A low-rank matrix equation method for solving PDE-constrained optimization problems

PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment and blood flow simulation. Discretization of the optimization problem and using a Lagrangian approach result in a large-scale saddle-point system, which is challenging to solve, and acquiring a full space-time solution is often infeasible. We present a new framework to efficiently compute a low-rank approximation to the solution by reformulating the KKT system into a Sylvester-like matrix equation. This matrix equation is subsequently projected onto a small subspace via an iterative rational Krylov method, and we obtain a reduced problem by imposing a Galerkin condition on its residual. In our work we discuss implementation details and dependence on the various problem parameters. Numerical experiments illustrate the performance of the new strategy also when compared to other low-rank approaches

Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32 cases, the result is very close to an integer that is a power of 2. In addition, this power of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute

Estimation of soil and vegetation temperatures with multiangular thermal infrared observations: IMGRASS, HEIFE, and SGP 1997 experiments

The potential of directional observations in the thermal infrared region for land surface studies is a largely uncharted area of research. The availability of the dual-view Along Track Scanning Radiometer (ATSR) observations led to explore new opportunities in this direction. In the context of studies on heat transfer at heterogeneous land surfaces, multiangular thermal infrared (TIR) observations offer the opportunity of overcoming fundamental difficulties in modeling sparse canopies. Three case studies were performed on the estimation of the component temperatures of foliage and soil. The first one included the use of multi-temporal field measurements at view angles of 0°, 23° and 52°. The second and third one were done with directional ATSR observations at view angles of 0° and 53° only. The first one was a contribution to the Inner-Mongolia Grassland Atmosphere Surface Study (IMGRASS) experiment in China, the second to the Hei He International Field Experiment (HEIFE) in China and the third one to the Southern Great Plains 1997 (SGP 1997) experiment in Oklahoma, United States. The IMGRASS experiment provided useful insights on the applicability of a simple linear mixture model to the analysis of observed radiance. The HEIFE case study was focused on the large oasis of Zhang-Ye and led to useful estimates of soil and vegetation temperatures. The SGP 1997 contributed a better understanding of the impact of spatial heterogeneity on the accuracy of retrieved foliage and soil temperatures. Limitations in the approach due to varying radiative and boundary layer forcing and to the difference in spatial resolution between the forward and the nadir view are evaluated through a combination of modeling studies and analysis of field data

Production of three-body Efimov molecules in an optical lattice

We study the possibility of associating meta-stable Efimov trimers from three free Bose atoms in a tight trap realised, for instance, via an optical lattice site or a microchip. The suggested scheme for the production of these molecules is based on magnetically tunable Feshbach resonances and takes advantage of the Efimov effect in three-body energy spectra. Our predictions on the energy levels and wave functions of three pairwise interacting 85Rb atoms rely upon exact solutions of the Faddeev equations and include the tightly confining potential of an isotropic harmonic atom trap. The magnetic field dependence of these energy levels indicates that it is the lowest energetic Efimov trimer state that can be associated in an adiabatic sweep of the field strength. We show that the binding energies and spatial extents of the trimer molecules produced are comparable, in their magnitudes, to those of the associated diatomic Feshbach molecule. The three-body molecular state follows Efimov's scenario when the pairwise attraction of the atoms is strengthened by tuning the magnetic field strength.Comment: 21 pages, 8 figures (final version

Design, simulation and characterization of integrated photonic spectrographs for astronomy: generation-I AWG devices based on canonical layouts

We present an experimental study on our first generation of custom-developed arrayed waveguide gratings (AWG) on a silica platform for spectroscopic applications in near-infrared astronomy. We provide a comprehensive description of the design, numerical simulation and characterization of several AWG devices aimed at spectral resolving powers of 15,000-60,000 in the astronomical H-band. We evaluate the spectral characteristics of the fabricated devices in terms of insertion loss and estimated spectral resolving power and compare the results with numerical simulations. We estimate resolving powers of up to 18,900 from the output channel 3-dB transmission bandwidth. Based on the first characterization results, we select two candidate AWGs for further processing by removal of the output waveguide array and polishing the output facet to optical quality with the goal of integration as the primary diffractive element in a cross-dispersed spectrograph. We further study the imaging properties of the processed AWGs with regards to spectral resolution in direct imaging mode, geometry-related defocus aberration, and polarization sensitivity of the spectral image. We identify phase error control, birefringence control, and aberration suppression as the three key areas of future research and development in the field of high-resolution AWG-based spectroscopy in astronomy

Pseudopotential Approaches to Ca, Sr and Ba Hybrides. Why are some Alkaline Earth MX2_2 Compounds Bent?

