Applied Symmetry for Crystal Structure Prediction

This thesis presents an original open-source Python package called PyXtal (pronounced pi-crystal ) that generates random symmetric crystal structures for use in crystal structure prediction (CSP). The primary advantage of PyXtal over existing structure generation tools is its unique symmetrization method. For molecular structures, PyXtal uses an original algorithm to determine the compatibility of molecular point group symmetry with Wyckoff site symmetry. This allows the molecules in generated structures to occupy special Wyckoff positions without breaking the structure\u27s symmetry. This is a new feature which increases the space of search-able structures and in turn improves CSP performance. It is shown that using already-symmetric initial structures results in a higher probability of finding the lowest-energy structure. Ultimately, this lowers the computational time needed for CSP. Structures can be generated for any symmetry group of 0, 1, 2, or 3 dimensions of periodicity. Either atoms or rigid molecules may be used as building blocks. The generated structures can be optimized with VASP, LAMMPS, or other computational tools. Additional options are provided for the lattice and inter-atomic distance constraints. Results for carbon and silicon crystals, water ice crystals, and molybdenum clusters are presented as usage examples

Are we all on the same page? Teacher, graduate and student perceptions of the importance of skills thought to enhance employability

Graduate employability is a key issue for Higher Education Institutions (HEIs), academic faculty and of course for students themselves. It is recognised that to be employable graduates require both discipline specific skills/knowledge and more generic skills for employment. A key step to the development of the latter is an understanding of their significance on the part of those designing courses and the students who take them. Here we compare the perceived importance of key skills from the perspective of teachers, current students and recent graduates. We find that the three groups differ in the relative importance they ascribe to several key skills. Staff rated all skills as being important and saw many as being more important than did their students. With hindsight, graduates prioritized skills that were not seen as being very important by current students. As a result of our synthesizing the views of current undergraduates, employed graduates and lecturing staff, we recommend that proper signposting of the significance of key skills to students is vital

Tidal oscillations at the head of Monterey Submarine Canyon and their relation to oceanographic sampling and the circulation of water in Monterey Bay. Annual report, Part 6, September 1972

During a 25-hour hydrographic times series at two stations near the head of Monterey Submarine Canyon, an internal tide was observed with an amplitude of 80 to 115 m in water depths of 120 and 220 m respectively. These large oscillations produced daily variations in hydrographic and chemical parameters that were of the same magnitude as seasonal variations in Monterey Bay. Computed velocities associated with the internal tide were on the order of 10 em/sec, and this tidally induced circulation may have a significant role in the exchange of deep water between Monterey Submarine Canyon and the open ocean. (PDF contains 49 pages

The Prevention of the Ice Hazard on Airplanes

A review of various methods to prevent ice formation and adhesion to aircraft surfaces is given. It was concluded that the adhesion of ice to a surface may be reduced somewhat by the application of certain waxes and varnishes. In the experiments described, the varnishes containing calcium stearate and calcium oleate gave the best results. In wind tunnel tests, the adhesion was further reduced by the application of these waxes and varnishes to a thin, heat insulating layer of rubber. The adhesion of ice is greatly reduced when the surface consists of a vehicle which carries an oil in sufficient quantity so that the surface of the vehicle is self lubricating. Ice may be removed from wings, struts, wires and other parts of an airplane during flight by the inflation of properly constructed pneumatic rubber members, providing that these members have been previously treated with a suitable low adhesion oil

Matrix Convex Hulls of Free Semialgebraic Sets

This article resides in the realm of the noncommutative (free) analog of real algebraic geometry - the study of polynomial inequalities and equations over the real numbers - with a focus on matrix convex sets $C$ and their projections $\hat C$. A free semialgebraic set which is convex as well as bounded and open can be represented as the solution set of a Linear Matrix Inequality (LMI), a result which suggests that convex free semialgebraic sets are rare. Further, Tarski's transfer principle fails in the free setting: The projection of a free convex semialgebraic set need not be free semialgebraic. Both of these results, and the importance of convex approximations in the optimization community, provide impetus and motivation for the study of the free (matrix) convex hull of free semialgebraic sets. This article presents the construction of a sequence $C^{(d)}$ of LMI domains in increasingly many variables whose projections $\hat C^{(d)}$ are successively finer outer approximations of the matrix convex hull of a free semialgebraic set $D_p=\{X: p(X)\succeq0\}$. It is based on free analogs of moments and Hankel matrices. Such an approximation scheme is possibly the best that can be done in general. Indeed, natural noncommutative transcriptions of formulas for certain well known classical (commutative) convex hulls does not produce the convex hulls in the free case. This failure is illustrated on one of the simplest free nonconvex $D_p$. A basic question is which free sets $\hat S$ are the projection of a free semialgebraic set $S$? Techniques and results of this paper bear upon this question which is open even for convex sets.Comment: 41 pages; includes table of contents; supplementary material (a Mathematica notebook) can be found at http://www.math.auckland.ac.nz/~igorklep/publ.htm