Augusto Muracchini

Continuum approach to phonon gas and shape changes of second sound via shock waves theory

SummaryA continuum approach, based on the principles of modern extended thermodynamics, describing the model of a phonon gas is performed. The main difference with the ideal phonon gas theory consists in the presence of athermal inertia. We apply the shock wave theory and discuss the selection rules for physical shocks (theLax conditions and theentropy growth). In this way the existence of two new kinds of shocks (hot andcold shocks) in rigid heat conductors at low temperature is pointed out. In particular a critical temperature, characteristic of each material, changing the structure of the previous types of shocks is analytically deduced. This characteristic temperature permits also to explain the modification of the received second sound wave form with respect to the initial wave profile. Finally, the results are applied to the case of high-purity crystals (NaF, Bi,3He and4He) and compared with experimental results.

Dispersion relation in the high frequency limit and non linear wave stability for hyperbolic dissipative systems

We consider a quasi-linear first order hyperbolic dissipative system in a one-dimensional space, and we prove that, if the constant solutions are stable for the linearized system, then they are also non-linear asymptotically λ-stable, i.e. the amplitude of the discontinuity wave vanishes, when t increases, provided that the initial amplitude is sufficiently small. In order to give the proof an evaluation of the dispersion law in the limit of high frequencies is accomplished, and the results are applied to the case of the Extended Thermodynamics for a non-equilibrium monatomic classical gas.

On the Müller paradox for thermal-incompressible media

In his monograph Thermodynamics, I. Müller proves that for incompressible media the volume does not change with the temperature. This Müller paradox yields an incompatibility between experimental evidence and the entropy principle. This result has generated much debate within the mathematical and thermodynamical communities as to the basis of Boussinesq approximation in fluid dynamics. The aim of this paper is to prove that for an appropriate definition of incompressibility, as a limiting case of quasi-thermal-incompressible body, the entropy principle holds for pressures smaller than a critical pressure value. The main consequence of our result is the physically obvious one that for very large pressures, no body can be perfectly incompressible. The result is first established in the fluid case. In case of hyperelastic media subject to large deformations, the approach is similar, but with a suitable definition of the pressure associated with a convenient stress tensor decomposition.

On the symmetric conservative form of Landau's superfluid equations

SummaryIt is shown how to obtain Landaus equations for a superfluid in a symmetric conservative form. On account of the constraints involved, this case is more complicated than those of the classical theory developed by Godunov and by other authors.SuntoSi dimostra che è possibile porre in forma simmetrica conservativa il sistema di equazioni di Landau del superfluido. A causa dei vincoli a cui é soggetto il moto del sistema la teoria che si usa risulta piú complessa di quella classica sviluppata da Godunov e da altri autori.

Travelling waves near a critical point of a binary fluid mixture

Abstract Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal form of the free energy near critical conditions and can be integrated by a rescaling process where the binary mixture is similar to a single fluid. Nevertheless, density solution profiles obtained are not necessarily monotonic. As indicated in Appendix, the results might be extended to other topics like in finance or biology.

On a special symmetric form of the hydrodynamic superfluid equations

SummaryA particular case of Landaus superfluid equations is investigated by assuming as viewpoint the theory of the symmetric hyperbolic systems with constraints. Some results on the symmetrization and hyperbolicity are obtained; then they are compared with those of the general case, studied in a previous paper [5].SuntoSi studia un caso particolare delle equazioni di Landau del superfluido dal punto di vista della teoria dei sistemi iperbolici quasi lineari con vincoli. Si ottengono alcuni risultati sulla simmetrizzazione e sulla iperbolicità del sistema di equazioni; tali risultati sono poi confrontati con quelli già ottenuti, nel caso generale, in un lavoro precedente [5].

Acceleration waves, shock formation and stability in a gravitating atmosphere

The shock formation in a gravitating atmosphere is studied by following the general nonlinear theory of discontinuity waves. In particular, we perform a discussion on the stability of an isothermal and isoentropic atmosphere and we evaluate, when the shock appears, the critical time and the critical height. Some numerical results for the solar and terrestrial atmospheres are also given.

Characteristic shocks of crossing velocities in magnetohydrodynamics

We illustrate, in the framework of magnetohydrodynamics, an application of crossing shock formulas to a characteristic shock moving perpendicularly to the magnetic field.

Fluid mixtures in nanotubes

The aim of the paper is the study of fluid mixtures in nanotubes by the methods of continuum mechanics. The model starts from a statistical distribution in mean-field molecular theory and uses a density expansion of Taylor series. We get a continuous expression of the volume free energy with densitys spatial derivatives limited at the second order. The nanotubes can be filled with liquid or vapor according to the chemical characteristics of the walls and of liquid or vapor mixture bulks. An example of a two-fluid mixture constituted of water and ethanol inside carbon nanotubes at 20^{∘}C is considered. When diameters are small enough, nanotubes are filled with a liquid mixture whatever are the liquid or vapor mixture bulks. The carbon wall influences the ratio of the fluid components in favor of ethanol. The fluid mixture flows across nanotubes can be much more important than classical ones and if the external bulk is vapor, then the flow can be several hundred thousand times larger than Poiseuille flow.