We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of non-degenerate wells. These follow WKB ansatz; error is O(exp(--cN)), where c > 0 and N $\rightarrow$ +$\infty$ inverse semiclassical parameter.

Abstract. Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the probability distribution of the population size is transformed into an evolution equation for the probability generating function. Spectral decomposition the...

We develop a theory of particle acceleration inside relativistic rotating electron-positron force–free jets with spiral magnetic fields. We considered perturbation of the stationary magnetic field structure and found that acceleration takes place in the regions where the Alfvén resonant condition with the eigenmodes in the jet is fulfilled, i.e. where the local Alfvén speed is equal to the phas...

An energetic particle Landau-fluid closure model (TAEFL) is applied to a case where both RSAE (Reversed Shear Alfvén Eigenmode) and TAE (Toroidal Alfvén Eigenmode) modes are destabilized by beam ions. The nonlinear evolution of the coupled modes are followed for about 104 Alfvén times under the simplifying assumptions that a density source is present that exactly balances the quasi-linear fast ...

We describe the first analytically tractable example of an instability of a nonorientable minimal surface under parametric variation of its boundary. A one-parameter family of incomplete Meeks Möbius surfaces is defined and shown to exhibit an instability threshold as the bounding curve is opened up from a double-covering of the circle. Numerical and analytical methods are used to determine the...

With its unique structure, the Akiyama probe is a type of tuning fork atomic force microscope probe. The long, soft cantilever makes it possible to measure soft samples in tapping mode. In this article, some characteristics of the probe at its second eigenmode are revealed by use of finite element analysis (FEA) and experiments in a standard atmosphere. Although the signal-to-noise ratio in thi...

The radial structure of the shear Alfvén wave continuous spectrum is calculated inside the separatrix of a magnetic island. We find that, within a magnetic island, there is a continuous spectrum very similar to that of tokamak plasmas, where a generalized safety factor q can be defined and a wide frequency gap is formed, analogous to the ellipticity induced Alfvén eigenmode gap in tokamaks. Thi...