Avalanches triggered by random extractions. (a) Arrangement of fruits on the market. The bottom panels show a numerical simulation for a system of 90 spheres, colored randomly. (b) Shows an overall view of the system, tilted at an angle. In panel (c), the first sphere is extracted and the second in panel (d). In panel (e), an avalanche takes place after extracting 12 spheres. The inset in panel (c) highlights the fence delimiting the system. Credit: Physical examination E (2023). DOI: 10.1103/PhysRevE.108.064904
A small team of physicists and mechanical engineers from the University of Antofagasta, the Autonomous University of Chile and the University of O’Higgins, all located in Chile, have found a way to find the points of stability of monolayers arranged in a granular manner in a single pile with inclined slopes.
In their study, published in the journal Physical examination EThe group used computer simulations to model spheres, such as oranges, stacked with varying slope edges to discover the point at which the stack would collapse when one or more spheres were removed from one edge.
Many grocery stores display the fruits for sale in piles aimed at showcasing their deliciousness. These piles tend to have slanted edges, which paints an overall picture of instability: unwary shoppers who grab a single orange from the wrong part of the pile can trigger a collapse and the fruit will roll off the shelf and onto floor. In this new effort, the research team discovered the tipping points of these piles.
The researchers created simulations depicting stacked spheres of different sizes, stacked with different edge slopes, and ran them under several configurations, from modest to extreme slopes. They found that stacked spheres with extreme slopes can indeed collapse if just one sphere is removed from the edge of the slope. They also found that for modest slopes, almost any number of spheres can be removed without causing collapse. It is between these extremes that things have become more difficult to predict.
Slowly increasing slope angle, they argued, led to situations where removing multiple spheres rather than just one could result in collapse. They also calculated that under normal circumstances, such as those typically found in a grocery store, up to 10 percent of the spheres (apples, oranges, or grapefruit, for example) must be removed before a collapse. Thus, it is unlikely that an individual buyer will cause a collapse if he removes a single piece of fruit – unless several buyers before him have done the same from the same location.
The researchers plan to continue their work by examining other possible collapse scenarios, such as rock piles of different sizes.
More information:
Eduardo Rojas et al, Stability of an inclined granular monolayer: how many spheres can we sample before collapse?, Physical examination E (2023). DOI: 10.1103/PhysRevE.108.064904. On arXiv: DOI: 10.48550/arxiv.2206.03016
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