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Journal articles on the topic 'Biot Savart's law'

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Published: 4 June 2021

Last updated: 9 February 2022

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1

Qihou, Z. "Proof of Biot-Savart's law for a discontinuous current-or another example of displacement current." European Journal of Physics 8, no. 2 (April 1, 1987): 128–30. http://dx.doi.org/10.1088/0143-0807/8/2/010.

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2

Kim, Ki-Chan. "Comparison of Biot-Savart's Law and 3D FEM in the Study of Electromagnetic Forces Acting on End Winding." Journal of Electrical Engineering and Technology 6, no. 3 (May 2, 2011): 369–74. http://dx.doi.org/10.5370/jeet.2011.6.3.369.

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3

Zhou, Zhen, Z. H. Guan, J. Luo, L. J. Wang, Y. Qin, and G. F. Sun. "Finite Element Analysis of Inductance Sensor Structure in the Measuring System of the Grade of the Iron Concentrate." Key Engineering Materials 458 (December 2010): 155–60. http://dx.doi.org/10.4028/www.scientific.net/kem.458.155.

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According to the Biot-Savart's Law, the principle of the detecting system which measures the grade of the iron concentrate is analysed in this paper. It carries out an analysis of influence of inductance sensor coil structure parameters on the performance of sensor. The finite element model of the air core coil is established and analysis of finite element simulation is done to inductance sensors by using orthogonal method. According to different structural parameters, the relation of magnetic permeability of the iron concentrate and the inductance of the sensor coil can be established. Moreover, the effect of the sensor coil’s parameter on the linearity and the sensitivity of the sensor can also be determined. All the above provide a reference for the design of coil structure parameter of the inductance sensors.

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4

BARBOSA, DISTERFANO L. M., JERSON R. P. VAZ, SÁVIO W. O. FIGUEIREDO, MARCELO DE OLIVEIRA E. SILVA, ERB F. LINS, and ANDRÉ L. A. MESQUITA. "An Investigation of a Mathematical Model for the Internal Velocity Profile of Conical Diffusers Applied to DAWTs." Anais da Academia Brasileira de Ciências 87, no. 2 (April 28, 2015): 1133–48. http://dx.doi.org/10.1590/0001-3765201520140114.

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The Diffuser Augmented Wind Turbines (DAWTs) have been widely studied, since the diffusers improve the power coefficient of the wind turbine, particularly of small systems. The diffuser is a device which has the function of causing an increase on the flow velocity through the wind rotor plane due to pressure drop downstream, therefore resulting in an increase of the rotor power coefficient. This technology aids the turbine to exceed the Betz limit, which states that the maximum kinetic energy extracted from the flow is 59.26%. Thus, the present study proposes a mathematical model describing the behavior of the internal velocity for three conical diffusers, taking into account the characteristics of flow around them. The proposed model is based on the Biot-Savart's Law, in which the vortex filament induces a velocity field at an arbitrary point on the axis of symmetry of the diffusers. The results are compared with experimental data obtained for the three diffusers, and present good agreement.

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5

Ganushkina, N. Yu, M. W. Liemohn, and T. I. Pulkkinen. "Storm-time ring current: model-dependent results." Annales Geophysicae 30, no. 1 (January 17, 2012): 177–202. http://dx.doi.org/10.5194/angeo-30-177-2012.

