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Related Concept Videos

Phase Transitions02:31

Phase Transitions

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 occupy...
Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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...
Dynamic Equilibrium02:20

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

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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Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR
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Cascading dynamics on random networks: crossover in phase transition.

Run-Ran Liu1, Wen-Xu Wang, Ying-Cheng Lai

  • 1Institute for Information Economy, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China. runranliu@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 3, 2012
PubMed
Summary
This summary is machine-generated.

Complex network failures can cause cascading events, similar to phase transitions. This study shows these transitions occur even without interdependent links, with a theory matching numerical results.

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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Complex networks are vulnerable to cascading failures initiated by random attacks or node malfunctions.
  • Previous research linked interdependent links to first- and second-order phase transitions in networks.
  • A critical system parameter determines the crossover between these transition types.

Purpose of the Study:

  • To investigate if cascading failures and phase transitions occur in networks lacking interdependent links.
  • To develop a theoretical framework for understanding these phenomena in a more general network setting.
  • To validate the theoretical predictions with numerical simulations.

Main Methods:

  • Analysis of complex network dynamics under random node failures.
  • Development of a heuristic theory to model cascading failure phenomena.
  • Numerical simulations to compute phase transition and crossover points.
  • Comparison of theoretical predictions with simulation outcomes.

Main Results:

  • Cascading failures and phase transitions are demonstrated in networks without interdependent links.
  • A heuristic theory accurately predicts crossover and phase transition points.
  • The findings generalize previous observations on network robustness and fragility.
  • Numerical results show remarkable agreement with the derived theoretical estimates.

Conclusions:

  • Network fragility and cascading failures are not solely dependent on interdependent links.
  • The developed heuristic theory provides a valuable tool for analyzing network resilience.
  • This research expands the understanding of phase transitions in complex systems.
  • The findings have implications for designing more robust and reliable complex networks.