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Updated: Oct 17, 2025

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
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Adaptive Brownian Dynamics.

Florian Sammüller1, Matthias Schmidt1

  • 1Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany.

The Journal of Chemical Physics
|October 9, 2021
PubMed
Summary
This summary is machine-generated.

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This study introduces adaptive Brownian Dynamics (BD) simulations using an embedded Heun-Euler integrator. This novel approach enhances performance and stability for complex systems by optimizing simulation timesteps.

Area of Science:

  • Computational physics
  • Molecular dynamics
  • Statistical mechanics

Background:

  • Traditional Brownian Dynamics (BD) simulations face performance and stability challenges, particularly with non-adaptive timestepping methods like Euler-Maruyama.
  • Simulating complex systems often involves concurrent slow and fast processes, demanding efficient and accurate computational approaches.

Purpose of the Study:

  • To present a novel framework for performant Brownian Dynamics (BD) many-body simulations utilizing adaptive timestepping.
  • To address the limitations of conventional non-adaptive BD methods in handling complex systems and long-time simulations.

Main Methods:

  • Implementation of an embedded Heun-Euler integrator for propagating overdamped coupled Langevin equations.
  • Development of a local error estimation for adaptive stepsize control, including acceptance/rejection criteria.

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  • Utilizing rejection sampling with memory (Rackauckas and Nie) to avoid bias in random forces, ensuring correct random process generation.

    • Main Results:

    • The adaptive BD framework demonstrates improved performance and stability compared to conventional non-adaptive BD.
    • Test cases involving Lennard-Jones fluids in bulk and confinement show the adaptive method's superiority.
    • The approach effectively manages issues arising from concurrent slow and fast processes in simulations.

    Conclusions:

    • The proposed adaptive timestepping framework offers a significant advancement for Brownian Dynamics simulations.
    • This method is expected to be particularly beneficial for long-time simulations of complex systems, including non-equilibrium scenarios.
    • The adaptive BD approach enhances computational efficiency and accuracy for molecular simulations.