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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

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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.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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¹H NMR Signal Multiplicity: Splitting Patterns01:13

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When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Nuclear Fusion02:45

Nuclear Fusion

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The process of converting very light nuclei into heavier nuclei is also accompanied by the conversion of mass into large amounts of energy, a process called fusion. The principal source of energy in the sun is a net fusion reaction in which four hydrogen nuclei fuse and ultimately produce one helium nucleus and two positrons.
A helium nucleus has a mass that is 0.7% less than that of four hydrogen nuclei; this lost mass is converted into energy during the fusion. This reaction produces about...
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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.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Related Experiment Video

Updated: May 29, 2025

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
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Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

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Explosive synchronization in coupled stars.

Ruby Varshney1, Kaustubh Manchanda2,3, Haider Hasan Jafri1

  • 1Aligarh Muslim University, Department of Physics, Aligarh 202 002, India.

Physical Review. E
|February 7, 2025
PubMed
Summary
This summary is machine-generated.

We investigated how network structure impacts oscillator synchronization. Increasing coupling between star networks amplifies explosive synchronization, a sudden shift from disorder to order.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Oscillator ensembles exhibit collective dynamics.
  • Network topology significantly influences system behavior.
  • Explosive synchronization is a phenomenon characterized by abrupt transitions.

Purpose of the Study:

  • To investigate the effect of network topology on collective dynamics.
  • To explore explosive synchronization in interacting star networks.
  • To analyze the impact of inter-star coupling strength on synchronization dynamics.

Main Methods:

  • Modeling an ensemble of Kuramoto oscillators.
  • Coupling multiple star networks via their central hubs.
  • Analyzing emergent dynamics as a function of coupling strength.

Main Results:

  • Hysteresis width in explosive synchronization increases with inter-star coupling strength.
  • This effect is independent of individual network size.
  • The backward transition point remains constant regardless of the number of coupled networks or coupling strength.

Conclusions:

  • Inter-star coupling strength is a critical parameter for controlling explosive synchronization in star network ensembles.
  • The backward transition point offers a robust characteristic of the system's dynamics.
  • Findings are consistent with established theories like Watanabe and Strogatz.