Aims. In the approximation of linear dissipative magnetohydrodynamics (MHD) it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén (or slow) frequency of a magnetic surface. This near resonant behaviour is confined to a thin region, known as the dissipative layer, which ...

In this paper, the problem of pseudo-Hamiltonian realization of a control system is studied. Several sufficient conditions are obtained. The stability of a dynamic system is investigated via dissipative pseudo-Hamiltonian realization, and the stabilization of a control system is also investigated via feedback dissipative pseudo-Hamiltonian realization. Some relations between the stability (asym...

We discuss two important topics of turbulence theory: inviscid limit and decay of the Fourier spectrum for the 2-D dissipative quasi-geostrophic (QGS) equations. In the first part we consider inviscid limits for both smooth and weak solutions of the 2-D dissipative QGS equations and prove that the classical solutions with smooth initial data tend to the solutions of the corresponding non-dissip...

Nonequilibrium stationary states (NESS) describe the state of a mechanical system driven and maintained out of equilibrium by external forces. The main characteristic of a NESS is that it sustains sustain steady flows or equivalently that it exhibits positive entropy production. We discuss general features of the fluctuations of the entropy production and corresponding flows. The NESS and the e...

A controllable distributed dynamical system described by a system of linear constant-coeecient partial diierential equations is said to be conservative if for compact support trajectories the integral of the supply rate is zero. It is said to be dissipative if this integral is non-negative. The question that we consider is whether these global versions of conservation and dissipativeness are eq...

This paper is devoted to the mathematical analysis of a degenerate nonlinear parabolic equation. This kind of equations stems either from the modeling of a compressible two phase flow in porous media or from the modeling of a chemotaxis-fluid process. In the degenerate equation, the strong nonlinearities are technically difficult to be controlled by the degenerate dissipative term because the e...

The coefficient of restitution is a measure of energy dissipation in a system across impact events. Often, the dissipative qualities of a pair of impacting components are neglected during the design phase. This research looks at the effect of applying a thin layer of metallic coating, using thermal spray technologies, to significantly alter the dissipative properties of a system. The dissipativ...

We first summarize features of free, forced and stochastic harmonic oscillations and, following an idea first proposed by Lord Rayleigh in 1883, we discuss the possibility of maintaining them in the presence of dissipation. We describe how phonons appear in a harmonic (linear) lattice and then use the Toda exponential interaction to illustrate solitonic excitations (cnoidal waves) in a one-dime...