Stats for this track
In 2 Groups
- User Image
ELECTRO - TECHNO - HOUSE - TECH ... Group for the eternal lovers of Electro - Techno - House - Tech House - Progressive house and Minimal (Tracks that are not electro,Techno,house,tech house, progressive and minimal will be removed)
- User Image
ELECTRONIC MUSIC WORLD The Planet Is Music
We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of non-local particle-particle interactions. We derive a self-similar linear wave operator describing the dynamics of a quasi-continuous linear chain of infinite length with a spatially self-similar distribution of nonlocal inter-particle springs. The self-similarity of the nonlocal harmonic particle-particle interactions results in a dispersion relation of the form of a Weierstrass-Mandelbrot function which exhibits self-similar and fractal features. We also derive a continuum approximation which relates the self-similar Laplacian to fractional integrals and yields in the low-frequency regime a power law frequency-dependence of the oscillator density.