Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.

Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice

Motivated by the unconventional properties and rich phase diagram of NaxCoO2 we consider the electronic and magnetic properties of a two-dimensional Hubbard model on an isotropic triangular lattice doped with electrons away from half-filling. Dynamical mean-field theory (DMFT) calculations predict that for negative intersite hopping amplitudes (t < 0) and an on-site Coulomb repulsion, U, comparable to the bandwidth, the system displays properties typical of a weakly correlated metal. In contrast, for t > 0 a large enhancement of the effective mass, itinerant ferromagnetism, and a metallic phase with a Curie-Weiss magnetic susceptibility are found in a broad electron doping range. The different behavior encountered is a consequence of the larger noninteracting density of states (DOS) at the Fermi level for t > 0 than for t < 0, which effectively enhances the mass and the scattering amplitude of the quasiparticles. The shape of the DOS is crucial for the occurrence of ferromagnetism as for t > 0 the energy cost of polarizing the system is much smaller than for t < 0. Our observation of Nagaoka ferromagnetism is consistent with the A-type antiferromagnetism (i.e., ferromagnetic layers stacked antiferromagnetically) observed in neutron scattering experiments on NaxCoO2. The transport and magnetic properties measured in NaxCoO2 are consistent with DMFT predictions of a metal close to the Mott insulator and we discuss the role of Na ordering in driving the system towards the Mott transition. We propose that the Curie-Weiss metal phase observed in NaxCoO2 is a consequence of the crossover from a bad metal with incoherent quasiparticles at temperatures T > T-* and Fermi liquid behavior with enhanced parameters below T-*, where T-* is a low energy coherence scale induced by strong local Coulomb electron correlations. Our analysis also shows that the one band Hubbard model on a triangular lattice is not enough to describe the unusual properties of NaxCoO2 and is used to identify the simplest relevant model that captures the essential physics in NaxCoO2. We propose a model which allows for the Na ordering phenomena observed in the system which, we propose, drives the system close to the Mott insulating phase even at large dopings.

A methodology for current density calculations in high-frequency RF resonators

As nuclear magnetic resonance imaging and spectroscopy move inexorably toward higher field-strength magnets in search of improved signal-to-noise ratio, spectral resolution, and spatial resolution, the way in which radiofrequency (RF) probes are designed changes. At higher frequencies, resonant cavities become the favored RF ''coil'' type and may be built using streamline elements to reduce the inductance of the system. In modeling such systems, the quasi-static approach of assuming that current flows evenly in all conductor cross sections and that adjacent conductors do not affect each other becomes less reasonable. The proximity of RF conductors in resonators typically causes RF eddy currents to flow, whereby the current density in each rung is altered by the RF fields generated by nearby conductors. The proper understanding and prediction of how resonators will perform require a model of the current densities flowing in conducting sections, including all RF eddy current effects. Very few models of this type have been presented in the literature. This article presents an overview of one such model and of how it may be applied to a variety of resonators, both shielded and unshielded, circular, and elliptical, in cross section. Results are presented from a shielded head coil operating at 2 tesla. (C) 1997 John Wiley & Sons, Inc.

Altered loading patterns and femoral bone mineral density in children with unilateral Legg-Calve-Perthes disease

Maximization of bone accrual during the growing years is thought to be an important factor in minimizing fracture risk in old age. Mechanical loading through physical activity has been recommended as a modality for the conservation of bone mineral in adults; however, few studies have evaluated the impact of different loading regimes in growing children. The purpose of this study was to compare bone mineral density (BMD) in weight-bearing and non-weight-bearing limbs in 17 children with unilateral Legg Calve Perthes Disease (LCPD). Children with this condition have an altered weight-bearing pattern whereby there is increased mechanical loading on the noninvolved normal hip and reduced loading on the involved painful hip. Thus, these children provide a unique opportunity to study the impact of differential mechanical loading on BMD during the growing years while controlling for genetic disposition. BMD at four regions of the proximal femur (trochanter, intertrochanter, femoral neck, total of the regions) was measured using dual energy x-ray absorptiometry (DXA), and the values were compared between the involved and noninvolved sides of the children with LCPD. The BMD of both sides also were compared with normative values based on both chronological and skeletal age data. A significantly higher BMD was found on the noninvolved side over the involved side for all regions (P

A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Heritability and gene-environment interactions for melanocytic nevus density examined in a U.K. adolescent twin study

Risk factors for melanoma include environmental (particularly ultraviolet exposure) and genetic factors. In rare families, susceptibility to melanoma is determined by high penetrance mutations in the genes CDKN2A or CDK4, with more common, less penetrant genes also postulated. A further, potent risk factor for melanoma is the presence of large numbers of melanocytic nevi so that genes controlling nevus phenotype could be such melanoma susceptibility genes. A large Australian study involving twins aged 12 y of predominantly U.K. ancestry showed strong evidence for genetic influence on nevus number and density. We carried out essentially the same study in the U.K. to gain insight into gene-environment interactions for nevi. One hundred and three monozygous (MZ) and 118 dizygous (DZ) twin pairs aged 10-18 y were examined in Yorkshire and Surrey, U.K. Nevus counts were, on average, higher in boys (mean = 98.6) than girls (83.8) (p = 0.009) and higher in Australia (110.4) than in the U.K. (79.2, adjusted to age 12 y, p < 0.0001), and nevus densities were higher on sun-exposed sites (92 per m(2)) than sun-protected sites (58 per m(2)) (p < 0.0001). Correlations in sex and age adjusted nevus density were higher in MZ pairs (0.94, 95% CI 0.92-0.96) than in DZ pairs (0.61, 95%CI 0.49-0.72), were notably similar to those of the Australian study (MZ = 0.94, DZ = 0.60), and were consistent with high heritability (65% in the U.K., 68% in Australia). We conclude that emergence of nevi in adolescents is under strong genetic control, whereas environmental exposures affect the mean number of nevi.

