A Note on Commuting Diffeomorphisms on Surfaces

Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by any family of elements in V then the elements of G have common fixed points. This result generalizes a similar result due to Bonatti and announced in his paper "Diffeomorphismes commutants des surfaces et stabilite des fibrations en tores".Comment: 16 page

Fire behaviour of reinforced concrete slab strips strengthened with prestressed NSM-CFRP laminates

Carbon fibre reinforced polymer (CFRP) composites are now widely used to strengthen reinforced concrete (RC) structures. Among the strengthening systems available, near-surface mounted (NSM)-prestressed CFRP laminates offer several advantages, as they significantly increase the load carrying capacity and also the serviceability performance of RC structures. However, as for other CFRP systems, there is a concern about their behaviour at elevated temperature and under fire exposure due to the glass transition process undergone by their polymeric components. Nevertheless, the fire performance of NSM-prestressed-CFRP strengthening systems has not yet been investigated. This paper presents an experimental study about the fire resistance behaviour of RC slab strips strengthened with prestressed NSM-CFRP laminates; the slabs were simultaneously subjected to a mechanical (fire) load and the ISO 834 fire curve, and the influence of the following parameters on their fire resistance behaviour was assessed: (i) the prestress level (0 %, 25 % and 50 % of the CFRP tensile strength), and (ii) the presence of passive fire protection, comprising up to 48 mm thick calcium silicate (CS) boards. The results obtained showed that: (i) without fire protection, the strengthening system remained effective during a very low period of fire exposure, which significantly decreased with the prestress level, from 16 min (0 %) to less than 5 min (50 %); (ii) with fire protection, even with 50 % of prestress, the strengthening system remained effective for more than 120 min; and (iii) the “critical” temperatures in the anchorages of the strengthening systems were found to be about 2.5Tg, 2.0Tg and 1.5Tg, for the prestress levels of 0 %, 25 % and 50 %, respectively, with Tg being the glass transition temperature of the adhesive.The authors wish to acknowledge FCT (project FireComposite PTDC/ECM-EST/1882/2014 and CERIS project UIDB UIDB/04625/2020); Secil and Unibet˜ao for supplying the concrete; and S&P Clever Reinforcement for supplying the CFRP laminates and the epoxy adhesive. The first author also wishes to thank the financial support of FCT through the scholarship SFRH/BD/145256/2019

Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking

The existence of electronic symmetry breaking in the underdoped cuprates, and its disappearance with increased hole-density $p$, are now widely reported. However, the relationship between this transition and the momentum space ($\vec{k}$-space) electronic structure underpinning the superconductivity has not been established. Here we visualize the $\vec{Q}$=0 (intra-unit-cell) and $\vec{Q}\neq$0 (density wave) broken-symmetry states simultaneously with the coherent $\vec{k}$-space topology, for Bi$_2$Sr$_2$CaCu$_2$O$_{8+d}$ samples spanning the phase diagram 0.06$\leq p \leq$0.23. We show that the electronic symmetry breaking tendencies weaken with increasing $p$ and disappear close to $p_c$=0.19. Concomitantly, the coherent $\vec{k}$-space topology undergoes an abrupt transition, from arcs to closed contours, at the same $p_c$. These data reveal that the $\vec{k}$-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.Comment: Journal reference added. Main materials: 13 pages, 4 figures. Supplementary materials: 18 pages, 9 figure