Relevant bibliographies by topics / Modeling Magnetic Anisotropy

Academic literature on the topic 'Modeling Magnetic Anisotropy'

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Published: 6 September 2023

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Journal articles on the topic "Modeling Magnetic Anisotropy"

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Ben, Tong, Yuqi Kong, Long Chen, Fangyuan Chen, and Xian Zhang. "Magnetostriction property modeling of silicon steel considering stress-induced and magnetocrystalline anisotropy." AIP Advances 13, no. 2 (February 1, 2023): 025031. http://dx.doi.org/10.1063/9.0000421.

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This paper proposed an improved magnetostriction model for correlation of anisotropy in non-oriented (NO) silicon steel based on the free energy, which considers stress-induced and magnetocrystalline anisotropy. Firstly, the free energy model, which includes stress-induced anisotropy energy, the energy of magnetic field, and the anisotropic energy of magnetic crystals, is incorporated into the anhysteretic magnetization parameter M an. Then, to obtain the magnetic field and proposed model parameters related to stress-induced and magnetocrystalline anisotropy, the magnetostrictive strain loops at different magnetization directions of NO silicon steel are measured. Finally, based on the parameters obtained from experimental data of the proposed model, magnetostrictive strain loops under varying magnetization directions are simulated. This improved magnetostriction model can be applied to the calculation of the vector magnetostriction of the motor core.
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Yamaguchi, Shinichi, Akihiro Daikoku, and Norio Takahashi. "Cogging torque calculation considering magnetic anisotropy for permanent magnet synchronous motors." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 23, no. 3 (September 1, 2004): 639–46. http://dx.doi.org/10.1108/03321640410540548.

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This paper describes the cogging torque of the permanent magnet synchronous (PM) motors due to the magnetic anisotropy of motor core. The cogging torque due to the magnetic anisotropy is calculated by the finite element method using two kinds of modeling methods: one is the 2D magnetization property method, and the other is the conventional method. As a result, the PM motors with parallel laminated core show different cogging torque waveform from the PM motors with the rotational laminated core due to the influence of the magnetic anisotropy. The amplitudes of the cogging torque are different depending on the modeling methods in the region of high flux density.
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Nowicki, Michał, Roman Szewczyk, and Paweł Nowak. "Experimental Verification of Isotropic and Anisotropic Anhysteretic Magnetization Models." Materials 12, no. 9 (May 11, 2019): 1549. http://dx.doi.org/10.3390/ma12091549.

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The anhysteretic magnetization curve is the key element of modeling magnetic hysteresis loops. Despite the fact that it is intensively exploited, known models of anhysteretic curve have not been verified experimentally. This paper presents the validation of four anhysteretic curve models considering four different materials, including isotropic, such as Mn-Zn soft ferrite, as well as anisotropic amorphous and nanocrystalline alloys. The presented results indicate that only the model that considers anisotropic energy is valid for a wide set of modern magnetic materials. The most suitable of the verified models is the anisotropic extension function-based model, which considers uniaxial anisotropy.
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Akin, Meriem, Autumn Pratt, Jennifer Blackburn, and Andreas Dietzel. "Paper-Based Magneto-Resistive Sensor: Modeling, Fabrication, Characterization, and Application." Sensors 18, no. 12 (December 11, 2018): 4392. http://dx.doi.org/10.3390/s18124392.

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In this work, we developed and fabricated a paper-based anisotropic magneto-resistive sensor using a sputtered permalloy (Ni 81 Fe 19 ) thin film. To interpret the characteristics of the sensor, we proposed a computational model to capture the influence of the stochastic fiber network of the paper surface and to explain the physics behind the empirically observed difference in paper-based anisotropic magneto-resistance (AMR). Using the model, we verified two main empirical observations: (1) The stochastic fiber network of the paper substrate induces a shift of 45 ∘ in the AMR response of the paper-based Ni 81 Fe 19 thin film compared to a Ni 81 Fe 19 film on a smooth surface as long as the fibrous topography has not become buried. (2) The ratio of magnitudes of AMR peaks at different anisotropy angles and the inverted AMR peak at the 90 ∘ -anisotropy angle are explained through the superposition of the responses of Ni 81 Fe 19 inheriting the fibrous topography and smoother Ni 81 Fe 19 on buried fibrous topographies. As for the sensitivity and reproducibility of the sensor signal, we obtained a maximum AMR peak of 0 . 4 % , min-max sensitivity range of [ 0 . 17 , 0 . 26 ] % , average asymmetry of peak location of 2 . 7 kA m within two consecutive magnetic loading cycles, and a deviation of 250–850 A m of peak location across several anisotropy angles at a base resistance of ∼100 Ω . Last, we demonstrated the usability of the sensor in two educational application examples: a textbook clicker and interactive braille flashcards.
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Ježek, J., and F. Hrouda. "Software for modeling the magnetic anisotropy of strained rocks." Computers & Geosciences 28, no. 9 (November 2002): 1061–68. http://dx.doi.org/10.1016/s0098-3004(02)00023-7.

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Rogovoy, Anatoli A., and Olga S. Stolbova. "Microstructural Modeling of the Magnetization Process in Ni2MnGa Alloy Polytwin Crystals." Magnetochemistry 8, no. 8 (July 25, 2022): 78. http://dx.doi.org/10.3390/magnetochemistry8080078.

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In this article, based on the theory of micromagnetism, a microstructural model of the behavior of the Heusler alloy in a magnetic field is constructed. The dynamics of the magnetic process is described by the Landau–Lifshitz–Gilbert equation. Using the Galerkin procedure, variational equations corresponding to the differential relations of the magnetic problem are written out. For numerical simulation, we consider the problem of magnetization of a Ni2MnGa alloy polytwin crystals, each grain of which is a twinned variant of martensite and has pronounced anisotropic properties. First, we consider the process of magnetization of a single grain, when an external magnetic field is applied at different angles to the anisotropy axes of twinned variants, and then, based on the results obtained, we plot magnetization curves for various (isotropic and texture-oriented) polycrystalline samples. This paper does not consider the process of detwinning, which can occur in such a material during the magnetization at a sufficiently high external field strength.
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Xiao, Xiao, Fabian Müller, Martin Marco Nell, and Kay Hameyer. "Modeling anisotropic magnetic hysteresis properties with vector stop model by using finite element method." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 41, no. 2 (December 2, 2021): 752–63. http://dx.doi.org/10.1108/compel-06-2021-0213.

