The Potts model representation and a Robinson–Schensted correspondence for the partition algebra

We construct a correspondence between the set of partitions of a finite set M and the set of pairs of walks to the same vertex on a graph giving the Bratteli diagram of the partition algebra on M. This is the precise analogue of the correspondence between the set of permutations of a finite set and the set of pairs of Young tableaux of the same shape, called the Robinson–Schensted correspondence.     

High temperature NMR approach of mixtures of rare earth and alkali fluorides: An insight into the local structure

In situ high temperature nuclear magnetic resonance in molten fluoride mixtures gives some structural picture of the complexes existing in the melt, i.e. of their nature and relative proportion. Thanks to the development of a laser heating system associated with a close crucible in boron nitride, we can describe experimentally the evolution of these complexes from the anions and the cations point of view. By ¹⁹F NMR, we have shown the existence of three kinds of fluorine atoms depending on the composition: free fluorine like in pure LiF (non-bonded), bridging fluorine in melts rich in LnF₃ in addition with terminal fluorine singly bonded to one rare earth. Data obtained by NMR spectroscopy are also combined with EXAFS measurements, again thanks to a specific development of the sample holder adapted with molten fluorides and high temperature. This study is a part of our systematic investigation of the different Alk-LnF₃ systems by NMR and EXAFS spectroscopy.     

Reflection <Emphasis Type="Italic">k</Emphasis>-matrices related to Temperley-Lieb <Emphasis Type="Italic">R</Emphasis>-matrices

We construct general solutions of the reflection equation associated with Temperley-Lieb R-matrices. We find their parameterization and obtain the Hamiltonians of the corresponding integrable spin systems.     

1H and 19F ultra-fast MAS double-quantum single-quantum NMR correlation experiments using three-spin terms of the dipolar homonuclear Hamiltonian

Measuring internuclear distances through dipolar interaction is a major challenge for solid-state nuclear magnetic resonance (NMR) spectroscopy. Obtaining reliable interatomic distances provides an access to the local structure in ordered or disordered solids. We show that at magic angle spinning (MAS) frequencies larger than ca. 50 kHz, some of the three-spin terms of the homogeneous homonuclear dipolar Hamiltonian can be used to promote the creation of double-quantum coherences between neighbouring (1)H or (19)F spins without using dipolar recoupling pulse sequences in the Dipolar Homonuclear Homogeneous Hamiltonian (DH(3)) double-quantum/single-quantum correlation experiment. This makes it possible to probe inter-nuclear spatial proximity with limited risk of probe or sample damage from radio-frequency (RF) irradiation, and is fully appropriate for fast repetition rate offering sensitivity gains in favourable cases. Experimental demonstrations are supported by multi-spin numerical simulations, which points to new possibilities for the characterization of spin-system geometries.     

Discrete symmetry groups of vertex models in statistical mechanics

We analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations. They can be seen as generated by involutions corresponding respectively to two kinds of transformations onq×q matrices: the inversion of theq×q matrix and an (involutive) permutation of the entries of the matrix. We show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics. This approach enables one to analyze two-dimensionalq ⁴-state vertex models as simply as three-dimensional vertex models, or higher-dimensional vertex models. Various examples of birational symmetries of vertex models are analyzed. A particular emphasis is devoted to a three-dimensional vertex model, the 64-state cubic vertex model, which exhibits a polynomial growth of the complexity of the calculations. A subcase of this general model is seen to yield integrable recursion relations. We also concentrate on a specific two-dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes Yang-Baxter integrable. It is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces, or higher-dimensional algebraic varieties.     

