2014 Fiscal Year Final Research Report
Construction of digital-analogue-hybrid mathematical model by ultradiscretization method
| Project/Area Number |
24654028
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Waseda University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 可積分系 / セルオートマトン / ソリトン / 超離散化 / 保存量 / 非線形波動 / 差分方程式 |
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| Outline of Final Research Achievements |
Our purpose is to propose a common analyzing method among nonlinear systems with different levels of discretization. We obtained the following concrete results. (1) We expressed the time-evolution equations of elementary cellular automata using lattice operations. We proposed the exact general solutions solving their initial value problem. (2) We solved exactly the initial value problems for the particle systems expressed by cellular automata with multi-neighbors. Moreover, we analyzed the cellular automata with higher-order conserved quantity reducing them to those with first-order. (3) We introduced the stochastic parameters to the systems obtained in (2) preserving their conserved quantity and derived the exact theoretical expression for their fundamental diagram.
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| Free Research Field |
離散可積分系
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