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Related Experiment Videos

Stability of flow- and diffusion-distributed structures to inlet noise effects.

Pavel V Kuptsov1, Razvan A Satnoianu

  • 1Centre for Mathematical Science, City University, Northampton Square, London EC1V 0HB, United Kingdom. kupav@mail.ru

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
Summary

Noise can disrupt stationary flow- and diffusion-distributed structures (FDS) in reaction-diffusion-advection systems. However, increasing the flow rate restores these patterns, with stabilization depending on noise amplitude via a power-law relationship.

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Area of Science:

  • Chemical Engineering
  • Nonlinear Dynamics
  • Fluid Dynamics

Background:

  • Reaction-diffusion-advection systems can exhibit stationary flow- and diffusion-distributed structures (FDS) under constant inlet forcing.
  • These complex patterns are fundamental in understanding various chemical and biological processes.

Purpose of the Study:

  • To investigate the impact of noise on FDS in a reaction-diffusion-advection system.
  • To determine the conditions under which FDS can be restored despite noise-induced instabilities.
  • To analyze the relationship between flow rate, noise amplitude, and pattern stabilization.

Main Methods:

  • Simulations of a reaction-diffusion-advection model with stochastic forcing at the inlet.
  • Analysis of pattern stability using concepts from nonlinear dynamics, including Hopf bifurcations.

Related Experiment Videos

  • Quantification of the critical flow rate required for pattern restoration as a function of noise amplitude.

    • Main Results:

    • Constant forcing in reaction-diffusion-advection systems generates stable FDS.
    • Introduction of noise can destroy FDS through a noise-induced Hopf instability.
    • FDS patterns are restored above a critical flow rate, which exhibits a power-law dependence on noise amplitude.

    Conclusions:

    • Noise-induced instabilities can destabilize stationary patterns in driven systems.
    • Sufficiently high flow rates can stabilize these patterns against noise.
    • The critical flow rate for stabilization follows a power-law relationship with noise amplitude, offering insights into pattern formation and control in complex systems.