A square-well model for the structural and thermodynamic properties of simple colloidal systems

A model for the radial distribution function $g(r)$ of a square-well fluid of variable width previously proposed [S. B. Yuste and A. Santos, J. Chem. Phys. {\bf 101}, 2355 (1994)] is revisited and simplified. The model provides an explicit expression for the Laplace transform of $rg(r)$, the coefficients being given as explicit functions of the density, the temperature, and the interaction range. In the limits corresponding to hard spheres and sticky hard spheres the model reduces to the analytical solutions of the Percus-Yevick equation for those potentials. The results can be useful to describe in a fully analytical way the structural and thermodynamic behavior of colloidal suspensions modeled as hard-core particles with a short-range attraction. Comparison with computer simulation data shows a general good agreement, even for relatively wide wells.Comment: 23 pages, 10 figures; Figs. 4 and 5 changed, Fig. 6 new; to be published in J. Chem. Phy

Heat capacity of square-well fluids of variable width

We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibility factor. This is illustrated by comparing the reported simulation data for the heat capacity with the theoretical predictions given by the Barker-Henderson perturbation theory as well as with those given by a non-perturbative theoretical model based on Baxter's solution of the Percus-Yevick integral equation for sticky hard spheres. Both theories give accurate predictions for the equation of state. By contrast, it is found that the Barker-Henderson theory strongly underestimates the excess heat capacity for low to moderate temperatures, whereas a much better agreement between theory and simulation is achieved with the non-perturbative theoretical model, particularly for small well widths, although the accuracy of the latter worsens for high densities and low temperatures, as the well width increases.Comment: 11 pages, 4 figures; figures now include additional perturbation data; to be published in Mol. Phy

On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.Comment: 22 pages, 6 figure

Participatory Approach to Optimizing Cabbage Fertilization System for Improved Yield, Quality and Shelf Life

Cabbage fertilization system was optimized following the participatory approach by factoring in farmers’ practices, conducting optimization trials on farmers’ field, and employing farmer-researcher co-management of on-farm trials. Five different rates of fertilizer application were documented in the survey of farmers in a vegetable-growing area in Central Philippines. They served as basis for the fertilizer treatments (2 organic fertilizer levels using chicken dung or CD and 5 inorganic fertilizer levels using complete fertilizer 14-14-14 and urea 46-0-0) tested in on-farm trials in the dry season (December to May) and wet season (June to November). Other cultural practices were those employed by farmers with some good practices introduced. Optimum fertilization rate was 2.3 tons CD/ha + 112-47-47 (336 kg 14-14-14 and 141 kg 46-0-0 per hectare) for both dry and wet season crops, giving yields of 29.5 and 10.7 tons/ha, respectively, with net profit-cost ratio of 4.41 and 2.14, respectively, or more than 2-3 times higher than that of unfertilized crops. In addition, the heads produced were flatter and more compact and had longer shelf life due to lower weight loss and trimming loss, particularly for dry-season crop, compared to other fertilizer treatments. The participatory approach equipped farmers with first-hand knowledge and skills on how to improve existing cultural practices to generate high quality yields and farm profits