Steady-state analytical solutions for the lattice boltzmann equation

A general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.     

Synthesis and Raman analysis of 1D-ZnO nanostructure via vapor phase growth

1D-nanostructural zinc oxide (ZnO) with different shapes have been synthesized on p-type Si(1 0 0) and glass substrates via vapor phase growth by heating pure zinc powder at temperatures between 480 and 570 °C. The different ZnO nanostructures depend on the substrates and the growth temperatures. Scanning electron microscopy and X-ray diffraction revealed that a well-aligned nanowires array, which are vertical to the substrate of Si(1 0 0) with 18 sides on their heads, but six sides on their stems, has been formed at 480 °C. Raman study on the ZnO nanostructures shows that the coupling strength between electron and phonon determined by the ratio of the second- to the first-order Raman scattering cross-sections declines with decreasing diameter of the nanowires. However, a little changes of the coupling strength in terms of the width of the nanobelts have been observed.     

On two theorems for flat,affine group schemes over a discrete valuation ring

We include short and elementary proofs of two theorems that characterize reductive group schemes over a discrete valuation ring, in a slightly more general context.     

Dynamical and Topological Methods in the Theory of Geodesically Equivalent Metrics

We suggest a new, more global, approach to the study of geodesically equivalent metrics which is based on application of the theory of integrable geodesic flows. Bibliography: 17 titles.     

Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures

The vibrational response of finite periodic lattice structures subjected to periodic loading is investigated. Special attention is devoted to the response in frequency ranges with gaps in the band structure for the corresponding infinite periodic lattice. The effects of boundaries, viscous damping, and imperfections are studied by analyzing two examples; a 1-D filter and a 2-D wave guide. In 1-D the structural response in the band gap is shown to be insensitive to damping and small imperfections. In 2-D the similar effect of damping is noted for one type of periodic structure, whereas for another type the band gap effect is nearly eliminated by damping. In both 1-D and 2-D it is demonstrated how the free structural boundaries affect the response in the band gap due to local resonances. Finally, 2-D wave guides are considered by replacing the periodic structure with a homogeneous structure in a straight and a 90° bent path, and it is shown how the vibrational response is confined to the paths in the band gap frequency ranges.     

Hawking Radiation of Dirac Particles in a Nonuniformly Rectilinearly Accelerating Black Hole

The Hawking radiation of Dirac particles on the event horizon of a nonuniformly rectilinearly accelerating black hole is studied in this paper. First, we construct the symmetrized null tetrad from which the spin coefficients and Dirac equation are derived. Next, by proposing generalized tortoise coordinate transformation, the decoupling problem of the Dirac equation with nonzero rest mass is solved. Finally, by analytic continuation, the Hawking thermal spectrum formula of Dirac particle for nonuniformly rectilinearly accelerating black hole is obtained.     

Dynamical exchange corrections to the dielectric function in a two-dimensional electron gas

The effect of dynamical exchange interactions on the dielectric function of a two-dimensional electron gas is studied using a variational approach. Exchange effects are introduced via the local-field correction. The variationally obtained local-field factor is compared to the earlier perturbative result to first order in the electron-electron interaction.