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Stochastic interface dynamics in the Hele-Shaw cell.

Oleg Alekseev1

  • 1Department of Mathematics and Mechanics, Chebyshev Laboratory, Saint-Petersburg State University, 14th Line, 29b, 199178 Saint-Petersburg, Russia.

Physical Review. E
|September 11, 2019
PubMed
Summary
This summary is machine-generated.

A new stochastic model for Hele-Shaw cell interface dynamics generates complex, chaotic patterns. This research connects Laplacian growth to conformal field theory, introducing time-constant observables.

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Area of Science:

  • Complex Systems
  • Fluid Dynamics
  • Statistical Physics

Background:

  • Hele-Shaw cells exhibit complex interface dynamics.
  • Previous models often struggle with cusp formation and chaotic behavior.

Purpose of the Study:

  • Introduce a one-parametric stochastic regularized dynamics for Hele-Shaw cell interfaces.
  • Investigate the generation of complex patterns and chaotic dynamics.
  • Establish a connection between Laplacian growth and conformal field theory.

Main Methods:

  • Developed a stochastic aggregation model for short-distance regularization.
  • Analyzed interface dynamics, pattern formation (fjords and fingers).
  • Coupled conformal field theory to the stochastic growth process for long-time analysis.

Main Results:

  • The model stabilizes interface growth, preventing cusps and inducing chaotic dynamics.
  • Universal complex patterns with oil fjords and water fingers are generated.
  • Introduced time-constant observables (martingales) linked to Virasoro algebra representations.

Conclusions:

  • The stochastic regularization provides a novel approach to modeling Hele-Shaw dynamics.
  • A direct link between Laplacian growth and conformal Liouville field theory (c≥25) is proposed.
  • The martingales offer new tools for analyzing complex growth processes.