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1
Sugaya, R. "Momentum-space diffusion due to resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma." Journal of Plasma Physics 56, no. 2 (October 1996): 193–207. http://dx.doi.org/10.1017/s0022377800019206.
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The momentum-space diffusion equation and the kinetic wave equation for resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma are derived from the relativistic Vlasov–Maxwell equations by perturbation theory. The p-dependent diffusion coefficient and the nonlinear wave—wave coupling coefficient are given in terms of third-order tensors which are amenable to analysis. The transport equations describing energy and momentum transfer between waves and particles are obtained by momentum-space integration of the momentum-space diffusion equation, and are expressed in terms of the nonlinear wave—wave coupling coefficient in the kinetic wave equation. The conservation laws for the total energy and momentum densities of waves and particles are verified from the kinetic wave equation and the transport equations. These equations are very useful for the theoretical analysis of transport phenomena or the acceleration and generation of high-energy or relativistic particles caused by quasi-linear and resonant wave—wave scattering processes.
2
Vegt, Wim. "4-Dimensional Relativistic Quantum Mechanical Equilibrium in Gravitational-Electromagnetic Confinements." International Science Review 1, no. 2 (November 21, 2020): 34–61. http://dx.doi.org/10.47285/isr.v1i2.59.
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An important milestone in quantum physics was reached by the publication of the Relativistic Quantum Mechanical Dirac Equation in 1928. However, the Dirac equation represents a 1-Dimensional quantum mechanical equation which is unable to describe the 4-Dimensional Physical Reality. In this article, the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation expressed in the vector probability functions and the complex conjugated vector probability function will be discussed. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time more than 200 years ago before the Dirac Equation had been published. Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics was in Harmony with Science and Religion. Newton found the concept of “Universal Equilibrium” which he mentioned in his famous third equation, Action = Reaction. This article presents a New Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity. The physical concept of quantum mechanical probability waves has been originated during the famous 5th Solvay Conference in 1927. During that period there were several circumstances that came together and made it possible to create a unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrödinger published his well-known material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrödinger's wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell, this was impossible. According to Maxwell's equations, Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason, these material waves in Schrödinger's wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrödinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function. In the New Theory, it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined Electromagnetic waves could not be considered to be the material waves expressed in Schrödinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge, and magnetic spin at discrete values.
3
Sugaya, Reiji. "Velocity-space diffusion due to resonant wave–wave scattering of electromagnetic and electrostatic waves in a plasma." Journal of Plasma Physics 45, no. 1 (February 1991): 103–13. http://dx.doi.org/10.1017/s002237780001552x.
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The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation.
4
Vegt, Wim. "The Illusion of Quantum Mechanical Probability Waves." European Journal of Engineering Research and Science 5, no. 10 (October 11, 2020): 1212–24. http://dx.doi.org/10.24018/ejers.2020.5.10.2153.
Full textAbstract:
An important milestone in quantum physics has been reached by the publication of the Relativistic Quantum Mechanical Dirac Equation in 1928. However, the Dirac equation represents a 1-Dimensional quantum mechanical equation which is unable to describe the 4-Dimensional Physical Reality.
In this article the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation expressed in the vector probability functions and the complex conjugated vector probability function will be published. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time 300 years ago. More than 200 years ago before the Dirac Equation had been published.
A Return to the Inception of Physics. The time of Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics which was in Harmony with Science and Religion. The Universal Path, the Leitmotiv, the Universal Concept in Physics. Newton found the concept of “Universal Equilibrium” which he formulated in his famous third equation Action = - Reaction. This article presents a New Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity.
The physical concept of quantum mechanical probability waves has been created during the famous 1927 5th Solvay Conference. During that period there were several circumstances which came together and made it possible to create an unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrödinger published his famous material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrödinger’s wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell this was impossible. According to Maxwell’s equations Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason, these material waves in Schrödinger’s wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrödinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function.
In the New Theory it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined Electromagnetic waves could not be considered to be the material waves expressed in Schrödinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge and magnetic spin at discrete values.
5
Vegt, Wim. "The Illusion of Quantum Mechanical Probability Waves." European Journal of Engineering and Technology Research 5, no. 10 (October 11, 2020): 1212–24. http://dx.doi.org/10.24018/ejeng.2020.5.10.2153.
Full textAbstract:
An important milestone in quantum physics has been reached by the publication of the Relativistic Quantum Mechanical Dirac Equation in 1928. However, the Dirac equation represents a 1-Dimensional quantum mechanical equation which is unable to describe the 4-Dimensional Physical Reality.
In this article the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation expressed in the vector probability functions and the complex conjugated vector probability function will be published. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time 300 years ago. More than 200 years ago before the Dirac Equation had been published.
A Return to the Inception of Physics. The time of Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics which was in Harmony with Science and Religion. The Universal Path, the Leitmotiv, the Universal Concept in Physics. Newton found the concept of “Universal Equilibrium” which he formulated in his famous third equation Action = - Reaction. This article presents a New Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity.
The physical concept of quantum mechanical probability waves has been created during the famous 1927 5th Solvay Conference. During that period there were several circumstances which came together and made it possible to create an unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrödinger published his famous material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrödinger’s wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell this was impossible. According to Maxwell’s equations Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason, these material waves in Schrödinger’s wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrödinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function.
In the New Theory it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined Electromagnetic waves could not be considered to be the material waves expressed in Schrödinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge and magnetic spin at discrete values.
