Spot dynamics of the volume preserving reaction-diffusion systems
| Project/Area Number |
25610029
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Hokkaido University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAMURA Ken-Ichi 金沢大学, 数物科学系, 准教授 (40293120)
TERAMOTO Takashi 旭川医科大学, 医学部, 准教授 (40382543)
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| Project Period (FY) |
2013-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 体積保存型反応拡散系 / 振動進行スポット / 自励往復運動スポット / 楕円形状定常解 / ピーナッツ形状定常解 / 自励往復スポット / 反応拡散系 / スポット運動 / 分岐数値計算 / 液滴運動モデル / 計算機援用解析 |
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| Outline of Final Research Achievements |
We have performed a mathematical analysis of model equations for fixed-form particle motions, as well as for one that utilizes droplet-like motions to incorporate shape deformations. In particular, droplet deformations are incorporated through the combination of a volume preserving phase-field equation within a two-component reaction diffusion system. By use of computer-aided analysis, we have also investigated the pattern dynamics within the mathematical model. We observe a parameter for which traveling spots bifurcate from stable standing spot solutions. Traveling spots, moreover, destabilize by means of a Hopf bifurcation, which leads to the appearance of an oscillatory travelling spot. We have also clarified the existence of stable elliptical-shaped and peanut-shaped equilibrium solutions.
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Report
(3 results)
Research Products
(14 results)
