软物质准晶广义流体动力学的一个应用——圆柱绕流的近似解

范天佑

doi:10.21656/1000-0887.370251

软物质准晶广义流体动力学的一个应用——圆柱绕流的近似解

doi: 10.21656/1000-0887.370251

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; O753^+.3
计量
- 文章访问数: 1212
- HTML全文浏览量: 181
- PDF下载量: 519
- 被引次数: 0
出版历程
- 收稿日期: 2016-08-14
- 修回日期: 2016-09-29
- 刊出日期: 2017-03-15

An Application of the Generalized Hydrodynamics for Soft-Matter Quasicrystals—Flow Past a Cylinder

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: 文中报道了笔者建议的软物质准晶广义流体动力学的一个应用——软物质准晶圆柱绕流的近似解.人们熟知,在普通流体动力学中, 二维圆柱绕流问题遇到很大的困难,Stokes求解它,未能成功,这就是著名Stokes佯谬.为了克服这一困难, Oseen分析了原因不在边界条件的提法,也不在Stokes的求解,问题出在Navier-Stokes方程, 他对方程进行了修改, 得到了二维绕流问题的有物理意义的近似分析解.本文借助于Oseen的方法讨论12次对称软物质准晶广义流体动力学二维绕流问题.由于问题比普通流体动力学复杂得多,严格的求解,在目前的条件下是根本不可能的.笔者提出一种近似方法——交替程序去构造其零级近似解,并且把该结果用于软物质准晶的位错问题.
- 软物质 /
- 准晶 /
- 广义流体动力学 /
- StokesOseen流 /
- 近似解 /
- 位错
Abstract: An application of the generalized hydrodynamics for soft-matter quasicrystals with 12-fold symmetry—flow past a cylinder, was demonstrated by means of an alternating procedure, and a zeroth-order approximate analytic solution was obtained, in which the classical Oseen solution was used. The flow velocity field and the phonon stress field were approximately determined, and the possible solution of the phason stress field was also discussed. At last a possible modification to dislocation of soft-matter quasicrystals due to the present solution was considered.
- soft matter /
- quasicrystal /
- generalized hydrodynamics /
- Stokes-Oseen flow /
- approximate solution /
- dislocation

HTML全文

参考文献(13)

[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]	ZENG Xiang-bing, Ungar G, LIU Yong-song, et al. Supramolecular dendritic liquid quasicrystals[J]. Nature,2004,428: 157-160.
[3]	Takano A, 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.
[4]	Hayashida K, Dotera T, Takano A, et al. Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers[J]. Physical Review Letters,2007,98: 195502. doi: 10.1103/PhysRevLett.98.195502.
[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]	FAN Tian-you. Mathematical Theory of Elasticity of Quasicrystals and Its Applications[M]. Beijing: Science Press, 2010.
[8]	Oseen C W. ber die Stokes’ sche formel, und über eine verwandte Aufgabe in der Hydrodynamik[J]. Arkiv f?r Matematik, Astronomi och Fysik,1910,6(29).
[9]	Sleozkin N A. Incompressible Viscous Fluid Dynamics [M]. Chapter 7. Moscow: Gostehizdat Press, 1959.(in Russian).
[10]	Kochin N E, Kibel’ I A, Rose N V. Theoretical Fluid Mechanics [M]. Vol2. Moscow: Governing Press of Physics-Mathematics, 1963: 516-534.(in Russian)
[11]	FAN Tian-you. Generalized Dynamics of Soft-Matter Quasicrystals—Mathematical Models and Solutions [M]. Beijing: Beijing Institute of Technology Press, 2017.
[12]	Li X F, Fan T Y. Dislocations in the second kind two-dimensional quasicrystals of soft matter[J]. Physica B: Physics of Condebsed Matter,2016,502: 175-180.
[13]	Cheng H, Fan T Y, Wei H. Characters of deformation and motion of soft-matter quasicrystals[J]. Results in Physics,2016.