• Corpus ID: 244478052

High Spots for the Ice-Fishing Problem with Surface Tension

  title={High Spots for the Ice-Fishing Problem with Surface Tension},
  author={N. Parker Willis and Chee Han Tan and Christel Hohenegger and Braxton Osting},
In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (“the ice”) with a hole. In this paper, we investigate the ice-fishing problem including the effects of surface tension on the free surface. The dimensionless number that describes the effect of surface tension is called the Bond number. For holes that are infinite parallel strips or circular holes, we transform the problem to an equivalent eigenvalue integro-differential equation on an interval and expand in… 


An Isoperimetric Sloshing Problem in a Shallow Container with Surface Tension
In 1965, B. A. Troesch solved the isoperimetric sloshing problem of determining the container shape that maximizes the fundamental sloshing frequency among two classes of shallow containers:
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  • T. Kulczycki, N. Kuznetsov
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2010
We study an eigenvalue problem with a spectral parameter in a boundary condition. The problem describes sloshing of a heavy liquid in a container, which means that the unknowns are the frequencies