Mathematicians may have uncovered the mystery of the form of “stone forest”


in great shape / Stone forest (shilin) ​​in Yunnan province of China can be the result of solids dissolving in liquids in the presence of gravity, producing a natural convection current.

From the Giant Causeway in Ireland to the Castellan Tower in Utah, there are many miraculous geological formations in nature, and the various processes by which such structures have long been of interest to scientists. A team of applied mathematicians from New York University has focused their attention on so-called “stone forests” in some areas of China and Madagascar. According to the NYU team, these pointed stone structures, like the famous stone forest in Yunnan province, China, are the result of solids dissolving in liquids, creating a natural convection flow. He described his findings in a recent paper published in the Proceedings of the National Academy of Sciences.

Co-author Leaf Ristrof told Aers that his group at NYU’s Applied Math Lab is interested in studying stone forests (technically a type of karst topography) somewhat indirectly. They were using simulations and experiments to detect interesting shapes that develop in the landscape due to a number of “shaping” processes, most notably erosion and disintegration.

“We first discovered spikes formed by disintegration when we released the candy into a water tank and later came back to find a needle-like spire,” he said. “The first author, Mac Huang, a graduate student, also accidentally cut himself off while he was looking at the figure. It got us into the problem, and when we were feeling the connection to the stone forests and the stone forests, We were very excited, which was very mysterious. In their development. We hope that our experiments will tell a simple ‘origin story’ behind these landscapes. ”

To test their simulations in the lab, the team combined water in granulated table sugar, corn syrup, and molds to create blocks of solid and hard (hard-cracked candy) and single pillars — an approximation for soluble rocks. Are those that usually make cast stography. . The mold for the block involves leveling an array of homogeneous metal rods into “seeds”, adjacent to the holes along the block. They placed these candy blocks and pillars in a plexiglass tank filled with room-temperature water – so deep that the dissolved sugar settled downstream, away from the test of objects. He captured the disintegration process by taking digital photographs at intervals of one minute each.

You can watch a time-lapse video of the experiment below, in which a brittle block the size of a candy can be seen in an array of sharp spikes similar to a nail bed. The block starts from the internal pores and sinks completely under water, where it dissolves and becomes a “candy forest” before collapsing.

It still occurs in water. “We found that the disintegration process itself generates the flow responsible for engraving the spike shape,” Ristrof said. “Basically, the mineral – or, in our experiments, the lollipop candy serving as ‘mock rock’ – dissolves and the surrounding fluid becomes heavier and then flows downward due to gravity. So our system Does not require any special flow conditions or other external conditions. Or environmental conditions: This recipe only involves dissolving in liquid and gravity. ”

Ristroph and others. Suggest that a similar mechanism is working in the construction of stone forests, just on a much longer time scale. Soluble rocks such as limestone, dolomite, and gypsum submerge under water, where minerals slowly dissolve in the surrounding water. The heavy water is then submerged under gravity, and the flow slowly builds up the topography. When the water fills, pillars and stone forests emerge.

On the surface, these stone forests resemble “penitents”: snowy pillars of ice that form in very dry air, found high in the Andaman glaciers. Some physicists have suggested that when sunlight evaporates directly into steam, without passing through the water phase (sublimation), when the peritants are formed. Smaller peaks and troughs are formed, and sunlight is trapped within them, creating additional heat, which also ejects deeper troughs, and those curved surfaces act as a lens, which is high Makes the making process even faster. An alternative proposal is added to an additional mechanism, which accounts for the odd periodic fixed interval of the periodant: a combination of vapor diffusion and heat transport that produces a steep temperature gradient, and therefore a higher rate of change.

Physicists have been able to recreate artificial versions of the penitent in the laboratory. But austerities and stone forests actually differ greatly in terms of the mechanisms involved in their formation. “I think the similarities are very superficial,” Ristrof said. “Of course, the ‘skulping’ process is very different in terms of the main driving effects. Primarily, our spikes are carved a lot by the flow, which I don’t think plays a big role in the creation of the penitent . ”

Granted, NYU researchers got their results under ideal conditions – intentionally therefore, according to the authors, better to clearly identify and characterize the incisive process, the underlying mechanism, and the mathematical structure. As a result, “this study suggests that a minimal set of materials required for the motifs of needle and bed nails,” the authors wrote. In the future, they hope to test this formation process in the laboratory under varying environmental conditions, such as precipitation and surface runoff, or being buried under loose sediment, may affect peak formation.

DOI: PNAS, 2020. 10.1073 / pnas.2001524117 (about DOIs).