’épaisseur, la mouillabilité ainsi que les propriétés anticorrosion des revêtements organosilicés ont été caractérisées en utilisant différentes techniques telles que FTIR, RMN solide, MEB, OCP, SIE,.... Ensuite l’effet du prétraitement de la surface de l’acier sur les performances anticorrosion des couches déposées a été étudié en utilisant la phosphatation amorphe, un plasma d’argon (Ar) ou un plasma d’azote (N2). Les résultats montrent une amélioration significative de la protection anticorrosion de l’acier lorsqu’un prétraitement par plasma d’azote (N2) est utilisé. Les caractérisations par EIS montrent que les propriétés anticorrosion des revêtements sont stables en fonction du temps. En effet, le module d’impédance à basse fréquence (0,01 Hz) reste largement supérieur en comparaison avec celui du substrat non revêtu même après plusieurs jours d’immersion dans NaCl 3%. / This thesis was carried out within Hubert Curien Program (PHC Toubkal). The goal of the project consists in developing efficient coatings for corrosion protection of carbon steel. In this context, a process has been developed which allows to obtain organosilicon coatings from 1,1,3,3-tetramethyldisiloxane (TMDSO) using Plasma Enhanced Chemical Vapor Deposition (PECVD) technique. In this solvent free process, nitrogen plasma gas was used to deposit the thin films. One of the main advantage of plasma processes is the wide range of modifiable parameters that allows to control the characteristics of the growing films. Firstly, an experimental design was used to optimize several experimental parameters such as, deposition time, nitrogen flow rate, oxygen flow rate, monomer flow rate and microwave power. The microstructure, adhesion, thickness, wettability as well as the anticorrosion properties of the organosilicon coatings were characterized using different techniques such as FTIR, solid NMR, SEM, OCP, EIS, ...). Then, the effect of surface pretreatments on the anticorrosion performances of the deposited coatings was studied using amorphous phosphatation, argon plasma (Ar) or nitrogen plasma (N2). The results show that a significant increase in the corrosion protection performance when nitrogen plasma pretreatment is used. EIS characterizations give evidence that the barrier properties of the coatings remain very stable versus immersion time in the corrosive medium. Indeed, the impedance modulus values at low frequency (0,01 Hz) remain higher than that of uncoated steel even after several days of immersion in 3% weight NaCl.

Sun Siu-wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 50-51). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Equation without viscosity --- p.5 / Chapter 3 --- Equation with standard viscosity --- p.8 / Chapter 3.1 --- "Particular convective flux, f(x) =u2" --- p.8 / Chapter 3.2 --- Convex convective flux --- p.10 / Chapter 4 --- Equation with monotonic dissipative flux --- p.11 / Chapter 4.1 --- Large initial data --- p.12 / Chapter 4.2 --- Small initial data --- p.19 / Chapter 4.3 --- Unbounded dissipative flux --- p.28 / Chapter 5 --- Equation with non-monotonic dissipative flux --- p.31 / Chapter 5.1 --- Large initial data --- p.32 / Chapter 5.2 --- Small initial data --- p.37 / Chapter 6 --- Comparison and conclusions --- p.39 / Appendices --- p.42 / Chapter A --- Hopf-Cole transformation --- p.42 / Chapter B --- Dirichlet problem --- p.45 / Bibliography --- p.50

Cho, Chi Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 63-65). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

