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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
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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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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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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.
Guven, Jemal +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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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
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A Survey of the Elastic Flow of Curves and Networks [PDF]
Milan Journal of Mathematics, 2021 AbstractWe collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and smooth convergence to critical points of the solution of the elastic flow of closed curves in$${\mathbb {R}}^2$$
Carlo Mantegazza +2 more
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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
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Bifurcation of elastic curves with modulated stiffness [PDF]
European Journal of Applied Mathematics, 2022 We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the minimisation of a bending energy with respect to shape and density and can be considered as a one-dimensional ...
K Brazda +3 more
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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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