Scattering of plane, elastic waves by a plane crack of finite width

The diffraction of time-harmonic, vertically polarized, plane elastic waves by a crack of finite width is investigated with the aid of the integral-equation method. Using the integral representation for the particle displacement of the scattered field together with the constitutive equation, it is shown that the resulting integral equations uncouple for this kind of obstacle. In them, the amount by which the components of particle displacement jump across the crack occur as unknown quantities. The integral equations are solved numerically. Normalized power scattering characteristics and scattering cross-sections are computed.The research reported in this paper has been supported by the Netherlands organization for the advancement of pure research (Z.W.O.).     

Relativistic corrections and very small g-shifts in solids

The relativistic Breit-Margenau correction to the Zeeman-interaction has been calculated for a group of atoms in the periodic table with Herman Skillman wave functions and potentials. The results are applied to the S-state ions Mn²⁺ and Gd³⁺, to the F-center and V_k-center, and to the shallow donors in Si.     

Magnetohydrodynamic Couette flow with transpiration cooling

Transpiration cooling with magnetohydrodynamic effects is studied in a porous-wall Couette flow of a steadily moving, incompressible, electrically conducting fluid. The flow, induced by the motion of the moving wall, is subject to a uniform transverse magnetic field. A coolant fluid, with the same properties as the main-stream fluid, is uniformly injected into (or extracted from) the flow through a porous stationary wall. Solutions are presented for the velocity and induced magnetic field distributions across the parallel walls, the pressure difference induced by the magnetic drag, and the friction factor in such a flow configuration. Considerations are further given to the heat transfer characteristics wherein viscous and Ohmic heating are significant. In this connection, the recovery factor and the Nusselt number are also presented over a wide range of blowing and suction rates.Nomenclature B magnetic field vector with components (B _x , B _y , B _z ) in (x, y, z) directions - B _x dimensionless magnetic field, B _x /B ₀ - B ₀ uniform applied magnetic field - C _p specific heat at constant pressure - E electric field vector - dimensionless electric field, E _z /U ₁ B ₀ - Ek Eckert number, U ₁ ² /C _p (T ₁–T ₀) - f friction factor, ₀/U ₁ ² - h heat transfer coefficient - I total electric current across parallel walls - J electric current density - L distance between parallel walls - M Hartmann number, B ₀ L - Nu Nusselt number, hL/ - p pressure - dimensionless pressure, pL/U ₁ - Pr Prandtl number, C _p / - Pm magnetic Prandtl number, Rm/Re - q ₀ heat flux density at stationary lower wall - r recovery factor, (T _r –T ₁)/(U ₁ ² /C _p ) - Re Reynolds number, U ₁ L/ - Rm magnetic Reynolds number, _e U ₁ L - T temperature, with T ₀ and T ₁ as temperatures of the lower and upper walls - dimensionless temperature, (T–T ₀)/(T ₁–T ₀) - T _r recovery temperature - U ₁ uniform velocity of upper wall - dimensionless velocity, u/U ₁ - V fluid velocity vector with components (u, v, w) in (x, y, z) directions - dimensionless velocity, v/U ₁=v ₀/U ₁ - v ₀ velocity of injection or suction at the walls - (x, y, z) rectangular coordinates - dimensionless height, y/L - viscous dissipation function - thermal conductivity - _e magnetic permeability - kinematic viscosity - fluid density - electrical conductivity - ₀ shear stress at stationary lower wall     

Dipole oscillator strengths for the photoabsorption,photoionization and fragmentation of molecular oxygen

The photoabsorption, photoionization and fragmentation of O₂ have been studied using electron impact coincidence methods to obtain branching ratios and dipole oscillator strengths (cross-sections). The photoabsorption measurements cover the energy range 5–300 eV while the formation of electronic states of O₂⁺ (photoelectron spectroscopy) and the resulting ionic fragmentation (photoionization mass spectrometry) are both measured from close to threshold up to photon energies of 75 eV. The binding energy spectra of O₂ show peaks at 33, 47 and 57 eV in addition to those reported elsewhere in the literature. These peaks are assigned to multiple final ion states arising from photoionization of the inner valence orbitals. Structure in the O₂⁺ electronic state partial oscillator strength curves is in good agreement with recent theoretical work which predicts the existence of several shape resonances. A quantitative picture of the dipole-induced breakdown of O₂ is obtained for the energy range 12–75 eV. The photoionization efficiency is found to be constant above 20 eV.     

Two theorems on graceful trees

Let T be a tree on n vertices which are labelled by the integers in N = {1,2,…,n} such that each vertex of T is associated with a distinct number in N. The weight of an edge is defined to be the absolute value of the difference between the two numbers labelled at its end vertices. If the weights of all edges of T are distinct, we call T a graceful tree. In this note, two methods for constructing bigger graceful trees from a given one and a given pair of graceful trees are provided.     

An experimental investigation of upstream flow characteristics of viscoelastic fluids in an annular die entry

Flow behaviour of viscoelastic polymer solutions on the upstream side of an annular die entry has been experimentally investigated and compared with published results on entry flow in circular die. Stable and unstable flow patterns were observed depending on the magnitudes of Reynolds and elasticity numbers. The latter number represents the relative effects of elastic and inertial forces. The stable flow region consists of an elasticity-controlled vortex growth regime and an inertia-controlled divergent flow regime. These two flow regimes have also been observed in circular entry flow. The criteria for the onset of flow instability in an annulus, based on the maximum vortex size, agree qualitatively with various criteria proposed for polymer metls and solutions in circular entry flow. The unstable flow patterns revealed a two-stage instability with a metastable region in between. The first-stage instability is characterised by low frequency disruption of the stationary vortex; while the second-stage instability, which occurs at high Reynolds numbers, is characterised by high frequency random distortion of the flow field.     

Gas-phase observation of multiply charged C60 anions

Gas-phase observation of C60(1-), C60(3-), and C60(4-) anions generated at platinum and gold electrodes and detected by electrochemical/electrospray mass spectrometry is reported. The anions were electrochemically generated from solutions of C60 dissolved in toluene/acetonitrile as well as from reduction of C60 films on gold electrode surfaces. The gas-phase observation of C60(3-) and C60(4-), despite the fact that they have negative electron affinities, is a result of a Coulombic barrier to electron loss. The fact that C60(2-) was not detected in these experiments is ascribed to its limited solubility under the reaction conditions. These studies, which demonstrate the gas-phase kinetic stability of C60(3-) and C60(4-), illustrate the promise of electrochemical/electrospray mass spectrometry for the study of metastable anions.     

A simple extrusion method for the synthesis of aligned silica nanowires using the template of a rigid surfactant mesophase

Long range alignment of silica nanowires has been accomplished by extrusion of a novel surfactant mesophase prior to silica synthesis.