A dropped vase, a crushed sugar cube and an exploding bubble all have something in common: They break apart in similar ways, a new mathematical equation reveals.
A French scientist recently discovered the mathematical equation, which describes the size distribution of fragments that form when something shatters. The equation applies to a variety of materials, including solids, liquids and gas bubbles, according to a new study, published Nov. 26 in the journal Physical Review Letters.
Though cracks spread through an object in often unpredictable ways, research has shown that the size distribution of the resulting fragments seems to be consistent, no matter what they’re made of — you can always expect a certain ratio of larger fragments to smaller ones. Scientists suspected that this consistency pointed to something universal about the process of fragmenting.
Rather than focusing on how fragments form, Emmanuel Villermaux, a physicist at Aix-Marseille University in France, studied the fragments themselves. In the new study, Villermaux argued that fragmenting objects follow the principle of “maximal randomness.” This principle suggests that the most likely fragmentation pattern is the messiest one — the one that maximizes entropy, or disorder.
Ferenc Kun, a physicist at the University of Debrecen in Hungary, told New Scientist that understanding fragmentation could help scientists determine how energy is spent on shattering ore in industrial mining or how to prepare for rockfalls.
Future work could involve determining the smallest possible size a fragment could have, Villermaux told New Scientist.
It’s also possible that the shapes of different fragments could follow a similar relationship, Kun wrote in an accompanying viewpoint article.