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Abstract. The main point of the paper is to investigate how much the modeled ring current depends on the representations of magnetic and electric fields and boundary conditions used in simulations. Two storm events, one moderate (SymH minimum of −120 nT) on 6–7 November 1997 and one intense (SymH minimum of −230 nT) on 21–22 October 1999, are modeled. A rather simple ring current model is employed, namely, the Inner Magnetosphere Particle Transport and Acceleration model (IMPTAM), in order to make the results most evident. Four different magnetic field and two electric field representations and four boundary conditions are used. We find that different combinations of the magnetic and electric field configurations and boundary conditions result in very different modeled ring current, and, therefore, the physical conclusions based on simulation results can differ significantly. A time-dependent boundary outside of 6.6 RE gives a possibility to take into account the particles in the transition region (between dipole and stretched field lines) forming partial ring current and near-Earth tail current in that region. Calculating the model SymH* by Biot-Savart's law instead of the widely used Dessler-Parker-Sckopke (DPS) relation gives larger and more realistic values, since the currents are calculated in the regions with nondipolar magnetic field. Therefore, the boundary location and the method of SymH* calculation are of key importance for ring current data-model comparisons to be correctly interpreted.

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6

Hovey, Arthur. "The Biot-Savart Law—Another Approach." Physics Teacher 46, no. 5 (May 2008): 261–62. http://dx.doi.org/10.1119/1.2909737.

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7

Oliveira, Mário H., and José A. Miranda. "Biot-Savart-like law in electrostatics." European Journal of Physics 22, no. 1 (January 1, 2001): 31–38. http://dx.doi.org/10.1088/0143-0807/22/1/304.

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8

Pyati, Vittal P. "Simplified Biot-Savart Law for Planar Circuits." IEEE Transactions on Education E-29, no. 1 (February 1986): 32–33. http://dx.doi.org/10.1109/te.1986.5570681.

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9

Kabbary, F. M., B. G. Stewart, and M. C. Hately. "Displacement Current and the Biot-Savart Law." International Journal of Electrical Engineering Education 27, no. 4 (October 1990): 344–55. http://dx.doi.org/10.1177/002072099002700412.

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10

Phillips, Jeffrey A., and Jeff Sanny. "The Biot-Savart Law: From Infinitesimal to Infinite." Physics Teacher 46, no. 1 (January 2008): 44–47. http://dx.doi.org/10.1119/1.2824000.

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11

Yan, C. C. "Theoretical experimentation with the law of Biot-Savart." Foundations of Physics 24, no. 1 (January 1994): 163–75. http://dx.doi.org/10.1007/bf02053913.

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12

Ferreira, J. M., and Joaquim Anacleto. "Using Biot–Savart’s law to determine the finite tube’s magnetic field." European Journal of Physics 39, no. 5 (July 12, 2018): 055202. http://dx.doi.org/10.1088/1361-6404/aace84.

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13

Caparelli, E. C., and D. Tomasi. "An Analytical Calculation of the Magnetic Field Using the Biot Savart Law." Revista Brasileira de Ensino de Física 23, no. 3 (September 2001): 284–88. http://dx.doi.org/10.1590/s1806-11172001000300005.

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This work presents an analytical method to calculate the magnetic field at any point of the space, by solving the Biot Savart equation in the reciprocal space. This is applied to express the magnetic field due to a circular current distributions as a convergent series. The comparison between the proposed method with the standard numerical integration of the Biot Savart law has shown a good agreement.

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14

Pelloni, S., A. Ligabue, and P. Lazzeretti. "Ring-Current Models from the Differential Biot-Savart Law." Organic Letters 6, no. 24 (November 2004): 4451–54. http://dx.doi.org/10.1021/ol048332m.

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15

Khosropour, B., and S. K. Moayedi. "Application of Biot–Savart law and generalized uncertainty principle." International Journal of Geometric Methods in Modern Physics 16, no. 04 (April 2019): 1950065. http://dx.doi.org/10.1142/s0219887819500658.

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In the recent decade, many investigations have been done in the framework of generalized uncertainty principle (GUP), but the phenomenology of models in this framework are less studied. In this work, the applications of Biot–Savart law in the presence of a minimal length scale are investigated. We obtain the modified magnetostatic field from an infinitely long, straight wire carrying current [Formula: see text]. Also, the modified magnetostatic field from a circular loop carrying current [Formula: see text] and the modified magnetostatic field of an ideal solenoid are found. It is interesting to note that in the limit [Formula: see text], all of the modified magnetostatic fields become their usual forms.

