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Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed
Stefano Martiniani1, K Julian Schrenk1, Jacob D Stevenson1,2
1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
Physical Review. E
|February 13, 2016
Summary
We numerically calculated disordered jammed configurations for spheres. A strong correlation was found between pressure and the volume of stable packing basins, described by a power law.
Area of Science:
- Physics
- Statistical Mechanics
- Computational Physics
Background:
- Disordered jammed configurations of particles are crucial in various physical systems.
- Understanding the configurational entropy is key to characterizing these states.
- Previous methods for calculating these properties were computationally intensive.
Purpose of the Study:
- To numerically calculate the total number of disordered jammed configurations (Ω) for N repulsive, 3D spheres in a fixed volume (V).
- To enhance computational efficiency for calculating configurational entropy as a function of pressure.
- To explore the relationship between pressure and the volume of basins of attraction in the potential energy landscape.
Main Methods:
- Improved computational efficiency of existing methods (Xu et al., Asenjo et al.).
- Sampling the absolute volume of basins of attraction for stable packings.
- Calculating configurational entropy as a function of pressure.
Main Results:
- A surprisingly strong correlation between configuration pressure and basin of attraction volume was observed.
- This relationship is accurately described by a power law.
- The number of minima in the potential energy landscape was computed.
Conclusions:
- The developed methodology offers a more efficient way to study disordered jammed states.
- The power-law relationship provides a new insight into the physics of jammed matter.
- The approach is broadly applicable to enumeration problems in diverse scientific fields.
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