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.

How does a colony of Apoica flavissima (Hymenoptera: Vespidae, Epiponini) maintain a constant temperature?

The thermal characteristics of a colony of Apoica flavissima, an epiponine wasp, were examined. The nest, with a diameter of slightly less than 30 cm, was built on a twig of an orange tree. The temperature of the roof surface fluctuated greatly, ranging between 19.1 and 41.5 degrees C. However, the temperature in the central cell was kept constant at around 27 degrees C throughout a day. Although heavy rain pelted the nest roof in the morning, the central cell maintained temperatures higher than 25 degrees C. On the contrary, after all immature and adult wasps were removed the temperature in the nest fluctuated considerably. The presence of immature individuals and adult wasps densely covering the under surface of the comb seemed to function as an effective insulator. The smaller temperature fluctuation in the central cell than on the roof surface, when the nest was in the empty state, suggests that the thick spongy tissue of the roof made from curled plant leaf hairs serves as an insulator to prevent the conduction of solar heat into the cells and the outward flow of heat generated in cells, especially at night.

Determination of the force constant of a single-beam gradient trap by measurement of backscattered light

A single-beam gradient trap could potentially be used to hold a stylus for scanning force microscopy. With a view to development of this technique, we modeled the optical trap as a harmonic oscillator and therefore characterized it by its force constant. We measured force constants and resonant frequencies for 1-4-mu m-diameter polystyrene spheres in a single-beam gradient trap using measurements of back-scattered light. Force constants were determined with both Gaussian and doughnut laser modes, with powers of 3 and 1 mW, respectively. Typical values for spring constants were measured to be between 10(-6) and 4 x 10(-6) N/m. The resonant frequencies of trapped particles were measured to be between 1 and 10 kHz, and the rms amplitudes of oscillations were estimated to be around 40 nm. Our results confirm that the use of the doughnut mode for single-beam trapping is more efficient in the axial direction. (C) 1996 Optical Society of America.

Analysis and implementation of a new constant acceleration subcycling algorithm

An algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps. With integer time step ratios, the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle. The algorithm is shown to have good accuracy, and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms. The implementation of a generalised form of the algorithm with non-integer time step ratios is presented. (C) 1997 by John Wiley & Sons, Ltd.