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Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

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Published on: February 3, 2014

Maximal width of the separatrix chaotic layer.

S M Soskin¹, R Mannella

¹Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This summary is machine-generated.

This study identifies universal sharp peaks in the width of chaotic layers in Hamiltonian systems. These findings predict a significantly larger maximal chaotic layer width than previously understood.

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Area of Science:

Nonlinear Dynamics
Chaos Theory
Mathematical Physics

Background:

The theory of separatrix chaos addresses the behavior of dynamical systems with a separatrix.
Understanding the width of the chaotic layer is crucial for predicting system dynamics.
Previous theories have underestimated the potential width of chaotic layers.

Purpose of the Study:

To determine the absolute maximum width of the separatrix chaotic layer.
To investigate the width's dependence on the frequency of time-periodic perturbations.
To address a major unsolved problem in the theory of separatrix chaos.

Main Methods:

Analysis of one-dimensional Hamiltonian systems with a separatrix.
Developing asymptotic expressions for low-frequency peak shapes.
Utilizing an approach based on Soskin's prior work [Phys. Rev. E 77, 036221 (2008)].

Main Results:

The chaotic layer width exhibits sharp, universal peaks at specific perturbation frequencies.
These peaks arise from nonlinear resonance dynamics within the chaotic motion.
The absolute maximum width is proportional to perturbation amplitude, amplified by large logarithmic or numerical factors.

Conclusions:

The derived theory predicts a maximal chaotic layer width significantly exceeding previous estimates.
This enhanced understanding has implications for the onset of global chaos.
The theoretical predictions are validated through numerical simulations.