New paper and an interview on planetary surface mosaics

Decoding planetary surfaces by counting cracks
Sophie Silver, Douglas Jerolmack, Krisztina Regős, Gábor Domokos.

Abstract: Planets are often covered with thin cracked shells. From mud films to lithospheres of rock or ice, fracture networks form two-dimensional (2D) tessellations of convex polygons whose geometry encodes their genesis. Here, we chart the geometry of 2D fracture mosaics across the solar system, and decode their formative conditions using a new dynamical crack model. We show that mosaics can be projected onto a Symbolic Ternary Diagram, where the relative proportions of “T,” “X,” and “Y” junctions are uniquely related to contributions from distinct modes of fracture. Most planetary mosaics cluster in a region associated with hierarchical fracture networks, where sequential cracking favors formation of T junctions. Exceptions to this rule may betray the presence of water. Europa’s fracture networks stand apart due to the predominance of X junctions; this is a special feature of ice, where healing of cracks by refreezing of water allows new fractures to overprint older ones. Several fracture networks on Mars appear as outliers due to the high proportion of Y junctions. These patterns—previously interpreted as ancient mudcracks and frozen polar terrain, based on geological evidence—are consistent with the twisting of crack junctions by cyclic volume change. Our findings suggest that counting cracks could aid in the identification of other water-influenced planetary environments.

(See also the related interview at the website of BME.)

Public lecture of Sándor Bozóki on monostable convex polyhedra

A public lecture has been presented within the framework of Celebration of Hungarian Science (“Magyar tudomány ünnepe”) by Sándor Bozóki. The lecture (in Hungarian) is available at the following link:
Proof of non-existence of mono-unstable polyhedra by means of inequalities (Monoinstabil poliéderek nemlétezésének igazolása egyenlőtlenségekkel)

Gomboc software in sailing

The Gomboc simulation software – whose name was chosen after the Gömböc of Gábor Domokos and Péter Várkonyi – played a crucial role in the the 36th America’s cup.

Read more (in Hungarian): A MAGYAR GÖMBÖCRŐL ELNEVEZETT GOMBOC SZOFTVERREL DIADALMASKODOTT A GYŐZTES CSAPAT A VILÁG LEGELITEBB VITORLÁSVERSENYÉN

An article about the Gomboc software in the 35th America’s cup (in English): Gomboc: A design high-flier for ETNZ

New paper on fragmentation

Plato’s cube and the natural geometry of fragmentation
G. Domokos, D.J. Jerolmack, F. Kun, J. Török
arxiv:1912.04628

Abstract: Plato envisioned Earth’s building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra—shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth’s tectonic plates, has two attractors: “Platonic” quadrangles and “Voronoi” hexagons. In three dimensions (3D), the Platonic attractor is dominant: Remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato’s forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation.

 

The article was followed by increased media attention. Here is a list of the international and national mentions of the MTA-BME Morphodynamics Research Group: Media mentions.