When the large diameter pile exists in the wave field, because of diffraction effect, the

cylindrical wave of each direction can cause the outward divergence effect.

When the incidence angle between the

cylindrical wave and tube wall exceeds some critical value, Mach reflection occurs.

Trifunac, "Zero-stress,

cylindrical wave functions around a circular underground tunnel in a flat, elastic half-space: incident P-waves," Soil Dynamics and Earthquake Engineering, vol.

The

cylindrical wave is a common type of wave motion in homogeneous medium [1].

* The vector C both includes the case of a plane wave propagating at the scalar velocity c, and three-dimensional cases such as those of a

cylindrical wave where C has at least two spatial components.

In order to obtain the dispersion curves of the surface wave modes for the plasma column loaded

cylindrical wave guide, two different techniques have been used.

The presence of the vias fence was included considering the field scattered from the metallic cylinders expanded in terms of the

cylindrical wave functions and enforcing the condition that the electric field tangent on each cylinder was zero.

According to

cylindrical wave transformation, the incident electric field can be expanded by an infinite sum of

cylindrical wave functions [13]

Consequently, in the case of

cylindrical wave of amplitude A, the hypothesis m(r) = [m.sub.0] leads (1) to become:

Wang Zhi-Liang, "On the Expansion of First-Kind Spherical Wave Functions in Terms of

Cylindrical Wave Functions." An expansion of the first-kind scalar spherical wave functions in terms of the scalar

cylindrical wave functions is given in this paper.

To this aim, the hypothesis that the omnidirectional field, in terms of an omnidirectional

cylindrical wave, locally interacts with the annular metasurface as the corresponding plane wave interacts with the linearized structure is assumed.

In order to transform generalized wave functions to a specific s pile's coordinate [[beta].sub.s], [r.sub.s], through employing the boundary conditions, incident SH wave is expanded to a Fourier-Bessel series in

cylindrical wave functions [28]: