Generalized treatment for diffusion waves

Abstract

Intended for teaching purposes, the phenomenon of diffusion in the presence of periodical sources is described, taking into account a characteristic operator, $\hat {F}(t)$, leading to a generalized hyperbolic equation. The essential features of the accompanying harmonic flux are presented. For this purpose the solution to the problem is interpreted in terms of diffusion waves, a peculiar class of waves with complex wave numbers whose generation, propagation and detection constitute the basis of modern analytical techniques able to measure optical and transport properties of materials in the condensed or gaseous phase. A generalized mathematical equation describing this kind of waves is shown and the existence of critical modulation frequencies, at which the diffusive fluxes change their behaviour, is demonstrated for different physical phenomena involving diffusion waves. The dispersion equation for diffusion waves is given, and different particular cases in modulation frequency ``spectrum'' are discussed.