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Mathematical Modelling and Analysis Volume 15, 2010 - Issue 2
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Original Articles

Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles

O. Lavrova Department of Computational Mathematics, Belarusian State University, Independence Ave. 4, Minsk, 220030, Belarus E-mail: [email protected]
,
V. Polevikov Department of Computational Mathematics, Belarusian State University, Independence Ave. 4, Minsk, 220030, Belarus E-mail: [email protected]
&
L. Tobiska Institute for Analysis and Computational Mathematics, Otto von Guericke University Magdeburg, PF4120, Magdeburg, D‐39106, Germany E-mail: [email protected]
Pages 223-233 | Received 11 Oct 2009, Published online: 09 Jun 2011

References

  • Bacri , J.‐C. and Salin , D. 1984 . First order transition in the instability of a magnetic fluid interface . J. Phys. Lett., , 45 (11) : 558 – 564 .
  • Bashtovoi , V. , Lavrova , O. , Polevikov , V. and Tobiska , L. 2002 . Computer modeling of the instability of a horizontal magnetic‐fluid layer in a uniform magnetic field . J. Magnetism and Magnetic Materials, , 252 : 299 – 301 .
  • Čiegis , R. 2006 . Parallel numerical algorithms for 3D parabolic problem with nonlocal boundary condition . Informatica, , 17 (3) : 309 – 324 .
  • Čiegis , R. , Štikonas , A. , Štikonien?e , O. and Suboč , O. 2001 . Stationary problems with nonlocal boundary conditions . Math. Model. Anal., , 6 (2) : 178 – 191 .
  • Cowley , M. and Rosensweig , R. 1967 . The interfacial stability of a ferromagnetic fluid . J. Fluid Mech., , 30 (4) : 671 – 688 .
  • Gailitis , A. 1977 . Formation of the hexagonal pattern on the surface of a ferromagnetic fluid in an applied magnetic field . J. Fluid Mech., , 82 (3) : 401 – 413 .
  • Gollwitzer , C. , Matthies , G. , Richter , R. , Rehberg , I. and Tobiska , L. 2007 . The surface topography of a magnetic fluid ‐ a quantitative comparison between experiment and numerical simulation . J. Fluid Mech., , 571 : 455 – 474 .
  • Lavrova , O. 2006 . Numerical methods for axisymmetric equilibrium magnetic fluid shapes , Fakultät für Mathematik : Otto‐von‐Guericke Universität Magdeburg . PhD Thesis
  • Lavrova , O. , Matthies , G. and Tobiska , L. 2008 . Numerical study of soliton‐like surface configurations on a magnetic fluid layer in the Rosensweig instability . Communications in Nonlinear Science and Numerical Simulation, , 13 : 1302 – 1310 . Doi:10.1016/j.cnsns.2006.12.006.
  • Polevikov , V. 2004 . Methods for numerical modeling of two‐dimensional capillary surfaces . Computational Methods in Applied Mathematics, , 4 (1) : 66 – 93 .
  • Polevikov , V. and Tobiska , L. 2008 . On the solution of the steady‐state diffusion problem for ferromagnetic particles in a magnetic fluid . Math. Model. Anal., , 13 (2) : 233 – 240 .
  • Richter , R. and Barashenkov , I. 2005 . Two‐dimensional solitons on the surface of magnetic fluids . Phys. Rev. Lett., , 94 : 184503 – 184506 .
  • Rosensweig , R. 1997 . Ferrohydrodynamics. , New York : Dover Publ. Inc. .

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