Results 11 to 20 of about 413,318 (238)
Environmental bias and elastic curves on surfaces [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 The behavior of an elastic curve bound to a surface will reflect the geometry of its environment. This may occur in an obvious way: the curve may deform freely along directions tangent to the surface, but not along the surface normal. However, even if the energy itself is symmetric in the curve's geodesic and normal curvatures, which control these ...
Dulce María Valencia +2 more
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Some minimization problems for planar networks of elastic curves
, 2017 In this note we announce some results that will appear in [6] (joint work with also Matteo Novaga) on the minimization of the functional $F(\Gamma)=\int_\Gamma k^2+1\,\mathrm{d}s$, where $\Gamma$ is a network of three curves with fixed equal angles at ...
Anna Dall’Acqua, Alessandra Pluda
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Elastic curves and phase transitions [PDF]
Mathematische Annalen, 2019 This paper is devoted to classical variational problems for planar elastic curves of clamped endpoints, so-called Euler's elastica problem. We investigate a straightening limit that means enlarging the distance of the endpoints, and obtain several new results concerning properties of least energy solutions.
Tatsuya Miura, Tatsuya Miura
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Weak elastic energy of irregular curves
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023 A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Ourp-energy is defined through a relaxation process, where a suitablep-rotation of inscribed polygons is adopted. The discretep-rotation we choose has a geometric flavour: a polygon is viewed as an approximation to a smooth curve, and ...
D. Mucci, A. Saracco
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Evolution characteristics of elastic energy storage of marble under creep loading
矿业科学学报, 2022 In order to study the energy absorption and transformation characteristics of marble, the release of strain energy and dissipation mechanism during creep process, this paper tested the stress-strain relationship of marble under uniaxial cyclic loading ...
Li Dongyang +4 more
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On nonlocal mechanics of curved elastic beams [PDF]
International Journal of Engineering Science, 2019 Curved beams are basic structural components of Nano-Electro-Mechanical-Sistems (NEMS) whose design requires appropriate modelling of scale effects. In the present paper, the size-dependent static behaviour of curved elastic nano-beams is investigated by stress-driven nonlocal continuum mechanics. Axial strain and flexural curvature fields are integral
Barretta R. +2 more
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Variational analysis of inextensible elastic curves
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022 We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers’ method. Finally, some examples arising from the applications are discussed and also numerical experiments are presented.
Bevilacqua, G. +2 more
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Black rubber and the non-linear elastic response of scale invariant solids
Journal of High Energy Physics, 2020 We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry.
Matteo Baggioli +2 more
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Curves in the Lorentz-Minkowski plane with curvature depending on their position
Open Mathematics, 2020 Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in the Lorentz-Minkowski plane, focusing on spacelike
Castro Ildefonso +2 more
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Elastic Sturmian spirals in the Lorentz-Minkowski plane
Open Mathematics, 2016 In this paper we consider some elastic spacelike and timelike curves in the Lorentz-Minkowski plane and obtain the respective vectorial equations of their position vectors in explicit analytical form.
Uçum Ali +2 more
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