Selfconsistent Approximations in Mori's Theory

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time dependent correlation functions and products of operators at $t=0$, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the Heisenberg dynamics of the observables are obtained as an expansion of the same type. The dynamic equations for correlation functions result to be selfconsistent nonlinear equations of the type known from mode-mode coupling approximations. The approach yields a neccessary condition for the validity of the presented equations. As a third consequence the static correlations can be calculated from fluctuation-dissipation theorems, if the observables obey a Lie algebra. For a simple spin model the convergence of the expansion is studied. As a further test, dynamic and static correlations are calculated for a Heisenberg ferromagnet at low temperatures, where the results are compared to those of a Holstein Primakoff treatment.Comment: 51 pages, Latex, 3 eps figures included, elsart and epsf style files included, also available at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html and ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram

HIV-1 VPR impairs cell growth through the inactivation of two genetically distinct host cell proteins

International audiencen.

Optimisation of accurate rutile TiO2TiO_2 (110), (100), (101) and (001) surface models from periodic DFT calculations

In this paper, geometric bulk parameters, bulk moduli, energy gaps and relative stabilities of the TiO2 anatase and rutile phases were determined from periodic DFT calculations. Then, for the rutile phase, structures, relaxations and surface energies of the (110), (100), (101) and (001) faces were computed. The calculated surface energies are consistent with the natural rutile powder composition, even if a dependence on the number of layers of the slab used to model the surface was identified. Internal constraints, consisting in freezing some internal layers of the slab to atomic bulk positions, were thus added to mimic the bulk hardness in order to stabilise the computed surface energies for thinner systems. In parallel, the influence of pseudopotentials was studied and it appears that four valence electrons for titanium atoms are sufficient. The aim of this study was to optimise accurate rutile TiO2 surface models that will be used in further calculations to investigate water and uranyl ion sorption mechanisms

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

Actions of the braid group, and new algebraic proofs of results of Dehornoy and Larue

This article surveys many standard results about the braid group with emphasis on simplifying the usual algebraic proofs. We use van der Waerden's trick to illuminate the Artin-Magnus proof of the classic presentation of the algebraic mapping-class group of a punctured disc. We give a simple, new proof of the Dehornoy-Larue braid-group trichotomy, and, hence, recover the Dehornoy right-ordering of the braid group. We then turn to the Birman-Hilden theorem concerning braid-group actions on free products of cyclic groups, and the consequences derived by Perron-Vannier, and the connections with the Wada representations. We recall the very simple Crisp-Paris proof of the Birman-Hilden theorem that uses the Larue-Shpilrain technique. Studying ends of free groups permits a deeper understanding of the braid group; this gives us a generalization of the Birman-Hilden theorem. Studying Jordan curves in the punctured disc permits a still deeper understanding of the braid group; this gave Larue, in his PhD thesis, correspondingly deeper results, and, in an appendix, we recall the essence of Larue's thesis, giving simpler combinatorial proofs.Comment: 51`pages, 13 figure

Combined investigation of water sorption on TiO2TiO_2 rutile (1 1 0) single crystal face: XPS vs. periodic DFT

XPS and periodic DFT calculations have been used to investigate water sorption on the TiO2 rutile (1 1 0) face. Two sets of XPS spectra were collected on the TiO2 (1 1 0) single crystal clean and previously exposed to water: the first set with photoelectrons collected in a direction parallel to the normal to the surface; and the second set with the sample tilted by 70°, respectively. This tilting procedure promotes the signals from surface species and reveals that the first hydration layer is strongly coordinated to the surface and also that, despite the fact that the spectra were recorded under ultra-high vacuum, water molecules subsist in upper hydration layers. In addition, periodic DFT calculations were performed to investigate the water adsorption process to determine if molecular and/or dissociative adsorption takes place. The first step of the theoretical part was the optimisation of a dry surface model and then the investigation of water adsorption. The calculated molecular water adsorption energies are consistent with previously published experimental data and it appears that even though it is slightly less stable, the dissociative water sorption can also take place. This assumption was considered, in a second step, on a larger surface model where molecular and dissociated water molecules were adsorbed together with different ratio. It was found that, due to hydrogen bonding stabilisation, molecular and dissociated water molecules can coexist on the surface if the ratio of dissociated water molecules is less than ≈33%. These results are consistent with previous experimental works giving a 10–25% range

Characterization of Tbc2, a nucleus-encoded factor specifically required for translation of the chloroplast psbC mRNA in Chlamydomonas reinhardtii

Genetic analysis has revealed that the three nucleus-encoded factors Tbc1, Tbc2, and Tbc3 are involved in the translation of the chloroplast psbC mRNA of the eukaryotic green alga Chlamydomonas reinhardtii. In this study we report the isolation and phenotypic characterization of two new tbc2 mutant alleles and their use for cloning and characterizing the Tbc2 gene by genomic complementation. TBC2 encodes a protein of 1,115 residues containing nine copies of a novel degenerate 38–40 amino acid repeat with a quasiconserved PPPEW motif near its COOH-terminal end. The middle part of the Tbc2 protein displays partial amino acid sequence identity with Crp1, a protein from Zea mays that is implicated in the processing and translation of the chloroplast petA and petD RNAs. The Tbc2 protein is enriched in chloroplast stromal subfractions and is associated with a 400-kD protein complex that appears to play a role in the translation of specifically the psbC mRNA

Smooth stable and unstable manifolds for stochastic partial differential equations

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's method. Then, we prove the smoothness of these invariant manifolds

Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions

This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.Comment: 28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9, Trends in Mathematics, Birkh\"auser Basel, 201