Zhang Kai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 99-102). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- The Generalized PML Theory --- p.6 / Chapter 1.1.1 --- Background --- p.6 / Chapter 1.1.2 --- Derivation --- p.8 / Chapter 1.1.3 --- Reflection Properties --- p.11 / Chapter 1.2 --- Unified Formulation --- p.12 / Chapter 1.2.1 --- "Face-, Edge- and Corner-PMLs" --- p.12 / Chapter 1.2.2 --- Unified PML Equations in 3D --- p.15 / Chapter 1.2.3 --- Unified PML Equations in 2D --- p.16 / Chapter 1.2.4 --- Examples of PML Formulations --- p.16 / Chapter 1.3 --- Inhomogeneous Initial Conditions --- p.23 / Chapter 2 --- Numerical Analysis of PMLs --- p.25 / Chapter 2.1 --- Continuous PMLs --- p.26 / Chapter 2.1.1 --- PMLs for Wave Equations --- p.27 / Chapter 2.1.2 --- Finite PMLs for Wave Equations --- p.31 / Chapter 2.1.3 --- Berenger's PMLs for Maxwell Equations --- p.33 / Chapter 2.1.4 --- Finite Berenger's PMLs for Maxwell Equations --- p.35 / Chapter 2.1.5 --- PMLs for Acoustic Equations --- p.38 / Chapter 2.1.6 --- Berenger's PMLs for Acoustic Equations --- p.39 / Chapter 2.1.7 --- PMLs for 1-D Hyperbolic Systems --- p.42 / Chapter 2.2 --- Discrete PMLs --- p.44 / Chapter 2.2.1 --- Discrete PMLs for Wave Equations --- p.44 / Chapter 2.2.2 --- Finite Discrete PMLs for Wave Equations --- p.51 / Chapter 2.2.3 --- Discrete Berenger's PMLs for Wave Equations --- p.53 / Chapter 2.2.4 --- Finite Discrete Berenger's PMLs for Wave Equations --- p.56 / Chapter 2.2.5 --- Discrete PMLs for 1-D Hyperbolic Systems --- p.58 / Chapter 2.3 --- Modified Yee schemes for PMLs --- p.59 / Chapter 2.3.1 --- Stability of the Yee Scheme for Wave Equation --- p.61 / Chapter 2.3.2 --- Decay of the Yee Scheme Solution to the Berenger's PMLs --- p.62 / Chapter 2.3.3 --- Stability and Convergence of the Yee Scheme for the Berenger's PMLs --- p.67 / Chapter 2.3.4 --- Decay of the Yee Scheme Solution to the Hagstrom's PMLs --- p.70 / Chapter 2.3.5 --- Stability and Convergence of the Yee Scheme for the Hagstrom's PMLs --- p.75 / Chapter 2.4 --- Modified Lax-Wendroff Scheme for PMLs --- p.80 / Chapter 2.4.1 --- Exponential Decays in Parabolic Equations --- p.80 / Chapter 2.4.2 --- Exponential Decays in Hyperbolic Equations --- p.82 / Chapter 2.4.3 --- Exponential Decays of Modified Lax-Wendroff Solutions --- p.86 / Chapter 3 --- Numerical Simulation --- p.93 / Bibliography --- p.99

在本文中，我們為了三維空間的馬克士威方程組(Maxwell’s equation)制定和分析了一套新種類的交錯間斷伽遼金(discontinuous Galerkin)方法，同時考慮了時間依賴性和時間諧波的馬克士威方程組。我們用了空間離散上交錯笛卡兒網格，這種方法具有許多良好的性質。首先，我們的方法所得出的數值解保留了電磁能量，並自動符合了高斯定律的離散版本。第二，質量矩陣是對角矩陣，從而時間推進是顯式和非常有效的。第三，我們的方法是高階準確，最佳收斂性在這裏會被嚴格地證明。第四，基於笛卡兒網格，它也很容易被執行，並可視為是典型的Yee’s Scheme的以及四邊形的邊有限元的推廣。最後，超收斂結果也會在這裏被證明。 / 在本文中，我們還提供了幾個數值結果驗證了理論的陳述。我們計算了時間依賴性和時間諧波的馬克士威方程組數值收斂結果。此外，我們計算時間諧波馬克士威方程組特徵值問題的數值特徵值，並與理論特徵值比較結果。最後，完美匹配層(Perfect Matching Layer)吸收邊界的問題也有實行其數值結果。 / We develop and analyze a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations in this paper. Both time-dependent and time-harmonic Maxwell’s equations are considered. The spatial discretization is based on staggered Cartesian grids which possess many good properties. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Second, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Third, our method is high order accurate and the optimal order of convergence is rigorously proved. Fourth, it is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee’s scheme as well as the quadrilateral edge finite elements. Lastly, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. / In this paper, we also provide several numerical results to verify the theoretical statements. We compute the numerical convergence order using L2-norm and discrete-norm respectively for both the time-dependent and time-harmonic Maxwell’s equations. Also, we compute the numerical eigenvalues for the time-harmonic eigenvalue problem and compare the result with the theoretical eigenvalues. Lastly, applications to problems in unbounded domains with the use of PML are also presented. