An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.     

SSCP markers provide a useful alternative to microsatellites in genotyping and estimating genetic diversity in populations and germplasm collections of plant specialty crops

For well-studied plant species with whole genome sequence or extensive EST data, SNP markers are the logical choice for both genotyping and whole genome association studies. However, SNP markers may not address the needs of researchers working on specialty crops with limited available genomic information. Microsatellite markers have been frequently employed due to their robustness, but marker development can be difficult and may result in few polymorphic markers. SSCP markers, such as microsatellites, are PCR-based and scored by electrophoretic mobility but, because they are based on SNPs rather than length differences, occur more frequently and are easier to develop than microsatellites. We have examined how well correlated the estimation of genetic diversity and genetic distance are in a population or germplasm collection when measured by 13 highly polymorphic microsatellite markers or 20 SSCP markers. We observed a significant correlation in pairwise genetic distances of 82 individuals in an international cacao germplasm collection (Mantel test Rxy=0.59, p<0.0001 for 10 000 permutations). Both sets of markers could distinguish each individual in the population. These data provide strong support for the use of SSCP markers in the genotyping of plant species where development of microsatellites would be difficult or expensive.