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Related Concept Videos

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
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P-value is one of the most crucial concepts in statistics.
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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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Related Experiment Video

Updated: Nov 17, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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High-degeneracy Potts coarsening.

J Denholm1

  • 1SUPA, Department of Physics, University of Strathclyde, Glasgow, G4 0NG Scotland, United Kingdom.

Physical Review. E
|February 19, 2021
PubMed
Summary

A kinetic ferromagnet quench to zero temperature favors the ground state, reached in ~71% of simulations. Other states like three-hexagon and spanning stripe configurations appear less frequently in this spin-flip dynamics study.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Investigating the behavior of magnetic systems quenched to low temperatures is crucial for understanding phase transitions and emergent phenomena.
  • High ground-state degeneracy in kinetic ferromagnets presents complex dynamics and diverse possible final configurations.

Purpose of the Study:

  • To determine the final states of a kinetic Potts ferromagnet after a deep quench to zero temperature.
  • To quantify the probabilities of various emergent configurations, including ground states, three-hexagon states, spanning stripes, and blinkers.

Main Methods:

  • Simulated single spin-flip dynamics on triangular lattices with linear dimensions ranging from 8 to 128.
  • Set the number of spin states (q) equal to the number of lattice sites (L×L) to explore high degeneracy.

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  • Analyzed the distribution of final configurations after the quench.

    • Main Results:

    • The ground state emerged as the most abundant final state, achieved with a probability of approximately 0.71.
    • Three-hexagon states were observed with a probability of approximately 0.26.
    • Spanning stripe states occurred with ~0.03 probability, while more complex hexagonal tessellations and blinker configurations appeared with vanishingly small probabilities.

    Conclusions:

    • Deep quenches in this kinetic ferromagnet model strongly favor the system's ground state.
    • The dynamics lead to a limited set of dominant final configurations, with rare occurrences of more complex patterns.
    • System size influences the probability of certain configurations, particularly blinkers, which become exceedingly rare.