Travelling Waves with a Singularity in Magnetic Nanowires

References

• Atkinson , D. , Xiong , G. , Faulkner , C. , Allwood , D. , Petit , D. , Cowburn , R. ( 2005 ). Magnetic domain wall logic . Science 309 : 1688 – 1692 .
   PubMedGoogle Scholar
• Berestycki , H. , Nirenberg . L. ( 1992 ). Travelling fronts in cylinders . Ann. Inst. H. Poincaré Anal. Non Linéaire 9 : 497 – 572 .
   Web of Science ®Google Scholar
• Bertsch , M. , Muratov , C. B. , Primi , I. ( 2006 ). Traveling wave solutions of harmonic heat flow . Calc. Var. Partial Differential Equations 26 : 489 – 509 .
   Web of Science ®Google Scholar
• Carbou , G. , Labbé , S. ( 2006 ). Stability for static walls in ferromagnetic nanowires . Discrete Contin. Dyn. Syst. Ser. B 6 : 273 – 290 .
   Google Scholar
• DeSimone , A. , Kohn , R. V. , Müller , S. , Otto , F. ( 2005 ). Recent analytical developments in micromagnetics . In: Bertotti , G. , Mayergoyz , I. , eds. The Science of Hysteresis . London : Academic Press, Inc.
   Google Scholar
• Forster , H. , Schrefl , T. , Suess , D. , Scholz , W. , Tsiantos , V. , Dittrich , R. , Fidler , J. (2002). Domain wall motion in nanowires using moving grids. J. Appl. Phys. 91:6914–6919.
   Google Scholar
• Gilbarg , D. , Trudinger , N. S. ( 2001 ). Elliptic Partial Differential Equations of Second Order, Classics in Mathematics . Berlin : Springer-Verlag .
   Google Scholar
• Heinze , S. ( 2001 ). A variational approach to travelling waves . Preprint. Available at: www.mis.mpg.de/preprints/2001.mis.mpg.de/preprints/2001
   Google Scholar
• Hertel , R. , Kirschner , J. ( 2004 ). Magnetization reversal dynamics in nickel nanowires . Physica B 343 : 206 – 210 .
   Google Scholar
• Hubert , A. , Schäfer , R. ( 2000 ). Magnetic Domains . New York : Springer-Verlag .
   Google Scholar
• Korenev , B. G. ( 2002 ). Bessel Functions and Their Applications . Volume 8 of Analytical Methods and Special Functions. Translated from the Russian by E. V. Pankratiev . London : Taylor & Francis .
   Google Scholar
• Kühn , K. ( 2007 ). Reversal modes in magnetic nanowires . PhD Thesis , Universität Leipzig , Leipzig , Germany .
   Google Scholar
• Kühn , K. Energy scaling of domain walls in magnetic nanowires . Arch. Rat. Mech. Anal. To appear .
   Google Scholar
• Kühn , K. ( 2007 ). Regularity of domain walls in magnetic nanowires . Preprint. Available at: www.mis.mpg.de/preprints/2007/prepr2007.mis.mpg.de/preprints/2007/prepr2007 106 .
   Google Scholar
• Kühn , K. ( 2008 ). Moving domain walls in magnetic nanowires . Ann. Inst. H. Poincaré Anal. Non Linéaire 26 : 1346 – 1360 .
   Google Scholar
• Lucia , M. , Muratov , C. B. , Novaga , M. ( 2004 ). Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium . Comm. Pure Appl. Math. 57 : 616 – 636 .
   Web of Science ®Google Scholar
• Lucia , M. , Muratov , C. B. , Novaga. M. ( 2008 ). Existence of traveling wave solutions for Ginzburg-Landau-type problems in infinite cylinders . Arch. Rat. Mech. Anal. 188 : 475 – 508 .
   Web of Science ®Google Scholar
• Muratov , C. B. ( 2004 ). A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type . Discrete Contin. Dyn. Syst. Ser. B 4 : 867 – 892 .
   Web of Science ®Google Scholar
• Muratov , C. B. , Novaga , M. ( 2008 ). Front propagation in infinite cylinders, I. A variational approach . Commun. Math. Sci. 6 : 799 – 826 .
   Google Scholar
• Sanchez , D. Behaviour of the Landau-Lifschitz equation in a ferromagnetic wire . Math. Methods Appl. Sci. To appear .
   Google Scholar
• Struwe , M. ( 1996 ). Variational Methods . Ergebnisse der Mathematik und ihrer Grenzgebiete (3) , Vol. 34 . Berlin : Springer-Verlag .
   Google Scholar
• Wieser , R. , Nowak , U. , Usadel , K. D. ( 2004 ). Domain wall mobility in nanowires: Transverse versus vortex walls . Phys. Rev. B 69 : 0604401 .
   Google Scholar