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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...

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The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
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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).

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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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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Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions

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Coupled Dynamical Phase Transitions in Driven Disk Packings.

Akash Ghosh¹, Jaikumar Radhakrishnan², Paul M Chaikin³

¹Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai 400005, India.

Physical Review Letters

|November 14, 2022

Summary

This summary is machine-generated.

Granular disks under shear flow show two surprising phase transitions occurring at the same critical point. Disk trajectories form unique loops, breaking time-reversal symmetry.

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Area of Science:

Physics
Materials Science
Complex Systems

Background:

Granular materials exhibit complex behaviors under external forces.
Oscillatory shear is a common method to study dynamical transitions in condensed matter systems.
Understanding phase transitions in non-equilibrium systems is a key challenge in physics.

Purpose of the Study:

To investigate the dynamical phase transitions in a monolayer of frictional granular disks subjected to oscillatory shear.
To determine if the observed phase transitions occur at the same critical point.
To characterize the nature of these transitions using disk trajectories.

Main Methods:

Simulating a 2D monolayer of frictional granular disks.
Applying oscillatory shear flow to the system.
Analyzing system dynamics, including order parameters and particle trajectories.
Identifying critical points and phase transition behaviors.

Main Results:

Two distinct dynamical phase transitions were observed: disorder-to-crystal and active-absorbing transitions.
Both transitions were found to occur at the same critical point, contrary to initial expectations.
Disk trajectories were characterized by non-trivial loops, indicating a breaking of time-reversal invariance.

Conclusions:

The study reveals a surprising synchronization of two distinct phase transitions in granular matter under shear.
The observed non-trivial loop trajectories offer new insights into the broken time-reversal symmetry in these dynamic systems.
This work contributes to the understanding of non-equilibrium phase transitions and collective behavior in granular materials.