Table of contents

Quantum field renormalisation group results of the theory of developed turbulence are reviewed. Background information about quantum field renormalisation theory, including operator expansion and the renormalisation of composite operators is given. As an example problem, the stochastic model of isotropic homogeneous turbulence is considered for which, using the renormalisation technique, the existence of infrared scaling with Kholmogorov dimensions is proved. The dimension of composite operators and the infrared asymptotic behaviour of various correlation functions are discussed, and numerical amplitude factors of scaling laws are calculated.

The state of the art of the problem of the analytical continuation of wave fields is reviewed. The problem is a multidisciplinary subject which involves radiophysics, acoustics, and optics on the one hand, and mathematical physics and the theory of differential equation, on the other. The qualitative aspects of the problem are examined. A computational algorithm for field singularities is given. The relation between the singularities and the 'computational catastrophes' of scattering models is discussed. To illustrate the theoretical material, numerous examples are discussed in great detail.

The state of the art of the Monte Carlo studies of randomly modulated optical waves in regular and randomly inhomogeneous nonlinear media is reviewed. A wide range of phenomena dealt with in nonlinear statistical optics are discussed, including self-phase noise pulse modulation, the self-action of partially coherent beams, the formation and instability of solitons, stimulated Raman scattering, intensive light beams in a turbulent atmosphere, and adaptive radiation focusing. Special attention is given to the justification of the phase screen model for a randomly inhomogeneous nonlinear continuum, and the numerical simulation of random light fields is discussed in detail.