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Exotic containers for capillary surfaces

In this paper we discuss ‘exotic’ rotationally symmetric containers that admit an entire continuum of distinct equilibrium capillary free surfaces. The paper extends earlier work to a larger class of parameters and clarifies and simplifies the governing differential equations, while expressing them in a parametric form appropriate for numerical integration. A unified presentation suitable for both zero and non-zero gravity is given. Solutions for the container shapes are depicted graphically along with members of the free-surface continuum, and comments are given concerning possible physical experiments.