Cette thèse porte sur certaines familles à un paramètre de surfaces de Riemann compactes de genre 2 définies par des surfaces de translation. Les familles que nous considérons constituent des géodésiques de Teichmüller dans l'espace des modules.Nous nous attachons en particulier à décrire ces surfaces par leurs matrices des périodes et par les équations des courbes algébriques associées.Nous étudions notamment les automorphismes admissibles par les surfaces de certaines de ces familles.Le principal résultat consiste en une caractérisation explicite des matrices des périodes des courbes réelles à trois composantes réelles appartenant à la famille obtenue par projection dans l'espace des modules de la SL(2,R)-orbite de la surface de translation en «L» pavée par trois carreaux.Nous montrons enfin, grâce à une interprétation en termes de transformations de Schwarz-Christoffel, comment calculer numériquement une équation de la courbe algébrique définie par une surface de translation en «L». / In this thesis we study some one parameter families of compact Riemann surfaces of genus 2 defined by translation surfaces.The families we consider are Teichmüller geodesics in the moduli space.We mainly describe these surfaces by means of period matrices and equations of the associated algebraic curves.We study admissible automorphisms for surfaces in some of those families.The main result is an explicit characterisation of period matrices of real curves with three real components belonging to the family obtained by projecting the SL(2,R)-orbit of the «L»-shaped translation surface tiled by three squares into the moduli space.We finally show, using an interpretation in terms of Schwarz-Christoffel transformations, how to numerically compute an equation of the algebraic curve defined by a «L»-shaped translation surface.

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硅對現今科技至關重要。而有機物吸附於硅表面可能大大擴展硅的用途。在本論文中，我採用密度泛函理論研究了六種分子於硅表面的反應。本論文大致可分為四部分。 / 第一部分包含四個分子（吡嗪、吡啶、嘧啶與1,3,5-三氮嗪）的吸附研究。它們都擁有類似於苯的結構而環中又包含氮原子。分子可以用氮原子與表面形成配位鍵並作為進一步反應的前體故其反應更為容易預測。而反應通常只消除π 鍵而不會使分子分解這使得分子可以在平衡狀態下與表面生成最為穩定的結構。此兩種特性使它們成為硅表面吸附的絶佳研究對象。不同的實驗都顯示出吡嗪於硅表面只會生成Cross-row bridge 結構加熱硅表面更會促進納米線的生成。過往的計算無法解釋實驗結果而我的計算表明范德華力對導出正確計算結果非常重要加入范德華力的修正可以同時解釋單一產物與納米線的生成。吡啶的吸附實驗結果相比之下較為複雜。低溫下的吸附與飽和只生成兩種產物可是室溫下的實驗卻顯示多種產物並存於表面。加入范德華力的計算結果指出覆蓋度和溫度與吸附密切相關並指出對低溫下形成的飽和表面加溫可能促使納米線的生成。而於室溫下吡啶可進入多條反應路徑致使多種產物於表面並存。基於范德華力對這兩個分子的顯著影響我又將此效應加諸於嘧啶與1,3,5-三氮嗪的吸附研究。結果表明於低覆蓋度與低溫下它們只生成Double-dative 產物。然而增加覆蓋度會使Double-dative 的能量高於其它產物導致多種產物並存。由於嘧啶與1,3,5-三氮嗪都可生成一種特別的tight-bridge 結構加溫會使它們輕易解離。對此四種分子的研究顯示出氮原子的數量與位置如何影響吸附過程。 / 第二部分包含對1,2-環己二酮的吸附研究。於室溫下此分子會以互變異構體形式存在。之前的實驗指出它會先變回二酮才進行後續反應這種硅表面輔助互變反應的現象是前所未見的卻無後續研究以驗証其說。我的計算結果指出雖然互變反應的能壘被硅表面大幅降低可是仍不足以與其他反應路徑相匹敵。其中三種新產物既與實驗譜相吻合而反應能壘和能量都低故比之前所提產物更為可取。 / 第三部分包含對氰基苯的吸附研究。之前的三個實驗給出完全不同的結論。探明其與覆蓋度和溫度的關係後我提出氰基苯於低溫下飽和只會生成一種產物。而在室溫下的吸附會先生成valley-bridge 結構增加覆蓋度將使多種產物並存。計算結果不但表明有序吸附的可能性同時又解釋為何不同實驗給出看似不相容的結論。 / Silicon is an important material and substrate in modern technologies. Adsorption of organic molecules on silicon surface has attracted much attention due to the possibility of functionalizing the surface. In this thesis, density functional theory has been applied to study the adsorption of several organic molecules on Si(100) surface. / Results on the adsorption of benzene-like N-heteroaromatic molecules on Si(100)surface, including pyrazine, pyridine, pyrimidine and s-triazine, are presented in Chapters 2-4. This class of molecules, containing nitrogen atoms, can datively attach to dimer and act as precursor for further