In this work, we present a statistical analysis of the wave motion through random media with perfect spatial disorder of inclusions. It is assumed that such a disorder can be tackled with the random potential function theory, whence the propagation of waves naturally turns to a diffusion process. The associated Itoô drift-diffusion process, and its Fokker-Planck equation are derived. It is found that the “ensemble” wave, i.e., the collective wave motion, fluctuates in space as a geometric Brownian motion. Finally, the effect of a double-well potential with random (vibrating) valleys is studied qualitatively by the Monte Carlo method. In practice, this situation occurs for high concentration and perfect dispersion of conductive/dielectric fillers, i.e., whose location and orientation are completely randomized.
Stochastic differential equation for wave diffusion in random media / Gradoni, Gabriele; Roberto, Pastore; Davide, Micheli; Moglie, Franco; MARIANI PRIMIANI, Valter; Mario, Marchetti. - STAMPA. - (2013), pp. 1176-1177. (Intervento presentato al convegno 013 International Conference on Electromagnetics in Advanced Applications (ICEAA) tenutosi a Torino (Turin), Italy nel 9-13 Sept. 2013) [10.1109/ICEAA.2013.6632429].
Stochastic differential equation for wave diffusion in random media
GRADONI, GABRIELE;MOGLIE, FRANCO;MARIANI PRIMIANI, Valter;
2013-01-01
Abstract
In this work, we present a statistical analysis of the wave motion through random media with perfect spatial disorder of inclusions. It is assumed that such a disorder can be tackled with the random potential function theory, whence the propagation of waves naturally turns to a diffusion process. The associated Itoô drift-diffusion process, and its Fokker-Planck equation are derived. It is found that the “ensemble” wave, i.e., the collective wave motion, fluctuates in space as a geometric Brownian motion. Finally, the effect of a double-well potential with random (vibrating) valleys is studied qualitatively by the Monte Carlo method. In practice, this situation occurs for high concentration and perfect dispersion of conductive/dielectric fillers, i.e., whose location and orientation are completely randomized.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.