| Budget Amount *help |
¥12,740,000 (Direct Cost: ¥9,800,000、Indirect Cost: ¥2,940,000)
Fiscal Year 2016: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2014: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
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| Outline of Final Research Achievements |
In this project, we aimed to develop mathematical technique to analyze the interacting motion of localized patterns and succeeded to get results for the motions for a curved surface, asymmetric localized patterns and traveling localized ones. Clearly speaking, we first clarified the relation between geometrical properties of a surface and motions of interacting patterns. We also derived the equation explicitly to determine a stable spatial distribution of patterns. Secondly, we established a general theory to deal with asymmetric patterns and applied it to the analysis of interacting motion of two camphor discs on water surface. We also checked the theoretical prediction in a real experiment. Finally, we mention to succeed to construct stable pairs of traveling patterns by using the interaction between fast and slow traveling ones. The result is shown to be applicable to the analysis of breathing traveling motions appearing in heart muscles.
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