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Related Concept Videos

Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
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 Diagrams of Ternary Systems01:28

Phase Diagrams of Ternary Systems

Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
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...

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Related Experiment Video

Updated: Jun 22, 2026

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms
08:36

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms

Published on: March 21, 2019

Topological transition in dynamic complex networks.

Nobuharu Kami1, Hideo Ikeda

  • 1Department of Electrical Engineering, Stanford University, Stanford, California 94305-9510, USA. n-kami@ak.jp.nec.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

This study explores complex network topology changes using a statistical mechanics model. Results show a transition from nonclustered to clustered networks based on randomness levels.

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Area of Science:

  • Statistical mechanics
  • Network science
  • Complex systems

Background:

  • Complex networks exhibit evolving structures.
  • Understanding network topology transitions is crucial.

Purpose of the Study:

  • To investigate topological transitions in complex networks with evolving wiring.
  • To model network evolution using statistical mechanics.

Main Methods:

  • Developed a network model incorporating statistical mechanics.
  • Included a wiring decision metric (local clustering coefficient) for structure.
  • Incorporated thermal fluctuation for randomness.
  • Utilized Monte Carlo simulations to analyze network behavior.

Main Results:

  • Observed a dramatic topological transition in network structure.
  • The transition occurs between nonclustered and clustered network states.
  • The degree of randomness significantly influences the transition.

Conclusions:

  • Network topology is sensitive to the balance between structuring and randomization.
  • The local clustering coefficient plays a key role in network evolution.
  • Randomness acts as a control parameter for network clustering.