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16

Szalek, Marek A. "Pauli versus the Maxwell Equations and the Biot‐Savart Law." Physics Essays 10, no. 1 (March 1997): 95–102. http://dx.doi.org/10.4006/1.3028706.

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17

ESİN, Yunus Emre, and Ferda Nur ALPASLAN. "MRI image enhancement using Biot--Savart law at 3 tesla." TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES 25 (2017): 3381–96. http://dx.doi.org/10.3906/elk-1604-348.

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18

Kalhor, H. A. "The degree of intelligence of the law of Biot-Savart." IEEE Transactions on Education 33, no. 4 (1990): 365–66. http://dx.doi.org/10.1109/13.61093.

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19

Evans, M. W. "The Biot-Savart-Ampère law and the vacuum fieldB (3)." Foundations of Physics Letters 8, no. 4 (August 1995): 381–88. http://dx.doi.org/10.1007/bf02187818.

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20

Buschauer, Robert. "Derivation of the Biot-Savart Law from Ampere's Law Using the Displacement Current." Physics Teacher 51, no. 9 (December 2013): 542–43. http://dx.doi.org/10.1119/1.4830067.

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21

Kalhor, H. A. "Comparison of Ampere's circuital law (ACL) and the law of Biot-Savart (LBS)." IEEE Transactions on Education 31, no. 3 (August 1988): 236–38. http://dx.doi.org/10.1109/13.2322.

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22

Afjeh, A. A., and T. G. Keith. "A Vortex Lifting Line Method for the Analysis of Horizontal Axis Wind Turbines." Journal of Solar Energy Engineering 108, no. 4 (November 1, 1986): 303–9. http://dx.doi.org/10.1115/1.3268110.

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The present paper utilizes an earlier analytical wake model, which essentially applies to helicopter load analysis, to determine the performance of horizontal axis wind turbines. The advantage of this method is that it makes use of an integrated version of the Biot-Savart law for each part of the wake and thereby avoids some of the numerical difficulties present in the Biot-Savart law. Numerical computations were performed for a number of two-bladed rotor geometries and operating conditions. Results were compared with experimental data as well as with predictions of a full free wake method. Good overall agreement with both was observed.

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23

Ruppeiner, George, Michael Grossman, and Ali Tafti. "Test of the Biot–Savart law to distances of 15 m." American Journal of Physics 64, no. 6 (June 1996): 698–705. http://dx.doi.org/10.1119/1.18235.

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24

Neuenschwander, Dwight E., and Brian N. Turner. "Generalization of the Biot–Savart law to Maxwell’s equations using special relativity." American Journal of Physics 60, no. 1 (January 1992): 35–38. http://dx.doi.org/10.1119/1.17039.

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25

Shi-De, Feng, Dong Ping, and Zhong Lin-Hao. "A Conceptual Model of Somali Jet Based on the Biot–Savart Law." Chinese Physics Letters 25, no. 12 (December 2008): 4321–24. http://dx.doi.org/10.1088/0256-307x/25/12/038.

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26

Feng Shi-De and Feng Tao. "Biot-Savart law and the formation mechanism of Somali low-level jet." Acta Physica Sinica 60, no. 2 (2011): 029202. http://dx.doi.org/10.7498/aps.60.029202.

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27

van den Broeh, S. P., H. Zhou, and M. J. Peters. "Computation of neuromagnetic fields using finite-element method and Biot-Savart law." Medical and Biological Engineering and Computing 34, no. 1 (January 1996): 21–26. http://dx.doi.org/10.1007/bf02637018.

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28

Takeda, Harunori, and David Dowell. "Modeling the APLE injector solenoid magnetic field with the Biot-Savart law." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 331, no. 1-3 (July 1993): 384–89. http://dx.doi.org/10.1016/0168-9002(93)90076-t.