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Purpose This paper aims to use a history-dependent vector stop hysteresis model incorporated into a two dimensional finite elements (FE) simulation environment to solve the magnetic field problems in electrical machines. The vector stop hysteresis model is valid for representing the anisotropic magnetization characteristics of electrical steel sheets. Comparisons of the simulated results with measurements show that the model is well appropriate for the simulation of electrical machines with alternating, rotating and harmonic magnetic flux densities. Design/methodology/approach The anisotropy of the permeability of an electrical steel sheet can be represented by integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model. The parameters of the vector stop hysteresis model were identified by minimizing the errors between the simulated results and measurements. In this paper, a damped Newton method is applied to solve the nonlinear problem, which ensures a robust convergence of the finite elements simulation with vector stop hysteresis model. Findings Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows the importance to consider the anisotropic and saturation behavior of the material. Comparing the calculated and measured data corroborates the hypothesis that the presented energy-based vector stop hysteresis model is able to represent these magnetic properties appropriately. To ensure a unique way of hysteresis loops during finite elements simulation, the memory of the vector stop hysteresis model from last time step is kept unchanged during the Newton iterations. Originality/value The results of this work demonstrates that the presented vector hysteresis stop model allows simulation of vector hysteresis effects of electrical steel sheets in electrical machines with a limited amount of measurements. The essential properties of the electrical steel sheets, such as phase shifts, the anisotropy of magnetizations and the magnetization characteristics by alternating, rotating, harmonic magnetization types, can be accurately represented.
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Liu, Yikuo, Anton Ziolkowski, and Paul L. Stoffa. "Time evolution of the electric field using the rapid expansion method with pseudospectral evaluation of spatial derivatives — Part 2: Inclusion of anisotropy and the earth-air interface." GEOPHYSICS 84, no. 5 (September 1, 2019): E323—E335. http://dx.doi.org/10.1190/geo2018-0143.1.

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We have evaluated an extension of the 3D 3C rapid-expansion method for time-domain electromagnetic modeling with pseudospectral evaluation of spatial derivatives that includes anisotropic conductivity and the earth-air interface. We found that transverse isotropic anisotropy can be included in the modeling with the manipulation of the conductivity tensor. We model the response of the earth-air interface by using the upward continuation of the time derivative of the magnetic induction. All three electric field components are collocated with the electric conductivities and are modeled independently and simultaneously with spectral accuracy in space and time. Numerical tests against the analytical solution for a half-space and spectral methods for 1D anisotropic layered earth models demonstrate the excellent accuracy of this approach.
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Zhao, Yang, and H. Neal Bertram. "Micromagnetic modeling of magnetic anisotropy in textured thin‐film media." Journal of Applied Physics 77, no. 12 (June 15, 1995): 6411–15. http://dx.doi.org/10.1063/1.359114.

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Zhang, Yue, Weisheng Zhao, Yahya Lakys, Jacques-Olivier Klein, Joo-Von Kim, Dafiné Ravelosona, and Claude Chappert. "Compact Modeling of Perpendicular-Anisotropy CoFeB/MgO Magnetic Tunnel Junctions." IEEE Transactions on Electron Devices 59, no. 3 (March 2012): 819–26. http://dx.doi.org/10.1109/ted.2011.2178416.

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Dissertations / Theses on the topic "Modeling Magnetic Anisotropy"

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Seaux, Gage E. "Analog Modeling of Anisotropy of Magnetic Susceptibility as Affected by Pure Shear Strain on Original Magnetic Fabrics of Sedimentary Rocks." Thesis, University of Louisiana at Lafayette, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10683064.

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Analysis of the anisotropy of magnetic susceptibility (AMS) is an easy, non-destructive method to determine the preferred orientations of minerals in rocks and rock analogs. The orientations of the principal susceptibility axes (Kmax≥Kint≥Kmin) of the AMS ellipsoid are generally parallel to the principal axes of the strain ellipsoid (X≥Y≥Z). The orientations of the AMS axes as well as the magnitudes change in response to strain, though a generally accepted correlation between the magnitudes of the principal axes of AMS and strain has not yet been established. A successful correlation of the magnitudes of the principal susceptibility axes of AMS and strain would allow an easy and non-destructive method of quantitative strain analysis. This would also allow quantitative strain analyses of rocks where traditional methods using strain markers fail. In this study, the quantitative aspect of the relationship between strain and AMS is investigated experimentally using artificial mineral mixtures with a sedimentary initial magnetic fabric in an attempt to correlate strain to AMS. Mineral mixtures of magnetite, biotite, and specular hematite with a matrix of Art Time Dough® (similar to Playdoh®) were mixed separately. To create a random magnetic fabric, the samples were kneaded by hand for approximately 15 minutes. The samples were then strained to 70% strain in one direction to create a sedimentary initial magnetic fabric. The orientation of this strain became the Z axis of the strain ellipsoid. The samples were then strained perpendicular to this axis incrementally from 0% to 40% strain in 5% increments, with the AMS measured at each interval. The orientation of this strain became the Y axis of the strain ellipsoid. The data from these experiments resulted in the quantitative correlation of strain and AMS for the magnetite mineral mixtures. The biotite and specular hematite mixtures contain enough magnetite inclusions and magnetite conversion respectively to dominate the AMS. This creates a more complex relationship that is not easily correlated quantitatively to strain. The experiments demonstrate that a strong qualitative relationship exists between both the orientations and the magnitudes of the axes of the strain and AMS ellipsoids.

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Fard, Samad Moemen Bellah. "Modelling anisotropy in electrotechnical steels." Thesis, Cardiff University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263551.

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Pera, Thierry. "Lois d'aimantation anisotropes et non linéaires : modélisation et validation expérimentale." Grenoble INPG, 1994. http://www.theses.fr/1994INPG0038.