reaction. Thus, their reactions on surface can be easily predicted. Their reaction with surface would sacrifice π bond rather than dissociation under very mild condition such that the most stable adsorption product can be obtained under thermal equilibrium. These two properties of N-heteroaromatic compounds makes them good models for the study of reaction on surface Experiments repeatedly showed that pyrazines formed cross-row bridge structures on Si(100) under various conditions, and thermal annealing led to the formation of ordered nano-lines. Previous calculations did not explain these observations. This thesis demonstrates that addition of van der Waals (vdW) correction is critical to explain the formation of both the cross-row bridge and the nano-lines. For pyridine, the situation is more complex. Only two products were observed in low temperature adsorption experiments. In contrast, room temperature experiments yielded a mixture of products. With vdW corrections added, results show that pyridine adsorption is dependent on both coverage and temperature. Adsorption and saturation started at low temperature and followed by annealing may produce nano-lines consisted of cross-row bridge structures. Adsorption at room temperature opens up all reaction channels such that nano-line formation becomes difficult, which explains the discrepancy among experimental studies. In light of these results, the pyrimidine and s-triazine adsorption on Si(100) are also explored. The results show that they form double-dative structures at low coverage and low temperature. Increasing coverage will destabilize it and lead to mixture of products. These structures decompose easily upon heating due to the formation of a particular tight-bridge structure. These results show that the position and number of heteroatom are important to explain the difference in reaction selectivity among N-heteroaromatic molecules. For all four molecules, cooperative effect and the addition of vdW correction, which are almost neglected in similar study, are shown to be important in surface adsorption process. / In Chapter 5, the adsorption of 1,2-cyclohexanedione (1,2-CHD) on surface is studied. Gas molecule of 1,2-CHD exists in the tautomeric form (2-hydroxylcyclohex-2-ene-1-one) at room temperature. Previous experimental studies claimed that surface assisted tautomerization back to 1,2-CHD took place before further reaction, although there was no follow-up study. Computational results showed that although surface adsorption lowers the barrier for tautomerization, the barrier is still at least 5 times larger than other reaction channels. Three new structures are proposed, which are in better agreement with previous spectroscopic results. / In the final chapter, the adsorption of benzonitrile on Si(100) is studied. Three previous experimental studies presented conflicting results. With the coverage and temperature dependence effects clarified, my results suggest that adsorption at saturation and low temperature leads to a single product. Adsorption at room temperature first leads to a valley-bridge structure, while a mixture of adsorption structures is produced upon increasing coverage, which explained the conflicting experimental results. The last two chapters show the importance of computational modeling for interpretation and summarizing experimental results. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Ng, Kwok Hung. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references. / Abstracts also in Chinese. / Ng, Kwok Hung.

