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.

PH-dependent leaching behaviour and other performance properties of cement-treated mixed contaminated soil

Portland cement has been widely used for stabilisation/solidification (S/S) treatment of contaminated soils. However, there is a dearth of literature on pH-dependent leaching of contaminants from cement-treated soils. This study investigates the leachability of Cu, Pb, Ni, Zn and total petroleum hydrocarbons (TPH) from a mixed contaminated soil. A sandy soil was spiked with 3000 mg/kg each of Cd, Cu, Pb, Ni and Zn, and 10,000 mg/kg of diesel, and treated with ordinary Portland cement (CEM I). Four different binder dosages, 5%, 10%, 15% and 20% (m/m) and different water contents ranging from 13%-19% dry weight were used in order to find a safe operating envelope for the treatment process. The pH-dependent leaching behaviour of the treated soil was monitored over an 84-day period using a 3-point acid neutralisation capacity (ANC) test. The monolithic leaching test was also conducted. Geotechnical properties such as unconfined compressive strength (UCS), hydraulic conductivity and porosity were assessed over time. The treated soils recorded lower leachate concentrations of Ni and Zn compared to the untreated soil at the same pH depending on binder dosage. The binder had problems with Pb stabilisation and TPH leachability was independent of pH and binder dosage. The hydraulic conductivity of the mixes was generally of the order, 10-8 m/sec, while the porosity ranged from 26%-44%. The results of selected performance properties are compared with regulatory limits and the range of operating variables that lead to acceptable performance described. © 2012 The Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences.

New application of temperature-dependent modelling of high temperature superconductors: Quench propagation and pulse magnetization

We present temperature-dependent modeling of high-temperature superconductors (HTS) to understand HTS electromagnetic phenomena where temperature fluctuation plays a nontrivial role. Thermal physics is introduced into the well-developed H-formulation model, and the effect of temperature-dependent parameters is considered. Based on the model, we perform extensive studies on two important HTS applications: quench propagation and pulse magnetization. A micrometer-scale quench model of HTS coil is developed, which can be used to estimate minimum quench energy and normal zone propagation velocity inside the coil. In addition, we study the influence of inhomogeneity of HTS bulk during pulse magnetization. We demonstrate how the inhomogeneous distribution of critical current inside the bulk results in varying degrees of heat dissipation and uniformity of final trapped field. The temperature- dependent model is proven to be a powerful tool to study the thermally coupled electromagnetic phenomena of HTS. © 2012 American Institute of Physics.

Fabrication of high-aspect-ratio polymer microstructures and hierarchical textures using carbon nanotube composite master molds

Scalable and cost effective patterning of polymer structures and their surface textures is essential to engineer material properties such as liquid wetting and dry adhesion, and to design artificial biological interfaces. Further, fabrication of high-aspect-ratio microstructures often requires controlled deep-etching methods or high-intensity exposure. We demonstrate that carbon nanotube (CNT) composites can be used as master molds for fabrication of high-aspect-ratio polymer microstructures having anisotropic nanoscale textures. The master molds are made by growth of vertically aligned CNT patterns, capillary densification of the CNTs using organic solvents, and capillary-driven infiltration of the CNT structures with SU-8. The composite master structures are then replicated in SU-8 using standard PDMS transfer molding methods. By this process, we fabricated a library of replicas including vertical micro-pillars, honeycomb lattices with sub-micron wall thickness and aspect ratios exceeding 50:1, and microwells with sloped sidewalls. This process enables batch manufacturing of polymer features that capture complex nanoscale shapes and textures, while requiring only optical lithography and conventional thermal processing. © 2011 The Royal Society of Chemistry.

The Random Forest Kernel and other kernels for big data from random partitions

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random Forest. To demonstrate the potential of this method, we propose two new kernels, the Random Forest Kernel and the Fast Cluster Kernel, and show that these kernels consistently outperform standard kernels on problems involving real-world datasets. Finally, we show how the form of these kernels lend themselves to a natural approximation that is appropriate for certain big data problems, allowing $O(N)$ inference in methods such as Gaussian Processes, Support Vector Machines and Kernel PCA.