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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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 slanted or...
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

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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Related Experiment Video

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High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements
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High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

Published on: May 12, 2023

Nonconverging hysteresis cycles in random spin networks.

O Hovorka1, G Friedman

  • 1Electrical and Computer Engineering Department, Drexel University, Philadelphia, PA 19104, USA.

Physical Review Letters
|March 21, 2008
PubMed
Summary

Investigating random networks of binary spins reveals distinct hysteretic behaviors based on network structure. Unexpectedly, non-converging hysteretic trajectories were found, linked to specific topological elements like fully interconnected spin groups.

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Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement
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Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement

Published on: November 7, 2017

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Last Updated: Jul 6, 2026

High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements
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High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

Published on: May 12, 2023

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement
09:43

Optimized Setup and Protocol for Magnetic Domain Imaging with In Situ Hysteresis Measurement

Published on: November 7, 2017

Area of Science:

  • Statistical physics
  • Network science
  • Complex systems

Background:

  • Hysteresis is a common phenomenon in physical systems, often studied in magnetic materials and neural networks.
  • The behavior of complex systems can be highly dependent on their underlying network architecture.
  • Random networks provide a simplified yet powerful model for understanding emergent properties.

Purpose of the Study:

  • To investigate the influence of internal network structure on hysteretic trajectory behavior under cyclical input.
  • To identify different regimes of hysteretic behavior linked to network connectivity and topology.
  • To explore the origins of unexpected hysteretic phenomena in random spin networks.

Main Methods:

  • Modeling a system using a classical random network of binary spins.
  • Applying cyclical input to observe system dynamics.
  • Analyzing hysteretic trajectories as a function of network connectivity and topology.
  • Identifying specific topological elements associated with observed behaviors.

Main Results:

  • Discovered distinct regimes of hysteretic behavior correlating with network connectivity and topology.
  • Observed hysteretic trajectories that exhibit non-convergence, a surprising finding.
  • Associated non-converging trajectories with the presence of fully interconnected spin groups (size ≥ 4).

Conclusions:

  • The internal structure, particularly topology, critically dictates hysteretic behavior in random spin networks.
  • Specific topological motifs, such as large fully interconnected spin groups, can lead to fundamentally different system dynamics.
  • Further research into topological elements is crucial for understanding complex system behavior and hysteresis.