Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct new Lagrangian ROMs. We show that the new Lagrangian ROMs are orders of magnitude more accurate than the standard Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis

Jahn-Teller Distortions and the Supershell Effect in Metal Nanowires

A stability analysis of metal nanowires shows that a Jahn-Teller deformation breaking cylindrical symmetry can be energetically favorable, leading to stable nanowires with elliptic cross sections. The sequence of stable cylindrical and elliptical nanowires allows for a consistent interpretation of experimental conductance histograms for alkali metals, including both the shell and supershell structures. It is predicted that for gold, elliptical nanowires are even more likely to form since their eccentricity is smaller than for alkali metals. The existence of certain metastable ``superdeformed'' nanowires is also predicted

Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry

We show how accurate benchmark values of the surface formation energy of crystalline lithium hydride can be computed by the complementary techniques of quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry. To demonstrate the high accuracy of the QMC techniques, we present a detailed study of the energetics of the bulk LiH crystal, using both pseudopotential and all-electron approaches. We show that the equilibrium lattice parameter agrees with experiment to within 0.03 %, which is around the experimental uncertainty, and the cohesive energy agrees to within around 10 meV per formula unit. QMC in periodic slab geometry is used to compute the formation energy of the LiH (001) surface, and we show that the value can be accurately converged with respect to slab thickness and other technical parameters. The quantum chemistry calculations build on the recently developed hierarchical scheme for computing the correlation energy of a crystal to high precision. We show that the hierarchical scheme allows the accurate calculation of the surface formation energy, and we present results that are well converged with respect to basis set and with respect to the level of correlation treatment. The QMC and hierarchical results for the surface formation energy agree to within about 1 %.Comment: 16 pages, 4 figure

Chasing the second gamma-ray bright isolated neutron star: 3EG J1835+5918/RX J1836.2+5925

The EGRET telescope aboard NASAs Compton GRO has repeatedly detected 3EG J1835+5918, a bright and steady source of high-energy gamma-ray emission with no identification suggested until recently. The long absence of any likely counterpart for a bright gamma-ray source located 25 degrees off the Galactic plane initiated several attempts of deep observations at other wavelengths. We report on counterparts in X-rays on a basis of a 60 ksec ROSAT HRI image. In order to conclude on the plausibility of the X-ray counterparts, we reanalyzed data from EGRET at energies above 100 MeV and above 1 GeV, including data up to CGRO observation cycle 7. The gamma-ray source location represents the latest and probably the final positional assessment based on EGRET data. The X-ray counterparts were studied during follow-up optical identification campaigns, leaving only one object to be likely associated with the gamma-ray source 3EG J1835+5918. This object, RX J1836.2+5925, has the characteristics of an isolated neutron star and possibly of a radio-quiet pulsar.Comment: 5 pages, 3 figures. To appear in the Proceedings of the 270. WE-Heraeus Seminar on Neutron Stars, Pulsars and Supernova Remnants, Jan. 21-25, 2002, Physikzentrum Bad Honnef, eds W. Becker, H. Lesch & J. Truemper. Proceedings are available as MPE-Report 27

Odd-parity perturbations of self-similar Vaidya spacetime

We carry out an analytic study of odd-parity perturbations of the self-similar Vaidya space-times that admit a naked singularity. It is found that an initially finite perturbation remains finite at the Cauchy horizon. This holds not only for the gauge invariant metric and matter perturbation, but also for all the gauge invariant perturbed Weyl curvature scalars, including the gravitational radiation scalars. In each case, `finiteness' refers to Sobolev norms of scalar quantities on naturally occurring spacelike hypersurfaces, as well as pointwise values of these quantities.Comment: 28 page

Hybrid density functional theory description of N- and C-doping of NiO

The large intrinsic bandgap of NiO hinders its potential application as a photocatalyst under visible-light irradiation. In this study, we have performed first-principles screened exchange hybrid density functional theory with the HSE06 functional calculations of N- and C-doped NiO to investigate the effect of doping on the electronic structure of NiO. C-doping at an oxygen site induces gap states due to the dopant, the positions of which suggest that the top of the valence band is made up primarily of C 2p-derived states with some Ni 3d contributions, and the lowest-energy empty state is in the middle of the gap. This leads to an effective bandgap of 1.7 eV, which is of potential interest for photocatalytic applications. N-doping induces comparatively little dopant-Ni 3d interactions, but results in similar positions of dopant-induced states, i.e., the top of the valence band is made up of dopant 2p states and the lowest unoccupied state is the empty gap state derived from the dopant, leading to bandgap narrowing. With the hybrid density functional theory (DFT) results available, we discuss issues with the DFT corrected for on-site Coulomb description of these systems

A CNO Dichotomy among O2 Giant Spectra in the Magellanic Clouds

From a survey of the 3400 Å region in the earliest O-type spectra, we have found that two of the four O2 giants observed in the Large Magellanic Cloud have O IV lines there that are stronger than the N IV lines, while the other two have the opposite. A Small Magellanic Cloud counterpart also has N IV stronger than O IV. Inspection of the blue spectra of these stars shows that the former pair have weaker N lines in all ionization states (III, IV, and V) present as well as lines of C IV λ4658, while the latter three have stronger N lines and greater He/H. Space ultraviolet observations of two of the N-strong stars show N V wind profiles substantially stronger than those of C IV, while in the N-weak stars the C IV features are equal to or stronger than the N V. The N-strong stars are now reclassified as ON2 III(f*), newly defining that category. These characteristics strongly suggest a larger fraction of processed material in the atmospheres of the ON2 stars, which we confirm by modeling the optical spectra. In the context of current models, it is in turn implied that the ON2 stars are in a more advanced evolutionary state than the others, and/or that they had higher initial rotational velocities. The recent formulation of the effects of rotation on massive stellar evolution introduces an additional fundamental parameter, which the CNO abundances are in principle able to constrain. We present some illustrative comparisons with current Geneva evolutionary models for rotating massive stars. It is possible that these very hot, nitrogen-rich objects are products of homogeneous evolution. Our results will provide motivation for further physical modeling of the atmospheres and evolutionary histories of the most massive hot stars.Fil: Walborn, Nolan Revere. Space Telescope Science Institute; Estados UnidosFil: Morrell, Nidia Irene. Las campanas observatory; ChileFil: Howarth, Ian D.. University College London; Estados UnidosFil: Crowther, Paul A.. University of Sheffield; Reino UnidoFil: Lennon, Daniel J.. Isaac Newton Group of Telescopes; EspañaFil: Massey, Philip. Lowell Observatory; Estados UnidosFil: Arias, Julia Ines. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin