445 research outputs found
On the energy-based variational model for vector magnetic hysteresis
We consider the quasi-static magnetic hysteresis model based on a dry-friction like representation of magnetization. The model has a consistent energy interpretation, is intrinsically vectorial, and ensures a direct calculation of the stored and dissipated energies at any moment in time, and hence not only on the completion of a closed hysteresis loop. We discuss the variational formulation of this model and derive an efficient numerical scheme, avoiding the usually employed approximation which can be inaccurate in the vectorial case. The parameters of this model for a nonoriented steel are identified using a set of first order reversal curves. Finally, the model is incorporated as a local constitutive relation into a 2D finite element simulation accounting for both the magnetic hysteresis and the eddy current
Energetics and switching of quasi-uniform states in small ferromagnetic particles
We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size
On the critical nature of plastic flow: one and two dimensional models
Steady state plastic flows have been compared to developed turbulence because
the two phenomena share the inherent complexity of particle trajectories, the
scale free spatial patterns and the power law statistics of fluctuations. The
origin of the apparently chaotic and at the same time highly correlated
microscopic response in plasticity remains hidden behind conventional
engineering models which are based on smooth fitting functions. To regain
access to fluctuations, we study in this paper a minimal mesoscopic model whose
goal is to elucidate the origin of scale free behavior in plasticity. We limit
our description to fcc type crystals and leave out both temperature and rate
effects. We provide simple illustrations of the fact that complexity in rate
independent athermal plastic flows is due to marginal stability of the
underlying elastic system. Our conclusions are based on a reduction of an
over-damped visco-elasticity problem for a system with a rugged elastic energy
landscape to an integer valued automaton. We start with an overdamped one
dimensional model and show that it reproduces the main macroscopic
phenomenology of rate independent plastic behavior but falls short of
generating self similar structure of fluctuations. We then provide evidence
that a two dimensional model is already adequate for describing power law
statistics of avalanches and fractal character of dislocation patterning. In
addition to capturing experimentally measured critical exponents, the proposed
minimal model shows finite size scaling collapse and generates realistic shape
functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science
for the special issue in honor of Victor Berdichevsky, 201
Micromagnetics and spintronics: Models and numerical methods
Computational micromagnetics has become an indispensable tool for the
theoretical investigation of magnetic structures. Classical micromagnetics has
been successfully applied to a wide range of applications including magnetic
storage media, magnetic sensors, permanent magnets and more. The recent advent
of spintronics devices has lead to various extensions to the micromagnetic
model in order to account for spin-transport effects. This article aims to give
an overview over the analytical micromagnetic model as well as its numerical
implementation. The main focus is put on the integration of spin-transport
effects with classical micromagnetics
Stabilization methods in relaxed micromagnetism
The magnetization of a ferromagnetic sample solves a
non-convex variational problem, where its relaxation by convexifying
the energy density resolves relevant
macroscopic information.
The numerical analysis of the relaxed model
has to deal with a constrained convex
but degenerated, nonlocal energy functional in mixed formulation for
magnetic potential u and magnetization m.
In [C. Carstensen and A. Prohl, Numer. Math. 90
(2001) 65â99], the conforming P1 - (P0)d-element in d=2,3 spatial
dimensions is shown to lead to
an ill-posed discrete problem in relaxed micromagnetism, and suboptimal
convergence.
This observation motivated a
non-conforming finite element method which leads to
a well-posed discrete problem, with solutions converging at
optimal rate.
In this work, we provide both an a priori and a posteriori error analysis for two
stabilized conforming methods which account for inter-element jumps of the
piecewise constant magnetization.
Both methods converge at optimal rate;
the new approach is applied to a macroscopic nonstationary
ferromagnetic model [M. KruĆŸĂk and A. Prohl, Adv. Math. Sci. Appl. 14 (2004) 665â681 â M. KruĆŸĂk and T. RoubĂÄek, Z. Angew. Math. Phys. 55 (2004) 159â182â]
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