Renormalon Singularities of the QCD Vacuum Polarization Function to Leading Order in 1/Nf1/N_{f}

We explicitly determine the residues and orders of all the ultra-violet (UV) and infra-red (IR) renormalon poles in the Borel plane for the QCD vacuum polarization function (Adler D-function), to leading order in an expansion in the number of quark flavours, $N_{f}$. The singularity structure is precisely as anticipated on general grounds. In particular, the leading IR renormalon is absent, in agreement with operator product expansion ideas. There is a curious and unexplained symmetry between the third and higher UV and IR renormalon residues. We are able to sum up separately UV and IR contributions to obtain closed form results involving $\zeta$-functions. We argue that the leading UV renormalon should have a more complicated structure than conventionally assumed. The disappearance of IR renormalons in flavour-saturated SU($N$) QCD is shown to occur for $N=3,6$ or 9.Comment: 22 pages of LaTeX, revisions to this paper are mainly typographica

Effect of core cross-linking on the physical properties of poly(dimethylsiloxane)-based diblock copolymer worms prepared in silicone oil

A trithiocarbonate-capped poly(dimethylsiloxane) (PDMS) precursor is chain-extended via reversible addition–fragmentation chain transfer dispersion polymerization of 2-(dimethylamino)ethyl methacrylate (DMA) in decamethylcyclopentasiloxane (D5) silicone oil at 90 °C. For a fixed mean degree of polymerization (DP) of 66 for the PDMS steric stabilizer block, targeting core-forming PDMA block DPs of between 105 and 190 enables the preparation of either well-defined worms or vesicles at a copolymer concentration of 25% w/w. The as-synthesized linear PDMS66–PDMA100 worms exhibit thermoresponsive behavior in D5, undergoing a worm-to-sphere transition on heating to 100 °C. Variable temperature 1H NMR spectroscopy indicates that this thermal transition is driven by reversible solvent plasticization of the PDMA cores. This change in copolymer morphology is characterized by transmission electron microscopy (TEM) studies, variable temperature dynamic light scattering and small-angle X-ray scattering experiments. Oscillatory rheology studies indicate that degelation occurs at 32 °C, but shear-induced polarized light imaging measurements suggest that full conversion of worms into spheres requires significantly higher temperatures (∼110 °C). 1,2-Bis(2-iodoethoxy)ethane (BIEE) is evaluated as a cross-linker for PDMS66–PDMAx diblock copolymer nano-objects in D5. This bifunctional reagent quaternizes the tertiary amine groups on the DMA residues within the worm cores, introducing cross-links via the Menshutkin reaction. TEM studies confirm that such covalently-stabilized worms no longer undergo a worm-to-sphere transition when heated to 100 °C. Kinetic studies performed on PDMS66–PDMA176 vesicles suggest that cross-linking requires approximately 13 h at 20 °C to ensure that these nano-objects remain intact when dispersed in chloroform, which is a good solvent for both blocks. Oscillatory rheology studies of a PDMS66–PDMA100 worm gel indicated that covalent stabilization using a BIEE/DMA molar ratio of 0.15 increased its dynamic elastic modulus (G′) by almost two orders of magnitude. Furthermore, such cross-linked worms exhibit a much lower critical gelation concentration (∼2% w/w) compared to that of the linear precursor worms (∼12% w/w)

Assessing the accuracy of industrial robots through metrology for the enhancement of automated non-destructive testing

This work presents the study of the accuracy of an industrial robot KR5 arc HW, used to perform quality inspections of components with complex shapes. Metrology techniques such as laser tracking and large volume photogrammetry were deployed to quantify both pose and dynamic path accuracies of the robot in accordance with ISO 9283:1998. The overall positioning pose inaccuracy of the robot is found to be almost 1 mm and path inaccuracy at 100% of the robot rated velocity is 4.5 mm. The maximum pose orientation inaccuracy is found to be 14 degrees and the maximum path orientation inaccuracy is 5 degrees. Despite of the significant maximum inaccuracies, uncertainty of a robotic scanning application is estimated to be 0.5mm. Local positional errors manifest pronounced dependence on the position of the robot end effector in the working envelope. The uncertainties of the measurements are discussed and deemed to be caused by the tool center point calibration, the reference coordinate system transformation and the low accuracy of the photogrammetry system

AdS Wormholes

We obtain a large class of smooth Lorentzian p-brane wormholes in supergravities in various dimensions. They connect two asymptotically flat spacetimes. In cases where there is no dilaton involved in the solution, the wormhole can connect an AdS_n\times S^m in one asymptotic region to a flat spacetime in the other. We obtain explicit examples for (n,m)=(4,7), (7,4), (5,5), (3,3), (3,2). These geometries correspond to field theories with UV conformal fixed points, and they undergo decompactification in the IR region. In the case of AdS_3, we compute the central charge of the corresponding conformal field theory.Comment: 20 pages, references adde

