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

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

The influence of experimental confederate peers on children's food intake: A systematic review and meta-analysis

Confederates influence eating behaviour. Systematic reviews and meta-analyses have been conducted on this topic, however, the majority have examined adults, or a combination of adults and children, therefore, an up-to-date meta-analysis is needed to examine the impact of confederate peers on children’s food intake. We systematically reviewed and meta-analysed the influence of confederate peers on children’s food intake in research using present and remote-confederates. Six publications summarising findings from seven studies were included in this review. One publication was excluded from the meta-analysis because it was not possible to extract the required data. The meta-analysis showed that children were influenced by confederate peers; eating more when exposed to a high-intake compared to a no or low-intake confederate. Larger effects were observed when children were exposed to a remote-than a present-confederate, and for studies using healthy snacks compared to high fat high sugar (HFHS) snacks. No difference in effect size was observed when children were exposed to a high-vs. low-intake confederate compared to a high-vs. no-intake confederate. In the narrative synthesis, confederate intake influenced children’s eating behaviour 24-h later, and possible moderators and a potential mechanism underlying the influence of confederates were identified. Caution is needed when interpreting the results, as the sub-groups were not compared statistically due to high heterogeneity, and a small number of studies were included in this review. Furthermore, all studies using the present-confederate design examined HFHS snack intake, therefore, it is unclear whether observed differences in effect sizes between present- and remote-confederates may be due to confederate or food type. Research is needed to further examine the influence of confederate peers on children’s food intake and to examine mechanisms and moderators

Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model

We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$ of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$, versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ``Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ``connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of $\chi^{(3)}$ and $\chi^{(4)}$. We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the $n$-particle contributions $\chi^{(n)}$ and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlev\'e oriented approach.Comment: 21 pages Proceedings of the Counting Complexity conferenc

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Rigorous Polynomial Approximation using Taylor Models in Coq

International audienceOne of the most common and practical ways of representing a real function on machines is by using a polynomial approximation. It is then important to properly handle the error introduced by such an approximation. The purpose of this work is to offer guaranteed error bounds for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq proof assistant, with a special focus on genericity and efficiency for our implementation. We give an abstract interface for rigorous polynomial approximations, parameter- ized by the type of coefficients and the implementation of polynomials, and we instantiate this interface to the case of Taylor models with inter- val coefficients, while providing all the machinery for computing them. We compare the performances of our implementation in Coq with those of the Sollya tool, which contains an implementation of Taylor models written in C. This is a milestone in our long-term goal of providing fully formally proved and efficient Taylor models

The Effects of Playing with Thin Dolls on Body Image and Food Intake in Young Girls

This study experimentally tested the effects of playing with thin dolls on body image and food intake in 6- to 10-year-old Dutch girls (N = 117). Girls were randomly assigned to play with a thin doll, an average-sized doll, or Legos in a no doll control condition. After 10 min, they participated in a taste-test and completed questionnaires about body image. No differences were found between conditions for any of the body image variables. However, girls who played with the average-sized doll ate significantly more food than girls in other exposure conditions. Although no support was found for the assumption that playing with thin dolls influences body image, the dolls directly affected actual food intake in these young girls