Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Infiltration from surface and buried point sources: The average wetting water content

The assumption in analytical solutions for flow from surface and buried point sources of an average water content, (θ) over bar, behind the wetting front is examined. Some recent work has shown that this assumption fitted some field data well. Here we calculated (θ) over bar using a steady state solution based on the work by Raats [1971] and an exponential dependence of the diffusivity upon the water content. This is compared with a constant value of (θ) over bar calculated from an assumption of a hydraulic conductivity at the wetting front of 1 mm day(-1) and the water content at saturation. This comparison was made for a wide range of soils. The constant (θ) over bar generally underestimated (θ) over bar at small wetted radii and overestimated (θ) over bar at large radii. The crossover point between under and overestimation changed with both soil properties and flow rate. The largest variance occurred for coarser texture soils at low-flow rates. At high-flow rates in finer-textured soils the use of a constant (θ) over bar results in underestimation of the time for the wetting front to reach a particular radius. The value of (θ) over bar is related to the time at which the wetting front reaches a given radius. In coarse-textured soils the use of a constant value of (θ) over bar can result in an error of the time when the wetting front reaches a particular radius, as large as 80% at low-flow rates and large radii.

Prevalence and comorbidity of behavioral problems of children aged three to six: Results of the Braunschweiger Kindergartenstudie

Prevalence and comorbidity of behavioral problems of children aged three to six: Results of the Braunschweiger Kindergartenstudie Objectives: To analyze the frequency of behavioral and emotional problems and comorbidity of kindergarten children in Braunschweig as rated by their parents. Method: The analysis is part of the Braunschweiger Kindergartenstudie. In a sample of N = 809 children aged three to six the parents rated their children using a modified version of the Child Behavior Checklist/CBCL 4-18. Results: The prevalence rates range from 0.5% to 5.0%. The most frequent behavioral problems in kindergarten children were aggressive behavior and attention problems, followed by social problems. The study also provides bidirectional comorbidity rates. Conclusion: Finally the prevalence rates and the implications of the findings for prevention of behavioral problems in children are discussed.

Quantum analysis of the nondegenerate optical parametric oscillator with injected signal

In this paper we study the nondegenerate optical parametric oscillator with injected signal, both analytically and numerically. We develop a perturbation approach which allows us to find approximate analytical solutions, starting from the full equations of motion in the positive-P representation. We demonstrate the regimes of validity of our approximations via comparison with the full stochastic results. We find that, with reasonably low levels of injected signal, the system allows for demonstrations of quantum entanglement and the Einstein-Podolsky-Rosen paradox. In contrast to the normal optical parametric oscillator operating below threshold, these features are demonstrated with relatively intense fields.

Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales

Based on a self-similar array model, we systematically investigated the axial Young's modulus (Y-axis) of single-walled carbon nanotube (SWNT) arrays with diameters from nanometer to meter scales by an analytical approach. The results show that the Y-axis of SWNT arrays decreases dramatically with the increases of their hierarchy number (s) and is not sensitive to the specific size and constitution when s is the same, and the specific Young's modulus Y-axis(s) is independent of the packing configuration of SWNTs. Our calculations also show that the Y-axis of SWNT arrays with diameters of several micrometers is close to that of commercial high performance carbon fibers (CFs), but the Y-axis(s) of SWNT arrays is much better than that of high performance CFs. (C) 2005 American Institute of Physics.

Transgenic expression of a viral oncoprotein exclusively in K14(+) epithelial cells results in peripheral but not central CD8 T cell tolerance

The role of thymic versus peripheral epithelial cells in the negative selection of the peptide-specific CD8 T cell repertoire is still largely unresolved. We have generated TCRb chain transgenic mice in which 20–35% of peripheral CD8 T cells recognize an epitope from a viral, nuclear oncoprotein (human papillomavirus type 16 E7) in the context ofMHC class I, H-2Db. When T cells from these transgenic mice develop through the thymus of a second transgenic mouse expressing E7 from a keratin 14 promoter, no major perturbation to thymic T cell development is observed over a 7 month period. In contrast, peripheral CD8 T cell responses in these same mice (E7TCRxK14E7 double transgenic) become reduced over time. This data suggests that peripheral tolerance mechanisms predominate over thymic negative selection in controlling CD8 T cell responses to this epithelial, nuclear oncoprotein.