Efforts to find solutions that can be used for verification of numerical techniques for solving the Richards equation have generated a wealth of approximate and exact analytical solutions. Coefficients of this equation involve two highly non-linear functions related to the soil water potential, the unsaturated hydraulic conductivity, and the soil water content. The known exact solutions for rea...

Lipid peroxidation is a common feature of many chemical and biological processes, and is governed by a complex kinetic scheme. A fundamental stage in kinetic investigations of lipid peroxidation is the accurate determination of the rate of peroxidation, which in many instances is heavily reliant on the method of finite differences. Such numerical approximations of the first derivative are commo...

This study compared the use of various models to describe growth in lambs of 2 contrasting breeds from birth to slaughter. Live BW records (n = 7559) from 240 Texel and 231 Scottish Blackface (SBF) lambs weighed at 2-wk intervals were modeled. Biologically relevant variables were estimated for each lamb from modified versions of the logistic, Gompertz, Richards, and exponential models, and from...

Richards and Hamers (2009) aim in their paper to ‘consider the place of randomised controlled trials in nursing’. In doing so, they make a number of largely unsubstantiated observations about ‘those that reject the positivist approach to science’, assuming that ‘readers will be familiar with the case made by objectors’. In fact, the only source cited by Richards and Hamers for the arguments aga...

Thoroughbred horses are seasonal mating animals, raised in northern regions or countries. Foals born yearly in spring generally show a typical seasonal compensatory growth pattern, in which their growth rate declines in the first winter and increases in the next spring. In this study, a new empirical adjustment approach is proposed to adjust for this compensatory growth when growth curve equati...

The objective of this study was to introduce application of the Richards equation on modelling and prediction of stand diameter distribution. The long-term repeated measurement data sets, consisted of 309 diameter frequency distributions from Chinese fir (Cunninghamia lanceolata) plantations in the southern China, were used. Also, 150 stands were used as fitting data, the other 159 stands were ...

We analyze regularization schemes for the Richards equation and a time discrete numerical approximation. The original equations can be doubly degenerate, therefore they may exhibit fast and slow diffusion. Additionally, we treat outflow conditions that model an interface separating the porous medium from a free flow domain. In both situations we provide a regularization with a non-degenerate eq...

Fluid flow in the vadose zone is governed by Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Saturation or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysi...