Off-Shell Hodge Dualities in Linearised Gravity and E11

In a spacetime of dimension n, the dual graviton is characterised by a Young diagram with two columns, the first of length n-3 and the second of length one. In this paper we perform the off-shell dualisation relating the dual graviton to the double-dual graviton, displaying the precise off-shell field content and gauge invariances. We then show that one can further perform infinitely many off-shell dualities, reformulating linearised gravity in an infinite number of equivalent actions. The actions require supplementary mixed-symmetry fields which are contained within the generalised Kac-Moody algebra E11 and are associated with null and imaginary roots.Comment: 33 pages, 2 figures, nomenclature changed and comments added to the conclusion

Many-body Green's function GW and Bethe-Salpeter study of the optical excitations in a paradigmatic model dipeptide

We study within the many-body Green's function GW and Bethe-Salpeter formalisms the excitation energies of a paradigmatic model dipeptide, focusing on the four lowest-lying local and charge-transfer excitations. Our GW calculations are performed at the self-consistent level, updating first the quasiparticle energies, and further the single-particle wavefunctions within the static Coulomb-hole plus screened-exchange approximation to the GW self-energy operator. Important level crossings, as compared to the starting Kohn-Sham LDA spectrum, are identified. Our final Bethe-Salpeter singlet excitation energies are found to agree, within 0.07 eV, with CASPT2 reference data, except for one charge-transfer state where the discrepancy can be as large as 0.5 eV. Our results agree best with LC-BLYP and CAM-B3LYP calculations with enhanced long-range exchange, with a 0.1 eV mean absolute error. This has been achieved employing a parameter-free formalism applicable to metallic or insulating extended or finite systems.Comment: 25 pages, 5 figure

Relative Effectiveness of Repellents for Preventing Deer Damage to Japanese Yews

Homeowners whose landscape plants are repeatedly browsed by white-tailed deer (Odocoileus virginianus) are interested in repellent products that are effective and long-lasting. New products come to market with limited experimental testing. We conducted a 10-week trial from Feb. through Apr. 1999 to test the duration and efficacy of six commercial deer repellents [Deer-Away Big Game Repellent (BGR) mix, BGR spray, Deer-Off, Deer Stopper II, Repellex, Tree Guard] and two experimental deer repellents (CU-A and CU-B) relative to each other and to untreated plants. Treated and control balled japanese yew (Taxus cuspidata) shrubs were placed at each of 10 homeowner sites with known white-tailed deer damage near Ithaca, NY. Yews are frequently eaten by deer during winter and provide a good bioassay for testing repellents, especially during the winter months. We checked shrubs once weekly and took photographs of damaged yews to measure the amount of deer browsing. We calculated the surface area of shrubs in each photograph by using digital analysis software. To determine significant differences over time, we applied statistical analysis using analysis of variance. Deer repellents that provided the most consistent protection were BGR spray, BGR mix, Deer-Off, and Deer Stopper II. The japanese pachysandra (Pachysandra terminalis) extracts in experimental repellents CU-A and CU-B were not effective. The performance of other commercial repellents varied considerably among sites, and these products were unreliable

Accurate and efficient linear scaling DFT calculations with universal applicability

Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear scaling algorithms, which have been developed during the last few decades. In this way it becomes possible to perform ab-initio calculations for several tens of thousands of atoms or even more within a reasonable time frame. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis -- which offers ideal properties for accurate linear scaling calculations -- we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large systems with only a moderate demand of computing resources

Etudes ab initio des effets de la température sur le spectre optique des semi-conducteurs

Thèse réalisée en cotutelle avec l'Université Catholique de Louvain (Belgique)La dépendance en température des spectres optiques des semi-conducteurs est discutée en fonction de la variation des énergies propres électroniques induite par l’interaction électron-phonon. Une démonstration formelle de la théorie de Allen-Heine-Cardona (AHC), la plus populaire dans le domaine, est présentée. Cette théorie est basée sur la théorie des perturbations et les approximations adiabatique, harmonique et des ions rigides. Une revue complète des applications semi-empiriques de cette théorie est aussi incluse dans ce document. Un nouveau formalisme ab initio basé sur la théorie des perturbations de la fonctionnelle de la densité (DFPT) est développé dans cette thèse. Ce formalisme est implémenté dans la distribution ABINIT. Dans cette nouvelle formulation, les fonctions d’onde de premier ordre sont déterminées grâce au principe variationnel et ne sont donc pas construites à partir des fonctions d’onde non perturbées, comme c’est le cas pour la théorie AHC. La théorie AHC présente une convergence lente sur le nombre d’états intermédiaires inclus dans la simulation : il faut inclure 2000 états pour un traitement adéquat de la molécule de H2 et 400 états pour le silicium. Le formalisme DFPT, quant à lui, ne nécessite que l’inclusion des états étudiés, ce qui mène à une diminution du temps de calcul par un facteur 20. Pour les molécules diatomiques,les résultats obtenus reproduisent ceux provenant de la méthode des différences finies. Pour le silicium, les résultats des études semi-empiriques antérieures sont retrouvés. Par contre, dans le cas du diamant, les résultats sont grandement sous-estimés. Ceci semble provenir de l’utilisation de la LDA. La méthode des différences finies utilisée dans le cas des molécules diatomiques a permis l’évaluation directe de la validité de l’approximation des ions rigides en évaluant le terme de Debye-Waller non diagonal (NDDW). Le terme NDDWcontribue entre 11 % pour la molécule de CO et 60 % pour la molécule de LiF ce qui signifie que l’approximation des ions rigide n’est pas valide. Cette approximation est donc perçue comme étant la cause du mauvais accord entre les observations expérimentales et les simulations théoriques pour les semi-conducteurs cristallins.The thermal corrections to the optical spectra of semiconductors are discussed interms of the variation of the single electron eigenenergies and the electron-phonon coupling. A formal derivation of the leading Allen-Heine-Cardona theory is presented. This theory is based on standard perturbation theory within the adiabatic, the harmonic and rigid-ion approximations. A full review of the successful application of this theory in the semi-empirical literature is also included. A new ab initio formalism based on DFPT is developed and implemented in the ABINIT package. In this new formulation of the theory of the electron-phonon coupling, the first-order wave functions are determined by a variational principle and are thus not constructed using the unperturbed wave functions. This is in contrast to the Allen- Heine-Cardona theory in which a slow convergence on the number of included states his observed : one must include 2000 states for the correct treatment of H2 and 400 states for silicon. Using the DFPT formalism with only 10 bands yields a decrease in calculation times by a factor of 20. This new implementation of the DFPT formalism was tested using the cases studies of diatomic molecules, silicon and diamond. The results obtained for the diatomic molecules reproduce finite difference calculations up to the numerical error present in the finite difference approach. The procedure reproduces the result of previous semi-empirical studies for silicon but underestimates drastically the electron-phonon coupling in diamond. This is shown to originate from the LDA. Finally, the finite difference method used in the diatomic molecules permitted the direct evaluation of the validity of the rigid-ion approximation by evaluating the non-site-diagonal Debye-Waller term. It was found that this term partially cancels the sum of the site-diagonal Debye-Waller and Fan term. It contributes from 11 % of this sum for CO to 60 % for LiF and is by no means negligible in any system considered. The mismatch between experimental observations and theoretical simulations in crystalline semiconductors is thus believed to originate from this approximation

Calcul des propriétés électroniques de polymères à base de métallocènes, de polymères pontés et du C60

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

The temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g. Density-Functional Theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak's theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak's theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principle context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the Density-Functional Perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion terms. For the two different numerical approaches without rigid-ion terms, the agreement is better than 7 $\mu$eV in the case of diamond, which represent an agreement to 5 significant digits. The magnitude of the non rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies

Elements for a comprehensive assessment of public indicators

There is no shortage of discussions and even criticisms of prominent indicators such as the Global Competitiveness Index, the Environmental Performance Index, or the Human Development Index, nor of proposals for supposedly better indices of prosperity, environmental sustainability or human progress. We certainly need them and probably others more. However, one cannot help thinking that a theory is missing that would offer a conception of indicators in general, and of social indicators in particular. Such a framework should recognize the complex and hybrid nature of these measures, and help assessing their quality. In other words, what we need is comprehensive assessments that considers indicators altogether as pieces of knowledge, instruments of governance and socially communicated signs; a perspective that combines the knowledge requirements of governance and the political dimension of public knowledge. We believe that such a perspective can be found at the juncture of three discourses or perspectives. The first one is Peirce’s theory of signs, or semiotics for short, that highlights the communicative nature of indicators, their role in the survival and reproduction of all living organisms and their link with action and behavior. In particular, Peirce’s classification of signs and notably his distinction between icons, indices and symbols is especially relevant here. Our second source of inspiration is John Dewey’s pragmatic theory of the public and of social inquiry which help conceptualizing the connection between indicators and public policy and understanding their role in the management of public problems. We underline the connection between Dewey’s conception of the public and more recent advances in cognitive politics, which highlights the importance of the way public problems are framed and the role of indicators in such framing. We find our third source of inspiration in the analysis by Gibbons, Limoges, Nowotny and their colleagues of the “Mode 2” of production of knowledge which can be looked at as an updating and empirical confirmation of Dewey’s theory of social inquiry. We conceive of the production of indicators as a typically “mode 2” activity, which is therefore to be assessed against the social robustness criteria. We attempt to show how Peirce’s distinction between the iconic, the indexical and the symbolic dimension of signs on one hand, and Dewey’s theory of democracy, on the other hand, provide us insightful tools for conducing comprehensive evaluations of the social robustness of indicators and designing more robust alternatives to the existing ones.JRC.DDG.01-Econometrics and applied statistic