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.
Burbulo paviršiaus mažų žadinimų dinamika vertikalioje Hele-Shaw ląstelėje, užpildytoje magnetiniu skysčių veikiamo normaliniu magnetiniu lauku
Santrauka. Dujų burbulo, judančio vertikalią Hele‐Shaw ląstelę užpildančiu magnetiniu skysčiu, paviršiaus dinamikos matematinis modelis yra suformuluotas kaip spektrinis uždavinys tam tikram tiesiniam operatoriui su periodinėmis kraštinėmis sąlygomis. Pastarasis uždavinys yra išspręstas skaitmeniškai išsigimstančių matricų metodu.
Cirulis, T., Lietuvietis, O., & Cēbers, A. (2004). Dynamics of small bubble interface perturbations in vertical hele‐shaw cell with magnetic liquid under the action of normal magnetic field. Mathematical Modelling and Analysis, 9(4), 287-298. https://doi.org/10.3846/13926292.2004.9637260
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.