Surface dynamics is sometimes used to determine the rheological properties of soft materials. In typical data analyses, surface capillary waves are included without incorporating thermal noise. A phenomenological expression for the time-dependent power spectral density has been proposed to account for thermal noise and shown to agree well with experiment. In this paper, we investigate the surfa...

We derive simplified formulas for analyzing the moment stability of stochastic parametrically forced linear systems. This analysis extends the results in [3], where, assuming the stochastic excitation is small, the stability of such systems was computed using a weighted sum of the extended power spectral density over the eigenvalues of the unperturbed operator. In this paper, we show how to con...