確率微分方程式による流体粒子の挙動 : (測度論的)確率論と数値解析

概要

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The purposes of this paper are (1) to develop the probability theory with the measure one. (2) to derive the stochastic differential equation from the martingale decomposition (Doob-Mayer theorem) and to define the it's strong and weak solutions. (3) to compute the path line of a fluid particle which is a strong solution of the stochastic diffrential eguation. In this paper, I gave up the plan of the purpose (4) which was to derive the dominant equations of the flow fields from the nonequilibrium statistical physics because of lack of space. The results of the numerical simulation were represented as the sumple path of a fluid particle in the turburent boundary layer on the plane. 0n the occasion of the numerical simulation, I set up two assumptions, i. e., (1) the fluid particle has the fluctuation on every position. (2) the velocity field are computed in advance. I think the true or false of this numerical computation will be clear by the fluctuation dissipation principle in the near future.
広島文化学園大学の論文
2002-07-22