First order generalized symmetries of Maxwell's equations

1988 ◽  
Vol 129 (3) ◽  
pp. 148-150 ◽  
Author(s):  
Juha Pohjanpelto
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
First Order ◽  
Generalized Symmetries

scholarly journals Calculation of Maxwell’s Equations Using MATLAB

2021 ◽  
Vol 09 (10) ◽  
Author(s):  
Subhi Abdalazim Aljily Osman ◽  
Keyword(s):  
Mathematical Method ◽  
Analytical Solution ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
System Of Equations ◽  
First Order ◽  
Mathematical Programs ◽  
Mathematical Problems ◽  
Micro Radio

Maxwell’s equations describe electromagnetic Phenomena. This includes micro- , radio and radar waves .The Maxwell equations are discussed in more detail Faraday's and Amperes laws constitute a first - order hyperbolic system of equations .Matlab is one of the most famous mathematical programs in calculating mathematical problems .The aims of this study is to calculate Maxwell’s equations using Matlab .We followed the applied mathematical method by using Matlab .We found that the solution of Matlab is more accuracy and speed than the analytical solution.

Low valence Killing spinors in Gödel's Universe

2017 ◽  
Vol 26 (13) ◽  
pp. 1750147 ◽  
Author(s):  
S. A. Cook
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Geodesic Equation ◽  
First Integrals ◽  
Coordinate Systems ◽  
Killing Spinors ◽  
Killing Tensors ◽  
Generalized Symmetries ◽  
Related Notion

Killing tensors have been of interest historically primarily for generating first integrals for the geodesic equation and for their use in finding separable coordinate systems. A related notion, that of Killing spinors, has recently been shown to be important in the study of generalized symmetries of Maxwell's equations. In a given spacetime, the generalized symmetries depend on the existence of Killing spinors of the spacetime of certain valences. The existence of Killing spinors for the curved metric of Gödel's Universe is investigated. There are five (1,1) Killing spinors, 14 (2,2) and five (1,5) Killing spinors of the spacetime, in addition to the unique (0,2) and (0,4) Killing spinors which are exhibited here as well.

scholarly journals Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials

2017 ◽  
Vol 21 (5) ◽  
pp. 1350-1375 ◽  
Author(s):  
Adérito Araújo ◽  
Sílvia Barbeiro ◽  
Maryam Khaksar Ghalati
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mesh Size ◽  
Element Space ◽  
First Order ◽  
Balance Accuracy ◽  
The Stability

AbstractIn this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability and error estimates, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-Müller. The bounds of the stability region point out the influence of not only the mesh size but also the dependence on the choice of the numerical flux and the degree of the polynomials used in the construction of the finite element space, making possible to balance accuracy and computational efficiency. In the model we consider heterogeneous anisotropic permittivity tensors which arise naturally in many applications of interest. Numerical results supporting the analysis are provided.

scholarly journals The first and second order equations of the quantum theory

1929 ◽  
Vol 124 (793) ◽  
pp. 143-150 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electromagnetic Theory ◽  
Second Order ◽  
Electromagnetic Mass ◽  
First Order ◽  
Second Order Equations

The form of the wave equation for a non-rotating electron suggests that it enters into the theory very much in the same way as the wave equation associated with electromagnetic theory. It would be expected to be derivable from equations of the first order corresponding to Maxwell's equations. It has been suggested that the function Ψ might enter by means of a relation such as s = grad Ψ (1) where s replaces the current four vector of the electromagnetic theory. The difficulty in connection with this procedure is to account for the phenomena associated with electronic rotation. Dirac has shown how to overcome this difficulty and has derived first order equations which can be derived from generalisations of Maxwell's equations. There are certain difficulties with regard to the form of Dirac's results which have been much discussed and some of them have been removed. There are two unsatisfactory points in the treatment of this question. One is the introduction of an operator ( h /2 πi ∂/∂ x α - eϕ α ) into the equations when it is desired to pass from a non-electromagnetic problem to one in which an electromagnetic field is present. The second difficulty lies in the occurrence of a term in mc . Darwin has pointed out this difficulty and considers that it is due to our inability to calculate electromagnetic mass in the quantum theory.

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

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