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SIAM Journal on Applied Mathematics, 2010 We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values +1 on the inside and -1 on the outside of the curve.
Dondl, Patrick W. +2 more
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Environmental bias and elastic curves on surfaces [PDF]
, 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.
Guven, Jemal +2 more
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Approximation by planar elastic curves [PDF]
Advances in Computational Mathematics, 2016 We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for
Brander, David +2 more
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A Property of Euler's Elastic Curve
Elemente der Mathematik, 2000 Euler and Legendre found formulas for certain products of elliptic integrals. Legendre's proof is sketched, and Euler's method is generalized to prove a more general formula which may be interpreted as a property of a curve generalizing Euler's elastic curve.
Victor H. Moll +3 more
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Constrained Willmore Tori and Elastic Curves in 2-Dimensional Space Forms [PDF]
, 2014 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.
Heller, Lynn
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On the elastic closed plane curves [PDF]
Kodai Mathematical Journal, 1985 Studying the variational problem for the functional \(E(C)=(1/2)\int_{C}k^ 2(s)ds\) (C a closed curve, s the arc length parameter of C, k(s) the curvature of C), under the condition \(\int_{C}ds=L=const.\), the author finds the following result: if E(C) is critical for a closed plane curve with \(L=const.\), then the curve C is either the plane circle \
Hiroshi Yanamoto
openalex +3 more sources
Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive ...
Samira Latifi +2 more
doaj +1 more source
Geometric and topological approaches to shape variation in
Royal Society Open Science, 2021 Leaf shape is a key plant trait that varies enormously. The range of applications for data on this trait requires frequent methodological development so that researchers have an up-to-date toolkit with which to quantify leaf shape. We generated a dataset
Haibin Hang +3 more
doaj +1 more source
Rolling Geodesics, Mechanical Systems and Elastic Curves
Mathematics, 2022 This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem.
Velimir Jurdjevic
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Additive Manufacturing Letters, 2022 The near-net-shape manufacturing in additive manufactured and cast of Al-Si alloys results in a heterogeneous solidification and cooling of the parts, leading to significant gradients in microstructural and defect features as well as deformation behavior.
Jochen Tenkamp +3 more
doaj +1 more source