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yu, Tang Fei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 46-49). / Abstracts also in Chinese. / Chapter 1 --- Introduction and Model Problems --- p.1 / Chapter 2 --- Staggered DG Spaces --- p.4 / Chapter 2.1 --- Review on Gauss-Radau and Gaussisan points --- p.5 / Chapter 2.2 --- Basis functions --- p.6 / Chapter 2.3 --- Finite Elements space --- p.7 / Chapter 3 --- Method derivation --- p.14 / Chapter 3.1 --- Method --- p.14 / Chapter 3.2 --- Time discretization --- p.17 / Chapter 4 --- Energy conservation and Discrete Gauss law --- p.19 / Chapter 4.1 --- Energy conservation --- p.19 / Chapter 4.2 --- Discrete Gauss law --- p.22 / Chapter 5 --- Error analysis --- p.24 / Chapter 6 --- Numerical examples --- p.29 / Chapter 6.1 --- Convergence tests --- p.30 / Chapter 6.2 --- Diffraction by a perfectly conducting object --- p.30 / Chapter 6.3 --- Perfectly matched layers --- p.37 / Chapter 7 --- Time Harmonic Maxwell’s equations --- p.40 / Chapter 7.1 --- Model Problems --- p.40 / Chapter 7.2 --- Numerical examples --- p.40 / Chapter 7.2.1 --- Convergence tests --- p.41 / Chapter 7.2.2 --- Eigenvalues tests --- p.41 / Chapter 8 --- Conclusion --- p.45 / Bibliography --- p.46

在本文中， 我們將主要討論一種在求解一類波動方程反問題中很有價值的數值方法：線性化方法。 / 在介紹上述的數值方法之前， 我們將首先討論波動方程的一些重要的特質，主要包括四類典型的波動方程模型，方程的基本解和一般解，以及波動方程解的性質。 / 接下來，在本文的第二部分中，我們會首先介紹所求解的模型以及其反問題。此反問題主要研究求解波動方程[附圖]中的系數c. 線性化方法的主要思想在於將速度c分解成兩部分：c₁ 和c₂ ，並且滿足關系式：[附圖]，其中c₁ 是一個小的擾動量。另一方面，上述波動方程的解u 可以被線性表示：u = u₀ + u₁ ，其中u₀ 和u₁ 分別是一維問題和二維問題的解。相應的，我們將運用有限差分方法和傅利葉變換方法求解上述一維問題和二維問題，從而分別求解c₁ 和c₂ ，最終求解得到係數c. 在本文的最後，我們將進行一些數值試驗，從而驗證此線性化方法的有效性和可靠性。 / In this thesis, we will discuss a numerical method of enormous value, a linearized method for solving a certain kind of inverse wave equations. / Before the introduction of the above-mentioned method, we shall discuss some important features of the wave equations in the first part of the thesis, consisting of four typical mathematical models of wave equations, there fundamental solutions, general solutions and the properties of those general solutions. / Next, we shall present the model and its inverse problem of recovering the coefficient c representing the propagation velocity of wave from the wave equation [with mathematic formula] The linearized method aims at dividing the velocity c into two parts, c₀ and c₁, which satisfying the relation [with mathematic formula], where c₁ is a tiny perturbation. On the other hand, the solution u can be represented in the linear form, u = u₀ + u₁, where u₀ and u₁ are the solutions to one-dimensional problem and two- dimensional problem respectively. Accordingly, we can use the numerical methods, finite difference method and Fourier transform method to solve the one-dimensional forward problem and two-dimensional inverse problem respectively, thus we can get c₀ and c₁, a step before we recover the velocity c. In the numerical experiments, we shall test the proposed linearized numerical method for some special examples and demonstrate the effectiveness and robustness of the method. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Xu, Xinyi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 64-65). / Abstracts also in Chinese. / Chapter 1 --- Fundamental aspects of wave equations --- p.6 / Chapter 1.1 --- Introduction --- p.6 / Chapter 1.1.1 --- Four important wave equations --- p.6 / Chapter 1.1.2 --- General form of wave equations --- p.10 / Chapter 1.2 --- Fundamental solutions --- p.11 / Chapter 1.2.1 --- Fourier transform --- p.11 / Chapter 1.2.2 --- Fundamental solution in three-dimensional space --- p.14 / Chapter 1.2.3 --- Fundamental solution in two-dimensional space --- p.16 / Chapter 1.3 --- General solution --- p.19 / Chapter 1.3.1 --- One-dimensional wave equations --- p.19 / Chapter 1.3.2 --- Two and three dimensional wave equations --- p.26 / Chapter 1.3.3 --- n dimensional case --- p.28 / Chapter 1.4 --- Properties of solutions to wave equation --- p.31 / Chapter 1.4.1 --- Properties of Kirchhoff’s solutions --- p.31 / Chapter 1.4.2 --- Properties of Poisson’s solutions --- p.33 / Chapter 1.4.3 --- Decay of the solutions to wave equation --- p.34 / Chapter 2 --- Linearized method for wave equations --- p.36 / Chapter 2.1 --- Introduction --- p.36 / Chapter 2.1.1 --- Background --- p.36 / Chapter 2.1.2 --- Forward and