Pattern formation in spatially heterogeneous Turing reaction-diffusion models

The Turing reaction–diffusion model [Phil. Trans. R. Soc. 237 (1952) 37–72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially homogeneous parameters. The case of parameters which vary spatially has received less attention. Here, we show that a simple step function heterogeneity in a kinetic parameter can lead to spatial pattern formation outside the classical Turing space parameter regime for patterning. This reduces the constraints on the model parameters, extending possible applications. Furthermore, it highlights the potential importance of boundaries during pattern formation

Australian Organic Market Report 2010

This is the second report the Biological Farmers of Australia has commissioned to help industry bench mark the growth and health of its sectors. This report - another significant milestone in the two decade plus history of the rapidly developing Australian certified organic sector - builds the information base for industry to benchmark production and market value against past and current claims and estimates and will enable monitoring of future growth of the certified organic market in Australia and its farming and production base. In an industry characterised by operational diversity, this report allows for performance assessment by sector. The next publication in this series is planned in 2012 (biennial since the inaugural report in 2008) as a means of providing the wider industry with invaluable and realistic market information

Wave-number-explicit bounds in time-harmonic scattering

In this paper we consider the problem of scattering of time-harmonic acoustic waves by a bounded sound soft obstacle in two and three dimensions, studying dependence on the wave number in two classical formulations of this problem. The first is the standard variational/weak formulation in the part of the exterior domain contained in a large sphere, with an exact Dirichletto-Neumann map applied on the boundary. The second formulation is as a second kind boundary integral equation in which the solution is sought as a combined single- and double-layer potential. For the variational formulation we obtain, in the case when the obstacle is starlike, explicit upper and lower bounds which show that the inf-sup constant decreases like k −1 as the wave number k increases. We also give an example where the obstacle is not starlike and the inf-sup constant decreases at least as fast as k −2. For the boundary integral equation formulation, if the boundary is also Lipschitz and piecewise smooth, we show that the norm of the inverse boundary integral operator is bounded independently of k if the coupling parameter is chosen correctly. The methods we use also lead to explicit bounds on the solution of the scattering problem in the energy norm when the obstacle is starlike in which the dependence of the norm of the solution on the wave number and on the geometry are made explicit

Progress Towards Modeling the Ablation Response of NuSil-Coated PICA

The Mars Science Laboratory (MSL) Entry, Descent and Landing Instrumentation (MEDLI) collected in-flight data largely used by the ablation community to verify and validate physics-based models for the response of the Phenolic Impregnated Carbon Ablator (PICA) material [1-4]. MEDLI data were recently used to guide the development of NASAs high-fidelity material response models for PICA, implemented in the Porous material Analysis Toolbox based on OpenFOAM (PATO) software [5-6]. A follow-up instrumentation suite, MEDLI2, is planned for the upcoming Mars 2020 mission [7] after the large scientific impact of MEDLI. Recent analyses performed as part of MEDLI2 development draw the attention to significant effects of a protective coating to the aerothermal response of PICA. NuSil, a silicone-based overcoat sprayed onto the MSL heatshield as contamination control, is currently neglected in PICA ablation models. To mitigate the spread of phenolic dust from PICA, NuSil was applied to the entire MSL heatshield, including the MEDLI plugs. NuSil is a space grade designation of the siloxane copolymer, primarily used to protect against atomic oxygen erosion in the Low Earth Orbit environment. Ground testing of PICA-NuSil (PICA-N) models all exhibited surface temperature jumps of the order of 200 K due to oxide scale formation and subsequent NuSil burn-off. It is therefore critical to include a model for the aerothermal response of the coating in ongoing code development and validation efforts

The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved

Neon and Sulfur Abundances of Planetary Nebulae in the Magellanic Clouds

The chemical abundances of neon and sulfur for 25 planetary nebulae (PNe) in the Magellanic Clouds are presented. These abundances have been derived using mainly infrared data from the Spitzer Space Telescope. The implications for the chemical evolution of these elements are discussed. A comparison with similarly obtained abundances of Galactic PNe and HII regions and Magellanic Clouds HII regions is also given. The average neon abundances are 6.0x10(-5) and 2.7x10(-5) for the PNe in the Large and Small Magellanic Clouds respectively. These are ~1/3 and 1/6 of the average abundances of Galactic planetary nebulae to which we compare. The average sulfur abundances for the LMC and SMC are respectively 2.7x10(-6) and 1.0x10(-6). The Ne/S ratio (23.5) is on average higher than the ratio found in Galactic PNe (16) but the range of values in both data sets is similar for most of the objects. The neon abundances found in PNe and HII regions agree with each other. It is possible that a few (3-4) of the PNe in the sample have experienced some neon enrichment, but for two of these objects the high Ne/S ratio can be explained by their very low sulfur abundances. The neon and sulfur abundances derived in this paper are also compared to previously published abundances using optical data and photo-ionization models.Comment: 13 pages, 4 tables, 5 figures. Accepted for publication in Ap

Auxin influx importers modulate serration along the leaf margin

Leaf shape in Arabidopsis is modulated by patterning events in the margin that utilize a PIN-based auxin exporter/CUC2 transcription factor system to define regions of promotion and retardation of growth, leading to morphogenesis. In addition to auxin exporters, leaves also express auxin importers, notably members of the AUX1/LAX family. In contrast to their established roles in embryogenesis, lateral root and leaf initiation, the function of these transporters in leaf development is poorly understood. We report that three of these genes (AUX1, LAX1 and LAX2) show specific and dynamic patterns of expression during early leaf development in Arabidopsis, and that loss of expression of all three genes is required for observation of a phenotype in which morphogenesis (serration) is decreased. We used these expression patterns and mutant phenotypes to develop a margin-patterning model that incorporates an AUX1/LAX1/LAX2 auxin import module that influences the extent of leaf serration. Testing of this model by margin-localized expression of axr3–1 (AXR17) provides further insight into the role of auxin in leaf morphogenesis

Heatshield Entry Modeling Using a Design, Analysis, and Optimization Toolbox

The Mars Science Laboratory (MSL) was protected during its Mars atmospheric entry by an instrumented heatshield that used NASA's Phenolic Impregnated Carbon Ablator (PICA). PICA is a lightweight carbon fiber/polymeric resin material that offers excellent performances for protecting probes during planetary entry. The Mars Entry Descent and Landing Instrument (MEDLI) suite on MSL offers unique in-flight validation data for models of atmospheric entry and material response. MEDLI recorded, among others, time-resolved in-depth temperature data of PICA using thermocouple sensors assembled in the MEDLI Integrated Sensor Plugs (MISP). The objective of this work is to showcase the capability of the Design, Analysis, and Optimization of Thermal Protection Materials (DAOTPM) software. DAO-TPM is a Python based framework that works as a link between mission design, aerothermal and radiative environment computation, Thermal Protection Systems (TPS) microstructure analysis, material response and optimization tools. The toolbox has a Graphical User Interface (GUI) that allows the user to build as well as run the various software and utilities used to design, analyze and optimize a heatshield during atmospheric entry