1,502 research outputs found
Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations
In this paper we develop magnetic induction conforming multiscale
formulations for magnetoquasistatic problems involving periodic materials. The
formulations are derived using the periodic homogenization theory and applied
within a heterogeneous multiscale approach. Therefore the fine-scale problem is
replaced by a macroscale problem defined on a coarse mesh that covers the
entire domain and many mesoscale problems defined on finely-meshed small areas
around some points of interest of the macroscale mesh (e.g. numerical
quadrature points). The exchange of information between these macro and meso
problems is thoroughly explained in this paper. For the sake of validation, we
consider a two-dimensional geometry of an idealized periodic soft magnetic
composite.Comment: Paper accepted for publication in the SIAM MMS journa
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
The Surface Topography of a Magnetic Fluid -- a Quantitative Comparison between Experiment and Numerical Simulation
The normal field instability in magnetic liquids is investigated
experimentally by means of a radioscopic technique which allows a precise
measurement of the surface topography. The dependence of the topography on the
magnetic field is compared to results obtained by numerical simulations via the
finite element method. Quantitative agreement has been found for the critical
field of the instability, the scaling of the pattern amplitude and the detailed
shape of the magnetic spikes. The fundamental Fourier mode approximates the
shape to within 10% accuracy for a range of up to 40% of the bifurcation
parameter of this subcritical bifurcation. The measured control parameter
dependence of the wavenumber differs qualitatively from analytical predictions
obtained by minimization of the free energy.Comment: 21 pages, 16 figures; corrected typos, added reference to Kuznetsov
and Spector(1976), S.J. Fortune(1995) and Harkins&Jordan (1930). Figures
revise
Nonlinear force-free reconstruction of the global solar magnetic field: methodology
We present a novel numerical method that allows the calculation of nonlinear
force-free magnetostatic solutions above a boundary surface on which only the
distribution of the normal magnetic field component is given. The method relies
on the theory of force-free electrodynamics and applies directly to the
reconstruction of the solar coronal magnetic field for a given distribution of
the photospheric radial field component. The method works as follows: we start
with any initial magnetostatic global field configuration (e.g. zero, dipole),
and along the boundary surface we create an evolving distribution of tangential
(horizontal) electric fields that, via Faraday's equation, give rise to a
respective normal field distribution approaching asymptotically the target
distribution. At the same time, these electric fields are used as boundary
condition to numerically evolve the resulting electromagnetic field above the
boundary surface, modelled as a thin ideal plasma with non-reflecting,
perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear
force-free configuration that satisfies the given normal field distribution on
the boundary. This is different from existing methods relying on a fixed
boundary condition - the boundary evolves toward the a priori given one, at the
same time evolving the three-dimensional field solution above it. Moreover,
this is the first time a nonlinear force-free solution is reached by using only
the normal field component on the boundary. This solution is not unique, but
depends on the initial magnetic field configuration and on the evolutionary
course along the boundary surface. To our knowledge, this is the first time
that the formalism of force-free electrodynamics, used very successfully in
other astrophysical contexts, is applied to the global solar magnetic field.Comment: 18 pages, 5 figures, Solar Physic
Magnetic Cellular Nonlinear Network with Spin Wave Bus for Image Processing
We describe and analyze a cellular nonlinear network based on magnetic
nanostructures for image processing. The network consists of magneto-electric
cells integrated onto a common ferromagnetic film - spin wave bus. The
magneto-electric cell is an artificial two-phase multiferroic structure
comprising piezoelectric and ferromagnetic materials. A bit of information is
assigned to the cell's magnetic polarization, which can be controlled by the
applied voltage. The information exchange among the cells is via the spin waves
propagating in the spin wave bus. Each cell changes its state as a combined
effect of two: the magneto-electric coupling and the interaction with the spin
waves. The distinct feature of the network with spin wave bus is the ability to
control the inter-cell communication by an external global parameter - magnetic
field. The latter makes possible to realize different image processing
functions on the same template without rewiring or reconfiguration. We present
the results of numerical simulations illustrating image filtering, erosion,
dilation, horizontal and vertical line detection, inversion and edge detection
accomplished on one template by the proper choice of the strength and direction
of the external magnetic field. We also present numerical assets on the major
network parameters such as cell density, power dissipation and functional
throughput, and compare them with the parameters projected for other
nano-architectures such as CMOL-CrossNet, Quantum Dot Cellular Automata, and
Quantum Dot Image Processor. Potentially, the utilization of spin waves
phenomena at the nanometer scale may provide a route to low-power consuming and
functional logic circuits for special task data processing
Effects of Line-tying on Magnetohydrodynamic Instabilities and Current Sheet Formation
An overview of some recent progress on magnetohydrodynamic stability and
current sheet formation in a line-tied system is given. Key results on the
linear stability of the ideal internal kink mode and resistive tearing mode are
summarized. For nonlinear problems, a counterexample to the recent
demonstration of current sheet formation by Low \emph{et al}. [B. C. Low and
\AA. M. Janse, Astrophys. J. \textbf{696}, 821 (2009)] is presented, and the
governing equations for quasi-static evolution of a boundary driven, line-tied
magnetic field are derived. Some open questions and possible strategies to
resolve them are discussed.Comment: To appear in Phys. Plasma
On the use of mixed potential formulation for finite-element analysis of large-scale magnetization problems with large memory demand
The finite-element analysis of three-dimensional magnetostatic problems in
terms of magnetic vector potential has proven to be one of the most efficient
tools capable of providing the excellent quality results but becoming
computationally expensive when employed to modeling of large-scale
magnetization problems in the presence of applied currents and nonlinear
materials due to subnational number of the model degrees of freedom. In order
to achieve a similar quality of calculation at lower computational cost, we
propose to use for modeling such problems the combination of magnetic vector
and total scalar potentials as an alternative to magnetic vector potential
formulation. The potentials are applied to conducting and nonconducting parts
of the problem domain, respectively and coupled together across their common
interfacing boundary. For nonconducting regions, the thin cuts are constructed
to ensure their simply connectedness and therefore the consistency of the mixed
formulation. The implementation in the finite-element method of both
formulations is discussed in detail with difference between the two emphasized.
The numerical performance of finite-element modeling in terms of combined
potentials is assessed against the magnetic vector potential formulation for
two magnetization models, the Helmholtz coil, and the dipole magnet. We show
that mixed formulation can provide a substantial reduction in the computational
cost as compared to its vector counterpart for a similar accuracy of both
methods.Comment: 14 pages, 7 figure, 2 table
- …