In this paper a multi-scaled diiusion-approximation theorem is proved so as to unify various applications in wave propagation in random media: transmission of optical modes through random planar waveguides; time delay in scattering for the linear wave equation; decay of the transmission coeecient for large lengths with xed output and phase diierence in weakly nonlinear random media. 1. Introduc...

The shortand long-scale behaviour of tangled wave vortices (nodal lines) in random three-dimensional wave fields is studied via computer experiment. The zero lines are tracked in numerical simulations of periodic superpositions of threedimensional complex plane waves. The probability distribution of local geometric quantities such as curvature and torsion are compared to previous analytical and...

The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random medium and the rough boundaries, and the second one which corresponds to the unperturbed Green functions describes the scattering by an homogeneous layer with ...

We analyze the solutions of the Schrödinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that the dynamics generates a non-trivial energy in the high frequencies, which do not homogenize – the high frequency component of the wave field remains random and...

We study the square-lattice XY model in the presence of random phase shifts. We consider two different disorder distributions with zero average shift and investigate the low-temperature quasi-long-range order phase which occurs for sufficiently low disorder. By means of Monte Carlo simulations we determine several universal quantities which are then compared with the analytic predictions of the...