TY - JOUR AU - Almádi, G. AU - MacG., Dawson R.J. AU - Domokos, Gábor AU - Regős, Krisztina TI - On Equilibria of Tetrahedra JF - MATHEMATICAL INTELLIGENCER J2 - MATH INTELL VL - 46 PY - 2024 SP - 247 EP - 254 PG - 8 SN - 0343-6993 DO - 10.1007/s00283-023-10294-2 UR - https://m2.mtmt.hu/api/publication/34168012 ID - 34168012 N1 - HUN-REN-BME Morphodynamics Research Group, Budapest University of Technology and Economics, Műegyetem Rakpart 1-3., Budapest, 1111, Hungary Department of Mathematics and Computing Science, Saint Mary’s University, Halifax, NS B3H 3C3, Canada Department of Morphology and Geometric Modeling and ELKH-BME Morphodynamics Research Group, Budapest University of Technology and Economics, Műegyetem Rakpart 1-3., Budapest, 1111, Hungary Export Date: 2 October 2023 Correspondence Address: Almádi, G.; HUN-REN-BME Morphodynamics Research Group, Műegyetem Rakpart 1-3., Hungary; email: gergo.almadi14@gmail.com LA - English DB - MTMT ER - TY - JOUR AU - Bárány, Balázs AU - Domokos, Gábor AU - Szesztay, Ágoston Péter TI - On an abrasion-motivated fractal model JF - NONLINEARITY J2 - NONLINEARITY VL - 37 PY - 2024 IS - 12 PG - 25 SN - 0951-7715 DO - 10.1088/1361-6544/ad8c0f UR - https://m2.mtmt.hu/api/publication/35598288 ID - 35598288 N1 - Department of Stochastics, Institute of Mathematics, Budapest University of Technology and Economics, Muegyetem rpk. 1-3., Budapest, H-1111, Hungary Department of Morphology and Geometric Modeling, Budapest University of Technology and Economics, Muegyetem rpk. 1-3., Budapest, H-1111, Hungary HUN-REN-BME Morphodynamics Research Group, Budapest University of Technology and Economics, Muegyetem rpk. 1-3., Budapest, H-1111, Hungary Department of Mechanics,Materials and Structures, Budapest University of Technology and Economics, Muegyetem rpk. 1-3., Budapest, H-1111, Hungary Export Date: 25 November 2024 Correspondence Address: Bárány, B.; Department of Stochastics, Muegyetem rpk. 1-3., Hungary; email: barany.balazs@ttk.bme.hu Funding details: Budapesti Műszaki és Gazdaságtudományi Egyetem, BME Funding details: Nemzeti Kutatási, Fejlesztési és Innovaciós Alap, NKFIA Funding details: 134199, 149429 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, KKP144059, K142169, FK134251 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH Funding text 1: BB acknowledges support from Grants NKFI FK134251, NKFI K142169 and NKFI KKP144059 \\u2018Fractal geometry and applications\\u2019 Research Group. GD acknowledges support from the NKFIH Hungarian Research Fund Grants 134199 and 149429, and BME FIKP-V\\u00CDZ. \\u00C1Sz is supported by the Doctoral Excellence Fellowship Programme (DCEP) is funded by the National Research Development and Innovation Fund of the Ministry of Culture and Innovation and the Budapest University of Technology and Economics under a grant agreement with the National Research, Development and Innovation Office. AB - In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping. LA - English DB - MTMT ER - TY - JOUR AU - Barany, Imre AU - Domokos, Gábor TI - Same average in every direction JF - SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE. BULLETIN MATHEMATIQUE J2 - B MATH SOC SCI MATH VL - 67 PY - 2024 IS - 2 SP - 125 EP - 138 PG - 14 SN - 1220-3874 UR - https://m2.mtmt.hu/api/publication/34979527 ID - 34979527 LA - English DB - MTMT ER - TY - JOUR AU - Domokos, Gábor AU - Goriely, Alain AU - G. Horváth, Ákos AU - Regős, Krisztina TI - Soft cells and the geometry of seashells JF - PNAS NEXUS J2 - PNAS NEXUS VL - 3 PY - 2024 IS - 9 PG - 10 SN - 2752-6542 DO - 10.1093/pnasnexus/pgae311 