| Project/Area Number |
18K13452
|
|---|
| Research Category |
Grant-in-Aid for Early-Career Scientists
|
| Allocation Type | Multi-year Fund |
|---|
| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
|
|---|
| Research Institution | SALESIAN POLYTECHNIC (2019-2021)
Hokkaido University (2018) |
|---|
Principal Investigator |
Sushida Takamichi サレジオ工業高等専門学校, その他部局等, 講師 (00751158)
|
|---|
| Project Period (FY) |
2018-04-01 – 2022-03-31
|
| Project Status |
Completed (Fiscal Year 2021)
|
| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | 葉序 / ボロノイ図 / 連分数展開 / 複素力学系 / タイリング / 円板充填 / 反応拡散方程式 / バーテックスモデル |
|---|
| Outline of Final Research Achievements |
Voronoi tilings with parabolic spiral lattices has been proposed as a geometric model of spiral phyllotaxis which are observed to plants such as sunflowers. However, its mathematical structure was not mathematically clear. In this study, about Voronoi tilings with generalized Archimedean spiral lattices including the parabolic spiral lattices, we showed comprehensively mathematical structures as follows. Grain boundaries consist of heptgons, hexagons, and pentagons, and the number of polygons is determined by denominators of convergents obtained from the regular continued fraction expansion of the divergence angle; the denseness of bifurcation curves of parameters; and the area convergence of Voronoi tiles. Moreover, as a ripple effect of the geometric study of Voronoi tiling for phyllotactic patterns, it was clarified from the statistical analysis of experimental data that patterns of compound eyes of Drosophila follow Voronoi tessellations.
|
| Academic Significance and Societal Importance of the Research Achievements |
20世紀後半に提案された放物螺旋格子を含む一般アルキメデス螺旋格子のボロノイタイリングの数理構造を明らかにした。さらに、ボロノイタイルの面積に対する収束および発散の条件を明らかにし、放物螺旋格子の場合に限り、面積が円周率に収束することを示した。対数螺旋格子や放物螺旋格子などではエネルギー的に最適な配置は黄金比で記述されることが知られているが、複素力学系分野で研究されている複雑な数理構造を有する超冪乗点列においても黄金比が関連することを数値的に示し、新たな展開を与えた。さらに、ショウジョウバエの複眼に対する幾何学的研究では、ボロノイ分割が細胞組織の形態形成で見られる例を新たに示すことができた。
|
