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Journal articles on the topic 'Maxwell's equations'

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Published: 4 June 2021

Last updated: 10 August 2024

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1

CIARLET, PATRICK, and SIMON LABRUNIE. "NUMERICAL ANALYSIS OF THE GENERALIZED MAXWELL EQUATIONS (WITH AN ELLIPTIC CORRECTION) FOR CHARGED PARTICLE SIMULATIONS." Mathematical Models and Methods in Applied Sciences 19, no. 11 (November 2009): 1959–94. http://dx.doi.org/10.1142/s0218202509004017.

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When computing numerical solutions to the Vlasov–Maxwell equations, the source terms in Maxwell's equations usually fail to satisfy the continuity equation. Since this condition is required for the well-posedness of Maxwell's equations, it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. These approaches, which involve a hyperbolic, a parabolic and an elliptic correction, have been recently analyzed mathematically. The goal of this paper is to carry out the numerical analysis for several variants of Maxwell's equations with an elliptic correction.

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2

Carey, A. L., and K. McNamara. "Degenerate forms of Maxwell's equations." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 31, no. 3 (January 1990): 277–300. http://dx.doi.org/10.1017/s0334270000006652.

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AbstractThis paper studies degenerate forms of Maxwell's equations which arise from approximations suggested by geophysical modelling problems. The approximations reduce Maxwell's equations to degenerate elliptic/parabolic ones. Here we consider the questions of existence, uniqueness and regularity of solutions for these equations and address the problem of showing that the solutions of the degenerate equations do approximate those of the genuine Maxwell equations.

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3

McCrea, W. H. "Maxwell's equations." Contemporary Physics 26, no. 3 (May 1985): 297. http://dx.doi.org/10.1080/00107518508223687.

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4

BARTHELMÉ, RÉGINE, PATRICK CIARLET, and ERIC SONNENDRÜCKER. "GENERALIZED FORMULATIONS OF MAXWELL'S EQUATIONS FOR NUMERICAL VLASOV–MAXWELL SIMULATIONS." Mathematical Models and Methods in Applied Sciences 17, no. 05 (May 2007): 657–80. http://dx.doi.org/10.1142/s0218202507002066.

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When solving numerically approximations of the Vlasov–Maxwell equations, the source terms in Maxwell's equations coming from the numerical solution of the Vlasov equation do not generally satisfy the continuity equation which is required for Maxwell's equations to be well-posed. Hence it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. Different such formulations have been introduced previously. The aim of this paper is to perform their mathematical analysis and verify the existence and uniqueness of the solution.

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5

Zhao, Yang, Dumitru Baleanu, Carlo Cattani, De-Fu Cheng, and Xiao-Jun Yang. "Maxwell’s Equations on Cantor Sets: A Local Fractional Approach." Advances in High Energy Physics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/686371.

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Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.

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6

Dawson, Peter, and Jim Grozier. "Maxwell's famous equations." Physics World 28, no. 4 (April 2015): 21–22. http://dx.doi.org/10.1088/2058-7058/28/4/29.

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7

Arbab, A. I. "Complex Maxwell's equations." Chinese Physics B 22, no. 3 (March 2013): 030301. http://dx.doi.org/10.1088/1674-1056/22/3/030301.

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8

Arbab, A. I. "Quantized Maxwell's equations." Optik 136 (May 2017): 64–70. http://dx.doi.org/10.1016/j.ijleo.2017.01.067.

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9

Hillion, Pierre. "Paraxial Maxwell's equations." Optics Communications 107, no. 5-6 (May 1994): 327–30. http://dx.doi.org/10.1016/0030-4018(94)90340-9.

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10

LONG, EAMONN. "EXISTENCE AND STABILITY OF SOLITARY WAVES IN NON-LINEAR KLEIN–GORDON–MAXWELL EQUATIONS." Reviews in Mathematical Physics 18, no. 07 (August 2006): 747–79. http://dx.doi.org/10.1142/s0129055x06002784.

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We prove the existence and stability of non-topological solitons in a class of weakly coupled non-linear Klein–Gordon–Maxwell equations. These equations arise from coupling non-linear Klein–Gordon equations to Maxwell's equations for electromagnetism.

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11

Holland, Peter. "Hydrodynamic construction of the electromagnetic field." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2063 (September 19, 2005): 3659–79. http://dx.doi.org/10.1098/rspa.2005.1525.

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We present an alternative Eulerian hydrodynamic model for the electromagnetic field in which the discrete vector indices in Maxwell's equations are replaced by continuous angular freedoms, and develop the corresponding Lagrangian picture in which the fluid particles have rotational and translational freedoms. This enables us to extend to the electromagnetic field the exact method of state construction proposed previously for spin 0 systems, in which the time-dependent wavefunction is computed from a single-valued continuum of deterministic trajectories where two spacetime points are linked by at most a single orbit. The deduction of Maxwell's equations from continuum mechanics is achieved by generalizing the spin 0 theory to a general Riemannian manifold from which the electromagnetic construction is extracted as a special case. In particular, the flat-space Maxwell equations are represented as a curved-space Schrödinger equation for a massive system. The Lorentz covariance of the Eulerian field theory is obtained from the non-covariant Lagrangian-coordinate model as a kind of collective effect. The method makes manifest the electromagnetic analogue of the quantum potential that is tacit in Maxwell's equations. This implies a novel definition of the ‘classical limit’ of Maxwell's equations that differs from geometrical optics. It is shown that Maxwell's equations may be obtained by canonical quantization of the classical model. Using the classical trajectories a novel expression is derived for the propagator of the electromagnetic field in the Eulerian picture. The trajectory and propagator methods of solution are illustrated for the case of a light wave.

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12

SHINDO, Takatoshi. "Comic Dialogue: Maxwell's Equations." Journal of The Institute of Electrical Engineers of Japan 141, no. 2 (February 1, 2021): 97–98. http://dx.doi.org/10.1541/ieejjournal.141.97.

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13

Boozer, Allen H. "Mathematics and Maxwell's equations." Plasma Physics and Controlled Fusion 52, no. 12 (November 15, 2010): 124002. http://dx.doi.org/10.1088/0741-3335/52/12/124002.

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14

Uyeda, Seiya, and Haruo Tanaka. "Maxwell's equations and earthquakes." Physics World 17, no. 2 (February 2004): 21–22. http://dx.doi.org/10.1088/2058-7058/17/2/30.

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15

Campbell, A. M. "Maxwell's Equations in Superconductors." IEEE Transactions on Applied Superconductivity 17, no. 2 (June 2007): 2531–36. http://dx.doi.org/10.1109/tasc.2007.900042.

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16

Diener, Gerhard, Jürgen Weissbarth, Frank Grossmann, and Rüdiger Schmidt. "Obtaining Maxwell's equations heuristically." American Journal of Physics 81, no. 2 (February 2013): 120–23. http://dx.doi.org/10.1119/1.4768196.

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17

Bartsch, Michael, Micha Dehler, Martin Dohlus, Frank Ebeling, Peter Hahne, Reinhard Klatt, Frank Krawczyk, et al. "Solution of Maxwell's equations." Computer Physics Communications 73, no. 1-3 (December 1992): 22–39. http://dx.doi.org/10.1016/0010-4655(92)90026-u.

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18

COSTABEL, MARTIN, MONIQUE DAUGE, and CHRISTOPH SCHWAB. "EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS." Mathematical Models and Methods in Applied Sciences 15, no. 04 (April 2005): 575–622. http://dx.doi.org/10.1142/s0218202505000480.

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The time-harmonic Maxwell equations do not have an elliptic nature by themselves. Their regularization by a divergence term is a standard tool to obtain equivalent elliptic problems. Nodal finite element discretizations of Maxwell's equations obtained from such a regularization converge to wrong solutions in any non-convex polygon. Modification of the regularization term consisting in the introduction of a weight restores the convergence of nodal FEM, providing optimal convergence rates for the h version of finite elements. We prove exponential convergence of hp FEM for the weighted regularization of Maxwell's equations in plane polygonal domains provided the hp-FE spaces satisfy a series of axioms. We verify these axioms for several specific families of hp finite element spaces.

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19

Chesnokov, Yevgen V., and Ivan V. Kazachkov. "Analysis of the Doppler Effect Based on the Full Maxwell Equations." EQUATIONS 2 (July 2, 2022): 100–103. http://dx.doi.org/10.37394/232021.2022.2.16.

