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Related Concept Videos

Phase Transitions02:31

Phase Transitions

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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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Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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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

Phase Transitions: Sublimation and Deposition

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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

Phase Transitions: Vaporization and Condensation

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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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Phase Diagram01:19

Phase Diagram

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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).
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Phase Diagrams02:39

Phase Diagrams

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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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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
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Topological persistence machine of phase transitions.

Quoc Hoan Tran1, Mark Chen1, Yoshihiko Hasegawa1

  • 1Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

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Summary

This study introduces a novel topological persistence machine for analyzing phase transitions using data-driven methods. This framework effectively detects complex transitions in physical systems without prior knowledge.

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Area of Science:

  • Physics
  • Data Science
  • Materials Science

Background:

  • Analyzing phase transitions with data-driven methods is challenging, particularly with limited prior system knowledge.
  • Topological data analysis (TDA) shows promise in detecting structural transitions but struggles with non-explicit data shapes from physical states.

Purpose of the Study:

  • To propose a general framework, the "topological persistence machine," for constructing data shapes from state correlations.
  • To enable deciphering phase transitions through qualitative shape changes in data.
  • To provide a unified and effective approach for phase transition analysis.

Main Methods:

  • Developed a "topological persistence machine" to infer data topology from correlations.
  • Applied the framework to analyze the Berezinskii-Kosterlitz-Thouless transition in the XY model.
  • Investigated quantum phase transitions in the transverse Ising and Bose-Hubbard models.

Main Results:

  • Successfully detected the Berezinskii-Kosterlitz-Thouless phase transition.
  • Characterized quantum phase transitions in the transverse Ising and Bose-Hubbard models.
  • Demonstrated effective analysis without requiring prior knowledge of system phases.

Conclusions:

  • The topological persistence machine offers a powerful, unified approach for analyzing phase transitions.
  • The framework excels in detecting transitions that are difficult for traditional methods.
  • Expected to be widely applicable to experimental physical systems for phase exploration.