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| We introduce a method for computing interfacial motions governed by curvature dependent acceleration. Our method is a thresholding algorithm of the BMO-type which, instead of utilizing a diffusion process, thresholds evolution by the wave equation to obtain the desired interfacial dynamics. We also develop the numerical method and present the results of its application, including an investigation of the volume preserving motions.
Curvature dependent accelerations (oscillating interfaces) contrast mean curvature flow, and it is natural to search for a thresholding algorithm to approximate their dynamics. The target of the current study is to construct such a method. Moreover, from the point of view of applications, since interfaces in nature are often observed to oscillate (e.g., elastic membranes, soap bubbles, and liquid droplets), we remark this class of motions includes interesting physical phenomena. |
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