Predicting PDF tails in systems with logarithmic non-linearity

TL;DR

This paper analytically predicts power-law tails in the flux PDF of systems with logarithmic non-linearity, attributing broad, intermittent distributions to short-lived coherent structures called instantons.

Contribution

It introduces an analytical method to predict the power-law tails of flux PDFs in systems with logarithmic non-linearity, linking them to intermittency and instantons.

Findings

PDF tails are broader than Gaussian distributions.

Power-law behavior is analytically derived for flux PDFs.

Intermittency is caused by short-lived coherent structures (instantons).

Abstract

The probability density function (PDF) of flux $R$ is computed in systems with logarithmic non-linearity using a model non-linear dynamical equation. The PDF tails of the first moment flux are analytically predicted to be power law. These PDF tails are shown to be broader than a Gaussian distribution and are a manifestation of intermittency caused by short lived coherent structures (instantons).