Theoretical interpretation of scanning tunneling microscopy images: Application to the molybdenum disulfide family of transition metal dichalcogenides

We have performed ab initio quantum mechanical calculations to describe scanning tunneling microscopy (STM) images of MoS_2 and MoTe_2. These results indicate that the interpretation of the STM images of these and related materials depends sensitively on experimental conditions. For example, determining whether the maximum tunneling current correlates to the top atom (S or Te) or to the second‐layer atom (Mo) requires information on the tip‐sample separation. Based on these results we discuss some STM experimental procedures which would allow assignment of the chemical identity of STM spots with greater certainty

Saccharomyces cerevisiae: a nomadic yeast with no niche?

Different species are usually thought to have specific adaptations, which allow them to occupy different ecological niches. But recent neutral ecology theory suggests that species diversity can simply be the result of random sampling, due to finite population sizes and limited dispersal. Neutral models predict that species are not necessarily adapted to specific niches, but are functionally equivalent across a range of habitats. Here we evaluate the ecology of S. cerevisiae, one of the most important microbial species in human history. The artificial collection, concentration, and fermentation of large volumes of fruit for alcohol production produces an environment in which S. cerevisiae thrives, and therefore it is assumed that fruit is the ecological niche that S. cerevisiae inhabits and has adapted to. We find very little direct evidence that S. cerevisiae is adapted to fruit, or indeed to any other specific niche. We propose instead a neutral nomad model for S. cerevisiae, which we believe should be used as the starting hypothesis in attempting to unravel the ecology of this important microbe

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

Quantum-mechanical calculations of the stabilities of fluxional isomers of C_4H_7^+ in solution

Although numerous quantum calculations have been made over the years of the stabilities of the fluxional isomers of C4H7+, none have been reported for other than the gas phase (which is unrealistic for these ionic species) that exhibit exceptional fluxional properties in solution. To be sure, quantum-mechanical calculations for solutions are subject to substantial uncertainties, but nonetheless it is important to see whether the trends seen for the gas-phase C4H7+ species are also found in calculations for polar solutions. Of the C4H7+ species, commonly designated bisected-cyclopropylcarbinyl 1, unsym-bicyclobutonium-2, sym-bicyclobutonium 3, allylcarbinyl 4, and pyramidal structure 6, the most advanced gas-phase calculations available thus far suggest that the order of stability is 1 ≥ 2 ≥ 3 >> 4 >> 6 with barriers of only ~1 kcal/mol for interconversions among 1, 2, and 3. We report here that, when account is taken of solvation, 2 turns out to be slightly more stable than 1 or 3 in polar solvents. The pattern of the overall results is unexpected, in that despite substantial differences in structures and charge distributions between the primary players in the C4H7+ equilibria and the large differences in solvation energies calculated for the solvents considered, the differential solvent effects from species to species are rather small

Modelling inelastic granular media using Dynamical Density Functional Theory

We construct a new mesoscopic model for granular media using Dynamical Density Functional Theory (DDFT). The model includes both a collision operator to incorporate inelasticity and the Helmholtz free energy functional to account for external potentials, interparticle interactions and volume exclusion. We use statistical data from event-driven microscopic simulations to determine the parameters not given analytically by the closure relations used to derive the DDFT. We numerically demonstrate the crucial effects of each term in the DDFT, and the importance of including an accurately parametrised pair correlation function

Comparing league formats with respect to match importance in Belgian football

Recently, most clubs in the highest Belgian football division have become convinced that the format of their league should be changed. Moreover, the TV station that broadcasts the league is pleading for a more attractive competition. However, the clubs have not been able to agree on a new league format, mainly because they have conflicting interests. In this paper, we compare the current league format, and three other formats that have been considered by the Royal Belgian Football Association. We simulate the course of each of these league formats, based on historical match results. We assume that the attractiveness of a format is determined by the importance of its games; our importance measure for a game is based on the number of teams for which this game can be decisive to reach a given goal. Furthermore, we provide an overview of how each league format aligns with the expectations and interests of each type of club