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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
73/2009

Floating criteria in three dimensions

Robert Finn and Thomas Vogel

Abstract

We extend to objects of general convex form an earlier criterion given by Finn for ensuring a local energy minimum corresponding to floating of a heavy horizontal cylinder on a liquid surface. We obtain a formal analogue of Finn’s criterion, and additionally a condition on interfacial surface energies under which an object of given shape with density exceeding that of the liquid must float if it is scaled to be sufficiently small. In analogy with Finn’s earlier work, we show also in the more physical case presently considered that if a body is lowered rigidly from a position above the undisturbed liquid surface to a position below the surface, the liquid configuration must change during the motion in a discontinuous way.

Received:
Dec 9, 2009
Published:
Dec 10, 2009
MSC Codes:
76B45, 49Q10, 53A10
Keywords:
capillarity, surface tension, floating bodies

Related publications

inJournal
2009 Repository Open Access
Robert Finn and Thomas I. Vogel

Floating criteria in three dimensions

In: Analysis, 29 (2009) 4, pp. 387-402