Community overlays upon real-world complex networks

An approximation for the dynamic structure factor S(q, ω) of the linear harmonic chain with periodic boundary conditions is obtained from a recurrence relation approach. It is compared with (numerically) exact results for S(q, ω). Explicit expressions for the moments of the structure factor are obtained from the short time expansion up to order n = 12. For the long-wavelength as well as the deep-inelastic limit, simple expressions are derived permitting to some extent analytic results for S(q, ω). Introducing a linear regression, an approximation scheme is defined which shows excellent agreement with the numerical results.