Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations

This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Pairwise Correlations in a Multicomponent Anisotropic Liquid

We investigate a multicomponent anisotropic liquid system. The first spatial moment of the direct correlation function is taken into account to obtain asymptotic expressions for the pairwise correlation functions. In this approximation, we obtain the pairwise correlation functions that describe the system behavior not only in the critical-state neighborhood but also in the noncritical domain. We show that the critical parameters for the anisotropic system differ from those for the isotropic system.     

On hyperbolic virtual polytopes and hyperbolic fans

Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness conjecture: Let K ⊂ ℝ³ be a smooth convex body. If for a constant C, at every point of ∂K, we have R ₁ ≤ C ≤ R ₂ then K is a ball. (R ₁ and R ₂ stand for the principal curvature radii of ∂K.) This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples to the conjecture. In particular, a hyperbolic virtual polytope (and therefore, a hyperbolic hérisson) with odd an number of horns is constructed. Moreover, various properties of hyperbolic virtual polytopes and their fans are discussed.     

Scattering from infinite rough tubular surfaces

We study the Helmholtz equation in the exterior of an infinite perturbed cylinder with a Dirichlet boundary condition. Existence and uniqueness of solutions are established using the variational technique introduced (SIAM J. Math. Anal. 2005; 37 (2):598–618). We also provide stability estimates with explicit dependence of the constants in terms of the frequency and the perturbed cylinder thickness. Copyright © 2006 John Wiley & Sons, Ltd.     

Growth Behavior of CdS Nanoparticles Embedded in Polymer and Sol-Gel Silica Matrices: Relationship with Surface-State Related Luminescence

Chemical techniques were employed to synthesize CdS nanoparticles embedded in polymer (PEG 300) and sol-gel silica matrices. Systematic growth of particles (radius 3–9 nm) was obtained by adjusting post-deposition annealing temperature and time to examine the dependence of surface-state–related luminescence on particle size. Photoluminescence (PL) peak energy showed a linear dependence with a gentle slope in the weak confinement region and a steep slope in the strong confinement region, the divergence being observed near the excitonic Bohr radius for CdS. The empirical relation proposed for the weak confinement region could be used for estimating chemically prepared CdS nanoparticle size with a high degree of reliability from PL peak energy.     

An efficient calculation algorithm for focusing by plane ultrasonic transducers

In the present paper, we simulate focused wave fields generated by a system of plane transducers used in an immersion ultrasonic technique. The ultrasonic beam penetrates into the elastic medium through the fluid-solid boundary. A real-time computer algorithm is proposed to calculate stress components in the solid medium. It is shown that a good focusing wave structure can be provided by a pair of plane rectangular transducers, inclined with respect to each other and to the beam acoustic axis.     

Theoretical STM images of alkaline-earth metal adsorbed Si(1 1 1)3 × 2 surfaces

We have performed total-energy calculations to study theoretical scanning tunneling microscopy (STM) images of the Si(1 1 1)3 × 2 surfaces induced by the adsorption of alkaline-earth metals (AEMs). Previously, in a series of works on Ba/Si(1 1 1) system, we have found that the observed Si(1 1 1)3 × 1-Ba LEED phase indeed has a 3 × 2 periodicity with a Ba coverage of 1/6 ML and the HCC substrate structure. Based on results of the Ba case, we proposed that the HCC structure is also adopted for other AEM atoms, which was confirmed by our recent work. In this paper, we mainly report the STM simulations for different AEM systems to compare with existing experimental data. We discuss the difference in the detailed STM images for different AEM adsorbates. Especially, the difference in filled-state images between Mg and other AEM atoms is attributed to the strong Mg-Si interaction.     

A family of maximal surfaces in Lorentz-Minkowski three-space

We prove the existence of an infinite family of complete spacelike maximal surfaces with singularities in Lorentz-Minkowski three-space and study their properties. These surfaces are distinguished by their number of handles and have two elliptic catenoidal ends.

     

Effects of saturation on optical bistability with coupled surface plasmons

We present exact numerical results for a symmetric layered medium (prism/Ag film/nonlinear dielectric/Ag film/prism) where the middle dielectric slab is assumed to have a saturation-type nonlinearity. We show bistable behaviour in the power dependence of the reflectivity ofp-polarized light under the condition when coupled surface modes are excited in the structure. Moreover, we study the effect of saturation on the bistable behaviour to show that multivalued character is inhibited by saturation effects. The field distributions corresponding to the minimum reflectivity states of the nonlinear structure are also presented.