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Running and Tumbling Localized Structures: A Non-Brownian Motion.

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Summary
This summary is machine-generated.

Localized structures in noisy systems exhibit complex movement patterns. Our study reveals a transition from diffusive to ballistic motion and back, explained by a minimal model.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Macroscopic systems can exhibit particle-like solutions.
  • Spontaneous symmetry-breaking leads to directional movement.
  • Random fluctuations can induce running and tumbling behaviors.

Purpose of the Study:

  • Investigate the running and tumbling dynamics of localized structures.
  • Analyze pattern formation in a one-dimensional model with noise.
  • Understand the statistical behavior of these structures.

Main Methods:

  • Observation of localized structures in a prototype model.
  • Statistical examination of dynamics, focusing on mean square displacement over time.
  • Derivation of a minimal model for structure position and velocity.

Main Results:

  • Observed initial diffusive behavior in mean square displacement.
  • Identified a subsequent transition to ballistic motion.
  • Noted a final return to diffusive behavior.
  • Developed a minimal model explaining these dynamics.

Conclusions:

  • The running and tumbling of localized structures are driven by noise and symmetry-breaking.
  • The observed mean square displacement transitions are characteristic of these dynamics.
  • A minimal model successfully captures the underlying physics of localized structure movement.