Asymptotic shape of isolated magnetic domains

Knüpfer, Hans; Stantejsky, Dominik

doi:10.1098/rspa.2022.0018

Cited by 4 publications

(2 citation statements)

References 67 publications

(88 reference statements)

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“…Other related vectorial models where the energy includes both interface type energies as well as a (dipolar) nonlocal interaction are ferromagnetic systems. The nucleation of magnetic domains during magnetization reversal and corresponding optimal magnetization patterns have been investigated in [44,47,48], see also [61]. The competition between a nonlocal repulsive potential and an attractive confining term is found also in other problems, for example in models studying the interaction of dislocations [41,67] or [14,15,59].…”

Section: Relation To the Literaturementioning

confidence: 99%

Minimal energy for geometrically nonlinear elastic inclusions in two dimensions

Akramov¹,

Knüpfer²,

Kružík³

et al. 2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from Conti and Schweizer (Commun. Pure Appl. Math.59 (2006), 830–868) and Knüpfer and Kohn (Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci.467 (2011), 695–717), we derive the lower scaling bound by invoking a two-well rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion.

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Section: Relation To the Literaturementioning

confidence: 99%

Minimal energy for geometrically nonlinear elastic inclusions in two dimensions

Akramov¹,

Knüpfer²,

Kružík³

et al. 2023

Proceedings of the Royal Society of Edinburgh: Section A Mathem

Self Cite

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show abstract

“…Other related vectorial models where the energy includes both interface type energies as well as a (dipolar) nonlocal interaction are ferromagnetic systems. The nucleation of magnetic domains during magnetization reversal and corresponding optimal magnetization patterns have been investigated in [43,44,45], see also [58]. The competition between a nonlocal repulsive potential and an attractive confining term is found also in other problems, for example in models studying the interaction of dislocations [64,38] or [56,13,14].…”

Section: Introductionmentioning

confidence: 99%

Minimal Energy for Geometrically Nonlinear Elastic Inclusions in Two Dimensions

Akramov¹,

Knüpfer²,

Kružík³

et al. 2022

Preprint

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We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion of a fixed volume for which the energy is determined by a surface and an (anisotropic) elastic contribution. Following ideas from [26] and [40], we derive the lower scaling bound by invoking a twowell rigidity argument and a covering result. The upper bound follows from a well-known construction for a lens-shaped elastic inclusion.

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On Scaling Laws for Multi-Well Nucleation Problems Without Gauge Invariances

Rüland

Tribuzio

2023

J Nonlinear Sci

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In this article, we study scaling laws for simplified multi-well nucleation problems without gauge invariances which are motivated by models for shape-memory alloys. Seeking to explore the role of the order of lamination on the energy scaling for nucleation processes, we provide scaling laws for various model problems in two and three dimensions. In particular, we discuss (optimal) scaling results in the volume and the singular perturbation parameter for settings in which the surrounding parent phase is in the first-, the second- and the third-order lamination convex hull of the wells of the nucleating phase. Furthermore, we provide a corresponding result for the setting of an infinite order laminate which arises in the context of the Tartar square. In particular, our results provide isoperimetric estimates in situations in which strong nonlocal anisotropies are present.

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Asymptotic shape of isolated magnetic domains

Abstract: We investigate the energy of an isolated magnetized domain Ω ⊂ R n for n = 2 , 3 . In non-dimensionalized variables, the energy given by … Show more

Cited by 4 publications

References 67 publications

Minimal energy for geometrically nonlinear elastic inclusions in two dimensions

Minimal energy for geometrically nonlinear elastic inclusions in two dimensions

Minimal Energy for Geometrically Nonlinear Elastic Inclusions in Two Dimensions

On Scaling Laws for Multi-Well Nucleation Problems Without Gauge Invariances

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