Critical time for shock formation in radiative magnetogasdynamics

For the general case of magnetogasdynamics coupled to the radiation field, a differential scheme which is capable of dealing with variable optical depths, leads to a hyperbolic system of equations. To this system the standard techniques for evaluating the critical time of weak discontinuities is applied. In this paper the critical time for radiative magnetoacoustic waves propagating into a constant state is analyzed. Plane waves, spherical waves and cylindrical waves are studied.     

Extended thermodynamics of the Blotekjaer hydrodynamical model for semiconductors

The Blotekjaer hydrodynamical model for charge carriers transport in semiconductors is reconsidered from the viewpoint of extended thermodynamics. In particular the Blotekjaer original closure of the moment equations is shown to be equivalent to that obtained by applying the entropy principle.Work partially supported by C.N.R. (MMI-P.S IPPMI, U.O Mathematical Models of Semiconductors)     

Geometrical optics in dispersive media

We present a systematic derivation of Geometrical Optics in dispersive media from Maxwell's equation for the presence of charges and currents, by using the two-timing approximation technique. A propagation equation for the polarisation plane is also derived.     

Fluid models for relativistic electron beams

A system of equations is provided that may be used in the study of relativistic charged particle beams. The equations are based upon the equations of the kinetic theory for first, second and third order moments and the system is closed by letting the third order moment depend on the lower order ones. The form of that dependence is formally equal to the explicit constitutive function given by extended thermodynamics. However, here the contributions to the third order moment can be classed as being different in order of magnitude, because there is a smallness parameter characterizing the small dispersion of the particle beam. The resulting system of equations is quite specific, it is fully covariant and it is equivalent to a symmetric hyperbolic system thus ensuring existence and uniqueness of solutions.     

Hydrodynamical Modeling of Charge Carrier Transport in Semiconductors

Enhanced functional integration in modern electron devices requires an accurate modeling of energy transport in semiconductors in order to describe high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. The standard drift-diffusion models cannot cope with high-field phenomena because they do not comprise energy as a dynamical variable. Furthermore for many applications in optoelectronics one needs to describe the transient interaction of electromagnetic radiation with carriers in complex semiconductor materials and since the characteristic times are of order of the electron momentum or energy flux relaxation times, some higher moments of the distribution function must be necessarily involved. Therefore these phenomena cannot be described within the framework of the drift-diffusion equations (which are valid only in the quasi-stationary limit). Therefore generalizations of the drift-diffusion equations have been sought which would incorporate energy as a dynamical variable and also would not be restricted to quasi-stationary situations. These models are loosely speaking called hydrodynamical models. One of the earliest hydrodynamical models currently used in applications was originally put forward by Blotekjaer [1] and subsequently investigated by Baccarani and Wordeman [2] and by other authors [3]. Eventually other models have also been investigated, some including also non-parabolic effects [4–6, 8–20]. Most of the implemented hydrodynamical models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem (lacking a physically convincing motivation) and the modeling of the production terms (usually assumed to be of the relaxation type and this, as we shall see, leads to serious inconsistencies with the Onsager reciprocity relations). In these lectures we present a general overview of the theory underlying hydrodynamical models. In particular we investigate in depth both the closure problem and the modeling of the production terms and present a recently introduced approach based on the maximum entropy principle (physically set in the framework of extended thermodynamics [21, 22]). The considerations and the results reported in the paper are exclusively concerned with silicon.     

The algebraic behaviour of the weyl tensor in the geometrical optics approximation

Sunto In questo lavoro si studia la propagazione di un'onda gravitazionale nel vuoto, nell'approssimazione dell'ottica geometrica. Viene esaminato il tensore di Weyl dell'onda all'ordine zero e all'ordine uno della serie che rappresenta l'approssimazione dell'ottica geometrica. Questi termini sono gli unici invarianti per le trasformazioni infinitesime che preservano la forma dell'espansione del tensore metrico (trasformazioni di gauge). Perciò sono gli unici ad avere un significato fisico, cioè ad essere misurabili indipendentemente dalla convergenza della serie che li definisce. Viene caratterizzato il tipo algebrico del tensore di Weyl a questi due ordini in termini degli scalari ottici associati alla congruenza dei raggi su cui l'onda si propaga.

---

---

Entrata in Redazione l'8 luglio 1975.     

Propagation of weak shock waves

An asymptotic method is developed in order to treat the evolution of weak shock waves. One obtains a geometrical theory according to which weak shock waves propagate along rays and satisfy a transport law.