by Yu-san Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references. / ABSTRACT --- p.ii / ACKNOWLEDGMENTS --- p.iv / EDITORIAL NOTE --- p.v / CONTENTS --- p.vi / LIST OF TABLES --- p.ix / LIST OF FIGURES --- p.xii / Chapter CHAPTER 1. --- INTRODUCTION / Chapter 1.1 --- Potential Energy Surfaces --- p.1 / Chapter 1.2 --- Ab initio Method --- p.1 / Chapter 1.2.1 --- Basis Sets --- p.2 / Chapter 1.2.2 --- Correlation Methods --- p.4 / Chapter 1.3 --- Locations and Characterizatioiis of Stationary Points --- p.5 / Chapter 1.4 --- Refinements of Energy and the Gaussian-2 Method --- p.7 / REFERENCES --- p.10 / Chapter CHAPTER 2. --- AN AB INITIO MOLECULAR ORBITAL STUDY OF THE GaH4 POTENTIAL ENERGY SURFACE / Chapter 2.1 --- Introduction --- p.12 / Chapter 2.2 --- Computational Details --- p.12 / Chapter 2.3 --- Results and Discussion --- p.13 / Chapter 2.3.1 --- Jahn-Teller Distortion from Td Symmetry --- p.18 / Chapter 2.3.2 --- Transition Structures Connecting Various Equilibrium Structures --- p.19 / Chapter 2.3.3 --- The Dissociation Products --- p.20 / Chapter 2.4 --- Conclusion --- p.21 / REFERENCES --- p.22 / Chapter CHAPTER 3. --- A GAUSSIAN-2 AB INITIO STUDY OF THE CH3S2 AND CH3S2+ POTENTIAL ENERGY SURFACES / Chapter 3.1 --- Introduction --- p.24 / Chapter 3.2 --- Computational Details --- p.25 / Chapter 3.3 --- Results and Discussion --- p.26 / Chapter 3.3.1 --- The Potential Energy Surface of CH3S2 Radicals --- p.26 / Chapter 3.3.2 --- The Potential Energy Surface of CH3S2+ Cations --- p.37 / Chapter 3.3.3 --- The Equilibrium Structures of CH3S2- Anions --- p.40 / Chapter 3.3.4 --- Interpretation of Experimental Results with Theoretical Predictions --- p.40 / Chapter 3.4 --- Conclusion --- p.42 / REFERENCES --- p.43 / Chapter CHAPTER 4. --- A GAUSSIAN-2 AB INITIO STUDY OF THE CH3O2 AND CH302+ POTENTIAL ENERGY SURFACES / Chapter 4.1 --- Introduction --- p.46 / Chapter 4.2 --- Computational Details --- p.47 / Chapter 4.3 --- Results and Discussions --- p.48 / Chapter 4.3.1 --- The Equilibrium Structures of CH3O2 Radicals --- p.48 / Chapter 4.3.2 --- The Transition Structures of CH3O2 Radicals --- p.59 / Chapter 4.3.3 --- The Equilibrium Structures of CH3O2+ Cations --- p.62 / Chapter 4.3.4 --- The Transition Structures of CH3O2+ Cations --- p.66 / Chapter 4.3.5 --- "The Equilibrium Structures of CH3O2"" Anions" --- p.68 / Chapter 4.3.6 --- Comparisons with Available Experimental Results --- p.69 / Chapter 4.4 --- Conclusion --- p.59 / REFERENCES --- p.72 / Chapter CHAPTER 5. --- MISCELLANEOUS / Chapter 5.1 --- "A Gaussian-2 ab initio Study of CH3SSCH2,CH3SF and Their Cations" --- p.74 / Chapter 5.2 --- A Gaussian-2 ab initio Study of SF5 and SF5+ --- p.80 / Chapter 5.3 --- "A Gaussian-2 ab initio Study of SFn+/SFn/SFn -(n = 1, 2, 3)" --- p.84 / REFERENCES --- p.91 / Chapter CHAPTER 6. --- CONCLUSION --- p.93 / REFERENCES --- p.94 / "APPENDIX A. PROCEDURES IN THE G2, G2(MP3) AND G2(MP2) METHODS" / Chapter A.l --- Location of Geometry --- p.95 / Chapter A.2 --- "Approximation of the QCISD(T)/6-311+G(3df,2p) Energy" --- p.95 / Chapter A.3 --- High-Level Correlation (HLC) Correction --- p.96 / Chapter A.4 --- Zero-Point Vibrational Energy (ZPVE) --- p.96 / APPENDIX B ENTHALPY CALCULATION --- p.97

