13,504 research outputs found
Optimal prediction for moment models: Crescendo diffusion and reordered equations
A direct numerical solution of the radiative transfer equation or any kinetic
equation is typically expensive, since the radiative intensity depends on time,
space and direction. An expansion in the direction variables yields an
equivalent system of infinitely many moments. A fundamental problem is how to
truncate the system. Various closures have been presented in the literature. We
want to study moment closure generally within the framework of optimal
prediction, a strategy to approximate the mean solution of a large system by a
smaller system, for radiation moment systems. We apply this strategy to
radiative transfer and show that several closures can be re-derived within this
framework, e.g. , diffusion, and diffusion correction closures. In
addition, the formalism gives rise to new parabolic systems, the reordered
equations, that are similar to the simplified equations.
Furthermore, we propose a modification to existing closures. Although simple
and with no extra cost, this newly derived crescendo diffusion yields better
approximations in numerical tests.Comment: Revised version: 17 pages, 6 figures, presented at Workshop on Moment
Methods in Kinetic Gas Theory, ETH Zurich, 2008 2 figures added, minor
correction
Oriented Local Moves and Divisibility of the Jones Polynomial
For any virtual link that may be decomposed into a pair of
oriented -tangles and , an oriented local move of type
is a replacement of with the -tangle in a way that preserves the
orientation of . After developing a general decomposition for the Jones
polynomial of the virtual link in terms of various (modified)
closures of , we analyze the Jones polynomials of virtual links
that differ via a local move of type . Succinct divisibility
conditions on are derived for broad classes of local moves that
include the -move and the double--move as special cases. As a
consequence of our divisibility result for the double--move, we
introduce a necessary condition for any pair of classical knots to be
-equivalent
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