Biomolecular structure and interactions in aqueous environment are determined by a complicated interplay between physical and chemical forces including solvation, electrostatics, van der Waals forces, the hydrophobic effect and covalent bonding. Among them, electrostatics has been of particular interest due to its long-range nature and the tradeoff between desolvation and interaction effects [1]. In addition, electrostatic interactions play a significant role within a biomolecule as well as between biomolecules, making the balance between the two vital to the understanding of macromolecular systems. As a result, much effort has been devoted to accurate modeling and simulation of biomolecule electrostatics. One important application of this work is to compute the structure of electrostatic interactions for a biomolecule in an electrolyte solution, as well as the potential that the molecule generates in space. There are two valuable uses for these simulations. First, it provides a full picture of the electrostatic energetics of a biomolecular system, improving our understanding of how electrostatics contributes to stability, specificity, function, and molecular interaction [2]. Second, these simulations serve as a tool for molecular design, since electrostatic complementarity is an important feature of interacting molecules. Through examination of the electrostatics and potential field generated by a protein molecule, for example, it may be possible to suggest improvements to other proteins or drug molecules that interact with it, or perhaps even design new interacting molecules de novo [3]. There are two approaches in simulating a protein macromolecule in an aqueous solution with nonzero ionic strength. Discrete/atomistic approaches based on Monte-Carlo or molecular dynamics simulations treat the macromolecule and solvent explicitly at the atomic level. Therefore, an enormous number of solvent molecules are required to provide reasonable accuracy, especially when electric fields far away from macroscopic surface are of interest, leading to computational infeasibility. In this work, we adopt instead an approach based on a continuum description of the macromolecule and solvent. Although the continuum model of biomolecule electrostatics is widely used, the numerical techniques used to evaluate the model do not exploit fast solver approaches developed for analyzing integrated circuit interconnect. I will describe the formulation used for analyzing biomolecule electrostatics, and then derive an integral formulation of the problem that can be rapidly solved with precorrected-FFT method [4]. / Singapore-MIT Alliance (SMA)

In this paper, the precorrected-FFT method is used to solve the electromagnetic scattering from two-dimensional cavities of arbitrary shape. The integral equation is discretized by the method of moments and the resultant matrix equation is solved iteratively by the generalized conjugate residual method. Instead of directly computing the matrix-vector multiplication, which requires N² operations, this approach reduces the computation complexity to O(N log N) as well as avoids the storage of large matrices. At the same time, a technique known as the complexifying k is applied to accelerate the convergence of the iterative method in solving this resonance problem. Some examples are considered and excellent agreements of radar cross sections between these computed using the present method and those from the direct solution are observed, demonstrating the feasibility and efficiency of the present method. / Singapore-MIT Alliance (SMA)

This paper presents an accurate and efficient method-of-moments solution of the electrical-field integral equation (EFIE) for large, three-dimensional, arbitrarily shaped objects. In this method, the generalized conjugate residual method (GCR) is used to solve the matrix equation iteratively and the precorrected-FFT technique is then employed to accelerate the matrix-vector multiplication in iterations. The precorrected-FFT method eliminates the need to generate and store the usual square impedance matrix, thus leading to a great reduction in memory requirement and execution time. It is at best an O(N log N) algorithm and can be modified to fit a wide variety of systems with different Green’s functions without excessive effort. Numerical results are presented to demonstrate the accuracy and computational efficiency of the technique. / Singapore-MIT Alliance (SMA)

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Cette thèse s'inscrit dans la thématique classique de l'homogénéisation des milieux hétérogènes linéaires et a pour but l'étude et la prédiction du comportement optique de couches de peintures. L'objectif est double : d'une part caractériser et modéliser la microstructure hétérogène des matériaux utilisés dans les revêtements de peinture, d'autre part prédire le comportement optique de ces matériaux par des moyens numériques, et étudier l'influence de la morphologie sur les propriétés optiques. Ces travaux ont été faits dans le cadre du projet LIMA (Lumière Interaction Matière Aspect), soutenu par l'Agence Nationale de la Recherche et en partenariat avec le groupe PSA. Des images acquises par microscopie électronique à balayage (MEB) sont obtenues de différentes couches de peintures. On y distingue différentes échelles pigmentaires : microscopique et nanoscopique. Des images représentatives des échelles sont alors sélectionnées et segmentées, pour permettre la prise de mesures morphologiques. Ces mesures permettent l'élaboration de modèles aléatoires propres à chacune des échelles. Ces modèles sont ensuite validés, et optimisés pour le cas du modèle nanoscopique à deux échelles. La prédiction du comportement optique des modèles aléatoires de matériaux hétérogènes se fait ici avec l'utilisation de méthodes utilisant les transformées de Fourier rapides (FFT). La théorie de l'optique des milieux composites est rappelée, ainsi que les contraintes et limites des méthodes FFT. L'approximation quasi-statique est une contrainte, impliquant l'application de la méthode FFT au seul modèle nanoscopique. Le comportement optique du modèle nanoscopique optimisé est calculé numériquement, et comparé à celui mesuré de la peinture qui a servi de référence. Les fonctions diélectriques des matériaux constituants de la peinture ont été mesurées à l'ellipsomètre spectroscopique au Musée de Minéralogie des Mines de Paris. Les réponses mesurée et calculées sont comparées entre elles et à des estimations analytiques. Une caractérisation statistique est également faite sur le modèle aléatoire et sur les champs locaux de déplacement diélectrique, par le calcul du volume élémentaire représentatif (VER). / This work presents a numerical and theoretical study of the optical properties of paint layers, in the classical framework of homogenization of heterogeneous media. Objectives are : describing and modeling the heterogenous microstructures used in paint coatings, and predicting the optical response of such materials by numerical ways, depending of the pigments morphology. This work was carried out as part of the LIMA project (Light Interaction Materials Aspect), in partnership with the Agence Nationale de la Recherche and the PSA company. Images of differents paint layers are acquired by scanning electron microscopy (SEM). Different length scales are considered for the microstructures and pigments : microscopic and nanoscopic. Representatives images of these scales are chosen and segmented in order to estimate morphological measurements. Using these measurements, random models are developed depending on the scales. These models, of a multiscale nature, are optimized and validated. The prediction of the optical behaviour of random models describing heterogenous materials is carried out using numerical process based on fast Fourier transforms (FFT). Optics of composite materials theory is introduced, as well as the limits of FFT methods. The quasi-static approximation is a constraint which implies the use of the FFT method on the nanoscopic model only. Dielectric functions of the components of the paint have been measured on macroscopic samples at the Museum of Mineralogy of Mines de Paris by spectroscopic ellipsometry. The optical response of the optimized nanoscopic model is computed and compared to ellipsometry measurements carried out on a reference paint layer. The computed and measured responses are also compared with analytical estimates. In addition, a statistical characterization is made on the random model and the local dielectrical displacement fields, by using the representative volume element (RVE).