Generalized randomly amplified linear system driven by gaussian noises: extreme heavy tail and algebraic correlation decay in plasma turbulence.

The extreme heavy tail and the power-law decay of the turbulent flux correlation observed in hot magnetically confined plasmas are modeled by a system of coupled Langevin equations describing a continuous time linear randomly amplified stochastic process where the amplification factor is driven by a superposition of colored noises which, in a suitable limit, generate a fractional Brownian motion. An exact analytical formula for the power-law tail exponent beta is derived. The extremely small value of the heavy tail exponent and the power-law distribution of laminar times also found experimentally are obtained, in a robust manner, for a wide range of input values, as a consequence of the (asymptotic) self-similarity property of the noise spectrum. As a by-product, a new representation of the persistent fractional Brownian motion is obtained.

On the Earnshaw and the Van den Tempel-Lucassen Compositional Viscoelastic Theories.

We consider a diffusion-controlled solute transfer and discuss the reasons to study the complete convective-diffusive equation to determine the coupling resonant domain between capillary and longitudinal waves in terms of viscoelastic compositional behavior. A perturbation of the surface tension due to solute transfer has two contributions. One is proportional to the surface area change while the other, not considered in the Van den Tempel-Lucassen theory, is due to the surface velocity. Copyright 2000 Academic Press.