Distribution Of Particle Displacements Research Articles

Suppression of bulk wave radiation of leaky surface acoustic waves by proton exchange

This paper shows that the bulk wave that is radiated to the inside of the substrate in the excitation and propagation of a leaky surface acoustic wave (LSAW) can be suppressed by forming a proton-exchanged layer on the surface of the substrate. It is theoretically shown that, even if the electrical condition of the propagation path is a free surface, the particle displacement distribution of the LSAW particle is concentrated at the substrate surface by proton exchange, as in the case of a metallized surface. This result suggests that the bulk wave radiation in LSAW excitation can be suppressed. The bulk wave radiation loss is examined by measuring the insertion loss between the input and the output IDT on the 41° Y-X LiNbO3 substrate, and it is shown that the bulk wave can be reduced to zero by proton exchange. It is shown experimentally that the leak loss in the propagation due to the bulk wave radiation can be reduced to approximately one-third by the proton exchange. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(1): 44–52, 2000

Pore-Scale Flow and Dispersion

Pore-scale simulations of fluid flow and mass transport offer a direct means to reproduce and verify laboratory measurements in porous media. We have compared lattice-Boltzmann (LB) flow simulations with the results of NMR spectroscopy from several published flow experiments. Although there is qualitative agreement, the differences highlight numerical and experimental issues, including the rate of spatial convergence, and the effect of signal attenuation near solid surfaces. For the range of Reynolds numbers relevant to groundwater investigations, the normalized distribution of fluid velocities in random sphere packings collapse onto a single curve, when scaled with the mean velocity. Random-walk particle simulations in the LB flow fields have also been performed to study the dispersion of an ideal tracer. These simulations show an encouraging degree of quantitative agreement with published NMR measurements of hydrodynamic and molecular dispersion, and the simulated dispersivities scale in accordance with published experimental and theoretical results for the Peclet number rangek 1 ≤ Pe ≤1500. Experience with the random-walk method indicates that the mean properties of conservative transport, such as the first and second moments of the particle displacement distribution, can be estimated with a number of particles comparable to the spatial discretization of the velocity field. However, the accurate approximation of local concentrations, at a resolution comparable to that of the velocity field, requires significantly more particles. This requirement presents a significant computational burden and hence a numerical challenge to the simulation of non-conservative transport processes.

GUIDED WAVES IN A WATER LOADED HOLLOW CYLINDER

Abstract A study on the leakage of guided waves in hollow cylinders is presented to find suitable modes that are basically independent of water loading. In this study, a boundary value problem of leaky cylindrical guided wave propagation is derived and solved in complex domain by using a complex wave number to obtain velocity and attenuation dispersion curves. Cross–sectional displacement and power flow distributions are also calculated at some sampling points on the dispersion curves in order to extract physically based answers on their attenuative natures. It turns out that the cross-sectional particle displacement distribution of a leaky mode, named wave structure in this paper, is remarkably sensitive with respect to outside water loading, resulting in a significant profile change at an interface between water and a tube. However that of a non-leaky mode is nearly independent. Ratios of the radial and tangential power flows are calculated for estimations of portions of leaky ultrasonic energy. An expe...

Normal Faults and Their Hanging-Wall Deformation: An Experimental Study

We have used clay models to study the effects of fault shape and displacement distribution on deformation patterns in the hanging wall of a master normal fault. The experimental results show that fault shape influences the style of secondary faulting and folding. Mostly antithetic normal faults form above concave-upward fault bends, whereas mostly synthetic normal faults form above low-angle fault segments and convex-upward fault bends. Beds dip toward the master normal fault above concave-upward fault bends and away from the master normal fault above low-angle fault segments and convex-upward fault bends. Generally, secondary faulting and folding are youngest at fault bends and become progressively older past fault bends. Hanging-wall deformation patterns differ significantly when a basal plastic sheet imposes a constant-magnitude displacement distribution on the master normal fault. In models without a plastic sheet, numerous secondary normal faults form in the hanging wall of the master normal fault. Most secondary normal faults propagate upward and, consequently, have greater displacement at depth. In models with a plastic sheet, few visible secondary normal faults develop. Most of these faults propagate downward and, consequently, have less displacement at depth. Hanging-wall folding is wider and bedding dips are gentler in models without a plastic sheet than in identical models with a plastic sheet. The observed particle paths, displacement distributions, bedding dips, and orientations of the principal-strain axes in our physical models with and without a basal plastic sheet are compatible with the assumption that homogeneous, inclined simple shear accommodates the hanging-wall deformation. Not all of our modeling observations, however, are consistent with this assumption. Specifically, the observed variability with depth of the distribution and intensity of deformation is incompatible with homogeneous, inclined simple shear as the hanging-wall deformation mechanism.