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Le but de notre étude est de prendre en compte le comportement bidimensionnel non linéaire et anisotrope des tôles magnétiques, utilisées en génie électrique, afin de pouvoir effectuer une modélisation par éléments finis aussi réaliste que possible. Nous avons développé un modèle original de loi de comportement de tôles magnétiques (à grains orientés, à grains non orientés, à texture cubique) fondé sur l'équivalence entre la relation vectorielle B(H) et une représentation magnétique 11. Les données expérimentales nécessaires sont les courbes B(H) suivant la direction de laminage (axe x) et striant la direction travers qui lui est orthogonale (axe y). Le comportement magnétique des tôles est pris en compte par une représentation adéquate des lignes isovaleurs de coénergie dans le plan HxHy. La relation B(H) est ensuite restituée à partir de la densité de coénergie. Une vérification expérimentale du modèle a été effectuée grâce à un cadre en champs tournants. Nous avons implanté le modèle dans un logiciel éléments finis avec une formulation en potentiel scalaire. Des exemples d'application ont été traités (alternateur et transformateur)
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Seleznyova, Kira. "Magnetic properties and magnetic resonances of single crystals based on iron borate : Experimental studies and modelling." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0398/document.

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La thèse porte sur la synthèse et l'étude des propriétés magnétiques de borates de fer-gallium,FexGa1-xBO3 avec 0 supérieur ou égal à x supérieur ou égal à 1. Ces matériaux sont prometteurs pour les applications; en plus, grâce à la présence, en fonction de x, de différents types d’ordre magnétique, ils sont bien adaptés au traitement de nombreux problèmes du magnétisme des solides.Le borate de fer, FeBO3 est un antiferromagnétique possédant un plan de facile aimantation et un faible ferromagnétisme. Les caractéristiques du borate de fer sont radicalement modifiées par substitution isomorphe fer – gallium diamagnétique.Nous avons mis au point une route de synthèse de monocristaux FexGa1-xBO3 de haute qualité. Comme principales techniques expérimentales, nous avons choisi les résonances magnétiques électronique (RME) et nucléaire (RMN). Selon le contenu du fer, nous avons observé:(i) la résonance antiferromagnétique, (ii) la résonance de clusters magnétiques et (iii) la résonance paramagnétique électronique (RPE). Les différents états magnétiques ont été identifiés et leurs caractéristiques – la température de Néel, le champ de Dzyaloshinskii-Moriya; les paramètres de l’hamiltonien de spin de Fe3+, etc.– ont été déterminées. La coordinence et la symétrie de sites de 11B et 71Ga ont été précisées par RMN à rotation sous l’angle « magique » (MAS). Moyennant la simulation des spectres de RPE et de MAS RMN, à l’aide de codes mis au point ad hoc, les distributions de paramètres dues au désordre local ont été déterminées. L’analyse théorique, tenant compte de contributions du champ cristallin et de l’interaction dipôle-dipôle, permet d’expliquer l’anisotropie magnétocristalline de volume et de surface
The thesis is concerned with synthesis and studying magnetic properties of iron-galliumborates, FexGa1-xBO3 with [0 supérieur ou égal à x supérieur ou égal à 1]. These materials are promising candidates for applications;besides, occurrence of different types of magnetic ordering, depending on x, makes them suitablefor treating a number of fundamental problems in solid state magnetism.Iron borate, FeBO3 is a two-sublattice easy-plane antiferromagnet with weakferromagnetism. Physical characteristics of iron borate are radically modified by isomorphoussubstitution of a part of iron by diamagnetic gallium.We have started with developing a synthesis route for growing high-quality FexGa1-xBO3single crystals. As main experimental techniques, we have chosen Electron and Nuclear MagneticResonances (EMR, NMR). Depending on iron contents and temperature, we have observed:(i) Antiferromagnetic, (ii) Cluster Magnetic and (iii) Electron Paramagnetic Resonance (EPR).Different magnetic states have been identified and their characteristics: Néel temperature,Dzyaloshinskii-Moriya field; spin Hamiltonian parameters of isolated Fe3+ ion, etc., have beendetermined. Coordination and site symmetry of 11B and 71Ga nuclei have been specified by meansof Magic Angle Spininng (MAS) NMR. Carrying out computer simulations of EPR and MASNMR spectra with laboratory-developed codes, the parameter distributions caused by localdisorder have been determined. Theoretical analysis taking into account crystal field and dipoledipolecontributions allow interpreting volume and surface magnetocrystalline anisotropy of thecrystals
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Kergaravat, Charlie. "Dynamique de formation et de déformation de minibassins en contexte compressif : exemple du bassin de Sivas, Turquie Approche terrain et implications structurales multiéchelles." Thesis, Pau, 2016. http://www.theses.fr/2016PAUU3005/document.