6
SALTI, MUSTAFA, and ALI HAVARE. "ON THE EQUIVALENCE OF THE MASSLESS DKP EQUATION AND THE MAXWELL EQUATIONS IN THE SHUWER." Modern Physics Letters A 20, no. 06 (February 28, 2005): 451–65. http://dx.doi.org/10.1142/s0217732305015768.
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In this paper, a general relativistic wave equation is written to deal with electromagnetic waves in the background of the Shuwer. We obtain the exact form of this equation in a second-order form. On the other hand, by using spinor form of the Maxwell equations the propagation problem is reduced to the solution of the second-order differential equation of complex combination of the electric and magnetic fields. For these two different approaches, we obtain the spinors in terms of field strength tensor. We show that the Maxwell equations are equivalence to the mDKP equation in the Shuwer.
7
Gevorkyan E. A. "Transverse components of the electromagnetic field in a waveguide with modulated in space and in time magnetodielectric filling." Optics and Spectroscopy 130, no. 10 (2022): 1293. http://dx.doi.org/10.21883/eos.2022.10.54865.3813-22.
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The propagation of transverse magnetic (TM) and transverse electric (TE) electromagnetic waves in a regular ideal waveguide of arbitrary cross section is considered. It is assumed that the permittivity and permeability of the magnetodielectric filling of the waveguide are functions that depend on the coordinate and time. Analytical expressions for the transverse components of the magnetic and electric vectors of the TM- and TE-fields in the waveguide are obtained from the system of Maxwell equations. They are expressed in terms of the longitudinal components of the electric and magnetic vectors, which describe the transverse magnetic and transverse electric fields in the waveguide. For the above longitudinal components of the electric and magnetic vectors, the wave equations are given, which are also obtained from the system of Maxwell's equations. Keywords: Maxwell equations, propagation of electromagnetic waves, waveguide with modulated filling, transverse components, Helmholtz equations, Dirichlet and Neumann problems.
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Bruce, S. A. "Maxwell-Like Equations for Free Dirac Electrons." Zeitschrift für Naturforschung A 73, no. 4 (March 28, 2018): 331–35. http://dx.doi.org/10.1515/zna-2017-0328.
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AbstractIn this article, we show that the wave equation for a free Dirac electron can be represented in a form that is analogous to Maxwell’s electrodynamics. The electron bispinor wavefunction is explicitly expressed in terms of its real and imaginary components. This leads us to incorporate into it appropriate scalar and pseudo-scalar fields in advance, so that a full symmetry may be accomplished. The Dirac equation then takes on a form similar to that of a set of inhomogeneous Maxwell’s equations involving a particular self-source. We relate plane wave solutions of these equations to waves corresponding to free Dirac electrons, identifying the longitudinal component of the electron motion, together with the corresponding Zitterbewegung (“trembling motion”).
9
Li, Qingsong, and Simon Maher. "Deriving an Electric Wave Equation from Weber’s Electrodynamics." Foundations 3, no. 2 (June 7, 2023): 323–34. http://dx.doi.org/10.3390/foundations3020024.
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Weber’s electrodynamics presents an alternative theory to the widely accepted Maxwell–Lorentz electromagnetism. It is founded on the concept of direct action between particles, and has recently gained some momentum through theoretical and experimental advancements. However, a major criticism remains: the lack of a comprehensive electromagnetic wave equation for free space. Our motivation in this research article is to address this criticism, in some measure, by deriving an electric wave equation from Weber’s electrodynamics based on the axiom of vacuum polarization. Although this assumption has limited experimental evidence and its validity remains a topic of debate among researchers, it has been shown to be useful in the calculation of various quantum mechanical phenomena. Based on this concept, and beginning with Weber’s force, we derive an expression which resembles the familiar electric field wave equation derived from Maxwell’s equations.
10
Fedele, Renato. "From Maxwell's theory of Saturn's rings to the negative mass instability." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1871 (January 25, 2008): 1717–33. http://dx.doi.org/10.1098/rsta.2007.2181.
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The impact of Maxwell's theory of Saturn's rings, formulated in Aberdeen ca 1856, is discussed. One century later, Nielsen, Sessler and Symon formulated a similar theory to describe the coherent instabilities (in particular, the negative mass instability) exhibited by a charged particle beam in a high-energy accelerating machine. Extended to systems of particles where the mutual gravitational attraction is replaced by the electric repulsion, Maxwell's approach was the conceptual basis to formulate the kinetic theory of coherent instability (Vlasov–Maxwell system), which, in particular, predicts the stabilizing role of the Landau damping. However, Maxwell's idea was so fertile that, later on, it was extended to quantum-like models (e.g. thermal wave model), providing the quantum-like description of coherent instability (Schrödinger–Maxwell system) and its identification with the modulational instability (MI). The latter has recently been formulated for any nonlinear wave propagation governed by the nonlinear Schrödinger equation, as in the statistical approach to MI (Wigner–Maxwell system). It seems that the above recent developments may provide a possible feedback to Maxwell's original idea with the extension to quantum gravity and cosmology.
11
Weber, Hannes, Omar Maj, and Emanuele Poli. "Wigner-function-based solution schemes for electromagnetic wave beams in fluctuating media." Journal of Computational Electronics 20, no. 6 (October 19, 2021): 2199–208. http://dx.doi.org/10.1007/s10825-021-01791-8.
