软物质准晶广义流体动力学方程组

范天佑

doi:10.3879/j.issn.1000-0887.2016.04.001

软物质准晶广义流体动力学方程组

doi: 10.3879/j.issn.1000-0887.2016.04.001

范天佑

北京理工大学物理学院, 北京 100081

基金项目: 国家自然科学基金(11272053)

详细信息

作者简介:
范天佑(1939—)，男，教授(E-mail: tyfan2013@163.com).

中图分类号: O35|O469
计量
- 文章访问数: 1786
- HTML全文浏览量: 294
- PDF下载量: 997
- 被引次数: 0
出版历程
- 收稿日期: 2016-01-22
- 修回日期: 2016-03-07
- 刊出日期: 2016-04-15

Equation Systems of Generalized Hydrodynamics for Soft-Matter Quasicrystals

FAN Tian-you

School of Physics, Beijing Institute of Technology,Beijing 100081, P.R.China

Funds: The National Natural Science Foundation of China(11272053)

摘要

摘要: 建立了软物质准晶广义流体动力学方程组，其基础为广义Langevin方程，推导方法为Poisson括号，它参考了固体准晶的广义流体动力学方程组，但是两者存在原则的不同.固体准晶的广义流体动力学方程组考虑了固体粘性与声子弹性和相位子弹性的相互作用，没有状态方程问题；软物质准晶广义流体动力学方程组考虑的是软物质流体声子与声子弹性和相位子弹性的相互作用，按物理学术语多出了一种元激发，而且必须考虑状态方程问题，这是一个新课题，又增加了难点.实际应用的结果发现，软物质准晶广义流体动力学方程组大大激活了广义流体动力学的效能，为软物质准晶学科的发展提供了一个数学模型，为探讨有关物理问题的时间空间演化提供了可操作的实际可行的求解体系和分析工具，求解的结果令人满意.
- 软物质 /
- 准晶 /
- 广义流体动力学 /
- 状态方程
Abstract: The equation systems of generalized hydrodynamics for soft-matter quasicrystals were established based on the Langevin equation, with the derivation method of Poisson bracket. The derivation was done with reference to the work on solid quasicrystals, for which there were only 2 kinds of elementary excitations: phonons and phasons. However, the generalized hydrodynamics for soft-matter quasicrystals was essentially different from that for solid ones. In the generalized hydrodynamics for solid quasicrystals the effects of solid viscosity and the interaction among viscosity, phonons and phasons were considered, without the need of state equations. Nevertheless, the fluid phonon and the interaction among fluid phonons, phonons and phasons in soft-matter quasicrystals were to be considered, where 3 kinds of elementary excitations, i.e. phonons, phasons and fluid phonons meant state equations were indispensable. This difficult problem was solved with the present method. The results show the correctness and efficiency of the theoretical analysis.
- soft-matter /
- quasicrystal /
- generalized hydrodynamics /
- state equation

HTML全文

参考文献(24)

[1]	Zeng X, Ungar G, Liu Y, Percec V, Dulcey A E, Hobbs J K. Supramolecular dendritic liquid quasicrystals[J].Nature,2004,428: 157-160.
[2]	Takano A, Kawashima W, Noro A, Isono Y, Tanaka N, Dotera T, Matsushita Y. A mesoscopic Archimedean tiling having a new complexity in an ABC star polymer[J].Journal of Polymer Science Part B: Polymer Physics,2005,43(18): 2427-2432.
[3]	Hayashida K, Dotera T, Takano A, Matsushita Y. Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers[J].Physical Review Letters,2007,98(19): 195502.
[4]	Talapin V D, Shevchenko E V, Bodnarchuk M I, Ye X, Chen J, Murray C B. Quasicrystalline order in self-assembled binary nanoparticle superlattices[J].Nature,2009,461: 964-967.
[5]	Fischer S, Exner A, Zielske K, Perlich J, Deloudi S, Steurer W, Linder P, Frster S. 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.
[6]	CHENG Hui, FAN Tian-you, SUN Jun-jun, HAO Wei. Possible soft-matter quasicrystals with 5- and 10-fold symmetries and hydrodynamics[J].Computational Materials Science,2015,105: 47-54.
[7]	Landau L. Theory of the superfluidity of helium II[J].Physical Review,1941,60(4): 356.
[8]	Pitaevskii L, Stringari S.Bose-Einstein Condensation [M]. USA: Oxford University Press, 2003.
[9]	Dalfovo F, Lastri A, Pricaupenko L, Stringari S, Treiner J. Structural and dynamical properties of superfluid helium: a density functional approach[J].Physical Review B,1995,52(2): 1193-1200.
[10]	Lifshitz E M, Pitaevskii L P.Statistical Physics [M]. Part 2. Oxford: Butterworth-Heinemann Ltd, 1980.
[11]	Wensink H H. Equation of state of a dense columnar liquid crystal[J].Physical Review Letters,2004,93(15): 157801.
[12]	XU Wen-sheng, LI Yan-wei, SUN Zhao-yan, AN Li-jia. Hard ellipses: equation of state, structure and self-diffusion[J].Journal of Chemical Physics,2013,139(2): 024501.
[13]	Debye P. Die eigentuemlichkeit der spezifischen waermen bei tiefen temperaturen[J].Arch de Genéve,1912,33(4): 256-258.
[14]	Sommerfeld A.Mechanik der Deformierbaren Medien [M]. Vorlesungen Ueber Theoretische Physik. VolⅡ. Wiesbaden: Diederich-Verlag, 1952.
[15]	FAN Tian-you, SUN Jun-jun. Four-phonon model of soft-matter quasicrystals for studying thermodynamics[J].Philosophical Magazine Letters,2014,94(2): 112-117.
[16]	Lubensky T C, Ramaswamy S, Toner J. Hydrodynamics of icosahedral quasicrystals[J].Physical Review B,1985,32(11): 7444-7452.
[17]	Dzyaloshinskii I E, Volovick G E. Poisson brackets in condensed matter physics[J].Annals of Physics,1980,125(1): 67-97.
[18]	范天佑. Poisson括号方法及其在准晶、液晶和一类软物质中的应用[J]. 力学学报, 2013,45(4): 548-559.(FAN Tian-you. Poisson bracket method and its applications to quasicrystals, liquid crystals and a class of soft matter[J].Chinese Journal of Theoretical and Applied Mechanics,2013,45(4): 548-559.(in Chinese))
[19]	HU Cheng-zheng, DING Di-hua, YANG Wen-ge, WANG Ren-hui. Possible two-dimensional quasicrystal structures with a six-dimensional embedding space[J].Physical Review B,1994,49(14): 9423-9427.
[20]	Li X F, Xie L Y, Fan T Y. Elasticity and dislocations in quasicrystals with 18-fold symmetry[J].Physics Letters A,2013,377(39): 2810-2814.
[21]	邢修三. 非平衡统计物理概论[R]. 2016.(XING Xiu-san. An introduction to nonequilibrium statistical physics[R]. 2016.(in Chinese))
[22]	Fan T Y, Mai Y W. Elasticity theory, fracture mechanics and some relevant thermal properties of quasicrystalline materials[J].Applied Mechanics Reviews,2004,57(5): 325-344.
[23]	FAN Tian-you.Mathematical Theory of Elasticity of Quasicrystals and Its Applications[M]. Beijing: Science Press, Heidelberg: Springer-Verlag, 2010.
[24]	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.Elasticity and Relevant Topics of Solid and Soft-Matter Quasicrystals and Its Applications [M]. Beijing: Beijing Institute of Technology Press, 2014.(in Chinese))