Simplified Model of the Magnetic Benard Convection and Its Simulation(Special Features on Nuclear Fusion)

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  • 磁気ベナール対流の簡約化モデルとそのシミュレーション(<小特集>核融合)

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Abstract

A control problem of Benard convection by means of the magnetic field is very important from the engineering view point. It is also very interesting from the view point of the mathematical physics related to transition to chaos. In this problem the influence of the magnetic field to the fluid is our interests. It is so difficult to analyze directly this problem described as a system of partial differential equations, that in this paper following Lorenz the simplified problem described as a system of ordinary differential equations is introduced and analyzed. Numerical simulation gives the following interesting results. The stabilizing effect of the magnetic field to the fluid motion is confirmed. The various structures of transition to chaos are obtained.

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