Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers

We prove conjectures of the third author [L. Tevlin, Proc. FPSAC’07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by means of two composition-valued statistics on permutations and packed words, which generalize the combinatorics of Genocchi numbers.      

Three-dimensional opal-like silica foams

The synthesis of novel meso-/macroporous SiO2 monoliths by combining a nano-building-blocks-based approach with the confined geometry of a tailored air-liquid foam structure is described. The resulting macrostructure in which ordered close-packed colloidal silica nanoparticles constitute the monolith's scaffolds very closely resembles the tailored periodic air-liquid foam template. The void spaces between adjacent particles create textural mesoporosity; therefore, the as-prepared silica networks are characterized by hierarchical porosity at the macroscopic and mesoscopic length scales. The fine-tuning of both the liquid foam's fraction and the bubble size allows a rational design over the macroscopic cell morphologies (shape, Plateau border's length, and width). Striking results of this approach are the weak shrinkage of the as-synthesized opal-like scaffolds during the thermally induced sintering process and, in contrast with previous studies, the formation of closed-cell structures. Particle organization and the foam film surface roughness are investigated by atomic force microscopy (AFM), showing the influence of the liquid flow, within the foams' Plateau borders and films, on the final assemblies.     

Structural transitions and melting in LJ(74-78) Lennard-Jones clusters from adaptive exchange Monte Carlo simulations

Phase changes in Lennard-Jones (LJ) clusters containing between 74 and 78 atoms are investigated by means of exchange Monte Carlo simulations in the canonical ensemble. The replica temperatures are self-adapted to facilitate the convergence. Although the 74- and 78-atom clusters have icosahedral global minima, the clusters with 75-77 atoms have decahedral ground-state structures and they undergo a structural transition to icosahedral minima before melting. The structural transitions are characterized by quenching and by looking at the Q4 and Q6 orientational bond order parameters. The transition temperatures are estimated to be 0.114, 0.065, and 0.074 reduced units for LJ75, LJ76, and LJ77, respectively. These values, their ordering and the associated latent heats are compared with other estimates based on the harmonic superposition approach.     

Theoretical study of the hydrated Gd3+ ion: structure, dynamics, and charge transfer

The dynamical processes taking place in the first coordination shells of the gadolinium (III) ion are important for improving the contrast agent efficiency in magnetic-resonance imaging. An extensive study of the gadolinium (III) ion solvated by a water cluster is reported, based on molecular dynamics simulations. The AMOEBA force field [P. Y. Ren and J. W. Ponder, J. Phys. Chem. B 107, 5933 (2003)] that includes many-body polarization effects is used to describe the interactions among water molecules, and is extended here to treat the interactions between them and the gadolinium ion. In this purpose accurate ab initio calculations have been performed on Gd(3+)-H(2)O for extracting the relevant parameters. Structural data of the first two coordination shells and some dynamical properties such as the water exchange rate between the first and second coordination shells are compared to available experimental results. We also investigate the charge transfer processes between the ion and its solvent, using a fluctuating charges model fitted to reproduce electronic structure calculations on [Gd(H(2)O)(n)](3+) complexes, with n ranging from 1 to 8. Charge transfer is seen to be significant (about one electron) and correlated with the instantaneous coordination of the ion.     

Biochemistry of the para-sulfonato-calix[n]arenes

The biochemistry of the para-sulfonato-calix[n]arenes has shown rapid development during the past ten years, the highly diverse biomedical applications of these molecules now include anti-viral, anti-thrombotic activities, enzyme blocking and protein complexation. The future is even more promising as para-sulfonato-calix[n]arenes have, now, been shown to have potential in the diagnosis of prion-based diseases. Their innocuous nature, as far as is known at present, may open up their future use in medications.     

Existence of a Fixed Point of a Nonsmooth Function Arising in Numerical Mechanics

A recent work (Acary et al. 2010) introduces a formulation as a nonsmooth fixed-point problem of a basic problem in numerical mechanics (namely the dynamical Coulomb friction problem in finite dimension with discretized time). Using this new formulation, the existence of a solution to the problem and its numerical resolution are then guaranteed under a strong assumption on the data of this problem. In this paper, we show that the fixed point problem admits solution under a natural, weaker assumption. This existence proof uses a perturbation argument combined with continuity properties of a set-valued mapping associated with the constraints of the problem.     

Inversion of some series of free quasi-symmetric functions

We give a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form where I runs over compositions with parts in a prescribed set C. This proves in particular three special cases (no restriction, even parts, and all parts equal to 2) which were conjectured by B.C.V. Ung in [B.C.V. Ung, Combinatorial identities for series of quasi-symmetric functions, in: Proc. FPSAC’08, Toronto, 2008].