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Front propagation up a reaction rate gradient.

Elisheva Cohen1, David A Kessler, Herbert Levine

  • 1Department of Physics, Bar-Ilan University, Ramat-Gan IL52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
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This study investigates particle number reaction-diffusion systems with a reaction rate gradient. We found that front velocity diverges with infinite particle density, influenced by lattice diffusion effects.

Area of Science:

  • Physics
  • Physical Chemistry
  • Nonlinear Dynamics

Background:

  • Reaction-diffusion systems are fundamental models in various scientific fields.
  • Previous studies explored fronts in these systems, but the role of fluctuations and density dependence requires further investigation.
  • Finite particle number effects and reaction rate gradients introduce complexities in front dynamics.

Purpose of the Study:

  • To analyze the behavior of fronts in finite particle number reaction-diffusion systems with a reaction rate gradient.
  • To investigate the influence of fluctuations and particle density on front velocity.
  • To derive an analytic approximation for front velocity dependence on bulk particle density.

Main Methods:

  • Utilizing reaction-diffusion equations to model the system.

Related Experiment Videos

  • Implementing a cutoff in the reaction rate below a critical density to represent fluctuations.
  • Employing an approximate analytic treatment for large particle densities.
  • Analyzing the impact of nearest-neighbor hopping on a lattice for diffusion.

    • Main Results:

    • An analytic approximation for front velocity dependence on bulk particle density was derived.
    • The study confirms that front velocity diverges in the infinite density limit.
    • The specific implementation of diffusion, such as lattice hopping, significantly affects the nature of this divergence.

    Conclusions:

    • Fluctuations, particularly those arising from finite particle numbers and reaction rate cutoffs, play a crucial role in front dynamics.
    • Front velocity in these systems exhibits a divergence at infinite bulk particle density.
    • The underlying diffusion mechanism, like lattice-based hopping, is essential in determining the characteristics of this velocity divergence.