Prediction of Novel High Pressure H2O-NaCl and Carbon Oxide Compounds with Symmetry-Driven Structure Search Algorithm

Crystal structure prediction with theoretical methods is particularly challenging when unit cells with many atoms need to be considered. Here we employ a symmetry-driven structure search (SYDSS) method and combine it with density functional theory (DFT) to predict novel crystal structures at high pressure. We sample randomly from all 1,506 Wyckoff positions of the 230 space groups to generate a set of initial structures. During the subsequent structural relaxation with DFT, existing symmetries are preserved, but the symmetries and the space group may change as atoms move to more symmetric positions. By construction, our algorithm generates symmetric structures with high probability without excluding any configurations. This improves the search efficiency, especially for large cells with 20 atoms or more. We apply our SYDSS algorithm to identify stoichiometric (H2O)_n-(NaCl)_m and C_nO_m compounds at high pressure. We predict a novel H2O-NaCl structure with Pnma symmetry to form at 3.4 Mbar, which is within the range of diamond anvil experiments. In addition, we predict a novel C2O structure at 19.8 Mbar and C4O structure at 44.0 Mbar with Pbca and C2/m symmetry respectively.Comment: 8 pages,8 figures, 3 table, Physical Review B, 201

Laplacian Distribution and Domination

Let $m_G(I)$ denote the number of Laplacian eigenvalues of a graph $G$ in an interval $I$, and let $\gamma(G)$ denote its domination number. We extend the recent result $m_G[0,1) \leq \gamma(G)$, and show that isolate-free graphs also satisfy $\gamma(G) \leq m_G[2,n]$. In pursuit of better understanding Laplacian eigenvalue distribution, we find applications for these inequalities. We relate these spectral parameters with the approximability of $\gamma(G)$, showing that $\frac{\gamma(G)}{m_G[0,1)} \not\in O(\log n)$. However, $\gamma(G) \leq m_G[2, n] \leq (c + 1) \gamma(G)$ for $c$-cyclic graphs, $c \geq 1$. For trees $T$, $\gamma(T) \leq m_T[2, n] \leq 2 \gamma(G)$

A Luddite Archaeology of Hobbyist Computation

The practice element of this research includes the How-To documented here, as well as the collected recordings and artist events I have documented. It also includes the forms I have chosen and experimented with for the publication of this. This text was written primarily as a website, and the styling of different sections here references the web version. To read the website version visit: http://bruise.in/research/luddite-archaeology.html. Some additional notes on the construction of the page are included in the code which can be viewed in the inspector. Excerpts of the code are included in the Code Practice section