Sulfone group (S=O, symmetric in PSU) wave number
(1150.00cm-1) shifted its peaks to 1128.05cm-1, 1121.41cm-1, and 1124.57cm-1, respectively, due to vibrational stretching.
In the 2D study in , different shape food samples could be classified as thin ([N.sub.w] [less than or equal to] 0.1), intermediate ([N.sub.w] > 0.1, [N.sub.p] < 3), and thick ([N.sub.p] [greater than or equal to] 3) size according to samples' wave number
and penetration number on the cross-section plane.
The decrease in intensity and shifting of peaks to lower wave number
might be due to the interaction of hydroxyl group of wood and clay with polymer which is reflected on acoustic properties shown in Figure 3 and also evident from SEM images in Figure 4.
From [25-28] and the references it can be found that, due to the so-called pollution effect , to compute approximate solutions of the Helmholtz equation for high wave numbers
by the standard finite element method (FEM) is unreliable, so, in (9), the wave number
should be not high.
i.e., the probability to find a wave number
k in the asymptotic transmitted wave packet is the same as in the initial state, which is as expected, since after a long enough time the initial wave packet will be transmitted with probability unit, as mentioned earlier.
In two-layer fluid system, the time-harmonic waves of a particular mode can propagate with two-different wave numbers
: waves with lower wave number
propagate in the upper layer and the waves with higher wave number
propagate in the lower layer.
The analysis was performed upon particles with diameters of 2 [micro]m and density of 600 kg/[m.sup.3] entrained by an oscillating flow with a phase velocity of 50 m/s (the angular frequency and the wave number
are [omega]=[10.sup.5] rad/s and k=2000 rad/m, respectively).
The wave number
[k.sub.i] of the ith wave and the relevant [[omega].sub.i] are as follows:
Two dispersion relations (9) and (25) are transcendent equations in which the wave frequency, [omega], is a complex quantity: Re([omega]) + Im([omega]), while the axial wave number
, [k.sub.z], is a real variable.
Normally, [k*.sub.0] is referred to as the absolute wave number
and [[omega]*.sub.0i] the absolute growth rate.
Where [[??].sub.i] abd [[??].sub.s] represent the combined vectors of incident and scattered wave number
, respectively; R is the distance from the observation to the facet centers; k is the electromagnetic wave number
; p and q are the polarization of the incident and scattered wave; [S.sub.pq] denotes the scattering amplitude that can be expressed as
We assume that a, b are real numbers and [m.sub.1], [m.sub.2] represent wave number
. Equation (54) shows that each nonlinear Rossby wave dispersion not only contains itself wave number
and amplitude, but also contains another wave amplitude, which is characteristic of the interaction between wave and wave.