Scientists have discovered a new mathematical equation that explains how objects break apart into fragments of different sizes. The equation, known as the “maximal randomness” principle, suggests that the most likely fragmentation pattern is the one with the highest disorder or randomness. This principle applies to various materials, including solids, liquids, and gas bubbles.
A French scientist named Emmanuel Villermaux studied the fragments themselves rather than how they formed. He combined two principles – maximal randomness and a conservation law discovered in 2015 – to derive the mathematical equation. The equation predicts that the size distribution of fragments will always follow a certain ratio of larger fragments to smaller ones, regardless of the material.
The scientist validated his equation by comparing it to years’ worth of fragmentation data collected on various objects, including glass, spaghetti, liquid droplets, gas bubbles, and even early stone tools. The results showed that all matched the predicted size distribution.
While the newly discovered law doesn’t always apply – it doesn’t apply in situations with no randomness or when fragments interact with each other – it could help scientists understand how energy is spent on shattering ore in industrial mining or prepare for rockfalls. Future work may also involve determining the smallest possible size a fragment could have and exploring whether the shapes of different fragments follow a similar relationship.
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Source: https://www.livescience.com/physics-mathematics/mathematics/law-of-maximal-randomness-explains-how-broken-objects-shatter-in-the-most-annoying-way-possible