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. © 2013 IEEE.
Stochastic differential equation for wave diffusion in random media / Gradoni, G.; Micheli, Davide; Moglie, F.; Primiani, V. Mariani; Marchetti, Mario; Pastore, Roberto. - ELETTRONICO. - (2013), pp. 1176-1177. (Intervento presentato al convegno 2013 15th International Conference on Electromagnetics in Advanced Applications, ICEAA 2013 tenutosi a Turin; Italy nel September 9-13, 2013) [10.1109/ICEAA.2013.6632429].
Stochastic differential equation for wave diffusion in random media
MICHELI, DAVIDE;MARCHETTI, Mario;PASTORE, Roberto
2013
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. © 2013 IEEE.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.