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Diffusion at finite speed and random walks.

Joseph B Keller1

  • 1Department of Mathematics, Stanford University, Stanford, CA 94305-2125, USA. keller@math.standford.edu

Proceedings of the National Academy of Sciences of the United States of America
|January 22, 2004
PubMed
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This study resolves the paradox of infinite-speed diffusion by proposing a modified diffusion equation. The new model accurately describes diffusion as a random walk with finite-speed steps, ensuring physical realism.

Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Classical diffusion models assume infinite propagation speed, contradicting physical principles.
  • The random walk model, a basis for diffusion, involves discrete steps at finite speeds.

Purpose of the Study:

  • To resolve the paradox between infinite-speed diffusion and finite-speed random walks.
  • To derive a modified diffusion equation that incorporates finite speed.

Main Methods:

  • Analysis of the random walk process at the microscopic level.
  • Mathematical derivation of a new diffusion equation based on finite-step speeds.

Main Results:

  • A modified diffusion equation is derived, accounting for finite step speeds.

Related Experiment Videos

  • The paradox of infinite speed in diffusion is resolved within the new framework.

    • Conclusions:

    • The derived modified diffusion equation provides a more physically accurate description of diffusion processes.
    • This work reconciles the conceptual discrepancy in classical diffusion theory.