Rapid Generation of Optimal Generalized Monkhorst-Pack Grids

Computational modeling of the properties of crystalline materials has become an increasingly important aspect of materials research, consuming hundreds of millions of CPU-hours at scientific computing centres around the world each year, if not more. A routine operation in such calculations is the evaluation of integrals over the Brillouin zone. We have previously demonstrated that performing such integrals using generalized Monkhorst-Pack k-point grids can roughly double the speed of these calculations relative to the widely-used traditional Monkhorst-Pack grids, and such grids can be rapidly generated by querying a free, internet-accessible database of pre-generated grids. To facilitate the widespread use of generalized k-point grids, we present new algorithms that allow rapid generation of optimized generalized Monkhorst-Pack grids on the fly, an open-source library to facilitate their integration into external software packages, and an open-source implementation of the database tool that can be used offline. We also present benchmarks of the speed of our algorithms on structures randomly selected from the Inorganic Crystal Structure Database. For grids that correspond to a real-space supercell with at least 50 angstroms between lattice points, which is sufficient to converge density functional theory calculations within 1 meV/atom for nearly all materials, our algorithm finds optimized grids in an average of 0.19 seconds on a single processing core. For 100 angstroms between real-space lattice points, our algorithm finds optimal grids in less than 5 seconds on average

Directed searches for continuous gravitational waves from binary systems: parameter-space metrics and optimal Scorpius X-1 sensitivity

We derive simple analytic expressions for the (coherent and semi-coherent) phase metrics of continuous-wave sources in low-eccentricity binary systems, both for the long-segment and short- segment regimes (compared to the orbital period). The resulting expressions correct and extend previous results found in the literature. We present results of extensive Monte-Carlo studies comparing metric mismatch predictions against the measured loss of detection statistic for binary parameter offsets. The agreement is generally found to be within ~ 10%-30%. As an application of the metric template expressions, we estimate the optimal achievable sensitivity of an Einstein@Home directed search for Scorpius X-1, under the assumption of sufficiently small spin wandering. We find that such a search, using data from the upcoming advanced detectors, would be able to beat the torque- balance level [1,2] up to a frequency of ~ 500 - 600 Hz, if orbital eccentricity is well-constrained, and up to a frequency of ~ 160 - 200 Hz for more conservative assumptions about the uncertainty on orbital eccentricity.Comment: 25 pages, 8 figure

Design degrees of freedom and mechanisms for complexity

We develop a discrete spectrum of percolation forest fire models characterized by increasing design degrees of freedom (DDOF’s). The DDOF’s are tuned to optimize the yield of trees after a single spark. In the limit of a single DDOF, the model is tuned to the critical density. Additional DDOF’s allow for increasingly refined spatial patterns, associated with the cellular structures seen in highly optimized tolerance (HOT). The spectrum of models provides a clear illustration of the contrast between criticality and HOT, as well as a concrete quantitative example of how a sequence of robustness tradeoffs naturally arises when increasingly complex systems are developed through additional layers of design. Such tradeoffs are familiar in engineering and biology and are a central aspect of the complex systems that can be characterized as HOT