D Generalized Hydrodynamics of Soft-Matter Quasicrystals
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摘要: 讨论了软物质准晶三维广义流体动力学.主要是给出了已经发现的和可能发现的第一类二维软物质准晶的动力学方程组,也简单地讨论了一下它们的解,以及这些解和固体准晶解的结果的巨大差别.Abstract: The 3D generalized hydrodynamics of soft-matter quasicrystals was investigated, and the governing equations for observed and possibly observed soft-matter quasicrystals were derived. The solving procedure for the equations was discussed briefly. Some results obtained reveal the gigantic dissimilarities between soft-matter quasicrystals and solid ones.
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[1] 范天佑. 软物质准晶广义流体动力学方程组[J]. 应用数学和力学, 2016,37(4): 331-344.(FAN Tian-you. Equation systems of generalized hydrodynamics for soft-matter quasicrystals[J]. Applied Mathematics and Mechanics,2016,37(4): 331-344.(in Chinese)) [2] 范天佑. 软物质第二类二维准晶广义流体动力学[J]. 应用数学和力学, 2017,38(2): 189-199.(FAN Tian-you. Generalized hydrodynamics for second 2D soft-matter quasicrystals[J]. Applied Mathematics and Mechanics,2017,38(2): 189-199.(in Chinese)) [3] ZENG Xiang-bing, Ungar G, LIU Yong-song, et al. Supramolecular dendritic liquid quasicrystals[J]. Nature,2004,428: 157-160. [4] Takano K, Kawashima W, Noro A, et al. A mesoscopic archimedian tiling having a complexity in polymeric stars[J]. Journal of Polymer Science Part B: Polymer Physics,2005,43(18): 2427-2432. [5] Talapin D V, Shevechenko E V, Bodnarchuk M I, et al. Quasicrystalline order in self-assembled binary nanoparticle superlattices[J]. Nature,2009,461: 964-967. [6] Fischer S, Exner A, Zielske K, et al. Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry[J]. Proceedings of the National Academy of Sciences of the United States of America,2011,108(5): 1810-1814. [7] YUE Kan, HUANG Ming-jun, Marson R, et al. Geometry induced sequence of nanoscale Frank-Kasper and quasicrystal mesophases in giant surfactants[J]. Proceedings of the National Academy of Sciences of the United States of America,2016,113(50): 14195-14200. [8] Lubensky T C, Ramaswamy S, Toner J. Hydrodynamics of icosahedral quasicrystals[J]. Physical Review B: Condensed Matter,1985,32(11): 7444-7452. [9] Lubensky T C. Symmetry, elasticity and hydrodynamics of quasicrystals[M]// Introduction to Quasicrystals . Jaric V M, ed. Boston: Academic Press, 1988: 199-280. [10] Lifshitz E M, Petaevskii L P. Statistical Physics Part 〖STBX〗2: Landau and Lifshitz Course of Theoretical Physics [M]. Vol 9. Oxford: Pergamon Press, 1980. [11] Wensink H H. Equation of state of a dense columnar liquid crystal[J]. Physical Review Letters,2004,93: 157801. [12] Dzyaloshinskii I E, Volovick G E. Poisson brackets in condensed matter physics[J]. Annals of Physics,1980,125(1): 67-97. [13] HU Cheng-zheng, WANG Ren-hui, DING Di-hua. Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals[J]. Reports on Progress in Physics,2000,63(1): 1-39. [14] 杨顺华, 丁棣华. 晶体位错理论基础[M]. 第2卷. 北京: 科学出版社, 1998.(YANG Shun-hua, DING Di-hua. Theoretical Foundations of Crystal Dislocation [M]. Vol 2. Beijing: Science Press, 1998.(in Chinese)) [15] FAN Tian-you. Mathematical Theory of Elasticity of Quasicrystals and Its Applications [M]. 2nd ed. Beijing: Science Press, 2016. [16] 范天佑. 固体与软物质准晶数学弹性与相关理论及应用[M]. 北京: 北京理工大学出版社, 2014.(FAN Tian-you. Mathematical Theory of Elasticity and Relevant Topics of Solid and Softmatter Quasicrystals and Its Applications [M]. Beijing: Beijing Institute of Technology Press, 2014.(in Chinese)) [17] Li X F, Fan T Y. Dislocations in the second kind two-dimensional quasicrystals of soft matter[J]. Physica B: Condensed Matter,2016,502(1): 175-180. [18] CHENG Hui, FAN Tian-you, WEI Hao. Solutions for hydrodynamics of solid quasicrystals with 5- and 10-fold symmetry[J]. Applied Mathematics and Mechanics(English Edition),2016,37(10): 1393-1404. [19] Metere A, Oleynikov P, Dzugutov M, et al. A smectic dodecagonal quasicrystal[J]. Soft Matter,2016,12(43): 8869-8876.
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