Angular Shear Research Articles

Fermi surface of lead under homogeneous strain

The uniaxial stress and angular shear dependence of several extremal cross sections of the Fermi surface of the simple metal lead were obtained by a simultaneous measurement of the oscillatory magnetostriction and the de Haas---van Alphen torque. For six of the seven experimentally studied orbits all the uniaxial stress derivatives were determined and their sum compares well with the directly measured hydrostatic pressure dependence of other authors. The response of the Fermi surface to homogeneous strain is discussed in terms of volume-conserving shears (tetragonal or angular) and volume changes. A theoretical study of the Fermi surface and its strain dependence, based on a local pseudopotential model, is presented. New values for the relevant pseudopotential matrix elements in the absence of strain obtained from a fit to high-precision de Haas---van Alphen frequencies are given for different sizes [(4\ifmmode\times\else\texttimes\fi{}4), (8\ifmmode\times\else\texttimes\fi{}8), (16\ifmmode\times\else\texttimes\fi{}16)] of the secular matrix. The Fermi energy and its derivatives are computed by summing over occupied states. Eight orthogonalized plane waves are required in the secular matrix in order to describe the effect of a general homogeneous deformation on the Fermi surface. The strain response of ten carefully extremalized orbits has been calculated, with the slopes of the form factor at the first two reciprocal-lattice vectors as the only free parameters. Good agreement with our uniaxial stress data, as well with the hydrostatic pressure data of Anderson et al. is found, without invoking the spin-orbit interaction as an extra free parameter.

Variation of interlayer slip in space and time during flexural folding

This paper describes the results of an experiment which was performed with a Plasticine model to investigate the progressive evolution of flexural-slip folds. The model analyses the relationship between bulk shortening and the amount of flexural slip on fold limbs and in hinge zones. In the light of the experimental results, the theoretical relationship between limb dip and angular shear strain proposed by Ramsay (1967, p. 393) needs modifying to take into account the effect of hinge dilation and limb thinning at large deformations.

Angular shear deformation of the Fermi surface of molybdenum

Angular shear deformation of the Fermi surface of molybdenum

AN EXPERIMENTAL TEST OF THE RIGID-MUFFIN-TIN APPROXIMATION USED IN THE THEORY OF ELECTRON-PHONON INTERACTION

AN EXPERIMENTAL TEST OF THE RIGID-MUFFIN-TIN APPROXIMATION USED IN THE THEORY OF ELECTRON-PHONON INTERACTION

Homogeneous strain response of the Fermi surface of molybdenum

The response of the Fermi surface of a cubic transition metal to homogeneous uniaxial deformation of the lattice is investigated in detail both experimentally and theoretically for the first time. The uniaxial stress dependence of several cross sections of the Fermi surface of molybdenum is measured by the combined oscillatory magnetostriction and torque method, and the results are analyzed to yield separately the dependence on tetragonal shear and isotropic dilation. The Korringa-Kohn-Rostoker method of band-structure calculation is extended to include the effects of uniaxial strain. The experimental results are compared with those calculated from a phase-shift model derived from measured Fermi-surface cross sections, and the volume dependence of the phase shifts is determined from the dilation data. Quantitative predictions of the angular shear dependence of the areas of principal orbits on the Fermi surface of molybdenum are made on the basis of the phase-shift model.

Influence of Shear Velocity on Vane Shear Strength

Comparisons of field and laboratory vane shear strength measurements from geotechnical test areas in the San Diego Trough and Gulf of Maine were made to evaluate the influence of vane size, rotation rate, and sample disturbance on vane shear strength. Field vane strengths were observed to be significantly higher than laboratory strengths in both test areas. In-situ strengths obtained with large diameter vanes were consistently higher than strengths obtained with smaller vanes. Comparison of field and laboratory vane strengths with angular shear velocity at the vane blade edges indicated that angular shear velocity can significantly influence vane shear strength measurements. It is recommended that laboratory and field vane shear strengths be determined at a standard angular shear velocity to eliminate many of the uncertainties associated with differences in vane size and rotation rate. An angular shear velocity of 0.5 x 10 - ³ fps (0.15 mm/s) is proposed as the standard for both laboratory and field vane shear strength measurements.

Vlasov equilibrium and electrostatic stability properties of a nonrelativistic nonneutral E layer

Vlasov equilibrium and stability properties of a nonrelativistic nonneutral E layer are investigated for the class of thin (a ≪R0) E-layer equilibria in which all electrons have the same value of the energy H and the same value of canonical angular momentum Pϑ, i.e., fe0(H, Pϑ) = (n0R0/2πm) δ (H+eφ̄0−mV02/2) δ (Pϑ−P0), where n0, R0, φ̄0, V0, and P0 are constants. No a priori restriction is made that the density is low (ωp02≪ωc2), and equilibrium and stability behavior is studied for both fast (P0≳0) and slow (P0<0) rotational equilibria. Equilibrium space-charge effects are shown to have a large (defocusing) effect on the radial thickness of the E layer when ωp02≈ωc2. The electrostatic stability analysis includes both negative-mass (orbit variations with Pϑ) and diocotron (angular velocity shear) effects. The system is shown to be stable whenever the equilibrium flow is space-charge neutralized, i.e., whenever f=1, where f=ni0/ne0 is the fractional charge neutralization. For f≪1, a necessary and sufficient condition for instability is given by (l−2) a/R0≳f, where l is the azimuthal mode number of the perturbation. Moreover, depending on system parameters, the growth rate can be a substantial fraction of the electron plasma frequency ωp0.

Angular-Shear Deformation of the Fermi Surface of Tungsten

The derivatives of extremal cross-sectional areas of the Fermi surface of tungsten with respect to angular shear have been determined by simultaneous measurements of quantum oscillations in ultrasound velocity and in torque. The results are in good agreement with the predictions of a simple model in which the angular shear is assumed to produce no effect other than to distort the geometry of the crystal lattice. (AIP)

Three-dimensional acoustic-ray tracing in an inhomogeneous anisotropic atmosphere using Hamilton's equations

Three-dimensional ray-tracing equations are presented for tracing acoustic rays in an inhomogeneous anisotropic atmosphere which are based on Hamilton's equations for geometrical optics. The equations are converted to a form suitable for direct numerical integration. Simplified ray equations for the special case of horizontal stratification are obtained. Results of ray tracing in an atmosphere with both vertical and angular wind shear are outlined, and the formation of a shadow zone in the downwind direction is demonstrated.

Dynamic properties of certain unvulcanized rubbers in the high-elastic and fluid states

The dynamic properties of a series of unvulcanized rubbers (cis-polybutadienes, Na-polybutadiene, cis-polyisoprene, butyl rubber, polyisobutylene, and ethylene-propylene copolymer) have been investigated in a low-frequency dynamic testing machine and a frequency rheometer on the frequency range from 5 · 10−2 to 4.5 · 103 Hz at temperatures of 25 and 60°C. At these temperatures the mechanical loss factor is the most sensitive criterion of transitions from one physical state of the polymer to another. For all the specimens investigated on the experimental range of angular frequencies the modulus of the complex dynamic viscosity and the effective viscosity determined under static conditions coincide, assuming the equivalence of angular frequencies and shear rates.

Acoustic Streaming Equations: Laws of Rotational Motion for Fluid Elements

It is shown that the third-order differential equations commonly used in connection with acoustic streaming are special approximations to the law of rotational motion for a fluid element. An expression is derived for the torque exerted by stresses on a spherical element of fluid, about its center of gravity. The average torque in a steady-state sound field consists partly of (1) a sonic torque, exerted by the sound field and partly of (2) a viscous torque due to the induced steady flow. Expressions are also derived for the instantaneous rate of increase of moment of momentum of a spherical fluid element, due to angular acceleration, expansion and shearing. Interpretation is given to individual terms in various streaming equations. In general, any field consisting of superposed elementary waves will give rise to a nonzero distribution of sonic torque. In the special case of a directional source the distribution is similar to that of the gradient of the magnitude of radiation pressure.