A DISCUSSION OF THE “FAULT” AND “DIKE” PROBLEMS IN MAGNETOTELLURIC THEORY

Geophysics ◽  
1963 ◽  
Vol 28 (3) ◽  
pp. 487-490 ◽  
Author(s):  
J. T. Weaver
Keyword(s):  
Boundary Condition ◽  
Electromagnetic Wave ◽  
Current Density ◽  
Normal Component ◽  
The Earth ◽  
Source Field ◽  
Vertical Fault ◽  
Explicit Mention

In two recent papers appearing in Geophysics, d’Erceville and Kunetz (1962) and Rankin (1962) have dealt with the magnetotelluric theory for a plane earth which contains a certain type of vertical fault. In both cases the results depend on a boundary condition which requires the assumption that the normal component of current density vanishes at the surface of the earth. While d’Erceville and Kunetz confine their attention to the region below the surface and thereby avoid explicit mention of the source field, Rankin follows Cagniard (1953) by considering a plane‐polarized electromagnetic wave normally incident on the surface of the earth. In this case, the assumed boundary condition is not correct, as we shall see later; indeed, it actually leads to a contradiction.

scholarly journals Quantum Vacuum Effects in Braneworlds on AdS Bulk

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 181
Author(s):  
Aram A. Saharian
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Normal Component ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Curvature Radius ◽  
Perfect Conductor ◽  
Quantum Vacuum ◽  
Local Properties

We review the results of investigations for brane-induced effects on the local properties of quantum vacuum in background of AdS spacetime. Two geometries are considered: a brane parallel to the AdS boundary and a brane intersecting the AdS boundary. For both cases, the contribution in the vacuum expectation value (VEV) of the energy–momentum tensor is separated explicitly and its behavior in various asymptotic regions of the parameters is studied. It is shown that the influence of the gravitational field on the local properties of the quantum vacuum is essential at distance from the brane larger than the AdS curvature radius. In the geometry with a brane parallel to the AdS boundary, the VEV of the energy–momentum tensor is considered for scalar field with the Robin boundary condition, for Dirac field with the bag boundary condition and for the electromagnetic field. In the latter case, two types of boundary conditions are discussed. The first one is a generalization of the perfect conductor boundary condition and the second one corresponds to the confining boundary condition used in QCD for gluons. For the geometry of a brane intersecting the AdS boundary, the case of a scalar field is considered. The corresponding energy–momentum tensor, apart from the diagonal components, has nonzero off-diagonal component. As a consequence of the latter, in addition to the normal component, the Casimir force acquires a component parallel to the brane.

The outgoing time-harmonic electromagnetic wave in a half-space with non-absorbing impedance boundary condition

2019 ◽  
Vol 53 (1) ◽  
pp. 325-350
Author(s):  
Sergio Rojas ◽  
Ignacio Muga ◽  
Carlos Jerez-Hanckes
Keyword(s):  
Boundary Condition ◽  
Electromagnetic Wave ◽  
Asymptotic Analysis ◽  
Radiation Pattern ◽  
Half Space ◽  
Existence And Uniqueness ◽  
Radiation Condition ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Time Harmonic

We show existence and uniqueness of the outgoing solution for the Maxwell problem with an impedance boundary condition of Leontovitch type in a half-space. Due to the presence of surface waves guided by an infinite surface, the established radiation condition differs from the classical one when approaching the boundary of the half-space. This specific radiation pattern is derived from an accurate asymptotic analysis of the Green’s dyad associated to this problem.

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