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Full-Text Articles in Physical Sciences and Mathematics
Supplementary Balance Laws For Cattaneo Heat Propagation, Serge Preston
Supplementary Balance Laws For Cattaneo Heat Propagation, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (conservation laws ) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature (λ0(ϑ),KA (ϑ), A = 1, 2, 3). The requirements of the II law of thermodynamics leads to the exclusion of three functional degrees (KA= 0, A …
Balance Systems And The Variational Bicomplex, Serge Preston
Balance Systems And The Variational Bicomplex, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian part and a complemental "pure non-Lagrangian" balance system. In the case when derivatives of the dynamical fields do not enter the constitutive relations of the balance system, the "pure non-Lagrangian" systems coincide with the systems introduced by S. Godunov [Soviet Math. Dokl. 2 (1961), 947–948] and, later, asserted as …
Supplementary Balance Laws And The Entropy Principle, Serge Preston
Supplementary Balance Laws And The Entropy Principle, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we study the mathematical aspects of the development in the continuum thermodynamics known as the “Entropy Principle”. It started with the pioneering works of B.Coleman, W.Noll and I. Muller in 60th of XX cent. and got its further development mostly in the works of G. Boillat, I-Shis Liu and T.Ruggeri. “Entropy Principle” combines in itself the structural requirement on the form of balance laws of the thermodynamical system (denote such system (C)) and on the entropy balance law with the convexity condition of the entropy density. First of these requirements has pure mathematical form defining so called …
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
Mathematics and Statistics Faculty Publications and Presentations
We study an indefinite metric G which was introduced by R. Mrugala and is defined on the contact phase space (P, θ) of a homogeneous thermodynamical system. We describe the curvature properties and the isometry group of the metric G. We established an isomorphism of the space (P, θ, G) with the Heisenberg Lie group Hn, endowed with the right invariant contact structure and the right invariant indefinite metric. The lift of the metric G to the symplectization of contact space (P, θ) and its properties are studied. Finally we introduce the "hyperbolic projectivization" of the space …
Curvature Of The Weinhold Metric For Thermodynamical Systems With 2 Degrees Of Freedom, Manuel Santoro, Serge Preston
Curvature Of The Weinhold Metric For Thermodynamical Systems With 2 Degrees Of Freedom, Manuel Santoro, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work the curvature of Weinhold (thermodynamical) metric is studied in the case of systems with two thermodynamical degrees of freedom. Conditions for the Gauss curvature R to be zero, positive or negative are worked out. Signature change of the Weinhold metric and the corresponding singular behavior of the curvature at the phase boundaries are studied. Cases of systems with the constant Cv, including Ideal and Van der Waals gases, and that of Berthelot gas are discussed in detail.