Overcoming the Rayleigh Criterion Limit with Optical Vortices

We experimentally and numerically tested the separability of two independent equally-luminous monochromatic and white light sources at the diffraction limit, using Optical Vortices (OV), related to the Orbital Angular Momentum (OAM) of light. The diffraction pattern of one of the two sources crosses a phase modifying device (fork-hologram) on its center generating the Laguerre-Gaussian (L-G) transform of an Airy disk. The second source, crossing the fork-hologram in positions different from the optical center, acquires different OAM values and generates non-symmetric L-G patterns. We formulated a criterion, based on the asymmetric intensity distribution of the superposed L-G patterns so created, to resolve the two sources at angular distances much below the Rayleigh criterion. Analogous experiments carried out in white light allow angular resolutions which are still one order of magnitude below the Rayleigh criterion. The use OVs might offer new applications for stellar separation in future space experiments.Comment: 4 pages, 5 figure

In situ measurement of root reinforcement using corkscrew extraction method

Mechanical root reinforcement is an important parameter to evaluate for stability analysis of rooted slopes. The contribution of roots is however difficult to quantify in situ without time-consuming methods or heavy equipment. Here we report field testing using the newly developed “corkscrew” method at two different sites with plantings of conifers and blackcurrant. In both sites we found positive correlations between root quantity and root reinforcement in surface layers where many roots were found. Below 125 mm depth, no correlations could be found, probably due to variability in soil stress and gravel content. Roots were shown not only to increase the soil peak strength, but also to add ductility to the soil, i.e., adding strength over much larger displacement ranges. Measured reinforcement, although similar to other experimental studies, was smaller than predicted using existing models. This may be attributed to the distinct difference in shear displacement required to mobilize the strength of rooted soil as compared with fallow soil. At displacements sufficient to mobilize root strength, the soil strength component has reduced from peak to a much smaller residual strength. The corkscrew method proved a promising tool to quantify root reinforcement in field conditions due to its ease of use and short test duration.</p

Towards developmental modelling of tree root systems

Knowledge of belowground structures and processes is essential for understanding and predicting ecosystem functioning, and consequently in the development of adaptive strategies to safeguard production from trees and woody plants into the future. In the past, research has mainly been concentrated on growth models for the prediction of agronomic or forest production. Newly emerging scientific challenges, e.g. climate change and sustainable development, call for new integrated predictive methods where root systems development will become a key element for understanding global biological systems. The types of input data available from the various branches of woody root research, including biomass allocation, architecture, biomechanics, water and nutrient supply, are discussed with a view to the possibility of incorporating them into a more generic developmental model. We discuss here the main focus of root system modelling to date, including a description of simple allometric biomass models, and biomechanical stress models, and then build in complexity through static growth models towards architecture models. The next progressive and logical step in developing an inclusive developmental model that integrates these modelling approaches is discussed.Knowledge of belowground structures and processes is essential for understanding and predicting ecosystem functioning, and consequently in the development of adaptive strategies to safeguard production from trees and woody plants into the future. In the past, research has mainly been concentrated on growth models for the prediction of agronomic or forest production. Newly emerging scientific challenges, e.g. climate change and sustainable development, call for new integrated predictive methods where root systems development will become a key element for understanding global biological systems. The types of input data available from the various branches of woody root research, including biomass allocation, architecture, biomechanics, water and nutrient supply, are discussed with a view to the possibility of incorporating them into a more generic developmental model. We discuss here the main focus of root system modelling to date, including a description of simple allometric biomass models, and biomechanical stress models, and then build in complexity through static growth models towards architecture models. The next progressive and logical step in developing an inclusive developmental model that integrates these modelling approaches is discussed.Knowledge of belowground structures and processes is essential for understanding and predicting ecosystem functioning, and consequently in the development of adaptive strategies to safeguard production from trees and woody plants into the future. In the past, research has mainly been concentrated on growth models for the prediction of agronomic or forest production. Newly emerging scientific challenges, e.g. climate change and sustainable development, call for new integrated predictive methods where root systems development will become a key element for understanding global biological systems. The types of input data available from the various branches of woody root research, including biomass allocation, architecture, biomechanics, water and nutrient supply, are discussed with a view to the possibility of incorporating them into a more generic developmental model. We discuss here the main focus of root system modelling to date, including a description of simple allometric biomass models, and biomechanical stress models, and then build in complexity through static growth models towards architecture models. The next progressive and logical step in developing an inclusive developmental model that integrates these modelling approaches is discussed.Peer reviewe

