Pattern formation its multiplicative stochastic processes
| Project/Area Number |
62460037
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Kyushu Institute of Technology |
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Principal Investigator |
KAI Shoichi Faculty of Engineering, Kyushu Institute of Technology, Prof., 工学部, 教授 (20112295)
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| Co-Investigator(Kenkyū-buntansha) |
HIROSHI Furukawa Faculty of Education, Yamaguchi Univ. Associate Prof., 教育学部, 助教授 (10108269)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥5,300,000 (Direct Cost: ¥5,300,000)
Fiscal Year 1988: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1987: ¥3,800,000 (Direct Cost: ¥3,800,000)
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| Keywords | convective instability / nematic liquid crystal / electrohydrodynamics / multiplicative noise / turbulence / precipitation pattern / 対流不安定性 / 乱流 / 構造転移 / 対流パターン / オストワルド熟成 / 磁界効果 / 確率過程 / ネマチック液晶 / スケーリンク |
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| Research Abstract |
The growth process of the convective pattern in the electrohydrodynamic instability(END) of nematic liquid crystals is basically devided into three evolution regimes; 1) the early stage(amplitude dynamics), 2)the late stage(phase dynamics) and 3)the final stage (defect dynamics). The scaling properties based on the noisy Landau equation for the amplitude and for the variances are experimentally observed in the early stage but not hold in both a late and a final stages. Both the correlation time _N and the intensity Q of the noise are the crucial parameters to control the bifurcation in multiplicative stochastic processes of EHD instability. With increasing a noise intensity the threshold for the onset of the first instability changes drastically. We observe that the curvature arising for the threshold changes as one is going e.g. from the onset of the williams domains(WD) to the onset of the GP. This result reflects the transition in the flow structure from WD to GP and dynamical scatt
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ering mode (DSM:turbulence). As the intensity of noise is increased further, the onset of the first instability becomes more complex. Defect motions, pattern selections, transition to chaos and these magnetic-field effect are also studied detailedly in WD to the fluctuating WD(FWD) regimes. The defect chaos(FWD) could occur slightly above the threshold, via the state with regular rolls without any defect for finite aspect ratio. In this state, defects never disappear whose number always changes nonperiodically in time. The power spectrum of the temporal change of this number shows l/f type-spectrum. A magnetic field can suppress a defect chaos and stabilized the system. The threshold of an applied electric field for the onset of EHD shifts upward increasing in a magnetic field. The magnetic field could change the direction of a roll axis into the direction perpendicular to its field. The quantitative dynamical studies on magnetic field and multiplicative noise effects are left to be investigated in future. Less
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Research Products
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