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AbstractElectromagnetic waves are described by Maxwell’s equations together with the constitutive equation of the considered medium. The latter equation in general may introduce complicated operators. As an example, for electron cyclotron (EC) waves in a hot plasma, an integral operator is present. Moreover, the wavelength and computational domain may differ by orders of magnitude making a direct numerical solution unfeasible, with the available numerical techniques. On the other hand, given the scale separation between the free-space wavelength $$\lambda _0$$ λ 0 and the scale L of the medium inhomogeneity, an asymptotic solution for a wave beam can be constructed in the limit $$\kappa = 2\pi L / \lambda _0 \rightarrow \infty$$ κ = 2 π L / λ 0 → ∞ , which is referred to as the semiclassical limit. One example is the paraxial Wentzel-Kramer-Brillouin (pWKB) approximation. However, the semiclassical limit of the wave field may be inaccurate when random short-scale fluctuations of the medium are present. A phase-space description based on the statistically averaged Wigner function may solve this problem. The Wigner function in the semiclassical limit is determined by the wave kinetic equation (WKE), derived from Maxwell’s equations. We present a paraxial expansion of the Wigner function around the central ray and derive a set of ordinary differential equations (phase-space beam-tracing equations) for the Gaussian beam width along the central ray trajectory.
12
ABREU, E. M. C., C. PINHEIRO, S. A. DINIZ, and F. C. KHANNA. "ELECTROMAGNETIC WAVES, GRAVITATIONAL COUPLING AND DUALITY ANALYSIS." Modern Physics Letters A 21, no. 02 (January 20, 2006): 151–58. http://dx.doi.org/10.1142/s0217732306019207.
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In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave equations are computed such that the electric field does not induce the magnetic field and vice versa. In a gravitational field, we analyze the Maxwell equations and the corresponding electromagnetic waves. A continuity equation is presented. A commutative and noncommutative analysis of the electromagnetic duality is described.
13
RAUCH, JEFFREY. "OPTIMAL FOCUSING FOR MONOCHROMATIC SCALAR AND ELECTROMAGNETIC WAVES." Reviews in Mathematical Physics 23, no. 08 (September 2011): 839–63. http://dx.doi.org/10.1142/s0129055x11004448.
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For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation, the electric field maximizing the value at the origin follows longitude lines on the sphere at infinity. In dimension d = 3, the highest electric field for Maxwell's equation is smaller by a factor 2/3 than the highest corresponding scalar waves. The highest electric field densities on the balls BR(0) occur as R → 0. The density dips to half max at R approximately equal to one third the wavelength. For these small R, the extremizing fields are identical to those that attain the maximum field intensity at the origin.
14
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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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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Tsidulko, Yuriy A., and Ivan S. Chernoshtanov. "Nonlinear Stage of Alfvén Ion-Cyclotron Instability." Siberian Journal of Physics 5, no. 3 (October 1, 2010): 90–94. http://dx.doi.org/10.54362/1818-7919-2010-5-3-90-94.
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A model describing nonlinear saturated state of Alfvén ion-cyclotron instability is presented. Spirally symmetric exact solutions of Vlasov – Maxwell equations describing nonlinear Alfvén waves in collisionless plasmas are presented. On their basis the equation describing ion distribution function in non-linear equilibrium of a weak-collision plasma with the wave is obtained, taking into account an uniform fast ion injection, ion drag caused by electrons and neglecting ion angle scattering. A solution of this equation and relations of the wave parameters with the injection parameters are obtained analytically in the case of the infinitely narrow velocity distribution of the injected ions
17
KOLOSNITSYN, N. I. "ELECTROMAGNETIC RADIATION INDUCED BY A GRAVITATIONAL WAVE." International Journal of Modern Physics D 04, no. 02 (April 1995): 207–13. http://dx.doi.org/10.1142/s0218271895000144.
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Conversion of a gravitational wave into an electromagnetic one in a laser coherent emission field is studied. As a result two electromagnetic waves are created. For calculation the Maxwell equations in three-dimensional vector form are used. Optimal detection of the gravitational wave is discussed. In a particular case it is the laser interferometric antenna. This approach is identical to those based on integration of the isotropic geodesic equation, the eikonal equation, giving the three-pulsing response of the electromagnetic signal obtained by Estabrook and Wahlquist. It also results in the matrix method developed by Vinet for calculation of laser interferometric antennae.
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Cai, Wenying, Fuhao Qin, and Gerard T. Schuster. "Electromagnetic velocity inversion using 2-D Maxwell’s equations." GEOPHYSICS 61, no. 4 (July 1996): 1007–21. http://dx.doi.org/10.1190/1.1444023.
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We adapt the wave‐equation traveltime inversion (WT) method to the reconstruction of the dielectric distribution from crosswell radar traveltime data. The data misfit gradient is computed using finite‐difference solutions to the 2-D Maxwell’s equations. An advantage of the wave‐equation method over ray‐tracing radar tomography is that it accounts for scattering and diffusion effects and works well in both resistive and moderately conductive rocks. Comparisons with ray‐tracing tomography show that the wave equation method is more robust and accurate when the rock conductivity is larger than .002 S/m. The methods are about equally effective when the conductivity is less than or equal to .001 S/m. The major disadvantage of the wave equation scheme is that it generally requires at least several orders of magnitude more computational time than ray tracing. We also derive the general equation for the waveform radar inversion method, which is closely related to the equations for the WT method and prestack radar migration.
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Zareei, Ahmad, and Mohammad-Reza Alam. "Cloaking in shallow-water waves via nonlinear medium transformation." Journal of Fluid Mechanics 778 (July 30, 2015): 273–87. http://dx.doi.org/10.1017/jfm.2015.350.
