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Updated: Feb 15, 2026

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Brownian systems with spatially inhomogeneous activity.

A Sharma1, J M Brader1

  • 1Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland.

Physical Review. E
|January 20, 2018
PubMed
Summary

We generalized the Green-Kubo approach for active particles to include spatial variations. This method accurately predicts particle orientation and density changes in inhomogeneous systems, validated by simulations.

Area of Science:

  • Soft Matter Physics
  • Statistical Mechanics
  • Theoretical Chemistry

Background:

  • The Green-Kubo approach is a standard method for calculating transport coefficients in bulk systems.
  • Previous work applied this method to bulk systems of spherically symmetric active particles.
  • Spatially inhomogeneous activity presents challenges for existing theoretical frameworks.

Purpose of the Study:

  • To generalize the Green-Kubo approach for active particles to systems with spatially inhomogeneous activity.
  • To develop a theoretical framework for predicting the spatial dependence of average particle orientation and density.
  • To validate theoretical predictions against simulation data.

Main Methods:

  • Generalization of the Green-Kubo formalism to incorporate spatial inhomogeneity in active particle systems.

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  • Analytical derivation of average particle orientation using the self part of the Van Hove function and a Gaussian approximation.
  • Application of dynamic density functional theory (DDFT) using analytical orientation results to approximate spatial density dependence.
  • Validation of theoretical predictions through Brownian dynamics simulations.

    • Main Results:

    • The generalized Green-Kubo approach successfully incorporates spatially inhomogeneous activity.
    • An accurate analytical expression for the spatial dependence of average particle orientation was derived.
    • Dynamic density functional theory, using the derived orientation, accurately approximates the spatial density dependence.
    • Theoretical predictions showed good agreement with Brownian dynamics simulation data.

    Conclusions:

    • The generalized Green-Kubo approach provides a powerful tool for studying active matter with spatial variations.
    • The developed analytical methods offer accurate predictions for particle orientation and density distributions.
    • This work bridges theoretical modeling and simulation for complex active matter systems.