セミナー発足に際してのごあいさつ(1997.4)


第 234 回 Q-NA セミナー
日     時2009 年 4月 14日 (火) 15:30 - 17:00
場     所九州大学箱崎キャンパス 理学部 3号館 3階 3311 号室
講 演 者Vladimír Chalupecký (九州大学大学院数理学研究院 GCOE研究員)
題     目Numerical solution and applications of some phase-field type models
概     要Many physical phenomena in materials science involving motion of interfaces can be formulated and studied in the phase field framework. In my talk I will start with an introduction to phase field modelling in order to motivate the rest of the presentation that consists of three parts, each concerning one particular phase field model. The main focus of the talk will be on the numerical approximation of these models by finite difference method and some possible applications in areas outside of computational materials science.
   In the first part, I present a modified Allen-Cahn equation that can be used for image processing tasks. I will summarize the previous developments in active contours models that also provide a motivation for the phase field approach. A finite difference approximation will be presented together with a number of numerical results showing the function of the algorithm.
   The second part of my talk concerns numerical solution of the Cahn-Hilliard equation, a well-known fourth-order nonlinear PDE model of phase separation in binary mixtures. I will show its several non-degenerate and degenerate forms, mention its relation to the motion of curves and study the convergence of a finite difference scheme. To conclude this part of the talk, I show again some numerical results.
   The third, last part of the talk will deal with a two-scale model of liquid phase epitaxy. First, a simpler model will be presented together with a numerical scheme and some computational results. Then, the full two-scale model will be shown with a preliminary approach to its numerical solution.

世話人
田上 大助 (九州大学 マス・フォア・インダストリ研究所)
渡部 善隆 (九州大学 情報基盤研究開発センター)

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