This paper presents a compact model of mutual inductance between two planar inductors, which is essential to design and optimize a wireless power transmission system. The tracks of the planar inductors are modeled as constant current carrying filaments, and the mutual inductance between individual filaments is determined by Neumann's integral. The proposed model is derived by solving Neumann's integral using a series expansion technique. This model can predict the mutual inductance at various axial and lateral displacements. Mutual coupling between planar inductors is computed by a 3-D electromagnetic (EM) solver, and the proposed model shows good agreement with these numerical results. Different types of planar inductors were fabricated on a printed circuit board (PCB) or silicon wafer. Using these inductors, wireless power links were constructed for applications like implantable biomedical devices and contactless battery charging systems. Mutual inductance was measured for each of the cases, and the comparison shows that the proposed model can predict mutual coupling suitably.

Modeling of Mutual Coupling Between Planar Inductors in Wireless Power Applications

Ferrofluids are suspensions of magnetic nanoparticles that have the attractive feature of being controlled by applied magnetic fields. Ferrofluids have been studied for decades in an ever growing number of applications that take advantage of their response to applied magnetic fields. Here, we provide a summary of recent advances in established and emerging applications of ferrofluids, including applications in optics, sensors, actuators, seals, lubrication, and static/dynamic magnetically driven assembly of structures.

Recent progress in ferrofluids research: novel applications of magnetically controllable and tunable fluids

Automated and accurate classiflcation of magnetic resonance (MR) brain images is a hot topic in the fleld of neuroimaging. Recently many difierent and innovative methods have been proposed to improve upon this technology. In this study, we presented a hybrid method based on forward neural network (FNN) to classify an MR brain image as normal or abnormal. The method flrst employed a discrete wavelet transform to extract features from images, and then applied the technique of principle component analysis (PCA) to reduce the size of the features. The reduced features were sent to an FNN, of which the parameters were optimized via an improved artiflcial bee colony (ABC) algorithm based on both fltness scaling and chaotic theory. We referred to the improved algorithm as scaled chaotic artiflcial bee colony (SCABC). Moreover, the K-fold stratifled cross validation was employed to avoid overfltting. In the experiment, we applied the proposed method on the data set of T2-weighted MRI images consisting of 66 brain images (18 normal and 48 abnormal). The proposed SCABC was compared with traditional training methods such as BP, momentum BP, genetic algorithm, elite genetic algorithm with migration, simulated annealing, and ABC. Each algorithm was run 20times to reduce randomness. The results show that our SCABC can obtain the least mean MSE and 100% classiflcation accuracy.

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Magnetic resonance brain image classification by an improved artificial bee colony algorithm

This paper presents a synthesis of analytical calculations of magnetic parameters (field, force, torque, stiffness) in cylindrical magnets and coils. By using the equivalence between the amperian current model and the coulombian model of a magnet, we show that a thin coil or a cylindrical magnet axially magnetized have the same mathematical model. Consequently, we present first the analytical expressions of the magnetic field produced by either a thin coil or a ring permanent magnet whose polarization is axial, thus completing similar calculations already published in the scientific literature. Then, this paper deals with the analytical calculation of the force and the stiffness between thin coils or ring permanent magnets axially magnetized. Such configurations can also be modeled with the same mathematical approach. Finally, this paper presents an analytical model of the mutual inductance between two thin coils in air. Throughout this paper, we emphasize why the equivalence between the coulombian and the amperian current models is useful for studying thin coils or ring permanent magnets. All our analytical expressions are based on elliptic integrals but do not require further numerical treatments. These expressions can be implemented in Mathematica or Matlab and are available online. All our models have been compared to previous analytical and semianalytical models. In addition, these models have been compared to the finite-element method. The computational cost of our analytical model is very low, and we find a very good agreement between our analytical model and the other approaches presented in this paper.

Cylindrical Magnets and Coils: Fields, Forces, and Inductances

This paper deals with the calculation of the force and the stiffness between two ring permanent magnets whose polarization is axial. Such a configuration corresponds to a passive magnetic bearing. All the calculations are determined by using the Coulombian model. The paper also discusses the optimal ring dimensions that provide a large force or stiffness between the rings. Such properties are commonly sought in passive magnetic bearings. We propose a three-dimensional method for optimizing these parameters. An important result is established in this paper: the exact relative position of the rings for which the force is the strongest depends on the air gap dimension. As the expressions in this paper give this exact relative position, manufacturers can easily optimize their passive magnetic bearings. This result is new because the curvature effect is taken into account. Such semianalytical expressions are more precise than the numerical evaluation of the magnetic forces obtained with the finite-element method. In addition, semianalytical expressions have a low computational cost whereas the finite-element method is computation-intensive. Such calculations make it easy to optimize quadripolar lenses and other devices utilizing permanent magnets.

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Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets. Part 2: Radial Magnetization

We present analytical formulations, based on a coulombian approach, of the magnetic field created by permanent-magnet rings. For axially magnetized magnets, we establish the expressions for the three components. We also give the analytical 3-D formulation of the created magnetic field for radially magnetized rings. We compare the results determined by a 2-D analytical approximation to those for the 3-D analytical formulation, in order to determine the range of validity of the 2-D approximation.

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Analytical Calculation of the Magnetic Field Created by Permanent-Magnet Rings

We present exact three-dimensional semi-analytical ex- pressions of the force exerted between two coaxial thick coils with rect- angular cross-sections. Then, we present a semi-analytical formulation of their mutual inductance. For this purpose, we have to calculate six and seven integrations for calculating the force and the mutual induc- tance respectively. After mathematical manipulations, we can obtain semi-analytical formulations based on only two integrations. It is to be noted that such integrals can be evaluated numerically as they are smooth and derivable. Then, we compare our results with the flla- ment and the flnite element methods. All the results are in excellent agreement.

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Mutual inductance and force exerted between thick coils

This paper presents three-dimensional expressions for the optimization of permanent-magnet couplings. First, we give a fully analytical expression of the azimuthal field created by one arc-shaped permanent magnet radially polarized which takes into account its magnetic pole volume density. Such an expression has a very low computational cost and is exact for all points in space. Then, we propose two semianalytical expressions of the azimuthal force and the torque exerted between two arc-shaped permanent magnets. These expressions are valid for thick or thin arc-shaped permanent magnets. Furthermore, this approach allows us to realize easily parametric studies and optimizations. The analytical approach taken in this paper, based on the Coulombian model, is a good alternative compared to the finite element method generally used to study such configurations.

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Romain Ravaud

Papers

Analytical Calculation of the Magnetic Field Created by Permanent-Magnet Rings

Cylindrical Magnets and Coils: Fields, Forces, and Inductances

Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets. Part 2: Radial Magnetization

Mutual inductance and force exerted between thick coils

Permanent Magnet Couplings: Field and Torque Three-Dimensional Expressions Based on the Coulombian Model