石けん膜の安定性をめぐって

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This paper shows a result of numerical calculation of a one-parameter family of surfaces with constant mean curvature spanning a Wiener contour. The method used here is founded on the theorems of H. C. Wente and K. Steffen concerning solutions to the volume constrained Plateau problem. The augmented Lagrangian method and Uzawa's algorithm are applied. The computed surfaces are classified according to the stability. An unstable minimal surface spanning a Wiener contour is obtained numerically. Considering a container which is filled with gas and has a fixed solid wall and a mouth covered with a free thin film, we state that, when the boundary of the mouth forms a Wiener contour with an appropriate proportion and when the pressure of the gas in the container changes so slowly that the free thin film passes through a succession of equilibrium states, the deformation of the film is discontinuous at some values of the pressure of the gas.
日本応用数理学会の論文
1992-03-16