The first-order small slope approximation is applied to model the scattering strength from a rough surface in underwater acoustics to account for seafloor for high frequencies from 10 kHz to hundreds of kilohertz. Emphasis is placed on simulating the response from two-dimensional anisotropic rough surfaces. Several rough surfaces are described based on structure functions such as the particular...

We show that a simple and straightforward rational approximation to the Thomas– Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Padé approximants are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas–Fermi equation for isolated atoms and for atoms in strong magnetic fields.

The small slope approximation (SSA) of Voronovich [Soy. Phys. JETP 62, 65-70 (1985)] is a promising method for application to scattering from many natural surfaces. The theory gives a systematic expansion that can be interpreted as a series in generalized surface slope. The SSA series for the T matrix satisfies the appropriate reciprocity condition at each order and reduces to the standard pert...

The small slope approximation !SSA" of Voronovich #Sov. Phys. JETP 62, 65–70 !1985"$ is a promising method for modeling wave scattering from rough surfaces. The SSA T-matrix series, which can be interpreted as an expansion in a generalized surface slope, satisfies the appropriate reciprocity condition at each order and reduces to the standard perturbation series for small surface roughness. Whe...

We use a rigorous numerical code based on the method of moments to test the accuracy and validity domains of two popular first-order approximations, namely the Kirchhoff and the small-slope approximation (SSA), in the case of two-dimensional rough surfaces. The experiment is performed on two representative types of surfaces: surfaces with Gaussian spectrum, which are the paradigm of single-scal...

The problem of a linguistic description of dependencies in data by a set of rules Rk: “If X is Tk then Y is Sk” is considered, where Tk’s are linguistic terms like SMALL, BETWEEN 5 AND 7 describing some fuzzy intervals Ak. Sk’s are linguistic terms like DECREASING and QUICKLY INCREASING describing the slopes pk of linear functions yk = pkx + qk approximating data on Ak. The decision of this pro...