Top

Hint

Swipe to navigate through the chapters of this book

Published in:

Read chapter Read first chapter

2022 | OriginalPaper | Chapter

12. Re-Discussion on Symmetry Breaking and Elementary Excitations

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

Published in: Generalized Dynamics of Soft-Matter Quasicrystals

Publisher: Springer Nature Singapore

Abstract

In the first 11 chapters, to establish the generalized dynamics theory of soft-matter quasicrystals, we used the general concepts from the conservation laws and symmetry breaking principle. Based on that some applications have been successfully demonstrated in Chaps. 7–11 via solving the initial- or boundary- or initial and boundary-condition problems of the governing equations of the dynamics.

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 The Possible 7-, 9-, and 14-fold Symmetry Quasicrystals in Soft Matter

next chapter An Application to the Thermodynamic Stability of Soft-Matter Quasicrystals

Planck, M.: Ueber irreversible Strahlungsvorgaenge. Ann. Phys. 1, 89–96 (1900)

Einstein, A.: Ueber einen die Erzeugung und Verwandlung des Lichits betreffenden heuristschen Gesichtspunkt. Ann. Phys. 17, 132–148 (1905) CrossRef

Wang, Z.X.: Statistical Physics. Peking University Press, Beijing, Chinese (2010)

Debye, P.: Die Eigentuemlichkeit der spezifischen Waermen bei tiefen Temperaturen. Arch de Genéve 33(4), 256–258 (1912)

Sommerfeld, A.: Vorlesungen ueber theoretische Physik, Band II, Mechanik der deformierbaren Medium. Verlag Harri Deutsch, Thun. Frankfurt/M (1992)

Born, M., von Kármán, Th.: Zur Theorie der spezifischen Waermen. Physikalische Zeitschrift 14(1), 15–19 (1913); Born, M., Huang, K.: Dynamic Theory of Crystal Lattices. Clarendon Press, Oxford (1954)

ter Harr, D. (ed.): Collected Papers of L D Landau. Pergamon Press, New York (1965)

Anderson, P.W.: Basic Notations of Condensed Matter Physics. Benjamin-Cummings, Menlo-Park (1984)

Lifshitz, M.E., Pitaevskii, L.: Statistical Physics, Part 2. Pergamon, Oxford (1980)

10.

Kittel, C.: Introduction to Solid State Physics, 5th edn. John, New York (1976) MATH

11.

Ren, S.Y.: Electronic State in Crystals of Finite Size. Springer, New York (2017) CrossRef

12.

Bak, P.: Phenomenological theory of icosahedral incommensurate (“quaisiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517–1519 (1985) ADSCrossRef

13.

Bak, P.: Symmetry, stability and elastic properties of icosahedral incommensurate crystals. Phys. Rev. B 32(9), 5764–5772 (1985) ADSMathSciNetCrossRef

14.

Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32(11), 7444–7452 (1985) ADSCrossRef

15.

Ding, D.H., Yang, W.G., Hu, C.Z., et al.: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48(10), 7003–7010 (1993) ADSCrossRef

16.

Hu, C.Z., Wang, R.H., Ding, D.H.: Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Rep. Prog. Phys. 63(1), 1–39 (2000) ADSMathSciNetCrossRef

17.

Hu, C.Z., Ding, D.H., Yang, W.G., Wang, R.H.: Possible two-dimensional quasicystal structure. Phys. Rev. B 49, 9423–9427 (1994) ADSCrossRef

18.

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

19.

Anderson, P.W.: More is different—broken symmetry and the nature of the hierarchical structure of science. Science 177, 393–396 (1972) ADSCrossRef

Title: Re-Discussion on Symmetry Breaking and Elementary Excitations
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_12