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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

21.5K
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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Energy Diagrams, Transition States, and Intermediates02:13

Energy Diagrams, Transition States, and Intermediates

21.0K
Free-energy diagrams, or reaction coordinate diagrams, are graphs showing the energy changes that occur during a chemical reaction. The reaction coordinate represented on the horizontal axis shows how far the reaction has progressed structurally. Positions along the x-axis close to the reactants have structures resembling the reactants, while positions close to the products resemble the products.  Peaks on the energy diagram represent stable structures with measurable lifetimes, while...
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Cooperative Allosteric Transitions01:58

Cooperative Allosteric Transitions

8.9K
Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
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Related Experiment Video

Updated: Feb 10, 2026

Optogenetic Phase Transition of TDP-43 in Spinal Motor Neurons of Zebrafish Larvae
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Absorbing phase transitions in deterministic fixed-energy sandpile models.

Su-Chan Park1

  • 1Department of Physics, The Catholic University of Korea, Bucheon 14662, Republic of Korea.

Physical Review. E
|May 20, 2018
PubMed
Summary
This summary is machine-generated.

We explored the difference between Abelian sandpile models (ASM) and deterministic fixed-energy sandpile models (DFES). DFES exhibit multiple absorbing phase transitions (APT) with universal critical phenomena, distinct from ASM steady states.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Dynamical Systems

Background:

  • Abelian sandpile models (ASM) exhibit steady-state behavior.
  • Deterministic fixed-energy sandpile models (DFES) present unique transition dynamics.
  • A noted difference exists between ASM steady states and DFES transition points.

Purpose of the Study:

  • Investigate the origin of the discrepancy between ASM steady state density and DFES transition points.
  • Analyze the absorbing phase transition (APT) in DFES.
  • Clarify the relationship between DFES dynamics and percolation theory.

Main Methods:

  • Theoretical analysis of DFES configuration space.
  • Numerical simulations of the 2D DFES with the Bak-Tang-Wiesenfeld (BTW-FES) toppling rule.
  • Examination of the impact of infinite-size and infinite-time limits.

Main Results:

  • DFES configuration space divides into classes leading to absorbing states or not.
  • Multiple transition points exist in DFES, dependent on initial configurations.
  • Critical phenomena at DFES transition points are universal.
  • The microscopic absorbing phase transition in BTW-FES relates to isotropic percolation, not self-organized criticality.

Conclusions:

  • The difference between ASM and DFES arises from their distinct dynamical behaviors and state spaces.
  • DFES can exhibit multiple absorbing phase transitions.
  • The transition dynamics of DFES are linked to percolation processes.
  • Recurrent ASM configurations do not yield nontrivial APT in DFES.