Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the Navier-Stokes equations and a modification to the Crank-Nicholson method for the Cahn-Hilliard equation. In particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn-Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the continuous free energy of the PDE system. Specifically, the discrete phase variable is shown to be bounded in $\ell^\infty \left(0,T;L^\infty\right)$ and the discrete chemical potential bounded in $\ell^\infty \left(0,T;L^2\right)$, for any time and space step sizes, in two and three dimensions, and for any finite final time $T$. We subsequently prove that these variables along with the fluid velocity converge with optimal rates in the appropriate energy norms in both two and three dimensions.Comment: 33 pages. arXiv admin note: text overlap with arXiv:1411.524

Deployable Optics for CubeSats

Since the beginning of the space age, many structures with different levels of complexity have been proposed for the deployment of equipment such as solar arrays, antennae, and scientific instruments. By increasing the packaging efficiency, stowing during launch and then deploying in orbit provides an opportunity for the improvement of the capabilities of small satellites payloads while maintaining a contained launch volume. The latter is particularly important when considering the launch of future constellations and, in particular, CubeSats where the volume is significantly constrained by the size of the pod. The focus of this work is the development of a camera/telescope barrel ideally suited for a Cassegrain configured space instrument, hosting the primary mirror at one (satellite side) end and the secondary mirror supported by a cruciform element at the other end (aperture). The barrel is stowed and deployed using a telescopic approach with three coaxial large diameter hollow cylinders making up the segments of the barrel. For an optical telescope, one of the most important challenges is in maintaining a highly accurate distance between the optical elements (in this case, primary and secondary mirrors which are positioned with an accuracy of a few micron). Thermo-mechanical distortions due to on orbit temperature variations and any micro-vibration excitation from sources on the spacecraft can cause significant degradation of the optical performance. To maintain the required shape stability, the main structural parts are made in a thermally invariable material and incorporate features to provide alignment and locking out. The large diameter of the structure, and low coefficient of thermal expansion, give the assembly excellent resilience to thermal and micro-vibration disturbances whilst keeping mass to a minimum. This “tube” arrangement also naturally fulfils the light baffling requirements of the telescope. Another significant challenge is the apparatus to drive the sequential deployment of the cylinders. Systems that use lead screws and gears have been proposed, however they present significant complexities and their mass has a substantial impact on the mass budget of the overall assembly. Here, a novel robust and simple wire-driven system is proposed to operate the deployment. The main advantages being the simplicity, light weight, and robustness with respect to severe vibration environments. This article will describe the development of the device and the testing of the proof of concept/qualification model

Studying in a Virtual Mobility Context:An International Pilot in the Domain of Educational Science

nonPeerReviewe

Developing Predictive Algorithm for Possible Fuel Stops for Private Aviation

Machine learning algorithms\u27 capacity to improve over time is one of their main advantages. When more and more data is handled, machine learning technology often becomes more effective and accurate. Machine learning can be used to address problems in industry. OneSky Flight is an aviation company under an umbrella of companies offering technology services for other private jet companies. One problem they face as a business is predicting when a flight will need a fuel stop upon a booking request. Given a data set of approximately 230,000 flights from OneSky, dating back to 2019, a prediction model will be made in order to achieve the overall objective of the project: a fuel stop predictor. Therefore, the customer is aware and can upgrade the aircraft or plan for the necessary fuel stop, saving the customer money and time

Lrp5 and Lrp6 exert overlapping functions in osteoblasts during postnatal bone acquisition

The canonical Wnt signaling pathway is critical for skeletal development and maintenance, but the precise roles of the individual Wnt co-receptors, Lrp5 and Lrp6, that enable Wnt signals to be transmitted in osteoblasts remain controversial. In these studies, we used Cre-loxP recombination, in which Cre-expression is driven by the human osteocalcin promoter, to determine the individual contributions of Lrp5 and Lrp6 in postnatal bone acquisition and osteoblast function. Mice selectively lacking either Lrp5 or Lrp6 in mature osteoblasts were born at the expected Mendelian frequency but demonstrated significant reductions in whole-body bone mineral density. Bone architecture measured by microCT revealed that Lrp6 mutant mice failed to accumulate normal amounts of trabecular bone. By contrast, Lrp5 mutants had normal trabecular bone volume at 8 weeks of age, but with age, these mice also exhibited trabecular bone loss. Both mutants also exhibited significant alterations in cortical bone structure. In vitro differentiation was impaired in both Lrp5 and Lrp6 null osteoblasts as indexed by alkaline phosphatase and Alizarin red staining, but the defect was more pronounced in Lrp6 mutant cells. Mice lacking both Wnt co-receptors developed severe osteopenia similar to that observed previously in mice lacking β-catenin in osteoblasts. Likewise, calvarial cells doubly deficient for Lrp5 and Lrp6 failed to form osteoblasts when cultured in osteogenic media, but instead attained a chondrocyte-like phenotype. These results indicate that expression of both Lrp5 and Lrp6 are required within mature osteoblasts for normal postnatal bone development

Optimising observing strategies for monitoring animals using drone-mounted thermal infrared cameras

The proliferation of relatively affordable off-the-shelf drones offers great opportunities for wildlife monitoring and conservation. Similarly the recent reduction in cost of thermal infrared cameras also offers new promise in this field, as they have the advantage over conventional RGB cameras of being able to distinguish animals based on their body heat and being able to detect animals at night. However, the use of drone-mounted thermal infrared cameras comes with several technical challenges. In this paper we address some of these issues, namely thermal contrast problems due to heat from the ground, absorption and emission of thermal infrared radiation by the atmosphere, obscuration by vegetation, and optimizing the flying height of drones for a best balance between covering a large area and being able to accurately image and identify animals of interest. We demonstrate the application of these methods with a case study using field data, and make the first ever detection of the critically endangered riverine rabbit (Bunolagus monticularis) in thermal infrared data. We provide a web-tool so that the community can easily apply these techniques to other studies (http://www.astro.ljmu.ac.uk/~aricburk/uav_calc/)