Sándor Bozóki, member of the HUN-REN Morphodynamics Research Group has been nominated full professor by the President of Republic on 5th September. Congratulations!
Conway’s Spiral and a Discrete Gömböc with 21 Point Masses
Gábor Domokos, Flórián Kovács.
Abstract: We show an explicit construction in three dimensions for a convex, mono-monostatic polyhedron (i.e., having exactly one stable and one unstable equilibrium) with 21 vertices and 21 faces. This polyhedron is a 0-skeleton, with equal masses located at each vertex. The above construction serves as an upper bound for the minimal number of faces and vertices of mono-monostatic 0-skeletons and complements the recently provided lower bound of 8 vertices. This is the first known construction of a mono-monostatic polyhedral solid. We also show that a similar construction for homogeneous distribution of mass cannot result in a mono-monostatic solid.
An Evolution Model for Polygonal Tessellations as Models for Crack Networks and Other Natural Patterns
Péter Bálint, Gábor Domokos, Krisztina Regős.
Abstract: We introduce and study a general framework for modeling the evolution of crack networks. The evolution steps are triggered by exponential clocks corresponding to local micro-events, and thus reflect the state of the pattern. In an appropriate simultaneous limit of pattern domain tending to infinity and time step tending to zero, a continuous time model, specifically a system of ODE is derived that describes the dynamics of averaged quantities. In comparison with the previous, discrete time model, studied recently by two of the present three authors, this approach has several advantages. In particular, the emergence of non-physical solutions characteristic to the discrete time model is ruled out in the relevant nonlinear version of the new model. We also comment on the possibilities of studying further types of pattern formation phenomena based on the introduced general framework.
Klaudia Nagy, member of the Morphodynamics Research Group, has been awarded as “Student of the Year” at the Faculty of Architecture of BME. Congratulations!
ENSHRINE is a group of volunteer researchers, dedicated to preserve the natural heritage of Tasmania, Australia. Their studies on the behaviour of rocking stones, found in a large number in the area, were also based on some results of the MTA-BME Research Group for Morphodynamics (https://listthemountain.org/natural-features/rocking-stone).
Krisztina Regős, PhD student of the Morphodynamics Research Group was mentioned among the top 30 of most successful people under 30 in Hungary by Forbes.
How things fall apart: The shape of failure across the solar system
Douglas J. Jerolmack, University of Pennsylvania
April 28, 2023
Our guest lecturer, second time since 2019, gave a talk on various aspects of fragmentation in Nature.
The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices
Dávid Papp, Krisztina Regős, Gábor Domokos, Sándor Bozóki
Abstract: In the study of monostatic polyhedra, initiated by John H. Conway in 1966, the main question is to construct such an object with the minimal number of faces and vertices. By distinguishing between various material distributions and stability types, this expands into a small family of related questions. While many upper and lower bounds on the necessary numbers of faces and vertices have been established, none of these questions has been so far resolved. Adapting an algorithm presented in Bozóki et al. (2022), here we offer the first complete answer to a question from this family: by using the toolbox of semidefinite optimization to efficiently generate the hundreds of thousands of infeasibility certificates, we provide the first-ever proof for the existence of a monostatic polyhedron with point masses, having minimal number (V=11) of vertices (Theorem 3) and a minimal number (F=8) of faces. We also show that V=11 is the smallest number of vertices that a mono-unstable polyhedron can have in all dimensions greater than 1.
The “Gömböc” is on permanent display since 17th April, 2023 at Pompidou Centre, Paris. The largest copy of Gömböc ever made of a single piece of material was introduced in the presence of one of its inventors, Gábor Domokos.
Several presentations were held in the session for Mathematics, Physics and Geosciences of the 36th National Scientific Students’ Associations Conference in relation with the Morphodynamics Research Group. Gergő Almádi has been awarded by 3rd prize for his presentation entitled Inhomogén politópok mechanikai komplexitása – avagy van-e egy tetraédernek lelke?, under the supervision of Gábor Domokos and Krisztina Regős. Ágoston Szesztay (Iteratív módon csonkolt poliéderek statikai egyenúlyáról) and Máté Szondi (A kvantummechanikai állapottér egy felbontása által indukált geometria) got special prizes.