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

Quasiparticle interference and strong electron-mode coupling in the quasi-one-dimensional bands of Sr2RuO4

The single-layered ruthenate Sr$_2$RuO$_4$ has attracted a great deal of interest as a spin-triplet superconductor with an order parameter that may potentially break time reversal invariance and host half-quantized vortices with Majorana zero modes. While the actual nature of the superconducting state is still a matter of controversy, it has long been believed that it condenses from a metallic state that is well described by a conventional Fermi liquid. In this work we use a combination of Fourier transform scanning tunneling spectroscopy (FT-STS) and momentum resolved electron energy loss spectroscopy (M-EELS) to probe interaction effects in the normal state of Sr$_2$RuO$_4$. Our high-resolution FT-STS data show signatures of the \beta-band with a distinctly quasi-one-dimensional (1D) character. The band dispersion reveals surprisingly strong interaction effects that dramatically renormalize the Fermi velocity, suggesting that the normal state of Sr$_2$RuO$_4$ is that of a 'correlated metal' where correlations are strengthened by the quasi 1D nature of the bands. In addition, kinks at energies of approximately 10meV, 38meV and 70meV are observed. By comparing STM and M-EELS data we show that the two higher energy features arise from coupling with collective modes. The strong correlation effects and the kinks in the quasi 1D bands may provide important information for understanding the superconducting state. This work opens up a unique approach to revealing the superconducting order parameter in this compound