A 16 moments model in relativistic extended thermodynamics of rarefied polyatomic gas

A model with 16 moments is here presented in the framework of RET of polyatomic gases. It furnishes as principal subsystem the relativistic counterpart of a work by Arima T., Ruggeri T., Sugiyama M.; this is present in literature and treats the non relativistic case which incorporates relaxation processes of molecular rotation and vibration. Another principal subsystem is the natural extension of the 14 moments model by Pennisi S. and Ruggeri T.; this is also present in literature in the relativistic framework but where the trace of the third balance equation is neglected. Its extension is found here for the case when this trace isn’t neglected.

     

Extended approaches to covariant Maxwell electrodynamics

The field equations of covariant Maxwell electrodynamics are a set I of 8 equations for the determination of 6 variables, i.e., the independent components of the skew-symmetric Maxwell tensorF . Obviously 2 of these equations are not evolutive; however they cannot be eliminated without losing manifest covariance. This paper presents a new hyperbolic set S of 8 equations in the 8 variablesF ,x, y, wherex, y are new auxiliary quantities. The solutions of S withx =y = 0 are those of the set I. Moreover, S is expressed in covariant form and is equivalent to a symmetric hyperbolic system.     

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)     

Quantum size effects and band structure in InSb

Quantum Size Effects (Q.S.E.) in InSb films have been detected by different experimental procedures.The work function dependence on thickness obtained from photoelectric emission threshold measurements is compared with prior results obtained with the retarding potential method. With both methods, the measured work function values are comparable. They are less than the corresponding bulk values, conforming to current theoretical predictions.The interband energy gap has been determined from photoelectric absorption band edge data: its value differs with respect to the bulk one, by the location of the first allowed energy subband in the conduction band due to the presence of Q.S.E.Some evidence is given for absence of a band structure dependence on Q.S.E.     

Quantum size effects and negative resistance in MOS structure with polycrystalline InSb (n-type)

Summary The tunnel characteristics (J vs. V) of Al−Al₂O₃−InSb (n type) structures with thin (100÷400)? semiconducting electrode are presented. They are analysed by utilizing the model proposed by Chang, Esaki and Styles. The data obtained by a nonlinear best fit on experimental points describe the MOS structure and the negative-resistance region exibited by the characteristics. Furthermore, the semiconductor gap shows a dependence on the thickness and this variation is explainable with the quantum effects presence in the thinnest films.

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Riassunto Le caratteristiche tunnel (J vs. V) di strutture Al−Al₂O₃−InSb (n type) con eletrodo semiconduttore sottile (100÷400) ? sono presentate. Esse sono analizzate utilizzando il modello proposto da Chang, Esaki e Styles; i dati ottenuti da un adattamento ottimale non lineare sui punti sperimentali descrivono la struttura MOS e la regione a resistenza negativa esibita dalle caratteristiche. Inoltre si osserva che il gap del semiconduttore varia con lo spessore; tale variazione è interpretata mediante la presenza di effetti quantistici di dimensione nei films più sottili.

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Резюме Приводятся туннельные характеристики (J в зависимости отV) для Al−Al₂O₃−InSb (n-типа) структур с тонким (100÷400) ? сверхпроводящим злектродом. Эти нарактеристики анализируются с помощью модели, предложенной Ченгом, Есаки и Стайлсом. Данные, полученные путем нелинейной подгонки, описывают MOS структуры и область отрицательного сопротивления, обнаруженного в характеристиках. Кроме того, щель в свернпроводнике обнаруживает зависимость от толщины. Изменение щели объясняется наличием квантовых эффектов, связанных с размерами образцов, в тончайших пленках.

     

A new method to exploit the Entropy Principle and galilean invariance in the macroscopic approach of Extended Thermodynamics

Abstract In extended thermodynamic the entropy principle and the Galilean invariance dictate respectively constraints for the constitutive equations and the velocity dependence. The entropy principle in particular requires the existence of a privileged field, the main field u^′, such that the original system becomes symmetric hyperbolic and is generated by four potentials. It is not easy to solve the restrictions of both principles, if we use as field the non convective main field and the velocity v. This is due to the fact that are not independent. Rather its components satisfy three scalar constraints. The aim of this paper is to solve the full problem using as new strategy to consider as independent variables and requiring an appropriate differential constraint. This new procedure is very efficient and we are able to solve the problem of 13 moments in the full non linear case (far from equilibrium). It turns out that the knowledge of only the equilibrium state function is sufficient to close the system. Keywords: Extended Thermodynamics, Entropy Principle, Galilean invariance, Rarefied Gas, Hyperbolic systems Mathematics Subject Classification (2000): 74A20, 76P05, 35l60     

From geometry to algebra: the Euclidean way with technology

In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products.     

A fourth order approach to relativistic extended thermodynamics

Relativistic Extended Thermodynamics is a very important scientific achievement of the last decades, and has inspired many subsequent authors to apply its methodology to lots of other possible applications. In short it furnishes field equations which are “closed” by imposing the relativity principle and the entropy principle up to second order, with respect to equilibrium; the linear closure is explicitly reported. Here these principles are imposed up to fourth order; the second order closure is explicitly reported, while the subsequent ones are reported as implicit functions. It is also proved that no internal inconsistencies are generated by the theory. In fact, in the process of computations many complicated conditions on the lower order terms are deduced, but they turn out to be identically satisfied. Received January 20, 1998     

Experimental investigation and analytical description of a vibro-impact NES coupled to a single-degree-of-freedom linear oscillator harmonically forced

In this paper, the dynamics of a system composed of a harmonically forced single-degree-of-freedom linear oscillator coupled to a vibro-impact nonlinear energy sink (VI-NES) is experimentally investigated. The mass ratio between the VI-NES and the primary system is about \(1\%\). Depending on the external force’s amplitude and frequency, either a strongly modulated response (SMR) or a constant amplitude response (CAR) is observed. In both cases, an irreversible transfer of energy occurs from the linear oscillator toward the VI-NES: process known in the literature as passive targeted energy transfer. Furthermore, the problem is analytically studied by using the method of multiple scales. The obtained slow invariant manifold shows the existence of a stable and of an unstable branch of solutions, as well as of an energy threshold (a saddle-node bifurcation) for the solutions to appear. Subsequently, the fixed points of the problem are calculated. When a stable fixed point is reached, the system is naturally drawn to it and a CAR is established, whereas when no stable point is attained, the system exhibits a SMR regime. Finally, a good correlation between the experimental and the analytical results is presented.