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Related Experiment Video

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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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Stochastic waves in a Brusselator model with nonlocal interaction.

Tommaso Biancalani¹, Tobias Galla, Alan J McKane

¹Theoretical Physics Division, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom. tommaso.biancalani@postgraduate.manchester.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 21, 2011

Summary

This summary is machine-generated.

Intrinsic noise can create complex spatiotemporal patterns like Turing patterns and traveling waves in nonlocal models. This study develops a theory to predict and characterize these stochastic waves, validated by simulations.

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Area of Science:

Chemical kinetics
Nonlinear dynamics
Statistical physics

Background:

The Brusselator model is a classic example of reaction-diffusion systems exhibiting complex dynamics.
Nonlocal interactions can significantly alter pattern formation in chemical and biological systems.
Intrinsic noise is often considered a perturbation, but can also drive pattern formation.

Purpose of the Study:

To investigate the role of intrinsic noise in inducing spatiotemporal patterns within a nonlocal Brusselator model.
To develop a theoretical framework for predicting and characterizing stochastic waves.
To explore the broader implications of these findings for other complex systems.

Main Methods:

System-size expansion applied to the nonlocal Brusselator model.
Analytical calculation of power spectra for stochastic waves.
Validation of theoretical predictions through numerical simulations.

Main Results:

Intrinsic noise is demonstrated to induce Turing patterns and traveling waves.
The system-size expansion accurately predicts and characterizes these stochastic waves.
Analytical power spectra match simulation results, confirming the theory's validity.

Conclusions:

Nonlocal interactions combined with intrinsic noise can lead to emergent spatiotemporal phenomena.
The developed theoretical approach provides a powerful tool for analyzing stochastic waves.
Similar noise-induced patterns may occur in diverse fields like epidemiology and social dynamics.