Dispersion relations and wave operators in self-similar quasicontinuous linear chains.

摘要: We construct self-similar functions and linear operators to deduce a variant of the Laplacian operator D'Alembertian wave operator. The exigence self-similarity as symmetry property requires introduction nonlocal particle-particle interactions. derive describing dynamics quasicontinuous chain infinite length with spatially distribution interparticle springs. harmonic interactions results in dispersion relation form Weierstrass-Mandelbrot function that exhibits fractal features. also continuum approximation, which relates fractional integrals, yields low-frequency regime power-law frequency-dependence oscillator density.