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.

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.

Environmental context explains Levy and Brownian movement patterns of marine predators

An optimal search theory, the so-called Levy-flight foraging hypothesis(1), predicts that predators should adopt search strategies known as Levy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey(2-4). Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Levy behaviour has recently been questioned(5,6). Consequently, whether foragers exhibit Levy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory's central predictions. Here we use maximum-likelihood methods to test for Levy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Levy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Levy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Levy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Levy-flight foraging hypothesis(1,7), supporting the contention(8,9) that organism search strategies naturally evolved in such a way that they exploit optimal Levy patterns.

Direct versus delayed pathways in strong-field non-sequential double ionization

We report full-dimensionality quantum and classical calculations of double ionization (DI) of laser-driven helium at 390 nm. Good agreement is observed. We identify the relative importance of the two main non-sequential DI pathways, the direct|with an almost simultaneous ejection of both electrons|and the delayed. We find that the delayed pathway prevails at small intensities independently of total electron energy but at high intensities the direct pathway predominates up to a certain upper-limit in total energy which increases with intensity. An explanation for this increase with intensity is provided.

Strong-field approximation for Coulomb explosion of H-2(+) and D-2(+) by short intense laser pulses

We present a simple quantum mechanical model to describe Coulomb explosion of H-2(+) and D-2(+) by short, intense infrared laser pulses. The model is based on the length gauge version of the molecular strong-field approximation and is valid when the process of dissociation prior to ionization is negligible. The results are compared with recent experimental data for the proton kinetic energy spectrum [Th. Ergler , Phys. Rev. Lett. 95, 093001 (2005); D. S. Murphy , J. Phys. B 40, S359 (2007)]. Using a Franck-Condon distribution over initial vibrational states, the theory reproduces the overall shape of the spectrum with only a small overestimation of slow protons. The agreement between theory and experiment can be made perfect by using a non-Frank-Condon initial distribution characteristic for H-2(+) (D-2(+)) targets produced by strong-field ionization of H-2 (D-2). For comparison, we also present results obtained by two different tunneling models for this process.

“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.

Redistribution of vibrational population in a molecular ion with nonresonant strong-field laser pulses

We present an experimental demonstration of nonresonant manipulation of vibrational states in a molecule by an intense ultrashort laser pulse. A vibrational wave packet is generated in D-2(+) through tunnel ionization of D-2 by a few-cycle pump pulse. A similar control pulse is applied as the wave packet begins to dephase so that the dynamic Stark effect distorts the electronic environment of the nuclei, transferring vibrational population. The time evolution of the modified wave packet is probed via the D-2(+) photodissociation yield that results from the application of an intense probe pulse. Comparing the measured yield with a quasiclassical trajectory model allows us to determine the redistribution of vibrational population caused by the control pulse. ©

Limitations of instantaneous water quality sampling in surface-water catchments: Comparison with near-continuous phosphorus time-series data.

The validity of load estimates from intermittent, instantaneous grab sampling is dependent on adequate spatial coverage by monitoring networks and a sampling frequency that re?ects the variability in the system under study. Catchments with a ?ashy hydrology due to surface runoff pose a particular challenge as intense short duration rainfall events may account for a signi?cant portion of the total diffuse transfer of pollution from soil to water in any hydrological year. This can also be exacerbated by the presence of strong background pollution signals from point sources during low flows. In this paper, a range of sampling methodologies and load estimation techniques are applied to phosphorus data from such a surface water dominated river system, instrumented at three sub-catchments (ranging from 3 to 5 km2 in area) with near-continuous monitoring stations. Systematic and Monte Carlo approaches were applied to simulate grab sampling using multiple strategies and to calculate an estimated load, Le based on established load estimation methods. Comparison with the actual load, Lt, revealed signi?cant average underestimation, of up to 60%, and high variability for all feasible sampling approaches. Further analysis of the time series provides an insight into these observations; revealing peak frequencies and power-law scaling in the distributions of P concentration, discharge and load associated with surface runoff and background transfers. Results indicate that only near-continuous monitoring that re?ects the rapid temporal changes in these river systems is adequate for comparative monitoring and evaluation purposes. While the implications of this analysis may be more tenable to small scale ?ashy systems, this represents an appropriate scale in terms of evaluating catchment mitigation strategies such as agri-environmental policies for managing diffuse P transfers in complex landscapes.

Temperature-dependent gap edge in strong-coupling superconductors determined using the Eliashberg-Nambu formalism

Using the theory of Eliashberg and Nambu for strong-coupling superconductors, we have calculated the gap function for a model superconductor and a selection of real superconductors includong the elements Al, Sn, Tl, Nb, In, Pb and Hg and one alloy, Bi2Tl. We have determined thetemperature-dependent gap edge in each and found that in materials with weak electron-phonon ($\lambda 1.20$), not only is the gap edge double valued but it also departs significantly from the BCS form and develops a shoulderlike structure which may, in some cases, denote a gap edge exceeding the $T = 0$ value. These computational results support the insights obtained by Leavens in an analytic consideration of the general problem. Both the shoulder and double value arise from a common origin seated in the form of the gap function in strong coupled materials at finite temperatures. From the calculated gap function, we can determine the densities of states in the materials and the form of the tunneling current-voltage characteristics for junctions with these materials as electroddes. By way of illustration, results are shown for the contrasting cases of Sn ($\lambda=0.74$) and Hg ($\lambad=1.63$). The reported results are distinct in several ways from BCS predictions and provide an incentive determinative experimental studies with techniques such as tunneling and far infrared absorption.