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29

White, Daniel A., and Benjamin J. Fasenfest. "Performance of Low-Rank QR Approximation of the Finite Element Biot–Savart Law." IEEE Transactions on Magnetics 43, no. 4 (April 2007): 1485–88. http://dx.doi.org/10.1109/tmag.2007.892274.

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30

Titov, V. S., C. Downs, T. Török, J. A. Linker, R. M. Caplan, and R. Lionello. "Optimization of Magnetic Flux Ropes Modeled with the Regularized Biot–Savart Law Method." Astrophysical Journal Supplement Series 255, no. 1 (July 1, 2021): 9. http://dx.doi.org/10.3847/1538-4365/abfe0f.

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31

Hey, J. D. "On the Biot–Savart law of electromagnetism applied to the atomic circulation current *." Journal of Physics A: Mathematical and Theoretical 54, no. 16 (March 26, 2021): 165302. http://dx.doi.org/10.1088/1751-8121/abe832.

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32

Falkowski, Krzysztof. "Second-Order Model of the Radial Passive Magnetic Bearing with Halbach's Array." Solid State Phenomena 198 (March 2013): 400–405. http://dx.doi.org/10.4028/www.scientific.net/ssp.198.400.

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In the paper is presented model of the passive magnetic bearing. The response of bearing is approximate by second order model. There are presented the damping and stiffness coefficient of suspension. The coefficients derived from Biot-Savards law, Ohms law and Lorenzs force. There is presented loop with molecular current as a model of magnet, final formula of damping and stiffness coefficients and static characteristic of passive magnetic bearing.

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33

WOOD, D. H., and J. BOERSMA. "On the motion of multiple helical vortices." Journal of Fluid Mechanics 447 (October 30, 2001): 149–71. http://dx.doi.org/10.1017/s002211200100578x.

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The analysis of the self-induced velocity of a single helical vortex (Boersma & Wood 1999) is extended to include equally spaced multiple vortices. This arrangement approximates the tip vortices in the far wake of multi-bladed wind turbines, propellers, or rotors in ascending, descending, or hovering flight. The problem is reduced to finding, from the Biot–Savart law, the additional velocity of a helix due to an identical helix displaced azimuthally. The resulting Biot–Savart integral is further reduced to a Mellin–Barnes integral representation which allows the asymptotic expansions to be determined for small and for large pitch. The Biot–Savart integral is also evaluated numerically for a total of two, three and four vortices over a range of pitch values. The previous finding that the self-induced velocity at small pitch is dominated by a term inversely proportional to the pitch carries over to multiple vortices. It is shown that a far wake dominated by helical tip vortices is consistent with the one-dimensional representation that leads to the Betz limit on the power output of wind turbines. The small-pitch approximation then allows the determination of the blade&s bound vorticity for optimum power extraction. The present analysis is shown to give reasonable estimates for the vortex circulation in experiments using a single hovering rotor and a four-bladed propeller.

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34

Kusiak, Dariusz, Tomasz Szczegielniak, and Zygmunt Piątek. "Magnetic field of a ribbon busbar of finite length." ITM Web of Conferences 19 (2018): 01010. http://dx.doi.org/10.1051/itmconf/20181901010.

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Using the analytic method based on the Biot-Savart law for the electromagnetic field, the distribution of the magnetic field of a ribbon busbar of finite length has been determined. The Mathematica program was used to visualize the solutions obtained. This allowed quick field analysis after changes of geometrical or electrical parameters of systems under examination.

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35

Rajaraman, K. C. "Ampere's Magnetic Circuital Law: A Simple and Rigorous Two-Step Proof." International Journal of Electrical Engineering & Education 38, no. 3 (July 2001): 246–55. http://dx.doi.org/10.7227/ijeee.38.3.7.