inverse problem --- p.38 / Chapter 2.2 --- Basic ideas of Linearized Method --- p.39 / Chapter 2.3 --- Theoretical analysis on linearized method --- p.41 / Chapter 2.3.1 --- One-dimensional forward problem --- p.42 / Chapter 2.3.2 --- Two-dimensional forward problem --- p.43 / Chapter 2.3.3 --- Existence and uniqueness of solutions to the inverse problem --- p.45 / Chapter 2.4 --- Numerical analysis on linearized method --- p.45 / Chapter 2.4.1 --- Discrete analog of the inverse problem --- p.46 / Chapter 2.4.2 --- Fourier transform --- p.48 / Chapter 2.4.3 --- Direct methods for inverse and forward problems --- p.52 / Chapter 2.5 --- Numerical Simulation --- p.54 / Chapter 2.5.1 --- Special Case --- p.54 / Chapter 2.5.2 --- General Case --- p.59 / Chapter 3 --- Conclusion --- p.63 / Bibliography --- p.64

Lee, Ho Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 75-79). / Abstracts in English and Chinese. / Chapter 1 --- Upscaling methods for high contrast problems --- p.6 / Chapter 1.1 --- Review on upscaling methods --- p.7 / Chapter 1.2 --- Upscaling method with high contrast of the conductivity --- p.11 / Chapter 2 --- Multiscale finite element methods for high contrast problems --- p.19 / Chapter 2.1 --- Review on Multiscale finite element methods --- p.20 / Chapter 2.2 --- Local spectral basis functions --- p.23 / Chapter 2.3 --- Discussion for MsFEM with spectral multiscale basis functions . --- p.25 / Chapter 3 --- Elliptic equations in high-contrast heterogeneous media --- p.28 / Chapter 3.1 --- Preliminaries --- p.29 / Chapter 3.2 --- Integral representation --- p.32 / Chapter 3.3 --- The well-posedness of the integral equation --- p.37 / Chapter 4 --- A numerical approach for the Elliptic equations in high-contrast heterogeneous media --- p.45 / Chapter 4.1 --- Introduction --- p.46 / Chapter 4.2 --- A new approach --- p.47 / Chapter 4.3 --- Discussion of the results --- p.50 / Chapter 4.4 --- Numerical experiment --- p.51 / Chapter 5 --- A preconditioner for high contrast problems using reduced-contrast approximations --- p.62 / Chapter 5.1 --- Reduced-contrast approximations for the solution of elliptic equations --- p.63 / Chapter 5.2 --- Review on multigrid methods --- p.66 / Chapter 5.3 --- Preconditioning and numerical experiments --- p.70 / Bibliography --- p.75

This thesis describes a novel microfluidic platform to control the macromolecular concentrations and their applications in constructing the phase diagram of polymer aqueous solutions and in the high-throughput screening of protein crystallization conditions at the nanoliter scale. The microfluidic platform was fabricated using the soft-lithography method and based on poly(dimethylsiloxane) (PDMS) material, which is widely used in microfluidic device. PDMS is gas and water permeable elastomer. By exploiting the permeability of the gas and water in PDMS, we developed the degassed-PDMS nanoliter liquid dispensing system, the controlled microevaporation method in constructing the phase diagram of polymer aqueous solution, and the screening platform of protein crystallization conditions. / This thesis describes two types of degassed-PDMS nanoliter liquid dispensing system. One is dispensing without the microvalve, in which various liquids are dispensed through the degassed PDMS microchannel. It involves two steps: in the first step, the PDMS microchannel patch (or the entire microchip) is placed in a vacuum chamber for a certain time; in the second step, the target liquid is deposited at the inlet of the PDMS channel and dispensed into the PDMS microchamber. The other method is dispensing with the aid of PDMS microvalve. This method combines the valve control and degassed PDMS pumping source, which provides more control over on the liquid dispensing, such as isolating, mixing, etc. / Zhou, Xuechang. / Adviser: Bo Zheng. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 53-56). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Wong Chak-fu. / "September 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 451-475). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