對流佔優擴散問題一直是一個俱有挑戰性的問題。眾所週知，解可能在邊界或者內部表現出局部斷層。傳統的數值解法在解決對流佔優擴散問題時不夠穩定和精確。因此有很多空間穩定技巧被提出和學習。 / 在這篇論文中，我們設計了一個全變分規則化方法來解對流佔優擴散方程。首先，選取一個較小的測試函數空間構造一個欠定模型。然後，通過附加條件最小化全變分來計算唯一解。這個想法是基於離散化解雙曲形偏微分方程的全變分遞減原理。為了實現這個全變分規則化方法，我們需要找出相應的拉格郎日方程的最優條件，並當做時間依賴方程進行求解。論文中涉及了三個運算符拆分方法，Peaceman-Rachford方法，Douglas-Rachford方法和Theta方法。數值實驗證明我們的方法可以準確的描繪出對流佔優擴散問題的邊界和內部斷層現象，因此可以在擴散系數很小的時候提供可靠的數值結果。 / The convection-dominated diffusion problem has been a challenge problem for a long time. It is well known that the solution may exhibit localized layer on the boundary or in the interior. Conventional numerical schemes for the convection-dominated diffusion problem are lacking in both stability and accuracy. Therefore many spatial stabilization techniques have been proposed and studied. / In this thesis, we devise a TV regularization method for solving convection-dominated diffusion equations. First, we form an underdetermined system by choosing a small test function space. Then, we find the unique solution by minimizing the total variation. The idea is based on the fact that total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equation. To implement this TV regularization approach, we find the optimality condition of the corresponding Lagrange function for the minimization problem, and then solve it as a time dependent problem. Three operator splitting methods, the Peaceman-Rachford method, the Douglas-Rachford method and the Theta scheme are studied. The numerical experiments demonstrate that our scheme can accurately capture the boundary and internal layer for the convection-dominated problem, and therefore provide reliable numerical result for small diffusivity. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Qi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 56-[58]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- TV scheme --- p.9 / Chapter 2.1 --- TV regularization --- p.9 / Chapter 2.1.1 --- The underdetermined system --- p.10 / Chapter 2.1.2 --- The minimization problem --- p.10 / Chapter 2.2 --- The optimality conditions --- p.11 / Chapter 2.3 --- Discrete version --- p.14 / Chapter 3 --- Numerical schemes --- p.17 / Chapter 3.1 --- Peachment-Rachford method --- p.17 / Chapter 3.2 --- Douglas-Rachford method --- p.18 / Chapter 3.3 --- Theta scheme --- p.19 / Chapter 3.4 --- Two systems --- p.22 / Chapter 3.4.1 --- System 1 --- p.23 / Chapter 3.4.2 --- System 2 --- p.25 / Chapter 3.5 --- Matrix representation --- p.26 / Chapter 4 --- Numerical examples --- p.29 / Chapter 4.1 --- Scenario --- p.30 / Chapter 4.1.1 --- Initial condition --- p.30 / Chapter 4.1.2 --- Notation --- p.30 / Chapter 4.1.3 --- Parameter --- p.31 / Chapter 4.2 --- Experiment 1 --- p.32 / Chapter 4.3 --- Experiment 2 --- p.38 / Chapter 4.4 --- Experiment 3 --- p.42 / Chapter 4.5 --- Experiment 4 --- p.48 / Chapter 5 --- Conclusion --- p.55

Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries. The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics.

Problems involving partial or ordinary differential equations arise in various fields of science. Therefore, the task of obtaining exact solutions of differential equations is of primary importance, and attracts high attention. The main purpose of the current thesis is the development of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, developed by Prof. Alexei Cheviakov. The reduction procedure is based on the Lie's classical symmetry reduction method involving canonical coordinates. The developed package is applicable for obtaining solutions arising from extension of Lie's method, in particular, nonlocal and approximate symmetries. The developed software is applied to a number of PDE problems to obtain exact invariant solutions. The considered equations include the one-dimensional nonlinear heat equation, the potential Burgers' equation, as well as equations arising in nonlinear elastostatics and elastodynamics.

Most of reports deal with bounded simply-connected domains; only a few involve in exterior and annular problems (Chen et al. [3], Katsuroda[10] and Ushijima and Chibu [30]). For exterior problems of Laplace's equations, there exist two kinds of infinity conditions, (1) |u|≤C and (2) u=O( ln r), which must be complied with by the fundamental solutions chosen. For u=O(ln r), the traditional fundamental solutions can be used. However, for |u|≤C, new fundamental solutions are explored, with a brief error analysis. Numerical experiments are carried out to verify the theoretical analysis made. Numerical experiments are also provided for annular domains, to show that the method of fundamental solutions (MFS) is inferior to the method of particular solutions (MPS), in both accuracy and stability. MFS and MPS are classified into the Trefftz method (TM) using fundamental solutions (FS) and particular solutions (PS), respectively. The remarkable advantage of MFS over MPS is the uniform $ln|overline{PQ_i}|$, to lead to simple algorithms and programming, thus to save a great deal of human power. Hence, we may reach the engineering requirements by much less efforts and a little payment. Besides, the crack singularity in unbounded domain is also studied. A combination of both PS and FS is also employed, called combination of MFS. The numerical results of MPS and combination of MFS are coincident with each other. The study in this thesis may greatly extend the application of MFS from bounded simply-connected domains to other more complicated domains.

Reprodcution de : Thèse de doctorat : Chimie physique : Clermont-Ferrand 2 : 2005. / Thèse avec annexes. Titre provenant de l'écran-titre. Bibliogr. p. 159-166.

Thesis (Ph. D.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains xii, 138 p. : ill. Includes abstract. Includes bibliographical references (p. 111-118).

Thesis (M.S.)--Tennessee Technological University, 2009. / Title from title page screen (viewed on Feb. 10, 2010). Includes bibliographical references.