Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 2: adjoint approximations and extensions

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] of discrete approximations to the linearized and adjoint equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. We consider a simple modified Lax–Friedrichs discretization on a uniform grid, and a key point is that the numerical smoothing increases the number of points across the nonlinear discontinuity as the grid is refined. It is proved that there is convergence in the discrete approximation of linearized output functionals even for Dirac initial perturbations and pointwise convergence almost everywhere for the solution of the adjoint discrete equations. In particular, the adjoint approximation converges to the correct uniform value in the region in which characteristics propagate into the discontinuity. Moreover, it is shown that the results of [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] and the present paper hold also for quite general nonlinear initial data which contain multiple shocks and for which shocks form at a later time and/or merge

Broad-line region structure and kinematics in the radio galaxy 3C 120

Broad emission lines originate in the surroundings of supermassive black holes in the centers of active galactic nuclei (AGN). One method to investigate the extent, structure, and kinematics of the BLR is to study the continuum and line profile variability in AGN. We selected the radio-loud Seyfert 1 galaxy 3C 120 as a target for this study. We took spectra with a high signal-to-noise ratio of 3C 120 with the 9.2m Hobby-Eberly Telescope between Sept. 2008 and March 2009. In parallel, we photometrically monitored the continuum flux at the Wise observatory. We analyzed the continuum and line profile variations in detail (1D and 2D reverberation mapping) and modeled the geometry of the line-emitting regions based on the line profiles. We show that the BLR in 3C 120 is stratified with respect to the distance of the line-emitting regions from the center with respect to the line widths (FWHM) of the rms profiles and with respect to the variability amplitude of the emission lines. The emission line wings of H{\alpha} and H{\beta} respond much faster than their central region. This is explained by accretion disk models. In addition, these lines show a stronger response in the red wings. However, the velocity-delay maps of the helium lines show a stronger response in the blue wing. Furthermore, the HeII{\lambda}4686 line responds faster in the blue wing in contradiction to observations made one and a half years later when the galaxy was in a lower state. The faster response in the blue wing is an indication for central outflow motions when this galaxy was in a bright state during our observations. The vertical BLR structure in 3C 120 coincides with that of other AGN. We confirm the general trend: the emission lines of narrow line AGN originate at larger distances from the midplane than AGN with broader emission lines.Comment: 18 pages, 25 figures, Astronomy & Astrophysics in pres

The Influence of Heart and Lung Dynamics on the Impedance Cardiogram — A Simulative Analysis

Impedance cardiography (ICG) is a simple and cheap method for acquiring hemodynamic parameters. Unfortunately, not all physiological influences on the ICG signal have yet been identified. In this work, the influence of heart and lung dynamics is analyzed using a simplified model of the human thorax with high temporal resolution. Simulations are conducted using the finite integration technique (FIT) with temporal resolution of 103 Hz. It is shown that changes in heart volume as well as conductivity changes of the lung have a high impact on the ICG signal, if analyzed separately. Considering the sum signal of both physiological sources, it can be shown that they compensate each other and thus do not contribute to the signal. This finding supports Kubicek’s model

Cyclones causing wind storms in the Mediterranean: characteristics, trends and links to large-scale patterns

A climatology of cyclones with a focus on their relation to wind storm tracks in the Mediterranean region (MR) is presented. Trends in the frequency of cyclones and wind storms, as well as variations associated with the North Atlantic Oscillation (NAO), the East Atlantic/West Russian (EAWR) and the Scandinavian variability pattern (SCAND) are discussed. The study is based on the ERA40 reanalysis dataset. Wind storm tracks are identified by tracking clusters of adjacent grid boxes characterised by extremely high local wind speeds. The wind track is assigned to a cyclone track independently identified with an objective scheme. Areas with high wind activity – quantified by extreme wind tracks – are typically located south of the Golf of Genoa, south of Cyprus, southeast of Sicily and west of the Iberian Peninsula. About 69% of the wind storms are caused by cyclones located in the Mediterranean region, while the remaining 31% can be attributed to North Atlantic or Northern European cyclones. The North Atlantic Oscillation, the East Atlantic/West Russian pattern and the Scandinavian pattern all influence the amount and spatial distribution of wind inducing cyclones and wind events in the MR. The strongest signals exist for the NAO and the EAWR pattern, which are both associated with an increase in the number of organised strong wind events in the eastern MR during their positive phase. On the other hand, the storm numbers decrease over the western MR for the positive phase of the NAO and over the central MR during the positive phase of the EAWR pattern. The positive phase of the Scandinavian pattern is associated with a decrease in the number of winter wind storms over most of the MR. A third of the trends in the number of wind storms and wind producing cyclones during the winter season of the ERA40 period may be attributed to the variability of the North Atlantic Oscillation

ProSAT2—Protein Structure Annotation Server

ProSAT2 is a server to facilitate interactive visualization of sequence-based, residue-specific annotations mapped onto 3D protein structures. As the successor of ProSAT (Protein Structure Annotation Tool), it includes its features for visualizing SwissProt and PROSITE functional annotations. Currently, the ProSAT2 server can perform automated mapping of information on variants and mutations from the UniProt KnowledgeBase and the BRENDA enzyme information system onto protein structures. It also accepts and maps user-prepared annotations. By means of an annotation selector, the user can interactively select and group residue-based information according to criteria such as whether a mutation affects enzyme activity. The visualization of the protein structures is based on the WebMol Java molecular viewer and permits simultaneous highlighting of annotated residues and viewing of the corresponding descriptive texts. ProSAT2 is available at

Theory of real space imaging of Fermi surfaces

A scanning tunneling microscope can be used to visualize in real space Fermi surfaces with buried impurities far below substrates acting as local probes. A theory describing this feature is developed based on the stationary phase approximation. It is demonstrated how a Fermi surface of a material acts as a mirror focusing electrons that scatter at hidden impurities.Comment: 10 pages, 4 figure

Distributed controller design for a class of sparse singular systems with privacy constraints

In the current research on distributed control of interconnected large-scale dynamical systems an often neglected issue is the desire to ensure privacy of subsystems. This gives motivation for the presented distributed controller design method which requires communication and the exchange of model data only with direct neighbors. Thus, no global system knowledge is required. An important property of many large-scale systems is the presence of algebraic conservation constraints, for example in terms of energy or mass flow. Therefore, the presented controller design takes these constraints explicitly into account while preserving the sparsity structure of the distributed system necessary for a distributed design. The computation is based on the simulation of the system states and of adjoint states. The control objective is represented by the finite horizon linear quadratic cost functional