Mathematical analysis of dendritic crystal growth

• Project/Area Number: 21654024
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Tohoku University
• Principal Investigator: TAKAGI Izumi 東北大学, 大学院・理学研究科, 教授 (40154744)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,040,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2009: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 針状結晶 / 側枝の形成 / Hele-Shaw流 / 粘性指 / 先端の分裂 / 樹枝状結晶 / 二相ステファン問題 / 進行波解 / 二層ステファン問題 / 表面張力 / 異方性

Research Abstract

A small disturbance in the overcooled liquid triggers the formation of paraboloidal interface growing into the bulk with constant speed, and side branches are formed, resulting in dendrites. To understand this phenomenon mathematically, we consider the existence of paraboloidal traveling wave solutions of the Stefan problemwith surface tension on the interface and their stability.

Research Products

• [Presentation] On the movement of a boundary-spike solution of a semilinear parabolic equation (2013)
  • Author(s): Izumi Takagi
  • Organizer: Applied and Computational Mathematics Seminar
  • Place of Presentation: University of California, Irvine,米国
  • Year and Date: 2013-03-11
• [Presentation] Introduction to a free boundary problem in crystal growth (2011)
  • Author(s): Izumi Takagi
  • Organizer: Complex Analysis Approaches to Free Boundary Problems
  • Place of Presentation: 仙台国際センター,宮城県
  • Year and Date: 2011-12-13
• [Presentation] Traveling spots and rotating spirals of the wave front interaction model (2011)
  • Author(s): Hirokazu Ninomiya
  • Organizer: Complex Analysis Approaches to Free Boundary Problems
  • Place of Presentation: 仙台国際センター,宮城県
  • Year and Date: 2011-12-12
• [Presentation] On the movement of a boundary-spike solution of a semilinear parabolic equation
  • Author(s): Izumi Takagi
  • Organizer: Applied and Computational Mathematics Seminar
  • Place of Presentation: University of California, Irvine, 米国
  • Invited
• [Remarks]
  • URL: http://morpho.sci.tohoku.ac.jp/~dendrites/
• [Remarks]
  • URL: http://morpho.sci.tohoku.ac.jp/~morpho/
• [Remarks] 樹枝状パターン形成の数理
  • URL: http://morpho.sci.tohoku.ac.jp/~dendrites/
• [Remarks] 生物の形づくりの数理
  • URL: http://morpho.sci.tohoku.ac.jp/~morpho/