Correlating the Energetics and Atomic Motions of the Metal-Insulator Transition of M1 Vanadium Dioxide

Materials that undergo reversible metal-insulator transitions are obvious candidates for new generations of devices. For such potential to be realised, the underlying microscopic mechanisms of such transitions must be fully determined. In this work we probe the correlation between the energy landscape and electronic structure of the metal-insulator transition of vanadium dioxide and the atomic motions occurring using first principles calculations and high resolution X-ray diffraction. Calculations find an energy barrier between the high and low temperature phases corresponding to contraction followed by expansion of the distances between vanadium atoms on neighbouring sub-lattices. X-ray diffraction reveals anisotropic strain broadening in the low temperature structure's crystal planes, however only for those with spacings affected by this compression/expansion. GW calculations reveal that traversing this barrier destabilises the bonding/anti-bonding splitting of the low temperature phase. This precise atomic description of the origin of the energy barrier separating the two structures will facilitate more precise control over the transition characteristics for new applications and devices.Comment: 11 Pages, 8 Figure

Chiminey: Reliable Computing and Data Management Platform in the Cloud

The enabling of scientific experiments that are embarrassingly parallel, long running and data-intensive into a cloud-based execution environment is a desirable, though complex undertaking for many researchers. The management of such virtual environments is cumbersome and not necessarily within the core skill set for scientists and engineers. We present here Chiminey, a software platform that enables researchers to (i) run applications on both traditional high-performance computing and cloud-based computing infrastructures, (ii) handle failure during execution, (iii) curate and visualise execution outputs, (iv) share such data with collaborators or the public, and (v) search for publicly available data.Comment: Preprint, ICSE 201

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl

Controlled non uniform random generation of decomposable structures

Consider a class of decomposable combinatorial structures, using different types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the random generation of such structures with respect to a size $n$ and a targeted distribution in $k$ of its \emph{distinguished} atoms. We consider two variations on this problem. In the first alternative, the targeted distribution is given by $k$ real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 < \TargFreq_i < 1 for all $i$ and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We aim to generate random structures among the whole set of structures of a given size $n$, in such a way that the {\em expected} frequency of any distinguished atom \At_i equals \TargFreq_i. We address this problem by weighting the atoms with a $k$-tuple \Weights of real-valued weights, inducing a weighted distribution over the set of structures of size $n$. We first adapt the classical recursive random generation scheme into an algorithm taking \bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw $m$ structures from the \Weights-weighted distribution. Secondly, we address the analytical computation of weights such that the targeted frequencies are achieved asymptotically, i. e. for large values of $n$. We derive systems of functional equations whose resolution gives an explicit relationship between \Weights and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in \bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies associated with a given $k$-tuple \Weights of weights, and an optimized version in \bigO{k n^2} in the case of context-free languages. This allows for a heuristic resolution of the weights/frequencies relationship suitable for complex specifications. In the second alternative, the targeted distribution is given by a $k$ natural numbers $n_1, \ldots, n_k$ such that $n_1+\cdots+n_k+r=n$ where $r \geq 0$ is the number of undistinguished atoms. The structures must be generated uniformly among the set of structures of size $n$ that contain {\em exactly} $n_i$ atoms \At_i ($1 \leq i \leq k$). We give a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating $m$ structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for regular specifications