A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary

We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the `edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on this `edge'. The ability to talk about the same objects, e.g., singularities, via different structures provides alternative routes for investigation which can be invaluable in the pursuit of physically motivated problems where certain types of information are unavailable or difficult to use.Comment: 23 page

Generalizations of the Abstract Boundary singularity theorem

The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.Comment: 24 page

Benchmarking a sustainable energy engineering undergraduate degree against curriculum frameworks and pedagogy standards from industry and academia

There is an urgent need for educational institutions to produce graduates with appropriate skills to meet the growing global demand for professionals in the sustainable energy industry. For universities to stay at the forefront of meeting this global demand from industry, universities need to ensure their curricula and pedagogies stay relevant. The use of benchmarking is a key means of achieving this and ensuring any gap between university curricula and the practical needs of industry is minimized. The aim of this paper is to present an approach to benchmarking a sustainable energy engineering undergraduate degree with respect to curriculum frameworks recommended by industry and pedagogy standards required and recommended by academia and education research. The method uses the Murdoch University renewable energy engineering degree major as a case study. The results show that the learning outcomes of the renewable energy engineering units, in general, align well with the recommended learning outcomes for a complete sustainable energy degree, as prescribed by the Australian Government Office for Learning and Teaching. In addition, assessment task and marking criteria for the capstone unit of the major were at Australian Universities’ standard. A similar approach to benchmarking can be adopted by developers of new or existing sustainable energy engineering degrees in order to align with curriculum frameworks and pedagogy standards required by industry and academic peers

Using TurbSim stochastic simulator to improve accuracy of computational modelling of wind in the built environment

Small wind turbines are often sited in more complex environments than in open terrain. These sites include locations near buildings, trees and other obstacles, and in such situations, the wind is normally highly three-dimensional, turbulent, unstable and weak. There is a need to understand the turbulent flow conditions for a small wind turbine in the built environment. This knowledge is crucial for input into the design process of a small wind turbine to accurately predict blade fatigue loads and lifetime and to ensure that it operates safely with a performance that is optimized for the environment. Computational fluid dynamics is a useful method to provide predictions of local wind flow patterns and to investigate turbulent flow conditions at small wind turbine sites, in a manner that requires less time and investment than actual measurements. This article presents the results of combining a computational fluid dynamics package (ANSYS CFX software) with a stochastic simulator (TurbSim) as an approach to investigate the turbulent flow conditions on the rooftop of a building where small wind turbines are sited. The findings of this article suggest that the combination of a computational fluid dynamics package with the TurbSim stochastic simulator is a promising tool to assess turbulent flow conditions for small wind turbines on the roof of buildings. In particular, in the prevailing wind direction, the results show a significant gain in accuracy in using TurbSim to generate wind speed and turbulence kinetic energy profiles for the inlet of the computational fluid dynamics domain rather than using a logarithmic wind-speed profile and a pre-set value of turbulence intensity in the computational fluid dynamics code. The results also show that small wind turbine installers should erect turbines in the middle of the roof of the building and avoid the edges of the roof as well as areas on the roof close to the windward and leeward walls of the building in the prevailing wind direction

A comparative analysis of built environment and open terrain wind data by higher order statistics and performance evaluation of 5 kW HAWT using FAST

Small wind turbines (SWT) that are designed as per the IEC 61400-2 standard suffer structural and operational complexities when operating in the built environment, because such environments impose stochastic variations in wind speed and turbulence. The wind conditions in flat terrain of Östergarnsholm (OG) Island, Sweden and built environment of Port Kennedy (PK), Australia are compared for turbulence intensity (TI) and intermittency. The TI of the PK wind field was 24% at mean wind speed of 15 m/s, which was higher than the Normal Turbulence Model (NTM) indicated in IEC 61400-2. The TI in the open terrain was below 18% for all mean wind speeds. Similarly, for three chosen wind speed bins within a SWT's operating range, the urban wind field had higher intermittency for smaller timescales but resulted in smaller intermittency as the time lag increased. The effect of these measured wind fields on the performance and loading of a turbine was studied at the three chosen wind speed bins using an aeroelastic model of a 5 kW SWT that was developed in FAST. The predicted output statistics using measured wind fields were compared with the assumed wind fields in the IEC 61400-2 standard. The rotor thrust and blade flapwise bending moment with PK wind data were higher than that of the IEC standard due to the increased turbulence in the inflowing wind indicating the inadequacy in the current wind standard applied for such SWTs for urban installations

Effect of the anionic counterpart: Molybdate vs. tungstate in energy storage for pseudo-capacitor applications

Nickel-based bimetallic oxides (BMOs) have shown significant potential in battery-type electrodes for pseudo-capacitors given their ability to facilitate redox reactions. In this work, two bimetallic oxides, NiMoO4 and NiWO4, were synthesized using a wet chemical route. The structure and electrochemical properties of the pseudo-capacitor cathode materials were characterized. NiMoO4 showed superior charge storage performance in comparison to NiWO4, exhibiting a discharge capacitance of 124 and 77 F·g−1, respectively. NiMoO4, moreover, demonstrates better capacity retention after 1000 cycles with 87.14% compared to 82.22% for NiWO4. The lower electrochemical performance of the latter was identified to result from the redox behavior during cycling. NiWO4 reacts in the alkaline solution and forms a passivation layer composed of WO3 on the electrode, while in contrast, the redox behavior of NiMoO4 is fully reversible

A longitudinal study assessing depression in hepatitis C: does gender play a role in the new onset depression during interferon-alpha treatment?

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Effects of spatial dispersion in near-field radiative heat transfer between two parallel metallic surfaces

We study the heat transfer between two parallel metallic semi-infinite media with a gap in the nanometer-scale range. We show that the near-field radiative heat flux saturates at distances smaller than the metal skin depth when using a local dielectric constant and investigate the origin of this effect. The effect of non-local corrections is analysed using the Lindhard-Mermin and Boltzmann-Mermin models. We find that local and non-local models yield the same heat fluxes for gaps larger than 2 nm. Finally, we explain the saturation observed in a recent experiment as a manifestation of the skin depth and show that heat is mainly dissipated by eddy currents in metallic bodies.Comment: Version without figures (8 figures in the complete version