Dynamical instability is shown to occur in differentially rotating polytropes with and . N p 3.33T/FWF տ 0.14 This instability has a strong mode, although the , 3, and 4 modes also appear. Such instability may m p 1 m p 2 allow a centrifugally hung core to begin collapsing to neutron star densities on a dynamical timescale. The gravitational radiation emitted by such unstable cores may be detectable with advanced ground-based detectors, such as LIGO-II. If the instability occurs in a supermassive star, it may produce gravitational radiation detectable by the spacebased detector LISA.
Understanding the impact of climate variability and change is of great importance for developing adaptation and mitigation strategies. Coarse resolution data sets (such as climate reanalysis, numerical weather predictions, satellite products, and simulations of general circulation models) are important for reconstructing historical climate and predicting the future. However, scale discrepancy limits the coarse resolution data sets from being directly used for impact assessments and decision making. One solution for bridging this gap is to downscale coarse resolution data to the local scale (
In this paper we describe in detail the computational algorithm used by our
parallel multigrid elliptic equation solver with adaptive mesh refinement. Our
code uses truncation error estimates to adaptively refine the grid as part of
the solution process. The presentation includes a discussion of the orders of
accuracy that we use for prolongation and restriction operators to ensure
second order accurate results and to minimize computational work. Code tests
are presented that confirm the overall second order accuracy and demonstrate
the savings in computational resources provided by adaptive mesh refinement.Comment: 12 pages, 9 figures, Modified in response to reviewer suggestions,
added figure, added references. Accepted for publication in J. Comp. Phy
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