Vertical Interface Research Articles

On the behaviour of the induction arrows over a buried conductive plate — a numerical model study

Two-dimensional numerical model calculations, employing a finite difference technique, are used to study the behaviour of the induction arrows, for a range of periods, for a conductive plate of (i) semi-infinite and (ii) finite width in uniform and layered resistive hosts. The results for the conductive plate at the surface of the host have application to a uniform-depth ocean, while the results for the plate buried at some depth in the resistive host have application to a conductive sill in a resistive Earth. The numerical results indicate that for a profile over the plate-host vertical interface the in-phase arrows for all periods and locations point towards the conductive plate, while the quadrature arrows at periods near the characteristic period of the model are oppositely directed on either side of the interface so as to point towards each other and towards the interface for nearby locations, both over the conductive plate and the resistive host. Further, the quadrature arrow undergoes a second reversal over the resistive host at a distance from the interface that is somewhat dependent on the period. Thus, at either side of the location of this second reversal, the quadrature induction arrows are again oppositely directed, but pointing away from each other, with the arrows near the interface pointing towards, and the more distant arrows pointing away from the conductive plate. The period range for the quadrature-arrow reversal is characteristic of conductivities and layer depths. The features of the quadrature-arrow sign reversals at and near the interface are in accordance with the earlier laboratory analogue model results of Hebert et al. for the Newfoundland coastal region and Nienaber et al. for a conductive plate in a resistive host. It is suggested that in practice the sign reversal of the quadrature arrow may aid in locating a conductor-host interface, and that if the conductivity of the host is known, the maximum in the anomalous vertical magnetic field response may permit an approximate determination of the conductive-layer depth.

The problem of time-dependent natural convection melting with conduction in the solid

This paper reports a theoretical and experimental study of the effect of solid-side subcooling on the phenomenon of melting by natural convection at the vertical interface between a solid body and a pool of its own liquid. The first part of the study consists of a conjugate boundary layer analysis of the transient melting process, in which the effect of solid subcooling leads to the formation of a time-dependent conduction boundary layer in the solid. The theoretical solution documents not only the effect of solid subcooling on the melting rate, but also the effects of liquid superheating (Stefan number) and thermal diffusivity ratio. The second part of the study consists of melting experiments conducted in a rectangular enclosure heated at a constant rate from the side. The solid subcooling parameter B covers the range 0.3–6.3, as the Rayleigh number remains fixed. The experiments show that in the conduction-dominated regime the Nusselt number increases as B increases. In the convection-dominated regime, the effect of the subcooling parameter B is insignificant. It is shown that these experimental observations agree with the trends anticipated theoretically in the first part of the study.

Analytic solutions for soil‐structure interaction in layered media

AbstractThe total system studied in this paper is a layered soil stratum with a rigid bedrock and a cylindrical cavity on the surface. Analytic solutions for the layered medium with prescribed harmonic displacement time history on the surface of the cylindrical cavity are presented. The whole soil domain is divided into interior and exterior domains. The interior domain is the projection of the cylindrical cavity down to the rigid bedrock, whereas the exterior domain is then the soil medium complement to the interior domain. The displacement and stress fields in both domains are expanded as an infinite series of Fourier components with respect to the azimuth. For each Fourier component in the infinite series, the solutions for both domains are found independently by solving the general differential equations of wave propagation satisfying the boundary conditions of the top surface and the lower rigid boundary. Displacement and stress continuity conditions are then imposed on the vertical interface between the two domains using the formulation of a weighted residual. For the soil‐structure interaction problem, the impedance matrix at the interface between the structure and the soil medium can be easily generated using the analytic solutions, which can then be combined with the finite element model of the structure. A simple example is presented to demonstrate the effectiveness of the procedure presented.

A parametric axisymmetric model study on the interface motions in porous-surfaced tibial implants.

The effects of a number of variables on the interface relative motions in porous-surfaced tibial implants are investigated using a simplified axisymmetric finite element model. The parameters considered are contact or link spacing, height of the central metal stem, presence of a circumferential metal flange, presence of a UHMWP articular plate resting freely on or fixed to the metal base, resting of the prosthesis edge on the cortical shell, and type of the metal alloy. In order to represent the immediate post-surgical situation with no bone ingrowth, the interface between the bone and porous-surfaced metal is modelled by frictionless rigid links oriented normal to the interface. Cases are also studied in which the horizontal interface is assumed to be fixed while the vertical interface remains frictionless. The magnitudes of the interface motion are negligibly affected by the variation in the link spacing from 0.3 mm to about 3.0 mm. The interface relative motion is predicted to decrease in cases with a shorter central metal stem, with the addition of a circumferential metal flange, with the use of more rigid prosthesis, and with the addition of a UHMWP articular plate.