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In the previous paper, a modification of Maxwell's equations was proposed, from which formula for Doppler effect follows. However, as was noted later, the equations proposed do not have symmetry with respect to the transformation B→-E, E→B, which the original Maxwell equations have and which was discovered by Heaviside in 1893. The equations proposed in present paper have this symmetry. The obtained equations are analyzed for several physical situations.

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20

Gupta, Vinay Kumar, and Manuel Torrilhon. "Higher order moment equations for rarefied gas mixtures." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2173 (January 2015): 20140754. http://dx.doi.org/10.1098/rspa.2014.0754.

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The fully nonlinear Grad's N ×26-moment ( N × G 26) equations for a mixture of N monatomic-inert-ideal gases made up of Maxwell molecules are derived. The boundary conditions for these equations are derived by using Maxwell's accommodation model for each component in the mixture. The linear stability analysis is performed to show that the 2×G26 equations for a binary gas mixture of Maxwell molecules are linearly stable. The derived equations are used to study the heat flux problem for binary gas mixtures confined between parallel plates having different temperatures.

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21

Kravchenko, Vladislav V. "Quaternionic Diagonalization of Maxwell's Equations." Telecommunications and Radio Engineering 56, no. 4-5 (2001): 8. http://dx.doi.org/10.1615/telecomradeng.v56.i4-5.30.

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22

Mismar, Mai. "Numerical Simulation of Maxwell's Equations." IOSR Journal of Engineering 7, no. 03 (March 2017): 01–10. http://dx.doi.org/10.9790/30210-703010110.

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23

Belgacem, Fethi Bin Muhammad. "Sumudu Applications to Maxwell's Equations." PIERS Online 5, no. 4 (2009): 355–60. http://dx.doi.org/10.2529/piers090120050621.

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24

Teixeira, Fernando Lisboa. "LATTICE MAXWELL'S EQUATIONS (Invited Paper)." Progress In Electromagnetics Research 148 (2014): 113–28. http://dx.doi.org/10.2528/pier14062904.

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25

Hiptmair, R. "Multigrid Method for Maxwell's Equations." SIAM Journal on Numerical Analysis 36, no. 1 (January 1998): 204–25. http://dx.doi.org/10.1137/s0036142997326203.

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26

Redžić, D. V. "Are Maxwell's equations Lorentz-covariant?" European Journal of Physics 38, no. 1 (October 31, 2016): 015602. http://dx.doi.org/10.1088/0143-0807/38/1/015602.

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27

Songoro, H., M. Vogel, and Z. Cendes. "Keeping Time with Maxwell's Equations." IEEE Microwave Magazine 11, no. 2 (April 2010): 42–49. http://dx.doi.org/10.1109/mmm.2010.935779.

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28

Graham, E. B., J. Pierrus, and R. E. Raab. "Multipole moments and Maxwell's equations." Journal of Physics B: Atomic, Molecular and Optical Physics 25, no. 21 (November 14, 1992): 4673–84. http://dx.doi.org/10.1088/0953-4075/25/21/030.

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29

Petropavlovsky, S. V., and S. V. Tsynkov. "Quasi-Lacunae of Maxwell's Equations." SIAM Journal on Applied Mathematics 71, no. 4 (January 2011): 1109–22. http://dx.doi.org/10.1137/100798041.

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30

Engheta, N. "150 years of Maxwell's equations." Science 349, no. 6244 (July 9, 2015): 136–37. http://dx.doi.org/10.1126/science.aaa7224.

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31

Turnbull, G. "Maxwell's equations [Scanning Our Past]." Proceedings of the IEEE 101, no. 7 (July 2013): 1801–5. http://dx.doi.org/10.1109/jproc.2013.2263616.

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32

Arbab, A. I., and Norah Alsaawi. "Maxwell's equations of dual photon." Optik 184 (May 2019): 499–507. http://dx.doi.org/10.1016/j.ijleo.2019.03.066.

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33

Pradhan, T. "Maxwell's equations from geometrical optics." Physics Letters A 122, no. 8 (June 1987): 397–98. http://dx.doi.org/10.1016/0375-9601(87)90735-3.

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34

Lin, Qun, and Ningning Yan. "Global superconvergence for Maxwell's equations." Mathematics of Computation 69, no. 229 (March 10, 1999): 159–77. http://dx.doi.org/10.1090/s0025-5718-99-01131-x.

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35

Upadhyay, C. S. "On Schelkunoff Symmetrical Maxwell's Equations." IETE Journal of Research 35, no. 5 (September 1989): 274–77. http://dx.doi.org/10.1080/03772063.1989.11436826.

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36

Guillemot, M. G. "Completing Maxwell's equations by symmetrization." Europhysics Letters (EPL) 53, no. 2 (January 2001): 155–61. http://dx.doi.org/10.1209/epl/i2001-00130-3.

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37

Kinzer, E. T., and J. Fukai. "Weber's force and Maxwell's equations." Foundations of Physics Letters 9, no. 5 (October 1996): 457–61. http://dx.doi.org/10.1007/bf02190049.

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38

Vasheghani, A., and N. Riazi. "Isovector solitons and Maxwell's equations." International Journal of Theoretical Physics 35, no. 3 (March 1996): 587–91. http://dx.doi.org/10.1007/bf02082826.

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39

Hyman, James M., and Mikhail Shashkov. "Mimetic Discretizations for Maxwell's Equations." Journal of Computational Physics 151, no. 2 (May 1999): 881–909. http://dx.doi.org/10.1006/jcph.1999.6225.

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40

Hillion, Pierre. "Beware of Maxwell's Divergence Equations." Journal of Computational Physics 132, no. 1 (March 1997): 154–55. http://dx.doi.org/10.1006/jcph.1996.5629.

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41

Buchanan, W. J., and N. K. Gupta. "Maxwell's Equations in the 21st Century." International Journal of Electrical Engineering & Education 30, no. 4 (October 1993): 343–53. http://dx.doi.org/10.1177/002072099303000408.

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Maxwell's equations in the 21st Century The finite-difference time-domain method is a novel method for solving Maxwell's curl equations, especially when parallel-processing techniques are applied. The next generation of computers will bring a revolution by exploiting the use of parallel processing in computation to the maximum.

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42

Jefimenko, Oleg D. "On the Relativistic Invariance of Maxwell's Equation." Zeitschrift für Naturforschung A 54, no. 10-11 (November 1, 1999): 637–44. http://dx.doi.org/10.1515/zna-1999-10-1113.

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It is common knowledge that Maxwell's electromagnetic equations are invariant under relativistic transformations. However the relativistic invariance of Maxwell's equations has certain heretofore over-looked peculiarities. These peculiarities point out to the need of reexamining the physical significance of some basic electromagnetic formulas and equations.

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43

Lin, T. W., and H. Lin. "Newton's Laws of Motion Based Substantial Aether Theory for Electro-Magnetic Wave." Journal of Mechanics 30, no. 4 (March 13, 2014): 435–42. http://dx.doi.org/10.1017/jmech.2014.18.

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AbstractEven though electro-magnetic wave can be calculated from Maxwell's equations, the cause of electro-magnetic waves has not been fully understood. This paper proposes a Newton's laws of motion based aether theory to derive identical results as those from Maxwell's equations for free field. The authors suggest that every aether particle has a mass and occupies a volume in space. Every aether particle has translational movement and particle spin movement. The translational movement is similar to the gas particle moving in the air and it does not produce an electro-magnetic wave. The particle spin movement generates shear and a spin wave that will be shown to have the same results as Maxwell's equations. Detailed derivation of electro-magnetic wave solutions from the proposed aether theory and Maxwell's equations is presented in this paper to show the validation of this model.

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44

Chubykalo, Andrew E., and Roman Smirnov-Rueda. "Convection Displacement Current and Generalized Form of Maxwell–Lorentz Equations." Modern Physics Letters A 12, no. 01 (January 10, 1997): 1–24. http://dx.doi.org/10.1142/s0217732397000029.