In Chapter 1, theories cited background of these studies as well as chemical synthesis methods used are introduced. / In Chapter 2, theories of static and dynamic light scattering (LLS) as well as details of the LLS instrumentation are introduced, especially the application of LLS to polymer solutions. / In Chapter 3, we present the study of the self-assembly of oligo( p-phenyteneethynylene)-based coil-rod-coil and rod-coil-rod triblock copolymers in the solvent mixture of toluene and hexane by using a combination of static and dynamic laser light scattering. UV-vis spectroscopy and fluorescence spectroscopy. Our results reveal that the aggregation in the solvent mixture is strongly influenced by the triblock copolymer structure. For the coil-rod-coil (PS-OPE-PS) triblock copolymer, small well-defined aggregates are formed in the solvent mixture with different toluene/hexane ratios. The coiled PS blocks entangle with the OPE block to restrict possible pi-pi stacking and make the OPE chain backbone more planar. The red-shift in the UV-vis and fluorescence spectra indicates the formation of 3-type aggregates. The rod-coil-rod (OPE-PS-OPE) triblock copolymer chains form large "disk-like" micelles with an ordered OPE core and a collapsed PS shell. The blue-shift in the UV-vis and fluorescence spectra shows the formation of H-type aggregates; namely, the OPE block in the core are parallel to each other so that there is stronger interchain pi-pi interaction. / In Chapter 4, we present the study of the aggregation of C60-PEO-C 60 chains in the chloronaphthalene/benzene solvent mixture with different ratios by using a combination of static and dynamic laser light scattering. Chloronaphthalene is a good solvent for C60 but a poor solvent for the PEO chain. On the other hand, benzene is a good solvent for the PEO chain but a poor solvent for Co. Individual polymer chains or small micelles coexist with large aggregates in solvent mixture. Our results show that the structures of the aggregates strongly depend on the composition of the solvent mixtures, which reflects in different ratios of <Rg>/<R h>, where <Rg> and <Rh> are z-average root-mean-square radius of gyration and hydrodynamic radius, respectively. / In Chapter 5, we present a study of reversible formation and decomposition of star polymer clusters. First, we synthesized 4-aim bromide-end star polystyrene chains by using atom transfer radical polymerization (ATRP), and then modified the end group from bromide to thiol since it can be slowly oxidized in air to induce the clustering among 4-arm star polystyrene chains. The clustering is reversible under a reduction condition. Such formation and fragmentation (decomposition) of the polymer clusters in toluene was followed by LLS. To induce the reduction, DTT was added. Our results reveal that in the clustering, the fast mode is attributed to the cooperative diffusion of individual 4-arm star polystyrene chains (unimers), while the slow mode is related to the diffusion of large clusters. In the fragmentation, the slow mode becomes fast and its intensity contribution decreases as the reduction time increases, reflecting the decreases of the size and the number of large polymer clusters. Our results suggest that the clusters fragmentation induced by thiol-functionalized 4-PS chains in toluene dilute solution follows the universal RLCA regime, but in a reversed fashion. / In this thesis, we did the following studies: (1) The association of two rod-coil triblock copolymers: polystyrene-oligo(p-phenyleneethynylene)-polystyrene (PS-OPE-PS) and oligo(p-phenyleneethynylene)-polystyrene-oligo( p-phenyleneethynylene) (OPE-PS-OPE) in a toluene/hexane mixture as well as of C60-Poly(ethylene oxide)-C60 in a chloronaphthalene/benzene mixture. (2) The formation and fragmentation of 4-arm-PS-SH cluster in toluene via the oxidization in air to form disulfide crosslink as well as the decomposition of the resultant cross-linked 4-arm star polystyrene clusters with reversible disulfide groups in toluene via reduction to thiol group by 2,3-dihydroxy-1,4-butanethiol (DTT). / Huo, Hong. / "August 2007." / Adviser: Chi Wu. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1037. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 109). / 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. / Abstract in English and Chinese. / School code: 1307.