The superior vena cava: conventional projections.

A S ALREADY noted, anomalies of the SVC are fairly common and are nicely demonmediastinal mass and lead to additional studies and even unnecessary surgery. In my own experistrated on CT. I have illustrated them here in conventional frontal projection so that you can suspect or recognize them from the plain films. Figure 1 illustrates double SVC and Fig 2 shows a left SVC entering the left coronary sinus. A left SVC can be recognized on the plain PA teleroentgenogram as a subtle vertical interface extending caudally from the left clavicle to the heart overlapping or lying just lateral to the aortic knob. This interface vanishes as it approaches the clavicle because of its location in the anterior mediastinum (the cervicothoracic sign’). From the Department of Radiology, University Hospital, Cincinnati. fDr Felson died Ott 22, 1988. Address reprint requests to Benjamin F&on, MD, Department of Radiology, #742, University Hospital, Cincinnati, OH 45247. Another variant of the SVC is idiopathic dilatation (Fig 3).2 The enlarged vessel may mimic a 0 I989 by W.B. Saunders Company.

Modal beamforming in a range‐dependent environment

Modal beamforming, previously developed for a range‐independent case [T. C. Yang, J. Acoust. Soc. Am. 82, 1736–1745 (1987)], is extended to a range‐dependent environment. The range‐dependent sound channel is partitioned into consecutive waveguides as a function of range. The normal modes in each waveguide are determined by the sound‐speed and bottom profile in that waveguide. The mode coefficients in adjacent waveguides are related by matching the boundary condition at the vertical interface. Modal beamforming is conducted for each waveguide. The array outputs from the waveguides are combined and plotted as a two‐dimensional surface with respect to range and depth. The source location is determined by the peak of this surface. A numerical example is given based on simulated data for a source propagating through a series of different sound‐speed profiles. The simulated data are created using an improved coupled‐mode program that was initially developed by R. B. Evans. Range and depth are estimated using a long vertical array of 3000‐m aperture, containing 50 phones. Modal beamforming for a range‐dependent environment can also be conducted directly using the coupled‐mode program or any other propagation code.

Buoyancy flow at a two‐fluid interface in a porous medium: Analytical studies

Analytical solutions for the pressure distribution and the flow field are derived for several idealized situations involving an injection well and a vertical plane or cylindrical interface between two fluids of different density and viscosity in an infinite anisotropic aquifer bounded by two horizontal planes. The interface, or transition zone, between the two fluids may be either sharp or of finite width. The buoyancy flow induced by the density difference will cause the two‐fluid interface to tilt. A characteristic time scale for the buoyancy tilting rate is deduced. The conditions at the well are found to have only a small influence on the buoyancy flow except very close to the well. The buoyancy flow decreases with increasing width of the transition zone.

Reactivity Analysis Model Based on Finite Difference Method for Three-Dimensional Fast Breeder Reactor Core Deformation

An analysis model has been proposed to evaluate reactivity due to horizontal fast breeder reactor (FBR) core deformation in seismic events by direct three-dimensional eigenvalue calculations, which are impossible for current neutronic analysis programs. The model is based on a current-centered finite difference neutron diffusion calculation method. Macroscopic neutron reaction cross sections are defined, which take into account changes in both mesh volume and material composition. Further, the expression of vertical neutron current is modified in such a way as to take into account changes in vertical mesh interface areas. By using these macroscopic neutron cross sections and the modified expression for vertical neutron current, it is possible to calculate the effective multiplication factor of a deformed FBR core within the bounds of a finite diffusion calculation method using the same mesh division used for the normal non-deformed core. Computation time and computer core memory required by the presented model are almost the same as in current finite difference methods. The calculated reactivities for simple one-dimensional slab, two-dimensional slab, and three-dimensional hexagonal systems agreed within 5% of those obtained by either a finite method or a finite difference method. The agreement was particularly good (within 2%) for cases in whichmore » fuel assembly pitches decrease around the horizontal core midplane; therefore, large reactivity is inserted.« less

A study in human subjects using a new device designed to mimic the protrusive functional appliances used previously in monkeys