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Cette thèse porte sur les interactions entre les déformations halocinétiques locales au sein des mini-bassins salifères et les déformations régionales compressives. L’étude s’appuie sur une analyse structurale multi-échelle détaillée d’une province à mini-bassins se développant dans le bassin d’avant pays de Sivas (Turquie). Une analyse de terrain approfondie, associée à une étude de données de subsurface, permet de proposer une révision des cartes géologiques ainsi qu’une évolution tectonosédimentaire identifiant les déformations liées à la tectonique salifère et celles liées à la propagation de la ceinture de plis et de chevauchements dans l’avant-pays. A partir de l’Eocène supérieur, le fluage del’évaporite autochtone, initié et entretenu par le chargement sédimentaire différentiel ainsi que par la déformation compressive, permet la formation d’une première génération de mini-bassins. Ces minibassins, constitués par une formation continentale Oligocène, vont être recouverts par une nappe d’évaporite allochtone accueillant une seconde génération de mini-bassins constitués de formations continentales et marines Oligo-Miocène. L’initiation du domaine de mini-bassins secondaires est caractérisée par une distribution polygonale du réseau de diapirs et de murs d’évaporites. Ces mini-bassins enregistrent localement les effets de la tectonique salifère par le développement d’une grande variété de structures halocinétiques à différentes échelles telles que les séquences halocinétiques unitaires (crochet et éventail), séquences composites (tabulaire ou fuseau) et megaflaps. Une série de modélisation analogique préliminaire amontré que ces structures peuvent se développer avec ou sans l’application d’une compression aux limites. De plus, les analogies géométriques entre les mini-bassins de Sivas et les provinces salifères connues suggèrent que la dynamique de formation de ces mini-bassins est au premier ordre contrôlée par le chargement sédimentaire différentiel, découplé partiellement de la compression régionale. Néanmoins, l’analyse du réseau de fractures et de l’endommagement matriciel souligne l’enregistrement précoce de la déformation compressive régionale lors de l’initiation des mini-bassins.L’influence du raccourcissement sur la structuration de la province à mini-bassins s’exprime de manière croissante par l’écrasement des corps salifères permettant : (i) le développement de dépocentres linéaires préférentiellement perpendiculaire à la direction de raccourcissement, (ii) l’émergence de corps allochtones d’évaporites en surface, ainsi que (iii) la rotation et translation des mini-bassins. Cette province à mini-bassins génère une discontinuité dans la propagation et l’accommodation de la déformation compressive : la déformation compressive est accommodée auniveau du réseau polygonal de murs d’évaporites formant des structures multidirectionnelles. De plus, cette concentration de la déformation par écrasement des structures salifères entraine la remobilisation des évaporites vers l’avant-pays générant alors un nouveau système salifère
This doctoral work studies the interaction between withdrawal of minibasins and regional shortening during evolution of a foreland fold-and-thrust belt. This is achieved by a multiscale structural analysis of the Sivas Basin (Turkey). Extensive field work and regional seismic lines interpretations helped to build a new and detailed geologic map of the central Sivas Basin and to provide a new tectonosedimentary framework highlighting the influence of salt tectonics and the regional shortening, starting in the Late Eocene by the autochthonous evaporite deposition. This level is remobilized by the northward migrating sedimentary load, shortening and tilting of the basin southern margin during propagation of the foreland fold-and-thrust belt. Evaporite flow is recorded by the withdrawal of a primary generation of continental Oligocene minibasins which are then covered by an evaporite canopy. The canopy extending northward allows the development of second generation of continental to shallow marine mini-basins from Oligocene to Middle Miocene. Secondary minibasins initiation in the central part of the Basin, is characterized by sub-circular minibasins surrounded by polygonal diapirs and walls. Flanking these minibasins, a large variety of halokinetic structures is described: halokinetic sequences (hooks and wedges), composite halokinetic sequences and megaflaps. Preliminary sand-box modeling study suggests the development of thesehalokinetic structures both with and without shortening. Furthermore, minibasins geometries are closely similar to those imaged or mapped in other salt provinces suggesting that mini-basin withdrew is first control by sedimentary load, probably due to decoupling by the salt. However, the fractures and anisotropy of magnetic susceptibility analyses suggests the record of shortening since the minibasins initiation. The increase influence of regional shortening on the minibasins domain is expressed by salt walls and diapirs squeezing inducing: (i) the development of linear mini-basins perpendicular to the shortening direction, (ii) salt sheet emplacement and (iii) the translation/rotation of minibasins. The minibasins province produces a discontinuity for the fold-and-thrust belt propagation. Indeed, the minibasins province accommodates the shortening deformation along the polygonal network of salt walls and diapirs forming multidirectional structures. Furthermore, the regional shortening accommodation by salt structures squeezing produce an evaporitic remobilization and migration of a salt canopy toward the foreland basin
Bu doktora tezi/çalışması, bir önülke kıvrım ve bindirme kuşağının evrimi sırasında minihavzaların çekilmesi ve bölgesel kısalma arasındaki etkileşimi konu edinir. Çoklu ölçekteki bu yapısal analiz Sivas Havzası (Türkiye) ölçeğinde gerçekleştirilmiştir. Kapsamlı saha çalışması ve bölgesel olarak sismik kesitlerden ortaya çıkarılan yorumlamalar, Sivas Havzası’nın orta kesiminde detaylı bir jeolojik haritalama yapımına yardımcı olmuş ve otokton evaporit depolanmasının başladığı Geç Eosen’den başlayarak havza için tuz tektoniği ve bölgesel kısalmanın etkisindeki yeni bir tektono-sedimanter çatının ortaya çıkarılmasına neden olmuştur. Söz konusu seviye, önülke kıvrım ve bindirme kuşağının ilerlemesisüresince kuzeye doğru sedimanter dolgunun göçüyle birlikte havzanın güney kenarında kısalıma uğrayarak ve eğim kazanarak remobilize olmuştur. Evaporit akışı, kıtasal Oligosen minihavzalarının ilksel olarak oluşumundan sonra çekilmesine bağlı olarak gözlenmiş ve sonrasında evaporit yaygılarıyla örtülmüştür. Kuzeye kadar uzanan bu yaygı, Oligosen-Orta Miyosen arasında kıtasaldan sonra sığ denizel tipteki ikincil minihavzaların gelişimine de neden olmuştur.Havzanın orta kesimindeki ikincil minihavza başlangıcı, poligonal diyapir ve duvarlar tarafından çevrelenen dairesel minihavzalarla karakterize olur. Bu minihavzaların kanatlarında halokinetik yapılar tanımlanmıştır. Kanca (hook) ve kama (wedge) tiplerde olmak üzere halokinetik seriler, kompozit halokinetik seriler ve megaflaplar bu yapılar arasında sayılabilir. Çalışmanın başlangıcında yapılan kum kutusu model deneyi, bu halokinetik yapıların kısalmayla veya kısalma olmaksızın geliştiğini göstermiştir. Buna ek olarak minihavzaların geometrisi, muhtemelen tuzun ayrışmasından dolayı tortul yükün ilkkontrolünden dolayı çekilen diğer tuz bölgelerinde önerilen haritalanmış minihavzalara benzerdir. Bununla birlikte kırık ve manyetik suseptibilite analizleri, minihavzaların başlangıcından itibaren kısalmanın kayıt edilebilmesi hakkında fikir vermektedir. Minihavza bölgelerindeki bölgesel kısalımın artışı, tuz duvarları ve diyapirlerin sıkışmasıyla birlikte(i) kısalma yönüne dik durumdaki çizgisel minihavzaların gelişimi, (ii) tuz örtülerinin yerleşimi ve (iii) minihavzaların yer değiştirmesi veya dönmesiyle açıklanır. Minihavzalar bölgesi, kıvrım ve bindirme kuşağının gelişimi için bir süreksizlik üretir. Aslında, minihavzalar birçok yönde yapılar oluşturarak tuz duvarları ve diyapirlerin polygonal şekildeki yerleşimi boyunca kısalma deformasyonuna eşlik eder. Üstelik, tuz yapılarının eşlik ettiği bölgesel kısalma önülke havzalarına doğru evaporitik bir göçe de neden olmaktadır
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Ferré, Giménez Ricardo. "Etude de nanoparticules magnétiques par simulation numérique." Université Joseph Fourier (Grenoble), 1995. http://www.theses.fr/1995GRE10224.

