Dynamics of small bubble interface perturbations in vertical hele-shaw cell with magnetic liquid under the action of normal magnetic field

A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is reduced to searching of eigenvalues and eigenfunctions for a linear operator with periodic boundary conditions. The obtained operator is presented...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical modelling and analysis Jg. 9; H. 4; S. 287 - 298
Hauptverfasser: Cirulis, T., Lietuvietis, O., Cēbers, A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis Group 01.01.2004
Schlagworte:
Chebyshev polynomials
eigenvalues and eigenfunctions problem
gas bubble
Hele-Shaw cell
magnetic liquid
the Degenerate Matrices method
ISSN:1392-6292, 1648-3510
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is reduced to searching of eigenvalues and eigenfunctions for a linear operator with periodic boundary conditions. The obtained operator is presented as a sum of two linear operators: the second order differential operator with varying coefficients and the integro - differential operator with the singularity of the Cauchy type. The spectral problem is solved by the Degenerate Matrices (DM) method using Chebyshev polynomials of the first and second kind.
AbstractList A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is reduced to searching of eigenvalues and eigenfunctions for a linear operator with periodic boundary conditions. The obtained operator is presented as a sum of two linear operators: the second order differential operator with varying coefficients and the integro - differential operator with the singularity of the Cauchy type. The spectral problem is solved by the Degenerate Matrices (DM) method using Chebyshev polynomials of the first and second kind.
Author Cēbers, A.
Lietuvietis, O.
Cirulis, T.
Author_xml – sequence: 1
  givenname: T.
  surname: Cirulis
  fullname: Cirulis, T.
  organization: Institute of Mathematics , Latvian Academy of Sciences and University of Latvia
– sequence: 2
  givenname: O.
  surname: Lietuvietis
  fullname: Lietuvietis, O.
  organization: Institute of Mathematics , Latvian Academy of Sciences and University of Latvia
– sequence: 3
  givenname: A.
  surname: Cēbers
  fullname: Cēbers, A.
  organization: Institute of Mathematics , Latvian Academy of Sciences and University of Latvia
BookMark eNpFUMtOwzAQtFCRaAufgOQfSPEjcdIbqDylSlzgHG2cNTFyHbATqv4CX40jijjtanZ2ZncWZOZ7j4RccrbirGJXXK6FEmuxEozlq7WSpVDshMy5yqtMFpzNUp842UQ6I4sY3xkrClGxOfm-PXjYWR1pb2jcgXO0GZvGIbV-wGBAI_3AMIyhgcH2PiacfiXAanC0Q4dZ7GBPNabNvR06uoM3j2lMnf0cbUtH32KgQ4cU9KQwGfk-JKt_qrHo2nNyasBFvDjWJXm9v3vZPGbb54enzc02s1yUQ2aUURUrBFdKF63gVYu8FOkf1NyIRjOeSyM1gFiXRsq2YVAYkSsoOTQcK7kk17-61pvpjn0fXFsPcHB9MAG8trGWnNVTtvVftvWUbX3MVv4AFCRx6w
ContentType Journal Article
Copyright Copyright Taylor & Francis Group, LLC 2004
Copyright_xml – notice: Copyright Taylor & Francis Group, LLC 2004
DOI 10.1080/13926292.2004.9637260
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1648-3510
EndPage 298
ExternalDocumentID 9637260
GroupedDBID .7F
.QJ
4.4
5GY
AAENE
ABCCY
ABFIM
ABJBJ
ABJNI
ABPEM
ABTAI
ACGFO
ACGFS
ACIPV
ACIWK
ADCVX
ADIYS
AENEX
AGMYJ
AGROQ
AIJEM
ALMA_UNASSIGNED_HOLDINGS
AQTUD
AVBZW
CE4
CRFIH
CS3
DMQIW
DU5
EBS
EJD
ESX
E~A
E~B
GROUPED_DOAJ
GTTXZ
H13
HZ~
H~P
IAO
M4Z
NA5
NY~
O9-
OK1
P2P
QCRFL
S-T
TDBHL
TFL
TFW
TR2
TUS
UT5
UU3
~S~
ID FETCH-LOGICAL-i127t-f6f68052166c5d218de172055ec1f2bc0143f3caa297f33db0a5f246a71ab1e83
IEDL.DBID TFW
ISSN 1392-6292
IngestDate Mon Oct 20 23:40:41 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 4
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-i127t-f6f68052166c5d218de172055ec1f2bc0143f3caa297f33db0a5f246a71ab1e83
PageCount 12
ParticipantIDs informaworld_taylorfrancis_310_1080_13926292_2004_9637260
PublicationCentury 2000
PublicationDate 1/1/2004
PublicationDateYYYYMMDD 2004-01-01
PublicationDate_xml – month: 01
  year: 2004
  text: 1/1/2004
  day: 01
PublicationDecade 2000
PublicationTitle Mathematical modelling and analysis
PublicationYear 2004
Publisher Taylor & Francis Group
Publisher_xml – name: Taylor & Francis Group
SSID ssj0055280
Score 1.5680853
Snippet A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is...