A new appliance is described that mimics in function the protrusive jaw-positioning devices used previously in monkeys. The appliance consists of maxillary and mandibular posterior biteplates separated by a sharp vertical interface perpendicular to the occlusal plane. Function of the appliance was evaluated in 35 consecutively treated patients and compared against matched controls. The patients, who ranged in age from 9 to 14 years, accepted the appliance readily and wore it 24 hours each day, even while eating. Although cephalometrics was the primary assessment tool, tomograms and/or transcranial x-ray films and models were also obtained. The rate of mandibular length increase, measured from articulare, was comparable to or better than that found in monkeys using similar devices. The dentoalveolar effects were also similar to those found in monkeys, including anterior migration of the mandibular dentition and posterior movement of the maxillary dentition. The mandibular molars moved forward 4.8 mm of which 73% was determined to have come from increased anterior movement of the mandible. Subtracting normal growth, the net mandibular length increase was 2.2 mm during the 9.4-month average treatment interval.

Monomolecular lipid layers on thin water films and on solid supports

Thin water layers in contact with a Langmuir film balance trough are prepared on solid supports. Onto these, monomolecular lipid layers are subsequently spread. The pressure—area isotherm of a monofilm on such a vertical liquid-air interface shows new features due to a very thin water layer that is carried along with the lipid film. Gravitational and frictional forces contribute to the observed additional lateral pressure. After the thinning of the water layer the monofilm is reversibly bound to the solid substrate. It is demonstrated that deposition is possible at all lateral pressures of the monofilm extending even far into the gaseous state region at virtually zero pressure. This allows for the ellipsometric characterization of monomolecular lipid layers on solid supports irrespective of their physical state.

Reflection and transmission at an interface separating transversely inhomogeneous acoustic half-spaces

Summary The problem of reflection and transmission at a vertical interface separating two stratified half-spaces is solved exactly, in principle, in the context of one-way propagation theory. The solution requires a generalization of the usual notions of reflection and transmission coefficients. These coefficients become (formally) pseudo-differential operators. For homogeneous half-spaces the operator symbols are recognized as the usual plane wave reflection and transmission coefficients. For stratified half-spaces the operator symbols should be calculated using approximate formulae that are consistent with whatever algorithm is to be used in the associated propagation problem. We derive formulae that are consistent with a high-frequency algorithm that has already been shown to be superior to other extended parabolic (one-way) theories. The connection between the exact theory and a number of other extended parabolic theories is explored by means of perturbation series.

Seismic waves generated by an impulsive point source in a solid/fluid configuration with a plane boundary

The space‐time acoustic wave motion generated by an impulsive point source in a solid/fluid configuration with a vertical plane boundary is calculated with the aid of the modified Cagniard method. Two types of sources are considered in detail, viz. (1) a point source of expansion (model for an explosive source), and (2) a point force parallel to the vertical interface (model for a mechanical vibrator). Numerical results are presented for the transmitted scalar traction in the fluid in those regions of space where head wave contributions occur. There is a marked difference in the time response observed for the two types of sources and for the different positions of the receiver in the fluid with respect to the position of the source in the solid. These waveform differences are important when the transmitted wave in the fluid is used to determine experimentally the elastic properties of the solid. Scholte waves are observed only when the source is close to the fluid/solid interface. As compared with the traditional Fourier‐Bessel integral transform method of handling this problem, the computation time with the method presented here is considerably less.

Characterisation and modelling of SIPOS on silicon high-voltage devices

The paper describes the way a semiconducting coating, such as SIPOS, controls the spread of the depletion region near the surface of simple planar high-voltage diodes. This is important to achieve the optimum breakdown performance for high-voltage devices. When an insulating oxide separates the SIPOS from the silicon, the surface layer acts as a resistive field plate and spreads a thin depletion region right across the surface at only a few volts reverse bias. Without the oxide, or if it is thin enough to be effectively transparent to electrons and holes, the depletion region spread in the surface is limited by current flow across the SIPOS silicon interface, and the depletion spread with bias becomes more like that expected for bulk silicon. For reverse biased planar diodes, with SIPOS directly over the junction, the leakage current is proportional to the voltage to the power of 0.7?0.8 when measured at temperatures where the current through the SIPOS dominates. These effects can be modelled, neglecting any effect from the p?n junction, using lateral and vertical SIPOS-silicon interface current measurement data.

