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Wave-number selection in pattern-forming systems.

S Saxena1, J M Kosterlitz1

  • 1Department of Physics, Brown University, Providence, Rhode Island 02912, USA.

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Summary
This summary is machine-generated.

Noise is key for wave-number selection in pattern-forming systems. Our study shows a unique wave number state emerges over time, regardless of noise strength or initial conditions, confirming noise

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Wave-number selection in pattern-forming systems is a complex problem.
  • External noise has been proposed as a potential mechanism for selection.

Purpose of the Study:

  • To investigate the role of noise in wave-number selection.
  • To explore the long-time behavior of pattern-forming systems under noise.

Main Methods:

  • Conducted extensive numerical simulations.
  • Utilized a fast spectral method for integration.
  • Studied the noisy stabilized Kuramoto-Sivashinsky equation for large system sizes and long times.

Main Results:

  • Identified a unique wave number state with the highest probability at very long times.
  • Observed that this selected state is independent of noise strength.
  • Confirmed the state's independence from initial conditions.

Conclusions:

  • Noise acts as a robust mechanism for state selection in pattern-forming systems.
  • The findings provide a convincing case for noise-induced wave-number selection.
  • This research advances understanding of pattern formation dynamics.