Nonlinear stationary vortices in gravitating fluid
The problem of nonlinear self-organization of perturbations in differentially rotating, nonuniform, gravitating systems is studied. Two types of stationary nonlinear solutions, in the form of tripolar vortices and vortex chains of gravitational potential and density, dependent on the spatial profiles of the basic state quantities, are found. They propagate with a constant velocity perpendicularly to the basic state gradients, and characteristic time scales for the creation of such vortical structures are shown to be much shorter than the corresponding intervals for gravitational contraction.
Nonlinear kink modes in the presence of charged dust grains
A set of coupled nonlinear equations, which govern the dynamics of electromagnetic perturbations in the presence of a spatially nonuniform electron current in a magnetized dusty plasma, is derived. The linear stability of such a system is discussed. It is shown that in the presence of the dust an oscillatory, kink-type instability can develop with a threshold for the instability far exceeding the value for an ordinary electron–ion plasma. In the nonlinear regime, the possibility for several types of stationary, coherent solutions is demonstrated. For specific profiles of spatially dependent functions describing the basic state, traveling dipolar and tripolar vortices, and vortex chains are found.
Natural history and long‐term evolution in families with autosomal dominant cortical tremor, myoclonus, and epilepsy
Purpose:  To investigate for the first time the natural history and long‐term evolution of “familial cortical tremor, myoclonus, and epilepsy.”