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A major obstacle in designing a perfect cloak for objects in shallow-water waves is that the linear transformation media scheme (also known as transformation optics) requires spatial variations of two independent medium properties. In the Maxwell’s equation and for the well-studied problem of electromagnetic cloaking, these two properties are permittivity and permeability. Designing an anisotropic material with both variable permittivity and variable permeability, while challenging, is achievable. On the other hand, for long gravity waves, whose governing equation maps one-to-one to the single polarization Maxwell’s equations, the two required spatially variable properties are the water depth and the gravitational acceleration; in this case changing the gravitational acceleration is simply impossible. Here we present a nonlinear transformation that only requires the change in one of the medium properties, which, in the case of shallow-water waves, is the water depth, while keeping the gravitational acceleration constant. This transformation keeps the governing equation perfectly intact and, if the cloak is large enough, asymptotically satisfies the necessary boundary conditions. We show that with this nonlinear transformation an object can be cloaked from any wave that merely satisfies the long-wave assumption. The presented transformation can be applied as well for the design of non-magnetic optical cloaks for electromagnetic waves.
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BENCI, VIERI, and DONATO FORTUNATO FORTUNATO. "SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS." Reviews in Mathematical Physics 14, no. 04 (April 2002): 409–20. http://dx.doi.org/10.1142/s0129055x02001168.
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This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.
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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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Bondarenko, Evgen. "Two basic systems of maxwell’s equations in a rotating frame: application in theory of ring laser gyro." MECHANICS OF GYROSCOPIC SYSTEMS, no. 40 (December 10, 2020): 64–73. http://dx.doi.org/10.20535/0203-3771402020249054.
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In the paper, using a linear in angular velocity approximation, two basic well-known systems of Maxwell’s equations in a uniformly rotating frame of reference are considered. The first system of equations was first obtained in the work [L. I. Schiff, Proc. Natl. Acad. Sci. USA 25, 391 (1939)] on the base of use of the formalism of the theory of general relativity, and the second one – in the work [W. M. Irvine, Physica 30, 1160 (1964)] on the base of use of the method of orthonormal tetrad in this theory. In the paper, in the approximation of plane waves, these two vectorial systems of Maxwell’s equations are simplified and rewritten in cylindrical coordinates in scalar component form in order to find the lows of propagation of transversal components of electromagnetic waves in a circular resonator of ring laser gyro in the case of its rotation about sensitivity axis. On the base of these two simplified systems of Maxwell’s equations, the well-known wave equation and its analytical solutions for the named transversal components are obtained. As a result of substitution of these solutions into the first and second simplified systems of Maxwell’s equations, it is revealed that they satisfy only the second one. On this basis, the conclusion is made that the second system of Maxwell’s equations is more suitable for application in the theory of ring laser gyro than the first one.
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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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ALLAIRE, GRÉGOIRE, MARIAPIA PALOMBARO, and JEFFREY RAUCH. "DIFFRACTION OF BLOCH WAVE PACKETS FOR MAXWELL'S EQUATIONS." Communications in Contemporary Mathematics 15, no. 06 (November 19, 2013): 1350040. http://dx.doi.org/10.1142/s0219199713500405.
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We study, for times of order 1/h, solutions of Maxwell's equations in an [Formula: see text] modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct accurate approximate solutions of three scale WKB type. The leading profile is both transported at the group velocity and dispersed by a Schrödinger equation given by the quadratic approximation of the Bloch dispersion relation. A weak ray average hypothesis guarantees stability. Compared to earlier work on scalar wave equations, the generator is no longer elliptic. Coercivity holds only on the complement of an infinite-dimensional kernel. The system structure requires many innovations.
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WILLETT, J. E., B. BOLON, U. H. HWANG, and Y. AKTAS. "Re-examination of the one-dimensional theory of a Raman free-electron laser." Journal of Plasma Physics 66, no. 5 (November 2001): 301–13. http://dx.doi.org/10.1017/s0022377801001519.
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A new one-dimensional analysis of the collective interaction in a free-electron laser with combined helical wiggler and uniform axial magnetic fields is presented. Maxwell's curl relations and the cold-fluid equations are employed, with the appropriate form of solution for right and left circularly polarized electromagnetic waves and space-charge waves. A set of three linear homogeneous algebraic equations for the electric field amplitudes of the three propagating waves is derived. This set may be employed to obtain the general dispersion relation in the form of a tenth-degree polynomial equation. With the left circular wave assumed to be nonresonant, the dispersion relation reduces to a seventh-degree polynomial equation corresponding to four space-charge modes and three right circular modes. The results of a numerical study of the spatial growth rate and radiation frequency are presented.
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Chanyal, B. C. "Quaternionic approach on the Dirac–Maxwell, Bernoulli and Navier–Stokes equations for dyonic fluid plasma." International Journal of Modern Physics A 34, no. 31 (November 10, 2019): 1950202. http://dx.doi.org/10.1142/s0217751x19502026.
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By applying the Hamilton’s quaternion algebra, we propose the generalized electromagnetic-fluid dynamics of dyons governed by the combination of the Dirac–Maxwell, Bernoulli and Navier–Stokes equations. The generalized quaternionic hydro-electromagnetic field of dyonic cold plasma consists of electrons and magnetic monopoles in which there exist dual-mass and dual-charge species in the presence of dyons. We construct the conservation of energy and conservation of momentum equations by equating the quaternionic scalar and vector parts for generalized hydro-electromagnetic field of dyonic cold plasma. We propose the quaternionic form of conservation of energy is related to the Bernoulli-like equation while the conservation of momentum is related to Navier–Stokes-like equation for dynamics of dyonic plasma fluid. Further, the continuity equation, i.e. the conservation of electric and magnetic charges with the dynamics of hydro-electric and hydro-magnetic flow of conducting cold plasma fluid is also analyzed. The quaternionic formalism for dyonic plasma wave emphasizes that there are two types of waves propagation, namely the Langmuir-like wave propagation due to electrons, and the ’t Hooft–Polyakov-like wave propagation due to magnetic monopoles.
