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Related Concept Videos

Couples: Scalar and Vector Formulation01:21

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One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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Nonlinear coupled-mode framework for coupled systems: From exact Hamiltonian models to improved reduced-order

Shubham Garg1, Kirankumar R Hiremath1

  • 1Department of Mathematics, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan 342030, India.

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A new nonlinear coupled-mode framework accurately models energy transfer in physical systems, overcoming limitations of conventional theories for strong coupling. This improved model precisely predicts dynamics in nonlinear circuits.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Circuit Theory

Background:

  • Accurate modeling of coupled nonlinear phenomena is crucial for understanding energy transfer in physical systems.
  • Conventional coupled-mode theory has limitations in moderate and strong coupling regimes due to approximations.

Purpose of the Study:

  • Develop a nonlinear coupled-mode framework that systematically includes nonlinear interactions and counter-propagating wave effects.
  • Improve the accuracy of reduced-order models for coupled nonlinear systems.

Main Methods:

  • Derived a reduced-order formulation from an exact Hamiltonian description for nonlinear LC circuits with Josephson junctions.
  • Incorporated essential nonlinear and self-coupling contributions, including rapidly oscillating terms.
  • Performed comparative analysis against exact Hamiltonian dynamics.

Main Results:

  • The proposed framework achieves quantitative agreement with exact Hamiltonian dynamics across weak-to-strong coupling regimes.
  • Conventional coupled-mode models show significant phase and amplitude errors outside the weak-coupling regime.
  • The new model overcomes limitations of traditional formulations.

Conclusions:

  • Established a systematic pathway for constructing accurate reduced-order descriptions of coupled nonlinear systems.
  • Clarified the limitations of existing phenomenological models.
  • Findings have implications for circuit dynamics, photonics, and energy transfer in complex media.