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
No keywords uploaded!
[ Download ] [ 2019-12-24 21:02:15 uploaded by Jack_Xin ] [ 470 downloads ] [ 0 comments ]
@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.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved