偏微分方程式セミナー (2014/6/16) : A variational method for curvature accelerated interfacial dynamics, Elliott Ginder 氏 (北海道大学)

開催日時
2014年   6月 16日 16時 30分 ~ 2014年   6月 16日 17時 30分
場所
北海道大学理学部3号館3-309室
講演者
Elliott Ginder 氏 (北海道大学電子科学研究所)
 
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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