Results 1 to 10 of about 55,376 (65)
Iterated Differential Forms II: Riemannian Geometry Revisited [PDF]
, 2006 A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.Comment: 12 pages, extended version of
A. M. Vinogradov +6 more
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DisMech: A Discrete Differential Geometry-Based Physical Simulator for Soft Robots and Structures [PDF]
IEEE Robotics and Automation Letters, 2023 Fast, accurate, and generalizable simulations are a key enabler of modern advances in robot design and control. However, existing simulation frameworks in robotics either model rigid environments and mechanisms only, or if they include flexible or soft ...
Andrew Choi +3 more
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Exploring differential geometry in neural implicits [PDF]
Computers & graphics, 2022 We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions.
Tiago Novello +5 more
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DG‐GL: Differential geometry‐based geometric learning of molecular datasets [PDF]
International Journal for Numerical Methods in Biomedical Engineering, 2018 Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding ...
D. Nguyen, G. Wei
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From Second-Order Differential Geometry to Stochastic Geometric Mechanics [PDF]
Journal of nonlinear science, 2022 Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton–Jacobi theory, are founded on geometric structures such as jets, symplectic and contact ones.
Qiao Huang, J. Zambrini
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On variational approach to differential invariants of rank two distributions [PDF]
, 2004 We construct differential invariants for generic rank 2 vector distributions on n-dimensional manifolds, where n ⩾ 5 . Our method for the construction of invariants is completely different from the Cartan reduction-prolongation procedure.
I. Zelenko
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Centro-affine differential geometry and the log-Minkowski problem [PDF]
Journal of the European Mathematical Society (Print), 2021 We interpret the log-Brunn-Minkowski conjecture of B\"or\"oczky-Lutwak-Yang-Zhang as a spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert-Brunn-Minkowski operator coincides with the centro-affine Laplacian ...
E. Milman
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Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map
International Electronic Journal of Geometry, 2023 The theory of finite type submanifolds was introduced by the first author in late 1970s and it has become a useful tool for investigation of submanifolds. Later, the first author and P.
Bang‐Yen Chen +3 more
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Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry [PDF]
bioRxiv, 2021 Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to approximation-based methods (
C. Zhu, Christopher T. Lee, P. Rangamani
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A quantum complexity lower bound from differential geometry [PDF]
Nature Physics, 2021 Quantum operations can be considered as points in a high-dimensional space in which distance reflects the similarity of two operations. Applying differential-geometric methods in this picture gives insights into the complexity of quantum systems ...
Adam R. Brown
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