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Nous avons etudie par simulation numerique les proprietes magnetiques d'une petite particule magnetique aussi bien que les proprietes d'un ensemble de telles particules. Dans la premiere partie de ce travail, un modele de petites particules est developpe. Ce modele, base sur les equations micromagnetiques, tient compte des interactions d'echange et dipolaire entre les moments magnetiques dans la particule aussi bien que de l'anisotropie magnetocristalline. Ce modele nous a permis d'etudier les configurations d'aimantation a l'equilibre pour des petites particules magnetiques. Nous avons aussi etudie plus en detail le retournement d'aimantation d'une particule isolee de ferrite de baryum d eforme aplatie. La deuxieme partie de ce travail est dediee a la modelisation d'un ensemble de petites particules en interaction dipolaire. Nous avons mis en evidence l'effet cruciale de la concentration de particules sur les proprietes magnetiques d'un tel agregat. Nous montrons que l'effet de l'augmentation de la concentration combine avec l'anisotropie de l'interaction dipolaire conduit a l'apparition d'une valeur maximale du champ coercitif pour les concentrations intermediaires. Nous avons aussi considere un terme d'anisotropie magnetique qui a comme effet la reduction de la portee des interactions dipolaires. La derniere partie de ce travail est dediee a une etude en temperature (monte carlo) de ces systemes de particules. Une transition de gel dynamique est observee comme a resultat de l'evaluation du parametre d'ordre d'edwards anderson pour notre modele ainsi que nombreux etats metastables sont possibles a basse temperature. Ces signatures, neanmoins, ne nous permettent pas d'affirmer l'existence d'une transition du type verre de spins
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Wei, Wei. "Characteristics of the late Mesozoic tectonic evolution of the South China block and geodynamic implications : Multi-approach study on the Qingyang-Jiuhua, Hengshan and Fujian coastal granitic massifs." Phd thesis, Université d'Orléans, 2013. http://tel.archives-ouvertes.fr/tel-01058791.

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The vast distribution and long duration of the Late Mesozoic magmatism in the eastern part of South China presents a unique case in the world. This offers a natural laboratory to study the process of magma genesis, the magma emplacement mode, the relationship between magmatism and tectonics, the geodynamic role on the magma emplacement and lithospheric evolution. Since 50's, particularly 90's of the last century, geoscientists have made important efforts in geological cartography and carried out numerous studies with remarkable scientific achievements, building a solid background to understand the tectonic evolution of the South China Block (SCB). However, certain fundamental questions mentioned above remain unsolved and/or are in hot debate. In order to make progress in these scientific issues, we have carried out in a multi-disciplinary study in the Late Mesozoic Qingyang-Jiuhua massif, Hengshan massif and Fujian coastal zone according to their distance with respect to the paleo subduction zone of the Paleo-Pacific plate, the ages of granitic massifs and related tectonics, including field observation on the structure geology, micro-observation on thin section, U-Pb dating on monazite, AMS, paleomagnetism, gravity modeling and P condition concern the granite emplacement. In the view of deformation in these granitic massifs and their country rocks, mode and influence of regional tectonics on the emplacement, though each studied zone reveals its distinguished characteristics, they show some intrinsic and common relationships between them. With our new results and integrating previous data, in this thesis, we discuss the tectonic context of emplacement of these Late Mesozoic magmatic massifs and the geodynamic evolution of the SCB., We propose a 3-step geodynamic model: (1) during 145-130 Ma period, the Paleo-Pacific plate subducted northwestwardly, the West Philippines micro-continent, approaching to SCB, important subduction-related arc volcanism was produced in the coastal areas of Southeast China coast (Zhejiang-Fujian-Guangdong), forming a back-arc extension tectonic system in SCB; (2) during 130-110 Ma period, due to the collision between the West Philippines microcontinent and SCB, the compressional tectonic structures were developed in the Changle-Na'ao coastal zone, producing ductile deformation zones. However, the inland of the eastern part of SCB was under a NW-SE extensional tectonic regime; (3) during 105-90 Ma period, a new subduction zone was developed in the SE flank of the West Philippines micro-continent, the subducting slab reached the Changle-Nan'ao tectonic belt, with the possible break-off of slab, the asthenospheric ascent was responsible for the important emplacement of plutonic massifs and dykes. The tectonics of the eastern part of SCB was characterized by a general extensional system in this period. This tectonic pattern has been significantly disturbed by the Oligocene-Eocene opening of the South China sea,and the Miocene shortening of the SCB margin in Taiwan. Of course, this model should be improved by more geological, geophysical and geochemical investigations.
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Wang, Lihui. "Modélisation et simulation de l’IRM de diffusion des fibres myocardiques." Thesis, Lyon, INSA, 2013. http://www.theses.fr/2013ISAL0004/document.

