Results 1 to 10 of about 3,090,394 (363)
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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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
core +8 more sources
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
core +9 more sources
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.
europepmc +2 more sources
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.
europepmc +3 more sources
ELASTIC MAGNETIC CURVES OF FERROMAGNETIC AND SUPERPARAMAGNETIC MODELS [PDF]
Mathematical methods in the applied sciences, 2020 In this paper, new energy functionals are described via the variational approach method. By doing this, a new class of elastic curves is described in the three‐dimensional ordinary space.
Talat K rp nar +2 more
openalex +2 more sources
Some minimization problems for planar networks of elastic curve [PDF]
, 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 ...
Dall'Acqua, Anna, Pluda, Alessandra
core +3 more sources
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
core +2 more sources
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
semanticscholar +1 more source
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
semanticscholar +1 more source