| Project/Area Number |
25610029
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
|
|---|
| 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)
|
|---|
| Project Period (FY) |
2013-04-01 – 2015-03-31
|
| Project Status |
Completed (Fiscal Year 2014)
|
| 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)
|
|---|
| 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 |
|---|
| 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.
|
