Solutions to problems from previous parts

  • Avner Friedman
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 67)


Chapters 1,9 and 17 dealt with magnetic material used, for instance, in floppy disks and magnetic tape. Such material is commonly modelled by the Landau-Lipshitz (LL) equation. Computation of the hysteresis loops are very expensive because (i) each time-step in the LL time-integration requires several evaluations of the magnetostatic field, and (ii) the nonlinear ODEs describing the motion of the magnetic particles have several kinds of stiffness. Solomonoff [1] has developed a scheme whereby he uses the LL equation only when the system is not near equilibrium; when the system is near equilibrium he lets the solution follow the equilibrium point (which varies in time, since the external field varies in time). Numerical results show that the method is very effective in reducing the computation time without sacrificing precision, especially in a range of parameters where the anisotropy is not too weak.


Capillary Number Magnetic Tape Previous Part Floppy Disk Electrorheological Fluid 
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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Avner Friedman
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

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