Stein factors for negative binomial approximation in Wasserstein distance

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burden, the Wasserstein metric is the appropriate choice.Comment: Published at http://dx.doi.org/10.3150/14-BEJ595 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Efficient Synthesis of Narrowly Dispersed Brush Polymers via Living Ring-Opening Metathesis Polymerization of Macromonomers

Various macromonomers (MMs) were efficiently synthesized through the copper-catalyzed “click” coupling of a norbornene moiety to the chain end of poly(methylacrylate), poly(t-butylacrylate), and polystyrene that were prepared using atom transfer radical polymerization. Ring-opening metathesis polymerization (ROMP) of these MMs was carried out using the highly active, fast-initiating ruthenium catalyst (H_2IMes)(pyr)_2(Cl)_2RuCHPh in THF at room temperature. ROMP of MMs was found to be living with almost quantitative conversions (>90%) of MMs, producing brush polymers with very low polydispersity indices of 1.01−1.07 and high Mn’s of 200−2600 kDa. The efficient ROMP of such MMs provides facile access to a variety of brush polymers and overcomes previous difficulties in the controlled polymerization of MMs. Atomic force microscopy of the brush polymer products revealed extended, wormlike shapes as a result of significant steric repulsion of densely grafted side chains

Strong ExB shear flows in the pedestal region in H-mode plasma

We report the first experimental observation of stationary zonal flows in the pedestal region of the H-mode plasma in the H-1 toroidal heliac. Strong peaks in E_r shear mark the top and foot of the density pedestal. Strong m=n=0 low-frequency (f < 0.6 kHz) zonal flows are observed in regions of increased E_r, suggesting substantial contribution of zonal flows to the spatial modulation of E_r radial profiles. Radial localization of zonal flows is correlated with a region of zero magnetic shear and low-order (7/5) rational surfaces.Comment: 4 pages, 5 figure

Efficient Synthesis of Narrowly Dispersed Brush Copolymers and Study of Their Assemblies: The Importance of Side Chain Arrangement

Efficient, one-pot preparation of synthetically challenging, high molecular weight (MW), narrowly dispersed brush block copolymers and random copolymers in high conversions was achieved by ring-opening metathesis (co)polymerization (ROMP) of various macromonomers (MMs) using the highly active, fast-initiating ruthenium olefin metathesis catalyst (H_2IMes)(pyr)_2(Cl)_2RuCHPh. A series of random and block copolymers were prepared from a pair of MMs containing polylactide (PLA) and poly(n-butyl acrylate) (PnBA) side chains at similar MWs. Their self-assembly in the melt state was studied by small-angle X-ray scattering (SAXS) and atomic force microscopy (AFM). In brush random copolymers containing approximately equal volume fractions of PLA and PnBA, the side chains segregate into lamellae with domain spacing of 14 nm as measured by SAXS, which was in good agreement with the lamellar thickness measured by AFM. The domain spacings and order−disorder transition temperatures of brush random copolymers were insensitive to the backbone length. In contrast, brush block copolymers containing approximately equal volume fractions of these MMs self-assembled into highly ordered lamellae with domain spacing over 100 nm. Their assemblies suggested that the brush block copolymer backbone adopted an extended conformation in the ordered state

Cyclic Ruthenium-Alkylidene Catalysts for Ring-Expansion Metathesis Polymerization

A series of cyclic Ru-alkylidene catalysts have been prepared and evaluated for their efficiency in ring-expansion metathesis polymerization (REMP). The catalyst structures feature chelating tethers extending from one N-atom of an N-heterocyclic carbene (NHC) ligand to the Ru metal center. The catalyst design is modular in nature, which provided access to Ru complexes having varying tether lengths, as well as electronically different NHC ligands. Structural impacts of the tether length were unveiled through 1H NMR spectroscopy as well as single-crystal X-ray analyses. Catalyst activities were evaluated via polymerization of cyclooctene, and key data are provided regarding propagation rates, intramolecular chain transfer, and catalyst stabilities, three areas necessary for the efficient synthesis of cyclic poly(olefin)s via REMP. From these studies, it was determined that while increasing the tether length of the catalyst leads to enhanced rates of polymerization, shorter tethers were found to facilitate intramolecular chain transfer and release of catalyst from the polymer. Electronic modification of the NHC via backbone saturation was found to enhance polymerization rates to a greater extent than did homologation of the tether. Overall, cyclic Ru complexes bearing 5- or 6-carbon tethers and saturated NHC ligands were found to be readily synthesized, bench-stable, and highly active catalysts for REMP

