Top

Hint

Swipe to navigate through the chapters of this book

Published in:

Read chapter Read first chapter

2022 | OriginalPaper | Chapter

5. Poisson Brackets and Derivation of Equations of Motion in Soft-Matter Quasicrystals

Authors : Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun

Published in: Generalized Dynamics of Soft-Matter Quasicrystals

Publisher: Springer Nature Singapore

Abstract

Previous chapters provided basic concepts of soft-matter quasicrystals. For practice, we need to establish the equations of motion of the matter, then one can give a quantitative description of their structures and dynamic properties.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

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

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

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

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Case Study of Equation of State in Several Structured Fluids

next chapter Oseen Theory and Oseen Solution

Einstein, A.: Ueber die von der molekularkinetischen Theorie der Waerme geforderte Bewegung von in ruhenden Fluessigkeiten suspendierten Teilchen. Ann d Phys 17, 549–560 (1905) ADSCrossRef

Perrin, J.B.: The Atoms. Nabu Press, New York (2010) (English Trans. D.L. Hammick)

Forster, D.: Hydrodynamic fluctuation, broken symmetry and correlation functions. In: Benjamin, W.A. (ed.) Frontier in Physics, A Lecture Note and Reprint Series, vol. 47. Incorporated, Massachusetts (1975)

Chaikin, P., Lubensky, T.C.: Principles of Condensed Matter Physics. Cambridge University Press, Cambridge (1995) CrossRef

Landau, L.D., Lifshitz, M.E.: Fluid Mechanics, Theory of Elasticity. Pergamon, Oxford (1998)

Landau, L.D.: The theory of superfluidity of heilium II. Zh. Eksp.Teor. Fiz, II, 592, J. Phys. USSR 5, 71–90 (1941)

Landau, L.D., Lifshitz, E.M.: Zur Theorie der Dispersion der magnetische Permeabilitaet der ferromagnetische Koerpern. Physik Zeitschrift fuer Sowjetunion 8, 158–164 (1935)

Dzyaloshinskii, I.E., Volovick, G.E.: Poisson brackets in condensed matter physics. AnnPhys. (NY) 125, 67–97 (1980) ADSMathSciNetCrossRef

Dzyaloshinskii, I.E., Volovick, G.E.: On the concept of local invariance in spin glass theory. J. de Phys. 39, 693–700 (1978) CrossRef

10.

Volovick, G.E.: Additional localized degrees of freedom in spin glasses. Zh Eksp Teor Fiz 75, 1102–1109 (1978)

11.

Martin, P.C., Paron, O., Pershan, P.S.: Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids. Phys. RevA 6, 2401–2420 (1972) ADSCrossRef

12.

Fleming, P.D., Cohen, C.: Hydrodynamics of solids. Phys. Rev. B 13, 500–516 (1976) ADSCrossRef

13.

Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32, 7444–7411 (1985) ADSCrossRef

14.

Lubensky, T.C.: Symmetry, elasticity and hydrodynamics of quasiperioic structures. In: Jaric, M.V. (ed.) Aperiodic Crystals, vol. I., pp. 199–280. Academic Press, Boston (1988)

15.

Fan, T.Y.: Poisson bracket method and it applications to quasicrystals, liquid crystals and a class of soft matter. Acta Mechanica Sinica 45, 548–559 in Chinese (2013)

16.

Rochal, S.B., Lorman, V.L.: Minimal model of the phonon-phason dynamics in icosahedral quasicrystals and its application to the problem of internal friction in the i-AlPdMn alloy. Phys. Rev. B 66, 144204 (2002)

17.

Coddens, G.: On the problem of the relation between phason elasticity and phason dynamics in quasicrystals. Euro. Phys. J. B 54, 37–65 (2006)

18.

Fan, T.Y.: Equation system of generalized hydrodynamics of soft-matter quasicrystals. Appl. Math. Mech. 37, 331–347 (2016) in Chinese; arXiv:1908.06425[cond-mat.soft] 15 Oct (2019)

19.

Fan, T.Y.: Generalized hydrodynamics of soft-matter second kind two-dimensional quasicrystals. Appl. Math. Mech. 38, 189–199 in Chinese (2017); arXiv:1908.06430[cond-mat.soft] 15 Oct (2019)

20.

Fan, T.Y., Tang, Z.Y.: Three-dimensional generalized dynamics of soft-matter quasicrystals. Appl. Math. Mech. 38, 1195–1207 (2017); Advances in Materials Science and Engineering, Vol. 2020, Article 1D4875854 (2020)

21.

Cheng, H., Fan, T.Y., Wei, H.: Solution of hydrodynamics of 5- and 10-fold symmetry quasicrystals. Appl. Math. Mech. 37, 1393–1404 (2016) MathSciNetCrossRef

22.

Cheng, H., Fan, T.Y., Wei, H.: Characters of deformation and motion of possible soft-matter quasicrystals with 5- and 10-fold symmetries. unpublished work (2016)

23.

Wang, F., Cheng, H., Fan, T.Y., Hu, H.Y.: A stress analysis of some fundamental specimens of soft-matter quasicrystals with 8-fold symmetry based on generalized dynamics. Adv. Mater. Sci. Eng. Vol 2019, Article 1D 8789151 (2019)

Title: Poisson Brackets and Derivation of Equations of Motion in Soft-Matter Quasicrystals
Authors: Tian-You Fan
Wenge Yang
Hui Cheng
Xiao-Hong Sun
Publisher: Springer Nature Singapore
Book: Generalized Dynamics of Soft-Matter Quasicrystals
Print ISBN: 978-981-16-6627-8

Electronic ISBN: 978-981-16-6628-5

Copyright Year: 2022
DOI: https://doi.org/10.1007/978-981-16-6628-5_5