Constructing a frame of cube : connecting 3D shapes with direction, location and movement

With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about 3D shapes with direction, location and movement, and how young children can mentally and visually construct virtual 3D shapes using movements in both egocentric and fixed frames of reference (FOR). Findings suggest that year 4 (aged 9) children can develop the capacity to construct a cube using egocentric FOR only, fixed FOR only or a combination of both FOR. However, these young participants were unable to articulate the effect of individual or combined FOR movements. Directions for future research are proposed.

A Satellite Selection Algorithm for Achieving High Reliability of Ambiguity Resolution with GPS and Beidou Constellations

Reliability of carrier phase ambiguity resolution (AR) of an integer least-squares (ILS) problem depends on ambiguity success rate (ASR), which in practice can be well approximated by the success probability of integer bootstrapping solutions. With the current GPS constellation, sufficiently high ASR of geometry-based model can only be achievable at certain percentage of time. As a result, high reliability of AR cannot be assured by the single constellation. In the event of dual constellations system (DCS), for example, GPS and Beidou, which provide more satellites in view, users can expect significant performance benefits such as AR reliability and high precision positioning solutions. Simply using all the satellites in view for AR and positioning is a straightforward solution, but does not necessarily lead to high reliability as it is hoped. The paper presents an alternative approach that selects a subset of the visible satellites to achieve a higher reliability performance of the AR solutions in a multi-GNSS environment, instead of using all the satellites. Traditionally, satellite selection algorithms are mostly based on the position dilution of precision (PDOP) in order to meet accuracy requirements. In this contribution, some reliability criteria are introduced for GNSS satellite selection, and a novel satellite selection algorithm for reliable ambiguity resolution (SARA) is developed. The SARA algorithm allows receivers to select a subset of satellites for achieving high ASR such as above 0.99. Numerical results from a simulated dual constellation cases show that with the SARA procedure, the percentages of ASR values in excess of 0.99 and the percentages of ratio-test values passing the threshold 3 are both higher than those directly using all satellites in view, particularly in the case of dual-constellation, the percentages of ASRs (>0.99) and ratio-test values (>3) could be as high as 98.0 and 98.5 % respectively, compared to 18.1 and 25.0 % without satellite selection process. It is also worth noting that the implementation of SARA is simple and the computation time is low, which can be applied in most real-time data processing applications.

Lattice-based threshold changeability for standard shamir sectret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a nonstandard scheme designed specifically for this purpose, or to have communication between shareholders. In contrast, we show how to increase the threshold parameter of the standard Shamir secret-sharing scheme without communication between the shareholders. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. Our method is a new positive cryptographic application for lattice reduction algorithms, inspired by recent work on lattice-based list decoding of Reed-Solomon codes with noise bounded in the Lee norm. We use fundamental results from the theory of lattices (geometry of numbers) to prove quantitative statements about the information-theoretic security of our construction. These lattice-based security proof techniques may be of independent interest.

Multiscale coupling and multiphysics approaches in earth sciences : theory

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.

Chemiluminescence imaging in supersonic combustors operating in radical-farming mode

Emission spectroscopy was used to investigate ignition and combustion characteristics of supersonic combustion ramjet engines. Two-dimensional scramjet models with inlet injection, fuelled with hydrogen gas, were used in the study. The scramjet engines were configured to operate in radical farming mode, where combustion radicals are formed behind shock waves reflected at the walls. The chemiluminescence emission signals were recorded in a two-dimensional, time-integrated fashion to give information on the location and distribution of the radical farms in the combustors. High signal levels were detected in localised regions immediately downstream of shock reflections, an indication of localised hydroxyl formation supporting the concept of radical farming. Results are presented for a symmetric as well as an asymmetric scramjet geometry. These data represent the first successful visualisation of radical farms in the hot pockets of a supersonic combustor. Spectrally resolved measurements have been obtained in the ultraviolet wavelength range between 300 and 400 nm. This data shows that the OH! chemiluminescence signal around 306nm is not the most dominant source of radiation observed in the radical farms.

Two-scale computational modelling of unsaturated flow in soils exhibiting small scale heterogeneities

