The role of calcite and gypsum in the leaching of potassium in a sandy soil

Pulses of potassium (K+) applied to columns of repacked calcium (Ca2+) saturated soil were leached with distilled water or calcium chloride (CaCl2) solutions of various concentrations at a rate of 12 mm h(-1). With increased Ca2+ concentration, the rate of movement of K+ increased, as did the concentration of K+ in the displaced pulse, which was less dispersed. The movement of K+ in calcite-amended soil leached with water was at a similar rate to that of the untreated soil leached with 1 mM CaCl2, and in soil containing gypsum, movement was similar to that leached with 15 mM CaCl2. The Ca2+ concentrations in the leachates were about 0.4 and 15 mM respectively the expected values for the dissolution of the two amendments. Soil containing native K+ was leached with distilled water or CaCl2 solutions. The amount of K+ leached increased as Ca2+ concentration increased, with up to 34% of the exchangeable K+ being removed in five pore volumes of 15 mM CaCl2. Soil amended with calcite and leached with water lost K+ at a rate between that for leaching the unamended soil with 1 mM CaCl2 and that with water. Soil containing gypsum and leached with water lost K+ at a similar rate to unamended soil leached with 15 mM CaCl2. The presence of Ca2+ in irrigation water and of soil minerals able to release Ca2+ are of importance in determining the amounts of K+ leached from soils. The LEACHM model predicted approximately the displacement of K+, and was more accurate with higher concentrations of displacing solution. The shortcomings of this model are its inability to account for rate-controlled processes and the assumption that K+:Ca2+ exchange during leaching can be described using a constant adsorption coefficient. As a result, the pulse is predicted to appear a little earlier and the following edge has less of a tail than chat measured. In practical agriculture, the model will be more useful in soils containing gypsum or leached with saline water than in either calcareous or non-calcareous soils leached with rainwater.

Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Müller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air-water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417-445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate F, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as proportional to 1/Gamma), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Surface and interstitial Ti diffusion at the rutile TiO2(110) surface

Diffusion of Ti through the TiO2 (110) rutile surface plays a key role in the growth and reactivity of TiO2. To understand the fundamental aspects of this important process, we present an analysis of the diffusion of Ti adspecies at the stoichiometric TiO2(110) surface using complementary computational methodologies of density functional theory corrected for on-site Coulomb interactions (DFT+U) and a charge equilibration (QEq) atomistic potential to identify minimum energy pathways. We find that diffusion of Ti from the surface to subsurface (and vice versa) follows an intersticialcy exchange mechanism, involving exchange of surface Ti with the 6-fold coordinated Ti below the bridging oxygen rows. Diffusion in the subsurface between layers also follows an interstitialcy mechanism. The diffusion of Ti is discussed in light of continued attempts to understand the re-oxidation of non-stoichiometric TiO2(110) surfaces.

Anharmonic force constant calculations

The relationship of the anharmonic force constants in curvilinear internal coordinates to the observed vibration-rotation spectrum of a molecule is reviewed. A simplified method of setting up the required non-linear coordinate transformations is described: this makes use of an / tensor, which is a straightforward generalization of the / matrix used in the customary description of harmonic force constant calculations. General formulae for the / tensor elements, in terms of the familiar L matrix elements, are presented. The use of non-linear symmetry coordinates and redundancies are described. Sample calculations on the water and ammonia molecules are reported.

Conservative upwind difference schemes for the Euler equations for real gas flows in a duct

In a recent paper [P. Glaister, Conservative upwind difference schemes for compressible flows in a Duct, Comput. Math. Appl. 56 (2008) 1787–1796] numerical schemes based on a conservative linearisation are presented for the Euler equations governing compressible flows of an ideal gas in a duct of variable cross-section, and in [P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480] schemes based on this philosophy are presented for real gas flows with slab symmetry. In this paper we seek to extend these ideas to encompass compressible flows of real gases in a duct. This will incorporate the handling of additional terms arising out of the variable geometry and the non-ideal nature of the gas.

Well-posed boundary value problems for integrable evolution equations on a finite interval

We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.

ASYM20: a program for force constant and normal coordinate calculations, with a critical review of the theory involved

The theory of harmonic force constant refinement calculations is reviewed, and a general-purpose program for force constant and normal coordinate calculations is described. The program, called ASYM20. is available through Quantum Chemistry Program Exchange. It will work on molecules of any symmetry containing up to 20 atoms and will produce results on a series of isotopomers as desired. The vibrational secular equations are solved in either nonredundant valence internal coordinates or symmetry coordinates. As well as calculating the (harmonic) vibrational wavenumbers and normal coordinates, the program will calculate centrifugal distortion constants, Coriolis zeta constants, harmonic contributions to the α′s. root-mean-square amplitudes of vibration, and other quantities related to gas electron-diffraction studies and thermodynamic properties. The program will work in either a predict mode, in which it calculates results from an input force field, or in a refine mode, in which it refines an input force field by least squares to fit observed data on the quantities mentioned above. Predicate values of the force constants may be included in the data set for a least-squares refinement. The program is written in FORTRAN for use on a PC or a mainframe computer. Operation is mainly controlled by steering indices in the input data file, but some interactive control is also implemented.

