As for the isometric volume cylindrical, cuboidal, and ellipsoidal samples, they can be classified into three groups by the
wave numbers and penetration numbers in the radial and axial directions.
Babuka, "Finite element solution of the Helmholtz equation with high
wave number part II: the h-p Version of the FEM," SIAM Journal on Numerical Analysis, vol.
Caption: Figure 3: 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 = 3, and [k.sub.0] [approximately equal to] 2.175932), with the initial state given by (18).
Figures 4(a)-(c) depict the first order reflection and transmission coefficients due to incident wave of mode [[lambda].sub.1] for depth ratio H/h = 2, amplitude of the sinusoidal ripple a/h = 0.1,
wave number of the ripples [gamma]h =1, density ratio [rho] = 0.5, surface tension parameter M/[h.sup.2] = 0.2, porosity Gh = 0.05 and for different number of ripples (different values of m and n).
That critical dimensionless
wave number for the m = 4 MHD mode (look at Figure 7) is equal to 0.528.
The superscript "p" represents the particular solution in the fixed layer, "h" the homogeneous solution in the fixed layer, "r" the solution to the counterforce in fixed end, and "k" the
wave number along the horizontal direction.
where [k.sup.([alpha]).sub.1] and [k.sup.([alpha]).sub.2] are the longitudinal and shear
wave numbers, respectively, and are given by
The hydrogen bond absorption band at 3,423 [cm.sup.-1] was shifted to a lower
wave number, which might cause the wood crystallinity to increase as temperature increases.
The standard procedure to generate random waves is via a discrete approximation of the spectral integral and, for discrete
wave numbers and frequencies, generate a discretized version of the integral (2),
where the
wave number k = [omega]/c = [square root of [rho][[omega].sup.2]/[mu]].