Asymptotic Solutions of Maxwell’s Equations in a Layered Periodic Structure

2017 ◽  
pp. 259-264
Author(s):  
M. V. Perel ◽  
M. S. Sidorenko
Keyword(s):  
Periodic Structure ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Asymptotic Solutions

Resonances for Maxwell's equations in a periodic structure

1997 ◽  
Vol 325 (2) ◽  
pp. 211-215 ◽  
Author(s):  
Habib Ammari ◽  
Natacha Béreux ◽  
Jean-Claude Nédélec
Keyword(s):  
Periodic Structure ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

Exact solutions of the three-dimensional scalar wave equation and Maxwell's equations from the approximate solutions in the wave zone through the use of the Radon transform

1989 ◽  
Vol 422 (1863) ◽  
pp. 351-365 ◽  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Radon Transform ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
Asymptotic Solutions ◽  
Scalar Wave ◽  
Wave Zone ◽  
One Dimensional

In our earlier paper we have shown that the solutions of both the three-dimensional scalar wave equation, which is also the three-dimensional acoustic equation, and Maxwell’s equations have forms in the wave zone, which, except for a factor 1/ r , represent one-dimensional wave motions along straight lines through the origin. We also showed that it is possible to reconstruct the exact solutions from the asymptotic forms. Thus we could prescribe the solutions in the wave zone and obtain the exact solutions that would lead to them. In the present paper we show how the exact solutions can be obtained from the asymptotic solutions and conversely, through the use of a refined Radon transform, which we introduced in a previous paper. We have thus obtained a way of obtaining the exact three-dimensional solutions from the essentially one-dimensional solutions of the asymp­totic form entirely in terms of transforms. This is an alternative way to obtaining exact solutions in terms of initial values through the use of Riemann functions. The exact solutions that we obtain through the use of the Radon transform are causal and therefore physical solutions. That is, these solutions for time t > 0 could have been obtained from the initial value problem by prescribing the solution and its time-derivative, in the acoustic case, and the electric and magnetic fields, in the case of Maxwell’s equations, at time t = 0. The role of time in the relation between the exact solutions and in the asymptotic solutions is made very explicit in the present paper.

scholarly journals Maxwell's Equations in a Periodic Structure

1991 ◽  
Vol 323 (2) ◽  
pp. 465 ◽  
Author(s):  
Xinfu Chen ◽  
Avner Friedman
Keyword(s):  
Periodic Structure ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

Resonances for Maxwell’s equations in a periodic structure

2000 ◽  
Vol 17 (2) ◽  
pp. 149-198 ◽  
Author(s):  
Habib Ammari ◽  
Natacha Béreux ◽  
Jean -Claude Nédélec
Keyword(s):  
Periodic Structure ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

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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