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Related Concept Videos

Multimachine Stability01:25

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
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...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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...
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,...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

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Related Experiment Video

Updated: Jun 5, 2026

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
14:58

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Published on: June 3, 2015

Making classical ground-state spin computing fault-tolerant.

I J Crosson1, D Bacon, K R Brown

  • 1Department of Physics, University of Washington, Seattle, Washington 98195, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

This study shows how to make classical computing models error-free using fault-tolerant techniques, enabling reliable computation below a critical temperature. It also links classical spin systems to computational complexity classes.

Related Experiment Videos

Last Updated: Jun 5, 2026

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
14:58

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Published on: June 3, 2015

Area of Science:

  • Classical computing
  • Quantum information science
  • Computational complexity theory

Background:

  • Classical deterministic computing models can utilize spatial histories as computational states.
  • These models are relevant to quantum dot cellular automata and adiabatic quantum computing.
  • Primitive forms of these systems exhibit errors at non-zero temperatures.

Purpose of the Study:

  • To develop an effectively error-free classical computing model.
  • To explore the connection between physical systems and computational complexity.
  • To demonstrate fault-tolerant computation in a spatial history model.

Main Methods:

  • Mapping the partition function of the spatial history model to probabilistic classical circuits.
  • Applying fault-tolerant classical computing techniques.
  • Analyzing computational complexity of finite temperature classical spin systems.

Main Results:

  • The classical computing model can be made effectively error-free below a critical temperature.
  • A specific problem in finite temperature classical spin systems is shown to be Merlin-Arthur complete.
  • Established a link between many-body spin systems and computational complexity.

Conclusions:

  • Fault-tolerant techniques enable error-free computation in spatial history models at low temperatures.
  • The study provides a novel connection between condensed matter physics and theoretical computer science.
  • The findings have implications for understanding the computational power of physical systems.