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Active fluids, like microtubule systems, create fractal patterns. A new model explains this fractal generation through local compressibility and periodic density variations, revealing a power-law decay in their structure.

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Area of Science:

  • Physics
  • Soft Matter Physics
  • Complex Systems

Background:

  • Active fluids, composed of self-propelled agents, exhibit complex emergent behaviors.
  • Microtubule-based active nematics, driven by kinesin motors, are a key experimental model for active fluids.
  • These systems display chaotic advection and fractal patterns in nematic contours.

Purpose of the Study:

  • To characterize the fractal structure in microtubule-based active nematics using power spectrum analysis.
  • To investigate the underlying physical mechanisms responsible for fractal generation in these systems.
  • To develop and validate a mathematical model that explains the observed fractal properties.

Main Methods:

  • Experimental characterization of fractal patterns using power spectrum analysis (k-β decay).
  • Development of a physically inspired mathematical model incorporating local compressibility and periodic density variations.
  • Linearization of the model to derive analytic relationships between fractal parameters and system properties.

Main Results:

  • The power spectrum of nematic contours decays as k-β, with β varying across experimental conditions.
  • The fractal parameter β is found to be constant in time for given experimental parameters.
  • The proposed mathematical model successfully reproduces the experimentally observed power-law decay.

Conclusions:

  • Fractal patterns in active nematics arise from a subtle interplay of local compressibility and large-scale density fluctuations.
  • The derived model provides a quantitative link between system compressibility and the observed fractal scaling (β).
  • This work offers fundamental insights into the physics of pattern formation in active matter systems.