Time Fractional Diffusion: A Discrete Random Walk Approach

The time fractional diffusion equation is obtained from the standarddiffusion equation by replacing the first-order time derivative with afractional derivative of order (0, 1). From a physicalview-point this generalized diffusion equation is obtained from afractional Fick law which describes transport processes with longmemory. The fundamental solution for the Cauchy problem is interpretedas a probability density of a self-similar non-Markovian stochasticprocess related to a phenomenon of slow anomalous diffusion. By adoptinga suitable finite-difference scheme of solution, we generate discretemodels of random walk suitable for simulating random variables whosespatial probability density evolves in time according to this fractionaldiffusion equation.     

Homogenization limit for electrical conduction in biological tissues in the radio-frequency rangeLimite d'homogénéisation pour la conduction électrique dans les tissus biologiques dans le domaine des radiofréquences

We study an evolutive model for electrical conduction in biological tissues, where the conductive intra-cellular and extracellular spaces are separated by insulating cell membranes. The mathematical scheme is an elliptic problem, with dynamical boundary conditions on the cell membranes. The problem is set in a finely mixed periodic medium. We show that the homogenization limit u₀ of the electric potential, obtained as the period of the microscopic structure approaches zero, solves the equation $\text{?}\text{div}\text{(σ}{}_0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+A}{}^0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+∫}{}_0{}^{\mathrm{t}}\text{A}{}^1\text{(t?τ)?}{}_{\mathrm{x}}\text{u}{}_0\text{(x,τ)}\text{d}\text{τ?}\text{F}\text{(x,t))=0}$ where σ₀>0 and the matrices A⁰, A¹ depend on geometric and material properties, while the vector function $\text{F}$ keeps trace of the initial data of the original problem. Memory effects explicitly appear here, making this elliptic equation of non standard type. To cite this article: M. Amar et al., C. R. Mecanique 331 (2003).     

Direct Evidence for a Peroxide Intermediate and a Reactive Enzyme–Substrate–Dioxygen Configuration in a Cofactor‐free Oxidase

Cofactor‐free oxidases and oxygenases promote and control the reactivity of O₂ with limited chemical tools at their disposal. Their mechanism of action is not completely understood and structural information is not available for any of the reaction intermediates. Near‐atomic resolution crystallography supported by in crystallo Raman spectroscopy and QM/MM calculations showed unambiguously that the archetypical cofactor‐free uricase catalyzes uric acid degradation via a C5(S)‐(hydro)peroxide intermediate. Low X‐ray doses break specifically the intermediate C5? OO(H) bond at 100 K, thus releasing O₂ in situ, which is trapped above the substrate radical. The dose‐dependent rate of bond rupture followed by combined crystallographic and Raman analysis indicates that ionizing radiation kick‐starts both peroxide decomposition and its regeneration. Peroxidation can be explained by a mechanism in which the substrate radical recombines with superoxide transiently produced in the active site.     

New biphasic mono-component composite material obtained by partial oxypropylation of bacterial cellulose

The present work evaluates the partial oxypropylation of dried bacterial cellulose (BC) performed by grafting propylene oxide with potassium hydroxide as the catalyst. Samples were characterized by scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray diffraction, differential scanning calorimetry, and thermogravimetric analysis. Partial transformation of BC was observed, with cellulose fibers being covered by the thermoplastic phase, leading to a new biphasic mono-component composite material. This synthesis can be considered a green chemical process, since it does not require the use of solvents nor the application of any processing operation, given the fact that the final product is ready for further exploitation as it is removed from the reactor. The obtained material can be used in various applications in the polymer field, i.e. composites, reinforced rigid polyurethane foams, and others.     

Analytical pyrolysis-based study on intra-skeletal organic matrices from Mediterranean corals

Off-line analytical pyrolysis combined with gas chromatography–mass spectroscopy (GC–MS), directly or after trimethylsilylation, along with infrared spectroscopy and amino acid analysis was applied for the first time to the characterization of the intra-skeletal organic matrix (OM) extracted from four Mediterranean hard corals. They were diverse in growth form and trophic strategy namely Balanophyllia europaea and Leptopsammia pruvoti—solitary corals, only the first having zooxanthelle—and Cladocora caespitosa and Astroides calycularis—colonial corals, only the first with zooxanthelle. Pyrolysis products evolved from OM could be assigned to lipid (e.g. fatty acids, fatty alcohols, monoacylglicerols), protein (e.g. 2,5-diketopiperazines, DKPs) and polysaccharide (e.g. anhydrosugars) precursors. Their quantitative distribution showed for all the species a low protein content with respect to lipids and polysaccharides. A chemometric approach using principal component analysis (PCA) and clustering analysis was applied on OM mean amino acidic compositions. The small compositional diversity across coral species was tentatively related with coral growth form. The presence of N-acetyl glucosamine markers suggested a functional link with other calcified tissues containing chitin. The protein fraction was further investigated using novel DKP markers tentatively identified from analytical pyrolysis of model polar linear dipeptides. Again, no correlation was observed in relation to coral ecology. These analytical results revealed that the bulk structure and composition of OMs among studied corals are similar, as it is the textural organization of the skeleton mineralized units. Therefore, they suggest that coral’s biomineralization is governed by similar macromolecules, and probably mechanisms, independently from their ecology.     

