具有分形分散律的链
Chains with Fractal Dispersion Law
摘要：
考虑了具有长程相互作用的链。相互作用被定义为使得每个第n个粒子仅与数目为n+a（m）和n-a（m）的链粒子相互作用，其中m= 1，2，3，.并且a（m）是整数值函数。指数型函数a（m）=b^m，其中b= 2，3，.，讨论了得到了相应的链振动拟微分方程。所建议的链的色散规律描述的Weierstrass和Weierstrass-Mandelbrot函数。
英文摘要：
Chains with long-range interactions are considered. The interactions are defined such that each nth particle interacts only with chain particles with the numbers n+a(m) and n-a(m), where m=1,2,3,... and a(m) is an integer-valued function. Exponential type functions a(m)=b^m, where b=2,3,.., are discussed. The correspondent pseudodifferential equations of chain oscillations are obtained. Dispersion laws of the suggested chains are described by the Weierstrass and Weierstrass-Mandelbrot functions.
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