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Fast reactions occurring in times shorter than the time needed to mix reactants pose a unique challenge for investigation. In a liquid-phase continuous-flow system, reactants A and B are swiftly pushed into the mixing chamber, where mixing occurs within 1 ms. The reaction mixture then flows through an observation tube, and one measures light absorption to determine species concentrations at various points of the tube. This method is most appropriate when relatively large volumes of reactants...
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Transient localized patterns in noise-driven reaction-diffusion systems.

Inbal Hecht1, David A Kessler, Herbert Levine

  • 1Center for Theoretical Biological Physics, University of California San Diego, La Jolla, California 92093-0319, USA.

Physical Review Letters
|May 21, 2010
PubMed
Summary
This summary is machine-generated.

Noise can trigger brief, localized activation in excitable systems. This study demonstrates how these spatiotemporal patches arise from reaction-diffusion equations, inspired by biological cell membrane excitability.

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Area of Science:

  • Complex Systems
  • Mathematical Biology
  • Nonlinear Dynamics

Background:

  • Excitable systems exhibit transitions between quiescent and active states.
  • External noise can induce these transitions, leading to transient activation.
  • Understanding localized activation is crucial in biological and physical systems.

Purpose of the Study:

  • To investigate the emergence of localized spatiotemporal activation patches in excitable media.
  • To determine the conditions under which noise-induced transitions occur locally.
  • To connect theoretical findings to biological observations of transiently excited cell membranes.

Main Methods:

  • Analysis of reaction-diffusion equations governing excitable media.
  • Investigation of parameter ranges supporting localized solutions.
  • Theoretical modeling of noise-induced phenomena in spatially extended systems.

Main Results:

  • Noise can indeed induce localized, time-limited transitions to active states.
  • Spatiotemporal patches of activation emerge in specific parameter regimes.
  • The existence of unstable localized solutions is key to this phenomenon.

Conclusions:

  • Localized activation patches can be generated by noise in excitable media.
  • This mechanism provides a theoretical framework for transient biological excitability.
  • The study highlights the role of reaction-diffusion dynamics in complex system behavior.