The wall shear rate distribution for flow in random sphere packings

The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1 <= phi <= 0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As phi --> 0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.Comment: 4 pages, 3 figures, 1 table, RevTeX 4; significantly revised with significantly extended scop

Determination of copper in tap water using solid-phase spectrophotometry

A new application of ion exchange films is presented. The films are used in a simple analytical method of directly determining low concentrations of Cu(2+) in aqueous solutions, in particular, drinking water. The basis for this new test method is the color and absorption intensity of the ion when adsorbed onto the film. The film takes on the characteristic color of the adsorbed cation, which is concentrated on the film by many orders of magnitude. The linear relationship between absorbance (corrected for variations in film thickness) and solution concentration makes the determinations possible. These determinations agree well with flame atomic absorption determinations

An assertion language for constraint logic programs

In an advanced program development environment, such as that discussed in the introduction of this book, several tools may coexist which handle both the program and information on the program in different ways. Also, these tools may interact among themselves and with the user. Thus, the different tools and the user need some way to communicate. It is our design principie that such communication be performed in terms of assertions. Assertions are syntactic objects which allow expressing properties of programs. Several assertion languages have been used in the past in different contexts, mainly related to program debugging. In this chapter we propose a general language of assertions which is used in different tools for validation and debugging of constraint logic programs in the context of the DiSCiPl project. The assertion language proposed is parametric w.r.t. the particular constraint domain and properties of interest being used in each different tool. The language proposed is quite general in that it poses few restrictions on the kind of properties which may be expressed. We believe the assertion language we propose is of practical relevance and appropriate for the different uses required in the tools considered

Estimating cropland requirements for global food system scenario modeling

IntroductionThe production of plant crops is foundational to the global food system. With the need for this system to become more sustainable while feeding an increasing global population, tools to investigate future food system scenarios can be useful to aid decision making, but are often limited to a calorie- or protein-centric view of human nutrition.MethodsHere, a mathematical model for forecasting the future cropland requirement to produce a given quantity of crop mass is presented in conjunction with the DELTA Model®: an existing food system scenario model calculating global availability of 29 nutrients against human requirements. The model uses national crop yield data to assign yield metrics for 137 crops.ResultsThe crops with the greatest variation between high and low yielding production were specific nuts, fruits, and vegetables of minor significance to global nutrient availability. The nut crop group showed the greatest overall yield variation between countries, and thus the greatest uncertainty when forecasting the cropland requirement for future increases in production. Sugar crops showed the least overall yield variation. The greatest potential for increasing global food production by improving poor yielding production was found for the most widely grown crops: maize, wheat, and rice, which were also demonstrated to be of high nutritional significance.DiscussionThe combined cropland and nutrient availability model allowed the contribution of plant production to global nutrition to be quantified, and the cropland requirement of future food production scenarios to be estimated. The unified cropland estimation and nutrient availability model presented here is an intuitive and broadly applicable tool for use in global food system scenario modeling. It should benefit future research and policy making by demonstrating the implications for human nutrition of changes to crop production, and conversely the implications for cropland requirement of food production scenarios aimed at improving nutrition