Development of a hybrid multi-scale simulation approach for spray processes

This paper presents a multi-scale approach coupling a Eulerian interface-tracking method and a Lagrangian particle-tracking method to simulate liquid atomisation processes. This method aims to represent the complete spray atomisation process including the primary break-up process and the secondary break-up process, paving the way for high-fidelity simulations of spray atomisation in the dense spray zone and spray combustion in the dilute spray zone. The Eulerian method is based on the coupled level-set and volume-of-fluid method for interface tracking, which can accurately simulate the primary break-up process. For the coupling approach, the Eulerian method describes only large droplet and ligament structures, while small-scale droplet structures are removed from the resolved Eulerian description and transformed into Lagrangian point-source spherical droplets. The Lagrangian method is thus used to track smaller droplets. In this study, two-dimensional simulations of liquid jet atomisation are performed. We analysed Lagrangian droplet formation and motion using the multi-scale approach. The results indicate that the coupling method successfully achieves multi-scale simulations and accurately models droplet motion after the Eulerian–Lagrangian transition. Finally, the reverse Lagrangian–Eulerian transition is also considered to cope with interactions between Eulerian droplets and Lagrangian droplets.This work was supported by the Engineering and Physical Sciences Research Council of the UK (grant number EP/L000199/1)

Linear Rheological Response of a Series of Densely Branched Brush Polymers

We have examined the linear rheological responses of a series of welldefined, dense, regularly branched brush polymers. These narrow molecular weight distribution brush polymers had polynorobornene backbones with degrees of polymerization (DP) of 200, 400, and 800 and polylactide side chains with molecular weight of 1.4 kDa, 4.4 kDa, and 8.7 kDa. The master curves for these brush polymers were obtained by time temperature superposition (TTS) of the dynamic moduli over the range from the glassy region to the terminal flow region. Similar to other long chain branched polymers, these densely branched brush polymers show a sequence of relaxation. Subsequent to the glassy relaxation, two different relaxation processes can be observed for samples with the high molecular weight (4.4 and 8.7 kDa) side chains, corresponding to the relaxation of the side chains and the brush polymer backbone. Influenced by the large volume fraction of high molecular weight side chains, these brush polymers are unentangled. The lowest plateau observed in the dynamic response is not the rubbery entanglement plateau but is instead associated with the steady state recoverable compliance. Side chain properties affect the rheological responses of these densely branched brush polymers and determine their glassy behaviors

Test of the τ-model of Bose–Einstein correlations and reconstruction of the source function in hadronic Z-boson decay at LEP

Bose–Einstein correlations of pairs of identical charged pions produced in hadronic Z decays are analyzed in terms of various parametrizations. A good description is achieved using a Lévy stable distribution in conjunction with a model where a particle’s momentum is correlated with its space–time point of production, the τ-model. Using this description and the measured rapidity and transverse momentum distributions, the space–time evolution of particle emission in two-jet events is reconstructed. However, the elongation of the particle emission region previously observed is not accommodated in the τ-model, and this is investigated using an ad hoc modification

Charge collective modes in an incommensurately modulated cuprate

We report the first measurement of collective charge modes of insulating Sr14Cu24O41 using inelastic resonant x-ray scattering over the complete Brillouin zone. Our results show that the intense excitation modes at the charge gap edge predominantly originate from the ladder-containing planar substructures. The observed ladder modes (E vs. Q) are found to be dispersive for momentum transfers along the "legs" but nearly localized along the "rungs". Dispersion and peakwidth characteristics are similar to the charge spectrum of 1D Mott insulators, and we show that our results can be understood in the strong coupling limit (U >> t_{ladder}> t_{chain}). The observed behavior is in marked contrast to the charge spectrum seen in most two dimensional cuprates. Quite generally, our results also show that momentum-tunability of inelastic scattering can be used to resolve mode contributions in multi-component incommensurate systems.Comment: 4+ pages, 5 figure