2004 Fiscal Year Final Research Report Summary
Euler-Lagrange correspondence of ultra-discrete systems
| Project/Area Number |
15560055
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Engineering fundamentals
|
|---|
| Research Institution | Ryukoku University |
|---|
Principal Investigator |
MATSUKIDAIRA Junta Ryukoku University, Faculty of Science and Technology, Professor, 理工学部, 教授 (60231594)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NISHINARI Katsuhiro Ryukoku University, Faculty of Science and Technology, Associate Professor, 理工学部, 助教授 (40272083)
|
|---|
| Project Period (FY) |
2003 – 2004
|
| Keywords | solution / cellular automata / ultra-discrete system / Euler-Lagrange correspondence |
|---|
| Research Abstract |
It is well known that Burgers cellular automaton includes Rule184 elementary cellular automaton, which is the basic traffic flow model Burgers CA is an Euler representation equation, in which variable expresses a strength of a field. Recently, Lagrange representation of Rule 184 has been found, in which variable expresses a position of particles. As this representation is expressed in a form of Max-Plus algebra, it is natural to consider the link between two representations. In the paper "Euler-Lagrange correspondence of cellular automaton for traffic-flow models, J.Matsukidaira and KNishinari, Phys.Rev.Lett.Vol.90,No.8,p088701(2003)", we have found the transformation formula between Euler representation and Lagrange representation We have been able to obtain this formula by using a new algebraic formula between Max-Plus algebra and Step function. We have also applied this method to multi-value, multi-velocity traffic flow models and have been able to obtain Euler-Lagrange correspondence of the Fukui-Ishibashi model and the quick-start model Furthermore, we have applied this method to soliton cellular automata and have succeeded to find the Euler-Lagrange correspondence of Box and Ball system. We are now preparing the paper for this result.
|
