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An iterative domain decomposition method is developed to solve a singular perturbation problem. The problem consists of a convection-diffusion equation with a discontinuous (piecewise-constant) diffusion coefficient, and the problem domain is decomposed into two subdomains, on each of which the coefficient is constant. After showing that the boundary value problem is well posed, we indicate a specific numerical implementation of the iterative technique that combines the finite element method on one subdomain with the method of matched asymptotic expansions on the other subdomain. This procedure extends work by Carlenzoli and Quarteroni, which was originally intended for a boundary layer problem with an outer region and an inner region. Our extension carries over to a problem where the domain consists of the outer and inner boundary layer regions plus a region in which the diffusion coefficient is constant and significant in magnitude. An unexpected benefit of our new implementation is its efficiency, which is due to the fact that at each iteration the problem needs to be solved explicitly only on one subdomain. It is only when the final approximation on the entire domain is desired that the matched asymptotic expansions approximation need be computed on the second subdomain. Two-dimensional convergence results and numerical results illustrating the method for a two-dimensional test problem are given.Received: February 12, 2004  相似文献   
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Polyhydroxyalkanoates are biodegradable polyesters produced by bacteria that can have a wide distribution in molecular weight, composition of monomers, and functionalities. This large distribution often leads to unpredictable physical properties making commercial applications challenging. To improve polymer homogeneity and obtain samples with a clear set of physical characteristics, poly-3-hydroxyvalerate-co-3-hydroxybutyrate copolymers were fractionated using gradient polymer elution chromatography (GPEC) as opposed to extensively used bulk fractionation. Separation was achieved using a reversed-phase column with chloroform and ethanol as the solvent and non-solvent, respectively. A separation was also conducted on a normal-phase column to compare elution patterns between columns of varied polarity. The fractions were analyzed using Size Exclusion Chromatography (SEC) and NMR to determine the percentage of 3-hydroxyvalerate in the copolymer as well as its molecular weight. It was found that as the percentage of "good" solvent was increased in the mobile phase, the polymers eluted with decreasing percentage of 3-hydroxyvalerate and increasing molecular weight which indicates the importance of precipitation/redissolution in the separation. The elution pattern of the polymer remained unchanged when using both a normal- and reversed-phase column which also illustrates the dominance of precipitation/redissolution in GPEC of polyhydroxyalkanoates. As such, GPEC is shown to be an excellent choice to provide polyhydroxyalkanoate samples with a narrower distribution in composition than the original bulk copolymer sample.  相似文献   
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2,2'-Dihydroxy-6,6'-dinaphthyldisulfide (DDD) forms a violet product with Fast Blue RR, which precipitates on standing. In presence of sulfhydryl compounds, DDD is reduced and when a monoazo coupling reagent is added, a green fluorescent product is obtained. Amino acids, amino acid derivatives, peptides, weak reducing agents, and water-soluble carbohydrates can be tolerated, but strongly oxidizing reagents or sulfhydryl-blocking reagents interfere. Strongly reducing inorganic compounds give a positive test even in the absence of sulfhydryls. The limit of detection is 5 μg of cysteine or 12 μg of glutathione.  相似文献   
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