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arXiv · 1804.10314

On the magnetorotational instability and elastic buckling

Geoff Vasil
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Abstract

This paper demonstrates an equivalence between rotating magnetised 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 nonlocal 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.

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Geoff Vasil. 2018-04-27. On the magnetorotational instability and elastic buckling. https://arxiv.org/abs/1804.10314

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