Wrapping the cube and other polyhedra

An infinite series of twofold, two-way weavings of the cube, corresponding to 'wrappings', or double covers of the cube, is described with the aid of the two-parameter Goldberg- Coxeter construction. The strands of all such wrappings correspond to the central circuits (CCs) of octahedrites (four-regular polyhedral graphs with square and triangular faces), which for the cube necessarily have octahedral symmetry. Removing the symmetry constraint leads to wrappings of other eight-vertex convex polyhedra. Moreover, wrappings of convex polyhedra with fewer vertices can be generated by generalizing from octahedrites to i-hedrites, which additionally include digonal faces. When the strands of a wrapping correspond to the CCs of a four-regular graph that includes faces of size greater than 4, non-convex 'crinkled' wrappings are generated. The various generalizations have implications for activities as diverse as the construction of woven-closed baskets and the manufacture of advanced composite components of complex geometry. © 2012 The Royal Society.

The unidirectional emptying box

A theoretical description of the turbulent mixing within and the draining of a dense fluid layer from a box connected to a uniform density, quiescent environment through openings in the top and the base of the box is presented in this paper. This is an extension of the draining model developed by Linden et al. (Annu. Rev. Fluid Mech. vol. 31, 1990, pp. 201-238) and includes terms that describe localized mixing within the emptying box at the density interface. Mixing is induced by a turbulent flow of replacement fluid into the box and as a consequence we predict, and observe in complementary experiments, the development of a three-layer stratification. Based on the data collated from previous researchers, three distinct formulations for entrainment fluxes across density interfaces are used to account for this localized mixing. The model was then solved numerically for the three mixing formulations. Analytical solutions were developed for one formulation directly and for a second on assuming that localized mixing is relatively weak though still significant in redistributing buoyancy on the timescale of the draining process. Comparisons between our theoretical predictions and the experimental data, which we have collected on the developing layer depths and their densities show good agreement. The differences in predictions between the three mixing formulations suggest that the normalized flux turbulently entrained across a density interface tends to a constant value for large values of a Froude number FrT, based on conditions of the inflow through the top of the box, and scales as the cube of FrT for small values of FrT. The upper limit on the rate of entrainment into the mixed layer results in a minimum time (tD) to remove the original dense layer. Using our analytical solutions, we bound this time and show that 0.2tE ≈tD tE, i.e. the original dense layer may be depleted up to five times more rapidly than when there is no internal mixing and the box empties in a time tE. © 2010 Cambridge University Press.

Investigation of critical state in melt processed YBa2Cu3O7-δ thick films

The magnetic moment of square planar melt processed YBa2Cu3O7-δ thick films is observed to scale with the cube of the sample width at 4.2 K, suggesting that current flow on the length scale of the film determines its magnetization at this temperature. A well-defined discontinuity in slope in the scaling data at a sample width corresponding to the average grain size (≈2 mm) implies the coexistence of distinct intra- and inter-grain critical current densities of 1.1 × 105Acm-2 and 0.4 × 105Acm-2 at 1 T and 4.2 K. The presence of a critical state in the films at 4.2T is confirmed by removing the central section from a specimen. The observed change in magnetic moment is in excellent agreement with theory for fields greater than ≈2 T. A critical state is not observed at 77 K which suggests that the grains are only weakly coupled at the higher temperature. © 1994.

LES and hybrid LES/RANS simulations for conjugate heat transfer over a matrix of cubes

Large Eddy Simulation (LES) and a novel k -l based hybrid LES/RANS approach have been applied to simulate a conjugate heat transfer problem involving flow over a matrix of surface mounted cubes. In order to assess the capability and reliability of the newly developed k -l based hybrid LES/RANS, numerical results are compared with new LES and existing RANS results. Comparisons include mean velocity profiles, Reynolds stresses and conjugate heat transfer. As well as for hybrid LES/RANS validation purposes, the LES results are used to gain insights into the complex flow physics and heat transfer mechanisms. Numerical simulations show that the hybrid LES/RANS approach is effective. Mean and instantaneous fluid temperatures adjacent to the cube surface are found to strongly correlate with flow structure. Although the LES captures more mean velocity field complexities, broadly time averaged wake temperature fields are found similar for the LES and hybrid LES/RANS. Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Tribological properties of mems materials measured on a small-scale device

Micro-electro-mechanical systems, MEMS, is a rapidly growing interdisciplinary technology within the general field of Micro-Systems Technology which deals with the design and manufacture of miniaturised machines with major dimensions at the scale of tens, to perhaps hundreds, of microns. Because they depend on the cube of a representative dimension, component masses and inertias rapidly become small as size decreases whereas surface and tribological effects, which often depend on area, become increasingly important. Although MEMS components and their areas of contact are small, tribological conditions, measured by contact pressures or acceptable wear rates, are demanding and technical and commercial success will require careful measurement and precise control of surface topography and properties. Fabrication of small numbers of MEMS devices designed to test potential material combinations can be prohibitively expensive and thus there is a need for small scale test facilities which mimic the contact conditions within a micro-machine without themselves requiring processing within a full semiconductor foundry. The talk will illustrate some initial experimental results from a small-scale experimental device which meets these requirements, examining in particular the performance of Diamond-Like-Carbon coatings on a silicon substrate. Copyright © 2005 by ASME.

The Trade-offs with Space Time Cube Representation of Spatiotemporal Patterns

Space time cube representation is an information visualization technique where spatiotemporal data points are mapped into a cube. Fast and correct analysis of such information is important in for instance geospatial and social visualization applications. Information visualization researchers have previously argued that space time cube representation is beneficial in revealing complex spatiotemporal patterns in a dataset to users. The argument is based on the fact that both time and spatial information are displayed simultaneously to users, an effect difficult to achieve in other representations. However, to our knowledge the actual usefulness of space time cube representation in conveying complex spatiotemporal patterns to users has not been empirically validated. To fill this gap we report on a between-subjects experiment comparing novice users error rates and response times when answering a set of questions using either space time cube or a baseline 2D representation. For some simple questions the error rates were lower when using the baseline representation. For complex questions where the participants needed an overall understanding of the spatiotemporal structure of the dataset, the space time cube representation resulted in on average twice as fast response times with no difference in error rates compared to the baseline. These results provide an empirical foundation for the hypothesis that space time cube representation benefits users when analyzing complex spatiotemporal patterns.

An evaluation of space time cube representation of spatiotemporal patterns.

Space time cube representation is an information visualization technique where spatiotemporal data points are mapped into a cube. Information visualization researchers have previously argued that space time cube representation is beneficial in revealing complex spatiotemporal patterns in a data set to users. The argument is based on the fact that both time and spatial information are displayed simultaneously to users, an effect difficult to achieve in other representations. However, to our knowledge the actual usefulness of space time cube representation in conveying complex spatiotemporal patterns to users has not been empirically validated. To fill this gap, we report on a between-subjects experiment comparing novice users' error rates and response times when answering a set of questions using either space time cube or a baseline 2D representation. For some simple questions, the error rates were lower when using the baseline representation. For complex questions where the participants needed an overall understanding of the spatiotemporal structure of the data set, the space time cube representation resulted in on average twice as fast response times with no difference in error rates compared to the baseline. These results provide an empirical foundation for the hypothesis that space time cube representation benefits users analyzing complex spatiotemporal patterns.