Search results for "Geometry"
showing 10 items of 4487 documents
Approximation of pore space with ellipsoids: a comparison of a geometrical method with a statistical one.
2018
International audience; We work with tomographic images of pore space in soil. The images have large dimensions and so in order to speed-up biological simulations (as drainage or diffusion process in soil), we want to describe the pore space with a number of geometrical primitives significantly smaller than the number of voxels in pore space. In this paper, we use the curve skeleton of a volume to segment it into some regions. We describe the method to compute the curve skeleton and to segment it with a simple segment approximation. We approximate each obtained region with an ellipsoid. The set of final ellipsoids represents the geometry of pore space and will be used in future simulations.…
Mechanical Detection of the De Haas–van Alphen Effect in Graphene
2022
Funding Information: We thank V. Falko, M. Kumar, and S. Paraoanu for useful discussions. This work was supported by the Academy of Finland projects 314448 (BOLOSE) and 336813 (CoE, Quantum Technology Finland) as well as by ERC (grant no. 670743). The research leading to these results has received funding from the European Unions Horizon 2020 Research and Innovation Programme, under Grant Agreement no 824109, and the experimental work benefited from the Aalto University OtaNano/LTL infrastructure. A.L. is grateful to Osk. Huttunen foundation for a scholarship. J.M. thanks the Väisälä Foundation of the Finnish Academy of Science and Letters for support. F.M. acknowledges financial support fr…
Geometry and quasisymmetric parametrization of Semmes spaces
2011
We consider decomposition spaces R 3 /G that are manifold factors and admit defining sequences consisting of cubes-with-handles of finite type. Metrics on R 3 /G constructed via modular embeddings of R 3 /G into a Euclidean space promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R 3 /G×R m by R 3+m for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, on the defining sequences for R 3 /G. We give a necessary condition and a sufficient condition for the existence of such a parametrization. The necessary condition answers negatively a question of Heinone…
Environmental control on granular clinoforms of ancient carbonate shelves
2006
The purpose of this paper is to document the influence of depositional environments on shallow-water, low-relief clinoforms from the description of five ancient carbonate platforms: the Neoproterozoic (Namibia), Middle Jurassic (France), Lower Cretaceous (France), Upper Cretaceous (Oman) and Miocene (Turkey). These examples have been investigated on the basis of field observations. The clinoforms are described with reference to geometric and compositional attributes: declivity, shape, height, sedimentary structures, sediment fabric and components. The results show great variability in stratal geometry, declivity and facies distribution: (1) depositional profiles vary from exponential, to si…
Lipschitz Functions on Submanifolds of Heisenberg Groups
2022
Abstract We study the behavior of Lipschitz functions on intrinsic $C^1$ submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation of Lipschitz functions on ${\mathbb {H}}$-rectifiable sets and a coarea formula on ${\mathbb {H}}$-rectifiable sets that completes the program started in [18].
Testing the Sobolev property with a single test plan
2020
We prove that in a vast class of metric measure spaces (namely, those whose associated Sobolev space is separable) the following property holds: a single test plan can be used to recover the minimal weak upper gradient of any Sobolev function. This means that, in order to identify which are the exceptional curves in the weak upper gradient inequality, it suffices to consider the negligible sets of a suitable Borel measure on curves, rather than the ones of the $p$-modulus. Moreover, on $\sf RCD$ spaces we can improve our result, showing that the test plan can be also chosen to be concentrated on an equi-Lipschitz family of curves.
Lipschitz Carnot-Carathéodory Structures and their Limits
2022
AbstractIn this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption on the limit vector-fields structure, the distances associated to equi-Lipschitz vector-fields structures that converge uniformly on compact subsets, and to norms that converge uniformly on compact subsets, converge locally uniformly to the limit Carnot-Carathéodory distance. In the case in which the limit distance is boundedly compact, we show that the convergence of the distances is uniform on compact sets. We show an example in which the limit distance is not…
Semigenerated Carnot algebras and applications to sub-Riemannian perimeter
2021
This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic: such a phenomenon happens if and only if the semigroup generated by each horizontal half-space is a vertical half-space. We call semigenerated those Carnot groups with this property. For Carnot groups of nilpotency step 3 we provide a complete characterization of semigeneration in terms of whether such groups do not have any Engel-type quotients. Engel-type groups, which are introduced here, are the minimal (in terms of quotients) counterexamples. In add…