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Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in the framework of Maxwellian theory, a novel convection displacement current is considered as additional and complementary to the famous Maxwell displacement current. It is shown that this form of the Maxwell–Lorentz equations is similar to that proposed by Hertz for electrodynamics of bodies in motion. Original Maxwell's equations can be considered as a valid approximation for a continuous and closed (or going to infinity) conduction current. It is also proved that our novel form of the Maxwell–Lorentz equations is relativistically invariant. In particular, a relativistically invariant gauge for quasistatic fields has been found to replace the non-invariant Coulomb gauge. The new gauge condition contains the famous relationship between electric and magnetic potentials for one uniformly moving charge that is usually attributed to the Lorentz transformations. Thus, for the first time, using the convection displacement current, a physical interpretation is given to the relationship between the components of the four-vector of quasistatic potentials. A rigorous application of the new gauge transformation with the Lorentz gauge transforms the basic field equations into a pair of differential equations responsible for longitudinal and transverse fields, respectively. The longitudinal components can be interpreted exclusively from the standpoint of the instantaneous "action at a distance" concept and leads to necessary conceptual revision of the conventional Faraday–Maxwell field. The concept of electrodynamics dualism is proposed for self-consistent classical electrodynamics. It implies simultaneous coexistence of instantaneous long-range (longitudinal) and Faraday–Maxwell short-range (transverse) interactions that resembles in this aspect the basic idea of Helmholtz's electrodynamics.

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45

Hussain, M. G. M. "A comparison of transient solutions of Maxwell's equations to that of the modified Maxwell's equations." IEEE Transactions on Electromagnetic Compatibility 34, no. 4 (1992): 482–86. http://dx.doi.org/10.1109/15.179282.

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46

Inskeep, Warren H. "Notizen: On Electromagnetic Spinors and Quantum Theory." Zeitschrift für Naturforschung A 43, no. 7 (July 1, 1988): 695–96. http://dx.doi.org/10.1515/zna-1988-0715.

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Abstract The Maxwell theory is related to the Dirac theory by two heuristic arguments based on electromagnetic spinors. First, given the condition to have spinors, if the free field Maxwell's equations are satisfied, then the spinors satisfy the Weyl equations. Second, a sufficient condition for electromagnetic spinors directly gives the Weyl equations with the usual substitutions for momentum and energy. It is proposed that the heuristic nature of the first argument is related to the idea of a point having a more general symmetry than a sphere.

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47

Kalauni, Pushpa, and J. C. A. Barata. "Reconstruction of symmetric Dirac–Maxwell equations using nonassociative algebra." International Journal of Geometric Methods in Modern Physics 12, no. 03 (February 27, 2015): 1550029. http://dx.doi.org/10.1142/s0219887815500292.

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In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the existence of magnetic monopoles for symmetrizing the Maxwell equations. In the present work, we obtain the fully symmetric Dirac–Maxwell's equations (i.e. with electric and magnetic charges and currents) as a single equation by using 4 × 4 matrix presentation of fields and derivative operators. This matrix representation has been derived with the help of the algebraic properties of quaternions and octonions. Such description gives a compact representation of electric and magnetic counterparts of the field in a single equation.

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48

Shaw, Simon. "Finite Element Approximation of Maxwell's Equations with Debye Memory." Advances in Numerical Analysis 2010 (December 27, 2010): 1–28. http://dx.doi.org/10.1155/2010/923832.

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Maxwell's equations in a bounded Debye medium are formulated in terms of the standard partial differential equations of electromagnetism with a Volterra-type history dependence of the polarization on the electric field intensity. This leads to Maxwell's equations with memory. We make a correspondence between this type of constitutive law and the hereditary integral constitutive laws from linear viscoelasticity, and we are then able to apply known results from viscoelasticity theory to this Maxwell system. In particular, we can show long-time stability by shunning Gronwall's lemma and estimating the history kernels more carefully by appeal to the underlying physical fading memory. We also give a fully discrete scheme for the electric field wave equation and derive stability bounds which are exactly analogous to those for the continuous problem, thus providing a foundation for long-time numerical integration. We finish by also providing error bounds for which the constant grows, at worst, linearly in time (excluding the time dependence in the norms of the exact solution). Although the first (mixed) finite element error analysis for the Debye problem was given by Li (2007), this seems to be the first time sharp constants have been given for this problem.

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49

Chen, Xinfu, and Avner Friedman. "Maxwell's Equations in a Periodic Structure." Transactions of the American Mathematical Society 323, no. 2 (February 1991): 465. http://dx.doi.org/10.2307/2001542.

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50

Volkov, B. "Stochastic Levy Divergence and Maxwell's Equations." Mathematics and Mathematical Modeling 15, no. 5 (October 3, 2015): 1–16. http://dx.doi.org/10.7463/mathm.0515.0820322.

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