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Method to Measure Tone of Axial and Proximal Muscle
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Published on: December 14, 2011

Resonantly driven wobbling kinks.

O F Oxtoby1, I V Barashenkov

  • 1CSIR Computational Aerodynamics, Building 12, P.O. Box 395, Pretoria 0001, South Africa. oliver.oxtoby@gmail.com

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

Resonant driving can compensate for energy losses in wobbling kinks within the varphi(4) theory. This study reveals complex amplitude behaviors and identifies optimal driving frequencies for parametric and direct resonance.

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Area of Science:

  • Nonlinear dynamics
  • Theoretical physics
  • Quantum field theory

Background:

  • Freely wobbling kinks in varphi(4) theory exhibit decaying oscillations due to second-harmonic radiation emission.
  • Understanding and controlling these oscillations are crucial for theoretical and computational physics applications.

Purpose of the Study:

  • To investigate the compensation of radiation and dissipative losses in wobbling kinks.
  • To analyze the effects of resonant driving (direct and parametric) on kink dynamics.
  • To derive and verify amplitude equations governing kink wobbling and velocity.

Main Methods:

  • Derivation of amplitude equations for wobbling and kink velocity.
  • Analysis of direct and parametric resonant driving at various frequencies.
  • Numerical simulations of the full partial differential equation to verify theoretical predictions.

Main Results:

  • Amplitude equations predict multistability and hysteretic transitions in wobbling amplitude.
  • Strongest parametric resonance occurs at the natural wobbling frequency, not double.
  • Direct driving shows strongest resonance at half the natural frequency, with a weaker resonance at the natural frequency accompanied by translational motion.

Conclusions:

  • Resonant driving effectively compensates for energy losses in wobbling kinks.
  • Driving frequency significantly influences resonance strength and associated phenomena like multistability and translational motion.
  • The study provides a comprehensive understanding of driven kink dynamics in varphi(4) theory.