Abstract
The discussion is mainly on elasticity and a few of on hydrodynamics of quasicrystals is ended up to Chap. 16.
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References
Sommerfeld A, 1952, Vorlesungen ueber theoretische Physik, Band II: Mechanik der deformirbaren Medien, Diederich Verlag, Wiesbaden.
Landau L D and Lifshitz E M, 1986, Theoretical Physics, Vol. VII: Theory of Elasticity, Pergamon Press, Oxford.
Debye P, 1912. Eigentuemlichkeit der spezifischen Waermen bei tiefen Temperaturen, Arch de Genéve, 33(7), 256-258.
Born M and von Kármán Th, Zur Theorie der spezifischen Waermen, Physikalische Zeitschrift, 14(1), 15-19, 1913; Born M and Huang K, 1954, Dynamic Theory of Crystal Lattices, Clarendon Press, Oxford.
Anderson P W, 1984, Basic Notation of Condensed Matter Physics, Menlo Park: Benjamin-Cummings.
Bak P, 1985, Symmetry, stability and elastic properties of icosahedral incommensurate crystals, Phys. Rev. B, 32(9), 5764-5772.
Horn P M, Malzfeldt W, DiVincenzo D P, Toner J et al, 1986, Systematics of Disorder in Quasiperiodic Material, Phys. Rev. Lett., 57(12), 1444-1447.
Lubensky T C, Ramaswamy S and Toner J, 1985, Hydrodynamics of icosahedral quasicrystals, Phys. Rev. B, 32(11), 7444-7452.
Lubensky T C, 1988, Introduction to Quasicrystals, ed by Jaric MÂ V, Boston: Academic Press.
De P, Pelcovits R A, 1987, Linear elasticity theory of pentagonal quasicrystals, Phys Rev B, 35(16), 8609-8620.
Ding D H, Yang W G, Hu C Z, Wang R H, 1993, Generalized elasticity theory of quasicrystals, Phys Rev B, 48(10), 7003-7010.
Li X F, Fan T Y, 1998, New method for solving elasticity problems of some planar quasicrystals and solution, Chin Phys Lett, 15(4), 278-280.
Feurbacher M and Urban K, 2003, Plastic behaviour of quasicrystalline materials, Quasicrystals (ed. Trebin H), Wiley Press, Berlin.
Messerschmidt U, 2010, Dislocation Dynamics during Plastic Deformation, Springer-Verlag, Heidelberg.
Fan T Y and Fan L, 2008, Plastic deformation of quasicrystals, Phil Mag, 88(4), 323-335.
Fan T Y and Fan L, 2011, Relation between generalized Eshelby integral and generalized BCS and generalized DB models for some one- and two-dimensional quasicrystals, Chin Phys B,20(4), 036102.
Yang S H, Ding D H, 1998, Crystal Dislocation Theory, Vol.2, Beijing, Science Press (in Chinese).
Li X F, Duan X Y, Fan T Y, Sun Y F, 1999, Elastic field for a straight dislocation in a decagonal quasicrystal, J Phys Condens Matter, 11(3), 703-711.
Fan T Y, Trebin H-R, Messerschmidt U, Mai Y W, 2004, Plastic flow coupled with a Griffith crack in some one- and two-dimensional quasicrystals, J Phys Condens Matter, 16(27),5229-5240.
Li X F, Fan T Y, Sun Y F, 1999, A decagonal quasicrystals with a Griffith crack, Phil Mag A, 79(8), 1943-1952.
Janssen T, 1992, The symmetry operations for n-dimensional periodic and quasi-periodic structures, Zeitschrift fuer Kristallographie, 198(1-2), 17-32.
Hu C Z, Wang R H, Ding D H, 2000, Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals, Rep. Prog. Phys., 63(1), 1-39.
Ding D H, Wang R H, Yang W G, Hu C Z, 1995, Elasticity theory of straight dislocation in quasicrystals, Phil Mag Lett, 72(5), 353-359.
Fan T Y, Guo L H, 2005, Final governing equation of plane elasticity of icosahedral quasicrystals, Phys Lett A, 341(5), 235-239.
Guo L H, Fan T Y, 2007, Solvability on boundary-value problems of elasticity of three-dimensional quasicrystals, Appl Math Mech, 28(8), 1061-1070.
Zhou WÂ M and Fan T Y, 2000, Axisymmetric elasticity problem of cubic quasicrystals, Chin Phys, 9(4), 294-303.
Fan T Y, Tang Z Y, Li L H, Li W, 2010, The strict theory of complex variable function method of sextuple harmonic equation and applications, J Math Phys, 51(5), 053519.
Zhu A Y, Fan T Y, 2008, Dynamic crack propagation in a decagonal Al-Ni-Co quasicrystal, J Phys Condens Matter, 20(29), 295217.
Dzyaloshinskii I E, Volovick G E, . Poisson brackets in condensed matter physics. Ann Phys (NY), 1980, 125(1): 67-97.
Zeng X ,Ungar G, Liu Y, Percec V, Dulcey A E and Hobbs JÂ K, 2004, Supramolecular dendritic liquid quasicrystals, Nature, 428, 157-159.
Takano K, 2005, A mesoscopic Archimedian tiling having a complexity in polymeric stars, J Polym Sci Pol Phys, 43, 2427-2432.
Hayashida K, Dotera T, Takano A, Matsushita Y, 2007, Polymeric quasicrystal : mesoscopic quasicrystalline tiling in ABC starpolymmers, Phys Rev Lett, 98, 195502 .
Talapin V D, Shevechenko E V, Bodnarchuk M I, Ye X C, Chen J and Murray C B, 2009, Quasicrystalline order in self-assembled binary nanoparticle superlattices, Nature, 461, 964-967.
Fischer S, Exner A, Zielske K, Perlich J, Deloudi S, Steuer W, Linder P and Foestor S, 2011, Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry, Proc Nat Ac Sci, 108, 1810-1814.
Fan T Y, 2016, Equation system of generalized hydrodynamics of soft-matter quasicrystals, Appl Math Mech, 37(4), 331-344.
Cheng H, Fan T Y, Sun JÂ J, Wei H, 2015, Possible soft-matter quasicrystals of 5- and 10-fold symmetries and hydrodynamics, Computational Materials Science, 205(7), 47-54.
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Fan, TY. (2016). Remarkable Conclusion. In: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer Series in Materials Science, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-10-1984-5_17
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