Abstract
The previous chapters provided knowledge for us to understanding soft-matter quasicrystals, an understanding quantitatively is needed to set up the equations of motion of the matter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Einstein, Ueber die von der molekularkinetischen Theorie der Waerme geforderte Bewegung von in ruhenden Fluessigkeiten suspendierten Teilchen. Ann d Phys 17(4), 549–560 (1905)
Perrin J B, The Atoms, Nabu Press, New York, 2010 (English translation, by Hammick D L)
D. Forster, Hydrodynamic Fluctuation, Broken Symmetry and Correlation Functions, vol. 47. Frontier in Physics, A Lecture Note and Reprint Series (W A Benjamin, Incorporated, Massachusetts, 1975)
J. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995)
L.D. Landau, M.E. Lifshitz, in Fluid Mechanics, Theory of Elasticity (Pergamon, Oxford, 1998)
L.D. Landau, The theory of superfluidity of heilium II, Zh. Eksp. Teor. Fiz, II, 592. J. Phys. USSR 5, 71–90 (1941)
L.D. Landau, E.M. Lifshitz, in Zur Theorie der Dispersion der magnetische Permeabilitaet der ferromagnetische Koerpern. Physik Zeitschrift fuer Sowjetunion 8(2), 158–164 (1935)
I.E. Dzyaloshinskii, G.E. Volovick, Poisson brackets in condensed matter physics. Ann. Phys. (NY) 125(1), 67–97 (1980)
I.E. Dzyaloshinskii, G.E. Volovick, On the concept of local invariance in spin glass theory. J. de Phys. 39(6), 693–700 (1978)
G.E. Volovick, Additional localized degrees of freedom in spin glasses. Zh. Eksp. Teor. Fiz. 75(7), 1102–1109 (1978)
P.C. Martin, O. Paron, P.S. Pershan, Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids. Phys. Rev. A 6(6), 2401–2420 (1972)
P.D. Fleming, C. Cohen, Hydrodynamics of solids. Phys. Rev. B 13(2), 500–516 (1976)
T.C. Lubensky, S. Ramaswamy, J. Toner, Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32(11), 7411–7444 (1985)
T.C. Lubensky, Symmetry, elasticity and hydrodynamics of quasiperioic structures, in Aperiodic Crystals, vol. I, ed. by M.V. Jaric (Academic Press, Boston, 1988), pp. 199–280
T.Y. Fan, Poisson bracket method and it applications to quasicrystals, liquid crystals and a class of soft matter. Acta. Mech. Sin. 45(4), 548–559 (2013). (in Chinese)
S.B. Rochal, V.L. Lorman, 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(14), 144204 (2002)
G. Coddens, On the problem of the relation between phason elasticity and phason dynamics in quasicrystals. Eur. Phys. J. B 54(1), 37–65 (2006)
T.Y. Fan, Equation system of generalized hydrodynamics of soft-matter quasicrystals. Appl. Math. Mech. 37(4), 331–347 (2016). (in Chinese)
T.Y. Fan, Generalized hydrodynamics of soft-matter second kind two-dimensional quasicrystals. Appl. Math. Mech. 38(2), 189–199 (2017). (in Chinese)
T.Y. Fan, Z.Y. Tang, Three-dimensional hydrodynamics of soft-matter quasicrystals. Appl. Math. Mech. 38 (2017). (in press, in Chinese)
H. Cheng, T.Y. Fan, H. Wei, Solution of hydrodynamics of 5- and 10-fold symmetry quasicrystals. Appl. Math. Mech. 37(10), 1393–1404 (2016)
H. Cheng, T.Y. Fan, H. Wei, Characters of deformation and motion of possible soft-matter quasicrystals with 5- and 10-fold symmetries. Appl. Phys. A (2017, in reviewing)
Wang F, Hu H Y, Fan T Y and Cheng H, Hydrodynamic analysis of octagonal soft-matter quasicrystals, Appl Math Mech, 2017, accepted
H. Cheng, T.Y. Fan, Flow of soft-matter quasicrystals past a circular cylinder. Unpublished work
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd. and Beijing Institution of Technology Press
About this chapter
Cite this chapter
Fan, TY. (2017). Poisson Brackets and Derivation of Equations of Motion of Soft-Matter Quasicrystals. In: Generalized Dynamics of Soft-Matter Quasicrystals. Springer Series in Materials Science, vol 260. Springer, Singapore. https://doi.org/10.1007/978-981-10-4950-7_5
Download citation
DOI: https://doi.org/10.1007/978-981-10-4950-7_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-4949-1
Online ISBN: 978-981-10-4950-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)