Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

A field method for integrating the equations of motion of mechanico--electrical coupling dynamical systems

A field method for integrating the equations of motion for mechanico-electrical coupling dynamical systems is studied. Two examples in mechanico-electrical engineering are given to illustrate this method.     

Structure properties and Noether symmetries for super-long elastic slender rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.     

Multiaxial constitutive modeling of aircraft engine materials

Based on a newly developed theory (Lu and Weng, Acta Mech., in press) the high temperature behavior of an aircraft engine material is studied under combined stress state. Both monotonic and cyclic deformations are examined to uncover its stress-strain response, as well as its cyclic hardening and strain-ratchetting characteristics. Under a biaxial loading it is disclosed that tensile cyclic hardening is greatly magnified with a superimposed lateral tension, whereas the strain-ratchetting process is led to an enhanced, unsettling state with a superimposed lateral compression. The biaxial transient and steady-state creep strains have also been calculated. The results suggest that while a superimposed lateral tension will inhibit the creep deformation, a lateral compression can greatly promote the inelastic flow. To reflect the practical service conditions of an aircraft engine, the theory is further applied to examine the effect of loading frequency on the development of inelastic strains under concurrent thermal and mechanical loading. It is found that a more frequently flying aircraft will have a greater accumulation of creep strains and, consequently, a greater possibility of material damage in its engine components over the same total flying time.     

Numerical study of the spin-Hall conductance in the Luttinger model

We present the first numerical studies of the disorder effect on the recently proposed intrinsic spin-Hall conductance in a three dimensional lattice Luttinger model. The results show that the spin-Hall conductance remains finite in a wide range of disorder strength, with large fluctuations. The disorder-configuration-averaged spin-Hall conductance monotonically decreases with the increase of disorder strength and vanishes before the Anderson localization takes place. The finite-size effect is also discussed.     

A novel fluorometric detection of Cu(2+) based on self-assembled bilayers

Fluorescent reagent sodium 1-naphthylamine diacetate (NADA) was assembled onto gold electrodes via its electrostatic interaction with cysteine (Cys) that was directly assembled on the gold electrode surface. Formation of the self-assembled bilayers was confirmed and primarily characterized by cyclic voltammetry and X-ray photoelectron spectra (XPS). The Cys modification of the gold electrode prevented direct adsorption of NADA onto the gold electrode and hence eliminated fluorescence quenching by gold. Strong fluorescence was observed from the NADA self-assembled bilayers at gold surface and was highly efficiently quenched by Cu²⁺ that allowed for an extremely highly sensitive detection of Cu²⁺ with a detection limit of 0.2 ppt and quantitative detection range of 0.5–9 ppt. The fluorescence from NADA/Cys/Au can be easily regenerated and therefore the present report showed a reusable method for immobilizing reagent in fabricating fluorescent chemosensors.     

-metrics, projective flatness and families of polarized abelian varieties

We compute the curvature of the -metric on the direct image of a family of Hermitian holomorphic vector bundles over a family of compact Kähler manifolds. As an application, we show that the -metric on the direct image of a family of ample line bundles over a family of abelian varieties and equipped with a family of canonical Hermitian metrics is always projectively flat. When the parameter space is a compact Kähler manifold, this leads to the poly-stability of the direct image with respect to any Kähler form on the parameter space.