Large spin systematics in CFT

20 pages; v2: version published in JHEPUsing conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.Peer reviewe

Lessons from crossing symmetry at large N

20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe

Structural characterisation of deposit layer during milk protein microfiltration by means of in-situ mri and compositional analysis

Milk protein fractionation by microfiltration membranes is an established but still growing field in dairy technology. Even under cross-flow conditions, this filtration process is impaired by the formation of a deposit by the retained protein fraction, mainly casein micelles. Due to deposition formation and consequently increased overall filtration resistance, the mass flow of the smaller whey protein fraction declines within the first few minutes of filtration. Currently, there are only a handful of analytical techniques available for the direct observation of deposit formation with opaque feed media and membranes. Here, we report on the ongoing development of a non-invasive and non-destructive method based on magnetic resonance imaging (MRI), and its application to characterise deposit layer formation during milk protein fractionation in ceramic hollow fibre membranes as a function of filtration pressure and temperature, temporally and spatially resolved. In addition, the chemical composition of the deposit was analysed by reversed phase high pressure liquid chromatography (RP-HPLC). We correlate the structural information gained by in-situ MRI with the protein amount and composition of the deposit layer obtained by RP-HPLC. We show that the combination of in-situ MRI and chemical analysis by RP-HPLC has the potential to allow for a better scientific understanding of the pressure and temperature dependence of deposit layer formation

Synthesis and characterization of uniform OCL-OEG block cooligomers

Block copolymers are an interesting class of materials, offering the opportunity to form nanostructured morphologies, making them suitable for a broad range of applications in nanotechnology, medicine, or biotechnology. Especially for the pharmaceutical sector, a uniform structure and a distinct structure–property relationship is desirable to manufacture highly reproducible and tailor-made materials. Herein, we report the synthesis and characterization of uniform (Đ = 1.01) oligo(ε-caprolactone)-oligo(ethylene glycol) (OCL-OEG) block co-oligomers (BCOs). Three different BCOs, varying in the length of the hydrophobic caprolactone segment, were obtained via Steglich esterification of the corresponding homo oligomers. A clear dispersity and composition dependent structure–property relationship based on the thermal properties is observed, compared to identical structures similar in M$_n$ and dispersities of Đ = 1.06, obtained via ring-opening polymerization (ROP) of ε-caprolactone. In addition, increased long-range-order distances L$_0$ with increasing dispersity of the BCOs are found for the formed morphologies after solvent vapor annealing (SVA). These results highlight the importance of uniform structures for a better understanding of the structure–property relationship of block copolymers

Corticosteroid injection for tennis elbow or lateral epicondylitis: a review of the literature

Lateral epicondylitis or tennis elbow is a painful and functionally limiting entity affecting the upperextremity and is frequently treated by hand surgeons. Corticosteroid injection is one of the most common interventions for lateral epicondylitis or tennis elbow. Here, a review of the medical literature on this treatment is presented