Dynamics of distributed sources

The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the Lagrangian invariants to dynamics. Possible applications of distributed sources and sinks to geophysical fluid dynamics and to the cosmology are indicated.Comment: 3 page

Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

A parametric oscillator with damping driven by white noise is studied. The mean square displacement (MSD) in the long-time limit is derived analytically for the case that the static force vanishes, which was not treated in the past work \cite{tashiro07}. The formula is asymptotic but is applicable to a general periodic function. On the basis of this formula, some periodic functions reducing MSD remarkably are proposed

Spectrum of pressure fluctuations in a turbulent flow

Spectrum of pressure fluctuations in turbulent flo