Research: The structure of ridges is universally similar

Research: The structure of ridges is universally similar

IFJ PAN scientists’ research on ridges using graphics and fractals has shown that the structures of land and mountain blocks on all continents are generally similar. Among other things, play in the Alps, Andes, Himalayas and Appalachians.

Mountain has its own characteristics. A series of gentle rolling hills and wide valleys known from the Carpathians, Appalachians and the lower Alps, with the towering peaks of the Tatras and Pyrenees, jagged The ridges and deep canyons are in sharp contrast, which is different from the inaccessible, snow-covered Himalayas or Andean giants, which have glacier tongues instead of slopes of currents. However, behind this huge change, there are surprisingly similar structures.

Scientists from the Institute of Nuclear Physics (IFJ PAN) of the Polish Academy of Sciences in Krakow used graphics and fractals to study the structure of our planet’s mountain blocks. The statistical review includes the Alps, the Pyrenees, the Scandinavian mountains, the Bettich mountains, the Himalayas, the Andes, the Appalachians, the Atlas mountains and the Southern Alps. Kind of area. The analysis was published in an article in the “Complex Network Journal” and led to unexpected findings. Facts have proved that the structure of the earth’s mountain blocks has universal similarities. You can see them in mountains on all continents, regardless of the size of their peaks, their ages, and even their origins in structures or volcanoes. Representatives of the PAS Institute of Nuclear Physics informed the research in a press release sent to PAP.

“The seemingly only common feature of each mountain range is that you must look high when you look at them. Only by converting a common mountain topographic map to a ridge map, that is, a map showing the routes of all ridge axes, can you see the true similarity Sex. Jarosław Kwapień of IFJ PAN then added: “The axis of the ridge is a line that runs along the ridge, and the terrain drops on both sides. Therefore it is opposite to the axis of the valley. “

Ridges are not separate strata. They merge into a large branch structure, like a tree: in the main ridge (“trunk”) there are longer or shorter first-order lateral ridges (“branches”), from which there are second-order lateral ridges (” branch”), from the next to the next. The whole has a clear hierarchical structure, and the number of levels of complexity depends on the size of the area covered by the mountain, and may even reach a dozen. This type of structure is represented in different diagrams. For example, each ridge of a given lot can be considered a node. When the corresponding game is also connected, the two nodes are connected by a line (the edge of the graph). In this kind of graph, some nodes are large in number (they are connected to many nodes), while others are small.

“The distribution of spine knots is a multiple distribution, with power. This means that regardless of the selected multiplicity, the number of nodes with multiplicity, for example, the number of nodes with multiplicity 2 is in a constant relationship. The distribution increases by a certain constant. Each segment of the looks like a whole, which means that there is no scale to distinguish”-said Dr. Kwapień.

“Regardless of the type of mountain range, the index of distributed force is within a very narrow range of about 5/3. If we consider the accuracy of the method, then this narrow range of values ​​may even mean that the index is the same in every case! ” -Attention Dr. Kwapień.

The observed homogeneity is due to the fact that the main mechanism responsible for mountain relief is basically the same everywhere on our planet. Tectonic movement or volcanic activity is a necessary condition for the uplift of this area, but the most important mitigating factors are water and glacier erosion. Water and ice break and crush rocks, and then transport the crushed materials to lowlands. In this way, ravines, canyons and valleys are formed, and ridges are formed.

Since the waterways that form the drainage system of a given area have a tree structure in nature (except for desert areas, of course), a similar structure appears in the ridge system. But why is the relationship between ridges with different branches so similar for different types of mountains?

Dr. Kwapień explained: “In addition to water, we also considered gravity and the situation became clearer.”-When crushing rock material, regardless of its chemical composition, it will be affected by loose objects. Only when the inclination angle is not too large, can the bulk objects on the slope be kept. The slope cannot be too steep. This is why the depth of the valley in nature is limited by its own width. The narrow river valley with almost vertical walls only exists in the early stages of the formation of the reliefs. They are rare in mature mountains because their walls have been slanted.

The existence of a river system is to drain water from a given area, erosion to break rocks, hollow out valleys, and gravitational landslides of rock fragments, which means that the ridges cannot be close or far apart anywhere. Their best arrangement has nothing to do with the characteristics of the mountains, and gives them some universal characteristics.

The above observation is a supplement to another observation made by physicists from IFJ PAN on the fractal dimension of the ridge structure. The fractal dimension describes how rough the structure of the inspection object is.

The size of a ridge is 1. If the arrangement of lines (ridges) is very dense, their fractal size will correspond to the size of the surface, so it is 2.

Researchers in Krakow showed that if the ridge structure is represented as a graph, its nodes are the intersection points of the ridges (most often appearing at the intersection of peaks), and the edges of the graph are the ridges connecting the peaks. The fractal dimension of the class diagram will be roughly equal to… 5/3.

“In some pictures, you can see the hierarchical structure of the mountain structure, while in others you can see their fractal nature. In both cases, we will encounter the same number for all types of mountains The same value. This kind of universalism is thought-provoking”-said the professor. Dr. Hab. Stanisław Drożdż (IFJ PAN, Krakow University of Technology).

Since each mountain range is so similar in terms of analysis scale, where is the source of mountain diversity? Is it possible to study them with the help of graph theory and fractal geometry? Is it possible to create a model in which the evolution map will mimic the subsequent stages of mountain sculpture formation? Finally, can the conversion of ridge diagrams into graphics be applied in practice, for example in cartography? These and more questions will be answered in future research.

PAP-Science of Poland

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