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Measurement of granular entropy
Sean McNamara1, Patrick Richard, Sébastien Kiesgen de Richter
1Institut de Physique de Rennes, UMR UR1-CNRS 6251, Université de Rennes I, Bât 11A, 35042 Rennes Cedex, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
Researchers extended a method to test granular packing theory, finding it works for Voronoï volumes but not global volumes. The technique can also calculate packing entropy but may produce false positives with Gaussian data.
Area of Science:
- Physics
- Statistical Mechanics
- Materials Science
Background:
- The statistical mechanical theory of granular packings by Edwards and co-workers provides a framework for understanding these materials.
- Dean and Lefèvre developed a method to test this theory using volume histograms.
Purpose of the Study:
- To extend the Dean and Lefèvre method for testing granular packing theory.
- To investigate the method's ability to calculate packing entropy.
- To identify potential limitations, such as false positive results.
Main Methods:
- Applied the extended Dean and Lefèvre method to simulations and experiments of granular compaction.
- Analyzed the distribution of global volumes and Voronoï volumes.
- Assessed the ratio of overlapping volume histograms for exponential behavior.
Main Results:
- The distribution of global volumes in granular compaction was found to be nearly Gaussian, making theory validation difficult.
- The distribution of Voronoï volumes strongly supported the theoretical predictions.
- The extended method can calculate packing entropy.
- False positive results can occur when using Gaussian histograms with similar variances.
Conclusions:
- The Dean and Lefèvre method, when extended, provides a robust test for granular packing theory, particularly for Voronoï volumes.
- Care must be taken to avoid misinterpretations due to Gaussian distributions.
- The method offers a pathway to calculate the entropy of granular packings.
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