Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

On the propagation of plane waves above an impedance surface

The propagation of grazing incidence plane waves along a finite impedance boundary is investigated. A solution of the semi-infinite problem, where a harmonic motion, parallel to the boundary, is imposed along a line perpendicular to the boundary, is obtained. This solution consists of quasiplane waves, waves moving parallel to the boundary with amplitude and phase variations perpendicular to the boundary. Several approximations to the full solution are considered

Optimization of robustness of scale-free network to random and targeted attacks

The scale-fee networks, having connectivity distribution $P(k)\sim k^{-\alpha}$ (where $k$ is the site connectivity), is very resilient to random failures but fragile to intentional attack. The purpose of this paper is to find the network design guideline which can make the robustness of the network to both random failures and intentional attack maximum while keeping the average connectivity per node constant. We find that when $=3$ the robustness of the scale-free networks reach its maximum value if the minimal connectivity $m=1$, but when is larger than four, the networks will become more robust to random failures and targeted attacks as the minimal connectivity $m$ gets larger

First-principles study of stability and vibrational properties of tetragonal PbTiO_3

A first-principles study of the vibrational modes of PbTiO_3 in the ferroelectric tetragonal phase has been performed at all the main symmetry points of the Brillouin zone (BZ). The calculations use the local-density approximation and ultrasoft pseudopotentials with a plane-wave basis, and reproduce well the available experimental information on the modes at the Gamma point, including the LO-TO splittings. The work was motivated in part by a previously reported transition to an orthorhombic phase at low temperatures [(J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B {\bf 28}, 3866 (1983)]. We show that a linear coupling of orthorhombic strain to one of the modes at Gamma plays a role in the discussion of the possibility of this phase transition. However, no mechanical instabilities (soft modes) are found, either at Gamma or at any of the other high-symmetry points of the BZ.Comment: 8 pages, two-column style with 3 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#ag_pbt

Initial stage of the 2D-3D transition of a strained SiGe layer on a pit-patterned Si(001) template

We investigate the initial stage of the 2D-3D transition of strained Ge layers deposited on pit-patterned Si(001) templates. Within the pits, which assume the shape of inverted, truncated pyramids after optimized growth of a Si buffer layer, the Ge wetting layer develops a complex morphology consisting exclusively of {105} and (001) facets. These results are attributed to a strain-driven step-meandering instability on the facetted side-walls of the pits, and a step-bunching instability at the sharp concave intersections of these facets. Although both instabilities are strain-driven, their coexistence becomes mainly possible by the geometrical restrictions in the pits. It is shown that the morphological transformation of the pit surface into low-energy facets has strong influence on the preferential nucleation of Ge islands at the flat bottom of the pits.Comment: 19 pages, 7 figure