A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary's entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429-35) for two-dimensional non-interacting tidal waves. (C) 2000 Elsevier Science Ltd. All rights reserved.

Two-dimensional approximation for tidal dynamics in coastal aquifers: Capillarity correction

Most previous investigations on tide-induced watertable fluctuations in coastal aquifers have been based on one-dimensional models that describe the processes in the cross-shore direction alone, assuming negligible along-shore variability. A recent study proposed a two-dimensional approximation for tide-induced watertable fluctuations that took into account coastline variations. Here, we further develop this approximation in two ways, by extending the approximation to second order and by taking into account capillary effects. Our results demonstrate that both effects can markedly influence watertable fluctuations. In particular, with the first-order approximation, the local damping rate of the tidal signal could be subject to sizable errors.

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

Two-Dimensional Failure Modeling with Minimal Repair

In this paper, we discuss two-dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one-dimensional case to the two-dimensional case and characterize the failures over a two-dimensional region under minimal repair. An application of this important result to a rnanufacturer's servicing costs for a two-dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. (C) 2003 Wiley Periodicals, Inc.

Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter (epsilon), the amplitude parameter (a) and coastline parameter (beta) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations. (c) 2004 Elsevier Ltd. All rights reserved.

Efffluent flux prediction in variably saturated soil zones within a septic tank-soil absorption trench

The treatment and hydraulic mechanisms in a septic tank-soil absorption system ( SAS) are highly influenced by the clogging layer or biomat zone which develops on bottom and lower sidewall surfaces within the trench. Flow rates through the biomat and sub-biomat zones are governed largely by the biomat hydraulic properties (resistance and hydraulic conductivity) and the unsaturated hydraulic conductivity of the underlying soil. One- and 2-dimensional models were used to investigate the relative importance of sidewall and vertical flow rates and pathways in SAS. Results of 1-dimensional modelling show that several orders of magnitude variation in saturated hydraulic conductivity (Ks) reduce to a 1 order of magnitude variation in long-term flow rates. To increase the reliability of prediction of septic trench hydrology, HYDRUS-2D was used to model 2-dimensional flow. In the permeable soils, under high trench loading, effluent preferentially flowed in the upper region of the trench where no resistant biomat was present (the exfiltration zone). By comparison, flow was more evenly partitioned between the biomat zones and the exfiltration zones of the low permeability soil. An increase in effluent infiltration corresponded with a greater availability of exfiltration zone, rather than a lower resistance of biomat. Results of modelling simulations demonstrated the important role that a permeable A horizon may play in limiting surface surcharge of effluent under high trench hydraulic loading.

The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Optical study of a light diaphragm rupture process in an expansion tube

Rupture of a light cellophane diaphragm in an expansion tube has been studied by an optical method. The influence of the light diaphragm on test flow generation has long been recognised, however the diaphragm rupture mechanism is less well known. It has been previously postulated that the diaphragm ruptures around its periphery due to the dynamic pressure loading of the shock wave, with the diaphragm material at some stage being removed from the flow to allow the shock to accelerate to the measured speeds downstream. The images obtained in this series of experiments are the first to show the mechanism of diaphragm rupture and mass removal in an expansion tube. A light diaphragm was impulsively loaded via a shock wave and a series of images was recorded holographically throughout the rupture process, showing gradual destruction of the diaphragm. Features such as the diaphragm material, the interface between gases, and a reflected shock were clearly visualised. Both qualitative and quantitative aspects of the rupture dynamics were derived from the images and compared with existing one-dimensional theory.

Diagnostics of A Range of Highly Superorbital Carbon Dioxide Flows

Expansion tubes are impulse facilities capable of generating highly energetic hyper-sonic flows. This work surveys a broad range of flow conditions produced in the facility X1 with carbon dioxide test gas, for simulation of spacecraft entry into the Martian atmosphere. Conditions with nominal flow speeds of 7, 9, 11 and 13 km/s were tested. The freestream conditions were calibrated using static/Pitot pressure measurements and advanced optical diagnostics. An extensive set of holographic interferometry experiments was performed on flows over wedges for quantitative study of freestream and post-shock densities, and post-shock ionisation. A one-dimensional code with frozen and equilibrium chemistry capabilities was used to estimate the freestream conditions. An equilibrium chemistry model produced a good match to measured freestream quantities at the high enthalpy conditions which are a major aim of this facility's operation. The freestream in the lower enthalpy conditions was found to be heavily influenced by chemical non-equilibrium. Non-equilibrium in the final unsteady expansion process of flow generation was accounted for by switching from equilibrium to frozen chemistry at a predetermined point. Comparison between the freestream density results of holographic interferometry, pressure measurements and computations shows good agreement.

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments.

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

Quantum integrability is established for the one-dimensional supersymmetric U model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric U chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system. [S0163-1829(98)00425-1].

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].

Incoherent interlayer transport and angular-dependent magnetoresistance oscillations in layered metals

The effect of incoherent interlayer transport on the interlayer resistance of a layered metal is considered. We find that for both quasi-one-dimensional and quasi-two-dimensional Fermi liquids the angular dependence of the magnetoresistance is essentially the same for coherent and incoherent transport. Consequently, the existence of a three-dimensional Fermi surface is not necessary to explain the oscillations in the magnetoresistance that are seen in many organic conductors as the field direction is varied. [S0031-9007(98)07660-1].