Coupled convective instabilities at crystal-melt interfaces

The stability of the parallel flow between a vertical crystal-melt interface and a vertical wall held at a temperature above the melting point of the crystal is analyzed for Prandtl numbers, P, ranging from 10 -2 to 10 2. Three modes of instability occur: (1) a bouyant mode, (2) a shear mode, and (3) a coupled crystal-melt mode. The bouyant and shear modes are similar to those that occur for flow between two vertical rigid walls held at different temperatures. For Prandtl numbers greater than approximately two, the coupled crystal-melt mode occurs at a lower Grashof number than the other two modes. Specific results are given for succinonitrile ( P = 22.8) and lead ( P = 0.0225). These calculations and similar calculations for a cylindrical geometry were motivated by and are in general agreement with recent experiments on succinonitrile.

Flood Plain and Main Channel Flow Interaction

Experimental results are presented concerning the discharge characteristics, the boundary shear stress and boundary shear force distributions in a compound section comprising of one rectangular main channel and two symmetrically disposed flood plains. Equations are presented giving the shear force on the flood plains as a percentage of the total shear force in terms of two dimensionless parameters. The experimental shear force results are used to derive ancillary equations for the lateral and vertical transfer of momentum within the cross section. The apparent shear force acting on the vertical interface between one flood plain and the main channel is shown to increase rapidly for low relative depths and high flood plain widths. Equations are also presented giving the proportion of the total flow which occurs in the various sub areas. The division of flow based on linear proportion of the areas is shown to be inadequate on account of the interaction between the flood plain and main channel flows.

Discharge Assessment in Compound Channel Flow

A series of laboratory tests were performed to measure the boundary shear stresses in a compound channel consisting of a main channel and associated shallow floodplains. Four different floodplain roughnesses were used. From these results apparent shear stresses across three different assumed main channel/floodplain interface planes (vertical, horizontal and diagonal) were calculated. The data was used with data from previous studies to derive a statistical relationship between the apparent shear stress on the vertical interface and several easily calculated parameters of the channel geometry and hydraulic characteristics. The accuracies of different methods of discharge calculation were shown to be dependent upon the assumptions they make regarding the magnitude of the apparent shear stress on the particular interface chosen. An apparent shear stress ratio was proposed which was found to be a useful yardstick in selecting the best method of discharge calculation for particular channel and flow conditions. Generally it was found that at low floodplain depths using the horizontal or diagonal interfaces gave better discharge results than the vertical.

Consequences of interaction between sodium and concrete

The experimental program involved ten experiments of sodium-concrete interaction under neutral atmosphere. When the interface (hot face) is horizontal and the opposite face (cold face) is closed by a sheet-iron, sodium temperature plays an important part but concrete thickness does not appear as an important parameter. The involved mechanism seems to be melt soda attack. The only test which is made with vertical interface shows a very different reaction rate evolution from one observed in horizontal interface. A computer code which calculates the consequences of such interactions is under development.

Boundary integral equation solutions to moving interface between two fluids in porous media

The boundary integral equation method is formulated for and applied to problems concerning a moving interface between two fluids in porous media. The mixing between two fluids is assumed to be insignificant; a sharp interface exists between them. Numerical and experimental results are presented for the tilting of a vertical interface in a Hele‐Shaw cell. During the initial stage of the interfacial movement, nonlinear effects are clearly demonstrated. The BIEM results are also compared to experimental results for a transient salt water intrusion problem.

The rotation of a vertical interface in a porous medium

A solution is given of the problem of the simultaneous flow of two different fluids in a vertical plane, separated from each other by a vertical interface. It is shown that the viscosities of the two fluids influence the motion of the interface only through their average value. A simple formula for the rotation of the interface is derived in terms of the relative density difference.

Flying locust visual responses in a radial wind tunnel

1. In order to observe the response of a flying locust to stationary and moving patterns, a new wind tunnel has been developed, tested and described. 2. The flying locust, free to yaw and move laterally, is capable of flying stably and in a natural flight posture whilst fixated on simple visual patterns. Both rotational and translational movements were monitored by transducers. 3. Locusts can orientate towards a stripe and near but not directly towards a black-white vertical interface. 4. Removal of visual stimuli by switching off or gradually reducing the pattern illumination resulted in less accurately controlled flight in 92% of trials. 5. Locusts maintained orientation when one eye was covered. 6. Locusts responded to moving striped patterns. They could accurately follow speeds ranging from 1.2° s−1 to 90° s−1. Some animals ceased to follow the stripes after a period of time which varied from insect to insect.