Self-excitation of a nonlinear scalar field in a random medium.
We discuss the evolution in time of a scalar field under the influence of a random potential and diffusion. The cases of a short-correlation in time and of stationary potentials are considered. In a linear approximation and for sufficiently weak diffusion, the statistical moments of the field grow exponentially in time at growth rates that progressively increase with the order of the moment; this indicates the intermittent nature of the field. Nonlinearity halts this growth and in some cases can destroy the intermittency. However, in many nonlinear situations the intermittency is preserved: high, persistent peaks of the field exist against the background of a smooth field distribution. These widely spaced peaks may make a major contribution to the average characteristics of the field.
Zeldovich
Y B
YB
Institute of Physical Problems, Academy of Sciences, Moscow, U.S.S.R.
Molchanov
S A
SA
Ruzmaikin
A A
AA
Sokoloff
D D
DD