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. 
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129 Citations
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129 Citations

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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.
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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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References

SHOWING 1-10 OF 50 REFERENCES
A non-local anisotropic model for phase transitions: asymptotic behaviour of rescaled energies
In this paper we consider a non-local anisotropic model for phase separation in two-phase fluids at equilibrium, and show that when the thickness of the interface tends to zero in a suitable way, the…
A Nonlocal Continuum Model for Biological Aggregation
TLDR
A continuum model for biological aggregations in which individuals experience long-range social attraction and short-range dispersal is constructed, and energy arguments are used to understand the nonlinear selection of clump solutions, and to predict the internal density in the large population limit.
A Diffusion-Generated Approach to Multiphase Motion
In this article, we present a diffusion-generated approach for evolving multiple junctions. This work generalizes an earlier method by Merriman, Bence, and Osher which alternately diffuses and…
Large-scale simulations and parameter study for a simple recrystallization model
Distance function-based diffusion-generated motion, a highly efficient numerical algorithm, is used to simulate a classical model of recrystallization in unprecedented detail and in physically…
A numerical method for tracking curve networks moving with curvature motion
Abstract A finite difference method is proposed to track curves whose normal velocity is given by their curvature and which meet at different types of junctions. The prototypical example is that of…
Motion of multiple junctions: a level set approach
Abstract A coupled level set method for the motion of multiple junctions is proposed. The new method extends the "Hamilton-Jacobi" level set formulation of Osher and Sethian. It retains the feature…
Coarsening in Nonlocal Interfacial Systems
TLDR
A rigorous upper bound on the coarsening rate is proved and a geometric approach is developed which is applicable to a wider class of problems, which includes ones based on local, gradient-type energies.
Diffusion generated motion for grain growth in two and three dimensions
Two‐Dimensional Motion of Idealized Grain Boundaries
To represent ideal grain boundary motion in two dimensions, a rule of motion of plane curves is considered whereby any given point of a curve moves toward its center of curvature with a speed that is…
A MultiPhase Field Concept: Numerical Simulations of Moving Phase Boundaries and Multiple Junctions
We present numerical simulations which support the formal asymptotic analysis relating a multiorder parameter Allen--Cahn system to a multiphase interface problem with curvature-dependent evolution…
...
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