When is the Bloch–Okounkov q-bracket modular?

The Ramanujan Journal - We obtain a condition describing when the quasimodular forms given by the Bloch–Okounkov theorem as q-brackets of certain functions on partitions are actually modular....     

High pressure synthesis of late rare earth RFeAs(O,F) superconductors; R = Tb and Dy

New TbFeAs(O,F) and DyFeAs(O,F) superconductors with critical temperatures T(c) = 46 and 45 K and very high critical fields, >/=100 T, have been prepared at 1100-1150 degrees C and 10-12 GPa, demonstrating that high pressure may be used to synthesise late rare earth derivatives of the recently reported RFeAs(O,F) (R = La-Nd, Sm, Gd) high temperature superconductors.     

A Complete Multiscale Modelling Approach for Polymer–Clay Nanocomposites

We present an innovative, multiscale computational approach to probe the behaviour of polymer–clay nanocomposites (PCNs). Our modeling recipe is based on 1) quantum/force‐field‐based atomistic simulation to derive interaction energies among all system components; 2) mapping of these values onto mesoscopic bead–field (MBF) hybrid‐method parameters; 3) mesoscopic simulations to determine system density distributions and morphologies (i.e., intercalated versus exfoliated); and 4) simulations at finite‐element levels to calculate the relative macroscopic properties. The entire computational procedure has been applied to two well‐known PCN systems, namely Nylon 6/Cloisite 20A and Nylon 6/Cloisite 30B, as test materials, and their mechanical properties were predicted in excellent agreement with the available experimental data. Importantly, our methodology is a truly bottom‐up approach, and no “learning from experiment” was needed in any step of the entire procedure.     

Reactivity of Primary Phosphines and Primary Phosphine Sulfides towards Imines

Reactivity of primary phosphines with two stoichiometric equivalents of imine results in the formation of bis-α-aminophosphines ( 2 a – e ), which can be subsequently oxidized in the presence of S₈ or H₂O₂ to generate air stable bis-α-aminophosphine sulfides ( 2 b – m(S/O) ). To elucidate the mechanism of this three-component reaction, Hammett analysis, kinetic isotope effect (KIE), and trapping experiments were performed. Ultimately a P(V)–P(III) tautomerization is invoked, followed by nucleophilic attack by the P(III) species to generate the desired products.     

Nature's microfluidic transporter: rotational cytoplasmic streaming at high Péclet numbers

Cytoplasmic streaming circulates the contents of large eukaryotic cells, often with complex flow geometries. A largely unanswered question is the significance of these flows for molecular transport and mixing. Motivated by "rotational streaming" in Characean algae, we solve the advection-diffusion dynamics of flow in a cylinder with bidirectional helical forcing at the wall. A circulatory flow transverse to the cylinder's long axis, akin to Dean vortices at finite Reynolds numbers, arises from the chiral geometry. Strongly enhanced lateral transport and longitudinal homogenization occur if the transverse Péclet number is sufficiently large, with scaling laws arising from boundary layers.     

Characterisation of leather candidate certified reference materials for their mass fractions of aromatic amines

Three batches of leather samples were coloured with nine azo dyes that can yield eight proven or suspected carcinogenic aromatic amines under reduction conditions. The samples were milled to grains and bottled in jars. A group of five laboratories has established the mass fraction of the amines in a ring test using different analytical methods. The methods included a reduction step in order to cleave the azo dyes into the aromatic amines. Quantification was by standard addition: sub-samples of the leathers were spiked with known amounts of azo dyes of known purity. It was possible to establish the mass fractions of six of the eight aromatic amines in three of the leather samples.     

Ellipsometry studies of nonionic surfactant adsorption at the oil--water interface

In the presented study we have developed and implemented a methodology for ellipsometry measurements at liquid interfaces that makes it possible to determine the amount adsorbed without assumptions of refractive index or thickness of the adsorbed layer. It was demonstrated that this is possible by combined measurements from different aqueous phases, H(2)O and D(2)O, which were shown to have sufficiently different refractive indices. The methodology was tested by studying adsorption of two types of nonionic poly(ethylene glycol) alkyl ether surfactants, C(n)H(2)(n)(+1)(OC(2)H(4))(m)OH or C(n)E(m) at the decane--aqueous interface, where C(12)E(5) was adsorbed from the oil phase and C(18)E(50) from the aqueous phase. The observed plateau values of the adsorbed amounts were 1.38 and 0.93 mg/m(2) for C(12)E(5) and C(18)E(50), respectively, which is in agreement with the corresponding values of 1.49 and 1.15 mg/m(2) obtained from applying the Gibbs equation to interfacial tension data for the same systems. We will briefly discuss the adsorption behavior in relation to the molecular structure of the surfactant and the phase behavior of the oil--surfactant--aqueous systems in relation to our experimental results.     

Flow-induced crystallization of propylene/ethylene random copolymers

The influence of the co-monomer content and processing conditions on the crystallization kinetics of propylene/ethylene (P/E) random copolymers is studied using DSC and rheometry. The presence of ethylene lowers the melting and crystallization temperature compared to pure polypropylene, and the quiescent crystallization rate, [(X)\dot], \dot{X}, increases at equal nominal undercooling, because both the crystal growth rate, G, and number of nuclei, N, increases. The effect of flow on the kinetics of crystallization decreases with the ethylene content. Still, different regimes of flow-induced crystallization are observed, but their size and the position of the transitions between them depend on the ethylene content, and can be expressed in terms of the level of molecular orientation, molecular stretch, and crystallization capacity of the system.