Photochemical synthesis of perfluoropolyether (PFPE) nanocomposites containing PFPE oligomer stabilized magnetite nanoparticles

Magnetite nanoparticles were synthesized and their post-synthesis surface modification was carried out with triethoxy terminated perfluoropolyether (PFPE) oligomers. The surface-treated nanoparticles were then dispersed in a UV-curable difunctional methacrylic PFPE oligomer. Thin films prepared from the resulting stable suspensions were photopolymerized. The obtained nanocomposites showed good distribution of the surface-treated magnetite nanoparticles in the polymer matrix. The surface treatment of magnetite nanoparticles with perfluoropolyether oligomers thus was found to be effective in preventing nanoparticle segregation and aggregation, ensuring therefore an increased compatibility with the PFPE matrix.     

Benchmarking dispersion and geometrical counterpoise corrections for cost‐effective large‐scale DFT calculations of water adsorption on graphene

The physisorption of water on graphene is investigated with the hybrid density functional theory (DFT)‐functional B3LYP combined with empirical corrections, using moderate‐sized basis sets such as 6‐31G(d). This setup allows to model the interaction of water with graphene going beyond the quality of classical or semiclassical simulations, while still keeping the computational costs under control. Good agreement with respect to Coupled Cluster with singles and doubles excitations and perturbative triples (CCSD(T)) results is achieved for the adsorption of a single water molecule in a benchmark with two DFT‐functionals (Perdew/Burke/Ernzerhof (PBE), B3LYP) and Grimme's empirical dispersion and counterpoise corrections. We apply the same setting to graphene supported by epitaxial hexagonal boron nitride (h‐BN), leading to an increased interaction energy. To further demonstrate the achievement of the empirical corrections, we model, entirely from first principles, the electronic properties of graphene and graphene supported by h‐BN covered with different amounts of water (one, 10 water molecules per cell and full coverage). The effect of h‐BN on these properties turns out to be negligibly small, making it a good candidate for a substrate to grow graphene on. © 2014 Wiley Periodicals, Inc.     

Comparison of Different Sorbents in the QuEChERS Method for the Determination of Pesticide Residues in Strawberries by LC–MS/MS

A comparison of sample preparation based on the quick, easy, cheap, effective, rugged and safe (QuEChERS) method for analysis of pesticide residues in strawberries by LC–MS/MS was made using different sorbents in the clean-up by dispersive solid-phase extraction (d-SPE). Some sorbents were laboratory-made, prepared by depositing poly(methyloctadecylsiloxane) (PMODS), poly(methyloctylsiloxane) (PMOS), aminopropyl-terminated poly(dimethylsiloxane) (APPS) and copolymer of (52–48 %)dimethyl-(48–52 %)methylphenyl-siloxane (DMMPS) onto silica supports. The commercial sorbent primary–secondary amine (PSA) and mixtures of two sorbents, primary–secondary amine and poly(methyloctadecylsiloxane), were also used in the experiments. The performances of the sorbents were evaluated by parameters such as color of the final extract, gravimetric measurement, recovery and matrix effect at the fortification level of 100 ng g^?1 of the pesticide mixture in strawberries. The recoveries were in the range 70–120 %, and the RSD values were lower than 20 % for most of the pesticides using the modified QuEChERS method with different sorbents in the clean-up step. The strawberry extracts were cleaned more efficiently with the use of primary–secondary amine sorbent, which has the function of removing sugars, organic acids and especially pigments. The sample preparation method was efficient, and LC–MS/MS determination was optimal because of high selectivity and good detectivity for the multiresidue analyses.     

Stereospecific Couplings of Secondary and Tertiary Boronic Esters

This Minireview highlights advances in the Suzuki–Miyaura cross‐coupling of secondary boron reagents for the creation of C? C bonds with control of stereochemistry. It also includes non‐transition‐metal coupling of secondary and tertiary boronic esters to electron‐rich aromatics.