On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

Complex language functions and subcortical mechanisms: evidence from Huntington's disease and patients with non-thalamic subcortical lesions

The neuropathological changes associated with Huntington's disease (HD) are most marked in the head of the caudate nucleus and, to a lesser extent, in the putamen and globus pallidus, suggesting that at least part of the language impairments found in patients with HD may result from non-thalamic subcortical (NTS) pathology. The present study aimed to test the hypothesis that a signature profile of impaired language functions is found in patients who have sustained damage to the non-thalamic subcortex, either focally induced or resulting from neurodegenerative pathology. The language abilities of a group of patients with Huntington's disease (n=13) were compared with those of an age- and education-matched group of patients with chronic NTS lesions following stroke (n=13) and a non-neurologically impaired control group (n=13). The three groups were compared on language tasks that assessed both primary and more complex language abilities. The primary language battery consisted of The Western Aphasia Battery and The Boston Naming Test, whilst the more complex cognitive-linguistic battery employed selected subtests from The Test of Language Competence-Expanded, The Test of Word Knowledge and The Word Test-Revised. On many of the tests of primary language function from the Western Aphasia Battery, both the HD and NTS participants performed in a similar manner to the control participants. The language performances of the HD participants were significantly more impaired (p<0.05 using modified Bonferroni adjustments) than the control group, however, on various lexico-semantic tasks (e. g. the Boston Naming Test and providing definitions), on both single-word and sentence-level generative tasks (e. g. category fluency and formulating sentences), and on tasks which required interpretation of ambiguous, figurative and inferential meaning. The difficulties that patients with HD experienced with tasks assessing complex language abilities were strikingly similar, both qualitatively and quantitatively, to the language profile produced by NTS participants. The results provide evidence to suggest that a signature language profile is associated with damage to the non-thalamic subcortex resulting from either focal neurological insult or a degenerative disease.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

Is maximizing resilience compatible with established ecological goal functions?

Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] used a simple phytoplanktonzooplankton-nutrient model and a genetic algorithm to determine the parameter values that would maximize the value of certain goal functions. These goal functions were to maximize biomass, maximize flux, maximize flux to biomass ratio, and maximize resilience. It was found that maximizing goal functions maximized resilience. The objective of this study was to investigate whether the Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] result was indicative of a general ecosystem principle, or peculiar to the model and parameter ranges used. This study successfully replicated the Cropp and Gabric [Ecosystem adaptation: do ecosystems maximise resilience? Ecology. In press] experiment for a number of different model types, however, a different interpretation of the results is made. A new metric, concordance, was devised to describe the agreement between goal functions. It was found that resilience has the highest concordance of all goal functions trialled. for most model types. This implies that resilience offers a compromise between the established ecological goal functions. The parameter value range used is found to affect the parameter versus goal function relationships. Local maxima and minima affected the relationship between parameters and goal functions, and between goal functions. (C) 2003 Elsevier B.V. All rights reserved.

Unsaturated diffusivity functions for concrete derived from NMR images

Deterioration of concrete or reinforcing steel through excessive contaminant concentration is often the result of repeated wetting and drying cycles. At each cycle, the absorption of water carries new contaminants into the unsaturated concrete. Nuclear Magnetic Resonance (NMR) is used with large concrete samples to observe the shape of the wetting profile during a simple one-dimensional wetting process. The absorption of water by dry concrete is modelled by a nonlinear diffusion equation with the unsaturated hydraulic diffusivity being a strongly nonlinear function of the moisture content. Exponential and power functions are used for the hydraulic diffusivity and corresponding solutions of the diffusion equation adequately predict the shape of the experimental wetting profile. The shape parameters, describing the wetting profile, vary little between different blends and are relatively insensitive to subsequent re-wetting experiments allowing universal parameters to be suggested for these concretes.

Mapping the royal road and other hierarchical functions

In this paper we present a technique for visualising hierarchical and symmetric, multimodal fitness functions that have been investigated in the evolutionary computation literature. The focus of this technique is on landscapes in moderate-dimensional, binary spaces (i.e., fitness functions defined over {0, 1}(n), for n less than or equal to 16). The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present case-study explorations of three fitness functions: royal road, hierarchical-if-and-only-if (H-IFF), and hierarchically decomposable functions (HDF). The visualisation approach provides an insight into the properties of these functions, particularly with respect to the size and shape of the basins of attraction around each of the local optima.

Health education: the role and functions of the specialist and the generalist

Education for health is a process in which all public health and medical care personnel are involved. People learn both formally (planned learning experiences) and informally (unplanned learning experiences). Since the patient, the client, the consummer and the community expect public health and medical care personnel to assist them with health and disease issues and problems, the response of the professional "educates" the customer whether the professional intends to educate or not. Therefore, it is incumbent on all public health and medical care professionals to understand their educational functions and their role in health education. It is also important that the role of the specialist in education be clear. The specialist, as to all other specialists, has an in-depth knowledge of his area of expertise, i.e., the teaching/learning process; s/he may function as a consultant to others to enhance the educational potential of their role or s/he may work with a team or with communities or groups of patients. Specific competencies and knowledge are required of the health education specialist; and there is a body of learning and social change theory which provides a frame of reference for planning, implementing and evaluating educational programs. Working with others to enhance their potential to learn and to make informed decisions about health/disease issues is the hallmark of the health education specialist.

Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

Periodic dynamic systems for infected hosts and mosquitoes

A mathematical model for the purpose of analysing the dynamic of the populations of infected hosts anf infected mosquitoes when the populations of mosquitoes are periodic in time is here presented. By the computation of a parameter lambda (the spectral radius of a certain monodromy matrix) one can state that either the infection peters out naturally) (lambda <= 1) or if lambda > 1 the infection becomes endemic. The model generalizes previous models for malaria by considering the case of periodic coefficients; it is also a variation of that for gonorrhea. The main motivation for the consideration of this present model was the recent studies on mosquitoes at an experimental rice irrigation system, in the South-Eastern region of Brazil.

Stratification of the earth beneath the Azores from P and S receiver functions

Seismic recordings of IRIS/IDA/GSN station CMLA and of several temporary stations in the Azores archipelago are processed with P and S receiver function (PRF and SRF) techniques. Contrary to regional seismic tomography these methods provide estimates of the absolute velocities and of the Vp/Vs ratio up to a depth of similar to 300 km. Joint inversion of PRFs and SRFs for a few data sets consistently reveals a division of the subsurface medium into four zones with a distinctly different Vp/Vs ratio: the crust similar to 20 km thick with a ratio of similar to 1.9 in the lower crust, the high-Vs mantle lid with a strongly reduced VpNs velocity ratio relative to the standard 1.8, the low-velocity zone (LVZ) with a velocity ratio of similar to 2.0, and the underlying upper-mantle layer with a standard velocity ratio. Our estimates of crustal thickness greatly exceed previous estimates (similar to 10 km). The base of the high-Vs lid (the Gutenberg discontinuity) is at a depth of-SO km. The LVZ with a reduction of S velocity of similar to 15% relative to the standard (IASP91) model is terminated at a depth of similar to 200 km. The average thickness of the mantle transition zone (TZ) is evaluated from the time difference between the S410p and SKS660p, seismic phases that are robustly detected in the S and SKS receiver functions. This thickness is practically similar to the standard IASP91 value of 250 km. and is characteristic of a large region of the North Atlantic outside the Azores plateau. Our data are indicative of a reduction of the S-wave velocity of several percent relative to the standard velocity in a depth interval from 460 to 500 km. This reduction is found in the nearest vicinities of the Azores, in the region sampled by the PRFs, but, as evidenced by SRFs, it is missing at a distance of a few hundred kilometers from the islands. We speculate that this anomaly may correspond to the source of a plume which generated the Azores hotspot. Previously, a low S velocity in this depth range was found with SRF techniques beneath a few other hotspots.

Effect of the number of shells on the pressure and energy of two-dimensional free bubble clusters

We have performed Surface Evolver simulations of two-dimensional hexagonal bubble clusters consisting of a central bubble of area lambda surrounded by s shells or layers of bubbles of unit area. Clusters of up to twenty layers have been simulated, with lambda varying between 0.01 and 100. In monodisperse clusters (i.e., for lambda = 1) [M.A. Fortes, F Morgan, M. Fatima Vaz, Philos. Mag. Lett. 87 (2007) 561] both the average pressure of the entire Cluster and the pressure in the central bubble are decreasing functions of s and approach 0.9306 for very large s, which is the pressure in a bubble of an infinite monodisperse honeycomb foam. Here we address the effect of changing the central bubble area lambda. For small lambda the pressure in the central bubble and the average pressure were both found to decrease with s, as in monodisperse clusters. However, for large,, the pressure in the central bubble and the average pressure increase with s. The average pressure of large clusters was found to be independent of lambda and to approach 0.9306 asymptotically. We have also determined the cluster surface energies given by the equation of equilibrium for the total energy in terms of the area and the pressure in each bubble. When the pressures in the bubbles are not available, an approximate equation derived by Vaz et al. [M. Fatima Vaz, M.A. Fortes, F. Graner, Philos. Mag. Lett. 82 (2002) 575] was shown to provide good estimations for the cluster energy provided the bubble area distribution is narrow. This approach does not take cluster topology into account. Using this approximate equation, we find a good correlation between Surface Evolver Simulations and the estimated Values of energies and pressures. (C) 2008 Elsevier B.V. All rights reserved.

Symbolic dynamics and renormalization of non-autonomous k periodic dynamical systems

The purpose of this paper was to introduce the symbolic formalism based on kneading theory, which allows us to study the renormalization of non-autonomous periodic dynamical systems.