Hidden law behind chaos: Why do things break in the same way? | sciences

When a plate is dropped or a glass is broken, the result is pure chaos, with many shards of varying sizes scattered around. But some physicists see in this chaos a deep question: Why does one thing break down into such a large variety of sizes?

Physicist Emanuele Filermo, from the University of Aix-Marseille in Italy, proposes a simple and elegant law that describes the method of disintegration, not only in glass and ceramics, but also in liquid droplets and bubbles that explode.

The idea that has haunted scientists for a long time is that there is “something universal” in fragmentation. If you count the number of fragments within each size category and draw the distribution of sizes in the form of a curve, you may find that the shape of the curve is almost the same, no matter how different the fragmented body is, that is, the details differ, but the general statistical fingerprint may remain constant.

Maximum randomness

Filermo started from the observation that the breaking event is usually very chaotic and rapid, and he saw that the most likely outcome is often the most random and not the most regular, and he called this principle “maximum randomness.”

And according to the studywhich Filermo published in the journal Physical Review Letters, means that nature tends to take the “least resistance” and more scattered path.

But chaos, as the researcher asserts, is not without limits, so he introduced a physical constraint that he called the “law of conservation,” and his research group had previously arrived at it. This constraint works as a hidden rule that prevents the “general scale” of fragmentation (the ratio of large to small in the overall image) from changing arbitrarily during refraction.

Power law

By combining extreme randomness with the conservation constraint, Filermo arrived at what he calls a universal law of fragmentation, meaning that it applies to everything in the universe, from the fragmentation of a homemade dessert plate to the stars in the depths of space.

According to Filermo, this combination automatically leads to the distribution of fragment sizes taking the form of a “power law,” which is a way to describe a phenomenon in which the number of small objects is much greater than the number of large objects according to a fixed pattern, which is that the smaller the size, the greater the number, but not randomly, but in an exponential mathematical relationship.

In the context of glass fragmentation, for example, this means that you will find many very small fragments, and few large fragments, and a regular gradation between them. If you double the size of the fragment, its number does not decrease by a fixed amount, but rather it decreases by a rate that depends on an “exponent.” This is why it is said that fragmentation follows a “power law.”

Effective experiences

The new research is not limited to theoretical propositions, as Filermo compared the law’s predictions to a large amount of fragmentation data collected over decades, and found excellent agreement with many cases involving fragile materials and liquids.

The researcher then conducted a direct test of his method, crushing individual sugar cubes, and was able to accurately predict the pattern of fragment sizes based on the cube being a three-dimensional object.

However, the law does not claim to explain all breakage scenarios. It works best when the fragmentation is truly random, such as a cup suddenly hitting the ground.

However, despite this, the law fails or is weakened if the material is very soft (such as types of plastic), or if the disintegration is organized by nature, as the phenomenon of surface tension does when water is divided into drops of similar size. Here, the “geometry” of the separation becomes governed by a special mechanism, not by general chaos, so the universality that the law seeks is absent.