Drying front in a sloping aquifer: Nonlinear effects

[1] The profiles for the water table height h(x, t) in a shallow sloping aquifer are reexamined with a solution of the nonlinear Boussinesq equation. We demonstrate that the previous anomaly first reported by Brutsaert [1994] that the point at which the water table h first becomes zero at x = L at time t = t(c) remains fixed at this point for all times t > t(c) is actually a result of the linearization of the Boussinesq equation and not, as previously suggested [Brutsaert, 1994; Verhoest and Troch, 2000], a result of the Dupuit assumption. Rather, by examination of the nonlinear Boussinesq equation the drying front, i.e., the point x(f) at which h is zero for times t greater than or equal to t(c), actually recedes downslope as physically expected. This points out that the linear Boussinesq equation should be used carefully when a zero depth is obtained as the concept of an average'' depth loses meaning at that time.

On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

A master equation model for bimolecular reaction via multi-well isomerization intermediates

A reversible linear master equation model is presented for pressure- and temperature-dependent bimolecular reactions proceeding via multiple long-lived intermediates. This kinetic treatment, which applies when the reactions are measured under pseudo-first-order conditions, facilitates accurate and efficient simulation of the time dependence of the populations of reactants, intermediate species and products. Detailed exploratory calculations have been carried out to demonstrate the capabilities of the approach, with applications to the bimolecular association reaction C3H6 + H reversible arrow C3H7 and the bimolecular chemical activation reaction C2H2 +(CH2)-C-1--> C3H3+H. The efficiency of the method can be dramatically enhanced through use of a diffusion approximation to the master equation, and a methodology for exploiting the sparse structure of the resulting rate matrix is established.

Refining the risk-benefit equation for thrombolysis: How to identity the low risk patient before administering thrombolytic therapy

In view of the relative risk of intracranial haemorrhage and major bleeding with thrombolytic therapy, it is important ro identify as early as possible the low risk patient who may not have a net clinical benefit from thrombolysis in the setting of acute myocardial infarction. An analysis of 5434 hospital-treated patients with myocardial infarction in the Perth MONICA study showed that age below 60 and absence of previous infarction or diabetes, shock, pulmonary oedema, cardiac arrest and Q-wave or left bundle branch block on the initial ECG identified a large group of patients with a 28 day mortality of only 1%, and one year mortality of only 2%. Identification of baseline risk in this way helps refine the risk-benefit equation for thrombolytic therapy, and may help avoid unnecessary use of thrombolysis in those unlikely to benefit.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

A pore-size-dependent equation of state for multilayer adsorption in cylindrical mesopores

The chemical potential of adsorbed film inside cylindrical mesopores is dependent on the attractive interactions between the adsorbed molecules and adsorbent, the curvature of gas/adsorbed phase interface, and surface tension. A state equation of the adsorbed film is proposed to take into account the above factors. Nitrogen adsorption on model adsorbents, MCM-41, which exhibit uniform cylindrical channels, are used to verify the theoretical analysis. The proposed theory is capable of describing the important features of adsorption processes in cylindrical mesopores. According to this theory, at a given relative pressure, the smaller the pore radius is, the thicker the adsorbed film will be. The thickening of adsorbed films in the pores as the vapor pressure increases inevitably causes an increase in the interface curvature, which consequently leads to capillary condensation. Besides, this study confirmed that the interface tension depends substantially on the interface curvature in small mesopores. A quantitative relationship between the condensation pressure and the pore radius can be derived from the state equation and used to predict the pore radius from a condensation pressure, or vice versa.

Groundwater waves in a coastal aquifer: A new governing equation including vertical effects and capillarity

Groundwater waves, that is, water table fluctuations, are a natural phenomenon in coastal aquifers. They represent an important part of the interaction between the ocean and aquifer and affect the mass exchange between them. This paper presents a new groundwater wave equation. Because it includes the effects of vertical flows and capillarity, the new equation is applicable to both intermediate-depth aquifers and high-frequency waves. Compared with the wave equation derived by Nielsen ed al. [1997], the present equation provides a closer representation of groundwater waves. In particular, it predicts high-frequency water table fluctuations as observed in the field. A validation of the new equation has been carried out by comparing the analytical solutions to it with predictions from direct simulations using the numerical model SUTRA. The effects of various physical parameters and their relative importance are also discussed.

Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature.

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity

The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface. For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman-Lucassen-Reynders-Miller (FLM) 'Aggregation model'. Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species. (C) 2004 Elsevier B.V All rights reserved.

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.