A wavelet element method is developed to compute band structures of phononic crystals. It is based on combining biorthogonal wavelet systems with philosophy Of spectral element method. Biorthogonal spline wavelets on interval with boundary adaption are constructed. Boundary adaption of wavelet element is extended to first-order derivatives, due to which construction of basis functions that satisfy boundary conditions exactly is possible. The method takes advantage of structural features of phononic crystals and boundary conditions are satisfied exactly. Better accuracy and higher efficiency are obtained.

We present 2D and 3D discrete mathematical models for migratory response of endothelial cells inside and outside a metastasic tumor based on a physiological fact that some primary tumor can inhibit metastasic tumor growth quickly. In models we consider inhibitory effects of angiostatin excreted by primary tumor, chemotactic effects of TAF due to metastasic tumor and random movement of endothelial cells and simulate spatiotemporal evolution of microvascular network inside and outside the metastasic tumor. It shows that the angiostatin excreted by primary tumor has obviously inhibitory effects on vascular growth rates, bifurcation amount and development of microvascular network inside and outside the metastasic tumor. Inhibitory effects of angiostatin decrease revascularization of a metastasic tumor and suppress growth of the metastasic tumor in tumor therapy. It provides theoretical references for experimental research on clinical anti-angiogenesis.

Based on the principie of shooting method, an effective approach to the soiution of nonlinear eguations with boundary problem is proposed for modeling the Er-doped superfluorescent fiber sources (SFSs).The characteristics of SFS in doubie-pass backward configuration have been analyzed theoretically and well explained physically for the first time.