Stochastic differential equation modeled on a turbulent thermal convection field
Project/Area Number |
22560198
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Thermal engineering
|
Research Institution | Osaka University |
Principal Investigator |
HIDESHI ISHIDA 大阪大学, 基礎工学研究科, 助教 (80283737)
|
Project Period (FY) |
2010-04-01 – 2014-03-31
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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Keywords | 乱流 / 確率微分方程式 / ノイズ強度 / 有効粘性係数 / カルマン・ブーシーフィルタ / 大偏差関数 / エネルギーバランス / Takensの埋め込み / 蔵本方程式 / ノイズを含むバーガーズ方程式 / 伊藤過程 / 数値伊藤積分 / ノイズレベル / クラメル関数 / 確立微分方程式 / 蔵本・シバシンスキー方程式 / バーガーズ方程式 / 大偏差統計 |
Research Abstract |
The noisy Burgers equation (NBE) modeled on the Kuramoto-Sivashinky equation (KSE) has two coefficients of an effective viscosity nu_eff and a noise strength N. In this study, they are optimized by the numerical stochastic integration of NBE to recover the properties of KSE. Under the condition that the average and variance of the solution of NBE agree with those of KSE, the values of the two coefficients are found to have a degree of freedom, showing exponential manner for a wide range of nu_eff. Their optimal values are determined by the agreement of large deviation functions obtained from the solutions of KSE and NBE. The optimal value of nu_eff, far smaller than known values, is found to accord with the estimated one by the Kalman-Bucy filter, minimizing the noise level N on the exponential curve. The agreement numerically validates the Yakhot conjecture. The strength N estimated by the variance of a noise-related term of KSE agrees well with the optimal one near nu_eff/alpha=1.
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Report
(5 results)
Research Products
(7 results)