Nonparametric Estimates of Drift and Diffusion Profiles via Fokker-Planck Algebra

Published

October 13, 2014

Author(s)

Steven P. Lund, Michael W. Halter, Joseph B. Hubbard

Abstract

Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker–Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

Citation

Journal of Physical Chemistry B

Volume

118

Issue

44

Pub Type

Journals

Download Paper

https://doi.org/10.1021/jp5084357

Keywords

free-energy landscape, relaxation kinetics

Citation

Lund, S. , Halter, M. and Hubbard, J. (2014), Nonparametric Estimates of Drift and Diffusion Profiles via Fokker-Planck Algebra, Journal of Physical Chemistry B, [online], https://doi.org/10.1021/jp5084357 (Accessed October 28, 2025)