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Khadka, Chandra Bahadur. "Relative Nature of Electric Permittivity and Magnetic Permeability of Electromagnetic Wave." Indian Journal of Advanced Physics 1, no. 3 (April 30, 2022): 17–25. http://dx.doi.org/10.54105/ijap.c1021.041322.
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This research is about the special theory of relativity on electric permittivity and magnetic permeability of electromagnetic wave. For this, Four Maxwell's electromagnetic equations play an important role. James Clerk Maxwell suggested that the light travel as electromagnetic wave which require no material medium for propagation. The speed of light (C) in free space is always constant and is independent of the speed of source or observer or the relative motion of the inertial system and has velocity 'C' given by . So velocity of electromagnetic waves depend on obsolute magnetic permeability and obsolute electric permittivity of free space. These two physical quantities rely on relative motion of inertial system. So are not obsolute quantity but are dependent upon the relative motion between the observer and the phenomenon observed. Electric and magnetic field of a charge rely upon the value of obsolute electric permittivity of medium. Concisely, are variant quantity. Consequently electric and magnetic field get relative for electromagnetic wave. That is electric and magnetic field depend on relative motion of inertial system for electromagnetic waves.
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Akhmeteli, Andrey. "Some Classical Models of Particles and Quantum Gauge Theories." Quantum Reports 4, no. 4 (November 3, 2022): 486–508. http://dx.doi.org/10.3390/quantum4040035.
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The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodynamics), spinor electrodynamics (Dirac–Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, and the resulting modified Maxwell equations describe the independent evolution of the electromagnetic field. Similar results were obtained for spinor electrodynamics. Three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and the remaining component can be made real by a gauge transformation. A similar result was obtained for the Dirac equation in the Yang–Mills field. As quantum gauge theories play a central role in modern physics, the approach of this article may be sufficiently general. One-particle wave functions can be modeled as plasma-like collections of a large number of particles and antiparticles. This seems to enable the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative.
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MIRONOV, VICTOR L., and SERGEY V. MIRONOV. "OCTONIC FIRST-ORDER EQUATIONS OF RELATIVISTIC QUANTUM MECHANICS." International Journal of Modern Physics A 24, no. 22 (September 10, 2009): 4157–67. http://dx.doi.org/10.1142/s0217751x09045480.
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We demonstrate a generalization of relativistic quantum mechanics using eight-component octonic wave function and octonic spatial operators. It is shown that the second-order equation for octonic wave function describing particles with spin 1/2 can be reformulated in the form of a system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special types of wave functions the second-order equation can be reduced to the single first-order equation analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not have quantum fields.
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SUCU, YUSUF, and NURI UNAL. "SOLUTION OF MASSLESS SPIN ONE WAVE EQUATION IN ROBERTSON–WALKER SPACE–TIME." International Journal of Modern Physics A 17, no. 08 (March 30, 2002): 1137–47. http://dx.doi.org/10.1142/s0217751x02005852.
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We generalize the quantum spinor wave equation for photon into the curved space–time and discuss the solutions of this equation in Robertson–Walker space–time and compare them with the solution of the Maxwell equations in the same space–time.
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BINI, DONATO, SALVATORE CAPOZZIELLO, and GIAMPIERO ESPOSITO. "GRAVITATIONAL WAVES ABOUT CURVED BACKGROUNDS: A CONSISTENCY ANALYSIS IN DE SITTER SPACETIME." International Journal of Geometric Methods in Modern Physics 05, no. 07 (November 2008): 1069–83. http://dx.doi.org/10.1142/s0219887808003211.
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Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the de Donder gauge is imposed, its preservation under infinitesimal spacetime diffeomorphisms is guaranteed if and only if the associated covector is ruled by a second-order hyperbolic operator which is the classical counterpart of the ghost operator in quantum gravity. In such a wave equation, the Ricci term has opposite sign with respect to the wave equation for Maxwell theory in the Lorenz gauge. We are, nevertheless, able to relate the solutions of the two problems, and the algorithm is applied to the case when the curved background geometry is the de Sitter spacetime. Such vector wave equations are studied in two different ways: (i) an integral representation, (ii) through a solution by factorization of the hyperbolic equation. The latter method is extended to the wave equation of metric perturbations in the de Sitter spacetime. This approach is a step towards a general discussion of gravitational waves in the de Sitter spacetime and might assume relevance in cosmology in order to study the stochastic background emerging from inflation.
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Firdaus, R. A., M. Khoiro, Dzulkiflih, V. Rahayu, and Mutmainnah. "Two Dimensional Simulation of Electromagnetic Waves on Metal Materials Using the FDTD Method." Journal of Physics: Conference Series 2392, no. 1 (December 1, 2022): 012037. http://dx.doi.org/10.1088/1742-6596/2392/1/012037.
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Abstract It is challenging to picture the physical phenomenon known as electromagnetic wave simulation. The purpose of this work is to model the propagation of electromagnetic waves on a two-dimensional medium. FDTD is a method that is quite relevant to be used in visualizing electromagnetic waves. One can utilise Maxwell's equations to describe discrete electromagnetic waves having TM mode. The simulation is in the form of a Gaussian pulse with the magnetic field H and the electric field E having position and time domains, respectively. The proposed simulation conditions have considered the program's boundary conditions and numerical stability. The differential equation method methodology is used in the FDTD method. The simulation results show that the wave without PML is impeccably reflected, and with PML, the wave is reflected by the material utilized. Materials with high conductivity will make the waves decay and reduce their intensity. This research can be used in the investigation of materials and communication media innovation.
