Orientation, sphericity and roundness evaluation of particles using alternative 3D representations

Sphericity and roundness indices have been used mainly in geology to analyze the shape of particles. In this paper, geometric methods are proposed as an alternative to evaluate the orientation, sphericity and roundness indices of 3D objects. In contrast to previous works based on digital images, which use the voxel model, we represent the particles with the Extreme Vertices Model, a very concise representation for binary volumes. We define the orientation with three mutually orthogonal unit vectors. Then, some sphericity indices based on length measurement of the three representative axes of the particle can be computed. In addition, we propose a ray-casting-like approach to evaluate a 3D roundness index. This method provides roundness measurements that are highly correlated with those provided by the Krumbein's chart and other previous approach. Finally, as an example we apply the presented methods to analyze the sphericity and roundness of a real silica nano dataset.Postprint (published version

Plotting the Centre: Bramante’s Drawings for the New St. Peter’s Basilica

This paper examines the concept of 'centre' in the design and symbolism of the new St Peter's Basilica, executed by Donato Bramante in the early 16th century. Drawing upon theological and philosophical notions of centre in late Medieval and Renaissance culture (specifically Nicolas Cusanus), the study argues that Bramante's drawings for the project reveal a particular understanding of centre, and its constellations of sub-centres, that broadly follow Platonic cosmological principles highlighted in the Timaeus. The paper considers how this understanding of space was also communicated in the iconography of the frescoes in the Stanza della Segnatura in the Vatican Palace, executed by Raphael at the same time as Bramante's design for the new basilica, in which Bramante is also credited as the author of the perspective construction

Conforming restricted Delaunay mesh generation for piecewise smooth complexes

A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted, conforming restricted Delaunay representation for domains specified as a (non-manifold) collection of piecewise smooth surface patches and curve segments, (ii) a protection strategy for domains containing curve segments that subtend sharply acute angles, and (iii) a new class of off-centre refinement rules designed to achieve high-quality point-placement along embedded curve features. Experimental comparisons show that the new Frontal-Delaunay algorithm outperforms a classical (statically weighted) restricted Delaunay-refinement technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl

Hydrophobic interactions: an overview

We present an overview of the recent progress that has been made in understanding the origin of hydrophobic interactions. We discuss the different character of the solvation behavior of apolar solutes at small and large length scales. We emphasize that the crossover in the solvation behavior arises from a collective effect, which means that implicit solvent models should be used with care. We then discuss a recently developed explicit solvent model, in which the solvent is not described at the atomic level, but rather at the level of a density field. The model is based upon a lattice-gas model, which describes density fluctuations in the solvent at large length scales, and a Gaussian model, which describes density fluctuations at smaller length scales. By integrating out the small length scale field, a Hamiltonian is obtained, which is a function of the binary, large-length scale field only. This makes it possible to simulate much larger systems than hitherto possible as demonstrated by the application of the model to the collapse of an ideal hydrophobic polymer. The results show that the collapse is dominated by the dynamics of the solvent, in particular the formation of a vapor bubble of critical size. Implications of these findings to the understanding of pressure denaturation of proteins are discussed.Comment: 10 pages, 4 figure

Experimentation and Representation in Architecture: analyzing one’s own design activity

Architects materialize ideas on physical supports to register their thoughts and to discover new possibilities from hints and suggestions in their own drawings. Uncertainty is inherent to creative processes encouraging the production of different ideas through testing. This research brings to light that the re-examination of artefacts from new points of view allows for the review and generation of design ideas and decisions, capacitating students to make yet new discoveries from what they have done so far. Tacit knowledge aids specific decisions. Student reports become analytical records of their material registers (sketches, physical and virtual models) making it explicit that which is implicit in those artefacts. This apparently confirms previous studies that suggest that knowledge per se not always triggers or controls decisions in design. Many physical as well as perceptive actions actually lead the initial steps and play a crucial role in the whole course of production. Besides serving as external representations, sketches and models provide visual hints that will be checked later, favouring the upcoming of the unexpected, stimulating creativity. The intent here is to point out how these different means of representation and expression contribute in a peculiar manner to the whole process of discovery and solution to problems in architecture. The authors propose here a reflection on the process of design and its uncertainties in its initial phase, concentrating on sketches and real models as experimentations. They consider these means not from a graphic and physical register stand point, but in terms of conception and concepts they embody, as records of students thinking and knowledge. Keywords: Experimentation; Uncertainty; Representation; Design Process; Cognition; Education</p

How often is a random quantum state k-entangled?

The set of trace preserving, positive maps acting on density matrices of size d forms a convex body. We investigate its nested subsets consisting of k-positive maps, where k=2,...,d. Working with the measure induced by the Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes of these sets. Our results strongly suggest that the inner set of (k+1)-positive maps forms a small fraction of the outer set of k-positive maps. These results are related to analogous bounds for the relative volume of the sets of k-entangled states describing a bipartite d X d system.Comment: 19 pages in latex, 1 figure include

Tolkien and Alterity (2017) ed. by Christopher Vaccaro and Yvette Kisor

Book review by Gergely Nagy of Tolkien and Alterity (2017), edited by Christopher Vaccaro and Yvette Kiso

Incorporating interactive 3-dimensional graphics in astronomy research papers

Most research data collections created or used by astronomers are intrinsically multi-dimensional. In contrast, all visual representations of data presented within research papers are exclusively 2-dimensional. We present a resolution of this dichotomy that uses a novel technique for embedding 3-dimensional (3-d) visualisations of astronomy data sets in electronic-format research papers. Our technique uses the latest Adobe Portable Document Format extensions together with a new version of the S2PLOT programming library. The 3-d models can be easily rotated and explored by the reader and, in some cases, modified. We demonstrate example applications of this technique including: 3-d figures exhibiting subtle structure in redshift catalogues, colour-magnitude diagrams and halo merger trees; 3-d isosurface and volume renderings of cosmological simulations; and 3-d models of instructional diagrams and instrument designs.Comment: 18 pages, 7 figures, submitted to New Astronomy. For paper with 3-dimensional embedded figures, see http://astronomy.swin.edu.au/s2plot/3dpd