Skoltech mathematicians have revealed the secret of the formation of the most unusual natural structures - graceful columns, arches and other architectural elements that are often found in the mountains, and published their findings in Scientific Reports.
The appearance of the Earth changes almost every second due to the movement of continents, the circulation of rocks in its depths and various forms of erosion. The main “sculptors” of the planet's face are not people, but wind, rivers, rains, glaciers and other forces and phenomena. Over the past few centuries, scientists have discovered several hundred erosional landforms, in the formation of which dozens of different processes and factors are involved.
The most striking and unusual of these are the giant stone arches, bridges, columns and other complex structures that can be seen in the mountains, made of sandstone and other soft rocks. The history of their formation was one of the most interesting mysteries for mankind, and many ignorant people seriously assumed that they were sculpted by representatives of ancient civilizations or even "guests" from space.
Three years ago, mathematicians from Charles University in Prague (Czech Republic) found out that their "sculptor" was the wind, and not aliens or ancient architects. They found that these columns and arches result from an unusual process of self-organization of sand grains within sandstone strata that are eroded by the wind, which causes them to cling tighter to each other as the arch or column is "born".
Igor Ostanin, a Skoltech researcher, and his colleagues became interested in the discovery of their Czech colleagues when they noticed that the phenomenon they described is very similar to how the most "advanced" engineers and architects today optimize the shape and structure of man-made columns, arches and other structures, where both high strength and low weight are required.
“We could not help but notice that similar methods of finding optimal forms of structures are widely used in modern industry. These methods, evolutionary structural optimization, are based on the gradual removal of ineffective material. The most striking aspect of this similarity is that the mathematical criterion by which material is removed during optimization is almost exactly the same as the criterion that follows from the physics of the erosion process,”says Igor Ostanin, a researcher at Skoltech.
Guided by this guess, Ostanin and his colleagues created a set of mathematical formulas describing the process of wind erosion, and tried to "build" an arch with it using a computer model of the sandstone formation.
It was extremely simple - sandstone, in fact, consisted of many almost unrelated cubes that pressed on neighbors with a certain force. If this force exceeded a certain value, then the wind could not move this "cube" from its place, and otherwise it disappeared from the layer after a certain period of time.
Promotional video:
Experimenting with this model, Russian scientists confirmed the findings of their Czech counterparts and revealed several physical principles that explain how these columns and arches are born. In its most general form, they were able to show that the wind plays the role of a kind of "computer" that tries to shape the sandstone layer into a minimum amount of elastic deformation energy, very gradually and accidentally removing the weakest elements from the structure.
Initially, this process proceeds very quickly, but after several hundred years, when the shape of a column or arch is already approaching the ideal, erosion slows down sharply, since almost all "cubes" begin to cling to each other with great force. Thanks to this, real mountain arches and columns can exist for millions of years in an almost intact form.
Such conclusions, as Ostanin notes, are important not only for engineers and geologists, but also for people looking for traces of extraterrestrial life. Now, as Russian mathematicians emphasize, such structures, which, for example, can be discovered on Mars, in principle, cannot be considered traces of extraterrestrial civilizations.
