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Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Standing wave-like patterns in the Gray-Scott model.

Igal Berenstein1

  • 1Non-Linear Physical Chemistry Unit, Université Libre de Bruxelles (ULB), Campus Plaine, C.P. 231, B-1050 Brussels, Belgium.

Chaos (Woodbury, N.Y.)
|June 29, 2015
PubMed
Summary
This summary is machine-generated.

Standing wave patterns emerge in the Gray-Scott model by combining defect-mediated turbulence with Turing instability. Similar patterns are observed in the Oregonator model under comparable conditions.

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Area of Science:

  • Chemical kinetics
  • Pattern formation in reaction-diffusion systems

Background:

  • Reaction-diffusion systems exhibit complex spatio-temporal patterns.
  • Defect-mediated turbulence and Turing instability are key phenomena in pattern formation.

Purpose of the Study:

  • To investigate the emergence of standing wave-like patterns in the Gray-Scott model.
  • To explore the role of Turing instability (driven by differential or cross-diffusion) in pattern formation.
  • To compare findings with the Oregonator model.

Main Methods:

  • Simulations of the Gray-Scott reaction-diffusion model.
  • Analysis of pattern formation under conditions promoting defect-mediated turbulence and Turing instability.
  • Comparative analysis with the Oregonator model.

Main Results:

  • Standing wave-like patterns were successfully generated in the Gray-Scott model.
  • These patterns arise from the interaction between defect-mediated turbulence and Turing instability.
  • The Oregonator model also produced similar standing wave patterns under analogous conditions.

Conclusions:

  • The interplay between different instability mechanisms can lead to complex emergent patterns.
  • The Gray-Scott and Oregonator models share similarities in pattern formation under specific conditions.
  • This study contributes to understanding pattern dynamics in reaction-diffusion systems.