Oil-in-oil pickering emulsions stabilized by diblock copolymer nanoparticles

Hypothesis Diblock copolymer nanoparticles have been shown to be Pickering emulsifiers for both oil-in-water and water-in-oil emulsions. Recently, we reported the preparation of sterically-stabilized diblock copolymer spheres in a low-viscosity silicone oil (Macromolecules 53 (2020) 1785–1794). We hypothesized that such spheres could be used as a Pickering emulsifier for a range of oil-in-oil emulsions comprising droplets of a bio-sourced oil dispersed in silicone oil. Experiments Diblock copolymer spheres were prepared via reversible addition-fragmentation chain transfer (RAFT) dispersion polymerization of benzyl methacrylate in silicone oil and characterized by dynamic light scattering and transmission electron microscopy. These spheres were evaluated as Pickering emulsifiers for a series of oil-in-oil Pickering emulsions. The influence of both sphere size and core-forming block composition was investigated. Findings \ud Optimization of the nanoparticle size and core-forming block composition enabled stable bio-sourced oil-in-silicone emulsions to be obtained for nine out of the ten bio-sourced oils investigated. These emulsions were characterized in terms of their mean droplet size by optical microscopy

RAFT dispersion polymerization of benzyl methacrylate in silicone oil using a silicone-based methacrylic stabilizer provides convenient access to spheres, worms, and vesicles

Reversible addition–fragmentation chain transfer (RAFT) solution polymerization of 3-[tris(trimethylsiloxy)silyl] propyl methacrylate (SiMA) was conducted in toluene to prepare three PSiMA precursors with mean degrees of polymerization (DP) of 12, 13, or 15. Each precursor was then chain-extended in turn via RAFT dispersion polymerization of benzyl methacrylate (BzMA) in a low-viscosity silicone oil (decamethylcyclopentasiloxane, D5). 1H NMR studies confirmed that such polymerizations were relatively fast, with more than 99% BzMA conversion being achieved within 100 min at 90 °C. Moreover, gel permeation chromatography analysis indicated that these polymerizations were well controlled, with dispersities remaining below 1.25 when targeting PBzMA DPs up to 200. A phase diagram was constructed at a constant copolymer concentration of 20% w/w. Only spherical micelles were accessible when the PSiMA15 stabilizer was utilized, as determined by transmission electron microscopy and small-angle X-ray scattering (SAXS) studies. Nevertheless, these spheres exhibited narrow size distributions and tunable z-average diameters ranging between 19 and 49 nm, as determined by dynamic light scattering. In contrast, spheres, worms, or vesicles could be prepared depending on the target PBzMA DP when utilizing the relatively short PSiMA12 precursor. Moreover, each of these nano-objects could be obtained at copolymer concentrations as low as 5% w/w. To obtain more detailed structural information, these spheres, worms and vesicles were further characterized by SAXS. PSiMA12-PBzMA55 worms formed reasonably transparent free-standing gels when prepared at copolymer concentrations as low as 5% w/w and exhibited an elastic modulus (G′) of 90 Pa at 25 °C, as judged by oscillatory rheology studies. Finally, broadening of the molecular weight distribution was observed during the long-term storage of PSiMA-PBzMA dispersions at ambient temperature. We tentatively suggest that this instability is related to hydroxyl impurities in the SiMA, which leads to cross-linking side reactions. This problem also causes incipient flocculation of the spheres and worms during the long-term storage of such dispersions at 20 °C

Meson masses in large Nf QCD from the Bethe-Salpeter equation

We solve the homogeneous Bethe-Salpeter (HBS) equation for the scalar, pseudoscalar, vector, and axial-vector bound states of quark and anti-quark in large Nf QCD with the improved ladder approximation in the Landau gauge. The quark mass function in the HBS equation is obtained from the Schwinger-Dyson (SD) equation in the same approximation for consistency with the chiral symmetry. Amazingly, due to the fact that the two-loop running coupling of large Nf QCD is explicitly written in terms of an analytic function, large Nf QCD turns out to be the first example in which the SD equation can be solved in the complex plane and hence the HBS equation directly in the time-like region. We find that approaching the chiral phase transition point from the broken phase, the scalar, vector, and axial-vector meson masses vanish to zero with the same scaling behavior, all degenerate with the massless pseudoscalar meson. This may suggest a new type of manifestation of the chiral symmetry restoration in large Nf QCD.Comment: 33 pages, 16 figures. Typos are corrected. Minor corrections and references are added. Version to appear in Phys. Rev.

Instanton Cosmology and Domain Walls from M-theory and String Theory

The recent proposal by Hawking and Turok for obtaining an open inflationary universe from singular instantons makes use of low-energy effective Lagrangians describing gravity coupled to scalars and non-propagating antisymmetric tensors. In this paper we derive some exact results for Lagrangians of this type, obtained from spherical compactifications of M-theory and string theory. In the case of the S^7 compactification of M-theory, we give a detailed discussion of the cosmological solutions. We also show that the lower-dimensional Lagrangians admit domain-wall solutions, which preserve one half of the supersymmetry, and which approach AdS spacetimes near their horizons.Comment: 51 pages, Latex (3 times). Discussion and references adde

Microscopic Description of Black Rings in AdS/CFT

We discuss some aspects of the recently discovered BPS black ring solutions in terms of the AdS/CFT correspondence. In the type IIB frame in which the black ring carries the charges of the D1-D5-P system, we propose a microscopic description of the rings in the orbifold CFT governing this system. In our proposal, the CFT effectively splits into two parts: one part captures the supertube-like properties of the ring, and the other captures the entropy. We can also understand the black ring entropy by relating the geometry near the ring to BPS black holes in four dimensions, although this latter approach does not directly lead to an identification of black rings in terms of the D1-D5-P CFT.Comment: 18 pages, harvmac. v2 - minor typo