Top

previous chapter Critical Phenomena in Darcy and Euler Flows of ...

Hint

Swipe to navigate through the chapters of this book

2021 | OriginalPaper | Chapter

6. Differential Invariants for Flows of Fluids and Gases

Read first chapter

Authors: Anna Duyunova, Valentin V. Lychagin, Sergey Tychkov

Publisher: Springer International Publishing

Published in: Differential Geometry, Differential Equations, and Mathematical Physics

» Get access to the full-text

Abstract

The paper is an extended overview of the papers. The main extension is a detailed analysis of thermodynamic states, symmetries, and differential invariants. This analysis is based on consideration of Riemannian structure naturally associated with Lagrangian manifolds that represent thermodynamic states. This approach radically changes the description of the thermodynamic part of the symmetry algebra as well as the field of differential invariants.

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 69.000 Bücher
über 500 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 50.000 Bücher
über 380 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Maschinenbau + Werkstoffe

Testen Sie jetzt 30 Tage kostenlos.

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 58.000 Bücher
über 300 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

inform now

G. Batchelor, An introduction to fluid dynamics, Cambridge university press (2000).

J. W. Gibbs, A Method of Geometrical Representation of the Thermodynamic Properties by Means of Surfaces, Transactions of Connecticut Academy of Arts and Sciences, 382–404 (1873).

C. Carathéodory, Untersuchungen über die Grundlagen der Thermodynamik, Mathematische Annalen, Springer, 67, 355–386 (1909).

Ruppeiner, G. (1995). Riemannian geometry in thermodynamic fluctuation theory. Reviews of Modern Physics, 67(3), 605. MathSciNetCrossRef

A. Bravetti, Contact geometry and thermodynamics, Int. J. Geom. Meth. Mod. Phys., 16, 1940003, (2018). MathSciNetCrossRef

Ian M. Anderson and Charles G. Torre, The Differential Geometry Package (2016). Downloads. Paper 4. https://digitalcommons.usu.edu/dg_downloads/4

V. Lychagin, Contact Geometry, Measurement and Thermodynamics, in: Nonlinear PDEs, Their Geometry and Applications. Proceedings of the Wisla 18 Summer School, Springer Nature, Switzerland, 3–54 (2019).

B. Kruglikov, V. Lychagin, Mayer brackets and solvability of PDEs–I, Differential Geometry and its Applications, Elsevier BV, 17, 251–272 (2002). MATH

B. Kruglikov, V. Lychagin, Global Lie–Tresse theorem, Selecta Math., 22, 1357–1411 (2016). MathSciNetCrossRef

10.

A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for plane flows of inviscid fluids, Analysis and Mathematical Physics, Vol. 8, No. 1, 135–154 (2018). MathSciNetCrossRef

11.

A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical flows of inviscid fluid, Lobachevskii Journal of Mathematics, Vol. 39, No. 5, 655–663 (2018). MathSciNetCrossRef

12.

A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of inviscid fluids, Analysis and Mathematical Physics, doi.org/10.1007/s13324-018-0274-0 (2018).

13.

A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for plane flows of viscid fluids, Lobachevskii Journal of Mathematics, Vol. 38, No. 4, 644–652 (2017). MathSciNetCrossRef

14.

A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for flows of viscid fluids, Journal of Geometry and Physics, 121, 309–316 (2017). MathSciNetCrossRef

15.

A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical flows of a viscid fluid, Journal of Geometry and Physics, 124, 436–441 (2018). MathSciNetCrossRef

16.

A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130, 288–292 (2018). MathSciNetCrossRef

17.

M. Rosenlicht, A remark on quotient spaces, An. Acad. Brasil. Ci. 35, 487–489 (1963). MathSciNetMATH

Title

Differential Invariants for Flows of Fluids and Gases

Book

Differential Geometry, Differential Equations, and Mathematical Physics

Print ISBN: 978-3-030-63252-6

Electronic ISBN: 978-3-030-63253-3

https://doi.org/10.1007/978-3-030-63253-3

DOI

https://doi.org/10.1007/978-3-030-63253-3_6

Authors:

Anna Duyunova
Valentin V. Lychagin
Sergey Tychkov

Publisher

Springer International Publishing

Sequence number

Chapter number

Chapter 6

Premium Partner

Image Credits