Nonlinear dynamics of fluctuations in a marginally-stable self-gravitating system

Abstract

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity σ, ν, respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values δσ, δν for modeling such fluctuations. Perturbed values τ ^′ _i = τ _i + δτ _i ,v ^′ _i = _i + δv _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (〈δτ〉= 〈δv〉 =0,〈δτ²〉 =〈δv ²〉 = 10⁻⁸) grow many times in marginally-stable state.