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Phase Transitions

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 Transitions

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 Transitions: Sublimation and Deposition

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...

Phase Diagram

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 Diagram

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...

Phase Diagrams

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...

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Related Experiment Video

Updated: Jun 19, 2026

A Method for Investigating Age-related Differences in the Functional Connectivity of Cognitive Control Networks Associated with Dimensional Change Card Sort Performance

A Method for Investigating Age-related Differences in the Functional Connectivity of Cognitive Control Networks Associated with Dimensional Change Card Sort Performance

Published on: May 7, 2014

Structural phase transition in evolving networks.

Sang-Woo Kim¹, Jae Dong Noh

¹Department of Physics, University of Seoul, Seoul 130-743, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 2, 2009

Summary

This summary is machine-generated.

This study introduces a model where networks and diffusing particles co-evolve, revealing a phase transition. The research shows how particle traffic dynamics can lead to the emergence of network hubs.

Related Experiment Videos

Last Updated: Jun 19, 2026

A Method for Investigating Age-related Differences in the Functional Connectivity of Cognitive Control Networks Associated with Dimensional Change Card Sort Performance

A Method for Investigating Age-related Differences in the Functional Connectivity of Cognitive Control Networks Associated with Dimensional Change Card Sort Performance

Published on: May 7, 2014

Area of Science:

Complex systems
Network science
Statistical physics

Background:

Networks often exhibit dynamics that influence processes occurring on them.
Understanding coupled dynamics between network structure and agents is crucial for complex systems analysis.

Purpose of the Study:

To model and investigate the emergent structural properties of networks evolving with diffusing particles.
To explore the relationship between particle dynamics and network topology.

Main Methods:

A computational model simulating an undirected weighted network with diffusing particles.
Coupled dynamics where edge weights are influenced by traffic and edges are rewired based on weight.
Analysis of degree distribution to identify phase transitions.

Main Results:

The model exhibits a structural phase transition from a homogeneous to a heterogeneous network phase.
Emergence of network hubs in the heterogeneous phase is observed.
A positive feedback loop between particle traffic and edge dynamics drives hub formation.

Conclusions:

Coupled dynamics can lead to significant structural changes in networks.
The proposed model provides a mechanism for the spontaneous emergence of hubs in complex networks.
This work offers insights into self-organization in systems with interacting agents and evolving structures.