A falling vase, a crushed sugar cube, and a bursting bubble all have one thing in common – they burst in the same way. Portal livescience.com speakHow spaghetti and sugar helped a physicist find a new mathematical formula
According to research published in the journal Physical Review Letters by French scientist Emmanuel Villermeau, a mathematical equation can describe the size of the fragments that form when something breaks. He believes his formula applies to a wide range of materials, including solids, liquids and gas bubbles.
Although cracks propagate through an object in unpredictable ways, experiments have shown that the size of the fragments is constant regardless of the material. Proportionally, any object is divided into a certain number of large and small pieces – scientists previously suspected that this constancy was a general property of the process itself.
But Villermo focuses not on the formation of fragments but on the fragments themselves. The physicist believes that cracked objects follow the principle of “maximum randomness” – the type of cracking most likely to occur is the most chaotic. One that increases entropy, also known as disorder.
But this randomness must, one way or another, obey certain boundaries. To account for this nuance, Villermo applied the conservation law discovered by him and his colleagues in 2015. It adds physical boundaries to the density of debris in space when an object breaks up.
By adding the above two principles, the physicist obtained a mathematical equation that describes the size pattern of fragments. He then tested the results against years of data on fragile objects, from glass to pieces of plastic in the ocean, drops of liquid and even pasta. And all were consistent with the predicted size distribution. Willermo further tested the equation by dropping heavy objects on sugar cubes and watching them crack.
However, new laws are not always applied. For example, it does not deal with situations where there is no element of randomness, such as the breaking of a smooth stream of water into drops of the same size. The formula also does not take into account the conditions under which the pieces interact with each other, as in some plastics.
