Belated comments on electromagnetic cylinder scattering and the ubiquitous galvanic current contribution

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 449-450
Author(s):  
James R. Wait
Keyword(s):  
General Solution ◽  
Electromagnetic Fields ◽  
Series Expansion ◽  
Galvanic Current ◽  
Static Limit ◽  
Line Current ◽  
Current Contribution ◽  
General Derivation ◽  
Static Form ◽  
Homogeneous Cylinder

Many years ago (prior to the birth of many SEG members), I published a paper on the electromagnetic fields of a line current in the presence of a homogeneous cylinder (Wait, 1952). Although the general solution presented there was correct, an omission occurred in the reduction to the quasi‐static form. Indeed, Ward and Hohmann (1988) indicated the corresponding expression for [Formula: see text] in my 1952 paper was “wrong” after they had replicated my general derivation. Also, they correctly pointed out that I should not have omitted then n = 0 term in the series expansion for [Formula: see text] in the quasi‐static limit.

A Functionally Graded Plane With a Circular Inclusion Under Uniform Antiplane Eigenstrain

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
X. Wang ◽  
E. Pan ◽  
A. K. Roy
Keyword(s):  
General Solution ◽  
Shear Modulus ◽  
Helmholtz Equation ◽  
Series Expansion ◽  
Original Problem ◽  
Circular Inclusion ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Homogeneous Material

The problem of a functionally graded plane with a circular inclusion under a uniform antiplane eigenstrain is investigated, where the shear modulus varies exponentially along the x direction. By introducing a new function which satisfies the Helmholtz equation, the general solution to the original problem is derived in terms of series expansion. Numerical results are then presented which demonstrate clearly that for a functionally graded plane, the strain and stress fields inside the circular inclusion under uniform antiplane eigenstrains are intrinsically nonuniform. This phenomenon differs from the corresponding homogeneous material case where both the strain and stress fields are uniform inside the circular inclusion.

PETROV TYPE I, STATIONARY, AXISYMMETRIC, PERFECT FLUID SOLUTION OF EINSTEIN'S EQUATIONS

1999 ◽  
Vol 14 (01) ◽  
pp. 7-14
Author(s):  
E. KYRIAKOPOULOS
Keyword(s):  
Equation Of State ◽  
General Solution ◽  
Perfect Fluid ◽  
Petrov Type ◽  
Type I ◽  
Fluid Solution ◽  
Einstein’S Equations ◽  
Perfect Fluid Solution ◽  
Einstein's Equations ◽  
Static Limit

We present a four-parameter, algebraically general solution for the interior of a rigidly rotating, axisymmetric perfect fluid, with the equation of state μ = p + const . The solution is analytically simple and has a static limit.

scholarly journals Multicenter solutions in Eddington-inspired Born–Infeld gravity

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Gonzalo J. Olmo ◽  
Emanuele Orazi ◽  
Diego Rubiera-Garcia
Keyword(s):  
General Solution ◽  
Electromagnetic Fields ◽  
Arbitrary Number ◽  
Geodesic Completeness ◽  
Theories Of Gravity

AbstractWe find multicenter (Majumdar–Papapetrou type) solutions of Eddington-inspired Born–Infeld gravity coupled to electromagnetic fields governed by a Born–Infeld-like Lagrangian. We construct the general solution for an arbitrary number of centers in equilibrium and then discuss the properties of their one-particle configurations, including the existence of bounces and the regularity (geodesic completeness) of these spacetimes. Our method can be used to construct multicenter solutions in other theories of gravity.

On the image representation of the fields of a line current source above finitely conducting earth

1981 ◽  
Vol 59 (1) ◽  
pp. 117-121 ◽  
Author(s):  
A. Mohsen ◽  
L. Shafai
Keyword(s):  
Line Source ◽  
Image Representation ◽  
Current Source ◽  
Far Field ◽  
Static Limit ◽  
Line Current ◽  
Electric Line ◽  
Field Computation ◽  
Physical Resemblance

The problem of an electric line source above a conducting earth is investigated. Approximations to the integrals appearing in the solution of the problem are considered. An estimate of the neglected terms is given and interpretation of their physical resemblance is presented. The analysis does not restrict the relative magnitudes of earth and air propagation constants as in previous work. It is shown that the approximation presented is legitimate for far field computation and the results are comparable to those known for the quasi-static limit.

scholarly journals Electromagnetic resonance of nonlinear vacuum in one-dimensional cavity

2021 ◽  
Vol 75 (6) ◽  
Author(s):  
Kazunori Shibata
Keyword(s):  
General Solution ◽  
Standing Wave ◽  
Electromagnetic Fields ◽  
Maxwell's Equations ◽  
One Dimensional ◽  
Electromagnetic Resonance ◽  
Resonant Behavior ◽  
D 74 ◽  
Detailed Feature ◽  
Polarization Fluctuation

Abstract Nonlinear corrections on electromagnetic fields in vacuum have been expected. In this study, we have theoretically considered nonlinear Maxwell’s equations in a one-dimensional cavity for a classical light and external static electromagnetic fields. A general solution for the electromagnetic corrective components including that of a longitudinal standing wave was derived after a linearization. The main purpose is to give a detailed feature of the previously reported resonant behavior [Shibata, Euro. Phys. J. D 74:215 (2020)], such as the effect of external static fields and the polarization fluctuation. These results favor the development of new and effective method for experiment. Graphic abstract

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