Memory of past random wave conditions in submarine groundwater discharge

Submarine groundwater discharge (SGD) is an integral part of the hydrological cycle and represents an important aspect of land-ocean interactions. We used a numerical model to simulate flow and salt transport in a nearshore groundwater aquifer under varying wave conditions based on yearlong random wave data sets, including storm surge events. The results showed significant flow asymmetry with rapid response of influxes and retarded response of effluxes across the seabed to the irregular wave conditions. While a storm surge immediately intensified seawater influx to the aquifer, the subsequent return of intruded seawater to the sea, as part of an increased SGD, was gradual. Using functional data analysis, we revealed and quantified retarded, cumulative effects of past wave conditions on SGD including the fresh groundwater and recirculating seawater discharge components. The retardation was characterized well by a gamma distribution function regardless of wave conditions. The relationships between discharge rates and wave parameters were quantifiable by a regression model in a functional form independent of the actual irregular wave conditions. This statistical model provides a useful method for analyzing and predicting SGD from nearshore unconfined aquifers affected by random waves

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.

Flow of metal into the flash gap in the last stages of a plane-strain closed-die forging operation

In closed-die forging the flash geometry should be such as to ensure that the cavity is completely filled just as the two dies come into contact at the parting plane. If metal is caused to extrude through the flash gap as the dies approach the point of contact — a practice generally resorted to as a means of ensuring complete filling — dies are unnecessarily stressed in a high-stress regime (as the flash is quite thin and possibly cooled by then), which reduces the die life and unnecessarily increases the energy requirement of the operation. It is therefore necessary to carefully determine the dimensions of the flash land and flash thickness — the two parameters, apart from friction at the land, which control the lateral flow. The dimensions should be such that the flow into the longitudinal cavity is controlled throughout the operation, ensuring complete filling just as the dies touch at the parting plane. The design of the flash must be related to the shape and size of the forging cavity as the control of flow has to be exercised throughout the operation: it is possible to do this if the mechanics of how the lateral extrusion into the flash takes place is understood for specific cavity shapes and sizes. The work reported here is part of an ongoing programme investigating flow in closed-die forging. A simple closed shape (no longitudinal flow) which may correspond to the last stages of a real forging operation is analysed using the stress equilibrium approach. Metal from the cavity (flange) flows into the flash by shearing in the cavity in one of the three modes considered here: for a given cavity the mode with the least energy requirement is assumed to be the most realistic. On this basis a map has been developed which, given the depth and width of the cavity as well as the flash thickness, will tell the designer of the most likely mode (of the three modes considered) in which metal in the cavity will shear and then flow into the flash gap. The results of limited set of experiments, reported herein, validate this method of selecting the optimum model of flow into the flash gap.

Simultaneous display of spectrum and image in a single plane, and the realization of a lensless coherent optical processor

A novel method, designated the holographic spectrum reconstruction (HSR) method, is proposed for achieving simultaneous display of the spectrum and image of an object in a single plane. A study of the scaling behaviour of both the spectrum and the image has been carried out and based on this study, it is demonstrated that a lensless coherent optical processor can be realized.

An absolute method for the determination of surface tension of liquids using pendent drop profiles

Drop formation at conical tips which is of relevance to metallurgists is investigated based on the principle of minimization of free energy using the variational approach. The dimensionless governing equations for drop profiles are computer solved using the fourth order Runge-Kutta method. For different cone angles, the theoretical plots of XT and ZT vs their ratio, are statistically analyzed, where XT and ZT are the dimensionless x and z coordinates of the drop profile at a plane at the conical tip, perpendicular to the axis of symmetry. Based on the mathematical description of these curves, an absolute method has been proposed for the determination of surface tension of liquids, which is shown to be preferable in comparison with the earlier pendent-drop profile methods.

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.

