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On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the stability features of steady-states of a two-dimensional system of ferromagnetic nanowires.We constitute a systemwith the finite number of nanowires arranged on the (e⃗1, e⃗2) plane, where (e⃗1, e⃗2, e⃗3) is the canonical basis of ℝ3. We consider two cases: in the first case, each nanowire is considered to be of infinite length, whereas in the second case, we deal with finite length nanowires to design the system. In both cases, we establish a sufficient condition under which these steady-states are shown to be exponentially stable.
Wydawca
Rocznik
Strony
89--100
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
autor
  • Department of Mathematics, SRM University, Kattankulathur 603 203, India
autor
  • Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India
Bibliografia
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  • [3] A. Aharoni, Introduction to the Theory of Ferromagnetism, Oxford University Press, Oxford, 2000.
  • [4] F. Alouges, A new finite element scheme for Landau-Lifchitz equations, Discrete Contin. Dyn. Syst. Ser. S 1 (2008), no. 2, 187-196.
  • [5] F. Alouges, Mathematical models in micromagnetism: An introduction, ESAIM Proc. 22 (2008), 114-117.
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  • [7] L. Baňas, Stochastic Ferromagnetism: Analysis and Numerics, De Gruyter Stud. Math. 58, Walter de Gruyter, Berlin, 2014.
  • [8] L. Baňas, S. Bartels and A. Prohl, A convergent implicit finite element discretization of the Maxwell-Landau-Lifshitz-Gilbert equation, SIAM J. Numer. Anal. 46 (2008), no. 3, 1399-1422.
  • [9] S. Bartels and A. Prohl, Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation, SIAM J. Numer. Anal. 44 (2006), no. 4, 1405-1419.
  • [10] G. Boling and S. Fengqiu, Global weak solution for the Landau-Lifshitz-Maxwell equation in three space dimensions, J. Math. Anal. Appl. 211 (1997), no. 1, 326-346.
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  • [13] G. Carbou, Domain walls dynamics for one-dimensional models of ferromagnetic nanowires, Differential Integral Equations 26 (2013), no. 3-4, 201-236.
  • [14] G. Carbou and P. Fabrie, Time average in micromagnetism, J. Differential Equations 147 (1998), no. 2, 383-409.
  • [15] G. Carbou and P. Fabrie, Regular solutions for Landau-Lifschitz equation in a bounded domain, Differential Integral Equations 14 (2001), no. 2, 213-229.
  • [16] G. Carbou and P. Fabrie, Regular solutions for Landau-Lifschitz equation in ℝ3, Commun. Appl. Anal. 5 (2001), no. 1, 17-30.
  • [17] G. Carbou and S. Labbé, Stability for static walls in ferromagnetic nanowires, Discrete Contin. Dyn. Syst. Ser. B 6 (2006), no. 2, 273-290.
  • [18] G. Carbou and S. Labbé, Stabilization of walls for nano-wires of finite length, ESAIM Control Optim. Calc. Var. 18 (2012), no. 1, 1-21.
  • [19] G. Carbou, S. Labbé and E. Trélat, Control of travelling walls in a ferromagnetic nanowire, Discrete Contin. Dyn. Syst. Ser. S 1 (2008), no. 1, 51-59.
  • [20] I. Cimrák, A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism, Arch. Comput. Methods Eng. 15 (2008), no. 3, 277-309.
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Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-42985500-f744-419e-a0ed-91b6cd027933
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