近些年來，計算機輔助造型技術廣泛應用於工業設計領域。對於那些產品設計於三維空間，但是產品加工要使用二維材料的工業，一個急遞解決的問題是對於一件三維設計，如何找到對應的二維裁片。而且，得到的二維裁片應該可以在微小的拉伸下折疊使之還原其原始三綠的形狀。除此之外，工業界還有一些額外的要求例如在特徵線和邊界上的長度控制。為了解決上述問題，我們提出了一些解決方法。 / 關於長度的曲面攤平技術對於生成以可微小拉伸材料製成的二維裁片，是一項非常關鍵的技術。王昌凌教授於2007 年研發了WireWarping 攤平技街，可以在保持邊界和特徵線長度不變的情況下將三維模型攤平得到二維裁片。然而，在攤平過程中，嚴格地保證所有的邊界和特徵長度不變通常會導致得到的二維裁片誤差很大，尤其是當要攤平的三維模型非常不可展的時候。為解決上述問題，我們提出一種新的，可靠而又靈活的新攤平方法--WireWarping++。其基本思想是:我們首先將所有特徵線劃分為彈性特徵線和剛性特徵線。在攤平過程中，只有剛性特徵線的長度需要嚴格保證，而彈性特徵線的長度可以在給定的範圍內變化。為了實現這一功能，我們構架了一個多層優化體系，可以在保證剛性特徵線長度不變的前提下，在一定範圍內改變彈性特徵線的長度，從而使得到的二維裁片形狀最優。除此以外，我們也開發了一套拓撲處理的算法，可以處理那些使得計算不穩定的特徵線網絡拓撲結構。最終的實驗結果證明，我們的WireWarping++方法可以有效地獲得形狀更優的二維裁片，並擁有穩定的性能 / 除了曲面攤平技街，另外一項可以得到二維裁片的技街是可展曲回處理技街。可展曲面處理技術可以將輸入的三維模型處理成可展曲面，而可展曲面可以被無誤差地攤平到二維裁片。現有的方法要么只能處理簡單形狀的模型，要么處理得到的形狀與處理前的相差太遠。 / 為了解決上述困難，我們首先嘗試一種局部可展曲面處理方法。不同於現有的基於全局優化的方法，我們的局部可展曲面處理方法基於可控的拉普拉斯漸變，一個一個地調整頂點的位置。局部可展曲面處理方法的計算速度非常的快。基於此項特性，我們開發了一種實時交互工具去處理輸入的模型。這種工具可以迅速、有效地改進被處理模型的可展度;與王昌凌教授2007 年開發的FL-mesh 方法比，我們的局部處理方法可以得到更接近原始模型形狀的可展曲面。 / 為了進一步得到接近原始模型形狀的可展曲面，我們開發了一種擬合算法，可以擬合出接近原始模型形狀的可展曲面。其中，構成可展曲面的材料僅允許輕微拉伸，而且在擬合過程中，可展曲面與原始模型形狀的誤差被優化，同時可展曲面上的應變得到控制。我們首先提出一種新的曲面造型工具，通過進行一系列接近等量度變形使一個可展曲面的形狀變得更接近原始模型。其次，為了得到更好的擬合結果和克服拓撲死鎖，我們提出了一種隨機形狀擾動的方法來生成不同的初始形狀。最後，為了使我們的方法有可伸縮性，我們提出一套由粗疏到細密擬合的框架，可以處理網格非常細密的模型，而且處理後的模型可以保持原始模型的邊界形狀。 / 除了對輕微可拉伸材料製成的產品進行建模，我們希望將我們的研究拓展到對有壓力產品的建模。我們提出了基於實驗的建模方法，包括以下兩個方面的工作1 )為了建立長度變化--壓力而進行的材料測試2) 長度控制的攤平。目前，我們獲得了一些初步結果。 / In those industries whose products are designed in 3D but fabricated by planar materials, a challenge work is to find out a 2D pattern for a given 3D design, and the 2D pattern should be warped back to the 3D shape with slight extension. Constraints coming from industries like length control on feature curves and boundary interpolation are needed to be enforced. To solve the aforementioned problems, we have proposed several approaches. / Length-aware surface flattening is very useful for generating 2D patterns made of slightly-extensible materials. WireWarping method presented by Wang, 2008 is exploited to generate 2D patterns with invariant lengths of feature and boundary curves. However, strict length constraints on all feature curves sometimes cause large distortions on 2D patterns, especially for those 3D surfaces which are highly non-developable. Then, we present a flexible and robust extension of Wire Warping by introducing a new type of feature curves named elastic feature, which brings flexibility to shape control of the resultant 2D patterns. On these new feature curves, instead of strictly preserving the exact lengths, only the ranges of their lengths are controlled. To achieve this function, a multi-loop shape control optimization framework is proposed to find out the optimized 2D shape among all possible flattening results with different length variations on those elastic feature curves, while the lengths of other feature curves are kept unchanged. Besides, we also present a topology processing algorithm on the network of feature curves to eliminate cases that lead to numerical singularity. The new proposed method is named as WireWarping++. Experimental results show that the WireWarping++ can successfully flatten surface patches into 2D patterns with more flexible shape control and more robust numerical performance. / As an alternative to surface flattening, flattenable surface processing approaches try to process an input model into a flattenable surface where flattenable surface is a polygonal mesh surface that can be unfolded into a planar patch without stretching any polygon. Prior approaches result in either a flattenable surface that could be quite different from the input shape or a (discrete) developable surface has relative simple shape. / To overcome the aforementioned shortages, our first attempt is a local flattenable processing approach. In stead of processing the input model by a global optimization, the local approach adjusts the positions of vertices one by one via a controllable Laplacian evolution. The computation speed of local approach is quite fast so that we develop an interactive tool based on it. The interactive tool can improve the flattenability of the processed model efficiently meanwhile having better shape approximation compared with the result obtained by FL-mesh processing proposed by Wang, 2007. / To achieve a flattenable surface with good shape approximation to the input model, we also proposed a new method for computing a slightly stretched flattenable mesh surface M from a piece wise-linear surface patch P in 3D, where the shape approximation error between M and P is minimized and the strain of stretching on M is controlled. Firstly, we introduce a new surface modeling method to conduct a sequence of nearly isometric deformations to morph a flattenable mesh surface to a new shape which has a better approximation of the input surface. Secondly, in order to get better initial surfaces for fitting and overcome topological obstacles, a shape perturbation scheme is investigated to obtain the optimal surface fitting result. Lastly, to improve the scalability of our optimal surface fitting algorithm, a coarse-to-fine fitting framework is exploited so that very dense flattenable mesh surfaces can be modeled and boundaries of the input surfaces can be interpolated. / Besides modeling on products fabricated by slightly-extensible materials, we also try to extend our work to modeling on compression garment. A calibration based method is proposed consist two aspects: 1) a material testing for establishing the relationship between length change and compression; 2) a length control flattening. Some preliminary results are presented. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Yunbo. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 148-161). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.1 / Chinese Abstract --- p.4 / Acknowledgements --- p.6 / List of Figures --- p.10 / List of Tables --- p.12 / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation. --- p.1 / Chapter 1.2 --- Problems and Methodology. --- p.3 / Chapter 1.2.1 --- Surface Flat tening with Length Control --- p.4 / Chapter 1.2.2 --- Modeling on Flattenable Surfaces --- p.5 / Chapter 1.2.2.1 --- A Local Flat tenable Processing Approach --- p.6 / Chapter 1.2.2.2 --- Optimal Fitting of Strain-cont rolled Flattenable Mesh Surfaces --- p.6 / Chapter 1.2.3 --- Modeling on Compression Garment --- p.7 / Chapter 1.3 --- Thesis Organization --- p.7 / Chapter 2 --- Literature Review --- p.11 / Chapter 2.1 --- Developable Parametric Surfaces --- p.11 / Chapter 2.2 --- Discrete Developable Surface Modeling --- p.12 / Chapter 2.3 --- Mesh Parameterization and Surface Flattening --- p.13 / Chapter 2.4 --- Cloth Simulation --- p.16 / Chapter 2.5 --- Multi-resolution Techniques --- p.16 / Chapter 3 --- Robust and Flexible Surface Flattening with Length Control --- p.18 / Chapter 3.1 --- Const rained Optimizat ion based Surface Flattening --- p.20 / Chapter 3.1.1 --- Length Preserved WireWarping --- p.21 / Chapter 3.1.2 --- Multi-loop Optimization Framework --- p.23 / Chapter 3.1.3 --- Shape Error Function --- p.27 / Chapter 3.2 --- Topology Processing --- p.29 / Chapter 3.2.1 --- Processing on Hinged Feature Curves --- p.30 / Chapter 3.2.2 --- Connecting Separate Boundary Loops --- p.32 / Chapter 3.3 --- Metrics --- p.8 / Chapter 3.4 --- Experimental Results --- p.33 / Chapter 3.5 --- Ot her Applications --- p.34 / Chapter 3.6 --- Angle Constraints on Female Jeans-pants Design --- p.39 / Chapter 3.7 --- Summary --- p.40 / Chapter 4 --- Flattenable Mesh Processing : A Local Approach --- p.42 / Chapter 4.1 --- Problem Definitions --- p.43 / Chapter 4.2 --- Controllable Laplacian Evolution --- p.44 / Chapter 4.2.1 --- Laplacian Operator. --- p.45 / Chapter 4.2.2 --- Analys is on Laplacian Operator --- p.45 / Chapter 4.2.3 --- Localized Energy Function --- p.46 / Chapter 4.2.4 --- Numerical Solution --- p.48 / Chapter 4.3 --- Interactive Tool --- p.49 / Chapter 4.4 --- Summary and Limit ation --- p.50 / Chapter 5 --- Optimal Fitting of St rain-Cont rolled Flattenable Mesh Surfaces --- p.55 / Chapter 5.1 --- Introduction --- p.55 / Chapter 5.2 --- Toolbox --- p.56 / Chapter 5.2.1 --- FL-mesh Processing --- p.56 / Chapter 5.2.2 --- Inextensible Cloth Simulation --- p.57 / Chapter 5.2.3 --- Least-square Mesh --- p.59 / Chapter 5.2.4 --- Spring-mass System --- p.59 / Chapter 5.3 --- Optimal Shape Approximation --- p.61 / Chapter 5.3.1 --- Isometric Surface Fitting --- p.62 / Chapter 5.3.1.1 --- Nearly Isometric Deformation --- p.63 / Chapter 5.3.1.2 --- Surface Fitting --- p.64 / Chapter 5.3.1.3 --- Problem of Numerical Singularity --- p.66 / Chapter 5.3.2 --- Shape Perturbation for Optimal Fitting --- p.68 / Chapter 5.3.3 --- Relaxation for Accurate Strain Control --- p.71 / Chapter 5.4 --- Multi-scale Surface Fitting. --- p.72 / Chapter 5.4.1 --- Coarsening, Local update and Relaxation --- p.74 / Chapter 5.4.2 --- Boundary Constraints of Interpolation --- p.78 / Chapter 5.4.2.1 --- Propert ies of Isometric Deformation --- p.78 / Chapter 5.4.2.2 --- Existence of Solution --- p.80 / Chapter 5.4.2.3 --- Boundary Triangulation --- p.81 / Chapter 5.4.2.4 --- Optimal Boundary Coarsening --- p.83 / Chapter 5.5 --- Results --- p.85 / Chapter 5.6 --- Summary --- p.87 / Chapter 6 --- Towards Compression Garment --- p.89 / Chapter 6.1 --- Problem Formulation --- p.90 / Chapter 6.2 --- Testing on Elastic Materials --- p.92 / Chapter 6.2.1 --- Test ing Overview --- p.92 / Chapter 6.2.2 --- Quad Load Test --- p.92 / Chapter 6.2.3 --- Geometric Models --- p.9 / Chapter 6.2.4 --- Pressure Sensors --- p.94 / Chapter 6.2.5 --- Test -bed --- p.95 / Chapter 6.2.6 --- Data Analysis --- p.99 / Chapter 6.2.6.1 --- Results for Ellipsoid --- p.100 / Chapter 6.2.6.2 --- Results for Cone wit hout Head --- p.102 / Chapter 6.2.6.3 --- Results for Cylinder --- p.105 / Chapter 6.2.7 --- Summary --- p.107 / Chapter 6.3 --- Compression Generation via Length Control --- p.108 / Chapter 6.4 --- Summary and Discussion --- p.111 / Chapter 7 --- Conclusion and Discuss ion --- p.114 / Chapter 7.1 --- Summary --- p.114 / Chapter 7.2 --- Fut ure Work --- p.117 / Chapter A --- Appendix A: Work on An Wet suit Design system --- p.119 / Chapter A.1 --- Introduction --- p.119 / Chapter A.1.1 --- Tools Expect ed by Designers --- p.120 / Chapter A.1.2 --- Existing Met hods --- p.121 / Chapter A.1.3 --- Conventional Fabricat ion of User Customized Products --- p.124 / Chapter A.2 --- System Overview --- p.124 / Chapter A.3 --- System Implement at ion --- p.127 / Chapter A.3.1 --- Styling Design and Its Transformation --- p.127 / Chapter A.3.2 --- Trimming --- p.129 / Chapter A.3.3 --- Unfolding with Length-Preserved Feature Curves --- p.130 / Chapter A.3.4 --- Discrete Developable Mesh Processing --- p.133 / Chapter A.3.5 --- Map-guided Layout Arrangement --- p.135 / Chapter A.4 --- Result s and Applications --- p.137 / Chapter A.5 --- User Experience --- p.142 / Chapter A.6 --- Summary --- p.146 / Bibliography --- p.148

This thesis details the use of x-ray photoelectron spectroscopy to monitor in-situ surface processing of solid surfaces in real-time. The processing methods investigated were annealing, deposition of thin organic films and exposure to oxygen and hydrogen produced by in-situ microwave plasmas. Three solid surfaces were investigated; metals, diamond and zinc oxide. Clean copper and gold were annealed up to 1000 K while monitoring with real-time XPS. A temperature-dependent shift of the Cu 2p3/2 and Au 4f7/2 core-level to lower binding energy was measured, -1.29 ± 0.04 meV/10 K and -2.36 ± 0.01 meV/10 K respectively. The shift was identified as being due to a thermal expansion of the lattice. The removal of argon ion induced damage to the copper surface was monitored in real-time and a critical temperature of 680 ± 20 K for the removal of the damage was measured. The formation of an interface between aluminium and copper phthalocyanine was monitored in real-time. Hydrogen and oxygen terminated (111) natural diamond surfaces were prepared in-situ and surface reconstruction by annealing up to 1200 K was monitored in real-time. Large reversible shifts to core-level binding energies were attributed to a surface photovoltage that was persistent at high temperature on the hydrogen and oxygen terminated surfaces. A model of the surface photovoltage is given where the bulk resistance of the diamond is identified as sustaining the photovoltage at elevated temperature. The zinc oxide (0001) surface was found to have a temperature-dependent core-level binding energy shift that was fully reversible up to 900 K and symmetric with cooling. The shift was attributed to a diffusion of oxygen vacancies from the bulk into the sub-surface. The zinc oxide (0001) surface was found to exhibit different temperature dependence to the (0001) surface that was fully reversible up to 700K but not symmetric with cooling. The shift was attributed to an additional disruption to stabilizing charge transfer between the polar surfaces. The formation of interfaces between the (0001) surface with copper phthalocyanine and C60 were monitored in real-time.

