2024-03-28T15:12:56Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/693402022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A numerical study of anisotropic crystal growth with bunching under very singular vertical diffusionTsai, Y.Giga, Y.410We study numerically the anisotropic bunching effect in crystal growth under curvature and a singular vertical diffusive regularization. Our assumpÂtion is that the mobility of the growth depends on the height of the given crystal. This assumption may result in overhanging crystals if approached in a naive way. Instead, we embed the profile of the crystal as the zero level set of a continuous function and study the corresponding level set evolution. To prevent "overhanging", we regularize the equation with a singular diffuÂsion that vanishes everywhere except at the fonnation of "overhanging". In addition, we add the mean curvature regularization to keep the convexity of the level sets.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69340info:doi/10.14943/83736https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69340/1/pre591.pdfHokkaido University Preprint Series in Mathematics591192003-04engpublisher