| Budget Amount *help |
¥17,030,000 (Direct Cost: ¥13,100,000、Indirect Cost: ¥3,930,000)
Fiscal Year 2021: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2020: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2019: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
|
|---|
| Outline of Final Research Achievements |
We extended the discrete KdV equation so that it has the co-primeness property, which is considred as a quasi-integrable extension of the discrete KdV equation. Then, it was proved that the discrete equation is a two-dimensional extension of the Hietarinta-Viallet equation, and its reduction involves the Hietarinta-Viallet equation and its generalized eequations of higher orders. We also proved the relation between cluster algebras and co-primeness, which is an algebraic formulation of the singularity confinement. Furthermore, we succeeded to construct the quasi-integrable system of discrete equations with the same properties in arbitrary dimensions.
As an application, we proved the stability of the traffic flow model obtained by Fuzzification of the Rule 184 cell automaton (FCA184). The generalization of FCA184 incorporates the slow-to-start property and analytically determines the value of the density of the phase transition from the free-flow phase to the congested phase.
|
