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2022 | OriginalPaper | Chapter

3. Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals

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

Published in: Generalized Dynamics of Soft-Matter Quasicrystals

Publisher: Springer Nature Singapore

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Abstract

Elasticity and hydrodynamics of solid quasicrystals are the basis of the dynamics of soft-matter quasicrystals. A brief review of these topics is given in this chapter, which may be beneficial for understanding the dynamics of soft-matter quasicrystals.

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Literature
1.
go back to reference Bak, P.: Phenomenological theory of icosahedral incommensurate (“quasiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517–1519 (1985)ADSCrossRef Bak, P.: Phenomenological theory of icosahedral incommensurate (“quasiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517–1519 (1985)ADSCrossRef
2.
go back to reference Bak, P.: Symmetry, stability and elastic properties of icosahedral incommensurate crystals. Phys. Rev. B 32, 5764–5772 (1985)ADSMathSciNetCrossRef Bak, P.: Symmetry, stability and elastic properties of icosahedral incommensurate crystals. Phys. Rev. B 32, 5764–5772 (1985)ADSMathSciNetCrossRef
3.
go back to reference Landau, L.D., Lifshitz, E.M.: Theoretical Physics V: Statistical Physics, Part 1, 3rd edn. Pregamen Press, New York (1980) Landau, L.D., Lifshitz, E.M.: Theoretical Physics V: Statistical Physics, Part 1, 3rd edn. Pregamen Press, New York (1980)
4.
go back to reference Anderson, P. W.: Basic Notations of Condensed Matter Physics. Benjamin-Cummings, Menlo-Park (1984) Anderson, P. W.: Basic Notations of Condensed Matter Physics. Benjamin-Cummings, Menlo-Park (1984)
5.
go back to reference Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. 1st edn. Science Press, Beijing (2010); 2nd edn. Springer, Heidelberg (2016) Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. 1st edn. Science Press, Beijing (2010); 2nd edn. Springer, Heidelberg (2016)
6.
go back to reference Levine, D., Lubensky, T.C., Ostlund, S., Ramaswamy, S., Steinhardt, P.J., Toner, J.: Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Phys. Rev. Lett. 54, 1520–1523 (1985)ADSCrossRef Levine, D., Lubensky, T.C., Ostlund, S., Ramaswamy, S., Steinhardt, P.J., Toner, J.: Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Phys. Rev. Lett. 54, 1520–1523 (1985)ADSCrossRef
7.
go back to reference Lubensky, T.C., Ramaswamy, S., Toner, J.: Dislocation motion in quasicrystals and implications for macroscopic properties. Phys. Rev. B 33, 7715–7719 (1986)ADSCrossRef Lubensky, T.C., Ramaswamy, S., Toner, J.: Dislocation motion in quasicrystals and implications for macroscopic properties. Phys. Rev. B 33, 7715–7719 (1986)ADSCrossRef
8.
go back to reference Lubensky, T.C., Socolar, J.E.S., Steinhardt, P.J., Bancel, P.A., Heiney, P.A.: Distortion and peak broadening in quasicrystal diffraction patterns. Phys. Rev. Lett. 57, 1440–1443 (1986)ADSCrossRef Lubensky, T.C., Socolar, J.E.S., Steinhardt, P.J., Bancel, P.A., Heiney, P.A.: Distortion and peak broadening in quasicrystal diffraction patterns. Phys. Rev. Lett. 57, 1440–1443 (1986)ADSCrossRef
9.
go back to reference Lubensky, T.C.: Symmetry, elasticity and hydrodynamics in quasiperiodic structures. In: Jaric, M.V. (ed.) Introduction to Quasicrystals, pp. 199–289. Academic Press, Boston (1988)CrossRef Lubensky, T.C.: Symmetry, elasticity and hydrodynamics in quasiperiodic structures. In: Jaric, M.V. (ed.) Introduction to Quasicrystals, pp. 199–289. Academic Press, Boston (1988)CrossRef
10.
go back to reference Kalugin, P.A., Kitaev, A., Levitov, L.S.: 6-Dimensional properties of Al0.86Mn0.14 alloy. J. Phys. Lett. 46, 601–607 (1985)CrossRef Kalugin, P.A., Kitaev, A., Levitov, L.S.: 6-Dimensional properties of Al0.86Mn0.14 alloy. J. Phys. Lett. 46, 601–607 (1985)CrossRef
