Geoscience Reference
In-Depth Information
Fig. 5.24
An approximation of the form of a protuberance (
a
); dependence from Eq.
5.30
at
b
D
1(
b
)
Here
b
is the radius of the basis of the ellipsoidal asperity and
a
is its height. The
dependence given by Eq.
5.30
is shown in Fig.
5.24
b.
Having applied for simplicity the known approximation of the ionization and the
dissociative attachment sum of frequencies (Mayhan
1971
):
E
E
cr
1
!
; ˇ
ˇ
i
a
D
a
5:34;
(5.31)
and using Eq.
5.27
, we estimate the speed of the asperity development in the
coordinates of the front:
r
E
cr
Q.a;b/
ˇ
0
1
1
@
A
da
dt
D
V
fr
r
E
cr
ˇ
1
:
(5.32)
1
For small values of
a
the approximation is fair:
2
a
b
; a
Q.a;b/
1
C
b:
(5.33)
Taking Eq.
5.33
into account, it is easy to determine the increment of the asperity
development:
V
fr
b
ˇ
4
.E=E
cr
/
ˇ
:
max
(5.34)
