These are notes prepared for presentation at the workshop ”Challenges in Granular Matter” at the Abdus Salam Institute for Theoretical Physics, Trieste, August 2001. Revisions and figures will be added at a later date. Many features of real granular fluids under rapid flow are replicated by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply sta...

The basis for a hydrodynamic description of granular gases is discussed for a low density gas of smooth, inelastic hard spheres. The more fundamental mesoscopic description is taken to be the nonlinear Boltzmann kinetic equation. Two arguments are presented in favor of a hydrodynamics for granular gases. The first one is the concept of a ”normal” solution and its explicit approximate constructi...

Hydrodynamics is the appropriate “effective theory” for describing any fluid medium at sufficiently long length scales. This paper treats the vacuum as such a medium and derives the corresponding hydrodynamic equations. Unlike a normal medium the vacuum has no linear sound-wave regime; disturbances always “propagate” nonlinearly. For an “empty vacuum” the hydrodynamic equations are familiar one...

By applying the fluctuation dissipation theorem [1] to the Navier Stokes equation, Landau and Lifshitz developed long ago the standard theory of fluctuating hydrodynamics [2] [3] [4]. This theory is both appealing and successful, and it is consistent with the fluctuating hydrodynamics which is derived if fluctuation dissipation theory is first applied to the Boltzmann equation [5], and then the...

We derive the complete set of macroscopic dynamic equations for ferrogels under an external magnetic field, including the magnetization as an independent dynamic degree of freedom. The magnetoelasticity comes in the form of magnetostriction and through the magnetic part of the Maxwell stress. Various dynamic couplings of the elastic degree of freedom with the magnetization and the magnetic fiel...

We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.

In this review the basic principles of smooth particle hydrodynamics (SPH) are outlined in a pedagogical fashion. To start, a basic set of SPH equations that is used in many codes throughout the astrophysics community is derived explicitly. Much of SPH’s success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attentio...

The main purpose of the lecture was to lead students and young post-docs to the frontier of the hydrodynamic description of relativistic heavy-ion collisions (H.I.C.) in order for them to understand talks and posters presented in the Quark Matter 2008 (QM08) conference in Jaipur, India [1]. So the most recent studies were not addressed in this lecture as they would be presented during the QM08 ...

This paper investigates different Poisson structures that have been proposed to give a Hamiltonian formulation to evolution equations issued from fluid mechanics. Our aim is to explore the main brackets which have been proposed and to discuss the difficulties which arise when one tries to give a rigorous meaning to these brackets. Our main interest is in the definition of a valid and usable bra...