Browsing by Author "Melcher, Christof"
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Item Domain wall motion in ferromagnetic layers(2003-09) Melcher, ChristofWe consider the dynamics of one-dimensional micromagnetic domain walls in layers of uniaxial anisotropy. In the regime of bulk materials, i.e. when the thickness is assumed to be infinite, and the magnetostatic interaction terms appear as local quantities, explicit traveling wave solutions for the corresponding Landau-Lifshitz equation, known as Walker exact solutions, can be constructed. A natural question is whether this construction can be perturbed to the non-local regime of layers of finite thickness. Our stability analysis gives an affirmative answer.Item Dynamics for Ginzburg-Landau vortices under a mixed flow(2008-11-07) Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, DanielWe consider a complex Ginzburg-Landau equation that contains a Schrodinger term and a damping term that is proportional to the time derivative. Given well-prepared initial conditions that correspond to quantized vortices, we establish the vortex motion law until collision time.Item Existence of partially regular solutions for Landau-Lifshitz equations in R3(2003-11) Melcher, ChristofWe establish existence of partially regular weak solutions for the Landau-Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. We show that the singular set of such a solution has locally finite 3-dimensional parabolic Hausdorff measure. The construction relies on an approximation based on the Ginzburg-Landau energy.Item Logarithmic lower bounds for Néel walls(2003-03) Melcher, ChristofMost mathematical models for interfaces and transition layers in materials science exhibit sharply localized and rapidly decaying transition profiles. We show that this behavior can largely change when non-local interactions dominate and internal length scales fail to be determined by dimensional analysis: we consider a reduced model for the micromagnetic N\'eel wall which is observed in thin films. The typical phenomenon associated with this wall type is the very long logarithmic tail of transition profiles. Logarithmic upper bounds were recently derived by the author. In the present article we prove that the latter result is indeed optimal. In particular, we show that N\'eel wall profiles are supported by explicitly known comparison profiles that minimize relaxed variational principles and exhibit logarithmic decay behavior. This lower bound is established by a comparison argument based on a global maximum principle for the non-local field operator and the qualitative decay behavior of comparison profiles.