in an axisymmetric co2-n2-h2o gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. to obtain a maximal small signal gain, some authors have tested several families of curves for ?. to find the most general solution for ?, an application of pontryagin’s principle led to the conjuncture that the optimal ? must consist o...

L-band electromagnetic scattering from two-dimensional random rough sea surfaces are calculated by first- and second-order Small-Slope Approximation (SSA1, 2) methods. Both analytical and numerical computations are utilized to calculate incoherent normalized radar cross-section (NRCS) in mono- and bi-static cases. For evaluating inverse Fourier transform, inverse fast Fourier transform (IFFT) i...

In an axisymmetric CO2-N2-H2O gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. To obtain a maximal small signal gain, some authors have tested several families of curves for ?. To find the most general solution for ?, an application of Pontryagin’s principle led to the conjuncture that the optimal ? must consist o...

In this paper we present new results on the small-slope approximation method. We consider different three-dimensional structures like a randomly rough surface separating two different media and a slab delimited by one or two rough surfaces. We extend the small-slope approximation to the fourth order terms of the perturbative development, and give the expression of the cross-sections for the dif...

Firstand second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the secondorder reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized el...

In this paper the small slope approximation is applied to acoustic scattering from a randomly rough fluid-elastic-solid interface. Expressions for the zeroth-, first-, and second-order bistatic scattering cross sections are derived. Numerical results are obtained for the zeroth-order small slope approximation for Gaussian and modified power law surface roughness pectra and are compared with tho...

The lowest-order nonlocal small slope approximation (NLSSA) reflection coefficient is derived, and numerical results are presented for one-dimensional (1-D) surfaces, satisfying the Dirichlet boundary condition. Reduction to the perturbation expression occurs in the small height limit, and the first term of the reflection coefficient gives the Kirchhoff approximation (KA) result. Numerical resu...