Construction of time discrete geometric models based on discrete differential geometry
| Project/Area Number |
16K13763
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
Kajiwara Kenji 九州大学, マス・フォア・インダストリ研究所, 教授 (40268115)
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| Co-Investigator(Renkei-kenkyūsha) |
MARUNO Ken-ichi 早稲田大学, 理工学術院, 教授 (80380674)
KAKEI Saburo 立教大学, 理学部, 教授 (60318798)
HIROSE Sampei 芝浦工業大学, デザイン工学部, 助教 (20743230)
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| Research Collaborator |
Broadbridge Philip ラ・トローブ大学, 教授
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| Project Period (FY) |
2016-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 離散微分幾何 / 可積分系 / 曲線 / ソリトン方程式 / 弾性曲線 / 相似幾何 / 変分原理 / 対数型美的曲線 / 解析学 / 離散曲線 / 離散可積分系 |
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| Outline of Final Research Achievements |
In this project, the following three topics have been studied:(a)discrete models of curve deformation with extension and external force, (b)time discrete model of deformation of layer, (c) discrete model of one-dimensional elastic rod. As to (a) we succeeded in constructing a new discrete model of the curve shortening equation and discrete local induction equation. For (b) we obtained the bilinearization of the complex Dym equation describing the Hele-Shaw flow, and also succeeded in discretization of the Broadbridge-White model for the one-dimensional soil water infiltration and its numerical simulation. Regarding (c) we succeeded in formulating the integrable discrete model of the Euler's elastic curves by the discrete variational principle. Further we have shown that the elastic curves in the similarity geometry are nothing but the log-aesthetic curves used in the industrial design, and gave a sound mathematical foundation for their generalization.
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Report
(3 results)
Research Products
(24 results)
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[Journal Article] dNLS Flow on Discrete Space Curves2016
Author(s)
Sampei Hirose, Jun-ichi Inoguchi, Kenji Kajiwara,Nozomu Matsuura, Yasuhiro Ohta
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Journal Title
Mathematical Progress in Expressive Image Synthesis III, Mathematics for Industry
Volume: 24
Pages: 137-149
DOI
Related Report
Peer Reviewed / Acknowledgement Compliant
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[Presentation] dNLS flow on discrete space curves2017
Author(s)
Kenji Kajiwara
Organizer
The 10th IMACS Conference on Nonlinear and Evolution Equations and Wave Phe- nomena: Computation and Theory
Place of Presentation
University of Georgia, Athens,USA
Year and Date
2017-03-30
Related Report
Int'l Joint Research / Invited
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