Variational discretization of Euler's Elastica problem

Sogo K

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Variational discretization of Euler's Elastica problem

机译：欧拉弹性问题的变分离散化

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摘要

A discrete version of Enter's Elastica problem is formulated by a variational principle. Hirota's bilinear equations, Lax pair formalism and the exact solution are obtained explicitly. Geometrical properties are also discussed such as discrete Frenet-Serret equations.

机译：Enter的Elastica问题的离散版本是通过变分原理制定的。明确获得了Hirota的双线性方程，Lax对形式主义和精确解。还讨论了几何特性，例如离散Frenet-Serret方程。

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《Journal of the Physical Society of Japan》 |2006年第6期|共4页
作者
Sogo K;
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正文语种 eng
中图分类物理学;
关键词
Euler's Elastica problem; discrete sine-Gordon equation; discrete Frenet-Serret equations; EQUATION;

机译：欧拉弹性问题;离散正弦-戈登方程;离散Frenet-Serret方程;方程;

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1. Variational discretization of Euler's Elastica problem [J] . Sogo K Journal of the Physical Society of Japan . 2006,第6期

机译：欧拉弹性问题的变分离散化
2. Euler elastica as a -limit of discrete bending energies of one-dimensional chains of atoms [J] . Espanol Malena I., Golovaty Dmitry, Wilber J. Patrick Mathematics and mechanics of solids: MMS . 2018,第7期

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3. Poisson Noise Removal Based on Nonlocal Total Variation with Euler's Elastica Pre-processing [J] . LIU Hongyi, ZHANG Zhengrong, XIAO Liang, 上海交通大学学报（英文版） . 2017,第005期
4. Total Variation and Euler's Elastica for Supervised Learning [C] . Tong Lin, Hanlin Xue, Ling Wang, International Conference on Machine Learning . 2012

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6. Euler’s Elastica-Based Biomechanics of the Papillary Muscle Approximation in Ischemic Mitral Valve Regurgitation: A Simple 2D Analytical Model [O] . Francesco Nappi, Angelo Rosario Carotenuto, Sanjeet Singh Avtaar Singh, 2019

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7. Variational Image Regularization with Euler's Elastica Using a Discrete Gradient Scheme [O] . Torbjørn Ringholm, Jasmina Lazić, Carola-Bibiane Schönlieb 2018

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Variational discretization of Euler's Elastica problem

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