Caption: Figure 4: Top: the stationary transmission clock time [t.sup.T.sub.c] (k) (blue) and the wave number
distribution [rho](k) = [[absolute value of (S(k))].sup.2] (orange, dashed, and arbitrary scale), for [V.sub.0] = 7, a = 1, b = 5, and [k.sub.0] [approximately equal to] 2.175932), with the initial state given by (18).
When the incident wave is of wave number
Ai, we have derived the energy balance relation as
For the threshold Alfveen Mach number of 4.062 we obtained one instability window and instability starts at the critical dimensionless wave number
of 1.944, or equivalently at [[lambda].sup.m=4.sub.cr] [congruent to] 8.0 Mm.
in which [k.sub.b] = [omega]/[[beta].sub.b] represents the shear wave number
of the shear wall.
where [mathematical expression not reproducible] are spectral current density amplitudes of electric and magnetic sources, respectively; [k.sub.[rho]] = [square root of ([k.sup.2.sub.0] - [k.sup.2.sub.z])] is the radial wave number
; b is the source radial distance.
The corresponding frequency for these dimensionless wave numbers
is [omega] = 154.83 rad/s.
Based on the dispersion relation, it is possible to determine the travelling wave number
under certain frequencies.
Averaged curves from 32 repeated scans were obtained between wave numbers
of 4,000 and 400 [cm.sup.-1].
We will use the discrete approximation with evenly spaced [[omega].sub.k] with spacing [[DELTA].sun.[omega]] and corresponding wave numbers
[[kappa].sub.k] given by the dispersion relation.
where k = [omega]/c = 4[square root of [zeta][[omega].sup.2]/[xi] is the wave number
The wave number
and radius update function determine how fast algorithm approaches to solution.
Comparing this with spectrum of pure FeNi , we can see that there is no peak in wave number
2400 [cm.sup.-1] in pure FeNi, because there is no bond between Fe and Ni atoms in this condition and no optical mode excitation is expected.