In this thesis, we will address two most important topics in inverse acoustic and electromagnetic obstacle scattering problems: uniqueness and reconstruction algorithms. / The first part is devoted to the uniqueness issues. A detailed exposition of the background of this problem and a comprehensive discussion of the existing results are presented. The focus of this part is on our contribution to this field, especially on the unique determination of polygonal or polyhedral scatterers with a single or finitely many far-field measurements. In summary, we have shown the following results when the polyhedral type scatterers are concerned in inverse acoustic obstacle scattering: if the scatterer consists of finitely many solid polyhedral obstacles, which may be either sound-soft, sound-hard or two types mixed together, and it may also contain some crack-type obstacles but only sound-soft ones, then one can uniquely determine the scatterer by a single incident plane wave at some fixed k0 > 0 and d0 ∈ SN-1 . This statement is affirmatively verified in any dimensions whenever there is no any sound-hard obstacle present; when there is any sound-hard obstacle, the uniqueness is validated in the R2 case, but still incomplete in the RN case with N ≥ 3, which is proved to be true only by N different incident plane waves. Whenever the scatterer contains some sound-hard crack-type obstacles, we have constructed some examples to show that one cannot uniquely determine the scatterer by any less than N incident waves. So in the case with the additional presence of sound-hard crack-type obstacles, another result we have established that one can uniquely determine such a scatterer by N incident waves at any fixed wave number and arbitrary N linearly independent incident directions is optimal. We also consider more general polyhedral type scatterers with partially coated components, and some uniqueness results are established to determine the underlying physical properties. Besides, we have also collected a global uniqueness result for balls or discs. It is shown that in the resonance region, the shape of a sound-soft/sound-hard ball in R3 or a soundhard/sound-soft disc in R2 is uniquely determined by a single far-field datum measured at some fixed spot corresponding to a single incident plane wave. This seems to be an important result in the uniqueness study field as it is the first to establish the unique determination by a single far-field datum measured at one fixed spot. While all the other existing uniqueness results require far-field data observed at least in one open subset on the unit sphere with non-zero measure. To pave the way for the uniqueness study with such simple balls or discs, we also present a systematic and rather complete study of the interlacing character of the zeros for Bessel and spherical Bessel functions and their respective derivatives. Finally, all the uniqueness results for inverse acoustic obstacle scattering associated with general polyhedral scatterers have been extended to the inverse electromagnetic scattering. / The second part of this thesis is concerned with the reconstruction algorithms. We will present a novel multilevel linear sampling method (MLSM) which is developed in our recent work. The new method resembles the popular multi-level techniques in scientific computing and is shown to possess the asymptotically optimal computational complexity. For an n x n sampling mesh-grid in R2 or an n x n x n sampling mesh-grid in R3 , the proposed algorithm only requires to solve O (nN-1)( N = 2,3) far-field equations for a RN problem, and this is in sharp contrast to the original version of the linear sampling method which needs to solve n N far-field equations instead. Numerical experiments have illustrated the promising feature of the new algorithm in significantly reducing the computational costs. / Liu, Hongyu. / "June 2007." / Adviser: Jun Zou. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0354. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 161-168). / 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.

