Skip to main content

NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.

Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.

U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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

Published

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

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 7, 2025)

Issues

If you have any questions about this publication or are having problems accessing it, please contact [email protected].

Created October 13, 2014, Updated June 2, 2021
Was this page helpful?