Explicit examples of DIM constraints for network matrix models

Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries of a single identity.Comment: 46 page

Spectral Duality Between Heisenberg Chain and Gaudin Model

In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.Comment: 36 page

Anomaly in RTT relation for DIM algebra and network matrix models

We discuss the recent proposal of arXiv:1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a nontrivial, but essentially abelian anomaly cocycle, which we explicitly evaluate for the free field representations of the quantum toroidal algebra. This cocycle is responsible for the braiding, which permutes the external legs in the q-deformed conformal block and its 5d/6d gauge theory counterpart, i.e. the non-perturbative Nekrasov functions. Thus, it defines their modular properties and symmetry. We show how to cancel the anomaly using a construction somewhat similar to the anomaly matching condition in gauge theory. We also describe the singular limit to the affine Yangian (4d Nekrasov functions), which breaks the spectral duality

Autonomous self-healing in epoxy coatings provided by high efficiency isophorone diisocyanate (IPDI) microcapsules for protection of carbon steel

This work aims at investigating the self-healing ability of epoxy coatings, modified with microcapsules containing highly reactive isocyanate in their core. Highly efficient, thermally and chemically stable isophorone diisocyanate microcapsules were prepared via emulsification followed by interfacial polymerization at the surface of oil droplets of the oil-in-water (O/W) emulsion. The microcapsules were incorporated into an epoxy coating to protect carbon steel from corrosion. Scanning Electron Microscopy (SEM) was used to assess the microcapsules? and coating morphology. The physico-chemical characterization of the microcapsules was studied by Fourier Transformed Infrared Spectroscopy (FTIR) and Thermogravimetric Analysis (TGA). Electrochemical Impedance Spectroscopy (EIS) was employed to evaluate the protective performance of coated steel samples and results confirmed that the barrier properties of modified coatings increased over time. The self-healing ability was studied via Localized Impedance Spectroscopy (LEIS), Scanning Vibrating Electrode Technique (SVET) and Scanning Ion-Selective Electrode Techniques (SIET) on coated steel samples containing artificial defects. This comprehensive study confirmed the ability of the capsules to heal damaged areas in the coating and to mitigate corrosion thanks to the formation of a protective polymeric barrier layer.Authors from Portugal acknowledge FCT for the additional funding under the projects UID/QUI/00100/2013 and UID/QUI/00100/2019UID/ECI/04028/2019; Sherwin-Williams for providing the model formulation of the epoxy coating; VoestAlpine AG for providing the steel samples. L.M. Calado acknowledges FCT for PhD grant SFRH/BD/127341/2016. This work was supported by Qatar National Research Fund (a member of the Qatar Foundation) [Grant number NPRP-9-080-2-039 ].Scopu

Smart epoxy coating modified with isophorone diisocyanate microcapsules and cerium organophosphate for multilevel corrosion protection of carbon steel

This study investigates the corrosion resistance of steel plates coated with epoxy-based coatings modified with microcapsules loaded with isophorone diisocyanate and with pH-sensitive cerium tri(bis(2-ethylhexyl)phosphate (Ce(DEHP)3) particles serving as inhibitor. The healing effects were studied by combining different localized electrochemical techniques, namely localized impedance spectroscopy (LEIS), localized potentiometry (SIET) and the scanning vibrating electrode technique (SVET). The impact of the additives in the coating barrier properties was assessed by electrochemical impedance spectroscopy (EIS). EIS evidences a relevant multilevel protection effect when both additives are combined, effect that is characterized by higher and more stable coating barrier properties and absence of interfacial corrosion activity. The corrosion healing ability over defects formed in the coating formulated with the combination of the two additives was confirmed by LEIS. SVET and SIET also evidence that the overall healing process in the coating modified with both additives involves the combination of the protective role of each individual species, that reinforces significantly the corrosion protection conferred by the epoxy coating.Authors from Centro de Química Estrutural and CERENA acknowledge the financial support of Fundação para a Ciência e Tecnologia, through grants UIDB/00100/2020, UIDP/00100/2020 and UID/ECI/04028/2019, respectively; Sherwin-Williams for providing the model formulation of the epoxy coating; VoestAlpine AG for providing the steel samples. L.M. Calado acknowledges FCT for PhD grant SFRH/BD/127341/2016.Scopu