Independence Standards Board: Backgournd, Organization, Mission and General operation, September 16, 1998

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Compactness estimates for difference schemes for conservation laws with discontinuous flux

We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function $f(k(x,t),u)$, where the coefficient $k(x,t$ is $BV$-regular and may exhibit discontinuities along curves in the $(x,t)$ plane. Our approach, which is technically elementary, relies on a discrete interaction estimate and the existence of one strictly convex entropy. While the details are specifically outlined for the Lax-Friedrichs scheme, the same framework can be applied to other difference schemes. Notably, our compactness estimates are new even in the homogeneous case ($k\equiv 1$)

Introducing the Independence Standards Board: Background, Organization, Mission, and General Operation, May 30, 1998

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Public File Documents Relating to ISB Staff Interpretive Letter Dated 4/9/99

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Staff Recent Interpretation Ratified: Coopers & Lybrand of Australia

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Novel methods for spatial prediction of soil functions within landscapes (SP0531)

Previous studies showed that soil patterns could be predicted in agriculturally managed landscapes by modelling and extrapolating from extensive existing but related integrated datasets. Based on these results we proposed to develop and apply predictive models of the relationships between environmental data and known soil patterns to predict capacity for key soil functions within diverse landscapes for which there is little detailed underpinning soil information available. Objectives were: To develop a high-level framework in which the non-specialist user-community could explore questions. To generate digital soil maps for three selected catchments at a target resolution of 1:50000 to provide the base information for soil function prediction. To use a modelling approach to predict the performance of key soil functions in catchments undergoing change but where only sparse or low resolution soil survey data are available. To use a modelling approach to assess the impact of different management scenarios and/or environmental conditions on the delivery of multiple soil functions within a catchment. To create a detailed outline of the requirements for ground-truthing to test the predicted model outputs at a catchment scale. To contribute to the development of a high-level framework for decision makers

Retinoic acid influences the timing and scaling of avian wing development

A fundamental question in biology is how embryonic development is timed between different species. To address this problem, we compared wing development in the quail and the larger chick. We reveal that pattern formation is faster in the quail as determined by the earlier activation of 5′Hox genes, termination of developmental organizers (Shh and Fgf8), and the laying down of the skeleton (Sox9). Using interspecies tissue grafts, we show that developmental timing can be reset during a critical window of retinoic acid signaling. Accordingly, extending the duration of retinoic acid signaling switches developmental timing between the quail and the chick and the chick and the larger turkey. However, the incremental growth rate is comparable between all three species, suggesting that the pace of development primarily governs differences in the expansion of the skeletal pattern. The widespread distribution of retinoic acid could coordinate developmental timing throughout the embryo

Requirements for the spatial storage effect are weakly evident for common species in natural annual plant assemblages

Coexistence in spatially varying environments is theorised to be promoted by a variety of mechanisms including the spatial storage effect. The spatial storage effect promotes coexistence when: (i) species have unique vital rate responses to their spatial environment and, when abundant, (ii) experience stronger competition in the environmental patches where they perform better. In a naturally occurring southwest Western Australian annual plant system we conducted a neighbour removal experiment involving eleven focal species growing in high-abundance populations. Specifically, we measured species' fecundity across a variety of environmental gradients in both the presence and absence of neighbours. For the environmental variables that we measured, there was only limited evidence for species-specific responses to the environment, with a composite variable describing overstory cover and leaf litter cover being the best predictor of fecundity for a subset of focal species. In addition, although we found strong evidence for intra-specific competition, positive environment-competition covariance was only detected for one species. Thus, positive environment-competition covariance may not be as common as expected in populations of species growing at high abundance, at least when tested in natural assemblages. Our findings highlight the inherent limitations of using natural assemblages to study spatial coexistence mechanisms, and we urge empirical ecologists to take these limitations into account when designing future experiments

Multidimensional solitons in periodic potentials

The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA) and in direct simulations. The potential stabilizes the solitons against collapse. Direct physical realizations are a Bose-Einstein condensate (BEC) trapped in an optical lattice, and a light beam in a bulk Kerr medium of a photonic-crystal type. In the 2D case, the creation of the soliton in a weak lattice potential is possible if the norm of the field (number of atoms in BEC, or optical power in the Kerr medium) exceeds a threshold value (which is smaller than the critical norm leading to collapse). Both "single-cell" and "multi-cell" solitons are found, which occupy, respectively, one or several cells of the periodic potential, depending on the soliton's norm. Solitons of the former type and their stability are well predicted by VA. Stable 2D vortex solitons are found too.Comment: 13 pages, 3 figures, Europhys. Lett., in pres