Growth of Vector Fields in Random Media
Time: 2023-09-18
Published By: Wenqiong Li
Speaker(s): Egor, Illarionov (Moscow State University)
Time: 14:00-15:00 September 19, 2023
Venue: Room 29, Quan Zhai, BICMR
Instabilities in random media often arise in various branches of physics, in particular, in the context of astrophysical magnetohydrodynamics (MHD). To be specific, one can discuss them, say, in the context of magnetic field self-excitation in celestial bodies, namely, the dynamo theory. As early as 1964, Zeldovich proposed a simple model that mimics a lot of basic properties of instabilities in random media and is simple enough for analytical investigation. The model qualitatively describes how the intermittent structure of the universe (i.e. rare mass concentrations represented in the model by random curvature fluctuations) can lead to the systematic divergence of the two initially close trajectories of light. In the series of later publications this model was formulated in the precise mathematical terms. More detailed, the problem was formulated in terms of the Jacobi equation with the random curvature parameter. Various assumptions on the distribution of the curvature parameter and its memory time lead to a wide bulk of practical models. In the seminar we will discuss the mathematical aspects of these models (which reduce to the product of random matrices) and the physical consequences.
