We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The Hamiltonian constructed here couples a given system to auxiliary fields in the universal form of a so-called canonical heat bath. After integrating out the heat bath, the original dissipative evolution is exactly re...

We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by M.V. Berry are recovered in the present approach. We determine the necessary condition satisfied by ...

We study the asymptotic behavior of compressible isentropic flow through porous medium when the initial mass is finite. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey to the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. In this paper, we prove that any L∞ weak entropy sol...

The supernova-driven interstellar medium in star-forming galaxies has Reynolds numbers of the order of 10 or even larger. We study, by means of adaptive mesh refinement hydroand magnetohydrodynamical simulations that cover the full available range (from 10 kpc to sub-parsec) scales, the statistical properties of the turbulent interstellar gas and the dimension of the most dissipative structures...

We present a variety of dissipative solitons and breathing modes in a medium with localized gain and homogeneous linear dissipation. The system possesses a number of unusual properties, like exponentially localized modes in both focusing and defocusing media, existence of modes in focusing media at negative propagation constant values, simultaneous existence of stable symmetric and antisymmetri...

In an ensemble of noninteracting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medi...

The solution for multi-frequency plane waves propagating through a dissipative and nonlinear medium is shown for some examples of periodic conditions. The expression may for any given condition be expressed analytically as a ratio of Fourier series with Bessel function coefficients. In the examples are shown how the final appearance of any initial wave always is a pure periodic wave in the lowe...