It is of utmost interest to control the divergence of the magnetic flux in simulations of the ideal magnetohydrodynamic equations since, in general, divergence errors tend to accumulate and render the schemes unstable. This paper presents a higher-order extension of the locally divergence-preserving procedure developed in Torrilhon [M. Torrilhon, Locally divergence-preserving upwind finite volu...

The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature. A recent application of the Lanczos algorithm proposed by Bai, Fahey and Golub allows quadrature evaluation of inner products of the form ψ · ...

We show that the static force spectroscopy curve taken in an atomic force microscope is significantly modified due to presence of intrinsic cantilever instability which occurs as a result of its movement in a nonlinear force field. This instability acts in tandem with such instabilities as water bridge or molecular bond rupture and makes the static force spectroscopy curve (including 'jump-off-...

We present a theory for the generation of mesoscale (k rgT1, where rg is the cosmic-ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfvén waves scattering off ambient density perturbations in the shock environment naturally generates larger scale fields. For a broad spectrum of perturbations, the physical mechanis...

We present a theory for the generation of mesoscale (kr g ≪ 1, where r g is the cosmic ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfven waves scattering off ambient density perturbations in the shock environment naturally generates larger scale fields. For a broad spectrum of perturbations, the physical mecha...