Symmetry protection of topological order in one-dimensional quantum spin systems

We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $\pi$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys. Rev. B \textbf{81}, 064439 (2010)]. On the other hand, an even-$S$ Haldane phase is not topologically protected (i.e., it is indistinct from a trivial, site-factorizable phase). We show some numerical evidence that supports these claims, using concrete examples.Comment: 9 pages, 6 figures, extended version: several new examples and numerical results added. Journal reference adde

Sequentially generated states for the study of two dimensional systems

Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product States, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of Projected Entangled Pair States and investigate their suitability for approximating the ground states of local Hamiltonians.Comment: 10 pages, 4 figure

Using Multiple Fidelity Numerical Models for Floating Offshore Wind Turbine Advanced Control Design

This paper summarises the tuning process of the Aerodynamic Platform Stabiliser control loop and its performance with Floating Offshore Wind Turbine model. Simplified Low-Order Wind turbine numerical models have been used for the system identification and control tuning process. Denmark Technical University's 10 MW wind turbine model mounted on the TripleSpar platform concept was used for this study. Time-domain simulations were carried out in a fully coupled non-linear aero-hydro-elastic simulation tool FAST, in which wind and wave disturbances were modelled. This testing yielded significant improvements in the overall Floating Offshore Wind Turbine performance and load reduction, validating the control technique presented in this work.This work was partially funded by the Spanish Ministry of Economy and Competitiveness through the research project DPI2017-82930-C2-2-R

Real-time phasefront detector for heterodyne interferometers

We present a real-time differential phasefront detector sensitive to better than 3 mrad rms, which corresponds to a precision of about 500 pm. This detector performs a spatially resolving measurement of the phasefront of a heterodyne interferometer, with heterodyne frequencies up to approximately 10 kHz. This instrument was developed as part of the research for the LISA Technology Package (LTP) interferometer, and will assist in the manufacture of its flight model. Due to the advantages this instrument offers, it also has general applications in optical metrology

Investigations on micro-mechanical properties of polycrystalline Ti(C,N) and Zr(C,N) coatings

Micro-mechanical properties of Ti(C,N) and Zr(C,N) coatings deposited by chemical vapor deposition on a WC-Co cemented carbide substrate were examined by micro-compression testing using a nanoindenter equipped with a flat punch. Scanning Electron Microscopy, Focused Ion Beam, Electron Backscattered Diffraction and Finite Element Modeling were combined to analyze the deformation mechanisms of the carbonitride layers at room temperature. The results revealed that Ti(C,N) undergoes a pure intergranular crack propagation and grain decohesion under uniaxial compression; whereas the fracture mode of Zr(C,N) was observed to be inter/transgranular failure with unexpected plastic deformation at room temperature.Peer ReviewedPostprint (author's final draft

Weak branch and multimodal convection in rapidly rotating spheres at low Prandtl number

The focus of this study is to investigate primary and secondary bifurcations to weakly nonlinear flows (weak branch) in convective rotating spheres in a regime where only strongly nonlinear oscillatory sub- and supercritical flows (strong branch) were previously found [E. J. Kaplan, N. Schaeffer, J. Vidal, and P. Cardin, Phys. Rev. Lett. 119, 094501 (2017)]. The relevant regime corresponds to low Prandtl and Ekman numbers, indicating a predominance of Coriolis forces and thermal diffusion in the system. We provide the bifurcation diagrams for rotating waves (RWs) computed by means of continuation methods and the corresponding stability analysis of these periodic flows to detect secondary bifurcations giving rise to quasiperiodic modulated rotating waves (MRWs). Additional direct numerical simulations (DNS) are performed for the analysis of these quasiperiodic flows for which Poincaré sections and kinetic energy spectra are presented. The diffusion timescales are investigated as well. Our study reveals very large initial transients (more than 30 diffusion time units) for the nonlinear saturation of solutions on the weak branch, either RWs or MRWs, when DNS are employed. In addition, we demonstrate that MRWs have multimodal nature involving resonant triads. The modes can be located in the bulk of the fluid or attached to the outer sphere and exhibit multicellular structures. The different resonant modes forming the nonlinear quasiperiodic flows can be predicted with the stability analysis of RWs, close to the Hopf bifurcation point, by analyzing the leading unstable Floquet eigenmode.Peer ReviewedPostprint (author's final draft

3-D Photoionization Structure and Distances of Planetary Nebulae IV. NGC 40

Continuing our series of papers on the 3-D structure and accurate distances of Planetary Nebulae (PNe), we present here the results obtained for the planetary nebula NGC\,40. Using data from different sources and wavelengths, we construct 3-D photoionization models and derive the physical quantitities of the ionizing source and nebular gas. The procedure, discussed in detail in the previous papers, consists of the use of 3-D photoionization codes constrained by observational data to derive the three-dimensional nebular structure, physical and chemical characteristics and ionizing star parameters of the objects by simultaneously fitting the integrated line intensities, the density map, the temperature map, and the observed morphologies in different emission lines. For this particular case we combined hydrodynamical simulations with the photoionization scheme in order to obtain self-consistent distributions of density and velocity of the nebular material. Combining the velocity field with the emission line cubes we also obtained the synthetic position-velocity plots that are compared to the observations. Finally, using theoretical evolutionary tracks of intermediate and low mass stars, we derive the mass and age of the central star of NGC\,40 as $(0.567 \pm 0.06)$M$_{\odot}$ and $(5810 \pm 600)$yrs, respectively. The distance obtained from the fitting procedure was $(1150 \pm 120)$pc.Comment: 12 pages, 11 figures, accepted for publication in Ap

First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries

Gravitational-wave observations of binary black holes currently rely on theoretical models that predict the dominant multipoles (l,m) of the radiation during inspiral, merger and ringdown. We introduce a simple method to include the subdominant multipoles to binary black hole gravitational waveforms, given a frequency-domain model for the dominant multipoles. The amplitude and phase of the original model are appropriately stretched and rescaled using post-Newtonian results (for the inspiral), perturbation theory (for the ringdown), and a smooth transition between the two. No additional tuning to numerical-relativity simulations is required. We apply a variant of this method to the non-precessing PhenomD model. The result, PhenomHM, constitutes the first higher-multipole model of spinning black-hole binaries, and currently includes the (l,m) = (2,2), (3,3), (4,4), (2,1), (3,2), (4,3) radiative moments. Comparisons with numerical-relativity waveforms demonstrate that PhenomHM is more accurate than dominant-multipole-only models for all binary configurations, and typically improves the measurement of binary properties.Comment: 4 pages, 4 figure