Using the full wave approach, the quasi specular contributors to the scattered fields from the large scale surface roughness as well as the Bragg-like diffusely scattered fields from the small scale surface roughness are accounted for in a unified self-consistent manner. Thus the full wave computer codes for the scattering cross sections contain ground truth data only. It has been shown how the...

This paper is aimed at analyzing the electromagnetic (EM) scattering from the twodimensional (2-D) Gaussian rough surfaces characterized by textures. Visual appearances of the stripe texture can be generated through the angle rotating in Fourier transform when the ratio of the correlation lengths in two directions is large enough. The scattering field is derived in Cartesian coordinate system t...

The Kirchhoff integral is a fundamental in scattering theory, appearing both the approximation and small slope approximation. In this work, functional Taylor series to presented, under condition that roughness covariance function follows either an exponential or Gaussian form—in one-dimensional two-dimensional cases. Previous approximations [Gragg, Wurmser, Gauss (2001) J. Acoust. Soc. Am. 110(...

We have calculated the phonon frequencies of KC1 along symmetry directions using an approach which is a combination of the frozen phonon and force constants methods. We also calculated Griineisen parameters for all modes at X and L points in the Brillouin zone. Finally, the slope of acoustic dispersion curves around zone center were used to calculate the three independent elastic coefficien...

We use a simple picture based on the π electron approximation to study the bandgap variation of carbon nanotubes with uniaxial and torsional strain. We find (i) that the magnitude of slope of bandgap versus strain has an almost universal behaviour that depends on the chiral angle, (ii) that the sign of slope depends on the value of (n−m) mod 3 and (iii) a novel change in sign of the slope of ba...

The orbit SL(2,Z)x is dense in R2 when the initial point x ∈ R2 has irrational slope. We refine this result from a diophantine perspective. For any target point y ∈ R2, we introduce two exponents μ(x,y) and μ̂(x,y) that measure the approximation to y by elements γx of the orbit in terms of the size of γ. We estimate both exponents under various conditions. Our results are optimal when the slope ...

An innnite word x has nite index if the exponents of the powers of primitive words that are factors of x are bounded. F. Mignosi has proved that a Sturmian word has nite index if and only if the coeecients of the continued fraction development of its slope are bounded. Mignosi's proof relies on a delicate analysis of the approximation of the slope by rational numbers. We give here a proof based...

We use a simple picture based on the π electron approximation to study the bandgap variation of carbon nanotubes with tensile and torsional strain. We find (i) that the magnitude of slope of bandgap versus strain has an almost universal behaviour that depends on the chiral angle, (ii) that the sign of slope depends on the value of (n−m) mod 3 and (iii) a novel change in sign of the slope of ban...

The appearance of a horizontal array of linear lamps below the water surface when viewed from above is approximately in the form of contours of one component of the water surface slope. The degree of approximation is a fraction of one percent when this method is used to describe the slopes of a wind ruffled surface. An extension of the method to image both components of slope requires two array...

We develop a method to calculate the column density distribution of the Lyα forest for column densities in the range 10 − 10 cm. The Zel’dovich approximation, with appropriate smoothing, is used to compute the density and peculiar velocity fields. The effect of the latter on absorption profiles is discussed and it is shown to have little effect on the column density distribution. An approximati...