The roughness of glass surfaces after different stages of etching is investigated by reflection measurements with a spectrophotometer, light scattering, and atomic-force microscopy (in small scale), and Talysurf (in large scale). The results suggest, there are three regimes during etching, according to their optical reflectivity and roughness. The first and second regimes are studied by the Kir...

We propose a Landauerlike theory for nonlinear transport in networks of one-dimensional interacting quantum wires (Luttinger liquids). A concrete example of current experimental focus is given by carbon nanotube Y junctions. Our theory has three basic ingredients that allow one to explicitly solve this transport problem: (i) radiative boundary conditions to describe the coupling to external lea...

Comparison theorems on resistance distances and Kirchhoff indices of the so-called S& T -isomer graphs are established. Then these results are applied to compare Kirchhoff indices of hexagonal chains, showing that the straight chain is the unique chain with maximum Kirchhoff index, whereas the minimum Kirchhoff index is achieved only when the hexagonal chain is an ‘‘all-kink’’ chain. © 2014 Els...

Elaborating on a Maxwellian representation of longitudinal wave propagation in a viscothermal fluid, a general nonlocal macroscopic theory of sound propagation in homogeneous porous media saturated with a viscothermal fluid has been recently proposed. The present paper validates this new nonlocal Maxwellian theory by showing that, in the case of the propagation in straight circular tubes, it is...

The fundamental relationship between matrices over the rational numbers and a newly defined type of graph, a Kirchhoff graph, is discussed. For a given matrix, a Kirchhoff graph for that matrix represents the orthogonal complementarity of the null and row spaces of the matrix. A number of basic results are proven, and then a relatively complicated Kirchhoff graph is constructed for a matrix tha...

In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...

The diffraction theory of Kirchhoff is applied to the semi-infinite aperture of a black half-screen. The derivative of the spherical Green's function is taken into account without any approximation. The uniformly evaluated scattering integral is compared with the physical optics solution. It is shown that the non-omitted term causes the existence of fictitious diffracted waves.

The acoustic backscatter from pressure release prolate spheroids and a three-dimensional representation of a fish swimbladder (Chilean jack mackerel, Trachurus symmetricus murphyi) was calculated using four target strength models (Kirchhoff-approximation, Kirchhoff-ray-mode, finite element solution of the Helmholtz equation, and prolate-spheroid-modal-series). Smoothly varying errors were found...

In this paper, using theory of sheets, the deflection of suspended diaphragm has been obtained under uniform and circular loading. This type of diaphragm, unlike other diaphragms, has a central support which is recommended to be used in MEMS applications. The relationship between diaphragm deflection and static analysis of this diaphragm enjoys a great significance in investigating and understa...