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Transient waves in non-stationary media

Åberg, Ingegerd LU ; Kristensson, Gerhard LU and Wall, David LU (1994) In Technical Report LUTEDX/(TEAT-7037)/1-27/(1994)
Abstract
This paper treats propagation of transient waves in non-stationary media,

which has many applications in e.g. electromagnetics and acoustics. The underlying

hyperbolic equation is a general, homogeneous, linear, first order 2×2

system of equations. The coefficients in this system depend only on one spatial

coordinate and time. Furthermore, memory effects are modeled by integral

kernels, which, in addition to the spatial dependence, are functions of two different

time coordinates. These integrals generalize the convolution integrals,

frequently used as a model for memory effects in the medium. Specifically, the

scattering problem for this system of equations is... (More)
This paper treats propagation of transient waves in non-stationary media,

which has many applications in e.g. electromagnetics and acoustics. The underlying

hyperbolic equation is a general, homogeneous, linear, first order 2×2

system of equations. The coefficients in this system depend only on one spatial

coordinate and time. Furthermore, memory effects are modeled by integral

kernels, which, in addition to the spatial dependence, are functions of two different

time coordinates. These integrals generalize the convolution integrals,

frequently used as a model for memory effects in the medium. Specifically, the

scattering problem for this system of equations is addressed. This problem is

solved by a generalization of the wave splitting concept, originally developed

for wave propagation in media which are invariant under time translations,

and by an imbedding or a Green functions technique. More explicitly, the

imbedding equation for the reflection kernel and the Green functions (propagator

kernels) equations are derived. Special attention is paid to the problem

of non-stationary characteristics. A few numerical examples illustrate this

problem. (Less)
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publishing date
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Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7037)/1-27/(1994)
pages
27 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
298b488f-f72c-41e7-9d7e-44e1a9e7c39d (old id 530250)
date added to LUP
2007-09-06 11:15:28
date last changed
2016-04-16 11:54:08
@misc{298b488f-f72c-41e7-9d7e-44e1a9e7c39d,
  abstract     = {This paper treats propagation of transient waves in non-stationary media,<br/><br>
which has many applications in e.g. electromagnetics and acoustics. The underlying<br/><br>
hyperbolic equation is a general, homogeneous, linear, first order 2×2<br/><br>
system of equations. The coefficients in this system depend only on one spatial<br/><br>
coordinate and time. Furthermore, memory effects are modeled by integral<br/><br>
kernels, which, in addition to the spatial dependence, are functions of two different<br/><br>
time coordinates. These integrals generalize the convolution integrals,<br/><br>
frequently used as a model for memory effects in the medium. Specifically, the<br/><br>
scattering problem for this system of equations is addressed. This problem is<br/><br>
solved by a generalization of the wave splitting concept, originally developed<br/><br>
for wave propagation in media which are invariant under time translations,<br/><br>
and by an imbedding or a Green functions technique. More explicitly, the<br/><br>
imbedding equation for the reflection kernel and the Green functions (propagator<br/><br>
kernels) equations are derived. Special attention is paid to the problem<br/><br>
of non-stationary characteristics. A few numerical examples illustrate this<br/><br>
problem.},
  author       = {Åberg, Ingegerd and Kristensson, Gerhard and Wall, David},
  language     = {eng},
  pages        = {27},
  publisher    = {ARRAY(0x942d818)},
  series       = {Technical Report LUTEDX/(TEAT-7037)/1-27/(1994)},
  title        = {Transient waves in non-stationary media},
  year         = {1994},
}