The formation of learning sets by the chinchilla in an auditory discrimination procedure

This paper discusses a study conducted to test sound discrimination abilities of the chinchilla.

Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes

This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance $\mu \propto L^{-1}$ from the substrate, where $L$ is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance $\xi \propto L^{-1/3}$. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.

Water wave scattering by finite arrays of circular structures

The scattering of small amplitude water waves by a finite array of locally axisymmetric structures is considered. Regions of varying quiescent depth are included and their axisymmetric nature, together with a mild-slope approximation, permits an adaptation of well-known interaction theory which ultimately reduces the problem to a simple numerical calculation. Numerical results are given and effects due to regions of varying depth on wave loading and free-surface elevation are presented.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Preparation of consistent soil data sets for modelling purposes: Secondary SOTER data for four case study areas

The common GIS-based approach to regional analyses of soil organic carbon (SOC) stocks and changes is to define geographic layers for which unique sets of driving variables are derived, which include land use, climate, and soils. These GIS layers, with their associated attribute data, can then be fed into a range of empirical and dynamic models. Common methodologies for collating and formatting regional data sets on land use, climate, and soils were adopted for the project Assessment of Soil Organic Carbon Stocks and Changes at National Scale (GEFSOC). This permitted the development of a uniform protocol for handling the various input for the dynamic GEFSOC Modelling System. Consistent soil data sets for Amazon-Brazil, the Indo-Gangetic Plains (IGP) of India, Jordan and Kenya, the case study areas considered in the GEFSOC project, were prepared using methodologies developed for the World Soils and Terrain Database (SOTER). The approach involved three main stages: (1) compiling new soil geographic and attribute data in SOTER format; (2) using expert estimates and common sense to fill selected gaps in the measured or primary data; (3) using a scheme of taxonomy-based pedotransfer rules and expert-rules to derive soil parameter estimates for similar soil units with missing soil analytical data. The most appropriate approach varied from country to country, depending largely on the overall accessibility and quality of the primary soil data available in the case study areas. The secondary SOTER data sets discussed here are appropriate for a wide range of environmental applications at national scale. These include agro-ecological zoning, land evaluation, modelling of soil C stocks and changes, and studies of soil vulnerability to pollution. Estimates of national-scale stocks of SOC, calculated using SOTER methods, are presented as a first example of database application. Independent estimates of SOC stocks are needed to evaluate the outcome of the GEFSOC Modelling System for current conditions of land use and climate. (C) 2007 Elsevier B.V. All rights reserved.