Two-level stabilized finite element method for Stokes eigenvalue problem

A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h -- O（H2）, which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.

Phenotypic Diversity of Jatropha curcas L. from Diverse Origins

The study was conducted to assess intraspecific variation/interrelationships and to determine the association of geographical distribution and phenotypic diversity in the Jatropha curcas accessions studied. Ex situ morphological characterization of 13 Jatropha curcas genotypes from various sources was undertaken using 21 quantitative traits. The generated data was subjected to two phenetic analysis methods （principal components analysis and cluster analysis）. Principal Components Analysis （PCA） reduced the collected data to 5 principal components that cumulatively explained 88.81% of total variance. PCA also subdivided the Jatropha provenances into distinct groups on the basis of height. The two clustering mechanisms, Average Linkage-Unweighted Pair Group Method with Arithmetic Mean （UPGMA） and Centroid Method （UPGMC）, divided the provenances into two major groups and revealed the divergence of Tubao-Philbio from the rest of the provenances. However, the study failed to adequately establish a relationship between spatial dispersal and phenotypic divergence in the Jatropha genotypes implying possible genetic homogeneity for the accessions studied. Screening for more quantitative traits and the use of more advanced molecular marker technologies are therefore recommended for a more accurate estimation of genetic diversity in Jatropha.

Identifying the limiting distribution by a general approach of Stein's method

A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.

Simple Sequence Repeat Analysis of Genetic Diversity in Primary Core Collection of Peach(Prunus persica)

In this study, the genetic diversity of 51 cultivars in the primary core collection of peach （Prunus persica （L.） Batsch） was evaluated by using simple sequence repeats （SSRs）. The phylogenetic relationships and the evolutionary history among different cultivars were determined on the basis of SSR data. Twenty-two polymorphic SSR primer pairs were selected, and a total of 111 alleles were identified in the 51 cultivars, with an average of 5 alleles per locus. According to traditional Chinese classification of peach cultivars, the 51 cultivars in the peach primary core collection belong to six variety groups. The SSR analysis revealed that the levels of the genetic diversity within each variety group were ranked as Sweet peach 〉 Crisp peach 〉 Flat peach 〉 Nectarine 〉 Honey Peach 〉 Yellow fleshed peach. The genetic diversity among the Chinese cultivars was higher than that among the introduced cultivars. Cluster analysis by the unweighted pair group method with arithmetic averaging （UPGMA） placed the 51 cultivars into five linkage clusters. Cultivar members from the same variety group were distributed in different UPGMA clusters and some members from different variety groups were placed under the same cluster. Different variety groups could not be differentiated in accordance with SSR markers. The SSR analysis revealed rich genetic diversity in the peach primary core collection, representative of genetic resources of peach.

WAKE PATTERNS OF FLOW PAST A PAIR OF CIRCULAR CYLINDERS IN SIDE-BY-SIDE ARRANGEMENTS AT LOW REYNOLDS NUMBERS

A flow past two side-by-side identical circular cylinders was numerically investigated with the unstructured spectral element method. From the computational results at various non-dimensional distances between cylinder centers T/D and the Reynolds number Re, a total of nine kinds of wake patterns were observed： four steady wake patterns, including single bluff-body steady pattern, separated double-body steady pattern and transition steady pattern for sub-critical Reynolds numbers and biased steady pattern for super-critical Reynolds numbers, and five unsteady wake patterns, including single bluff-body periodic pattern, biased quasi-steady pattern, quasi-periodic （flip-flopping） pattern, in-phase-synchronized pattern and anti-phase-synchronized pattern. Time evolution of lift and drag coefficients corresponding to each unsteady wake pattern was given.