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Related Experiment Videos

Viscosity in the escape-rate formalism.

S Viscardy1, P Gaspard

  • 1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, Code Postal 231, B-1050 Brussels, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

We introduce a novel method to calculate shear viscosity using chaotic dynamics and fractal dimensions. This approach accurately models viscosity in systems like colliding disks, aligning with established formulas.

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Area of Science:

  • Statistical Mechanics
  • Dynamical Systems Theory
  • Non-equilibrium Physics

Background:

  • Shear viscosity is a fundamental property of fluids, crucial for understanding fluid dynamics.
  • Traditional methods for calculating shear viscosity include Green-Kubo and Einstein-Helfand formulas.
  • The relationship between chaotic dynamics and transport coefficients like viscosity is an active area of research.

Purpose of the Study:

  • To develop and apply a novel method for computing shear viscosity.
  • To connect shear viscosity to the fractal properties of microscopic dynamics.
  • To validate the proposed method using a minimal model system.

Main Methods:

  • Application of the escape-rate formalism.
  • Formulation of a first-passage problem for the Helfand moment.

Related Experiment Videos

  • Analysis of fractal repeller dimensions generated by absorbing boundaries.
  • Utilizing the Bunimovich-Spohn minimal model (two hard disks on a torus).

    • Main Results:

    • Shear viscosity is computed in terms of chaotic properties and fractal dimensions.
    • The fractal dimensions of the repeller are directly linked to shear viscosity and Lyapunov exponent.
    • The method yields values in excellent agreement with Green-Kubo and Einstein-Helfand formulas for the Bunimovich-Spohn model.

    Conclusions:

    • The escape-rate formalism provides an effective framework for calculating shear viscosity from microscopic chaotic dynamics.
    • Fractal properties of absorbing boundary-generated repellers offer a new route to determining transport coefficients.
    • This approach offers a complementary perspective to existing methods for viscosity computation.