2002 Fiscal Year Final Research Report Summary
Study on the singularity of spatio-temporal disorder in large degree-freedom systems
| Project/Area Number |
11214203
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Kyoto University |
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Principal Investigator |
KURAMOTO Yoshiki Kyoto University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (40037247)
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Michio Tokyo University, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (90166736)
YOSHIKAWA Ken-ichi Kyoto University, Graduate School of Sciences, Professor, 大学院・理学研究科, 教授 (80110823)
KAI Shoichi Kyushu University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (20112295)
TOH Sadayoshi Kyoto University, Graduate School of Sciences, Associate Professor, 大学院・理学研究科, 助教授 (10217458)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Pattern formation / Turbulence / Spatio-temporal chaos / Rhythm / Liquid crystals / Reaction-diffusion systems / Navier-Stokes equation / Synchronization |
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| Research Abstract |
Three representative classes of physical systems, i. e. (1) Navier-Stokes fluids, (2) liquid crystals, and (3) reaction-diffusion systems, were studied focusing on their complex spatio-temporal behavior through the underlying mathematical singularities Specifically.
1. New numerical algorithms were developed for the analysis of geophysically relevant Navier-Stokes turbulence on a rotating sphere. This tool turned out extremely useful for the study of large scale turbulent structure on a rotating sphere.
2. A remarkable progress was achieved in our understanding of developed turbulence through the analysis of certain mathematical and physical singular structures involved there. This was especially successful for turbulent thermal convection and wall turbulence where some characteristics of turbulent flows were approximately represented by some objects constructed using low-dimensional dynamical system.
3. A new type of spatio-temporal chaos named as "soft-mode turbulence" was discovered experimentally in electro-convection using nematic liquid crystals, and some unique features of this turbulence were revealed. A phase diagram was experimentally constructed in a two-dimensional parameter space. Anomalous diffusion in turbulent media was also studied in detail.
4. Regarding experiments on reaction-diffusion systems, it was found that nonlinear waves in excitable media can be controlled variously by changing the geometry of the system. Possibility of constructing "computer on a continuous field" was also argued. From a theoretical side, possibility of new classes of reaction-diffusion patterns was claimed. They include rotating spiral waves without phase singularity and spatio-temporal chaos with multi-fractal structure.
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