In the first part of this thesis, we proved a pseudo-locality theorem for a coupled Ricci flow, extending Perelman’s work on Ricci flow to the Ricci flow coupled with heat equation. By use of the reduced distance and the pseudo-locality theorem, we showed that the parabolic rescaling of a Type I coupled Ricci flow with respect to a Type I singular point converges to a non-trivial Ricci soliton. In the second part of the thesis, we prove the existence of infinitely many solutions to the Hull- Strominger system on generalized Calabi-Gray manifolds, more specifically compact non-K \"ahler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers. We also studied the behavior of the anomaly flow on the generalized Calabi-Gray manifolds, and reduced it to a scalar flow on a Riemann surface. We obtained the long-time existence and convergence after rescaling in the case when the curvature of initial metric is small.

In this thesis, we explore the restrictions imposed on the genus of a smooth curve $X$ which possesses at least three independent gonal morphisms to $\Pp^1$. We will prove a sharp lower bound on the dimension of global sections given by the sum of the divisors for the gonal morphisms. This inequality will provide an upper bound on the genus of a curve with the described properties. By considering the birational image of $X$ in $\Pp^1 \times \Pp^1 \times \Pp^1$ under the product of three pairwise independent morphisms, we observe that the boundary case for the previously mentioned inequality is closely related to the case where the image of $X$ is contained in a type 1-1-1 surface. Motivated by this phenomenon, we examine the constraints on the arithmetic genus of an irreducible curve in $\Pp^1 \times \Pp^1 \times \Pp^1$ whose natural projections are pairwise independent and all have degree 7.

It is well-known that del Pezzo surfaces of degree 9 -- n. are in one-to-one correspondence to flat En bundles over elliptic curves which are anti-canonical curves of such surfaces. In my thesis, we study a broader class of rational surfaces which are called ADE surfaces. We construct Lie algebra bundles of any type on these surfaces, and extend the above correspondence to flat G bundles over elliptic curves, where G is a simple, compact and simply-connected Lie group of any type. Concretely, we establish a natural identification between the following two very different moduli spaces for a Lie group G of any type: the moduli space of rational surfaces with G-configurations and the moduli space of flat G-bundles over a fixed elliptic curve. / Zhang, Jiajin. / "July 2007." / Adviser: Leung Nai Chung Conan. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 77-79). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Leung, Wai Sing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-62). / Abstracts in English and Chinese. / Chapter 0.1 --- Introduction --- p.6 / Chapter 1 --- Sphere Theorems --- p.8 / Chapter 1.1 --- Rauch-Berger-Klingenberg Sphere Theorem --- p.8 / Chapter 1.2 --- Maximal Diameter Theorem --- p.15 / Chapter 1.3 --- Minimal Diameter Theorem --- p.17 / Chapter 2 --- A Differentiable Sphere Theorem --- p.27 / Chapter 2.1 --- Definitions --- p.27 / Chapter 2.2 --- Preliminary results not related to curvature --- p.28 / Chapter 2.3 --- Preliminary result related to the curvature --- p.33 / Chapter 2.4 --- Differentiable Sphere Theorem --- p.35 / Chapter 3 --- The fundamental equations of Riemannian submer- sions --- p.43 / Chapter 3.1 --- Definitions --- p.43 / Chapter 3.2 --- The fundamental tensors T and A --- p.44 / Chapter 3.3 --- Covariant derivatives of T and A --- p.47 / Chapter 3.4 --- Fundamental equations and O'Neill's formulas --- p.49 / Chapter 4 --- A study on exotic spheres --- p.52 / Chapter 4.1 --- Construction of Milnor sphere --- p.52 / Chapter 4.2 --- Construction of GM-sphere (Σ7) --- p.53 / Chapter 4.3 --- The curvature of Σ7 --- p.54 / Chapter 4.4 --- Some recent results and open questions --- p.59 / Bibliography --- p.61