Naomi, I Moan

In this quiz the answer to each clue is a palindrome; to aid in the solution, word-divisions and all vowels are given. The first letters of all thirteen palindromes will spell out another palindrome when read from top to bottom. Answers are given in Answers and Solutions at the end of the issue

The Writhe of Permutations and Random Framed Knots

We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Gaussian limit distribution. This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model. The distribution of the framing in this model is equivalent to the writhe of random permutations

Cubic Polyhedra

A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears that many (but not all) of them can be relaxed to smooth minimal surfaces (under an appropriate smoothing flow, keeping their symmetries). Here we give a complete classification of the cubic polyhedra. Among these are five new infinite uniform polyhedra and an uncountable collection of new infinite semi-regular polyhedra. We also consider the somewhat larger class of all discrete minimal surfaces in the cubic lattice.Comment: 18 pages, many figure

Effect of 1 wt% LiF additive on the densification of nanocrystalline Y2O3 ceramics by spark plasma sintering

Densification of nanocrystalline cubic yttria (nc-Y2O3) powder, with 18 nm crystal size and 1 wt% LiF as a sintering additive was investigated. Specimens were fabricated by spark plasma sintering at 100 MPa, within the temperature range of 700–1500 °C. Sintering at 700 °C for 5 and 20 min resulted in 95% and 99.7% dense specimens, with an average grain size of 84 and 130 nm, respectively. nc-Y2O3 without additive was only 65% dense at 700 °C for 5 min. The presence of LiF at low sintering temperatures facilitated rapid densification by particle sliding and jamming release. Sintering at high temperatures resulted in segregation of LiF to the grain boundaries and its entrapment as globular phase within the fast growing Y2O3 grains. The sintering enhancement advantage of LiF was lost at high SPS temperatures

Evaluating functions of positive-definite matrices using colored noise thermostats

Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scales with the cube of the size of the matrix. We present here a method that can be used to evaluate the elements of a function of a positive-definite matrix with a scaling that is linear for sparse matrices and quadratic in the general case. This methodology is based on the properties of the dynamics of a multidimensional harmonic potential coupled with colored noise generalized Langevin equation (GLE) thermostats. This "$f-$thermostat" (FTH) approach allows us to calculate directly elements of functions of a positive-definite matrix by carefully tailoring the properties of the stochastic dynamics. We demonstrate the scaling and the accuracy of this approach for both dense and sparse problems and compare the results with other established methodologies.Comment: 8 pages, 4 figure

Densification and polymorphic transition of multiphase Y2O3 nanoparticles during spark plasma sintering

Multiphase (MP) monoclinic and cubic Y2O3 nanoparticles, 40 nm in diameter, were densified by spark plasma sintering for 5–15 min and100 MPa at 1000 °C, 1100 °C, and 1500 °C. Densification started with pressure increase at room temperature. Densification stagnated during heating compared to the high shrinkage rate in cubic single-phase reference nanopowder. The limited densification of the MP nanopowder originated from the vermicular structure (skeleton) formed during the heating. Interface controlled monoclinic to cubic polymorphic transformation above 980 °C led to the formation of large spherical cubic grains within the vermicular matrix. This resulted in the loss of the nanocrystalline character and low final density