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Related Experiment Video

Updated: Jun 2, 2026

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

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

Published on: February 3, 2014

Variational approximations to homoclinic snaking.

H Susanto1, P C Matthews

  • 1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG72RD, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 27, 2011
PubMed
Summary
This summary is machine-generated.

We reveal how localized patterns snake using a novel variational approximation. This method accurately captures snaking structures and predicts the stability of these complex physical states.

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Last Updated: Jun 2, 2026

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

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Area of Science:

  • Applied Mathematics
  • Mathematical Physics

Background:

  • Localized patterns are prevalent in various physical systems.
  • Understanding their complex dynamics, such as snaking, is crucial.

Purpose of the Study:

  • To investigate the snaking of localized patterns using a variational approximation.
  • To analyze symmetric snaking solutions and asymmetric ladder states.
  • To predict the stability of these localized states.

Main Methods:

  • A variational approximation method was employed.
  • This approach naturally incorporates exponentially small terms crucial for snaking.
  • Standard multiple-scales asymptotic techniques were insufficient.

Main Results:

  • Symmetric snaking solutions and asymmetric ladder states were obtained.
  • The stability of localized states was predicted.
  • Approximate formulas for the snaking region width showed good agreement with numerical data.

Conclusions:

  • The variational approximation is effective for studying snaking patterns.
  • This method provides insights into the stability and structure of localized states.
  • The findings offer a valuable tool for analyzing complex physical phenomena.