Seismic reliability assessment of external stability of reinforced soil walls using pseudo-dynamic method

The paper presents a method for the evaluation of external stability of reinforced soil walls subjected to earthquakes in the framework of the pseudo-dynamic method. The seismic reliability of the wall is evaluated by considering the different possible failure modes such as sliding along the base, overturning about the toe point of the wall, bearing capacity and the eccentricity of the resultant force. The analysis is performed considering properties of the reinforced backfill, foundation soil below the base of the wall, length of the geosynthetic reinforcement and characteristics of earthquake ground motions such as shear wave and primary wave velocity as random variables. The optimum length of reinforcement needed to maintain stability against four modes of failure by targeting various component reliability indices is obtained. Differences between pseudo-static and pseudo-dynamic methods are clearly highlighted in the paper. A complete analysis of pseudo-static and pseudo-dynamic methodologies shows that the pseudodynamic method results in realistic design values for the length of geosynthetic reinforcement under earthquake conditions.

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.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Out-of-plane deformation and failure of masonry walls with various forms of reinforcement

Out-of-plane behaviour of mortared and mortarless masonry walls with various forms of reinforcement, including unreinforced masonry as a base case is examined using a layered shell element based explicit finite element modelling method. Wall systems containing internal reinforcement, external surface reinforcement and intermittently laced reinforced concrete members and unreinforced masonry panels are considered. Masonry is modelled as a layer with macroscopic orthotropic properties; external reinforcing render, grout and reinforcing bars are modelled as distinct layers of the shell element. Predictions from the layered shell model have been validated using several out-of-plane experimental datasets reported in the literature. The model is used to examine the effectiveness of two retrofitting schemes for an unreinforced masonry wall.

A unified approach to the solution of plane problems of Magneto-elasticity with special reference to a hole in a thin infinite conducting plate

Under certain specific assumption it has been observed that the basic equations of magneto-elasticity in the case of plane deformation lead to a biharmonic equation, as in the case of the classical plane theory of elasticity. The method of solving boundary value problems has been properly modified and a unified approach in solving such problems has been suggested with special reference to problems relating thin infinite plates with a hole. Closed form expressions have been obtained for the stresses due to a uniform magnetic field present in the plane of deformation of a thin infinite conducting plate with a circular hole, the plate being deformed by a tension acting parallel to the direction of the magnetic field.

Experimental investigation of interaction of strong shock heated oxygen gas on the surface of ZrO2 - a novel method to understand re-combination heating

Interaction of shock heated test gas in the free piston driven shock tube with bulk and thin film of cubic zirconium dioxide (ZrO2) prepared by combustion method is investigated. The test samples before and after exposure to the shock wave are analyzed by X-ray diffraction (XRD), X-Ray Photoelectron Spectroscopy (XPS) and Scanning Electron Microscope (SEM). The study shows transformation of metastable cubic ZrO2 to stable monoclinic ZrO2 phase after interacting with shock heated oxygen gas due to the heterogeneous catalytic recombination surface reaction.

Studies on the out-of-plane behaviour of masonry walls

The prime aim of this PhD thesis is to contribute to the current body of knowledge on the out-of-plane performance of masonry walls through systematic investigation of the key parameters and provide insight into the design clauses of Australian Masonry Standard (AS3700-2011). The research work has been carried out through numerical simulation based on a 3D layered shell element model. The model demonstrated capability to simulate various forms of new and existing masonry systems commonly constructed in Australia such as unreinforced, internally and externally reinforced, confined and dry-stack masonry. In addition, the model simultaneously simulates in-plane and out-of-plane responses.

An accurate method for the experimental evaluation of the acoustical impedance of a black box

Among different methods, the transmission-line or the impedance tube method has been most popular for the experimental evaluation of the acoustical impedance of any termination. The current state of method involves extrapolation of the measured data to the reflecting surface or exact locations of the pressure maxima, both of which are known to be rather tricky. The present paper discusses a method which makes use of the positions of the pressure minima and the values of the standing-wave ratio at these points. Lippert's concept of enveloping curves has been extended. The use of Smith or Beranek charts, with their inherent inaccuracy, has been altogether avoided. The existing formulas for the impedance have been corrected. Incidentally, certain other errors in the current literature have also been brought to light.Subject Classification: 85.20.

Analytical method for solving a set of inhomogeneous infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of inhomogeneous infinite simultaneous equations encountered in the analysis of surface acoustic wave propagation along the periodically perturbed surface of a piezoelectric medium.