Design of spherical symmetric gradient index lenses

Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.

On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Instabilities in two-liquid layers subject to a horizontal temperature gradient

We study theoretically the stability of two superposed fluid layers heated laterally. The fluids are supposed to be immiscible, the interface undeformable and of infinite horizontal extension. Combined thermocapillary and buoyancy forces give rise to a basic flow when a temperature difference is applied. The calculations are performed for a melt of GaAs under a layer of molten B2 O3 , a configuration of considerable technological importance. Four dif- ferent flow patterns and five temperature configurations are found for the basic state in this system. A linear stability analysis shows that the basic state may be destabilized by oscilla- tory motions leading to the so-called hydrothermal waves. Depending on the relative height of the two layers these hydrothermal waves propagate parallel or perpendicular to the temperature gradient. This analysis reveals that these perturbations can alter significantly the liquid flow in the liquid-encapsulated crystal growth techniques.

Nitrogen deposition alters nitrogen cycling and reduces soil carbon content in low-productivity semiarid Mediterranean ecosystems.

Anthropogenic N deposition poses a threat to European Mediterranean ecosystems. We combined data from an extant N deposition gradient (4.3–7.3 kg N ha−1 yr−1) from semiarid areas of Spain and a field experiment in central Spain to evaluate N deposition effects on soil fertility, function and cyanobacteria community. Soil organic N did not increase along the extant gradient. Nitrogen fixation decreased along existing and experimental N deposition gradients, a result possibly related to compositional shifts in soil cyanobacteria community. Net ammonification and nitrification (which dominated N-mineralization) were reduced and increased, respectively, by N fertilization, suggesting alterations in the N cycle. Soil organic C content, C:N ratios and the activity of β-glucosidase decreased along the extant gradient in most locations. Our results suggest that semiarid soils in low-productivity sites are unable to store additional N inputs, and that are also unable to mitigate increasing C emissions when experiencing increased N deposition.

The application of inverse-dispersion and gradient methods to estimate ammonia emissions from a penguin colony.

Penguin colonies represent some of the most concentrated sources of ammonia emissions to the atmosphere in the world. The ammonia emitted into the atmosphere can have a large influence on the nitrogen cycling of ecosystems near the colonies. However, despite the ecological importance of the emissions, no measurements of ammonia emissions from penguin colonies have been made. The objective of this work was to determine the ammonia emission rate of a penguin colony using inverse-dispersion modelling and gradient methods. We measured meteorological variables and mean atmospheric concentrations of ammonia at seven locations near a colony of Adélie penguins in Antarctica to provide input data for inverse-dispersion modelling. Three different atmospheric dispersion models (ADMS, LADD and a Lagrangian stochastic model) were used to provide a robust emission estimate. The Lagrangian stochastic model was applied both in ‘forwards’ and ‘backwards’ mode to compare the difference between the two approaches. In addition, the aerodynamic gradient method was applied using vertical profiles of mean ammonia concentrations measured near the centre of the colony. The emission estimates derived from the simulations of the three dispersion models and the aerodynamic gradient method agreed quite well, giving a mean emission of 1.1 g ammonia per breeding pair per day (95% confidence interval: 0.4–2.5 g ammonia per breeding pair per day). This emission rate represents a volatilisation of 1.9% of the estimated nitrogen excretion of the penguins, which agrees well with that estimated from a temperature-dependent bioenergetics model. We found that, in this study, the Lagrangian stochastic model seemed to give more reliable emission estimates in ‘forwards’ mode than in ‘backwards’ mode due to the assumptions made.

A gradient-enhanced continuum damage model for fibre-reinforced materials

Modelo de daño no local definido a materiales fibrados. Este modelo se aplica al estudio de problemas típicos en la biomecánica de los tejidos blandos, como las paredes arteriales.

Surveillance of habitats and plant diversity indicators across a regional gradient in the Iberian Peninsula

Dentro del Proyecto EBONE (Red de Observación de la Biodiversidad Europea) se analizan diferentes tipos de paisaje en varias zonas de Madrid y norte de Portugal. Se realiza un estudio de los habitats y la diversidad de especies con el objetivo principal de preservarlos y conservalos.

Grain size gradient length scale in ballistic properties optimization of functionally graded nanocrystalline steel plates

The last few years have highlighted the existence of two relevant length scales in the quest to ultrahigh-strength polycrystalline metals. Whereas the microstructural length scale – e.g. grain or twin size – has mainly be linked to the well-established Hall–Petch relationship, the sample length scale – e.g. nanopillar size – has also proven to be at least as relevant, especially in microscale structures. In this letter, a series of ballistic tests on functionally graded nanocrystalline plates are used as a basis for the justification of a “grain size gradient length scale” as an additional ballistic properties optimization parameter.

