Analysis on singular behavior of interfaces by multiple interface dynamics
| Project/Area Number |
22740109
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Gunma University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 界面の発展方程式 / 等高線法 / 曲率流方程式 / 粘性解 / 結晶成長 / 退化放物型方程式 / 反応拡散方程式 / 結晶のスパイラル成長 / 拡散方程式 / 機械学習理論 / 画像処理問題 / 界面の発現方程式 / 平均曲率流方程式 / 渦巻曲線の運動 |
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| Research Abstract |
A level set method for evolving spirals by an eikonal-curvature equation on a crystal surface is studied. A level set equation for interlaced spiral is proposed and examined numerically. The stability of a bunch of spirals evolving with an eikonal-curvature equation is obtained. Growth rate of the crystal surface by a single or multiple spiral steps are estimated and examined numerically. Stationary solution to the level set equation with the situation of an inactive pair is obtained. A priori estimate for Lipschitz continuity of solutions to an approximating equation of the level set equation is obtained. A diffusion method for data separation is proposed as an application of the infinite propagation property on the heat equation.
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Report
(5 results)
Research Products
(70 results)
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[Presentation] 綾織り模様について2011
Author(s)
大塚岳
Organizer
表面・界面ダイナミクスの数理 I
Place of Presentation
東京大学大学院数理科学研究科
Year and Date
2011-05-12
Related Report
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[Presentation] 綾織り模様について2011
Author(s)
大塚岳
Organizer
表面・界面ダイナミクスの数理I
Place of Presentation
東京大学大学院数理科学研究科
Year and Date
2011-05-12
Related Report
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