A Note on the Uniqueness of Certain Water‐Wave Problems Involving Two Vertical Cylindrical Shells.
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| Title: | A Note on the Uniqueness of Certain Water‐Wave Problems Involving Two Vertical Cylindrical Shells. |
|---|---|
| Authors: | EVANS, D. V.1, SHIPWAY, B. J.1 |
| Source: | Quarterly Journal of Mechanics & Applied Mathematics. Aug2003, Vol. 56 Issue 3, p347-359. 13p. 6 Graphs. |
| Subjects: | Geometry problems & exercises, Cylinder (Shapes), Finite differences, Numerical analysis, Linear algebra |
| Abstract: | A simple geometric condition is derived under which certain problems relating to two partially or totally immersed vertical cylindrical shells in water of finite depth are unique. The method, using classical linear water wave theory, is based on an idea of F. John (1950), utilized by N. Kuznetsov and V. Maz'ya (2001) who proved uniqueness for all geometries and frequencies of a single cylindrical shell. The problem is particularly relevent to the possible existence of trapped modes that have been predicted numerically in the case of two circular cylindrical shells. The method is also applied to two pairs of symmetric vertical barriers and extends the results of Kuznetsov et al. (2001). A further example with a geometry defined by confocal ellipses is considered. [ABSTRACT FROM PUBLISHER] |
| Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 44552969 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Note on the Uniqueness of Certain Water‐Wave Problems Involving Two Vertical Cylindrical Shells. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22EVANS%2C+D%2E+V%2E%22">EVANS, D. V.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22SHIPWAY%2C+B%2E+J%2E%22">SHIPWAY, B. J.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Quarterly+Journal+of+Mechanics+%26+Applied+Mathematics%22">Quarterly Journal of Mechanics & Applied Mathematics</searchLink>. Aug2003, Vol. 56 Issue 3, p347-359. 13p. 6 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Geometry+problems+%26+exercises%22">Geometry problems & exercises</searchLink><br /><searchLink fieldCode="DE" term="%22Cylinder+%28Shapes%29%22">Cylinder (Shapes)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+differences%22">Finite differences</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+algebra%22">Linear algebra</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A simple geometric condition is derived under which certain problems relating to two partially or totally immersed vertical cylindrical shells in water of finite depth are unique. The method, using classical linear water wave theory, is based on an idea of F. John (1950), utilized by N. Kuznetsov and V. Maz'ya (2001) who proved uniqueness for all geometries and frequencies of a single cylindrical shell. The problem is particularly relevent to the possible existence of trapped modes that have been predicted numerically in the case of two circular cylindrical shells. The method is also applied to two pairs of symmetric vertical barriers and extends the results of Kuznetsov et al. (2001). A further example with a geometry defined by confocal ellipses is considered. [ABSTRACT FROM PUBLISHER] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Quarterly Journal of Mechanics & Applied Mathematics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1093/qjmam/56.3.347 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 347 Subjects: – SubjectFull: Geometry problems & exercises Type: general – SubjectFull: Cylinder (Shapes) Type: general – SubjectFull: Finite differences Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Linear algebra Type: general Titles: – TitleFull: A Note on the Uniqueness of Certain Water‐Wave Problems Involving Two Vertical Cylindrical Shells. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: EVANS, D. V. – PersonEntity: Name: NameFull: SHIPWAY, B. J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2003 Type: published Y: 2003 Identifiers: – Type: issn-print Value: 00335614 Numbering: – Type: volume Value: 56 – Type: issue Value: 3 Titles: – TitleFull: Quarterly Journal of Mechanics & Applied Mathematics Type: main |
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