Three dimensional extension of Nakaya-Kobayashi diagram including snow crystals in Antarctica

• Project/Area Number: 26610031
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Meiji University
• Principal Investigator: Yazaki Shigetoshi 明治大学, 理工学部, 専任教授 (00323874)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 界面現象 / 移動境界問題 / クリスタライン曲率流 / ヘレ・ショウ流れ / 負結晶 / 空像 / Hele-Shaw流れ / 雪結晶成長 / 結晶成長 / クリスタライン / ヘレ・ショウ流 / 異方性 / 雪結晶モデル

Outline of Final Research Achievements

We studied negative crystals, or vapor figures in the ice block, and their mathematical and numerical analysis were done. These results are mathematical justification of Dr. Ukichiro Nakaya's observation. We also considered the pioneering idea about geometric selection. These results are related to growth of snow crystals in wider sense. In addition, we studied Hele-Shaw flow, which contribute the future works.

Research Products

• [Journal Article] Method of fundamental solutions with weighted average condition and dummy points (2017)
  • Author(s): K. Sakakibara and S. Yazaki
  • Journal Title: JSIAM Letters Volume: 9 Issue: 0 Pages: 41-44
  • DOI: 10.14495/jsiaml.9.41
  • NAID: 130006900325
  • ISSN: 1883-0609, 1883-0617
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Instability of a free boundary in a Hele-Shaw cell with sink/source and its parameter dependence (2017)
  • Author(s): H. Tani and S. Yazaki
  • Journal Title: JSIAM Letters Volume: 9 Issue: 0 Pages: 37-40
  • DOI: 10.14495/jsiaml.9.37
  • NAID: 130006900379
  • ISSN: 1883-0609, 1883-0617
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Method of fundamental solutions with weighted average condition and dummy points (2017)
  • Author(s): K. Sakakibara and S. Yazaki
  • Journal Title: Applied Mathematics Letters Volume: 印刷中 Pages: 16-21
  • DOI: 10.1016/j.aml.2017.04.018
  • NAID: 130006900325
  • Peer Reviewed / Open Access
• [Journal Article] Exact solution for dislocation bowing and a posteriori numerical technique for dislocation touching-splitting (2015)
  • Author(s): P. Paus and S. Yazaki
  • Journal Title: JSIAM Letters Volume: 7 Issue: 0 Pages: 57-60
  • DOI: 10.14495/jsiaml.7.57
  • NAID: 130005097358
  • ISSN: 1883-0609, 1883-0617
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] A numerical scheme for the Hele-Shaw flow with a time-dependent gap by a curvature adjusted method (2015)
  • Author(s): S. Yazaki
  • Journal Title: Adv. Stud. Pure Math. Volume: 64
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion (2013)
  • Author(s): T. Ishiwata and S. Yazaki
  • Journal Title: Discrete Contin. Dynam. Systems A Volume: 34, Issue 5 Issue: 5 Pages: 2069-2090
  • DOI: 10.3934/dcds.2014.34.2069
  • Peer Reviewed / Open Access
• [Presentation] 界面現象に現れる移動境界の追跡法 (2017)
  • Author(s): 矢崎成俊
  • Organizer: 日本数学会
  • Place of Presentation: 首都大学東京
  • Invited
• [Presentation] A direct approach to image segmentation (2016)
  • Author(s): S. Yazaki
  • Organizer: Algoritmy 2016
  • Place of Presentation: Podbanske, Slovakia
  • Year and Date: 2016-03-15
  • Int'l Joint Research
• [Presentation] 代用電荷法と一様配置を用いたHele-Shaw問題の数値計算 (2015)
  • Author(s): 榊原航也 and 矢崎成俊
  • Organizer: 北陸応用数理研究会2015
  • Place of Presentation: 金沢大学サテライトプラザ
  • Year and Date: 2015-02-22
• [Presentation] 雪氷数学の構築に向けて (2015)
  • Author(s): 矢崎成俊
  • Organizer: 研究集会「偏微分方程式と現象 in 清里」
  • Place of Presentation: 明治大学清里セミナーハウス
  • Year and Date: 2015-02-04
• [Presentation] 代用電荷法による Hele-Shaw 問題の数値計算 (2014)
  • Author(s): 榊原航也 and 矢崎成俊
  • Organizer: 研究集会「新時代の科学技術を牽引する数値解析学」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-10-10
• [Presentation] Numerical experiments of the charge simulation method for Hele-Shaw flows (2014)
  • Author(s): K. Sakakibara and S. Yazaki
  • Organizer: 2nd Slovak-Japan conference on applied mathematics
  • Place of Presentation: Radzovce - Obrucna, Cerova vrchovina, Slovakia
  • Year and Date: 2014-09-15
• [Book] 界面現象と曲線の微積分 (2016)
  • Author(s): 矢崎成俊
  • Total Pages: 232
  • Publisher: 共立出版