Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

Some properties of the speciation model for food-web structure - Mechanisms for degree distributions and intervality

We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are derived. Properties of the speciation model are compared to those of other models that successfully describe empirical data. It is argued that the speciation model unities the underlying ideas of previous theories. In particular, it offers a mechanistic explanation for the success of the niche model of Williams and Martinez and the frequent observation of intervality in empirical food webs. (c) 2005 Elsevier Ltd. All rights reserved.

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes (approximate to hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given. [S1063-651X(00)09512-X].

Soil resource supply influences faunal size-specific distributions in natural food webs

The large range of body-mass values of soil organisms provides a tool to assess the ecological organization of soil communities. The goal of this paper is to identify graphical and quantitative indicators of soil community composition and ecosystem functioning, and to illustrate their application to real soil food webs. The relationships between log-transformed mass and abundance of soil organisms in 20 Dutch meadows and heathlands were investigated. Using principles of allometry, maximal use can be made of ecological theory to build and explain food webs. The aggregate contribution of small invertebrates such as nematodes to the entire community is high under low soil phosphorus content and causes shifts in the mass-abundance relationships and in the trophic structures. We show for the first time that the average of the trophic link lengths is a reliable predictor for assessing soil fertility responses. Ordered trophic link pairs suggest a self-organizing structure of food webs according to resource availability and can predict environmental shifts in ecologically meaningful ways.

“Superluminal” transmission via entanglement, superoscillations, and quasi-Dirac distributions

We analyze a system inwhich, due to entanglement between the spin and spatial degrees of freedom, the reduced transmitted state has the shape of the freely propagating pulse translated in the complex coordinate plane. In the case an apparently “superluminal” advancement of the pulse, the delay amplitude distribution is found to be a peculiar approximation to the Dirac d function, and the transmission coefficient exhibits a well-defined superoscillatory window. Analogies with potential tunneling and Wheeler’s delayed choice experiment are highlighted.

Entrapping homogeneous catalysts by sol-gel methods: the bottom-up synthesis of catalysts that recycle and cascade

Perspective and front cover article: Homogeneous catalysts entrapped in silica matrices, including ionic liquid containing 'ionogels', exhibit high selectivity, unexpected activity and excellent recyclability.

Blue bottle light: lecture demonstrations of homogeneous and heterogeneous photo-induced electron transfer reactions

The classic, non-photochemical blue bottle experiment involves the reaction of methylene blue (MB) with deprotonated glucose, to form a bleached form of the dye, leuco-methylene blue (LMB), and subsequent colour recovery by shaking with air. This reaction is a popular demonstrator of key principles in kinetics and reaction mechanisms. Here it is modified so as to highlight features of homogenous and heterogeneous photoinduced electron transfer (PET) (Pure Appl. Chem., 2007, 79, 293-465) reactions, i.e. blue bottle light experiments. The homogeneous blue bottle light experiment uses methylene blue, MB, as the photo-sensitizer and triethanolamine as the sacrificial electron donor. Visible light irradiation of this system leads to its rapid bleaching, followed by the ready restoration of its original colour upon shaking away from the light source. The heterogeneous blue bottle light experiment uses titania as the photo-sensitizer, MB as a redox indicator and glucose as the sacrificial electron donor. UVA light irradiation of this system leads to the rapid bleaching of the MB and the gradual restoration of its original colour with shaking and standing. The latter 'dark' step can be made facile and more demonstrator-friendly by using platinised titania particles. These two photochemical versions of the blue bottle experiment are used to explore the factors which underpin homogeneous and heterogeneous PET reactions and provide useful demonstrations of homogeneous and heterogeneous photochemistry.

Selective homogeneous snythesis of dimethyl ether from methanol

Selected Bronsted acidic ionic liquids were tested as homogeneous catalysts for the dehydration of methanol to dimethyl ether. Ionic liquids incorporating an alkanesulfonic acid as a part of the cation, a complex acidic anion, [A(2)H](-), or both, proved to be good catalysts for this process, providing high conversions and selectivities. Homogeneous catalysis in the liquid state represents a novel approach to dimethyl ether synthesis.

Study of ground-state titanium ion velocity distributions in laser-produced plasma plumes

The velocity distribution of ground-state titanium ions within a low-temperature plasma resulting from the laser ablation of a titanium target has been investigated. A KrF excimer laser was focused onto the target at moderate fluences (