to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

In 1982, the Belgian Pilots' Guild raised the question of what effect exposure to radar radiation--for example, that encountered in passing a pilot launch's radar--might have on the human body. Recapitulating investigations of this question, this article states that in 25 years of experience with radar, there have been no known incidents of pilots being affected by radar waves. In the future, however, involvement by some pilots with Vessel Traffic Service shore-based radar could affect pilots somewhat differently from limited exposure to pilot launch radar. Pilots who find themselves in new working conditions close to an emitting source should exercise care all times.

About heat waves

In the preceding chapters with few exceptions we studied systems at equilibrium. This means that the systems do not change or evolve over time.

Non-Equilibrium Thermodynamics

Der vorliegende Band enthált sechs Beitrage, in denen punktuell und exemplarisch der Stand der Forschung beleuchtet wird. Ein Beitrag von Codling und Frasinski beschreibt in erster Linie Experimente zum noch wenig verstandenen Phânomen der dissoziativen Ionisation von Molekülen, bei dem diese in einem intensiven Laserfeld mehrere Elektronén verlieren und in Ionen mit hoher kinetischer Energie zerfallen. Ein wesentlicher Teil dieses Beitrags widmet sich einer von den Autoren entwickelten Auswertungstechnik, welche die Korrelationen zwischen den Fiugzeiten emittierter Ionen und Elektronén sichtbar macht. Es folgen drei Beitrage zur Théorie. Schmelcher und Cederbaum beschreiben Effekte starker statischer Felder, die nur dann zu verstehen sind, wenn die Nicht-Separation der Schwerpunktsbewegung im auBeren Magnetfeld korrekt beriicksichtigt wird. Dies fiihrt

Extended Irreversible Thermodynamics

A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal transformation group (basic Nother’s identity) are obtained. These conditions extend the classical results, valid for integer order derivatives. A generalization of Nother’s theorem leading to conservation laws for fractional Euler–Lagrangian equation is obtained as well. Results are illustrated by several concrete examples. Finally, an approximation of a fractional Euler–Lagrangian equation by a system of integer order equations is used for the formulation of an approximated invariance condition and corresponding conservation laws.

Variational problems with fractional derivatives: Invariance conditions and Nöther’s theorem☆

In this chapter, we prove, in the case of polyatomic rarefied gases, that the maximum entropy principle (MEP) gives the same closure of the system as that obtained in the phenomenological ET theory with 14 fields discussed in Chap. 5 The main idea is to consider a generalized distribution function depending not only on the velocity but also on an extra variable that connects with the internal degrees of freedom of a constituent molecule. On the basis of MEP, we again obtain the same binary hierarchy introduced in the previous chapter: the one is the usual momentum-type, F-series, and the other is the energy-type, G-series. The extra variable plays a role in the G-series. Thus we prove the perfect agreement between the ET theory and the molecular ET theory at least within 14-field theories. The agreement for any number of moments will be proved in Chap. 10

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Maximum entropy principle for rarefied polyatomic gases

A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal transformation group (basic Nother's identity) are obtained. These conditions extend the classical results, valid for integer order derivatives. A generalization of Nother's theorem leading to conservation laws for fractional Euler-Lagrangian equation is obtained as well. Results are illustrated by several concrete examples. Finally, an approximation of a fractional Euler-Lagrangian equation by a system of integer order equations is used for the formulation of an approximated invariance condition and corresponding conservation laws.

Variational problems with fractional derivatives: Invariance conditions and N\"{o}ther's theorem

The first rational model of homogeneous mixtures of fluids was proposed by Truesdell in the context of rational thermodynamics. Afterwards, two different theories were developed: one with a single-temperature (ST) field of the mixture and the other one with several temperatures. The two systems are from the mathematical point of view completely different and the relationship between their solutions was not clarified.



In this paper, the hyperbolic multi-temperature (MT) system of a mixture of Eulerian fluids will be explained and it will be shown that the corresponding single-temperature differential system is a principal subsystem of the MT one. As a consequence, the subcharacteristic conditions for characteristic speeds hold and this gives an upper-bound esteem for pulse speeds in an ST model. Global behaviour of smooth solutions for large time for both systems will also be discussed through the application of the Shizuta–Kawashima condition. Finally, as an application, the particular case of a binary mixture is considered. Copyright © 2006 John Wiley & Sons, Ltd.

On the hyperbolic system of a mixture of Eulerian fluids: a comparison between single- and multi-temperature models

This paper treats the nonequilibrium processes in mixtures of fluids under the assumption that each constituent is characterized by its own velocity and temperature field. First we discuss the concept of the average temperature of mixture based upon considerations that the internal energy of the mixture is the same as in the case of a single-temperature mixture. As a consequence, it is shown that the entropy of the mixture reaches a local maximum in equilibrium. An illustrative example of homogeneous mixtures is given to support the theoretical considerations. Through the procedure of Maxwellian iteration a new constitutive equation for nonequilibrium temperatures of constituents is obtained in a classical limit, together with the Fick's law for the diffusion flux. These results obtained for n-species are in perfect agreement with a recent classical approach of thermodynamics of irreversible processes in multitemperature case due to Gouin and Ruggeri and generalize our previous papers concerning the case of a binary mixture.

Srboljub Simić

Papers

Variational problems with fractional derivatives: Invariance conditions and Nöther’s theorem☆

Maximum entropy principle for rarefied polyatomic gases

Variational problems with fractional derivatives: Invariance conditions and N\"{o}ther's theorem

On the hyperbolic system of a mixture of Eulerian fluids: a comparison between single- and multi-temperature models

Average temperature and Maxwellian iteration in multitemperature mixtures of fluids.