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Stochastic bifurcations in a prototypical thermoacoustic system
E A Gopalakrishnan1, J Tony1, E Sreelekha1
1Department of Aerospace Engineering, IIT Madras, Chennai, India.
Physical Review. E
|September 15, 2016
Summary
Noise can suppress bistable zones in thermoacoustic systems, preventing stochastic bifurcations. This study identifies parameter regimes for phenomenological bifurcations using amplitude distributions.
Area of Science:
- * Nonlinear dynamics
- * Thermoacoustics
- * Statistical physics
Background:
- * Thermoacoustic systems can exhibit nonlinear self-excited oscillations.
- * Bistable oscillators possess two stable states, influenced by system parameters.
- * Noise can alter the behavior and stability of nonlinear systems.
Purpose of the Study:
- * To investigate the influence of noise on a prototypical thermoacoustic system.
- * To identify the occurrence of stochastic bifurcations in a bistable thermoacoustic oscillator.
- * To determine parameter regimes relevant to phenomenological (P) bifurcations.
Main Methods:
- * Analysis of unsteady pressure time series from a horizontal Rijke tube.
- * Utilization of a mathematical model for the thermoacoustic system.
- * Calculation of stationary amplitude distribution by solving the Fokker-Planck equation.
Main Results:
- * Stochastic bifurcations were observed in the thermoacoustic system.
- * High-intensity noise led to the complete suppression of the bistable zone.
- * Suppression of the bistable zone correlated with the nonexistence of P bifurcations.
Conclusions:
- * Noise significantly impacts the dynamics of thermoacoustic systems.
- * The presence and intensity of noise are critical in determining the existence of bistable zones and P bifurcations.
- * The Fokker-Planck equation provides a framework for understanding noise-induced transitions in thermoacoustics.
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