542 research outputs found
An exact particle method for scalar conservation laws and its application to stiff reaction kinetics
An "exact" method for scalar one-dimensional hyperbolic conservation laws is
presented. The approach is based on the evolution of shock particles, separated
by local similarity solutions. The numerical solution is defined everywhere,
and is as accurate as the applied ODE solver. Furthermore, the method is
extended to stiff balance laws. A special correction approach yields a method
that evolves detonation waves at correct velocities, without resolving their
internal dynamics. The particle approach is compared to a classical finite
volume method in terms of numerical accuracy, both for conservation laws and
for an application in reaction kinetics.Comment: 14 page, 7 figures, presented in the Fifth International Workshop on
Meshfree Methods for Partial Differential Equation
Normal and conormal maps in homotopy theory
Let M be a monoidal category endowed with a distinguished class of weak
equivalences and with appropriately compatible classifying bundles for monoids
and comonoids. We define and study homotopy-invariant notions of normality for
maps of monoids and of conormality for maps of comonoids in M. These notions
generalize both principal bundles and crossed modules and are preserved by nice
enough monoidal functors, such as the normaliized chain complex functor.
We provide several explicit classes of examples of homotopy-normal and of
homotopy-conormal maps, when M is the category of simplicial sets or the
category of chain complexes over a commutative ring.Comment: 32 pages. The definition of twisting structure in Appendix B has been
reformulated, leading to further slight modifications of definitions in
Section 1. To appear in HH
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