Unsaturated water flow in soil is commonly modelled using Richards’ equation, which requires the hydraulic properties of the soil (e.g., porosity, hydraulic conductivity, etc.) to be characterised. Naturally occurring soils, however, are heterogeneous in nature, that is, they are composed of a number of interwoven homogeneous soils each with their own set of hydraulic properties. When the length scale of these soil heterogeneities is small, numerical solution of Richards’ equation is computationally impractical due to the immense effort and refinement required to mesh the actual heterogeneous geometry. A classic way forward is to use a macroscopic model, where the heterogeneous medium is replaced with a fictitious homogeneous medium, which attempts to give the average flow behaviour at the macroscopic scale (i.e., at a scale much larger than the scale of the heterogeneities). Using the homogenisation theory, a macroscopic equation can be derived that takes the form of Richards’ equation with effective parameters. A disadvantage of the macroscopic approach, however, is that it fails in cases when the assumption of local equilibrium does not hold. This limitation has seen the introduction of two-scale models that include at each point in the macroscopic domain an additional flow equation at the scale of the heterogeneities (microscopic scale). This report outlines a well-known two-scale model and contributes to the literature a number of important advances in its numerical implementation. These include the use of an unstructured control volume finite element method and image-based meshing techniques, that allow for irregular micro-scale geometries to be treated, and the use of an exponential time integration scheme that permits both scales to be resolved simultaneously in a completely coupled manner. Numerical comparisons against a classical macroscopic model confirm that only the two-scale model correctly captures the important features of the flow for a range of parameter values.

Web crippling tests of hollow flange channel beams – end one flange and interior one flange load cases

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. The LSBs were commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Due to the unique geometry of LSBs, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSBs. Many research studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions, predominant shear and combined actions. However, to date, no investigation has been conducted into the web crippling behaviour and strength of LSB sections. Hence detailed experimental studies were conducted to investigate the web crippling behaviour and strengths of LSBs under EOF (End One Flange) and IOF (Interior One Flange) load cases. A total of 26 web crippling tests was conducted and the results were compared with current AS/NZS 4600 design rules. This comparison showed that AS/NZS 4600 (SA, 2005) design rules are very conservative for LSB sections under EOF and IOF load cases. Suitable design equations have been proposed to determine the web crippling capacity of LSBs based on experimental results. This paper presents the details of this experimental study on the web crippling behaviour and strengths of LiteSteel beams under EOF and IOF load cases.

Web crippling tests of hollow flange channel beams : ETF AND ITF load cases

This paper presents the details of an experimental study of a cold-formed steel hollow flange channel beam known as LiteSteel Beam (LSB) subject to web crippling actions (ETF and ITF). Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSB. Experimental and numerical studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions, predominant shear actions and combined actions. To date, however, no investigation has been conducted into the web crippling behaviour and strength of LSB sections under ETF and ITF load conditions. Hence experimental studies were conducted to assess the web crippling behaviour and strengths of LSBs. Twenty eight web crippling tests were conducted and the results were compared with the current AS/NZS 4600[1] and AISI S100 [2]design equations. Comparison of the ultimate web crippling capacities from tests showed that AS/NZS 4600[1] and AISI S100 [2] design equations are unconservative for LSB sections under ETF and ITF load cases. Hence new equations were proposed to determine the web crippling capacities of LSBs. Suitable design rules were also developed under the DSM format.

Numerical studies and design of hollow flange channel beams subject to combined bending and shear actions

LiteSteel beam (LSB) is a cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. It is commonly used as floor joists and bearers in residential, industrial and commercial buildings. Design of the LSB is governed by the Australian cold-formed steel structures code, AS/NZS 4600. Due to the geometry of the LSB, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, currently available design equations for common cold-formed sections are not directly applicable to the LSB. Many research studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions and predominant shear actions. To date, however, no investigation has been conducted into the strength of LSB sections under combined bending and shear actions. Hence experimental and numerical studies were conducted to assess the combined bending and shear behaviour of LSBs. Finite element models of LSBs were developed to simulate their combined bending and shear behaviour and strength of LSBs. They were then validated by comparing the results with available experimental test results and used in a detailed parametric study. The results from experimental and finite element analyses were compared with current AS/NZS 4600 and AS 4100 design rules. Both experimental and numerical studies show that the AS/NZS 4600 design rule based on circular interaction equation is conservative in predicting the combined bending and shear capacities of LSBs. This paper presents the details of the numerical studies of LSBs and the results. In response to the inadequacies of current approaches to designing LSBs for combined bending and shear, two lower bound design equations are proposed in this paper.

The crystal structure and vibrational spectroscopy of jarosite and alunite minerals

The alunite supergroup of minerals is a large hydroxy-sulfate mineral group, which has seen renewed interest following their discovery on Mars. Numerous reviews exist concerning nomenclature, formation, and natural occurrence of this mineral group. Sulfate minerals in general are widely studied and their vibrational spectra are well characterized. However, no specific review concerning alunite and jarosite spectroscopy and crystal structure has been forthcoming. This review focuses on the controversial aspects of the crystal structure and vibrational spectroscopy of jarosite and alunite minerals. Inconsistencies regarding band assignments especially in the 1000–400 cm−1 region plague these two mineral groups and result in different band assignments among the various spectroscopic studies. There are significant crystallographic and magnetic structure ambiguities with regards to ammonium and hydronium end-members, namely, the geometry these two ions assume in the structure and the fact that hydronium jarosite is a spin glass. It was also found that the synthetic causes for the super cell in plumbojarosite, minamiite, huangite, and walthierite are not known.