Représentation de Feynman–Kac dans des domaines temps–espace et sensibilité par rapport au domaine

We consider the solution X=(X_t)_t?0 of a time-inhomogeneous stochastic differential equation and the exit time τ by (t,X_t)_t?0 of the time–space domain $\text{D}$. We prove the differentiability of expectations of functionals of X stopped at τ, with respect to the domain $\text{D}$: these results extend those in the literature, known in particular by the analysts for the issues of shape optimization. However from the probabilistic point of view, this is not standard. To cite this article: C. Costantini et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Microcanonical and canonical distributions and finite exchangeable random processes

A pure probabilistic approach to Gibbs' distributions is given, starting from the notion of finite exchangeable random process. The differences between bosons, fermions, and classical particles are ascribed to different values of correlation. The relationship between exchangeability and constraints on the energy distribution is investigated.     

The lattice automorphisms of simple algebraic groups over\bar F_2

We prove that if u is a unipotent element of a connected reductive algebraic group G over , there exists an involution σ in G such that σuσ=u⁻¹. We use this result to determine the group of lattice automorphisms of G, when G is simple.     

Polymer-surfactant and protein-surfactant interactions

The phase behavior and some physicochemical properties of homopolymers (HP) and hydrophobically modified (HMP) polymers, as well as of polyelectrolytes (PE) and proteins (PR), in the presence of aqueous surfactants, or their mixtures, are discussed. Mixing the above components gives rise to the formation of organized phases, whose properties are controlled by polymer and/or surfactant content, temperature, pH, and ionic strength. Depending on the nature, concentration, and net charge of both solutes, molecular solutions, polymer-surfactant complexes, adsorption onto micelles and vesicles, gels, liquid crystalline phases, and precipitates are observed. Such rich polymorphic behavior is the result of a complex balance between electrostatic, excluded volume, van der Waals, and other contributions to overall system stability. It is also modulated by the molecular details and architecture of both the polymer and the surfactant. Different experimental methods allow investigation of the above systems and getting information on the nature of polymer-surfactant interactions (PSI). Surface adsorption and thermodynamic methods, together with investigation of the phase diagrams, give information on the forces controlling PSI and on the existence of different phases. Conductivity, QELS and viscosity allow estimating the size and shape of polymer-surfactant (protein-surfactant) complexes. Optical microscopy, cryo-TEM, AFM, NMR, fluorescence, and relaxation methods give more information on the above systems. Use of the above mixtures in controlling gelation, surface covering, preparing dielectric layers, and drug release is suggested.     

Supramolecular association of a triblock copolymer in water

Solutions of a poly(oxyethylene)-poly(oxypropylene)-poly(oxyethylene) triblock copolymer, Pluronic F(68), were investigated in isothermal and isopleth mode. Surface tension, sigma, dynamic shear viscosity, n(omega), QELS experiments, and volumetric, colligative, and refractive index measurements characterize the system behavior in a wide range of compositions and temperatures. The thermodynamic properties associated with micelle formation, above the critical micellar temperature, were determined by different experimental methods. The large entropic contributions to the system stability are ascribed to significant dehydration of the oxypropylene portion in the copolymer, consequent to micelle formation. Temperature has a pronounced effect on the association features of F(68). It gives rise to abrupt changes in QELS and rheological properties when the critical micellar temperature is approached. Such effects are explained in terms of thermally driven micellization processes and interconnection between micelles.     

Removal of organic pollutants from water via molecular inclusion within a cavitand

The molecular inclusion chemistry of cavitands provides a useful way for the removal of organic pollutants from water. A wide range of lipophilic organic compounds, present at trace level in water, are efficiently extracted by cavitand1, which can be easily reactivated and reused.     

Easy hydrolysis of white phosphorus coordinated to ruthenium

The P4 molecule bound to ruthenium as an eta1-ligand in [CpRu(PPh3)2(eta1-P4)]Y (Y = PF6, CF3SO3) undergoes an easy reaction with water in exceedingly mild conditions to yield PH3, which remains coordinated to the [CpRu(PPh3)2] fragment, and oxygenated derivatives.     

Quantum calculation of the intrinsic torsional barrier of C-C and C-O bonds

PCILO and ab initio calculations have been performed to investigate the energies associated to rotation about the central bond in n-butane and methyl ethyl ether. Quantum mechanical energies have been fit to a classical intramolecular force field, containing torsional and nonbonded (Lennard-Jones 6–12 plus Coulomb) contributions, with a standard deviation comprised between 0.03 and 0.09 kcal mol^–1. Two conditions have proved indispensable to reach such level of accuracy: (a) the use of a torsional potential with threefold periodicity, which corrects for the part of the rotation barrier not covered by van der Waals repulsions and may be interpreted as bond-bond repulsion; (b) the introduction in the force field for ethers of terms accounting for orbital interaction effects of different nature than the normal molecular mechanics nonbonded interactions; these terms are represented either by low order rotational potential functions or preferably by interactions of atoms simulating lone-pair orbitals and bonded to oxygen in such a way as to render it sp ³-hybridized. According to ab initio, the height of the threefold torsional potential about C-C and C-O bonds is comparable and is of the order of 3 kcal mol^–1. According to PCILO, it is larger for C-C (ca. 1.5 kcal mol^–1) than for C-O (ca. 0.5 kcal mol^–1).     

Thermal transitions in associating aqueous block copolymers: light scattering,rheology and spectroscopy

Solutions containing a polyoxy-ethylene/polyoxy-propylene/polyoxy-ethylene (PEO–PPO–PEO) block copolymer, indicated as F68, in water were investigated as a function of composition and temperature. Hydrogen nuclear magnetic resonance (¹H NMR) line width, chemical shift, self-diffusion, spin-lattice relaxation times, laser light scattering and rheological methods were used. The monomer–micelle equilibrium and the micelle–liquid crystalline phase transitions depend on the F68 content in the mixture and temperature. Significant changes in light scattering intensity and apparent hydrodynamic radius are associated to micelle formation above the critical micellar temperature (CMT). According to a Contin analysis, this behaviour is reflected in the presence of two populations in the intensity–intensity autocorrelation functions. The contributions due to molecules and micelles can be evaluated separately. No such effects are observed below the CMT. Micelle onset is also associated to variations in ¹H NMR spectra, affecting the chemical shift, line width and spin-lattice relaxation time of the PPO methyl protons and self-diffusion, as well. Spin-lattice relaxation times of PEO chains, conversely, change significantly at temperatures close to the micelle–liquid crystalline thermal transition. Similar results were obtained from the line width of ²H NMR spectra as a function of T. Significant changes in both viscous and elastic modulus were also observed and ascribed to PPO dehydration, at the CMT, as well as to squeezing and dehydration of PEO units in liquid crystal formation, respectively.