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A new proof of Ampere's law from the Biot-Savart law is presented. In the first step, a physical interpretation of current as moving charges carrying their electric fields with them simplifies the derivation of the magnetic field of current in a straight infinitely long conductor. The m.m.f. of a finite electric circuit linking a magnetic path is synthesized from those of two infinitely long wires carrying equal currents in opposite directions, only one of them threading the path. This makes the second step rigorous, enabling a non-mathematical treatment of the magnetic effects of electric currents in free space.

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36

White, Daniel A., Ben Fasenfest, and Mark Stowell. "A Parallel Computer Implementation of Fast Low-rank QR Approximation of the Biot-savart Law." PIERS Online 2, no. 4 (2006): 420–24. http://dx.doi.org/10.2529/piers050901151739.

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37

WANG, JIN, GUOFENG LI, KE LIANG, and XIANHU GAO. "THE THEORY OF FIELD PARAMETERS FOR HELMHOLTZ COIL." Modern Physics Letters B 24, no. 02 (January 20, 2010): 201–9. http://dx.doi.org/10.1142/s0217984910022275.

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In this paper, the field parameters for the magnetic field of a Helmholtz coil is defined, as predicted by the theory of magnetic multipolar fields. In accordance with Biot–Savart law, eleven series of field parameters for the Helmholtz coil are calculated and the effect of each parameter thoroughly analyzed. This is then shown to provide a theoretical basis for obtaining a uniform magnetic field.

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38

Margineda, J., and P. Lorrain. "Comments, with reply, on "Comparison of Ampere's law (ACL) and the law of Biot-Savart (LBS)" by H.A. Kalhor." IEEE Transactions on Education 33, no. 2 (May 1990): 222–23. http://dx.doi.org/10.1109/13.54866.

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39

YEGHIAZARYAN, Alexandra S., and Lev S. ZIMIN. "VIBRATION PROTECTION OF POWERFUL INDUCTORS." Urban construction and architecture 6, no. 3 (September 15, 2016): 135–39. http://dx.doi.org/10.17673/vestnik.2016.03.22.

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Electrodynamic and vibroacoustic problems during induction heating of solids with variable curvature of surface - primarily heating of slabs for rolling - are viewed. It is recommended to perform electrodynamic calculation on numerical model developed through coupled circuits method and virtual displacement law. For numerical solution of vibration problem it is worth to use finite-element method. In the general case for calculating of distributed forces Biot-Savart-Laplaces law is used. This law permits to definite surface current density in a slab. Through inductor vibration model studies the form of inductor optimal shell is synthesized according to the criterion of minimal noise emissions.

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40

KLETSEL, Mark. "About the Biot-Savart-Laplace law and its use for calculations in high-voltage AC installations." PRZEGLĄD ELEKTROTECHNICZNY 1, no. 11 (November 5, 2017): 131–34. http://dx.doi.org/10.15199/48.2017.11.28.

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41

Moyssides, P. G. "Calculation of the sixfold integrals of the Biot-Savart-Lorentz force law in a closed circuit." IEEE Transactions on Magnetics 25, no. 5 (1989): 4298–306. http://dx.doi.org/10.1109/20.42596.

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42

Graneau, P. N. "Energy deficiency of the electromagnetic-impulse pendulum with respect to the Biot-Savart-Lorentz force law." Il Nuovo Cimento D 11, no. 4 (April 1989): 649–50. http://dx.doi.org/10.1007/bf02457517.

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43

AGISHTEIN, M. E., and A. A. MIGDAL. "COMPUTER SIMULATION OF THREE-DIMENSIONAL VORTEX DYNAMICS." Modern Physics Letters A 01, no. 03 (June 1986): 221–30. http://dx.doi.org/10.1142/s0217732386000312.

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The discrete model, approximating with exponential accuracy the set of interacting closed vortex lines in an ideal fluid, is proposed and investigated by means of the computer. The vortex lines move in their own velocity field according to the Biot-Savart law. This is a generalized Hamiltonian system possessing in addition an infinite number of conservation laws. Nevertheless, the motion becomes stochastic for certain initial conditions, and may be interpreted as marking the onset of turbulence.