On the continuity of stochastic models for the Lagrangian velocity in turbulence

Inertial sub-range statistics of stochastic models for the Lagrangian velocity in turbulent flow have been examined. For Markovian models it is shown that consistency with Kolmogorov's theory of local isotropy requires that the Lagrangian velocity be a continuous function of time. This limits suitable Markov models to those which can be represented by a stochastic differential equation. Markov models in which the velocity is discontinuous (and a class of non-Markovian jump models) are not consistent with Kolmogorov's theory. Modifications to (Kolmogorov's theory to account for the effects of intermittency are shown to be non-Markovian, but still correspond to a Lagrangian velocity which is continuous. In Gaussian homogeneous turbulence only continuous Markov models predict that the particle displacement is Gaussian. For a Markovian jump model, the particle displacement distribution is leptokurtic with a maximum excess of about 0.67, which is inconsistent with wind tunnel data in grid turbulence.

Chaotic advection and dispersion

The dispersion of passive tracers by chaotic advection is examined for the flow through a “twisted” pipe. The effect of long-time trapping by islands on particle dispersion is documented by numerical experiments. The trapping episodes lead to periods of quasi-ballistic motion, however these periods are intermittent and are interrupted by periods of chaotic motion. The effect of the longitudinal transport is to cause super-diffusive spreading of the tracer, Δ 2( t)≈ t v where v is empirically determined to be in the range 1 < v < 2. A simple model is presented thatleads to algebraic dispersion laws. This rapid dispersion is a consequence of the divergence of the second moment of the particle displacement distribution. It can also be interpretedin terms of the slow decay of the waiting-time distribution within a “cell” of the flow. The significance of the waiting-time distribution on dispersion in other spatially periodic flow geometries is discussed.

Double-thin-film waveguides for acoustic surface waves

To increase the degrees of freedom in the design of a thin-film surface acoustic waveguide, this paper proposes a waveguide of new configuration in which two kinds of strip thin films are placed on the substrate. Specifically, a double-thin-film waveguide is considered which consists of a Y-cut Z-propagation LiNb 03 substrate with a chromium coat and an additional gold coat on top of it. The velocity dispersion of the Rayleigh wave and the particle displacement distribution as a measure of the guiding effect have been studied theoretically. The results are compared with the structure coated with gold only or with chromium only. From the utility viewpoint, it is desirable to make the velocity dispersion small and the guiding effect substantial. The chromium-coated structure has a smaller velocity dispersion but the guiding effect is smaller. On the other hand, the gold-coated waveguide has a larger guiding effect but the velocity dispersion is also large. In the double-thin-film configuration, the velocity dispersion can be reduced without significantly degrading the guiding effect. This double-thin-film waveguide and the one coated with gold only have been fabricated and the experiments have been performed. It has been confirmed that the numerical results for the velocity dispersion are accurate.

Rupture propagation and focusing of energy in a foam rubber model of a stick slip earthquake

Dynamic displacements and velocities measured at the surface of a block of foam rubber are analyzed for stick slip events on faults with three different geometries; elliptical, rectangular (aspect ratio of 3.33), and long thin (aspect ratio of 12.66). Over 100 separate events were recorded, each with up to eight simultaneous point measurements of particle displacement. The positions of the measurements were along the fault trace and to distances of a few fault lengths. Acceleration of the rupture front is observed as the rupture propagates out from its point of nucleation. Deceleration of the rupture is also observed when it enters a region of lower effective stress. In the direction of rupture propagation the static displacements along the fault trace increase, and the rise times decrease. The combined effect causes a rapid increase in particle velocities. For a predominantly unilateral rupture, increases in particle velocities by a factor of 2 or 3 over those recorded near the center of the fault trace are common. At higher rupture velocities, there is a larger increase in the particle velocity (or decrease in the rise time) for a given increase in the static displacement. The amplitude of the far‐field displacement is similarly strongly dependent on the nature of the rupture. Differences in far‐field displacements of an order of magnitude are seen for measurements at equal distances from a unilateral rupture. When the rupture initiates at depth, a much more uniform distribution of particle displacements and velocities is obtained. Afterslip, i.e., motion occurring significantly slower than the time required for a shear wave to travel the length of the fault, is also observed. Comparison of our model results with surface static displacements following major earthquakes suggests that observed variation in static displacements may be due in part to variations in the bedrock stress field. Such stress heterogeneity can lead to a division of a major earthquake into a series of several subruptures, each of which rupture coherently, but the event as a whole behaves incoherently.

Measurement of flow velocity distribution by means of double-exposure holographic interferometry

A method for measuring flow velocity distribution in the interior of a transparent fluid is proposed. The method utilizes a thin sheet of laser light, which illuminates fluid containing small scattering particles. A double-exposure hologram is made with the scattered light as a signal wave. In the reconstructed image we can observe interference fringes which correspond to the distribution of particle displacements between the two exposures and consequently to the distribution of flow velocity. Simple experiments were performed that confirmed the usefulness of the method. A discussion of the relation of this method to laser Doppler velocimetry shows that the two methods utilize different aspects of the same phenomenon.

Propagation of Elasto-Plastic Stress Waves in Cylindrical High-Pressure Sections

An analysis is made of the axisymmetric elastic and plastic stresses and deformations in thick-wall cylindrical shells subjected to internal dynamic pressures. The study utilizes a direct numerical approach called the discontinuous-step analysis. This analysis is based on the direct use of the boundary conditions and the applicable physical laws to propagate dynamic changes in the cylinder by finite steps. Reflection of stress waves from both inner and outer boundaries is automatically generated. The validity of the method is checked by comparison of numerical results in the elastic range with published results for thick-wall cylinders. Comparison is made with experimentally measured strains from the high-pressure section of a hypervelocity launcher. This analysis assumes that the work hardening of the material is independent of the strain rate and is constant for a large variation of plastic strain. Stress-strain relationships are derived for the condition of plane strain in the cylinder which is held to be representative of the actual conditions in the launcher high-pressure section. The digital computer program developed from this study predicts the distribution of dynamic stress and strain throughout the cylinder, the internal radial growth, the distribution of particle displacement, the distribution of yield stress in an autofrettaged cylinder, and the residual stress.

Particle motion along a kinematic fault model

abstract Particle motion was examined along the following kinematic fault model: the fault plane is a rectangle so elongated that differences in particle motion in the shorter dimension can be neglected and rupture, once initiated, can be considered to propagate only in the longitudinal direction(s) at constant speed; the distribution of particle displacement along the ruptured fault segment maintains the same sinusoidal shape at different times until finally all particles stop simultaneously. It was found that the pattern of particle motion in this model depends on whether the rupture propagates unilaterally or bilaterally. For the bilateral case, particle displacement and velocity are nearly a finite ramp and a box-car function of time, respectively. The maximum particle velocity is the same everywhere along the final ruptured fault segment, but the average velocity is slightly higher for particles closer to the ends. For the unilateral case, particle velocity is approximately an impulse function of time for particles near the starting edge and gradually becomes a box-car function for particles near the ending edge of rupture. The maximum velocity is the same for all particles along the fault segment, but the average velocity is considerably higher for particles closer to the ending edge. It is not a good approximation for either of these cases to assume that all the particles along the fault segment have the same displacement-time function with only a time delay.