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Related Concept Videos

Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The orientation of the...
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Related Experiment Video

Updated: Jun 19, 2026

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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Published on: July 19, 2016

Wobbling kinks in varphi(4) theory.

I V Barashenkov1, O F Oxtoby

  • 1Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa. igor@odette.mth.uct.ac.za

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 2, 2009
PubMed
Summary
This summary is machine-generated.

We developed a new mathematical method to describe wobbling kink radiation. This confirms a previously observed decay law for the kink

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Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • Nonlinear Dynamics

Background:

  • Kinks are topological solitons with important applications in various fields of physics.
  • Understanding the long-range behavior and radiation of kinks is crucial for their theoretical and experimental study.
  • Previous studies suggested a specific decay law for kink radiation based on energy considerations.

Purpose of the Study:

  • To develop a uniform asymptotic expansion for the wobbling kink.
  • To describe the long-range radiation behavior of the wobbling kink.
  • To derive and confirm the decay law for the wobbling mode amplitude.

Main Methods:

  • Uniform asymptotic expansion of the wobbling kink to any order.
  • Matching asymptotic expansions in the far field and near the kink core.
  • Derivation of an ordinary differential equation for the complex amplitude of the wobbling mode.

Main Results:

  • A uniform asymptotic expansion for the wobbling kink is presented.
  • The long-range radiation is accurately described by matching expansions.
  • The complex amplitude follows a nonlinear damped ordinary differential equation.

Conclusions:

  • The study confirms the t(-1/2)-decay law for the wobbling kink amplitude.
  • The derived mathematical framework provides a comprehensive description of wobbling kink radiation.
  • This work offers new insights into the dynamics and behavior of topological solitons.