HOG-Like gradient-based descriptor for visual vehicle detection

One of the main challenges for intelligent vehicles is the capability of detecting other vehicles in their environment, which constitute the main source of accidents. Specifically, many methods have been proposed in the literature for video-based vehicle detection. Most of them perform supervised classification using some appearance-related feature, in particular, symmetry has been extensively utilized. However, an in-depth analysis of the classification power of this feature is missing. As a first contribution of this paper, a thorough study of the classification performance of symmetry is presented within a Bayesian decision framework. This study reveals that the performance of symmetry-based classification is very limited. Therefore, as a second contribution, a new gradient-based descriptor is proposed for vehicle detection. This descriptor exploits the known rectangular structure of vehicle rears within a Histogram of Gradients (HOG)-based framework. Experiments show that the proposed descriptor outperforms largely symmetry as a feature for vehicle verification, achieving classification rates over 90%.

Technical note: Comparison of automated ribosomal intergenic spacer analysis (ARISA) and denaturing gradient gel electrophoresis (DGGE) to assess bacterial diversity in the rumen of sheep

The aim of this study was to compare automated ribosomal intergenic spacer analysis (ARISA) and denaturing gradient gel electrophoresis (DGGE) techniques to assess bacterial diversity in the rumen of sheep. Sheep were fed 2 diets with 70% of either alfalfa hay or grass hay, and the solid (SOL) and liquid (LIQ) phases of the rumen were sampled immediately before feeding (0 h) and at 4 and 8 h postfeeding. Both techniques detected similar differences between forages, with alfalfa hay promoting greater (P < 0.05) bacterial diversity than grass hay. In contrast, whereas ARISA analysis showed a decrease (P < 0.05) of bacterial diversity in SOL at 4 h postfeeding compared with 0 and 8 h samplings, no variations (P > 0.05) over the postfeeding period were detected by DGGE. The ARISA technique showed lower (P < 0.05) bacterial diversity in SOL than in LIQ samples at 4 h postfeeding, but no differences (P > 0.05) in bacterial diversity between both rumen phases were detected by DGGE. Under the conditions of this study, the DGGE was not sensitive enough to detect some changes in ruminal bacterial communities, and therefore ARISA was considered more accurate for assessing bacterial diversity of ruminal samples. The results highlight the influence of the fingerprinting technique used to draw conclusions on factors affecting ruminal bacterial diversity.

A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

A gradient-enhanced continuum damage model with application to fibre-reinforced tissues at finite strains

A non-local gradient-based damage formulation within a geometrically non-linear set- ting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy function which is additively composed by an isotropic neo-Hookean matrix and by an anisotropic fibre-reinforced material based on the model proposed by T. Gasser, R. Ogden, and G. Holzapfel.

Changes in spatial point patterns of pioneer woody plants across a large tropical landslide

We assessed whether the relative importance of positive and negative interactions in early successional communities varied across a large landslide on Casita Volcano (Nicaragua). We tested several hypotheses concerning the signatures of these processes in the spatial patterns of woody pioneer plants, as well as those of mortality and recruitment events, in several zones of the landslide differing in substrate stability and fertility, over a period of two years (2001 and 2002). We identified all woody individuals with a diameter >1 cm and mapped them in 28 plots measuring 10 × 10-m. On these maps, we performed a spatial point pattern analysis using univariate and bivariate pair-correlation functions; g (r) and g12 (r), and pairwise differences of univariate and bivariate functions. Spatial signatures of positive and negative interactions among woody plants were more prevalent in the most and least stressful zones of the landslide, respectively. Natural and human-induced disturbances such as the occurrence of fire, removal of newly colonizing plants through erosion and clearcutting of pioneer trees were also identified as potentially important pattern-creating processes. These results are in agreement with the stress-gradient hypothesis, which states that the relative importance of facilitation and competition varies inversely across gradients of abiotic stress. Our findings also indicate that the assembly of early successional plant communities in large heterogeneous landslides might be driven by a much larger array of processes than previously thought.

All males are not created equal: Fertility differences depend on gamete recognition polymorphisms in sea urchins

Behaviors, morphologies, and genetic loci directly involved in reproduction have been increasingly shown to be polymorphic within populations. Explaining how such variants are maintained by selection is crucial to understanding the genetic basis of fertility differences, but direct tests of how alleles at reproductive loci affect fertility are rare. In the sea urchin genus Echinometra, the protein bindin mediates sperm attachment to eggs, evolves quickly, and is polymorphic within species. Eggs exposed to experimental sperm mixtures show strong discrimination on the basis of the males’ bindin genotype. Different females produce eggs that nonrandomly select sperm from different males, showing that variable egg–sperm interactions determine fertility. Eggs select sperm with a bindin genotype similar to their own, suggesting strong linkage between female choice and male trait loci. These experiments demonstrate that alleles at a single locus can have a strong effect on fertilization and that reproductive loci may retain functional polymorphisms through epistatic interactions between male and female traits. They also suggest that positive selection at gamete recognition loci like bindin involves strong selection within species on mate choice interactions.

Measurements of hydrogen, oxygen and carbon isotope variability in Sphagnum moss along a micro-topographical gradient in a southern Patagonian peatland

Funded by Natural Environment Research Council PRECIP and PATAGON