UR - https://m2.mtmt.hu/api/publication/35263008 ID - 35263008 AB - A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. However, many tilings in Nature are characterized by shapes with curved edges, nonflat faces, and few, if any, sharp corners. An important question is then to relate prototypical sharp tilings to softer natural shapes. Here, we solve this problem by introducing a new class of shapes, the soft cells, minimizing the number of sharp corners and filling space as soft tilings. We prove that an infinite class of polyhedral tilings can be smoothly deformed into soft tilings and we construct the soft versions of all Dirichlet–Voronoi cells associated with point lattices in two and three dimensions. Remarkably, these ideal soft shapes, born out of geometry, are found abundantly in nature, from cells to shells. LA - English DB - MTMT ER - TY - JOUR AU - Domokos, Gábor AU - Regős, Krisztina TI - A discrete time evolution model for fracture networks JF - CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH J2 - CEJOR VL - 32 PY - 2024 SP - 83 EP - 94 PG - 12 SN - 1435-246X DO - 10.1007/s10100-022-00838-w UR - https://m2.mtmt.hu/api/publication/33578682 ID - 33578682 AB - We examine geological crack patterns using the mean field theory of convex mosaics. We assign the pair \left({\overline{n } }^{*},{\overline{v } }^{*}\right) n ¯ ∗ , v ¯ ∗ of average corner degrees (Domokos et al. in A two-vertex theorem for normal tilings. Aequat Math https://doi.org/10.1007/s00010-022-00888-0 , 2022) to each crack pattern and we define two local, random evolutionary steps R 0 and R 1 , corresponding to secondary fracture and rearrangement of cracks, respectively. Random sequences of these steps result in trajectories on the \left({\overline{n } }^{*},{\overline{v } }^{*}\right) n ¯ ∗ , v ¯ ∗ plane. We prove the existence of limit points for several types of trajectories. Also, we prove that cell density \overline{\rho }= \frac{{\overline{v } }^{*}}{{\overline{n } }^{*}} ρ ¯ = v ¯ ∗ n ¯ ∗ increases monotonically under any admissible trajectory. LA - English DB - MTMT ER - TY - JOUR AU - Ludmány, Balázs AU - Lángi, Zsolt AU - Domokos, Gábor TI - Morse–Smale complexes on convex polyhedra JF - PERIODICA MATHEMATICA HUNGARICA J2 - PERIOD MATH HUNG VL - 89 PY - 2024 IS - 1 SP - 1 EP - 22 PG - 22 SN - 0031-5303 DO - 10.1007/s10998-024-00583-4 UR - https://m2.mtmt.hu/api/publication/34550819 ID - 34550819 AB - Motivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional Euclidean space. The resulting polyhedral Morse–Smale complex may be regarded, on one hand, as a generalization of the Morse–Smale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the Morse–Smale complex of the piecewise linear parallel distance function (measured from a plane), defining a polyhedral surface. Beyond similarities, our paper also highlights the marked differences between these three problems and it also relates our theory to other methods. Our work includes the design, implementation and testing of an explicit algorithm computing the Morse–Smale complex on a convex polyhedron. LA - English DB - MTMT ER - TY - JOUR AU - Bálint, Péter AU - Domokos, Gábor AU - Regős, Krisztina TI - An evolution model for polygonal tessellations as models for crack networks and other natural patterns JF - JOURNAL OF STATISTICAL PHYSICS J2 - J STAT PHYS VL - 190 PY - 2023 IS - 8 PG - 30 SN - 0022-4715 DO - 10.1007/s10955-023-03146-y UR - https://m2.mtmt.hu/api/publication/33665427 ID - 33665427 AB - 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. LA - English DB - MTMT