State-space realization of a describing function

The describing function is a powerful tool for characterizing nonlinear dynamical systems in the frequency domain. In some cases, it is the only available description of a nonlinear operator characterizing a certain subcomponent of the system. This paper presents a methodology to provide a state-space realization of one given describing function, in order to allow the study of the system in the time domain as well. The realization is based on Hammerstein models and Fourier–Bessel series. It can be embedded in time domain simulations of complex configurations with many nonlinear elements interacting, accurately describing the nonlinear saturation of the system. The technique is applied to an example application in the field of combustion instability, featuring self-excited thermoacoustic oscillations. We benchmark the performance of the tool comparing the results with a frequency domain analysis of the same system, obtaining good agreement between the two formulations.This work was supported by the European Research Council through project ALORS N.259620 and by the German Research Association for Combustion Engines (Forschungsvereinigung Verbrennungskraftmaschinen e.V. FVV).This is the accepted manuscript of a paper published in Nonlinear Dynamics (Ghirardo G, Ćosić B, Juniper MP, Moeck JP, Nonlinear Dynamics, 2015, doi:10.1007/s11071-015-2134-x). The final version is available at http://dx.doi.org/10.1007/s11071-015-2134-

Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors

Rotationally symmetric annular combustors are of practical importance because they generically resemble combustion chambers in gas turbines, in which thermoacoustically driven oscillations are a major concern. We focus on azimuthal thermoacoustic oscillations and model the fluctuating heat release rate as being dependent only on the local pressure in the combustion chamber. We study the dynamics of the annular combustor with a finite number of compact flames equispaced around the annulus, and characterize the flames’ response with a describing function. We discuss the existence, amplitude and the stability of standing and spinning waves, as a function of: (i) the number of the burners; (ii) the acoustic damping in the chamber; (iii) the flame response. We present the implications for industrial applications and the future direction of investigations. We then present as an example the first theoretical study of thermoacoustic triggering in annular combustors, which shows that rotationally symmetric annular chambers that are thermoacoustically unstable do not experience only stable spinning solutions, but can also experience stable standing solutions. We finally test the theory on one experiment with good agreement.European Research Council (Project ALORS

Well path design and stimulation treatments at the geothermal research well GtGrSk4/05 in Groß Schönebeck

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System Test of the ATLAS Muon Spectrometer in the H8 Beam at the CERN SPS

An extensive system test of the ATLAS muon spectrometer has been performed in the H8 beam line at the CERN SPS during the last four years. This spectrometer will use pressurized Monitored Drift Tube (MDT) chambers and Cathode Strip Chambers (CSC) for precision tracking, Resistive Plate Chambers (RPCs) for triggering in the barrel and Thin Gap Chambers (TGCs) for triggering in the end-cap region. The test set-up emulates one projective tower of the barrel (six MDT chambers and six RPCs) and one end-cap octant (six MDT chambers, A CSC and three TGCs). The barrel and end-cap stands have also been equipped with optical alignment systems, aiming at a relative positioning of the precision chambers in each tower to 30-40 micrometers. In addition to the performance of the detectors and the alignment scheme, many other systems aspects of the ATLAS muon spectrometer have been tested and validated with this setup, such as the mechanical detector integration and installation, the detector control system, the data acquisition, high level trigger software and off-line event reconstruction. Measurements with muon energies ranging from 20 to 300 GeV have allowed measuring the trigger and tracking performance of this set-up, in a configuration very similar to the final spectrometer. A special bunched muon beam with 25 ns bunch spacing, emulating the LHC bunch structure, has been used to study the timing resolution and bunch identification performance of the trigger chambers. The ATLAS first-level trigger chain has been operated with muon trigger signals for the first time

Crystallographic Education in the 21st Century

There are many methods that can be used to incorporate concepts of crystallography into the learning experiences of students, whether they are in elementary school, at university or part of the public at large. It is not always critical that those who teach crystallography have immediate access to diffraction equipment to be able to introduce the concepts of symmetry, packing or molecular structure in an age- and audience-appropriate manner. Crystallography can be used as a tool for teaching general chemistry concepts as well as general research techniques without ever having a student determine a crystal structure. Thus, methods for younger students to perform crystal growth experiments of simple inorganic salts, organic compounds and even metals are presented. For settings where crystallographic instrumentation is accessible (proximally or remotely), students can be involved in all steps of the process, from crystal growth, to data collection, through structure solution and refinement, to final publication. Several approaches based on the presentations in the MS92 Microsymposium at the IUCr 23rd Congress and General Assembly are reported. The topics cover methods for introducing crystallography to undergraduate students as part of a core chemistry curriculum; a successful short-course workshop intended to bootstrap researchers who rely on crystallography for their work; and efforts to bring crystallography to secondary school children and non-science majors. In addition to these workshops, demonstrations and long-format courses, open-format crystallographic databases and three-dimensional printed models as tools that can be used to excite target audiences and inspire them to pursue a deeper understanding of crystallography are described

