Threshold Dynamics for Networks with Arbitrary Surface Tensions

@article{EsedoLu2015ThresholdDF,
  title={Threshold Dynamics for Networks with Arbitrary Surface Tensions},
  author={Selim Esedoḡ Lu and Felix Otto},
  journal={Communications on Pure and Applied Mathematics},
  year={2015},
  volume={68}
}
We present and study a new algorithm for simulating the N‐phase mean curvature motion for an arbitrary set of (isotropic) N(N−1)2 surface tensions. The departure point is the threshold dynamics algorithm of Merriman, Bence, and Osher for the two‐phase case. 
Evolution of networks with multiple junctions
We consider the motion by curvature of a network of curves in the plane and we discuss existence, uniqueness, singularity formation and asymptotic behavior of the flow.
ALGORITHMS FOR MOTION OF NETWORKS BY WEIGHTED MEAN CURVATURE
  • S. Esedoglu
  • Computer Science
    Proceedings of the International Congress of Mathematicians (ICM 2018)
  • 2019
TLDR
I will report on recent developments in a class of algorithms, known as threshold dynamics, for computing the motion of interfaces by mean curvature, which can be extended to the multi-phase setting of networks of surfaces, and to motion by weighted (anisotropic) mean curvatures, while maintaining the simplicity of the original version.
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TLDR
A simplified version of the threshold dynamics algorithm given in Esedoḡlu and Otto is presented, which employs linear combinations of Gaussians in the convolution step of the algorithm, maintaining the efficiency of the original thresholding scheme.
An Efficient Boundary Integral Scheme for the Threshold Dynamics Method II: Applications to Wetting Dynamics
TLDR
The boundary integral scheme for the threshold dynamics method is extended to treat the case where the material interface is nonsmooth and may undergo topological changes, making accurate simulation of wetting dynamics on a chemically patterned solid surface in three dimensions within practical reach.
The Role of Surface Tension and Mobility Model in Simulations of Grain Growth.
We explore the effects of surface tension and mobility models in simulations of grain growth using threshold dynamics algorithms that allow performing large scale simulations, while naturally
De Giorgi’s inequality for the thresholding scheme with arbitrary mobilities and surface tensions
  • Tim Laux, Jona Lelmi
  • Mathematics
    Calculus of Variations and Partial Differential Equations
  • 2022
We provide a new convergence proof of the celebrated Merriman–Bence–Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general class of surface
Kernels with prescribed surface tension & mobility for threshold dynamics schemes
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