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BAL, GUILLAUME, and OLIVIER PINAUD. "IMAGING USING TRANSPORT MODELS FOR WAVE–WAVE CORRELATIONS." Mathematical Models and Methods in Applied Sciences 21, no. 05 (May 2011): 1071–93. http://dx.doi.org/10.1142/s0218202511005258.
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We consider the imaging of objects buried in unknown heterogeneous media. The medium is probed by using classical (e.g. acoustic or electromagnetic) waves. When heterogeneities in the medium become too strong, inversion methodologies based on a microscopic description of wave propagation (e.g. a wave equation or Maxwell's equations) become strongly dependent on the unknown details of the heterogeneous medium. In some situations, it is preferable to use a macroscopic model for a quantity that is quadratic in the wave fields. Here, such macroscopic models take the form of radiative transfer equations also referred to as transport equations. They can model either the energy density of the propagating wave fields or more generally the correlation of two wave fields propagating in possibly different media. In particular, we consider the correlation of the two fields propagating in the heterogeneous medium when the inclusion is absent and present, respectively. We present theoretical and numerical results showing that reconstructions based on this correlation are more accurate than reconstructions based on measurements of the energy density.
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VASY, ANDRÁS. "DIFFRACTION BY EDGES." Modern Physics Letters B 22, no. 23 (September 10, 2008): 2287–328. http://dx.doi.org/10.1142/s0217984908017035.
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In these expository notes we explain the role of geometric optics in wave propagation on domains or manifolds with corners or edges. Both the propagation of singularities, which describes where solutions of the wave equation may be singular, and the diffractive improvement under non-focusing hypotheses, which states that in certain places the diffracted wave is more regular than a priori expected, is described. In addition, the wave equation on differential forms with natural boundary conditions, which in particular includes a formulation of Maxwell's equations, is studied.
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LESCARRET, VINCENT. "WAVE TRANSMISSION IN DISPERSIVE MEDIA." Mathematical Models and Methods in Applied Sciences 17, no. 04 (April 2007): 485–535. http://dx.doi.org/10.1142/s0218202507002005.
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The aim of this paper is to study the reflection-transmission of geometrical optic rays described by semi-linear symmetric hyperbolic systems such as the Maxwell–Lorentz equations with the anharmonic model of polarisation. The framework is both that of Donnat and Williams since we consider dispersive media and profiles with hyperbolic (imaginary) phases and elliptic phases (complex with non-null real part). We first give hypothesis close to the Maxwell equation. Then we introduce a decomposition for both profile into boundary (tangential) and normal part and we solve the so-called "microscopic" equation of the small scales for each boundary frequency. Then we show that the non-linearities generate harmonics which interact at the boundary and generate new resonant profiles with harmonic tangential frequency. Lastly we make a WKB expansion at any order and give a precise description of the correctors.
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Khutieva A. B., Akimova B. R., Beginin E. N., and Sadovnikov A. V. "Control of the direction of propagation of spin waves in an ensemble of laterally and vertically connected ferrite microstrips." Physics of the Solid State 64, no. 9 (2022): 1279. http://dx.doi.org/10.21883/pss.2022.09.54166.20hh.
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The possibility of controlling the direction of propagation of spin waves in an ensemble of laterally and vertically connected microstrips of iron-yttrium garnet (YIG) is shown by numerical modeling. Using the finite element method, the magnitude of the coupling length of spin waves in lateral and vertical geometries was calculated. The numerical value of the spin wave coupling coefficients was found by the finite element method as a result of solving a system of Maxwell equations with a magnetic permeability tensor obtained from the linearization of the Landau-Lifshitz equation. By integrating the equation of coupled waves, the possibility of changing the direction of propagation of the spin-wave signal in the structure under consideration is shown. The signal transmission spectra obtained in micromagnetic modeling indicate a change in the nature of the localization of the spin wave power in the output sections of the microwave with a change in the frequency at the input of the structure. The system of laterally and vertically connected microwave diodes is an element of interconnections for three-dimensional topologies of magnon networks, while demonstrating the functionality of spatial-frequency signal demultiplexing. Keywords: spin waves, magnonics, lateral structures, magnonic crystal, ensembles of related structures. Keywords: spin waves, magnonics, lateral structures, magnonic crystal, ensembles of related structures.
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Tuomela, Jukka. "Fourth-order schemes for the wave equation, Maxwell equations, and linearized elastodynamic equations." Numerical Methods for Partial Differential Equations 10, no. 1 (January 1994): 33–63. http://dx.doi.org/10.1002/num.1690100104.
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Hao, Qi, and Tariq Alkhalifah. "Viscoacoustic anisotropic wave equations." GEOPHYSICS 84, no. 6 (November 1, 2019): C323—C337. http://dx.doi.org/10.1190/geo2018-0865.1.
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The wave equation plays a central role in seismic modeling, processing, imaging and inversion. Incorporating attenuation anisotropy into the acoustic anisotropic wave equations provides a choice for acoustic forward and inverse modeling in attenuating anisotropic media. However, the existing viscoacoustic anisotropic wave equations are obtained for a specified viscoacoustic model. We have developed a relatively general representation of the scalar and vector viscoacoustic wave equations for orthorhombic anisotropy. We also obtain the viscoacoustic wave equations for transverse isotropy as a special case. The viscoacoustic orthorhombic wave equations are flexible for multiple viscoacoustic models. We take into account the classic visocoacoustic models such as the Kelvin-Voigt, Maxwell, standard-linear-solid and Kjartansson models, and we derive the corresponding viscoacoustic wave equations in differential form. To analyze the wave propagation in viscoacoustic models, we derive the asymptotic point-source solution of the scalar wave equation. Numerical examples indicate a comparison of the acoustic waveforms excited by a point source in the viscoacoustic orthorhombic models and the corresponding nonattenuating model, and the effect of the attenuation anisotropy on the acoustic waveforms.
