Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)⁵ for the one-particle Green function in arbitrary dimension. The spectral weight is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented. Received 25 October 1999     

Patterning of polystyrene by scanning electrochemical microscopy. Biological applications to cell adhesion

Polystyrene surfaces may be patterned by Ag(II), NO(3)(?), and OH(?) electrogenerated at the tip of a scanning electrochemical microscope. These electrogenerated reagents lead to local surface oxidation of the polymer. The most efficient surface treatment is obtained with Ag(II). The patterns are evidenced by XPS and IR and also by the surface wettability contrast between the hydrophobic virgin surface and the hydrophilic pattern. Such Ag(II) treatment of a polystyrene Petri dish generates discriminative surfaces able to promote or disfavor the adhesion of proteins and also the adhesion and growth of adherent cells. The process is also successfully applied to a cyclo-olefin copolymer and should be suitable to pattern any hydrogenated polymer.     

Analyses of the factors for the demagnetization of permanent magnets caused by high‐energy electron irradiation

Demagnetization owing to high‐energy electron irradiation has been analyzed for permanent magnets used in insertion devices of synchrotron radiation sources, using the Monte Carlo code FLUKA. The experimental data of a thermally treated Nd₂Fe₁₄B permanent magnet with a copper or a tantalum block at electron energies ranging from 2 to 8 GeV were compared with the calculation data of the absorbed doses, photoneutron production distributions and star densities. The results indicate that low‐energy photoneutrons and bremsstrahlung photons are not involved in the demagnetization process, and suggest that the star density owing to the photoneutrons is strongly correlated with the demagnetization process.     

Neutron correlations in 6He viewed through nuclear break-up

The nuclear break-up of ⁶He on a ²⁰⁸Pb target was studied at 20A MeV using a secondary beam of ⁶He produced by the SPIRAL facility at GANIL. $ \alpha$ -particles were detected in coincidence with two neutrons with a large angular coverage and the reaction mechanism was identified. From the distribution of the relative angles between the two neutrons the correlation function was extracted. It shows a strong correlation at small relative angles attributed to the contribution of the di-neutron configuration of ⁶He .     

Descentwise inexact proximal algorithms for smooth optimization

The proximal method is a standard regularization approach in optimization. Practical implementations of this algorithm require (i)?an algorithm to compute the proximal point, (ii)?a rule to stop this algorithm, (iii)?an update formula for the proximal parameter. In this work we focus on?(ii), when smoothness is present??so that Newton-like methods can be used for?(i): we aim at giving adequate stopping rules to reach overall efficiency of the method. Roughly speaking, usual rules consist in stopping inner iterations when the current iterate is close to the proximal point. By contrast, we use the standard paradigm of numerical optimization: the basis for our stopping test is a ??sufficient?? decrease of the objective function, namely a fraction of the ideal decrease. We establish convergence of the algorithm thus obtained and we illustrate it on some ill-conditioned problems. The experiments show that combining the proposed inexact proximal scheme with a standard smooth optimization algorithm improves the numerical behaviour of the latter for those ill-conditioned problems.     

Synergistic extraction of europium and americium into nitrobenzene by using hydrogen dicarbollylcobaltate and 1,3-bis(diphenylphosphino)propane dioxide

Extraction of microamounts of europium and americium by a nitrobenzene solution of hydrogen dicarbollylcobaltate (H⁺B^?) in the presence of 1,3-bis(diphenylphosphino)propane dioxide (DPPPrDO, L) has been investigated. The equilibrium data have been explained assuming that the species $ {\text{HL}}^{ + } ,\,{\text{HL}}_{2}^{ + } ,\,{\text{ML}}^{3 + } \,{\text{and}}\,{\text{ML}}_{3}^{3 + } $ HL + , HL 2 + , ML 3 + and ML 3 3 + (M³⁺ = Eu³⁺, Am³⁺) are extracted into the organic phase. The values of extraction and stability constants of the complex species in nitrobenzene saturated with water have been determined. It was found that the stability constants of the corresponding complexes $ {\text{EuL}}_{n}^{ 3+ } \,{\text{and}}\,{\text{AmL}}_{n}^{ 3+ } , $ EuL n 3 + and AmL n 3 + , where n = 1, 3 and L is DPPPrDO, in water-saturated nitrobenzene are comparable.     

Sulfonic and Phosphonic Acid and Bifunctional Organic–Inorganic Hybrid Membranes and Their Proton Conduction Properties

Hybrid organic–inorganic approaches are used for the synthesis of bifunctional proton exchange membrane fuel cell (PEMFC) membranes owing to their ability to combine the properties of a functionalized inorganic network and an organic thermostable polymer. We report the synthesis of both sulfonic and phosphonic acid functionalized mesostructured silica networks into a poly(vinylidenefluoride‐co‐hexafluoropropylene) (poly(VDF‐co‐HFP) copolymer. These membranes, containing different amounts of phosphonic acid and sulfonic acid groups, have been characterized using FTIR and NMR spectroscopy, SA‐XRD, SAXS, and electrochemical techniques. The proton conductivity of the bifunctional hybrid membranes depends strongly on hydration, increasing by two orders of magnitude over the relative humidity (RH) range of 20 to 100 %, up to a maximum of 0.031 S cm⁻¹ at 60 °C and 100 % RH. This value is interesting as only half of the membrane conducts protons. This approach allows the synthesis of a porous SiO₂ network with two different functions, having  SO₃H and  PO₃H₂ embedded in a thermostable polymer matrix.     

Spin relaxation and band excitation of a dipolar Bose-Einstein condensate in 2D optical lattices

We observe interband transitions mediated by dipole-dipole interactions for an array of 1D quantum gases of chromium atoms, trapped in a 2D optical lattice. Interband transitions occur when dipolar relaxation releases an energy larger than the lattice band gap. For symmetric lattice sites, and a magnetic field parallel to the lattice axis, we compare the measured dipolar relaxation rate with a Fermi golden rule calculation. Below a magnetic field threshold, we obtain an almost complete suppression of dipolar relaxation, leading to metastable 1D gases in the highest Zeeman state.     

Water and biomolecules: an introduction

As an introduction to the eighth session ‘Water and Biosystems’ of the XVth ‘Horizon in Hydrogen Bond Research’, water molecules are presented with the stress on some elusive points which justify the existence of a session devoted to this topics. Thus, despite its familiar character, H₂O is a molecule which remains still poorly known, especially when it is part of large orderless systems such as liquid water or macromolecules. It is then difficult to observe it. It has consequently for long been ignored despite the fundamental role it may play, in biosystems for instance. The central importance it has in the reactivity of aqueous sytems is evocated, with a particular emphasis on the difference between proton transfers, which are encountered in the chemistry of acid/base in water, and H atoms transfers in cyclic hydrogen bonded structures by tautomerism. Arguments are given which suggest that this latter mechanism is the basic mechanism in bioreactivity and that it is the presence of water molecules that makes it efficient. In the final part the different lectures delivered during this session are presented in the line of this viewpoint.