The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes
Abstract We study an eignevalue problem with a spectral parameter in a boundary condition. This problem for the Laplace equation is relevant to sloshing frequencies that describe free oscillations of an inviscid, incompressible, heavy fluid in a half‐space covered by a rigid dock with some apertures...
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crwiley:10.1002/mma.442 2024-06-02T08:08:17+00:00 The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes Kozlov, Vladimir Kuznetsov, Nikolay Swedish Research Council Wenner-Gren foundation Russian foundation 2004 http://dx.doi.org/10.1002/mma.442 https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fmma.442 https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.442 en eng Wiley http://onlinelibrary.wiley.com/termsAndConditions#vor Mathematical Methods in the Applied Sciences volume 27, issue 3, page 289-312 ISSN 0170-4214 1099-1476 journal-article 2004 crwiley https://doi.org/10.1002/mma.442 2024-05-03T11:21:14Z Abstract We study an eignevalue problem with a spectral parameter in a boundary condition. This problem for the Laplace equation is relevant to sloshing frequencies that describe free oscillations of an inviscid, incompressible, heavy fluid in a half‐space covered by a rigid dock with some apertures (an ice sheet with fishing holes). The dependence of the fundamental eigenvalue on holes' geometry is investigated. We give conditions on a plane region guaranteeing that the fundamental eigenvalue corresponding to this region is larger than the fundamental eigenvalue corresponding to a single circular hole. Examples of regions satisfying these conditions and having the same area as the unit disk are given. New results are also obtained for the problem with a single circular hole. On the other hand, we construct regions for which the fundamental eigenfrequency is larger than the similar frequency for the circular hole of the same area and even as large as one wishes. In the latter examples, the hole regions are either not connected or bounded by a rather complicated curves. Copyright © 2004 John Wiley & Sons, Ltd. Article in Journal/Newspaper Ice Sheet Wiley Online Library Laplace ENVELOPE(141.467,141.467,-66.782,-66.782) Mathematical Methods in the Applied Sciences 27 3 289 312 |
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Wiley Online Library |
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English |
description |
Abstract We study an eignevalue problem with a spectral parameter in a boundary condition. This problem for the Laplace equation is relevant to sloshing frequencies that describe free oscillations of an inviscid, incompressible, heavy fluid in a half‐space covered by a rigid dock with some apertures (an ice sheet with fishing holes). The dependence of the fundamental eigenvalue on holes' geometry is investigated. We give conditions on a plane region guaranteeing that the fundamental eigenvalue corresponding to this region is larger than the fundamental eigenvalue corresponding to a single circular hole. Examples of regions satisfying these conditions and having the same area as the unit disk are given. New results are also obtained for the problem with a single circular hole. On the other hand, we construct regions for which the fundamental eigenfrequency is larger than the similar frequency for the circular hole of the same area and even as large as one wishes. In the latter examples, the hole regions are either not connected or bounded by a rather complicated curves. Copyright © 2004 John Wiley & Sons, Ltd. |
author2 |
Swedish Research Council Wenner-Gren foundation Russian foundation |
format |
Article in Journal/Newspaper |
author |
Kozlov, Vladimir Kuznetsov, Nikolay |
spellingShingle |
Kozlov, Vladimir Kuznetsov, Nikolay The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes |
author_facet |
Kozlov, Vladimir Kuznetsov, Nikolay |
author_sort |
Kozlov, Vladimir |
title |
The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes |
title_short |
The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes |
title_full |
The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes |
title_fullStr |
The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes |
title_full_unstemmed |
The ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes |
title_sort |
ice‐fishing problem: the fundamental sloshing frequency versus geometry of holes |
publisher |
Wiley |
publishDate |
2004 |
url |
http://dx.doi.org/10.1002/mma.442 https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fmma.442 https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.442 |
long_lat |
ENVELOPE(141.467,141.467,-66.782,-66.782) |
geographic |
Laplace |
geographic_facet |
Laplace |
genre |
Ice Sheet |
genre_facet |
Ice Sheet |
op_source |
Mathematical Methods in the Applied Sciences volume 27, issue 3, page 289-312 ISSN 0170-4214 1099-1476 |
op_rights |
http://onlinelibrary.wiley.com/termsAndConditions#vor |
op_doi |
https://doi.org/10.1002/mma.442 |
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Mathematical Methods in the Applied Sciences |
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27 |
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3 |
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289 |
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312 |
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1800753488877060096 |