Weak Spatial Dispersion of Elastic Waves in Anisotropic Solids

该提案寻求资金，以便将波传播和物理声学方面的国际权威带到英国进行为期四个月的两次访问。特别是，我们的目标是调查波在各向异性弹性介质，具有微观结构的传播。纤维夹杂物等微观结构的存在导致波速取决于波数，这通常称为空间色散。要考虑的特定类型的波是波长与特定微结构的典型尺寸相比较长的那些波。对于这样的波，由微结构引起的空间色散将平滑与相关联的非色散介质相关联的波前处的奇点。使用各种数学方法（奇异摄动，傅立叶型积分和突变理论）以前开发和利用的英国队，预计该项目将导致一个完整的分类

This proposal seeks finance to bring over to the UK a leading international authority in waves propagation and physical acoustics for two visits totalling four months. In particular, we aim to investigate the propagation of waves in anisotropic elastic media which possess a micro-structure. The existence of a micro-structure, such as a fibrous inclusion, lead the wave speed being dependent on wave number, this usually being termed spatial dispersion. The specific type of waves to be considered are those for which the wavelength is long compared to a typical dimension of the particular micro-structure. For such waves, the spatial dispersion brought about by the micro-structure will smooth the singularities at the wave fronts associated with the associated non-dispersive media. Using various mathematical methods (singular perturbation, Fourier-type integrals and Catastrophe Theory) previous developed and exploited by the UK team, it is envisaged that the project will result in a complete classification