Results 11 to 20 of about 3,008,618 (361)
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.
J. Guven +2 more
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Some minimization problems for planar networks of elastic curves [PDF]
, 2017 In this note we announce some results that will appear in [6] on the minimization of the functional F(Γ) = ∫Γk2 + 1 ds, where Γ is a network of three curves with fixed equal angles at the two junctions.
Anna Dall’Acqua, Alessandra Pluda
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Constrained Willmore Tori and Elastic Curves in 2-Dimensional Space Forms [PDF]
, 2013 In this paper we consider two special classes of constrained Willmore tori in the 3-sphere. The first class is given by the rotation of closed elastic curves in the upper half plane - viewed as the hyperbolic plane - around the x-axis.
Lynn Heller
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An obstacle problem for elastic curves: Existence results [PDF]
Interfaces and free boundaries (Print), 2019 We consider an obstacle problem for elastic curves with fixed ends. We attempt to extend the graph approach provided in [8]. More precisely, we investigate nonexistence of graph solutions for special obstacles and extend the class of admissible curves in
Marius Müller
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Lectures on Elastic Curves and Rods [PDF]
AIP Conference Proceedings, 2008 These five lectures constitute a tutorial on the Euler elastica and the Kirchhoff elastic rod. We consider the classical variational problem in Euclidean space and its generalization to Riemannian manifolds. We describe both the Lagrangian and the Hamiltonian formulation of the rod, with the goal of examining the (Liouville‐Arnol'd) integrability.
D. Singer
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Curve straightening and a minimax argument for closed elastic curves
Topology, 1985 The authors study the functional \(F=\oint k^ 2 ds\) (''total squared curvature'') on the space of smooth closed curves in \({\mathbb{R}}^ 3\) of fixed length. In particular they establish the Palais-Smale condition for F, so the gradient flow of F (''curve straightening'') is well-behaved.
Joel Langer, D. Singer
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The elastic flow of curves on the sphere
Geometric Flows, 2018 We consider closed curves on the sphere moving by the L2-gradient flow of the elastic energy both with and without penalisation of the length and show short-time and long-time existence of the flow.
Anna Dall’Acqua +4 more
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The second-order $L^2$-flow of inextensible elastic curves with hinged ends in the plane
, 2014 In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C∞-smooth solutions during the evolution, given the initial curves that are only C2-smooth with vanishing curvature at the ...
Chunchi Lin +2 more
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General rigidity principles for stable and minimal elastic curves [PDF]
Journal für die Reine und Angewandte Mathematik, 2023 For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks’ and Sachkov’s rigidity principles for Euler’
Tatsuya Miura, Kensuke Yoshizawa
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Constrained elastic curves and surfaces with spherical curvature lines [PDF]
Indiana University Mathematics Journal, 2021 In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be generated by a pair of initial data: a suitable curve of Lie sphere ...
Joseph Cho, M. Pember, Gudrun Szewieczek
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