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Systematic Onset of Periodic Patterns in Random Disk Packings.
Nikola Topic1, Thorsten Pöschel1,2, Jason A C Gallas1,2,3
1Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany.
Physical Review Letters
|April 26, 2018
Summary
Randomly deposited disks in tall piles surprisingly form periodic patterns. These patterns emerge regardless of pile width, with disordered phases preceding them, especially in wider channels.
Area of Science:
- Physics of granular materials
- Statistical mechanics of disordered systems
Background:
- Understanding pattern formation in randomly deposited granular materials is crucial.
- Previous studies have focused on different deposition methods or geometries.
Purpose of the Study:
- To investigate the emergence of periodic patterns in tall piles of randomly deposited disks.
- To analyze the influence of channel width on pattern formation and transient phases.
Main Methods:
- Simulations of monodisperse disk deposition between rigid walls.
- Analysis of the probability density function of disordered transient phase lengths.
- Examination of periodic pattern formation across varying channel widths.
Main Results:
- Periodic structures consistently observed in tall piles (up to 10^7 disks) irrespective of pile width.
- Probability density of transient phase lengths exhibits an exponential tail.
- Discrete peaks in periodic pattern probability for narrow channels are lost as width increases.
Conclusions:
- Random disk deposition can lead to systematic periodic pattern formation.
- Channel width significantly impacts the transition from disordered to ordered states.
- The observed phenomena offer insights into self-organization in granular systems.
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