Spatial Variability of the Depth of Weathered and Engineering Bedrock using Multichannel Analysis of Surface Wave Method

In this paper an attempt has been made to evaluate the spatial variability of the depth of weathered and engineering bedrock in Bangalore, south India using Multichannel Analysis of Surface Wave (MASW) survey. One-dimensional MASW survey has been carried out at 58 locations and shear-wave velocities are measured. Using velocity profiles, the depth of weathered rock and engineering rock surface levels has been determined. Based on the literature, shear-wave velocity of 330 ± 30 m/s for weathered rock or soft rock and 760 ± 60 m/s for engineering rock or hard rock has been considered. Depths corresponding to these velocity ranges are evaluated with respect to ground contour levels and top surface levels have been mapped with an interpolation technique using natural neighborhood. The depth of weathered rock varies from 1 m to about 21 m. In 58 testing locations, only 42 locations reached the depths which have a shear-wave velocity of more than 760 ± 60 m/s. The depth of engineering rock is evaluated from these data and it varies from 1 m to about 50 m. Further, these rock depths have been compared with a subsurface profile obtained from a two-dimensional (2-D) MASW survey at 20 locations and a few selected available bore logs from the deep geotechnical boreholes.

Wave propagation in multi-walled carbon nanotube

In this paper, wave propagation in multi-walled carbon nanotubes (MWNTs) are studied by modeling them as continuum multiple shell coupled through van der Waals force of interaction. The displacements, namely, axial, radial and circumferential displacements vary along the circumferential direction. The wave propagation are simulated using the wavelet based spectral finite element (WSFE) method. This technique involves Daubechies scaling function approximation in time and spectral element approach. The WSFE Method allows the study of wave properties in both time and frequency domains. This is in contrast to the conventional Fourier transform based analysis which are restricted to frequency domain analysis. Here, first, the wavenumbers and wave speeds of carbon nanotubes (CNTs) are Studied to obtain the characteristics of the waves. These group speeds have been compared with those reported in literature. Next, the natural frequencies of a single-walled carbon nanotube (SWNT) are studied for different values of the radius. The frequencies of the first five modes vary linearly with the radius of the SWNT. Finally, the time domain responses are simulated for SWNT and three-walled carbon nanotubes.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Monolithic surface acoustic wave resonator oscillator

A monolithic surface acoustic wave (SAW) resonator operating at 156 MHz, in which the frequency controlling element is a Fabry–Perot type of SAW resonator and the gain element is a monolithic SAW amplifier (SiOx/InSb/SiOx structure located inside the SAW resonator cavity) is described and experimental details presented. Based on the existing experimental data, an uhf monolithic ring resonator oscillator is proposed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

A fuzzy logic based dynamic wave model inversion algorithm for canal regulation

A fuzzy logic based centralized control algorithm for irrigation canals is presented. Purpose of the algorithm is to control downstream discharge and water level of pools in the canal, by adjusting discharge release from the upstream end and gates settings. The algorithm is based on the dynamic wave model (Saint-Venant equations) inversion in space, wherein the momentum equation is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. The fuzzy rule based model is developed on fuzzification of a new mathematical model for wave velocity, the derivational details of which are given. The advantages of the fuzzy control algorithm, over other conventional control algorithms, are described. It is transparent and intuitive, and no linearizations of the governing equations are involved. Timing of the algorithm and method of computation are explained. It is shown that the tuning is easy and the computations are straightforward. The algorithm provides stable, realistic and robust outputs. The disadvantage of the algorithm is reduced precision in its outputs due to the approximation inherent in the fuzzy logic. Feed back control logic is adopted to eliminate error caused by the system disturbances as well as error caused by the reduced precision in the outputs. The algorithm is tested by applying it to water level control problem in a fictitious canal with a single pool and also in a real canal with a series of pools. It is found that results obtained from the algorithm are comparable to those obtained from conventional control algorithms.

