Two researchers from the Higher Council for Scientific Research (CSIC), Alberto Enciso and Daniel Peralta, from the Institute of Mathematical Sciences (ICMAT), have managed to decipher a substantial mathematical enigma , unsolved by the scientific community for 140 years. The finding has been published in the journal Acta Mathematica .
The problem was originally raised in 1875 by the Scottish physicist William Thomson, first Baron Kelvin (creator, among many other things, of the Kelvin temperature scale) as a way of understanding the atomic structure of matter. Lord Kelvin suggested that knotted tubes could appear in stationary fluids that would explain the composition of matter; thus this would be formed by these same structures in the form of a loop (the atoms) that floated in the ether.
Although Kelvin’s atomic conception was incorrect, the results of the investigations of these two experts prove that the structures do correspond to the configuration of fluid matter . That is, fluids in equilibrium can accommodate twisted donut-shaped structures in a complex manner. These shapes, known as knotted vorticity tubes, are also related to fluid turbulence.
“Arc-shaped tongues of plasma appear on the surface of the Sun, which are vorticity tubes. Physicists had already observed these phenomena, but we have provided solid information: we have proven that structures such as those observed and others much more complicated are mathematically possible ”, the researchers explain.
The importance of this resolution , confirmed in the Irvine laboratory of the James Franck Institute of the University of Chicago in the USA (where they managed to reproduce some of these complex structures in fluids) lies not only in the world of physics, but also in pure mathematics. , specifically in the development of the well-known but complicated “Theory of Knots”.
“It is a very sophisticated demonstration and has required a detailed analysis of the fluid mechanics equations, using concepts we have worked on for the last 10 years, ” declare Enciso and Peralta.
