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Diffusing diffusivity model of a polymer moving on a spherical surface.

Xinyi Wu1, Daxin Nie1, Weihua Deng1,2

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Chaos (Woodbury, N.Y.)
|March 6, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a diffusing diffusivity (DD) model for polymer movement on a sphere. The model, using a coupled Langevin system, accurately predicts polymer behavior using Fokker-Planck and Feynman-Kac equations.

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Area of Science:

  • Polymer physics
  • Statistical mechanics
  • Theoretical chemistry

Background:

  • Polymer dynamics are often modeled using Brownian motion.
  • Fluctuating diffusion coefficients present unique challenges in modeling polymer movement.
  • Extending models to curved surfaces is crucial for understanding complex systems.

Purpose of the Study:

  • To extend the diffusing diffusivity (DD) model to a two-dimensional spherical surface.
  • To develop a theoretical framework for polymer dynamics on a sphere with fluctuating diffusivity.
  • To derive and validate governing equations for polymer position and functional observables.

Main Methods:

  • Developed a coupled Langevin system for polymer movement on a sphere.
  • Characterized the diffusion coefficient using a birth and death chain model.
  • Derived Fokker-Planck and Feynman-Kac equations for probability density functions (PDFs).
  • Employed Monte Carlo simulations and spectral methods for validation.

Main Results:

  • Successfully extended the DD model to a spherical surface.
  • Derived accurate Fokker-Planck and Feynman-Kac equations for the spherical DD model.
  • Achieved unification of numerical results from simulation and analytical methods.
  • Confirmed the correctness of the derived equations through cross-validation.

Conclusions:

  • The diffusing diffusivity model is effectively extended to spherical surfaces.
  • The derived Fokker-Planck and Feynman-Kac equations provide a robust framework for analyzing polymer dynamics.
  • The study validates the theoretical model through consistent numerical results.