Bonding studies of compounds of boron and the group IV elements : X. Photoelectron spectra of compounds Me4M (MC,Si, Ge,Sn, or Pb) and the lack of participation of M d-orbitals

The question of d-orbital participation by the central metal M in molecules containing second and higher row elements is critically examined in relation to the photoelectron spectra of the Group IV compounds Me₄M. It is shown that the splitting between the two strictly symmetry-determined CH levels 1t₁ and 1e drops monotonically from 1.3₅ eV in neopentane to approximately zeor in tetramethyl-plumbane, as is consistent with the decreasing through-space interactions in the (CH₃)₄ tetrahedron. Within the limits of the spectroscopic resolution, d-orbital participation is therefore discounted, as this would tend to increase the separation between these two levels on going down the series.     

A study of the action of wild fires on remote forests

A stochastic model is developed to describe interaction of fires and vegetation in remote forest regions to demonstrate that, given certain circumstances, fires have a dominant effect on the long term, as well as the short term, forest structure. The model describes interactions peculiar to rainforest regions of Tasmania, Australia, but can be adapted to any situation where a similar dependence of vegetation on fires exists.     

A modified Brent’s method for finding zeros of functions

Brent’s method, also known as zeroin, has been the most popular method for finding zeros of functions since it was developed in 1972. This method usually converges very quickly to a zero; for the occasional difficult functions encountered in practice, it typically takes $O(n)$ iterations to converge, where $n$ is the number of steps required for the bisection method to find the zero to approximately the same accuracy. While it has long been known that in theory Brent’s method could require as many as $O(n^2)$ iterations to find a zero, such behavior had never been observed in practice. In this paper, we first show that Brent’s method can indeed take $O(n^2)$ iterations to converge, by explicitly constructing such worst case functions. In particular, for double precision accuracy, Brent’s method takes $2{,}914$ iterations to find the zero of our function, compared to the $77$ iterations required by bisection. Secondly, we present a modification of Brent’s method that places a stricter complexity bound of $O(n)$ on the search for a zero. In our extensive testing, this modification appears to behave very similarly to Brent’s method for all the common functions, yet it remains at worst five times slower than the bisection method for all difficult functions, in sharp contrast to Brent’s method.     

New ideas in neutrino detection

What is new in the field of neutrino detection? In addition to new projects probing both the low and high ends of the neutrino energy scale, an inexpensive, effective technique is being developed to allow tagging of antineutrinos in water Cherenkov (WC) detectors via the addition to water of a solute with a large neutron cross-section and energetic γ daughters. Gadolinium is an excellent candidate since in recent years it has become very inexpensive, now less than $8 per kilogram in the form of commercially available gadolinium trichloride. This non-toxic, non-reactive substance is highly soluble in water. Neutron capture on gadolinium yields an 8.0 MeV gamma cascade easily seen in detectors like Super-Kamiokande. The uses of GdCl₃ as a possible upgrade for the Super-Kamiokande detector — with a view toward improving its performance as an antineutrino detector for supernova neutrinos and reactor neutrinos — are discussed, as are the ongoing R&;D efforts which aim to make this dream a reality within the next two years.