Effect of wave parameters on flood wave subsidence

A detailed analy~is on the propagation of a sinusoidal flood wave in a wide prismatic open channel b.as hen made by numc? ii.~ll~integrating We govemins nondimenional equations of unsteady flow in an open chamei. EmpE:dsis has been laid on the effect of wave parmefen on th propagation of 6.8 sinusoidal wave. Results show that the amount of subsidence is more in the case of small wave anplltude and wave duration cases. Further, wave duration has been noticed to have a relatively Vier influence on subsidence than wave amplitude. The speed at which the peak of the wave moves is observed to be a function of only the wave amplitude.

Generalized pencils of rays in statistical wave optics

The recently introduced generalized pencil of Sudarshan which gives an exact ray picture of wave optics is analysed in some situations of interest to wave optics. A relationship between ray dispersion and statistical inhomogeneity of the field is obtained. A paraxial approximation which preserves the rectilinear propagation character of the generalized pencils is presented. Under this approximation the pencils can be computed directly from the field conditions on a plane, without the necessity to compute the cross-spectral density function in the entire space as an intermediate quantity. The paraxial results are illustrated with examples. The pencils are shown to exhibit an interesting scaling behaviour in the far-zone. This scaling leads to a natural generalization of the Fraunhofer range criterion and of the classical van Cittert-Zernike theorem to planar sources of arbitrary state of coherence. The recently derived results of radiometry with partially coherent sources are shown to be simple consequences of this scaling.

XPES studies of oxides of second- and third-row transition metals including rare earths

X-ray photoelectron spectroscopy has been employed to investigate oxides of second- and third-row transition metals, including those of rare earths. Systematics in the spin—orbit splittings and binding energies of core levels of the metals are described. In most of the cases studied, the dependence of the spin—orbit splittings on the atomic number Z is given by the relation ΔE = a(Z - Z0)4, where a is the quantum defect parameter and Z0 is the effective screening. Core-level binding energies are found to increase with the oxidation state of the metal. Most of the core-level binding energies are related to the atomic number Z by the expression E = x(Z - Z0)2, giving rise to linear plots of ln E versus ln Z. Specific features of individual oxides, with respect to satellites, multiplet structure, configuration mixing, and other properties are also discussed. The spectra of PrO2, Pr6O11, TbO2 and Tb4O7 are reported for the first time.

Monolithic surface acoustic wave resonator oscillator

A monolithic surface acoustic wave (SAW) resonator operating at 156 MHz, in which the frequency controlling element is a Fabry–Perot type of SAW resonator and the gain element is a monolithic SAW amplifier (SiOx/InSb/SiOx structure located inside the SAW resonator cavity) is described and experimental details presented. Based on the existing experimental data, an uhf monolithic ring resonator oscillator is proposed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Acoustic-surface-wave generation along a cylindrical plasma column surrounded by a compressible gas

Acoustic surface waves can be generated along the plasma column in pressure equilibrium with a gas blanket in the presence of the uniform axial magnetic field. Unlike the case of volume-acoustic-wave generation in the magnetoplasma reported recently, the threshold magnetic field required for the generation of acoustic surface waves increases with increasing gas pressure.

Rise Time of a Surface-Acoustic-Wave Resonator

This paper presents the results of the rise time calculation of a SAW resonator. The total rise time is given by rise time = [(rise time of cavity)2 + (rise time of reflectors)2 + (rise time of IDT) 2 ]. 1/2 These rise times are calculated in terms of the effective length of the cavity , the characteristics of the reflector, and the number of finger pairs in the IDT. The rise time of a 38 MHz one-port resonator on Y-Z LiNb03 calculated using this approach is found to be in good agreement with experimental results .

Radiation induced depinning of a charge density wave system

The frequency-dependent response of a pinned charge density wave is considered in terms of forced vibration of an oscillator held in an anharmonic well. It is shown that the effective pinning-frequency can be reduced by applying a d.c. field. If a strong a.c. field, superposed on a d.c. field is applied on such a system “jumps” can be observed in the frequency dependent response of the system. The conditions at which these “jumps” occur are investigated with reference to NbSe3. The possibility of observing such phenomena in other systems like superionic conductors, non-linear dielectrics like ferroelectrics is pointed out. The characteristics are expressed in terms of some “scaled variables” — in terms of which the characteristics show a universal behaviour.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.