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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Phase Transitions: Sublimation and Deposition02:33

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Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
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Phase Transitions: Vaporization and Condensation02:39

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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
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Once a ligand binds to a receptor, the signal is transmitted through the membrane and into the cytoplasm. The continuation of a signal in this manner is called signal transduction. Signal transduction only occurs with cell-surface receptors, which cannot interact with most components of the cell, such as DNA. Only internal receptors can interact directly with DNA in the nucleus to initiate protein synthesis. When a ligand binds to its receptor, conformational changes occur that affect the...
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Cascading Failures as Continuous Phase-Space Transitions.

Yang Yang1, Adilson E Motter1,2

  • 1Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA.

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|December 30, 2017
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Summary
This summary is machine-generated.

Cascading failures in power grids can be larger than predicted. A new model shows these events are energy transitions, and perturbation timing significantly impacts outcomes, offering insights for grid control.

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Area of Science:

  • Network systems science
  • Power grid dynamics
  • Complex systems analysis

Background:

  • Local perturbations in network systems can escalate into large-scale cascading failures.
  • Understanding the dynamics of power grid failures is crucial for maintaining stability.

Purpose of the Study:

  • To develop a continuous model for analyzing cascading failures in power-grid networks.
  • To incorporate transmission line failures and generator desynchronization into cascade modeling.
  • To investigate the transient dynamics within cascade steps.

Main Methods:

  • Derivation of a continuous model for power-grid cascading failures.
  • Analysis of phase-space transitions using a global Hamiltonian-like function.
  • Inclusion of transient dynamics between cascade steps.

Main Results:

  • Cascade events are characterized as phase-space transitions from high to lower energy equilibrium states.
  • The model predicts that systems may experience larger cascades than quasi-steady-state models suggest.
  • The order and timing of multiple perturbations critically influence cascade outcomes.

Conclusions:

  • The derived model offers a more nuanced understanding of power-grid cascading failures.
  • Results challenge existing quasi-steady-state assumptions and highlight the importance of transient dynamics.
  • Findings have implications for developing effective control interventions for power grid stability.