Modeling for Spatio-Temporal Chaos
| Project/Area Number |
11837014
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
SAKAGUCHI Hidetsugu Kyushu Univ., Grad.Sc.of Eng.Sci., Ass.Prof., 総合理工学研究院, 助教授 (90192591)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1999: ¥2,300,000 (Direct Cost: ¥2,300,000)
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| Keywords | nonlinear equation / spatio-temporal chaos / Burgers equation |
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| Research Abstract |
To understand spatio-temporal chaos better, we have studied simple model eqations. The creation and annihilation processes of characteristics spatial structures is typical of the spatio-temporal chaos. The reconnection of roll structures is a fundamental process in defect chaos.
We have studied the Burgers equation with an additional instability term. A characteristic spatial structure in this system is the shock structure. In the spatio-temporal chaos, there appear many shocks and they collide with each other. Two shocks are merged into one shock as a resut of the collision. A new shock is spontaneously created in a long interval between two neighboring shocks. These creation and merging processes are characteristic of the spatio-temporal chaos in this model equation. We have constructed a simple model for the positions of the shocks and obtained a similar chaotic time evolution including the creation and merging of shocks.
We have studied a coupled Ginzburg-Landau equation for another example and found a pulse solution as an attractor. The pulse solution can exhibit breathing motion and splitting bifurcation.
As a result, spatio-temporal chaos appears spontaneously from a single pulse solution.
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Report
(3 results)
Research Products
(10 results)
