In superconductors where the coherence length is comparable to the Fermi wavelength , the electronic levels within a vortex core are quantized, and separated by energies of the order of the superconducting gap. The absence of a continuum modifies significantly the energy dissipation due to the motion of vortices. At zero temperature , dissipation is suppressed, and the system shows non ohmic be...

Anharmonic interactions in lattices may sustain robust oscillatory modes and (nonlinear) waves including solitons. This is illustrated here by using an exponentially repulsive interaction introduced by Toda. To cope with friction and dissipation -always present in real systemsand hence to make robust, e.g., solitons, following Lord Rayleigh, an appropriate input-output energy balance is added t...

An analytical theory is developed that describes asymptotically exactly the process of nonlinear saturation of the magnetorotational instability in a model problem employing a linear shear flow in a uniformly rotating channel. The theory shows that the instability saturates by modifying the shear responsible for it. The saturation process requires both viscous and Ohmic dissipation. The theory ...