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L’imagerie par résonance magnétique de diffusion (l’IRMd) est actuellement la seule technique non-invasive pour étudier l’architecture tridimensionnelle des fibres myocardiques du cœur humain à la fois ex vivo et in vivo. Cependant, il est difficile de savoir comment les caractéristiques de diffusion calculées à partir des images de diffusion reflètent les propriétés des microstructures du myocarde à cause de l’absence de la vérité-terrain sans parler de l’influence de divers facteurs tels que la résolution spatiale, le bruit et les artéfacts. L'objectif principal de cette thèse est donc de développer des simulateurs de l’IRM de diffusion basés sur des modèles réalistes afin de simuler, en intégrant différentes modalités d'imagerie, les images pondérées en diffusion des fibres myocardiques à la fois ex vivo et in vivo, et de proposer un outil générique permettant d’évaluer la qualité de l’imagerie et les algorithmes de traitement d’images. Pour atteindre cet objectif, le présent travail se focalise sur quatre parties principales. La première partie concerne la formulation de la théorie de simulation IRMd pour la génération d’images de diffusion et pour les applications sur les modèles simples de fibres cardiaques chez l’homme, et essaie de comprendre la relation sous-jacente entre les propriétés mesurées de la diffusion et les caractéristiques à la fois physiques et structurelles des fibres cardiaques. La seconde partie porte sur la simulation des images de résonance magnétique de diffusion à différentes échelles en s’appuyant sur des données du cœur humain issues de l'imagerie par lumière polarisée. En comparant les propriétés de diffusion à différentes échelles, la relation entre la variation de la microstructure et les propriétés de diffusion observée à l'échelle macroscopique est étudiée. La troisième partie consacre à l’analyse de l'influence des paramètres d'imagerie sur les propriétés de diffusion en utilisant une théorie de simulation améliorée. La dernière partie a pour objectif de modéliser la structure des fibres cardiaques in vivo et de simuler les images de diffusion correspondantes en combinant la structure des fibres cardiaques et le mouvement cardiaque connu a priori. Les simulateurs proposés nous fournissent un outil générique pour générer des images de diffusion simulées qui peuvent être utilisées pour évaluer les algorithmes de traitement d’images, pour optimiser le choix des paramètres d’IRM pour les fibres cardiaque aussi bien ex vivo que in vivo, et pour étudier la relation entre la structure de fibres microscopique et les propriétés de diffusion macroscopiques
Diffusion magnetic resonance imaging (dMRI) appears currently as the unique imaging modality to investigate noninvasively both ex vivo and in vivo three-dimensional fiber architectures of the human heart. However, it is difficult to know how well the diffusion characteristics calculated from diffusion images reflect the microstructure properties of the myocardium since there is no ground-truth information available and add to that the influence of various factors such as spatial resolution, noise and artifacts, etc. The main objective of this thesis is then to develop realistic model-based dMRI simulators to simulate diffusion-weighted images for both ex vivo and in vivo cardiac fibers by integrating different imaging modalities, and propose a generic tool for the evaluation of imaging quality and image processing algorithms. To achieve this, the present work focuses on four parts. The first part concerns the formulation of basic dMRI simulation theory for diffusion image generation and subsequent applications on simple cardiac fiber models, and tries to elucidate the underlying relationship between the measured diffusion anisotropic properties and the cardiac fiber characteristics, including both physical and structural ones. The second part addresses the simulation of diffusion magnetic resonance images at multiple scales based on the polarized light imaging data of the human heart. Through both qualitative and quantitative comparison between diffusion properties at different simulation scales, the relationship between the microstructure variation and the diffusion properties observed at macroscopic scales is investigated. The third part deals with studying the influence of imaging parameters on diffusion image properties by means of the improved simulation theory. The last part puts the emphasis on the modeling of in vivo cardiac fiber structures and the simulation of the corresponding diffusion images by combining the cardiac fiber structure and the a priori known heart motion. The proposed simulators provide us a generic tool for generating the simulated diffusion images that can be used for evaluating image processing algorithms, optimizing the choice of MRI parameters in both ex vivo and in vivo cardiac fiber imaging, and investigating the relationship between microscopic fiber structure and macroscopic diffusion properties
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Haldar, Sumit. "Modeling Magnetic Anisotropy in Single Chain Magnets." Thesis, 2020. https://etd.iisc.ac.in/handle/2005/4736.

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This thesis embodies work on modeling magnetic anisotropy in molecular magnets. Understanding the factors that govern the magnitude of anisotropy in these materials is crucial for tailoring molecules that can be used in magnetic devices. In chapter 1, we briefly discussed magnetism and magnetic materials, and in chapter 2, we have discussed the model Hamiltonian we have employed in our work. In chapter 3, we have studied the effect of on-site anisotropy on magnetic anisotropy, $D_M$. In principle, for strong anisotropy, we cannot define the molecular anisotropy parameters $D_M$ and $E_M$, which correspond to the axial and rhombic zero-field splitting parameters, respectively. However, the giant spin of the low-lying large $M_S$ states is very nearly an integer, and using this spin value; it is possible to construct an effective spin Hamiltonian and compute $D_M$ and $E_M$. We have also studied the effect of finite size, rotations of site anisotropies, and chain dimerization on the effective anisotropy of the spin chains. In chapter 4, we have studied the effect of exchange anisotropy as well as on-site anisotropy on molecular anisotropy, $D_M$. We find that the axial anisotropy parameter, $D_M$ is the sum of the individual contributions due to exchange and on-site anisotropies. We have also studied magnetic susceptibility, specific heat as a function of temperature, and magnetization as a function of the applied field. One of the possible applications of molecular magnets is in the area of the magnetocaloric effect. In chapter 5, we have studied two different spin models (i) spin chains with alternating ferro and antiferromagnetic interactions, and (ii) with an additional next nearest neighbor ferromagnetic interaction using both exact diagonalizations as well as the Monte Carlo technique. We have computed the magnetic Grüneisen parameter $(Γ_H )$, which is closely related to the magnetocaloric effect, for different parameters such as on-site anisotropy, exchange anisotropy as well as spin-dipolar interaction strength. We also show the dependence of $Γ_H$ on the dimensionality of the lattice for a fixed lattice constant. Modeling blocking temperature in molecular magnets has been a long-standing problem in the field of molecular magnetism. In chapter 6, we have studied the relaxation of magnetization on an assembly of 100,000 spin chains using an innovative rejection free kinetic Monte Carlo technique. We study this for different exchange anisotropy, on-site anisotropy, and strength of dipolar interactions. The magnetization relaxation times show non-Arrhenius behavior for weak on-site interactions. The energy barrier to magnetization relaxation increases with the increase in on-site anisotropy, strength of spin dipolar interactions, and exchange anisotropy. However, in all these cases, the barrier saturates at large on-site anisotropy. These studies throw light on why single ion rare-earth magnets have high blocking temperatures.
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Dibb, Russell. "Probing Tissue Microstructure Using Susceptibility Contrast Magnetic Resonance Imaging." Diss., 2016. http://hdl.handle.net/10161/12158.

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Magnetic resonance imaging is a research and clinical tool that has been applied in a wide variety of sciences. One area of magnetic resonance imaging that has exhibited terrific promise and growth in the past decade is magnetic susceptibility imaging. Imaging tissue susceptibility provides insight into the microstructural organization and chemical properties of biological tissues, but this image contrast is not well understood. The purpose of this work is to develop effective approaches to image, assess, and model the mechanisms that generate both isotropic and anisotropic magnetic susceptibility contrast in biological tissues, including myocardium and central nervous system white matter.

