Are power laws that estimate fractal dimension a good descriptor of soil structure and its link to soil biological properties?

The study of interrelationships between soil structure and its functional properties is complicated by the fact that the quantitative description of soil structure is challenging. Soil scientists have tackled this challenge by taking advantage of approaches such as fractal geometry, which describes soil architectural complexity through a scaling exponent (D) relating mass and numbers of particles/aggregates to particle/aggregate size. Typically, soil biologists use empirical indices such as mean weight diameters (MWD) and percent of water stable aggregates (WSA), or the entire size distribution, and they have successfully related these indices to key soil features such as C and N dynamics and biological promoters of soil structure. Here, we focused on D, WSA and MWD and we tested whether: D estimated by the exponent of the power law of number-size distributions is a good and consistent correlate of MWD and WSA; D carries information that differs from MWD and WSA; the fraction of variation in D that is uncorrelated with MWD and WSA is related to soil chemical and biological properties that are thought to establish interdependence with soil structure (e.g., organic C, N, arbuscular mycorrhizal fungi). We analysed observational data from a broad scale field study and results from a greenhouse experiment where arbuscular mycorrhizal fungi (AMF) and collembola altered soil structure. We were able to develop empirical models that account for a highly significant and large portion of the correlation observed between WSA and MWD but we did not uncover the mechanisms that underlie this correlation. We conclude that most of the covariance between D and soil biotic (AMF, plant roots) and abiotic (C. N) properties can be accounted for by WSA and MWD. This result implies that the ecological effects of the fragmentation properties described by D and generally discussed under the framework of fractal models can be interpreted under the intuitive perspective of simpler indices and we suggest that the biotic components mostly impacted the largest size fractions, which dominate MWD, WSA and the scaling exponent ruling number-size distributions. (C) 2010 Elsevier Ltd. All rights reserved.

The area-independent effects of habitat complexity on biodiversity vary between regions.

Potential explanatory variables often co-vary in studies of species richness. Where topography varies within a survey it is difficult to separate area and habitat-diversity effects. Topographically complex surfaces may contain more species due to increased habitat diversity or as a result of increased area per se. Fractal geometry can be used to adjust species richness estimates to control for increases in area on complex surfaces. Application of fractal techniques to a survey of rocky shores demonstrated an unambiguous area-independent effect of topography on species richness in the Isle of Man. In contrast, variation in species richness in south-west England reflected surface availability alone. Multivariate tests and variation in limpet abundances also demonstrated regional variation in the area-independent effects of topography. Community composition did not vary with increasing surface complexity in south-west England. These results suggest large-scale gradients in the effects of heterogeneity on community processes or demography.

Coherence and discontinuity in the scaling of species' distribution patterns

The spatial distribution of a species can be characterized at many different spatial scales, from fine-scale measures of local population density to coarse-scale geographical-range structure. Previous studies have shown a degree of correlation in species' distribution patterns across narrow ranges of scales, making it possible to predict fine-scale properties from coarser-scale distributions. To test the limits of such extrapolation, we have compiled distributional information on 16 species of British plants, at scales ranging across six orders of magnitude in linear resolution (1 in to 100 km). As expected, the correlation between patterns at different spatial scales tends to degrade as the scales become more widely separated. There is, however, an abrupt breakdown in cross-scale correlations across intermediate (ca. 0.5 km) scales, suggesting that local and regional patterns are influenced by essentially non-overlapping sets of processes. The scaling discontinuity may also reflect characteristic scales of human land use in Britain, suggesting a novel method for analysing the 'footprint' of humanity on a landscape.

An Investigation of the Flow Field through a Variable Geometry Turbine Stator with Vane Endwall Clearance

Variable geometry turbines provide an extra degree of flexibility in air management in turbocharged engines. The pivoting stator vanes used to achieve the variable turbine geometry necessitate the inclusion of stator vane endwall clearances. The consequent leakage flow through the endwall clearances impacts the flow in the stator vane passages and an understanding of the impact of the leakage flow on stator loss is required. A numerical model of a typical variable geometry turbine was developed using the commercial CFX-10 computational fluid dynamics software, and validated using laser doppler velocimetry and static pressure measurements from a variable geometry turbine with stator vane endwall clearance. Two different stator vane positions were investigated, each at three different operating conditions representing different vane loadings. The vane endwall leakage was found to have a significant impact on the stator loss and on the uniformity of flow entering the turbine rotor. The leakage flow changed considerably at different vane positions and flow incidence at vane inlet was found to have a significant impact.

Triply differential single ionization cross sections in coplanar and non-coplanar geometry for fast heavy ion-atom collisions

We have performed a kinematically complete experiment and calculations on single ionization in 100 MeV/amu C6+ + He collisions. For electrons ejected into the scattering plane (defined by the initial and final projectile momentum vectors) our first- and higher-order calculations are in good agreement with the data. In the plane perpendicular to the scattering plane and containing the initial projectile axis a strong forward-backward asymmetry is observed. In this plane both the first-order and the higher-order calculations do not provide good agreement neither with the data nor amongst each other.

An analytic geometry-variant approach to line ratio enhancement above the optically thin limit

We describe a simple theoretical model to investigate the anomalous effects of opacity on spectral line ratios, as previously studied in elements such as Fe XV and Fe XVII. The model developed is general: it is not specific to a particular atomic system, thus giving applicability to a number of coronal and chromospheric plasmas; furthermore, it may be applied to a variety of astrophysically relevant geometries. The analysis is underpinned by geometrical arguments, and we outline a technique for it to be used as a tool for the explicit diagnosis of plasma geometry in distant astrophysical objects.

Geometry- and diffraction-independent ionization probabilities in intense laser fields: Probing atomic ionization mechanisms with effective intensity matching

We report an experimental technique for the comparison of ionization processes in ultrafast laser pulses irrespective of pulse ellipticity. Multiple ionization of xenon by 50 fs 790 nm, linearly and circularly polarized laser pulses is observed over the intensity range 10 TW/cm(2) to 10 PW/cm(2) using effective intensity matching (EIM), which is coupled with intensity selective scanning (ISS) to recover the geometry-independent probability of ionization. Such measurements, made possible by quantifying diffraction effects in the laser focus, are compared directly to theoretical predictions of multiphoton, tunnel and field ionization, and a remarkable agreement demonstrated. EIM-ISS allows the straightforward quantification of the probability of recollision ionization in a linearly polarized laser pulse. Furthermore, the probability of ionization is discussed in terms of the Keldysh adiabaticity parameter gamma, and the influence of the precursor ionic states present in recollision ionization is observed.