645 research outputs found
A high-order Nystrom discretization scheme for boundary integral equations defined on rotationally symmetric surfaces
A scheme for rapidly and accurately computing solutions to boundary integral
equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The
scheme uses the Fourier transform to reduce the original BIE defined on a
surface to a sequence of BIEs defined on a generating curve for the surface. It
can handle loads that are not necessarily rotationally symmetric. Nystrom
discretization is used to discretize the BIEs on the generating curve. The
quadrature is a high-order Gaussian rule that is modified near the diagonal to
retain high-order accuracy for singular kernels. The reduction in
dimensionality, along with the use of high-order accurate quadratures, leads to
small linear systems that can be inverted directly via, e.g., Gaussian
elimination. This makes the scheme particularly fast in environments involving
multiple right hand sides. It is demonstrated that for BIEs associated with the
Laplace and Helmholtz equations, the kernel in the reduced equations can be
evaluated very rapidly by exploiting recursion relations for Legendre
functions. Numerical examples illustrate the performance of the scheme; in
particular, it is demonstrated that for a BIE associated with Laplace's
equation on a surface discretized using 320,800 points, the set-up phase of the
algorithm takes 1 minute on a standard laptop, and then solves can be executed
in 0.5 seconds.Comment: arXiv admin note: substantial text overlap with
arXiv:1012.56301002.200
Spatial Variation of Bacteria in Surface Waters of Paranaguá and Antonina Bays, Paraná, Brazil
Can sexual selection drive female life histories? A comparative study on Galliform birds
Sexual selection is an important driver of many of the most spectacular morphological traits that we find in the animal kingdom (for example see Andersson, 1994). As such, sexual selection is most often emphasized as
Equity as a Prerequisite for Stability of Cooperation on Global Public Good Provision
Analysing cooperative provision of a global public good such as climate protection, we explore the relationship between equitable burden sharing on the one hand and core stability on the other. To assess the size of the burden which a public good contribution entails for a country, we make use of a specific measure based on Moulin (Econometrica 55:963-977, 1987). In particular, we show that a Pareto optimal allocation which is not in the core can always be blocked by a group of countries with the highest Moulin sacrifices. In this sense, it is the 'overburdening' and thus 'unfair' treatment of some countries that provides the reason for core instability. By contrast, a Pareto optimal allocation is in the core if the public good contributions are fairly equally distributed according to their Moulin sacrifices. The potential implications of our theoretical analysis for global climate policy are also discussed
Retention and Separation Changes of Ternary and Quaternary Alkaloids from Chelidonium majus L. by TLC Under the Influence of External Magnetic Field
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