title: On the magnetorotational instability and elastic buckling.
abstract: This paper demonstrates an equivalence between rotating magnetized shear flows and a stressed elastic beam. This results from finding the same form of dynamical equations after an asymptotic reduction of the axis-symmetric magnetorotational instability (MRI) under the assumption of almost-critical driving. The analysis considers the MRI dynamics in a non-dissipative near-equilibrium regime. Both the magnetic and elastic systems reduce to a simple one-dimensional wave equation with a non-local nonlinear feedback. Under transformation, the equation comprises a large number of mean-field interacting Duffing oscillators. This system was the first proven example of a strange attractor in a partial differential equation. Finding the same reduced equation in two natural applications suggests the model might result from other applications and could fall into a universal class based on symmetry.
authors.affiliation: School of Mathematics and Statistics , The University of Sydney , Carslaw F07, Sydney, New South Wales 2006, Australia.
authors.forename: Geoffrey M
authors.initials: GM
authors.lastname: Vasil
keywords: asymptotics; magnetorotational instability; nonlinear dynamics; nonlinear elasticity