Information Technology Reference
In-Depth Information
In the first stage, the normal impedance of the one-dimensional background is
derived in the absence of the inclusion:
0
Z
N
[
Z
N
]
=
,
(7
.
120)
−
Z
N
0
where
−
i
o
h
Z
N
=
o
S
1
h
2
,
h
=
h
1
+
h
2
.
1
−
i
In the second stage, we find the electric and magnetic distortion tensors [
e
] and [
h
].
The tensor [
e
] is derived from the well-known problem on infinitely long ellipti-
cal cylinder in the uniform static field (Smythe, 1950). Restricting our consideration
to measurements along the
y
-axis, we get
e
xx
0
=
.
[
e
]
(7
121)
0
e
yy
where
b
2
S
1
a
2
a
2
S
1
−
ab
S
1
−
S
1
|
f
y
b
2
y
2
|
S
1
S
1
−
+
+
y
|
y
|
>
b
=
e
xx
bS
1
a
2
=
1
+
,
b
)
aS
1
+
(
a
−
−
b
2
+
y
2
a
+
b
S
1
|
y
|
<
b
=
e
xx
aS
1
+
bS
1
b
2
S
1
a
2
a
2
S
1
−
ab
S
1
−
S
1
|
f
y
−
b
2
+
y
2
+
y
|
S
1
S
1
|
y
|
>
b
=
e
yy
bS
1
a
2
=
1
+
,
b
)
aS
1
+
(
a
−
−
b
2
+
y
2
a
+
b
S
1
|
y
|
<
b
=
e
yy
aS
1
+
bS
1
.
(7
122)
and
1
S
1
S
1
S
1
ab
(1
−
)
|
y
|
f
(
y
,
)
=
−
a
2
,
=
or
S
1
.
(
a
−
b
)(
a
+
b
)
−
b
2
+
y
2
The tensor [
h
] is determined by (1.85). With a knowledge of [
Z
N
] and [
e
]we
have
h
xx
0
[
h
]
=
,
(7
.
123)
0
h
yy
where
