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Instanton solutions in the problem of wrinkled flame-front dynamics
1Solid State Electronics Department, Research Institute of Physics, St.-Petersburg State University, St. Petersburg, Russia. volchen@cpt.univ-mrs.fr
Summary
Quantum-field theory methods reveal how wrinkling flame statistics are shaped by kink configurations. These kinks drive flame acceleration and cusp formation, offering insights into flame dynamics.
Area of Science:
- Fluid dynamics
- Combustion science
- Statistical physics
Background:
- Wrinkling flames in channels exhibit complex statistical properties.
- Understanding flame front dynamics is crucial for combustion control.
- Previous models often simplify flame front behavior.
Purpose of the Study:
- To investigate the statistical properties of wrinkling flame slopes.
- To apply quantum-field theory methods to flame propagation.
- To elucidate the mechanisms behind flame acceleration and cusp formation.
Main Methods:
- Utilizing quantum-field theory (QFT) techniques.
- Employing the WKB approximation in functional integrals.
- Analyzing field-force configurations related to Sivashinsky equation solutions.
Main Results:
- Identified a coupled field-force configuration as the main contributor to flame statistics.
- Linked this configuration to kinks between metastable pole solutions.
- Demonstrated that these kinks cause new cusp formation and power-law flame acceleration.
Conclusions:
- QFT methods provide a powerful framework for analyzing wrinkling flames.
- Kink dynamics are central to understanding flame front evolution and acceleration.
- The study discusses the asymptotic stability of the derived solutions.