Static Maxwell System in Axially Symmetric Inhomogeneous Media

2009 ◽  
pp. 111-117
Keyword(s):  
Inhomogeneous Media ◽  
Maxwell System ◽  
Axially Symmetric

scholarly journals On the solution of the static Maxwell system in axially symmetric inhomogeneous media

2009 ◽  
Vol 33 (4) ◽  
pp. 439-447 ◽  
Author(s):  
Kira V. Khmelnytskaya ◽  
Vladislav V. Kravchenko ◽  
Héctor Oviedo
Keyword(s):  
Inhomogeneous Media ◽  
Maxwell System ◽  
Axially Symmetric

Green’s Functions for Axially Symmetric Elastic Waves in Unbounded Inhomogeneous Media Having Constant Velocity Gradients

1962 ◽  
Vol 29 (2) ◽  
pp. 293-298 ◽  
Author(s):  
J. F. Hook
Keyword(s):  
Elastic Waves ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Point Sources ◽  
Axially Symmetric ◽  
S Waves ◽  
Displacement Vectors ◽  
Unbounded Media ◽  
The Media ◽  
Scalar Potentials

This paper treats the propagation of elastic waves in one class of inhomogeneous media. The properties of the media are proportional to powers of the Cartesian co-ordinate z in such a way that Poisson’s ratio remains constant and the velocities of propagation of P and S waves are proportional to z. Exact expressions are obtained for the P, SV, and SH displacements generated by impulsive point sources buried in unbounded media of this class. The sources are taken to be symmetric about the z axis. Separation of the vector-wave equation is achieved by use of a potential representation that is a generalization of the familiar Stokes-Helmholtz representation; the P, SV, and SH displacement vectors are expressed in terms of scalar potentials that satisfy independent second-order wave equations. The SH displacement is solenoidal, but it is found that the products of the P and SV displacement vectors with appropriate weighting functions, rather than the displacement vectors themselves, are irrotational and solenoidal, respectively. The media are found to be dispersive, with the result that decaying tails follow the advancing wave fronts.

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

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