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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.
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The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
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Emergent marginality in frustrated multistable networks.

Dor Shohat1,2, Yoav Lahini1,2, Daniel Hexner3

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Disordered networks of elastic elements self-organize into a marginally stable state. This state exhibits vanishingly small activation barriers, leading to unique dynamics in amorphous solids.

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Area of Science:

  • Physics
  • Materials Science
  • Condensed Matter Physics

Background:

  • Amorphous solids exhibit complex mechanical behaviors not fully explained by traditional models.
  • Understanding the underlying network structure and dynamics is crucial for predicting material properties.

Purpose of the Study:

  • To investigate the self-organization and emergent properties of disordered networks of coupled bistable elastic elements.
  • To model amorphous solids and gain insights into their local and global stability characteristics.

Main Methods:

  • Development of a coarse-grained model for amorphous solids using coupled bistable elastic elements.
  • Direct measurement of pseudo-gaps in the excitation spectrum.
  • Analysis of fluctuations under shear and identification of unstable bond populations.

Main Results:

  • Networks self-organize to a state of marginal stability with vanishingly small local activation barriers.
  • Observation of pseudo-gaps in excitation spectra and diverging fluctuations under shear.
  • Identification of quasi-localized vibrational modes and scale-free avalanches driven by unstable bonds.

Conclusions:

  • The model provides a framework for understanding marginal stability in amorphous solids.
  • A correction to scaling laws relating pseudo-gaps and avalanche statistics is proposed.
  • The study offers novel insights into the behavior of diverse amorphous solid systems.