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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...
Phase Diagrams02:39

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
Phase Diagram01:19

Phase Diagram

The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
Phase Diagram01:24

Phase Diagram

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...

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Related Experiment Video

Updated: Jun 8, 2026

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke
06:37

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke

Published on: July 14, 2023

Griffiths phases on complex networks.

Miguel A Muñoz1, Róbert Juhász, Claudio Castellano

  • 1Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, 18071 Granada, Spain.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

This study reveals that quenched disorder causes slow relaxation in complex networks, similar to Griffiths phases. Surprisingly, these phases can also arise from network structure alone, impacting propagation dynamics.

Related Experiment Videos

Last Updated: Jun 8, 2026

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke
06:37

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke

Published on: July 14, 2023

Area of Science:

  • Complex systems
  • Statistical physics
  • Network science

Background:

  • Quenched disorder significantly influences dynamical processes and phase transitions.
  • The impact of quenched disorder on complex network dynamics remains under-explored.

Purpose of the Study:

  • To investigate the effects of quenched disorder on the contact process, a fundamental propagation model, within complex networks.
  • To identify and characterize emergent phenomena like Griffiths phases and their influence on relaxation dynamics.

Main Methods:

  • Analysis of the contact process on Erdos-Rényi networks with quenched disorder.
  • Investigation of network topologies with finite percolation thresholds.
  • Exploration of Griffiths phase emergence due to topological heterogeneity.

Main Results:

  • Quenched disorder induces Griffiths phases and rare-region effects, resulting in anomalously slow relaxation (algebraic, logarithmic) on Erdos-Rényi networks.
  • Similar slow relaxation effects are predicted for networks with finite percolation thresholds.
  • Griffiths phases can emerge even without quenched disorder, driven by topological heterogeneity in networks with finite topological dimension.

Conclusions:

  • The findings highlight the significant role of quenched disorder and network topology in dictating propagation dynamics.
  • The study broadens understanding of dynamical processes on networks, with implications for phenomena beyond simple propagation.