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Papas, Charles Herach. "On a differential equation for electromagnetic wave transmission in flare stars and the possible existance of cohesive wave solutions." Symposium - International Astronomical Union 137 (1990): 337–42. http://dx.doi.org/10.1017/s0074180900187972.
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Ambartsumian's celebrated hypothesis that stellar flares and other phenomena of stellar instability are due to a novel source of energy and a novel means of transporting this energy to the outer layers of the star has drawn the attention of electrodynamicists to a number of fundamental problems. One of these problems, namely the energy transport problem, is the subject of this communication. Herein, by assuming that the matter of the star is an isotropic collisionless plasma, from Maxwell's field equations and Newton's equation of motion with nonlinear Lorentz driving force, we have derived a vector differential equation for electromagnetic wave propagation. This equation contains the Debye radius and the plasma frequency as parameters, and reduces to the well-known wave equation when its nonlinear terms are neglected. We have indicated that the nonlinear equation has cohesive (solitary) wave solutions for both the longitudinal and transverse components of the electromagnetic field. Such cohesive waves are appropriate for transporting energy from the prestellar core of the star to its outer layers since they hold their shape, are free from dispersive distortion, and can carry energy in discrete amounts.
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MIRONOV, VICTOR L., and SERGEY V. MIRONOV. "SEDEONIC GENERALIZATION OF RELATIVISTIC QUANTUM MECHANICS." International Journal of Modern Physics A 24, no. 32 (December 30, 2009): 6237–54. http://dx.doi.org/10.1142/s0217751x09047739.
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We represent sixteen-component values "sedeons," generating associative noncommutative space–time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space–time operators. It is shown that the sedeonic second-order equation for the sedeonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. We showed that the sedeonic second-order wave equation can be reformulated in the form of the system of the first-order Maxwell-like equations for the massive fields. We proposed the sedeonic first-order equations analogous to the Dirac equation, which differ in space–time properties and describe several types of massive and massless particles. In particular we proposed four different equations, which could describe four types of neutrinos.
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Huang, Yunqing, Jichun Li, and Wei Yang. "Solving metamaterial Maxwell’s equations via a vector wave integro-differential equation." Computers & Mathematics with Applications 63, no. 12 (June 2012): 1597–606. http://dx.doi.org/10.1016/j.camwa.2012.03.035.
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ISLAM, SK ANARUL, A. BANDYOPADHYAY, and K. P. DAS. "Stability of ion–acoustic solitary waves in a multi-species magnetized plasma consisting of non-thermal and isothermal electrons." Journal of Plasma Physics 75, no. 5 (October 2009): 593–607. http://dx.doi.org/10.1017/s0022377809008113.
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AbstractA theoretical study of the first-order stability analysis of an ion–acoustic solitary wave, propagating obliquely to an external uniform static magnetic field, has been made in a plasma consisting of warm adiabatic ions and a superposition of two distinct populations of electrons, one due to Cairns et al. and the other being the well-known Maxwell–Boltzmann distributed electrons. The weakly nonlinear and the weakly dispersive ion–acoustic wave in this plasma system can be described by the Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation and different modified KdV-ZK equations depending on the values of different parameters of the system. The nonlinear term of the KdV-ZK equation and the different modified KdV-ZK equations is of the form [φ(1)]ν(∂φ(1)/∂ζ), where ν = 1, 2, 3, 4; φ(1) is the first-order perturbed quantity of the electrostatic potential φ. For ν = 1, we have the usual KdV-ZK equation. Three-dimensional stability analysis of the solitary wave solutions of the KdV-ZK and different modified KdV-ZK equations has been investigated by the small-k perturbation expansion method of Rowlands and Infeld. For ν = 1, 2, 3, the instability conditions and the growth rate of instabilities have been obtained correct to order k, where k is the wave number of a long-wavelength plane-wave perturbation. It is found that ion–acoustic solitary waves are stable at least at the lowest order of the wave number for ν = 4.
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Kalaee, M. J., Y. Katoh, A. Kumamoto, T. Ono, and Y. Nishimura. "Simulation of mode conversion process from upper-hybrid waves to LO-mode waves in the vicinity of the plasmapause." Annales Geophysicae 28, no. 6 (June 14, 2010): 1289–97. http://dx.doi.org/10.5194/angeo-28-1289-2010.
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Abstract. In order to clarify the role of the mode conversion process in the generation mechanism of LO-mode waves in the equatorial region of the plasmasphere, we have investigated the linear mode conversion process among upper-hybrid-resonance (UHR)-mode, Z-mode and LO-mode waves by a numerical simulation solving Maxwell's equations and the equation of motion of a cold electron fluid. The wave coupling process occurring in the cold magnetized plasma are examined in detail. In order to give a realistic initial plasma condition in the numerical experiments, we use initial parameters inferred from observation data obtained around the generation region of LO-mode waves obtained by the Akebono satellite. A density gradient is estimated from the observed UHR frequency, and wave normal angles are estimated from the dispersion relation of cold plasma by comparing observed wave electric fields. Then, we perform numerical experiments of mode conversion processes using the density gradient of background plasma and the wave normal angle of incident upper hybrid mode waves determined from the observation results. We found that the characteristics of reproduced LO-mode waves in each simulation run are consistent with observations.