NMR structure and backbone dynamics of a concatemer of epidermal growth factor homology modules of the human low-density lipoprotein receptor

The ligand-binding region of the low-density lipoprotein (LDL) receptor is formed by seven N-terminal, imperfect, cysteine-rich (LB) modules. This segment is followed by an epidermal growth factor precursor homology domain with two N-terminal, tandem, EGF-like modules that are thought to participate in LDL binding and recycling of the endocytosed receptor to the cell surface. EGF-A and the concatemer, EGF-AB, of these modules were expressed in Escherichia coli. Correct protein folding of EGF-A and the concatemer EGF-AB was achieved in the presence or absence of calcium ions, in contrast to the LB modules, which require them for correct folding. Homonuclear and heteronuclear H-1-N-15 NMR spectroscopy at 17.6 T was used to determine the three-dimensional structure of the concatemer. Both modules are formed by two pairs of short, anti-parallel beta -strands. In the concatemer, these modules have a fixed relative orientation, stabilized by calcium ion-binding and hydrophobic interactions at the interface. N-15 longitudinal and transverse relaxation rates, and {H-1}-N-15 heteronuclear NOEs were used to derive a model-free description of the backbone dynamics of the molecule. The concatemer appears relatively rigid, particularly near the calcium ion-binding site at the module interface, with an average generalized order parameter of 0.85 +/- 0.11. Some mutations causing familial hypercholesterolemia may now be rationalized. Mutations of D41, D43 and E44 in the EGF-B calcium ion-binding region may affect the stability of the linker and thus the orientation of the tandem modules. The diminutive core also provides little structural stabilization, necessitating the presence of disulfide bonds. The structure and dynamics of EGF-AB contrast with the N-terminal LB modules, which require calcium ions both for folding to form the correct disulfide connectivities and for maintenance of the folded structure, and are connected by highly mobile linking peptides. (C) 2001 Academic Press.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Optimal patch-leaving behaviour: a case study using the parasitoid Cotesia rubecular

1. Parasitoids are predicted to spend longer in patches with more hosts, but previous work on Cotesia rubecula (Marshall) has not upheld this prediction, Tests of theoretical predictions may be affected by the definition of patch leaving behaviour, which is often ambiguous. 2. In this study whole plants were considered as patches and assumed that wasps move within patches by means of walking or flying. Within-patch and between-patch flights were distinguished based on flight distance. The quality of this classification was tested statistically by examination of log-survivor curves of flight times. 3. Wasps remained longer in patches with higher host densities, which is consistent with predictions of the marginal value theorem (Charnov 1976). tinder the assumption that each flight indicates a patch departure, there is no relationship between host density and leaving tendency. 4. Oviposition influences the patch leaving behaviour of wasps in a count down fashion (Driessen et al. 1995), as predicted by an optimal foraging model (Tenhumberg, Keller & Possingham 2001). 5. Wasps spend significantly longer in the first patch encountered following release, resulting in an increased rate of superparasitism.

'Neighbourhood' size, dispersal and density estimates in the prickly forest skink (Gnypetoscincus queenslandiae) using individual genetic and demographic methods

Dispersal, or the amount of dispersion between an individual's birthplace and that of its offspring, is of great importance in population biology, behavioural ecology and conservation, however, obtaining direct estimates from field data on natural populations can be problematic. The prickly forest skink, Gnypetoscincus queenslandiae, is a rainforest endemic skink from the wet tropics of Australia. Because of its log-dwelling habits and lack of definite nesting sites, a demographic estimate of dispersal distance is difficult to obtain. Neighbourhood size, defined as 4 piD sigma (2) (where D is the population density and sigma (2) the mean axial squared parent-offspring dispersal rate), dispersal and density were estimated directly and indirectly for this species using mark-recapture and microsatellite data, respectively, on lizards captured at a local geographical scale of 3 ha. Mark-recapture data gave a dispersal rate of 843 m(2)/generation (assuming a generation time of 6.5 years), a time-scaled density of 13 635 individuals * generation/km(2) and, hence, a neighbourhood size of 144 individuals. A genetic method based on the multilocus (10 loci) microsatellite genotypes of individuals and their geographical location indicated that there is a significant isolation by distance pattern, and gave a neighbourhood size of 69 individuals, with a 95% confidence interval between 48 and 184. This translates into a dispersal rate of 404 m(2)/generation when using the mark-recapture density estimation, or an estimate of time-scaled population density of 6520 individuals * generation/km(2) when using the mark-recapture dispersal rate estimate. The relationship between the two categories of neighbourhood size, dispersal and density estimates and reasons for any disparities are discussed.

On a theorem of Cooper

In this paper we study some purely mathematical considerations that arise in a paper of Cooper on the foundations of thermodynamics that was published in this journal. Connections with mathematical utility theory are studied and some errors in Cooper's paper are rectified. (C) 2001 Academic Press.