Integrable evolution equations in time-dependent domains

We discuss the implementation of a method of solving initial boundary value problems in the case of integrable evolution equations in a time-dependent domain. This method is applied to a dispersive linear evolution equation with spatial derivatives of arbitrary order and to the defocusing nonlinear Schrödinger equation, in the domain l(t)

A rotating disc voltammetry study of the 1,8-dihydroxyanthraquinone mediated reduction of colloidal indigo

Colloidal indigo is reduced to an aqueous solution of leuco-indigo in a mediated two-electron process converting the water-insoluble dye into the water-soluble leuco form. The colloidal dye does not interact directly with the electrode surface, and to employ an electrochemical process for this reduction, the redox mediator 1,8-dihydroxyanthraquinone (1,8-DHAQ) is used to transfer electrons from the electrode to the dye. The mediated reduction process is investigated at a (500-kHz ultrasound-assisted) rotating disc electrode, and the quantitative analysis of voltammetric data is attempted employing the Digisim numerical simulation software package. At the most effective temperature, 353 K, the diffusion coefficient for 1,8-DHAQ is (0.84 +/- 0.08)x10(-9) m(2) s(-1), and it is shown that an apparently kinetically controlled reaction between the reduced form of the mediator and the colloidal indigo occurs within the diffusion layer at the electrode surface. The apparent bimolecular rate constant k (app)=3 mol m(-3) s(-1) for the rate law d[leuco-indigo]/dt = k(app) x [mediator] x [indigo] is determined and attributed to a mediator diffusion controlled dissolution of the colloid particles. The average particle size and the number of molecules per particles are estimated from the apparent bimolecular rate constant and confirmed by scanning electron microscopy.

Declining survival rates in a reintroduced population of the Mauritius kestrel: evidence for non-linear density dependence and environmental stochasticity

1. We studied a reintroduced population of the formerly critically endangered Mauritius kestrel Falco punctatus Temmink from its inception in 1987 until 2002, by which time the population had attained carrying capacity for the study area. Post-1994 the population received minimal management other than the provision of nestboxes. 2. We analysed data collected on survival (1987-2002) using program MARK to explore the influence of density-dependent and independent processes on survival over the course of the population's development. 3.We found evidence for non-linear, threshold density dependence in juvenile survival rates. Juvenile survival was also strongly influenced by climate, with the temporal distribution of rainfall during the cyclone season being the most influential climatic variable. Adult survival remained constant throughout. 4. Our most parsimonious capture-mark-recapture statistical model, which was constrained by density and climate, explained 75.4% of the temporal variation exhibited in juvenile survival rates over the course of the population's development. 5. This study is an example of how data collected as part of a threatened species recovery programme can be used to explore the role and functional form of natural population regulatory processes. With the improvements in conservation management techniques and the resulting success stories, formerly threatened species offer unique opportunities to further our understanding of the fundamental principles of population ecology.

Degradation products of clavulanic acid promote clavulanic acid production in cultures of Streptomyces clavuligerus

The role of clavulanic acid, an unstable antibiotic produced by Streptomyces clavuligerus, in biomass accumulation and production of clavulanic acid in batch cultures of the organism was examined. The organism was grown in a medium containing either 20 g/l lysine, 1 g/l lysine or 1 g/l lysine supplemented with degraded clavulanic acid as nitrogen sources. Biomass accumulation was highest in cultures grown with supplemented degraded clavulanic acid and reached a maximum of 2.2 g/l, compared with 1.5 g/l when lysine only was used. The yield coefficient for clavulanic acid production was again highest in cultures grown with supplemented degraded clavulanic acid, with a Y-p/x, value of 2 mg/g compared with Y-p/x value of 1.5 mg/g in 20 g/l lysine. No clavulanic acid was produced in cultures containing non-supplemented 1 g/l lysine. Non-degraded clavulanic, acid was added at 60 h to non-producing cultures of the organism containing 1 g/l lysine only. Clavulanic acid concentration immediately decreased on addition from 0.04 g/l over a period of 20 h, then remained constant at 0.02 g/l for a further 30 h until the end of the cultivation. This suggests that the rate of degradation was equivalent to the rate of production of clavulanic acid following a period of initial additive degradation. These results indicate that clavulanic acid is both produced and degraded in cultures of S. clavuligerus and that the products of degradation are used by the organism, resulting in further production of the antibiotic. (C) 2003 Elsevier Inc. All rights reserved.

New mathematical modeling approach for predicting microbial inactivation by high hydrostatic pressure

A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

On two rational difference equations

In this paper, we study the oscillating property of positive solutions and the global asymptotic stability of the unique equilibrium of the two rational difference equations [GRAPHICS] and [GRAPHICS] where a is a nonnegative constant. (c) 2005 Elsevier Inc. All rights reserved.

Approximate Riemann solutions of the two-dimensional shallow-water equations

A finite-difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow-water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gasdynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. An extension to the two-dimensional equations with source terms, is included. The scheme is applied to a dam-break problem with cylindrical symmetry.