Quantization Of Cyclotron Motion and Quantum Hall Effect

We present a two dimensional model of IQHE in accord with the cyclotron motion. The quantum equation of the QHE curve and a new definition of filling factor are also given.Comment: 13 Pages, Latex, 1 figure, to appear in Europhys. Lett. September 199

Surface wave ray tracing and azimuthal anisotropy: a generalized spherical harmonic approach

We explain in detail how azimuthally anisotropic maps of surface wave phase velocity can be parametrized in terms of generalized spherical harmonic functions, and why this approach is preferable to others; most importantly, generalized spherical harmonics are the only basis functions adequate to describe a tensor field everywhere on the unit sphere, including the poles of the reference frame. We introduce here a new algorithm, designed specifically for the generalized harmonic parametrization, to trace surface wave ray paths in the presence of laterally varying azimuthal anisotropy. We describe the algorithm, and prove its reliability in view of future application

On the parametrization of equilibrium stress fields in the Earth

A new method for parametrizing the possible equilibrium stress fields of a laterally heterogeneous earth model is described. In this method a solution of the equilibrium equations is first found that satisfies some desirable physical property. For example, we show that the equilibrium stress field with smallest norm relative to a given inner product can be obtained by solving a static linear elastic boundary value problem. We also show that the equilibrium stress field whose deviatoric component has smallest norm with respect to a given inner product can be obtained by solving a steady-state incompressible viscous flow problem. Having found such a solution of the equilibrium equations, all other solutions can be written as the sum of this equilibrium stress field and a divergence-free stress tensor field whose boundary tractions vanish. Given n divergence-free and traction-free tensor fields, we then obtain a simple n-dimensional parametrization of equilibrium stress fields in the earth model. The practical construction of such divergence- and traction-free tensor fields in the mantle of a spherically symmetric reference earth model is described using generalized spherical harmonics

Tomographic resolution of ray and finite-frequency methods: A membrane-wave investigation

The purpose of this study is to evaluate the resolution potential of current finite-frequency approaches to tomography, and to do that in a framework similar to that of global scale seismology. According to our current knowledge and understanding, the only way to do this is by constructing a large set of ‘ground-truth' synthetic data computed numerically (spectral elements, finite differences, etc.), and then to invert them using the various available linearized techniques. Specifically, we address the problem of using surface wave data to map phase-velocity distributions. Our investigation is strictly valid for the propagation of elastic waves on a spherical, heterogeneous membrane, and a good analogue for the propagation of surface waves within the outermost layers of the Earth. This amounts to drastically reducing the computational expense, with a certain loss of accuracy if very short-wavelength features of a strongly heterogeneous Earth are to be modelled. Our analysis suggests that a single-scattering finite-frequency approach to tomography, with sensitivity kernels computed via the adjoint method, is significantly more powerful than ray-theoretical methods, as a tool to image the fine structure of the Eart

Acoustics of the banjo: measurements and sound synthesis

Measurements of vibrational response of an American 5-string banjo and of the sounds of played notes on the instrument are presented, and contrasted with corresponding results for a steel-string guitar. A synthesis model, fine-tuned using information from the measurements, has been used to investigate what acoustical features are necessary to produce recognisable banjo-like sound, and to explore the perceptual salience of a wide range of design modifications. Recognisable banjo sound seems to depend on the pattern of decay rates of “string modes”, the loudness magnitude and profile, and a transient contribution to each played note from the “body modes”. A formant-like feature, peaking around 500–800 Hz on the banjo tested, is found to play a key role. At higher frequencies the dynamic behaviour of the bridge produces additional formant-like features, reminiscent of the “bridge hill” of the violin, and these also produce clear perceptual effects

Acoustics of the banjo: theoretical and numerical modelling

A previous paper [Woodhouse et al., Acta Acustica 5, 15 (2021) https://doi.org/10.1051/aacus/2021009] showed acoustical measurements of an American 5-string banjo alongside similar measurements on a guitar, revealing a strong contrast in bridge admittance. Theoretical and numerical modelling is now presented to probe the physics behind this contrast. Without the bridge and strings, the banjo membrane has a rising trend of admittance associated with its modal density, and it has a distinctive pattern of sound radiation because an ideal membrane has no critical frequency. When the bridge and strings are added to the banjo, three formants shape the amplitude envelope of the admittance. One is associated with local effects of mass and stiffness near the bridge, and is sensitive to bridge mass and the break angle of the strings over the bridge. The other two formants are associated with dynamical behaviour of the bridge, analogous to the “bridge hill” in the violin

Calculation of seismic displacement fields in self-gravitating earth models—applications of minors vectors and symplectic structure

An account is given of the minor vector method that allows for the stable numerical integration of the systems of linear ordinary differential equations occurring in a number of geophysical problems. In particular, new results are presented that allow for the application of the method to the solution of 6-D inhomogeneous boundary value problems, such as those encountered in the calculation of seismic displacement fields in spherically symmetric, self-gravitating earth models. In addition, the symplectic structure possessed by many of the ordinary differential equations of interest is described. It is shown how this structure can be used to simplify the numerical implementation of the minor vector method and also to concisely derive a number of theoretical results about the eigenfrequencies and eigenfunctions of a linearly anelastic earth model

An icon-based synoptic visualization of fully polarimetric radar data

The visualization of fully polarimetric radar data is hindered by traditional remote sensing methodologies for displaying data due to the large number of parameters per pixel in such data, and the non-scalar nature of variables such as phase difference. In this paper, a new method is described that uses icons instead of image pixels to represent the image data so that polarimetric properties and geographic context can be visualized together. The icons are parameterized using the alpha-entropy decomposition of polarimetric data. The resulting image allows the following five variables to be displayed simultaneously: unpolarized power, alpha angle, polarimetric entropy, anisotropy and orientation angle. Examples are given for both airborne and laboratory-based imaging

Effects of off great-circle propagation on the phase of long-period surface waves

Surface wave phase corrections for departures from great-circle propagation are computed using two-point ray-tracing through the aspherical earth model M84C of Woodhouse & Dziewonski (1984). For Rayleigh and Love waves with periods in the range 100–250 s, we determine whether these corrections provide significant variance reductions in source determinations compared with corrections calculated assuming great-circle propagation through the heterogeneous structure. For most source-receiver geometries, the off great-circle travel-time effects are small (< 10 s) for second and third orbits (e.g. R2 and R3), and their application in source determinations does not significantly reduce the data variance. This suggests that for the loworder heterogeneous models currently available the geometrical optics approximation is valid for long-period low orbit surface waves. Off great-circle phase anomalies increase quasi-linearly with increasing orbit number, indicating that the geometrical optics approximation degrades for higher orbits, which emphasizes the importance of developing higher order approximations for free-oscillation studies.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73147/1/j.1365-246X.1987.tb05217.x.pd