11.
go back to reference Torian, S.M., Mermin, D.: Mean-field theory of quasicrystalline order. Phys. Rev. Lett. 54, 1524–1527 (1985)ADSCrossRef Torian, S.M., Mermin, D.: Mean-field theory of quasicrystalline order. Phys. Rev. Lett. 54, 1524–1527 (1985)ADSCrossRef
12.
go back to reference Jaric, M.V.: Long-range icosahedral orientational order and quasicrystals. Phys. Rev. Lett. 55, 607–610 (1985)ADSCrossRef Jaric, M.V.: Long-range icosahedral orientational order and quasicrystals. Phys. Rev. Lett. 55, 607–610 (1985)ADSCrossRef
14.
go back to reference Socolar, J.E.S., Lubensky, T.C., Steinhardt, P.J.: Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34, 3345–3360 (1986)ADSCrossRef Socolar, J.E.S., Lubensky, T.C., Steinhardt, P.J.: Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34, 3345–3360 (1986)ADSCrossRef
15.
go back to reference Gahler, F., Rhyner, J.: Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings. J. Phys. A: Math. Gen. 19, 267–277 (1986)ADSMathSciNetCrossRef Gahler, F., Rhyner, J.: Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings. J. Phys. A: Math. Gen. 19, 267–277 (1986)ADSMathSciNetCrossRef
16.
go back to reference Dolinsek, J., Ambrosini, B., Vonlanthen, P., et al: Atomic motion in quasicrystalline Al70Re8.6Pd21.4: a two-dimensional exchange NMR study. Phys. Rev. Lett. 81, 3671–3674 (1998) Dolinsek, J., Ambrosini, B., Vonlanthen, P., et al: Atomic motion in quasicrystalline Al70Re8.6Pd21.4: a two-dimensional exchange NMR study. Phys. Rev. Lett. 81, 3671–3674 (1998)
17.
go back to reference Dolinsek, J., Apih, T., Simsic, M., et al.: Self-diffusion in icosahedral Al72.4Pd20.5Mn7.1 and phason percolation at low temperatures studied by 27Al NMR. Phys. Rev. Lett. 82, 572–575(1992) Dolinsek, J., Apih, T., Simsic, M., et al.: Self-diffusion in icosahedral Al72.4Pd20.5Mn7.1 and phason percolation at low temperatures studied by 27Al NMR. Phys. Rev. Lett. 82, 572–575(1992)
18.
go back to reference Ding, D.H., Yang, W.G., Wang, R.H., Hu, C.Z.: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48, 7003–7010 (1993)ADSCrossRef Ding, D.H., Yang, W.G., Wang, R.H., Hu, C.Z.: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48, 7003–7010 (1993)ADSCrossRef
19.
go back to reference Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32, 7444–7452 (1985)ADSCrossRef Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32, 7444–7452 (1985)ADSCrossRef
20.
go back to reference Rochal, S.B., Norman, V.L.: Minimal model of the phonon-phason dynamics of quasicrystals. Phys. Rev. B 66, 144204 (2002)ADSCrossRef Rochal, S.B., Norman, V.L.: Minimal model of the phonon-phason dynamics of quasicrystals. Phys. Rev. B 66, 144204 (2002)ADSCrossRef
21.
go back to reference Fan, T.Y., Wang, X.F., Li, W., Zhu, A.Y.: Elasto-hydrodynamics of quasicrystals. Phil. Mag. 89, 501–512 (2009)ADSCrossRef Fan, T.Y., Wang, X.F., Li, W., Zhu, A.Y.: Elasto-hydrodynamics of quasicrystals. Phil. Mag. 89, 501–512 (2009)ADSCrossRef
22.
go back to reference Martin, P.C., Parodi, O., Pershan, P.S.: Unified hydrodynamic theory for crystals, liquid crystals and normal fluids. Phys. Rev. A 6, 2401–2420 (1972)ADSCrossRef Martin, P.C., Parodi, O., Pershan, P.S.: Unified hydrodynamic theory for crystals, liquid crystals and normal fluids. Phys. Rev. A 6, 2401–2420 (1972)ADSCrossRef
23.
24.
go back to reference Cheng, H.: Fan T Yand Wei H, Solutions for hydrodynamics of 5- and 10-fold symmetry quasicrystals. Appl. Math. Mech. 37, 1393–1404 (2016)CrossRef Cheng, H.: Fan T Yand Wei H, Solutions for hydrodynamics of 5- and 10-fold symmetry quasicrystals. Appl. Math. Mech. 37, 1393–1404 (2016)CrossRef
Metadata
Title
Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals
Authors
Tian-You Fan
Wenge Yang
Hui Cheng
Xiao-Hong Sun
Copyright Year
2022
Publisher
Springer Nature Singapore
DOI
https://doi.org/10.1007/978-981-16-6628-5_3

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