| Project/Area Number |
11555023
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 展開研究 |
|---|
| Research Field |
Engineering fundamentals
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
TAKAHASHI Daisuke Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (50188025)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SHINZAWA Nobuhiko School of Science and Engineering, Research Associate, 理工学部, 助手 (20350473)
NISHINARI Katsuhiro Ryukoku University, Dept of Applied Mathematics, Associate Professor, 理工学部, 助教授 (40272083)
MATSUKIDAIRA Junta Ryukoku University, Dept of Applied Mathematics, Associate Professor, 理工学部, 助教授 (60231594)
廣田 良吾 早稲田大学, 理工学部, 教授 (00066599)
筧 三郎 早稲田大学, 理工学部, 助手 (60318798)
|
|---|
| Project Period (FY) |
1999 – 2002
|
| Project Status |
Completed (Fiscal Year 2002)
|
| Budget Amount *help |
¥6,900,000 (Direct Cost: ¥6,900,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2000: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1999: ¥2,200,000 (Direct Cost: ¥2,200,000)
|
|---|
| Keywords | soliton / ultradiscrete / difference equation / cellular autonatcn / traffic flow / box and ball system / digital / pattern formation / 超離散化 / 交通流モデル / 反応拡散系 / 再帰方程式 / max-plus方程式 / バーガーズ方程式 / 可積分系 / 可積分 / クリスタルベース |
|---|
| Research Abstract |
Ultradiscretization is a method to discretize a dependent variable of difference equation by using an non-analytic limit of exp type. Combination of this method and differentiation enables a series of discretizing process from differential to ultradiscrete via difference. We apply these methods to various equations and try to find their application in this research.
First, we succeeded to obtain a model which show a traffic jamming process by ultradiscretizing the well-known Burgers equation. The ultradiscrete analogue to Burgers equation is a rule-184 cellular automaton.
Next, we proposed a new digital equation which can show a pattern formation process. This digital equation is given by the max-plus algebra which is a base of the ultradiscretization method.
Finally, we ultradiscretized some nonlinear integrable differenece equations of second order and analyzed their solution structure. Ultradiscrete solutions are similar to the mod function. We clarified the behavior of the solutions from a view point of the dynamical system theory and obtained explicit solutions.
|
