Related Experiment Video
Updated: May 18, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Finite-size scaling at the jamming transition
Carl P Goodrich1, Andrea J Liu, Sidney R Nagel
1Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Physical Review Letters
|September 26, 2012
Summary
Finite-size effects in jammed sphere packings reveal corrections to scaling, showing the jamming transition behaves like a phase transition. This occurs above isostaticity, with implications for understanding material properties.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Jammed packings of soft spheres are crucial for understanding granular materials and glasses.
- Finite-size effects are known to influence phase transitions and critical phenomena.
Purpose of the Study:
- To analyze finite-size effects in jammed packings of soft, frictionless spheres at zero temperature.
- To investigate the impact of particle number (N) on the jamming transition and its associated properties.
Main Methods:
- Analysis of discrete jumps in contact number for packings of N spheres.
- Examination of power-law scalings for contact number and elastic moduli at low pressures.
- Investigation of scaling collapse as a function of N in 2D and 3D.
Main Results:
- A 1/N correction to the contact number jump indicates jammed packings exist only above isostaticity.
- Canonical power-law scalings break down at low pressures due to finite-size effects.
- Scaling collapse with a nontrivial scaling function demonstrates the jamming transition as a phase transition.
- Scaling is achieved as a function of N in both 2D and 3D, suggesting an upper critical dimension of 2.
Conclusions:
- Finite-size effects are critical for understanding the jamming transition in soft sphere packings.
- The jamming transition exhibits characteristics of a phase transition, particularly above isostaticity.
- The upper critical dimension for this transition is found to be 2.
Related Concept Videos
01:26Scaling
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
02:39Phase 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...
02:31Phase 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...
01:21Phase 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...
02:54Trends in Lattice Energy: Ion Size and Charge
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
01:10Entropy 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.
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.