SourceID informaworld
SourceType Publisher
StartPage 287
SubjectTerms Chebyshev polynomials
eigenvalues and eigenfunctions problem
gas bubble
Hele-Shaw cell
magnetic liquid
the Degenerate Matrices method
Title Dynamics of small bubble interface perturbations in vertical hele-shaw cell with magnetic liquid under the action of normal magnetic field
URI https://www.tandfonline.com/doi/abs/10.1080/13926292.2004.9637260
Volume 9
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor & Francis Journals Complete
  customDbUrl:
  eissn: 1648-3510
  dateEnd: 20100131
  omitProxy: false
  ssIdentifier: ssj0055280
  issn: 1392-6292
  databaseCode: TFW
  dateStart: 19960101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQxQADb8RbHlgDjZ04yYiAiqliKKJb5SeNlKaQpPAf-NXcOamokJhgjWInOV_On09330fIZWoU09LIgEuUMFPSBRmPAMhJp1waZyLmyotNJMNhOh5nj101Yd2VVeIZ2rVEET5W488tVb2siLsG0MIEyzyNZHQFHpQAKIcoDMgei_pGg-dlLI5jlrZ9whkLcMiyh-e3WX4Qlq5sNYPtf3jJHbLV4Ux60zrGLlmz5R7ZXGEf3Cefd60afU3njtYzWRRULZQqLEUOicpJbemrrWBPUm1aD65TL98M60qnsF8F9VR-UMz9U8zn0pl8KbEpkhb52yI3FBvUKgoQk7btE_igEj-7-L7Vl9AdkKfB_ej2IeikGYI8ZEkTOOGEF0MQQscGYIKxgITA3laHjimNrIGOaylZljjOjerL2LFIyCSUKrQpPyS9cl7aI2waj5zWLrUG1a95BIC0b0I4x_VDEynBjkm2uiSTxmcyXCs7MuFhx3G6tDfqakaTzt4nfxh7SjbaKh1Mt5yRXlMt7DlZ1-9NXlcX3s2-AJ3O0-I
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3JTsMwFLSgIAEHdsSOD1wDjZ31iICqiNJTEdwqrzRSmkKSwj_w1fg5iYiQOME1ip3k2bHHT29mEDqPJCeCSeZQBhZmnGknpp4BckxzHflx4FNuzSbC4TB6fo7bXBgoq4QztK6EIuxaDT83JKObkrhLg1pIQGKrI-ldmCkUGlS-iJbAnQ4OYKPeU7Ma-z6JKqZwTBxo07B4fuvmh2Rpa7PpbfzHa26i9Rpq4qtqbmyhBZVto7WWAOEO-rypDOkLPNO4mLI0xXzOeaowyEjkmgmFX1VutiVeZfbMdWwdnM3Q4onZspxiwj4wpP8xpHTxlL1kwIvEafI2TyQGjlqODcrEFYMCHpTBd6fft9oqul302LsdXfed2p3BSVwSlo4OdGD9EIJA-NIgBakMGDIBV8LVhAsQDtRUMEbiUFMqeZf5mngBC13GXRXRPdTJZpnaB964p4XQkZJggE09g0m70jVHua4rPR6QAxS3x2Rc2mSGrpxHxtStZU6beIO1pjeu4334h7ZnaKU_ehiMB3fD-yO0WhXtQPblGHXKfK5O0LJ4L5MiP7Vz7gv-sNgF
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3JTsMwELWgIAQHdsSOD1wDjZ31iCgRCFT1UERvkVcaKU1LksI_8NV4sogKiRNco9hJxhPP82jmPYQuA8mJYJJZlIGEGWfaCqljgBzTXAdu6LmUV2ITfr8fjEbhoKkmLJqySjhD65oootqr4eeeSd1WxF0b0EI8ElY0ks6V8SDfgPJltGKgswuOPYxe2s3YdUlQNwqHxIIxbRPPb9P8YCxdiDXR1j-85TbabIAmvqk9YwctqWwXbSzQD-6hz14tR1_gqcbFhKUp5nPOU4WBRCLXTCg8U7kJSrzO65nruNJvNguLxyZgWcWYfWBI_mNI6OIJe82gKxKnyds8kRg61HJsMCau-yfgQRl8dvp9a1VDt4-eo7vh7b3VaDNYiU380tKe9io1BM8TrjQ4QSoDhYy9lbA14QJoAzUVjJHQ15RK3mWuJo7HfJtxWwX0AHWyaaYOoWvc0ULoQEmQv6aOQaRdaZuDXNeWDvfIEQoXlyQuq1SGrnVHYmo3JKetvUFY04kbex__YewFWhv0ovjpof94gtbrih1IvZyiTpnP1RlaFe9lUuTnlcd9AZnh1rc
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Dynamics+of+small+bubble+interface+perturbations+in+vertical+hele-shaw+cell+with+magnetic+liquid+under+the+action+of+normal+magnetic+field&rft.jtitle=Mathematical+modelling+and+analysis&rft.au=Cirulis%2C+T.&rft.au=Lietuvietis%2C+O.&rft.au=C%C4%93bers%2C+A.&rft.date=2004-01-01&rft.pub=Taylor+%26+Francis+Group&rft.issn=1392-6292&rft.eissn=1648-3510&rft.volume=9&rft.issue=4&rft.spage=287&rft.epage=298&rft_id=info:doi/10.1080%2F13926292.2004.9637260&rft.externalDocID=9637260
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1392-6292&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1392-6292&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1392-6292&client=summon