@article{MTMT:34168012,
	title = {On Equilibria of Tetrahedra},
	url = {https://m2.mtmt.hu/api/publication/34168012},
	author = {Almádi, G. and MacG., Dawson R.J. and Domokos, Gábor and Regős, Krisztina},
	doi = {10.1007/s00283-023-10294-2},
	journal-iso = {MATH INTELL},
	journal = {MATHEMATICAL INTELLIGENCER},
	volume = {46},
	unique-id = {34168012},
	issn = {0343-6993},
	year = {2024},
	eissn = {1866-7414},
	pages = {247-254},
	orcid-numbers = {Regős, Krisztina/0000-0001-6866-2658}
}

@article{MTMT:35598288,
	title = {On an abrasion-motivated fractal model},
	url = {https://m2.mtmt.hu/api/publication/35598288},
	author = {Bárány, Balázs and Domokos, Gábor and Szesztay, Ágoston Péter},
	doi = {10.1088/1361-6544/ad8c0f},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {35598288},
	issn = {0951-7715},
	abstract = {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.},
	year = {2024},
	eissn = {1361-6544},
	orcid-numbers = {Bárány, Balázs/0000-0002-0129-8385}
}

@article{MTMT:34979527,
	title = {Same average in every direction},
	url = {https://m2.mtmt.hu/api/publication/34979527},
	author = {Barany, Imre and Domokos, Gábor},
	journal-iso = {B MATH SOC SCI MATH},
	journal = {SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE. BULLETIN MATHEMATIQUE},
	volume = {67},
	unique-id = {34979527},
	issn = {1220-3874},
	keywords = {Convex polytopes; Zonotopes; number of vertices; fragmentation.},
	year = {2024},
	eissn = {2065-0264},
	pages = {125-138}
}

@article{MTMT:35263008,
	title = {Soft cells and the geometry of seashells},
	url = {https://m2.mtmt.hu/api/publication/35263008},
	author = {Domokos, Gábor and Goriely, Alain and G. Horváth, Ákos and Regős, Krisztina},
	doi = {10.1093/pnasnexus/pgae311},
	journal-iso = {PNAS NEXUS},
	journal = {PNAS NEXUS},
	volume = {3},
	unique-id = {35263008},
	abstract = {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.},
	year = {2024},
	eissn = {2752-6542},
	orcid-numbers = {Goriely, Alain/0000-0002-6436-8483; G. Horváth, Ákos/0000-0003-2371-4818; Regős, Krisztina/0000-0001-6866-2658}
}

@article{MTMT:33578682,
	title = {A discrete time evolution model for fracture networks},
	url = {https://m2.mtmt.hu/api/publication/33578682},
	author = {Domokos, Gábor and Regős, Krisztina},
	doi = {10.1007/s10100-022-00838-w},
	journal-iso = {CEJOR},
	journal = {CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH},
	volume = {32},
	unique-id = {33578682},
	issn = {1435-246X},
	abstract = {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.},
	year = {2024},
	eissn = {1613-9178},
	pages = {83-94},
	orcid-numbers = {Regős, Krisztina/0000-0001-6866-2658}
}

@article{MTMT:34550819,
	title = {Morse–Smale complexes on convex polyhedra},
	url = {https://m2.mtmt.hu/api/publication/34550819},
	author = {Ludmány, Balázs and Lángi, Zsolt and Domokos, Gábor},
	doi = {10.1007/s10998-024-00583-4},
	journal-iso = {PERIOD MATH HUNG},
	journal = {PERIODICA MATHEMATICA HUNGARICA},
	volume = {89},
	unique-id = {34550819},
	issn = {0031-5303},
	abstract = {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.},
	year = {2024},
	eissn = {1588-2829},
	pages = {1-22},
	orcid-numbers = {Ludmány, Balázs/0000-0001-5373-7610; Lángi, Zsolt/0000-0002-5999-5343}
}

@article{MTMT:33665427,
	title = {An evolution model for polygonal tessellations as models for crack networks and other natural patterns},
	url = {https://m2.mtmt.hu/api/publication/33665427},
	author = {Bálint, Péter and Domokos, Gábor and Regős, Krisztina},
	doi = {10.1007/s10955-023-03146-y},
	journal-iso = {J STAT PHYS},
	journal = {JOURNAL OF STATISTICAL PHYSICS},
	volume = {190},
	unique-id = {33665427},
	issn = {0022-4715},
	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.},
	year = {2023},
	eissn = {1572-9613},
	orcid-numbers = {Regős, Krisztina/0000-0001-6866-2658}
}

@inproceedings{MTMT:34383912,
	title = {A Technique for the Measurement of the Morphological Evolution of Marine Pebbles},
	url = {https://m2.mtmt.hu/api/publication/34383912},
	author = {Bertoni, Duccio and Di Renzone, Gabriele and Domokos, Gábor and Favaretto, Chiara and Pozzebon, Alessandro and Sarti, Giovanni},
	booktitle = {2023 IEEE International Workshop on Metrology for the Sea; Learning to Measure Sea Health Parameters (MetroSea)},
	doi = {10.1109/MetroSea58055.2023.10317284},
	unique-id = {34383912},
	year = {2023},
	pages = {433-438}
}

@article{MTMT:34108939,
	title = {Conway’s Spiral and a Discrete Gömböc with 21 Point Masses},
	url = {https://m2.mtmt.hu/api/publication/34108939},
	author = {Domokos, Gábor and Kovács, Flórián},
	doi = {10.1080/00029890.2023.2241336},
	journal-iso = {AM MATH MON},
	journal = {AMERICAN MATHEMATICAL MONTHLY},
	volume = {130},
	unique-id = {34108939},
	issn = {0002-9890},
	year = {2023},
	eissn = {1930-0972},
	pages = {795-807},
	orcid-numbers = {Kovács, Flórián/0000-0002-8374-8035}
}

@article{MTMT:33742876,
	title = {A characterization of the symmetry groups of mono-monostatic convex bodies},
	url = {https://m2.mtmt.hu/api/publication/33742876},
	author = {Domokos, Gábor and Lángi, Zsolt and Várkonyi, Péter László},
	doi = {10.1007/s00605-023-01847-w},
	journal-iso = {MONATSH MATH},
	journal = {MONATSHEFTE FUR MATHEMATIK},
	volume = {201},
	unique-id = {33742876},
	issn = {0026-9255},
	abstract = {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.},
	year = {2023},
	eissn = {1436-5081},
	pages = {703-724},
	orcid-numbers = {Lángi, Zsolt/0000-0002-5999-5343}
}