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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
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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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Nonreciprocal Coupling Induced Self-Assembled Localized Structures.

D Pinto-Ramos1, K Alfaro-Bittner2,3, M G Clerc1

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|May 28, 2021
PubMed
Summary
This summary is machine-generated.

Nonreciprocal coupling in nonlinear chains creates traveling waves, a self-assembly of localized structures. This study characterizes the emergent wave patterns and their dependence on coupling levels.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • Coupled oscillator chains typically propagate energy via waves, pulses, and fronts.
  • Nonreciprocal coupling significantly alters these wave dynamics.

Purpose of the Study:

  • To investigate the nonlinear wave dynamics in chains with nonreciprocal nearest-neighbor coupling.
  • To understand the emergent phenomena arising from such coupling, specifically localized structures and traveling waves.

Main Methods:

  • Development of a prototype model for nonlinear chains with nonreciprocal coupling.
  • Analytical determination of the phase diagram.
  • Numerical simulations to validate analytical findings.

Main Results:

  • Nonreciprocal coupling induces a convective instability between stable and unstable equilibria.
  • Increased coupling leads to the emergence of a propagative pattern, identified as a traveling wave.
  • Characterization of the pattern wavelength as a function of the coupling strength.
  • Analytical phase diagram matches numerical simulation results.

Conclusions:

  • Nonreciprocal coupling is a key mechanism for generating self-assembled localized structures and traveling waves in nonlinear chains.
  • The study provides a framework for understanding emergent wave phenomena in systems with asymmetric interactions.