Differential (2+1) Jet Event Rates and Determination of alpha_s in Deep Inelastic Scattering at HERA

Events with a (2+1) jet topology in deep-inelastic scattering at HERA are studied in the kinematic range 200 < Q^2< 10,000 GeV^2. The rate of (2+1) jet events has been determined with the modified JADE jet algorithm as a function of the jet resolution parameter and is compared with the predictions of Monte Carlo models. In addition, the event rate is corrected for both hadronization and detector effects and is compared with next-to-leading order QCD calculations. A value of the strong coupling constant of alpha_s(M_Z^2)= 0.118+- 0.002 (stat.)^(+0.007)_(-0.008) (syst.)^(+0.007)_(-0.006) (theory) is extracted. The systematic error includes uncertainties in the calorimeter energy calibration, in the description of the data by current Monte Carlo models, and in the knowledge of the parton densities. The theoretical error is dominated by the renormalization scale ambiguity.Comment: 25 pages, 6 figures, 3 tables, submitted to Eur. Phys.

Multiplicity Structure of the Hadronic Final State in Diffractive Deep-Inelastic Scattering at HERA

The multiplicity structure of the hadronic system X produced in deep-inelastic processes at HERA of the type ep -> eXY, where Y is a hadronic system with mass M_Y< 1.6 GeV and where the squared momentum transfer at the pY vertex, t, is limited to |t|<1 GeV^2, is studied as a function of the invariant mass M_X of the system X. Results are presented on multiplicity distributions and multiplicity moments, rapidity spectra and forward-backward correlations in the centre-of-mass system of X. The data are compared to results in e+e- annihilation, fixed-target lepton-nucleon collisions, hadro-produced diffractive final states and to non-diffractive hadron-hadron collisions. The comparison suggests a production mechanism of virtual photon dissociation which involves a mixture of partonic states and a significant gluon content. The data are well described by a model, based on a QCD-Regge analysis of the diffractive structure function, which assumes a large hard gluonic component of the colourless exchange at low Q^2. A model with soft colour interactions is also successful.Comment: 22 pages, 4 figures, submitted to Eur. Phys. J., error in first submission - omitted bibliograph

Low Q^2 Jet Production at HERA and Virtual Photon Structure

The transition between photoproduction and deep-inelastic scattering is investigated in jet production at the HERA ep collider, using data collected by the H1 experiment. Measurements of the differential inclusive jet cross-sections dsigep/dEt* and dsigmep/deta*, where Et* and eta* are the transverse energy and the pseudorapidity of the jets in the virtual photon-proton centre of mass frame, are presented for 0 < Q2 < 49 GeV2 and 0.3 < y < 0.6. The interpretation of the results in terms of the structure of the virtual photon is discussed. The data are best described by QCD calculations which include a partonic structure of the virtual photon that evolves with Q2.Comment: 20 pages, 5 Figure

Hadron Production in Diffractive Deep-Inelastic Scattering

Characteristics of hadron production in diffractive deep-inelastic positron-proton scattering are studied using data collected in 1994 by the H1 experiment at HERA. The following distributions are measured in the centre-of-mass frame of the photon dissociation system: the hadronic energy flow, the Feynman-x (x_F) variable for charged particles, the squared transverse momentum of charged particles (p_T^{*2}), and the mean p_T^{*2} as a function of x_F. These distributions are compared with results in the gamma^* p centre-of-mass frame from inclusive deep-inelastic scattering in the fixed-target experiment EMC, and also with the predictions of several Monte Carlo calculations. The data are consistent with a picture in which the partonic structure of the diffractive exchange is dominated at low Q^2 by hard gluons.Comment: 16 pages, 6 figures, submitted to Phys. Lett.