This document contains the first report of MRI-measured susceptibility anisotropy in myocardium. Intact mouse heart specimens were scanned using MRI at 9.4 T to ascertain both the magnetic susceptibility and myofiber orientation of the tissue. The susceptibility anisotropy of myocardium was observed and measured by relating the apparent tissue susceptibility as a function of the myofiber angle with respect to the applied magnetic field. A multi-filament model of myocardial tissue revealed that the diamagnetically anisotropy α-helix peptide bonds in myofilament proteins are capable of producing bulk susceptibility anisotropy on a scale measurable by MRI, and are potentially the chief sources of the experimentally observed anisotropy.

The growing use of paramagnetic contrast agents in magnetic susceptibility imaging motivated a series of investigations regarding the effect of these exogenous agents on susceptibility imaging in the brain, heart, and kidney. In each of these organs, gadolinium increases susceptibility contrast and anisotropy, though the enhancements depend on the tissue type, compartmentalization of contrast agent, and complex multi-pool relaxation. In the brain, the introduction of paramagnetic contrast agents actually makes white matter tissue regions appear more diamagnetic relative to the reference susceptibility. Gadolinium-enhanced MRI yields tensor-valued susceptibility images with eigenvectors that more accurately reflect the underlying tissue orientation.

Despite the boost gadolinium provides, tensor-valued susceptibility image reconstruction is prone to image artifacts. A novel algorithm was developed to mitigate these artifacts by incorporating orientation-dependent tissue relaxation information into susceptibility tensor estimation. The technique was verified using a numerical phantom simulation, and improves susceptibility-based tractography in the brain, kidney, and heart. This work represents the first successful application of susceptibility-based tractography to a whole, intact heart.

The knowledge and tools developed throughout the course of this research were then applied to studying mouse models of Alzheimer’s disease in vivo, and studying hypertrophic human myocardium specimens ex vivo. Though a preliminary study using contrast-enhanced quantitative susceptibility mapping has revealed diamagnetic amyloid plaques associated with Alzheimer’s disease in the mouse brain ex vivo, non-contrast susceptibility imaging was unable to precisely identify these plaques in vivo. Susceptibility tensor imaging of human myocardium specimens at 9.4 T shows that susceptibility anisotropy is larger and mean susceptibility is more diamagnetic in hypertrophic tissue than in normal tissue. These findings support the hypothesis that myofilament proteins are a source of susceptibility contrast and anisotropy in myocardium. This collection of preclinical studies provides new tools and context for analyzing tissue structure, chemistry, and health in a variety of organs throughout the body.


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Book chapters on the topic "Modeling Magnetic Anisotropy"

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Bihlmayer, Gustav. "Density Functional Theory for Magnetism and Magnetic Anisotropy." In Handbook of Materials Modeling, 895–917. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-319-44677-6_73.

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Bihlmayer, Gustav. "Density Functional Theory for Magnetism and Magnetic Anisotropy." In Handbook of Materials Modeling, 1–23. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-42913-7_73-1.

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Křížek, Michal, and Pekka Neittaanmäki. "Nonlinear anisotropic heat conduction in a transformer magnetic core." In Mathematical Modelling: Theory and Applications, 162–96. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8672-6_9.

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Miller, Renee, Haodan Jiang, Ria Mazumder, Brett R. Cowan, Martyn P. Nash, Arunark Kolipaka, and Alistair A. Young. "Determining Anisotropic Myocardial Stiffness from Magnetic Resonance Elastography: A Simulation Study." In Functional Imaging and Modeling of the Heart, 346–54. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20309-6_40.

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Riel, Stefanie, Mohammad Bashiri, Werner Hemmert, and Siwei Bai. "Computational Models of Brain Stimulation with Tractography Analysis." In Brain and Human Body Modeling 2020, 101–17. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45623-8_6.

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AbstractComputational human head models have been used in studies of brain stimulation. These models have been able to provide useful information that can’t be acquired or difficult to acquire from experimental or imaging studies. However, most of these models are purely volume conductor models that overlooked the electric excitability of axons in the white matter of the brain. We hereby combined a finite element (FE) model of electroconvulsive therapy (ECT) with a whole-brain tractography analysis as well as the cable theory of neuronal excitation. We have reconstructed a whole-brain tractogram with 2000 neural fibres from diffusion-weighted magnetic resonance scans and extracted the information on electrical potential from the FE ECT model of the same head. Two different electrode placements and three different white matter conductivity settings were simulated and compared. We calculated the electric field and second spatial derivatives of the electrical potential along the fibre direction, which describes the activating function for homogenous axons, and investigated sensitive regions of white matter activation. Models with anisotropic white matter conductivity yielded the most distinctive electric field and activating function distribution. Activation was most likely to appear in regions between the electrodes where the electric potential gradient is most pronounced.
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Aghadavoudi Jolfaei, Mohsen, Jun Liu, Frenk van den Berg, and Claire Davis. "Measurement and Modelling Magnetic Anisotropy due to Crystallographic Texture in Interstitial Free (IF) Steels." In Electromagnetic Non-Destructive Evaluation (XXIV). IOS Press, 2023. http://dx.doi.org/10.3233/saem230004.

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A set of IF steel specimens, at different states of recrystallisation (commercially cold rolled and annealed to give partially recrystallised and fully recrystallised microstructures) and accordingly different texture components have been used to investigate the measurement and prediction of magnetic anisotropy. A finite element microstructure model that considers crystallographic texture has been used for the prediction of magnetic anisotropy to compare to the measured values, with comparable anisotropy being observed. The results show that the proposed deployable non-destructive approach (U-shaped electromagnetic sensor that can be placed onto a sheet sample) is promising for the quick evaluation of the magnetic anisotropy in IF steels.
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Conference papers on the topic "Modeling Magnetic Anisotropy"

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Teixeira, B., A. Timopheev, N. Caçoilo, S. Auffret, R. Sousa, B. Dieny, L. Cuchet, et al. "ION BEAM MODIFICATION OF MAGNETIC TUNNEL JUNCTIONS." In Mathematical modeling in materials science of electronic component. LLC MAKS Press, 2020. http://dx.doi.org/10.29003/m1517.mmmsec-2020/54-55.

