An exact fluid model for relativistic electron beams: The many moments case

An interesting and satisfactory fluid model has been proposed in literature for the the description of relativistic electron beams. It was obtained with 14 independent variables by imposing the entropy principle and the relativity principle. Here the case is considered with an arbitrary number of independent variables, still satisfying the above mentioned two principles; these lead to conditions whose general solution is here found. We think that the results satisfy also a certain ordering with respect to a smallness parameter $\epsilon$ measuring the dispersion of the velocity about the mean; this ordering generalizes that appearing in literature for the 14 moments case

Calculations for Extended Thermodynamics of dense gases up to whatever order and with all the symmetries

The 14 moments model for dense gases, introduced in the last years by Arima, Taniguchi Ruggeri, Sugiyama, is here considered. They have found the closure of the balance equations up to second order with respect to equilibrium; here the closure is found up to whatever order with respect to equilibrium, but for a more constrained system where more symmetry conditions are imposed and this in agreement with the suggestion of the kinetic theory. The results, when restricted at second order with respect to equilibrium, are the same of the previously cited model but under the further restriction of full symmetries.Comment: arXiv admin note: substantial text overlap with arXiv:1410.405

Relativistic Extended Thermodynamics of Polyatomic Gases with Rotational and Vibrational Modes

In a recent article, an infinite set of balance equations has been proposed to modelize polyatomic gases with rotational and vibrational modes in a non-relativistic context. To obtain particular cases, it has been truncated to obtain a model with 7 or 15 moments. Here the following objectives are pursued: 1) to obtain the relativistic counterpart of this model, which, at the non-relativistic limit, gives the same balance equations as in the known classical case; 2) to obtain the previous result for the model with an arbitrary but fixed number of moments; and 3) to obtain the closure of the resulting relativistic model so that all the functions appearing in the balance equations are expressed in terms of the independent variables. To achieve these goals, the following methods are used: 1) the principle of entropy is imposed. As a result, it is obtained that the closure is determined up to a single 4-vectorial function, usually called a 4-potential. 2) To determine this last function, a more restrictive principle is imposed, namely the Maximum Entropy Principle (MEP). 3) Since all the functions involved must be expressed in the covariant form so as not to depend on the observer, the Representation Theorems are used. The findings of this article exactly match the goals outlined earlier. They are clearly novel because they have never been achieved before. They can also be considered improvements because, if the aforementioned arbitrary number of moments is restricted to 16, the present work coincides with that already known in literature

A new model for polyatomic gases in an electromagnetic field

Significant progress has recently been made in the field of polyatomic gases, in particular by Professors T Ruggeri, M Sugiyama and collaborators. But so far it has not yet been seen how they interact with an electromagnetic field. This is realized in the present paper. As a first step, we consider here the case when the gas is described only by the Euler Equations and the electromagnetic field by Maxwell’s Equations in materials. To find the field equations, a supplementary conservation law is imposed which is the entropy principle for the Euler Equations, while for Maxwell’s Equations is the energy; this is useful because in this way the whole set of equations becomes a symmetric hyperbolic system as usual in Extended Thermodynamics. One of the results is a restriction on the law connecting the magnetic field in the empty space and the electric field in materials to the electromotive force and its dual: they are the gradients of a scalar function. Obviously, two Maxwell’s equations are not evolutive (The Gauss magnetic and electric laws)

Consistent Order Approximations in Extended Thermodynamics of Polyatomic Gases

In this article the known models are considered for relativistic polyatomic gases with an arbitrary number of moments, in the framework of Extended Thermodynamics. These models have the downside of being hyperbolic only in a narrow domain around equilibrium, called "hyperbolicity zone". Here it is shown how to overcome this drawback by presenting a new model which satisfies the hyperbolicity requirement for every value of the independent variables and without restrictions. The basic idea behind this new model is that hyperbolicity is limited in previous models by the approximations made there. It is here shown that hyperbolicity isn't limited also for an approximated model if terms of the same order are consistently considered, in a new way never used before in literature. To design and complete this new model, well accepted principles are used such as the "Entropy Principle" and the "Maximum Entropy Principle". Finally, new trends are analized and these considerations may require a modification of the results published so far; as a bonus, more manageable balance equations are obtained. This allows to obtain more stringent results than those so far known. For example, we will have a single quantity (the energy e) expressed by an integral and all the other constitutive functions will be expressed in terms of it and its derivatives with respect to temperature. Another useful consequence is its easier applicability to the case of diatomic and ultrarelativistic gases which are useful, at least for testing the model in simple cases

A novel topology for a HEMT negative current mirror

A new solution for the implementation of a HEMT negative current source is presented. The topology can be also profitably employed as a current mirror and as an active load in high-gain MMICs voltage amplifiers. A small-signal model of the proposed circuit is developed which allows to find accurate expressions for the required transfer functions (i.e., the output impedance of the current source, and the current gain of the circuit when operated as a current mirror). Design examples using Philips PML ED02AH GaAs PHEMT process are provided. Spice simulations show that a 10- kW output impedance for the current source and a 35dB voltage gain for a differential pair loaded with the proposed current mirror are easily achieved