35,937 research outputs found
Modified Renormalization Strategy for Sandpile Models
Following the Renormalization Group scheme recently developed by Pietronero
{\it et al}, we introduce a simplifying strategy for the renormalization of the
relaxation dynamics of sandpile models. In our scheme, five sub-cells at a
generic scale form the renormalized cell at the next larger scale. Now the
fixed point has a unique nonzero dynamical component that allows for a great
simplification in the computation of the critical exponent . The values
obtained are in good agreement with both numerical and theoretical results
previously reported.Comment: APS style, 9 pages and 3 figures. To be published in Phys. Rev.
Recursive partitioned inversion of large (1500 x 1500) symmetric matrices
A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models
Ill-posedness in the Einstein equations
It is shown that the formulation of the Einstein equations widely in use in
numerical relativity, namely, the standard ADM form, as well as some of its
variations (including the most recent conformally-decomposed version), suffers
from a certain but standard type of ill-posedness. Specifically, the norm of
the solution is not bounded by the norm of the initial data irrespective of the
data. A long-running numerical experiment is performed as well, showing that
the type of ill-posedness observed may not be serious in specific practical
applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of
Mathematical Physics (to appear August 2000
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