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44

Yang, Cheng Wei, Xiao Jiang Li, and Hao Ran Wu. "The Electromagnetic Force Influencing Research of a Rectangular Cross-Sectional Rail Launcher by Armature Position." Advanced Materials Research 791-793 (September 2013): 1828–31. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.1828.

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The electromagnetic force which influenced by rail launcher armature position have been researched in this paper. As an important indicator, Inductance Gradient (IG) denotes the performance of rail launch, which can make the railgun performance to achieve optimal results by better design. A rectangular cross-sectional rail launcher model was built based on the Biot-Savart law in this paper. Furthermore, the analytical expression of inductance gradient can be obtained by this model. Finally, the electromagnetic force can be calculated. Some numerical simulations are made to test the validity and capability of the proposed model.

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45

Davidson, P. A. "Long-range interactions in turbulence and the energy decay problem." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1937 (February 28, 2011): 796–810. http://dx.doi.org/10.1098/rsta.2010.0295.

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We discuss the long-range interactions that arise in homogeneous turbulence as a consequence of the Biot–Savart law. We note that, somewhat surprisingly, these long-range correlations are very weak in decaying, isotropic turbulence, and we argue that this should also be true for magnetohydrodynamic, rotating and stratified turbulence. If this is indeed the case, it is possible to make explicit predictions for the rate of decay of energy in these anisotropic systems, and it turns out that these predictions are consistent with the available numerical and experimental evidence.

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46

Liu, Li Kun, Zi Zi Ouyang, Sen Wang, Yi Wang, Xiao Dong Chen, and Dao Yin Yu. "A New Real-Time Position and Orientation Tracking System for Endoscopy." Applied Mechanics and Materials 130-134 (October 2011): 1196–99. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.1196.

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A New real-time position and orientation tracking system for endoscopy is described. Three coils sequentiallyfed with current comprise the excitation source which will produce magnetic field. According to Biot-Savart-Laplace law, flux intensity data detected by three-axis magnetic sensor could be interpreted into information that will reflect the sensor's specific position, thus realizing the position determination. Also, data detected by the magnetic sensor and gravity sensor changes in connection with the spatial angles. By researching the change law between the two, spatial angles of the sensor is calculated, thus realizing orientation determination. It is shown errors in position determination is,errors in orientation determination is , the tracking frequency of the system is 10 Hz.

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47

Guangming, Xue, Zhang Peilin, He Zhongbo, Li Xin, Zeng Wei, and Chu Yang. "Revised reluctance model of the axial magnetic field intensity within giant magnetostrictive rod." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 14 (March 22, 2016): 2718–29. http://dx.doi.org/10.1177/0954406216639076.

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A theoretical magnetic field intensity model within giant magnetostrictive material was presented. This model was established just like the reluctance model, while could describe the non-uniform distribution flexibly for its integral form. This model employed magnetic circuit theorem calculating the mean of the magnetic field, while used a normalized function describing the distributing character. The distributing function was determined by Biot–Savart law and relative permeability of the material. The model was validated with the help of the experimental device. At last, the fitting degree of the model with the tested results in predicting the performance of the actuator is researched.

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48

Moffatt, H. K., and Yoshifumi Kimura. "Towards a finite-time singularity of the Navier–Stokes equations Part 1. Derivation and analysis of dynamical system." Journal of Fluid Mechanics 861 (December 31, 2018): 930–67. http://dx.doi.org/10.1017/jfm.2018.882.

