ABSTRACT
Heeding the above warning, we now switch to a field where thermodynamics is not of central importance: waves in random media, also called stochastic wave propagation. That research activity, fast growing since the middle of the twentieth century, has primarily been motivated by various problems arising in acoustics, atmospheric physics, geophysics, and composite materials, see the reviews and books of Chernov (1960), Frisch (1968), Dence and Spence (1970), Uscinski (1977), Sobczyk (1985, 1986), Rytov et al. (1987), Papanicolaou (1998). Mathematical problems in all these applications have typically been set up as ordinary of partial differential equations on random fields with either discrete or continuous realizations. A key characteristic of random fields has been the correlation length, and most studies have focused on the most tractable situations of wavelengths being either much smaller or much larger than the typical size of heterogeneity; recall Section 2.2 in Chapter 2. Generally speaking, in stochastic wave propagation we must have three length scales: (1) the typical propagation distances Lmacro; (2) the typical wavelength λ or wavefront thickness L ; and (3) the typical size of inhomogeneity d.