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Marinescu, Nicolae, and Rudolf Nistor. "Quantum description of microwave passive circuits." Canadian Journal of Physics 68, no. 10 (October 1, 1990): 1122–25. http://dx.doi.org/10.1139/p90-157.
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The paper gives a formal analogy between the distribution of the electromagnetic field in a wave guide and microwave cavities and the quantum-mechanical probabilities distribution. We show that the wave guide of the cutoff frequency ωc acts on an electromagnetic wave as a quantum potential barrier [Formula: see text]. We also establish a nonhabitual time-independent Schrödinger equation that replaces Maxwell's equations in describing guided wave propagation.
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Das, A. "Discrete phase space - II: The second quantization of free relativistic wave fields." Canadian Journal of Physics 88, no. 2 (February 2010): 93–109. http://dx.doi.org/10.1139/p09-090.
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The Klein–Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential equations in the arena of discrete phase space and continuous time. The scalar field and electromagnetic fields are quantized with commutation relations. The spin-1/2 field is quantized with anti-commutation relations. Moreover, the total momentum, energy and charge of these free relativisitic quantized fields in the discrete phase space and continuous time are computed exactly. The results agree completely with those computed from the relativisitic fields defined on the space-time continuum.
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Halilsoy, M. "Colliding Einstein-Maxwell waves that admit a separable wave equation." General Relativity and Gravitation 26, no. 2 (February 1994): 213–17. http://dx.doi.org/10.1007/bf02105154.
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Nevdakh, V. V. "Electromagnetic Waves in Maxwell’s Theory." Science & Technique 21, no. 3 (June 2, 2022): 222–28. http://dx.doi.org/10.21122/2227-1031-2022-21-3-222-228.
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The description of a plane traveling electromagnetic wave existing in the physical literature by identical solutions of wave equations for the strengths of electric and magnetic fields is physically incorrect, since such solutions contradict the physical meaning of Maxwell’s equations and violate the energy conservation law. The paper gives a physically correct description of electromagnetic waves in the framework of Maxwell’s theory. New solutions of Maxwell’s wave equations for traveling electromagnetic wave are proposed, in which the strength of its electric and magnetic components change in time with shifts of a quarter of the period and a quarter of the wavelength along coordinate. The solutions describe a traveling electromagnetic wave, in which the energy of the electrical component is sequentially converted into the energy of the magnetic component and vice versa; the total energy density of the lossless wave remains constant in space at any time; the mutual orientation of the intensity vectors of the electric, magnetic fields and phase velocity changes from a left-handed three to a right-handed three every quarter of the wavelength; the energy flux density of the traveling wave is described by the Umov vector. It is shown that the formation of a standing electromagnetic wave does not require the loss of half a wave of one of the components of the wave reflected at the interface between the media. In a standing wave, the total energy density remains constant in time, but it is a function of coordinates: there are points in space where the total energy density of the wave at any time is zero – these are nodes, and there are points where it has a maximum value – these are antinodes. Due to the inhomogeneity of the distribution of the total energy density of the wave in space, a standing electromagnetic wave cannot be considered as a harmonic oscillator, but a lossless traveling electromagnetic wave can.
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Piro, Tristram de. "Some arguments for the wave equation in quantum theory 3." Open Journal of Mathematical Sciences 7, no. 1 (June 13, 2023): 196–235. http://dx.doi.org/10.30538/oms2023.0207.
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In this paper, we proved that solutions \((\rho,J)\) exist for the 1-dimensional wave equation on \([-\pi,\pi]\). When \((\rho,J)\) is extended to a smooth solution \((\rho,\overline{J})\) of the continuity equation on a vanishing annulus \(Ann(1,\epsilon)\) containing the unit circle \(S^1\), a corresponding causal solution \((\rho,\overline{J}' \overline{E}, \overline{B})\) to Maxwell's equations can be obtained from Jefimenko's equations. The power radiated in a time cycle from any sphere \(S(r)\) with \(r>0\) is \(O\left(\frac{1}{r}\right)\), which ensure that no power is radiated at infinity over a cycle.
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NOVOTNÝ, ANTONÍN, MICHAEL RŮŽIČKA, and GUDRUN THÄTER. "SINGULAR LIMIT OF THE EQUATIONS OF MAGNETOHYDRODYNAMICS IN THE PRESENCE OF STRONG STRATIFICATION." Mathematical Models and Methods in Applied Sciences 21, no. 01 (January 2011): 115–47. http://dx.doi.org/10.1142/s0218202511005003.
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We consider a low Mach, Péclet, Froude and Alfvén number limit in the complete Navier–Stokes–Fourier system coupled with Maxwell's equations for gases with large specific heat at constant volume. The target system is shown to be the anelastic Oberbeck–Boussinesq system coupled with Maxwell's equations. The proof allows an intrinsic view into the process of separation of fast oscillating acoustic waves, governed by a Lighthill-type equation, from the equations describing the slow fluid flows.
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Kulkarni, Raghavendra G. "Alternative derivations for the fields inside a waveguide." Journal of Electrical Engineering 72, no. 2 (April 1, 2021): 129–31. http://dx.doi.org/10.2478/jee-2021-0018.
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Abstract Generally, the longitudinal magnetic field of the transverse electric (TE) wave inside a waveguide is obtained by solving the corresponding Helmholtz wave equation, which further leads to the derivation of the remaining fields. In this paper, we provide an alternative way to obtain this longitudinal magnetic field by making use of one of the Maxwell’s equations instead of directly relying on the Helmholtz wave equation. The longitudinal electric field of the transverse magnetic (TM) wave inside a waveguide can also be derived in a similar fashion. These derivations, which are different from those found in the introductory textbooks on microwave engineering, make the study of waveguides more interesting.