Quasirelativistic and nonrelativistic lo-valence-electronp seudopotentialsf or Ca, Sr, and Ba are presented. Results of calculations with 6s6p5d basis sets for MH, MH$^+$ , and MH$_2$, are compared with all-electron and 2-valence-electron pseudopotential calculations with and , without core-polarization potentials. The lo-valence-electron pseudopotential approach agrees well with all-electron calculations. It circumvents problems for the 2-valence-electron pseudopotentials arising from an incomplete separation of valence and subvalence shells in polar molecular systems due to strongly contracted occupied (n - 1 )-d orbitals. All higherlevel calculations show SrH$_2$ and BaII$_2$, to be bent with angles of - 140° and 120°, respectively, while CaH$_2$ is linear with a flat potential-energy surface for the bending motion. The use of a core-polarization potential together with the 2-valence-electronp seudopotentiala pproach allows an investigation of the relative importance of core-polarization vs direct d-orbital bonding participation as reasons for the bent structures. The calculations strongly suggest that both contribute to the bending in SrH$_2$ and BaII$_2$. Even at the Hartree-Fock level of theory lovalence- electronp seudopotentialc alculations given reasonablea nglesw hen the potentialenergy surface is not exceedingly flat, and only moderately contracted basis sets including both compact d functions and diffuse p functions are used. The effect of core-valence correlation and the importance off functions also are discussed

Correlation effects in ionic crystals: I. The cohesive energy of MgO

High-level quantum-chemical calculations, using the coupled-cluster approach and extended one-particle basis sets, have been performed for (Mg2+)n (O2-)m clusters embedded in a Madelung potential. The results of these calculations are used for setting up an incremental expansion for the correlation energy of bulk MgO. This way, 96% of the experimental cohesive energy of the MgO crystal is recovered. It is shown that only 60% of the correlation contribution to the cohesive energy is of intra-ionic origin, the remaining part being caused by van der Waals-like inter-ionic excitations.Comment: LaTeX, 20 pages, no figure

Ferromagnetic coupling of mononuclear Fe centers in a self-assembled metal-organic network on Au(111)

The magnetic state and magnetic coupling of individual atoms in nanoscale structures relies on a delicate balance between different interactions with the atomic-scale surrounding. Using scanning tunneling microscopy, we resolve the self-assembled formation of highly ordered bilayer structures of Fe atoms and organic linker molecules (T4PT) when deposited on a Au(111) surface. The Fe atoms are encaged in a three-dimensional coordination motif by three T4PT molecules in the surface plane and an additional T4PT unit on top. Within this crystal field, the Fe atoms retain a magnetic ground state with easy-axis anisotropy, as evidenced by X-ray absorption spectroscopy and X-ray magnetic circular dichroism. The magnetization curves reveal the existence of ferromagnetic coupling between the Fe centers

Car-to-cyclist accidents from the car driver's point of view

A promising approach to prevent road traffic accidents between passenger cars and cyclists is the development of driver assistance systems. To develop such systems with maximum ef-fectiveness in road traffic, car-to-cyclist accidents have to be analysed from the car driver’s point of view to gain insight into the situations with which the drivers were faced and espe-cially why they failed to manage these crash situations. The EU funded project PROSPECT (Proactive Safety for Pedestrians and Cyclists) considered this approach and made the pre-sented research possible. This paper reports findings from a case-by-case analysis of 3,550 car-to-cyclist accidents in Germany. The results of the accident analysis confirm findings of previous studies showing that crossing scenarios play a predominant role in car-to-cyclist ac-cidents. Moreover, the results show that both the orientation of the cyclist and the driver’s task (in terms of the driver’s maneuver intention, road layout, traffic regulations) have an in-fluence on the distribution of those scenarios in so far as certain combinations lead to a higher or lower distribution. The results contribute towards a better understanding of possi-ble reasons why the driver failed to manage certain situations. Regarding PROSPECT, the most relevant use cases will be used to specify and develop advanced measures that will be implemented in the next generation of active safety systems

Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections

Long-range exchange and correlation effects, responsible for the failure of currently used approximate density functionals in describing van der Waals forces, are taken into account explicitly after a separation of the electron-electron interaction in the Hamiltonian into short- and long-range components. We propose a "range-separated hybrid" functional based on a local density approximation for the short-range exchange-correlation energy, combined with a long-range exact exchange energy. Long-range correlation effects are added by a second-order perturbational treatment. The resulting scheme is general and is particularly well-adapted to describe van der Waals complexes, like rare gas dimers.Comment: 8 pages, 1 figure, submitted to Phys. Rev.