PHASES High Precision Differential Astrometry of delta Equulei

delta Equulei is among the most well-studied nearby binary star systems. Results of its observation have been applied to a wide range of fundamental studies of binary systems and stellar astrophysics. It is widely used to calibrate and constrain theoretical models of the physics of stars. We report 27 high precision differential astrometry measurements of delta Equulei from the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES). The median size of the minor axes of the uncertainty ellipses for these measurements is 26 micro-arcseconds. These data are combined with previously published radial velocity data and other previously published differential astrometry measurements using other techniques to produce a combined model for the system orbit. The distance to the system is determined to within a twentieth of a parsec and the component masses are determined at the level of a percent. The constraints on masses and distance are limited by the precisions of the radial velocity data; we outline plans improve this deficiency and discuss the outlook for further study of this binary.Comment: Accepted by AJ. Complete versions of tables 2-7 now available at http://stuff.mit.edu/~matthew1/deltaEquTables/ (removed from astroph server

Root Structure and Growth in Diverse Soils

Unlike most biofuel species, Jatropha curcas has promise for use in marginal lands, but it may serve an additional role by stabilizing soils. We evaluated the growth and structural responsiveness of young J. curcas plants to diverse soil conditions. Soils included a sand, a sandy-loam, and a clay-loam from eastern Mexico. Growth and structural parameters were analyzed for shoots and roots, although the focus was the plasticity of the primary root system architecture (the taproot and four lateral roots). The sandy soil reduced the growth of both shoot and root systems significantly more than sandy-loam or clay-loam soils; there was particularly high plasticity in root and shoot thickness, as well as shoot length. However, the architecture of the primary root system did not vary with soil type; the departure of the primary root system from an index of perfect symmetry was 14 ± 5% (mean ± standard deviation). Although J. curcas developed more extensively in the sandy-loam and clay-loam soils than in sandy soil, it maintained a consistent root to shoot ratio and root system architecture across all types of soil. This strong genetic determination would make the species useful for soil stabilization purposes, even while being cultivated primarily for seed oil

Choice of a model for height-growth curves in maritime pine

A modelling procedure is presented for height-growth curves in maritime pine (Pinus pinaster Ait). We chose to fit 4 parameter nonlinear functions. Some of the parameters were fixed or estimated globally (1 value for all curves in a data set). The models were reparametrized to ensure good identifiability and better characterization of the data. The structural properties of parametrizations were investigated using sensitivity functions and the models were compared using a test file. We show that the estimation of 4 parameters for each curve is not possible in practice and that even the estimation of only 3 parameters should be avoided, in particular with the Lundqvist-Matern model or with short growth curves. With 2 local parameters, the Lundqvist-Matern model appears slightly more suitable than the Chapman-Richards model.Choix d'un modèle pour l'étude des courbes de croissance en hauteur du pin maritime. Une procédure de modélisation est présentée pour l'étude des courbes de croissance en hauteur de pins maritimes (Pinus pinaster Ait). Nous avons choisi l'ajustement à des fonctions non linéaires à 4 paramètres. Certains paramètres ont été fixés ou estimés globablement (une valeur commune à toutes les courbes). Les modèles ont été reparamétrés, de façon à améliorer l'identifiabilité ainsi que la caractérisation des données. Les propriétés des modèles et des paramétrisations ont été examinées à l'aide des fonctions de sensibilité. Les modèles ont été comparés sur un fichier test. Nous montrons que l'estimation de 4 paramètres pour chaque courbe est pratiquement impossible, et que même l'estimation de seulement 3 paramètres doit être évitée, en particulier avec le modèle de Lundqvist-Matern ou avec des courbes courtes. En revanche, avec 2 paramètres locaux, le modèle de Lundqvist-Matern semble un peu mieux adapté que le modèle de Chapman-Richards, ce dernier sous-estimant les hauteurs aux âges avancés