Guo Zhenhua. / "June 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 79-84). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Kwan Chi Man Simon. / Abstract also in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references. / Abstract --- p.i / Abstract (Chinese) --- p.iii / Acknowledgment --- p.iv / Contents --- p.v / Abbreviations --- p.viii / List of Figures --- p.xiv / List of Tables --- p.xvii / Chapter 1. --- Introduction --- p.1 / Chapter 2. --- Theoretical background --- p.4 / Chapter 2.1 --- Static laser light scattering --- p.5 / Chapter 2.2 --- Dynamic laser light scattering --- p.5 / Chapter 2.3 --- Gel Permeation Chromatography --- p.6 / Chapter 2.4 --- Chain Flexibility --- p.9 / Chapter 2.4.1 --- Flexible chains --- p.9 / Chapter 2.4.2 --- Stiff chains --- p.12 / Chapter 2.5 --- Calibration between translational diffusion coefficient D and molar mass M --- p.14 / Chapter 2.5.1 --- Conversion between line-Width and molar Mass distributions --- p.14 / Chapter 2.5.2 --- Using a set of Narrowly Distributed Standards --- p.15 / Chapter 2.5.3 --- Using Two or More Broadly Distributed Samples --- p.16 / Chapter 2.6 --- "Calibration by off-line GPC, Static and Dynamic LLS" --- p.16 / Chapter 2.7 --- References --- p.19 / Chapter 3. --- Experimental --- p.21 / Chapter 3.1 --- Laser Light Scattering Instrumentation --- p.21 / Chapter 3.2 --- Refractive index increment measurement --- p.23 / Chapter 3.3 --- Gel permeation chromatography --- p.24 / Chapter 3.4 --- References --- p.25 / Chapter 4. --- Laser Light Scattering Studies of Soluble High Performance Fluorine- containing Polyimides --- p.26 / Chapter 4.1 --- Introduction --- p.26 / Chapter 4.2 --- Sample Preparation --- p.28 / Chapter 4.3 --- Results and Discussion --- p.28 / Chapter 4.4 --- Conclusion --- p.40 / Chapter 4.5 --- References --- p.42 / Chapter 5. --- Characterization of novel optically active conjugated polyarylenes and poly(aryleneethynylene)s by a combination of Laser Light Scattering and Gel Permeation Chromatography --- p.45 / Chapter 5.1 --- Introduction --- p.45 / Chapter 5.2 --- Sample Preparation --- p.48 / Chapter 5.3 --- Results and Discussion --- p.48 / Chapter 5.4 --- Conclusion --- p.56 / Chapter 5.5 --- References --- p.61 / Appendix --- p.62 / Chapter A.1 --- Static laser light scattering --- p.62 / Chapter A.1.1 --- Scattering from a small particle --- p.62 / Chapter A. 1.2 --- Scattering from a large particle --- p.62 / Chapter A. 1.3 --- Scattering by macroscopic systems and Theory of Fluctuations --- p.65 / Chapter A.1.3.1 --- Scattering by gases and liquids --- p.67 / Chapter A. 1.4 --- Scattering by solutions of small molecules --- p.68 / Chapter A. 1.4.1 --- Scattering from polymer solution --- p.70 / Chapter A.2 --- Dynamic laser light scattering --- p.71 / Chapter A.2.1 --- Line-width measurement --- p.75 / Chapter A.2.2 --- Data analysis --- p.77