Nonlinear Excitation of Plasma Convection

Parametric excitations of electrostatic convective cells by drift waves as well as magnetostatic cells by Alfvén waves are considered. The growth rates are calculated for various limits of interest to plasma diffusion studies; our results agree with computer simulations. The problem of crossfield diffusion is also discussed. Finally, the coupling of magnetostatic modes with electrostatic modes is investigated and a variational principle for coalescence of magnetic islands is formulated.     

Field and pressure response of Yb compounds close to a quantum critical point

YbCu_5−x Al _x provides the possibility to tune ground state properties by a change of the valence due to the Cu/Al substitution, by pressure as well as by the application of a magnetic field. Near to the critical concentration x _cr≈1.5 non-Fermi-liquid properties (NFL) are obvious, obeying hyperscaling. If magnetic order sets in for x>1.5, the application of moderate magnetic fields quenches order and again NFL features become evident. Hyperscaling in this case indicates strongly interacting spin fluctuations.     

Stability of two-dimensional monopolies in plasmas

Monopole vortices, obeying the homogeneous Hasegawa-Mima equation or the convective cell equation in magnetized plasmas are considered. It is shown that two-dimensional perturbations of single vortices in the plane perpendicular to the external magnetic field do not grow in time. It is also argued that three-dimensional perturbations will not lead to an instability of monopoles.     

A complementary energy principle in magnetohydrodynamics

Variational principles for growth rates of instabilities in magnetohydrodynamics are derived. In addition to previous investigations, complementary expressions are presented. The latter are quite useful for numerical computations since they lead to upper and lower bounds for the exact growth rates.     

Onset of instability for a class of nonlinear lagrangian systems

For systems of real and complex (charged) fields derivable from Lorentz-invariant lagrangian densities a general criterion for dynamical instability of lump solutions is presented. This criterion complements the well-known Q-theorem for stability.     

Stability of activation-barrier-lowering solitons

A simple one-dimensional, nonlinear, scalar kink-bearing system is investigated. The possible types of kink solutions as well as the stability of the latter are discussed. The results have applications in biological and solid state systems.