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Diffusion-generated motion by mean curvature for filaments

Steven J Ruuth Barry Merriman Jack Xin Stanley Osher

Analysis of PDEs mathscidoc:1912.43852

Journal of Nonlinear Science, 11, (6), 473-493, 2001.12
Diffusion-generated motion by mean curvature is a simple algorithm for producing motion by mean curvature of a surface, in which the motion is generated by alternately diffusing and renormalizing a characteristic function. In this paper, we generalize diffusion-generated motion to a procedure that can be applied to the curvature motion of filaments, i.e., curves in <i>R</i> ^3, that may initially consist of a complex configuration of links. The method consists of applying diffusion to a complex-valued function whose values wind around the filament, followed by normalization. We motivate this approach by considering the essential features of the complex Ginzburg-Landau equation, which is a reaction-diffusion PDE that describes the formation and propagation of filamentary structures. The new algorithm naturally captures topological merging and breaking of filaments without fattening curves. We justify the new
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@inproceedings{steven2001diffusion-generated,
  title={Diffusion-generated motion by mean curvature for filaments},
  author={Steven J Ruuth, Barry Merriman, Jack Xin, and Stanley Osher},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210216002736416},
  booktitle={Journal of Nonlinear Science},
  volume={11},
  number={6},
  pages={473-493},
  year={2001},
}
Steven J Ruuth, Barry Merriman, Jack Xin, and Stanley Osher. Diffusion-generated motion by mean curvature for filaments. 2001. Vol. 11. In Journal of Nonlinear Science. pp.473-493. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210216002736416.
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