Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics

Two - wave interaction in ideal magnetohydrodynamics

The weakly nonlinear interaction of sound and linearly polarised Alfvén waves propagating in the same direction along an applied magnetic field is studied. It is found that a sound wave is coupled to the Alfvén wave with double period and wavelength when the sound and Alfvén speeds are equal. The Alfvén wave drives the sound wave through the ponderomotive force, while the sound wave returns ene...

Converging cylindrical shocks in ideal magnetohydrodynamics

Linear equivalence of ideal topologies

It is proved that whenever P is a prime ideal in a commutative Noethe-rian ring such that the P-adic and the P-symbolic topologies are equivalent, then the two topologies are equivalent linearly. Several explicit examples are calculated, in particular for all prime ideals corresponding to non-torsion points on nonsingular elliptic cubic curves. There are many examples of prime ideals P in commu...

Grothendieck Topologies and Ideal Closure Operations

We relate closure operations for ideals and for submodules to non-flat Grothendieck topologies. We show how a Grothendieck topology on an affine scheme induces a closure operation in a natural way, and how to construct for a given closure operation fulfilling certain properties a Grothendieck topology which induces this operation. In this way we relate the radical to the surjective topology and...

A Solution-Adaptive Upwind Schemefor Ideal Magnetohydrodynamics

A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics Kenneth G. Powell,∗ Philip L. Roe,∗ Timur J. Linde,∗ Tamas I. Gombosi,† and Darren L. De Zeeuw† ∗W. M. Keck Foundation CFD Laboratory, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109-2140; and †Space Physics Research Laboratory, Department of Atmospheric, Oceanic and Space Sciences, Universit...