ER - TY - CHAP AU - Bertoni, Duccio AU - Di Renzone, Gabriele AU - Domokos, Gábor AU - Favaretto, Chiara AU - Pozzebon, Alessandro AU - Sarti, Giovanni TI - A Technique for the Measurement of the Morphological Evolution of Marine Pebbles T2 - 2023 IEEE International Workshop on Metrology for the Sea; Learning to Measure Sea Health Parameters (MetroSea) PB - Institute of Electrical and Electronics Engineers (IEEE) CY - Piscataway (NJ) SN - 9798350340662 PY - 2023 SP - 433 EP - 438 PG - 6 DO - 10.1109/MetroSea58055.2023.10317284 UR - https://m2.mtmt.hu/api/publication/34383912 ID - 34383912 N1 - University of Pisa, Department of Earth Sciences, Pisa, Italy University of Pisa, Department of Information Engineering, Pisa, Italy Budapest University of Technology and Economics, Department of Morphology and Geometric Modeling, HUN-REN-BME Morphodynamics Research Group, Budapest, Hungary University of Padova, Department of Civil, Environmental and Architectural Engineering, Padova, Italy University of Padova, Department of Information Engineering, Padova, Italy Conference code: 194563 Export Date: 22 December 2023 Correspondence Address: Bertoni, D.; University of Pisa, Italy; email: duccio.bertoni@unipi.it LA - English DB - MTMT ER - TY - JOUR AU - Domokos, Gábor AU - Kovács, Flórián TI - Conway’s Spiral and a Discrete Gömböc with 21 Point Masses JF - AMERICAN MATHEMATICAL MONTHLY J2 - AM MATH MON VL - 130 PY - 2023 IS - 9 SP - 795 EP - 807 PG - 13 SN - 0002-9890 DO - 10.1080/00029890.2023.2241336 UR - https://m2.mtmt.hu/api/publication/34108939 ID - 34108939 N1 - Hungarian Academy of Sciences, Hungary Department of Morphology and Geometric Modeling and ELKH-BME Morphodynamics Research Group, Budapest University of Technology and Economics, Budapest, H-1111, Hungary Budapest University of Technology and Economics, Hungary Department of Structural Mechanics and ELKH-BME Morphodynamics Research Group, Budapest University of Technology and Economics, Budapest, H-1111, Hungary Export Date: 24 August 2023 LA - English DB - MTMT ER - TY - JOUR AU - Domokos, Gábor AU - Lángi, Zsolt AU - Várkonyi, Péter László TI - A characterization of the symmetry groups of mono-monostatic convex bodies JF - MONATSHEFTE FUR MATHEMATIK J2 - MONATSH MATH VL - 201 PY - 2023 IS - 3 SP - 703 EP - 724 PG - 22 SN - 0026-9255 DO - 10.1007/s00605-023-01847-w UR - https://m2.mtmt.hu/api/publication/33742876 ID - 33742876 N1 - ELKH-BME Morphodynamics Research Group, Budapest University of Technology, Műegyetem rakpart 1-3, Budapest, 1111, Hungary Department of Morphology and Geometric Modeling, Budapest University of Technology and Economics, Budapest, H-1111, Hungary Department of Geometry, Budapest University of Technology, Egry József utca 1, Budapest, 1111, Hungary Department of Mechanics, Materials and Structures, Budapest University of Technology, Műegyetem rakpart 1-3, Budapest, 1111, Hungary Export Date: 11 April 2023 Correspondence Address: Lángi, Z.; Department of Geometry, Egry József utca 1, Hungary; email: zlangi@math.bme.hu AB - Answering a question of Conway and Guy (SIAM Rev. 11:78-82, 1969), Langi (Bull. Lond. Math. Soc. 54: 501-516, 2022) proved the existence of a monostable polyhedron with n-fold rotational symmetry for any n = 3, and arbitrarily close to a Euclidean ball. In this paper we strengthen this result by characterizing the possible symmetry groups of all mono-monostatic smooth convex bodies and convex polyhedra. Our result also answers a stronger version of the question of Conway and Guy, asked in the above paper of Langi. LA - English DB - MTMT ER -