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In this work, the effect of bombardment with high-energy ions on the parameters of magnetic tunnel junctions based on CoFeB / MgO, such as magnetic anisotropy, magnetoresistance, and the damping coefficient of magnetization precession, is investigated. The modeling of the ferromagnetic resonance spectra was carried out within the framework of the Smit-Beljers and Landau-Lifshitz-Gilbert formalisms. The ion fluence limit is established, below which a controlled modulation of the magnetic anisotropy is achieved while maintaining a high tunneling magnetoresistance and stable magnetic configuration of the transition
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Tauki, Md Sadik Yasir, and Orchi Hassan. "Modeling Second Order Anisotropy of Monodomain Magnetic Body." In 2022 12th International Conference on Electrical and Computer Engineering (ICECE). IEEE, 2022. http://dx.doi.org/10.1109/icece57408.2022.10088553.

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Haji-Sheikh, M., Y. z. Yoo, O. Chmaissem, S. Kolesnik, and A. Ullah. "Modeling of Magnetic Anisotropy of SrRuO3 Thin Films Using Tensors." In 2006 SICE-ICASE International Joint Conference. IEEE, 2006. http://dx.doi.org/10.1109/sice.2006.315466.

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Wang, Manman, and Yanfeng Jiang. "Modeling of Single-Digit Nanometer Perpendicular Shape Anisotropy Magnetic Tunnel Junction Driven by Spin-Transfer-Torque." In 2021 IEEE International Magnetic Conference (INTERMAG). IEEE, 2021. http://dx.doi.org/10.1109/intermag42984.2021.9579780.

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Hirayama, S., S. Kasai, and S. Mitani. "Modeling and Evaluation of Interface Perpendicular Magnetic Anisotropy in Ta/NiFe/Pt Trilayers." In 2016 International Conference on Solid State Devices and Materials. The Japan Society of Applied Physics, 2016. http://dx.doi.org/10.7567/ssdm.2016.ps-12-10.

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Kiefer, Björn, Karsten Buckmann, Thorsten Bartel, and Andreas Menzel. "Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques." In ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/smasis2014-7436.

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This paper presents an energy relaxation-based approach for the modeling of single crystalline magnetic shape memory alloy response under general two-dimensional magneto-mechanical loading. It relies on concepts of energy relaxation in the context of non-convex free energy landscapes whose wells define preferred states of straining and magnetization. The constrained theory of magnetoelasticity developed by DeSimone and James [1] forms the basis for the model development. The key features that characterize the extended approach are (i) dissipative effects, accounted for in an incremental variational setting, and (ii) finite magnetocrystalline anisotropy energy. In this manner, important additional response features, e.g. the hysteretic nature, the linear magnetization response in the pre-variant reorientation regime, and the stress dependence of the maximum field induced strain, can be captured, which are prohibited by the inherent assumptions of the constrained theory. The enhanced modeling capabilities of the extended approach are demonstrated by several representative response simulations and comparison to experimental results taken from literature. These examples particularly focus on the response of single crystals under cyclic magnetic field loading at constant stress, and cyclic mechanical loading at constant magnetic field.
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Markozov, I. D. "Modeling pulse profiles in X-Ray pulsars with accretion column." In Всероссийская с международным участием научная конференция студентов и молодых ученых, посвященная памяти Полины Евгеньевны Захаровой «Астрономия и исследование космического пространства». Ural University Press, 2021. http://dx.doi.org/10.15826/b978-5-7996-3229-8.09.

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The pulse profiles of the radiation coming from X-ray pulsars with an accretion column were modeled. Gravitational lensing and redshift in the Schwarzschild metric, as well as the reflection of X-Ray photons from the surface of a neutron star, were taken into account. On the basis of the obtained pulse profiles an analysis of possible errors in the measurements of the luminosities of X-ray pulsars associated with the inability of the observer to correctly take into account the anisotropy in the radiation emerging from the neutron star, as well as the angles between the pulsar’s rotation axis, the magnetic axis and the line of sight, was carried out.
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Liu*, Yajun, Hongzhu Cai, Xiangyun Hu, and Ronghua Peng. "3D forward modeling and analysis for loop-source transient electromagnetic data based on finite-volume method in an arbitrarily anisotropy earth." In GEM 2019 Xi'an: International Workshop and Gravity, Electrical & Magnetic Methods and their Applications, Chenghu, China, 19-22 April 2015. Society of Exploration Geophysicists and Chinese Geophysical Society, 2019. http://dx.doi.org/10.1190/gem2019-069.1.

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Manabe, Hiroki, Shota Yabui, Hideyuki Inoue, and Tsuyoshi Inoue. "Development of Experimental Active Magnetic Bearing Device for Measurement of Mechanical Seal Reaction Force Acting on Rotor." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85883.

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In turbomachinery, seals are used to prevent fluid leakage. At seal part, rotordynamic fluid force (RD fluid force), which causes whirling motion of rotor, is generated. Under certain conditions, the RD fluid force may contribute to instability of the machine. There are several cases that the whirling is accompanied by eccentricity due to the influence of gravity, or the whirling orbit becomes elliptical due to the influence of the bearing support anisotropy. In these cases, mathematical modeling of the RD fluid forces becomes increasingly complex. As a result, the RD fluid force measurement is more preferable. To improve the measurement and evaluation technology of the RD fluid force, a method to arbitrarily control whirling of the orbit is required. In this paper, RD fluid force measurement by controlling the shape of the orbit using an active magnetic bearing (AMB) is proposed. A contact type mechanical seal is used as a test specimen. When the rotating shaft is whirling, the RD fluid force due to hydrodynamics lubrication and the frictional force due to contact occur on the sliding surface. The resultant force of these forces is taken as the reaction force of mechanical seal and the measurement is performed. The measured reaction force of the mechanical seal is compared with simulation results and the validity of the proposed measurement method is confirmed.
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Cardelli, E., E. Della Torre, and A. Faba. "Vector hysteresis modeling for anisotropic magnetic materials." In 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2010). IEEE, 2010. http://dx.doi.org/10.1109/cefc.2010.5481768.

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