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...

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Published in:Mathematical modelling and analysis Vol. 9; no. 4; pp. 287 - 298
Main Authors: Cirulis, T., Lietuvietis, O., Cēbers, A.
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.01.2004
Subjects:
Chebyshev polynomials
eigenvalues and eigenfunctions problem
gas bubble
Hele-Shaw cell
magnetic liquid
the Degenerate Matrices method
ISSN:1392-6292, 1648-3510
Online Access:Get full text
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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.
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  fullname: Cēbers, A.
  organization: Institute of Mathematics , Latvian Academy of Sciences and University of Latvia
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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...
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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
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