On the N-exciton normalization factor

The N-ground-state-exciton normalization factor, namely 〈v| B ₀ ^N B ₀ ^dagN| v〉 = N!F _N, with B ₀ ^d ag the exact ground state exciton creation operator, differs from N! because the excitons are not perfect bosons. The quantity F_N turns out to be crucial for problems dealing with interacting excitons. Indeed, the excitons feel each other not only through the Coulomb interaction but also through Pauli exclusion between their components. A quite novel purely Pauli contribution exists in their many-body effects, which relies directly on F_N. Following procedures used in the commutation technique we recently introduced to treat interacting close-to-bosons, and in the BCS theory of superconductivity, we rederive important relations verified by the F_N's. We also give new explicit expressions of F_N valid for η = Na _x ³/ small but N ² a _x ³/ large, as F_N does not read in terms of η but Nη, the exciton number N being possibly huge in macroscopic samples. Due to this superextensivity, F_N does not appear alone in physical quantities, but through ratios like F _{N + p}/F _N. We end this work by giving the η expansion of these ratios, useful for all purely Pauli many-body effects. Received 30 May 2002 / Received in final form 12 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Poly(trialkylsilyl methacrylate)s: A family of hydrolysable polymers with tuneable erosion profiles

Polymers containing hydrolytically labile trialkylsilyl ester side groups were synthesised via a conventional and a controlled radical polymerization. The trialkylsilyl methacrylate monomer unit was chosen for its capacity to hydrolyse into basic, acid or sea water varying the hydrophilic character of the resulting polymer backbone with time. The hydrolysis or saponification reaction of the ester bond of the trialkylsilyl methacrylate was monitored through a ¹H NMR study showing the formation of siloxane side-products. Several copolymers and polymer blends were prepared as matrixes for controlled erodible systems. Their capacity to hydrolyse was demonstrated through SEM investigations with selective dissolution of free films containing hydrolysable copolymers and PMMA blends. Well-defined random and diblock copolymers with methyl methacrylate were investigated to show the effect of the microstructure on the erosion properties of the corresponding coatings. Poly(methyl methacrylate-b-tert-butyldimethylsilyl methacrylate) diblock copolymers synthesised through the RAFT process showed a better control of the erosion with a constant erosion rate over a long-time service in sea water at pH = 8.2. In addition, experiments showed that the erosion rate could be modulated by varying the molar proportion of hydrolysable side groups onto the copolymer backbone and the weight amount of copolymers mixed with PMMA in toluene solution.     

A study of two-dimensional dispersion in unconsolidated porous media

An experimental and numerical investigation into the magnitude of longitudinal and transverse dispersion in a two-dimensional flow field over a particle Peclet number range of 50–8500 is reported. Numerical modelling using a Galerkin finite element method is used to test various models, notably those of Fried and combarnous and Koch and Brady. Dispersion at low Peclet numbers (< 200) is found to be described adequately by either model, which at large Peclet, the degree of dispersion is significantly underestimated. An improved dispersion model for Peclet numbers greater than 200 is proposed. The transverse dispersion term and the choice of inlet boundary condition are found to have a negligible effect on the shape of the breakthrough curve.Nomenclature A (z) Polynomial in the z plane - B (z) Polynomial in the z plane - C Concentration - C _f Feed concentration - C _o Concentration at the entrance - D Dispersion tensor - D _f Molecular diffusion coefficient - D ₁ Longitudinal dispersion coefficient - D _p Particle diameter - D _t Transverse dispersion coefficient - k Permeability/viscosity - k Dimensionless permiability in the Koch and Brady model - P Pressure - Pe _k Modified Peclet number, Pe _p k - Pe _p Particle Peclet number vD _p /D _f - v Velocity - z Axial coordinate or complex variable Greek letters Solution domain - Boundary - Porosity     

Poly(D,L-lactide)-block-poly(2-hydroxyethyl acrylate) block copolymers as potential biomaterials for peripheral nerve repair: in vitro and in vivo degradation studies

The properties of poly(D ,L ‐lactide)‐block‐poly(2‐hydroxyethyl acrylate) (PLA‐b‐PHEA) block copolymers by means of in vitro / in vivo (rat) degradation are investigated and compared to those of PLA homopolymer. Over 12 weeks, we observe mass loss and molecular weight decrease. In vitro and in vivo findings are very similar for each polymer tested. When a short PHEA block is used (PLA‐b‐PHEA 15 000–3 000 g · mol^?1, 85/15 wt%), the degradation process is found to be very similar to that of homo‐PLA, and to be typical of a bulk erosion mechanism, with no mass loss observed until week 7 and continuous decrease of molar mass within this timeframe. For a longer PHEA block length within the block copolymer (PLA‐b‐PHEA 15 000–7 500 g · mol^?1, 65/35 wt%), the degradation mechanism is modified, with a significant mass loss observed at early times and only a slight decrease in molar mass. The latter finding is related to the pronounced hydrophilicity and softness of the material induced by the PHEA block, which allow easy diffusion and rapid leakage of the degradation residues from the material towards the aqueous medium. Schwann cells are found to better adhere on spin‐coated films of PLA‐b‐PHEA (85/15 wt%) than on PLA ones. These results show the potential of such hydrophilized PLA‐based copolymers for use in peripheral nerve repair.

     

Électrochimie dans les mélanges NaF+AlF3 fondus

Results obtained by electrochemistry in molten cryolite and sodium tetrafluoroaluminate are related to the following points: self-dissociation constant of the melts, classification of fluoride-ion donors/acceptors, electrooxidation of so-called “dissolved” aluminium, anode effect, redox behaviour of phosphorous (V), boron (III+), and some metals, titration of alumina by CrF₃.     

Influence of the electron-hole density profile on the reflectivity of laser irradiated silicon

We study the influence of the spatial extension of the electron-hole plasma created by a pump pulse on the reflectivity of a probe pulse. We show that the density deduced from reflectivity measurements is the surface density value with a very good accuracy, except very close to the plasma resonance. We also show that the resonance broadening due to the spatial inhomogeneity can be larger than the one due to free carriers absorption and has to be included in the usual experimental determination of the plasma relaxation time.     

Iron pentacarbonyl mediated coupling of benzyl halides to ketones under mild phase transfer conditions.

In a two-phase system (saturated aqueous calcium hydroxide, tetrabutylamnonium sulfate, dichloromethane, iron pentacarbonyl) benzyl bromides are readily carbonylated to dibenzyl ketones; α-α′ dibromoorthoxylene yields the o-quinodimethane iron tricarbonyl complex 8. It is inferred that the reactions proceed through transient generation of the tetracarbonyl ferrate dianion.     

Lipschitz continuity of state functions in some optimal shaping

We prove local Lipschitz continuity of the solution to the state equation in two kinds of shape optimization problems with constraint on the volume: the minimal shaping for the Dirichlet energy, with no sign condition on the state function, and the minimal shaping for the first eigenvalue of the Laplacian. This is a main first step for proving regularity of the optimal shapes themselves.Received: 11 November 2003, Accepted: 10 May 2004, Published online: 8 February 2005Mathematics Subject Classification (2000): 49Q10, 35R35, 49K20, 35J20