Results 1 to 10 of about 3,008,618 (361)
Approximation by planar elastic curves [PDF]
Advances in Computational Mathematics, 2015 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
D. Brander, J. Gravesen, T. B. Nørbjerg
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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.
P. Dondl, Luca Mugnai, Matthias Röger
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Analysis of shape data: From landmarks to elastic curves. [PDF]
Wiley Interdiscip Rev Comput Stat, 2020 Proliferation of high‐resolution imaging data in recent years has led to substantial improvements in the two popular approaches for analyzing shapes of data objects based on landmarks and/or continuous curves.
Bharath K, Kurtek S.
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Elastic curves and phase transitions [PDF]
Mathematische Annalen, 2017 This paper is devoted to a classical variational problem 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 ...
Tatsuya Miura
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Variational analysis of inextensible elastic curves [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2021 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.
G. Bevilacqua, L. Lussardi, A. Marzocchi
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Bifurcation of elastic curves with modulated stiffness [PDF]
European Journal of Applied Mathematics, 2020 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.
K. Brazda +3 more
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Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves. [PDF]
J Am Stat Assoc, 2019 A population quantity of interest in statistical shape analysis is the location of landmarks, which are points that aid in reconstructing and representing shapes of objects.
Strait J, Chkrebtii O, Kurtek S.
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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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A Survey of the Elastic Flow of Curves and Networks [PDF]
Milan Journal of Mathematics, 2020 We 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.
C. Mantegazza +2 more
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Convergence of elastic flows of curves into manifolds [PDF]
Nonlinear Analysis, 2020 For a given $p\in[2,+\infty)$, we define the $p$-elastic energy $\mathscr{E}$ of a closed curve $ :\mathbb{S}^1\to M$ immersed in a complete Riemannian manifold $(M,g)$ as the sum of the length of the curve and the $L^p$--norm of its curvature (with respect to the length measure).
Marco Pozzetta
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