**13. Acknowledgments**

The authors are very greatful to Dr.Omar López for helpful discussions and advice.

**18** 

*China* 

**Elasto-Hydrodynamics of** 

Tian You Fan1 and Zhi Yi Tang2

(1)

**Quasicrystals and Its Applications** 

*1Department of Physics, Beijing Institute of Technology, Beijing 2Southwest Jiaotong University Hope College, Nanchong, Sichuan* 

Quasicrystal as a new structure of solids as well as a new material, has been studied over twenty five years. The elasticity and defects play a central role in field of mechanical behaviour of the material, see e.g. Fan [1]. Different from crystals and conventional engineering materials, quasicrystals have two different displacement fields: phonon field <sup>123</sup> *uu u u* (,,) and phason field 123 *ww w w* (,,) , which is a new degree of freedom to condensed matter physics as well as continuum mechanics, this leads to two strain tensors

<sup>1</sup> ( )

 

*j i*

 , *<sup>i</sup> ij*

*w*

*ij* and *Hij* .

*j w*

(2)

(3)

*x*

*j i u u x x*

We call the first of equation (1) as phonon strain tensor, the second as phason strain tensor,

*ij ijkl kl ijkl kl ij ijkl kl klij kl C Rw*

in which *Cijkl* denotes the phonon elastic tensor, *Kijkl* the phason one, and *Rijkl* the phononphason coupling one, respectively. It is evident that the appearance of the new degree

In the dynamic process of quasicrystals problem presents further complexity. According to the point of view of Lubensky et al. [2,3], phonon represents wave propagation, while phason represents diffusion in the dynamic process. Following the argument of Lubensky et al., Rochal and Lorman [4] and Fan [1,5] put forward the equations of motion of

> 2 2 *ij i j*

*u t x*

*H Kw R*

 

2

The constitutive law is the so-called generalized Hooke's law as follows

freedom yields a great challenge to the continuum mechanics.

*ij*

respectively. The corresponding stress tensor is

**1. Introduction** 

quasicrystals as follows

such as

#### **14. References**

