Three dimensional diffusion with helical persistence

TL;DR

This paper models three-dimensional persistent diffusion using Frenet--Serret equations, deriving a Fokker--Planck equation, effective diffusion constant, and correlation expressions, highlighting the complexity of 3D diffusion processes.

Contribution

It introduces a novel formulation of 3D persistent diffusion based on Frenet--Serret equations, deriving key equations and explicit correlation expressions.

Findings

Derived a Fokker--Planck equation for 3D persistent diffusion

Calculated the effective diffusion constant in 3D

Provided explicit expressions for tangent-normal-binormal correlations

Abstract

We formulate the the problem of persistent diffusion in three dimensions from the perspective of the Frenet--Serret equations. In contrast to one and two dimensional systems, in three dimensions persistent diffusion is, in general, a third order process. In this paper we derive a Fokker--Planck equation for the process and we calculate its effective diffusion constant. We also provide expressions for the asymptotic average displacement of the walk, as well as explicit expressions for the Fourier--Laplace transform of the correlations between the tangent, normal and binormal vectors of the motion.