Scalar probability density function mixing models need not comply with the linearity and independence hypothesis

TL;DR

This paper argues that scalar probability density function mixing models do not need to adhere to linearity and independence assumptions, as these properties are relaxed when using conditional expected values in diffusive processes.

Contribution

It challenges the traditional linearity and independence hypotheses in PDF mixing models, proposing that these assumptions are not necessary when considering conditional expectations.

Findings

Linearity and independence are not required in PDF models.

Conditional expected values relax these properties.

Models can be more flexible without these constraints.

Abstract

In a mixture of scalar fields undergoing diffusive processes governed by Fick's law, the concentration at each point evolves linearly in the concentrations at all points and independently from the other concentrations, when one considers a finite differences integration of their evolution equations. However, these properties must not necessarily be enforced in probability density function models, since they are relaxed when conditional expected values are taken.