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The evolution towards a finite-time singularity of the Navier–Stokes equations for flow of an incompressible fluid of kinematic viscosity$\unicode[STIX]{x1D708}$is studied, starting from a finite-energy configuration of two vortex rings of circulation$\pm \unicode[STIX]{x1D6E4}$and radius$R$, symmetrically placed on two planes at angles$\pm \unicode[STIX]{x1D6FC}$to a plane of symmetry$x=0$. The minimum separation of the vortices,$2s$, and the scale of the core cross-section,$\unicode[STIX]{x1D6FF}$, are supposed to satisfy the initial inequalities$\unicode[STIX]{x1D6FF}\ll s\ll R$, and the vortex Reynolds number$R_{\unicode[STIX]{x1D6E4}}=\unicode[STIX]{x1D6E4}/\unicode[STIX]{x1D708}$is supposed very large. It is argued that in the subsequent evolution, the behaviour near the points of closest approach of the vortices (the ‘tipping points’) is determined solely by the curvature$\unicode[STIX]{x1D705}(\unicode[STIX]{x1D70F})$at the tipping points and by$s(\unicode[STIX]{x1D70F})$and$\unicode[STIX]{x1D6FF}(\unicode[STIX]{x1D70F})$, where$\unicode[STIX]{x1D70F}=(\unicode[STIX]{x1D6E4}/R^{2})t$is a dimensionless time variable. The Biot–Savart law is used to obtain analytical expressions for the rate of change of these three variables, and a nonlinear dynamical system relating them is thereby obtained. The solution shows a finite-time singularity, but the Biot–Savart law breaks down just before this singularity is realised, when$\unicode[STIX]{x1D705}s$and$\unicode[STIX]{x1D6FF}/\!s$become of order unity. The dynamical system admits ‘partial Leray scaling’ of just$s$and$\unicode[STIX]{x1D705}$, and ultimately full Leray scaling of$s,\unicode[STIX]{x1D705}$and$\unicode[STIX]{x1D6FF}$, conditions for which are obtained. The tipping point trajectories are determined; these meet at the singularity point at a finite angle. An alternative model is briefly considered, in which the initial vortices are ovoidal in shape, approximately hyperbolic near the tipping points, for which there is no restriction on the initial value of the parameter$\unicode[STIX]{x1D705}$; however, it is still the circles of curvature at the tipping points that determine the local evolution, so the same dynamical system is obtained, with breakdown again of the Biot–Savart approach just before the incipient singularity is realised. The Euler flow situation ($\unicode[STIX]{x1D708}=0$) is considered, and it is conjectured on the basis of the above dynamical system that a finite-time singularity can indeed occur in this case.

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Paese, E., Pedro A. R. Rosa, Martin Geier, Roberto P. Homrich, and R. Rossi. "An Analysis of Electromagnetic Sheet Metal Forming Process." Applied Mechanics and Materials 526 (February 2014): 9–14. http://dx.doi.org/10.4028/www.scientific.net/amm.526.9.

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Electromagnetic forming (EMF) is a high-speed forming process that uses energy density of a pulsed magnetic field to deform metallic workpieces. This paper presents a method to calculate the electromagnetic force in thin flat plates using a flat spiral coil as an actuator. The method is based on the Biot-Savart law, and the solution of magnetic induction integral equations is performed inside Matlab®by a numerical method based on discretizing the EMF system in a system of ordinary differential equations that couple the electric and magnetic phenomena. Free bulging experiments and a comparison with Ansoft Maxwell®software are presented demonstrating a good correlation with the proposed implementation.

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Afjeh, A. A., and T. G. Keith. "A Simplified Free Wake Method for Horizontal-Axis Wind Turbine Performance Prediction." Journal of Fluids Engineering 108, no. 4 (December 1, 1986): 400–406. http://dx.doi.org/10.1115/1.3242595.

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Based on the assumption that wake geometry of a horizontal-axis wind turbine closely resembles that of a hovering helicopter, a method is presented for predicting the performance of a horizontal-axis wind turbine. A vortex method is used in which the wake is composed of an intense tip-vortex and a diffused inboard wake. Performance parameters are calculated by application of the Biot-Savart law along with the Kutta-Joukowski theorem. Predictions are shown to compare favorably with values from a more complicated full free wake analysis and with existing experimental data, but require more computational effort than an existing fast free wake method.

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