Monte Carlo simulation of mini TEPC microdosimetric spectra: Influence of low energy electrons

In the past few years, miniaturized tissue-equivalent gas detectors (mini TEPCs) have been developed for application of microdosimetry in radiotherapy. These mini-TEPCs are characterised by millimetric dimensions. They are equipped neither with an internal calibration source nor with electric field tubes, which would properly define the sensitive volume hence the simulated site size. In spite of these lacks, mini TEPCs working in gas flow conditions have proven to be precise and reliable detectors. However, for future therapeutic plans including microdosimetric data, consistency between experimental and calculated data is important. Existing general-purpose Monte Carlo codes have proven to be very useful to calculate the energy deposition due to ionization in macroscopic targets, even in various complex radiation fields. However, theoretical models implemented in these codes for simulating electron transport and straggling are valid only for energies above a few keV. This restricts their applicability for simulating radiation transport at a micrometric level, where low-energy electrons play a dominant role. In this work, we calculate frequency distributions of deposited energy in a mini TEPC (with sizes equivalent to 1 and 2 μm) due to photons using the Monte Carlo code FLUKA. Comparisons between simulated and experimental data show a rather good agreement. Differences due to different FLUKA settings are discussed.     

Elaboration of densely functionalized polylactide nanoparticles from N‐acryloxysuccinimide‐based block copolymers

Poly(N‐acryloxysuccinimide) (PNAS) and poly(N‐acryloxysuccinimide‐co‐N‐vinylpyrrolidone) (P(NAS‐co‐NVP)) of adjustable molecular weights and narrow polydispersities were prepared by nitroxide‐mediated polymerization (NMP) in N,N‐dimethylformamide in the presence of free SG1 (N‐tert‐butyl‐N‐1‐diethylphosphono‐(2,2‐dimethylpropyl) nitroxide), with MAMA‐SG1 (N‐(2‐methylpropyl)‐N‐(1‐diethylphosphono‐2,2‐dimethylpropyl)‐O‐(2‐carboxylprop‐2‐yl)hydroxylamine) alkoxyamine as initiator. The reactivity ratios of NAS and NVP were determined to be r_NAS = 0.12 and r_NVP = 0, indicating a strong alternating tendency for the P(NAS‐co‐NVP) copolymer. NAS/NVP copolymerization was then performed from a SG1‐functionalized poly(D ,L ‐lactide) (PLA‐SG1) macro‐alkoxyamine as initiator, leading to the corresponding PLA‐b‐P(NAS‐co‐NVP) block copolymer, with similar NAS and NVP reactivity ratios as mentioned above. The copolymer was used as a surface modifier for the PLA diafiltration and nanoprecipitation processes to achieve nanoparticles in the range of 450 and 150 nm, respectively. The presence of the functional/hydrophilic P(NAS‐co‐NVP) block, and particularly the N‐succinimidyl (NS) ester moieties at the particle surface, was evidenced by ethanolamine derivatization and zeta potential measurements. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Polymerization Initiated by Organic Electron Donors

Polymerization reactions with organic electron donors (OED) as initiators are presented herein. The metal‐free polymerization of various activated alkene and cyclic ester monomers was performed in short reaction times, under mild conditions, with small amounts of organic reducing agents, and without the need for co‐initiators or activation by photochemical, electrochemical, or other methods. Hence, OED initiators enabled the development of an efficient, rapid, room‐temperature process that meets the technical standards expected for industrial processes, such as energy savings, cost‐effectiveness and safety. Mechanistic investigations support an electron‐transfer initiation pathway that leads to the reduction of the monomer.     

Study of the casting of sulfonated polyimide ionomer membranes: structural evolution and influence on transport properties

A casting process has been studied for charged polymers: the sulfonated polyimide ionomer membrane. The formation of the membrane has been followed by X-ray reflectivity as a function of temperature. The effect of equivalent weight has been also investigated. The thickness loss presents two regimes: the first one is linear vs time indicating that the models developed for noncharged polymer may be suitable for ionomers in the early period of drying. The second one corresponds to the loss of X-ray reflectivity signal. Moreover, the X-ray reflectivity signal seems to be correlated to the characteristic time of the sample drying. In complement, we have studied the influence of casting on the properties of the dried ionomer membranes. The transport coefficients of N(CH(3))(4)(+) ions confined in two kinds of membranes that were differently cast were measured. The results show that shearing the ionomer solution during casting may lead to an enhancement of the anisotropy of structure and of transport. Moreover, we have studied the effect of both interfaces on the ion transport properties through the dried membranes.