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-

Degenerate perturbation theory in thermoacoustics: High-order sensitivities and exceptional points

In this study, we connect concepts that have been recently developed in thermoacoustics, specifically, (i) high-order spectral perturbation theory, (ii) symmetry induced degenerate thermoacoustic modes, (iii) intrinsic thermoacoustic modes, and (iv) exceptional points. Their connection helps gain physical insight into the behaviour of the thermoacoustic spectrum when parameters of the system are varied. First, we extend high-order adjoint-based perturbation theory of thermoacoustic modes to the degenerate case. We provide explicit formulae for the calculation of the eigenvalue corrections to any order. These formulae are valid for self-adjoint, non-self-adjoint or even non-normal systems; therefore, they can be applied to a large range of problems, including fluid dynamics. Second, by analysing the expansion coefficients of the eigenvalue corrections as a function of a parameter of interest, we accurately estimate the radius of convergence of the power series. Third, we connect the existence of a finite radius of convergence to the existence of singularities in parameter space. We identify these singularities as exceptional points, which correspond to defective thermoacoustic eigenvalues, with infinite sensitivity to infinitesimal changes in the parameters. At an exceptional point, two eigenvalues and their associated eigenvectors coalesce. Close to an exceptional point, strong veering of the eigenvalue trajectories is observed. As demonstrated in recent work, exceptional points naturally arise in thermoacoustic systems due to the interaction between modes of acoustic and intrinsic origin. The role of exceptional points in thermoacoustic systems sheds new light on the physics and sensitivity of thermoacoustic stability, which can be leveraged for passive control by small design modifications

Methods for the calculation of thermoacoustic stability margins and monte carlo-free uncertainty quantification

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible CFD computations. Frequency-domain approaches result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Nonlinear functions of the frequency are, for example, the n–τ model, impedance boundary conditions, etc. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, which are obtained by experiments with some uncertainty, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. It quantifies the uncertainty of a set of parameters in terms of the probability of a mode to become unstable. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters etc. Assessing also the influence of all possible combinations of these parameters on the risk factor is a numerically very costly task. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the eigenfrequency problem is using adjoint perturbation theory. Though adjoint perturbation methods were recently applied to accelerate the risk factor analysis, its potential to improve the theory has not yet been fully exploited. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental validation is available.</jats:p

Exceptional points in the thermoacoustic spectrum

Exceptional points are found in the spectrum of a prototypical thermoacoustic system as the parameters of the flame transfer function are varied. At these points, two eigenvalues and the associated eigenfunctions coalesce. The system's sensitivity to changes in the parameters becomes infinite. Two eigenvalue branches collide at the exceptional point as the interaction index is increased. One branch originates from a purely acoustic mode, whereas the other branch originates from an intrinsic thermoacoustic mode. The existence of exceptional points in thermoacoustic systems has implications for physical understanding, computing, modeling and control

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

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

Search for Supersymmetry with Gauge-Mediated Breaking in Diphoton Events with Missing Transverse Energy at CDF II

accepted to Phys. Rev. LettWe present the results of a search for supersymmetry with gauge-mediated breaking and \NONE\to\gamma\Gravitino in the $\gamma\gamma$+missing transverse energy final state. In 2.6$\pm$0.2 \invfb of $p{\bar p}$ collisions at $\sqrt{s}$$=$1.96 TeV recorded by the CDF II detector we observe no candidate events, consistent with a standard model background expectation of 1.4$\pm$0.4 events. We set limits on the cross section at the 95% C.L. and place the world's best limit of 149\gevc on the \none mass at $\tau_{\tilde{\chi}_1^0}$$We present the results of a search for supersymmetry with gauge-mediated breaking and χ˜10→γG˜ in the γγ+missing transverse energy final state. In 2.6±0.2  fb-1 of pp̅ collisions at √s=1.96  TeV recorded by the CDF II detector we observe no candidate events, consistent with a standard model background expectation of 1.4±0.4 events. We set limits on the cross section at the 95% C.L. and place the world’s best limit of 149  GeV/c2 on the χ˜10 mass at τχ˜10≪1  ns. We also exclude regions in the χ˜10 mass-lifetime plane for τχ˜10≲2  ns.Peer reviewe

Measurements of branching fraction ratios and CP asymmetries in B+/- ->D_CP K+/- decays in hadron collisions

We reconstruct B+/- -> D K+/- decays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to 1 fb-1 of integrated luminosity. We select decay modes where the D meson decays to either K- pi+ (flavor eigenstate) or K- K+, pi- pi+ (CP-even eigenstates), and measure the direct CP asymmetry A_CP+ = 0.39 +/- 0.17(stat) +/- 0.04(syst), and the double ratio of CP-even to flavor eigenstate branching fractions R_CP+ = 1.30 +/- 0.24(stat) +/- 0.12(syst). These measurements will improve the determination of the CKM angle gamma. They are performed here for the first time using data from hadron collisions.We reconstruct B±→DK± decays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to 1  fb-1 of integrated luminosity. We select decay modes where the D meson decays to either K-π+ (flavor eigenstate) or K-K+, π-π+ (CP-even eigenstates), and measure the direct CP asymmetry ACP+=0.39±0.17(stat)±0.04(syst), and the double ratio of CP-even to flavor eigenstate branching fractions RCP+=1.30±0.24(stat)±0.12(syst). These measurements will improve the determination of the Cabibbo-Kobayashi-Maskawa angle γ. They are performed here for the first time using data from hadron collisions.Peer reviewe

Measurement of the cross-section for b-jets produced in association with a Z boson at root s=7 TeV with the ATLAS detector ATLAS Collaboration

A measurement is presented of the inclusive cross-section for b-jet production in association with a Z boson in pp collisions at a centre-of-mass energy of root s = 7 TeV. The analysis uses the data sample collected by the ATLAS experiment in 2010, corresponding to an integrated luminosity of approximately 36 pb(-1). The event selection requires a Z boson decaying into high P-T electrons or muons, and at least one b-jet, identified by its displaced vertex, with transverse momentum p(T) > 25 GeV and rapidity vertical bar y vertical bar < 2.1. After subtraction of background processes, the yield is extracted from the vertex mass distribution of the candidate b-jets. The ratio of this cross-section to the inclusive Z cross-section (the average number of b-jets per Z event) is also measured. Both results are found to be in good agreement with perturbative QCD predictions at next-to-leading order

Inclusive Search for Standard Model Higgs Boson Production in the WW Decay Channel using the CDF II Detector

We present a search for standard model (SM) Higgs boson production using ppbar collision data at sqrt(s) = 1.96 TeV, collected with the CDF II detector and corresponding to an integrated luminosity of 4.8 fb-1. We search for Higgs bosons produced in all processes with a significant production rate and decaying to two W bosons. We find no evidence for SM Higgs boson production and place upper limits at the 95% confidence level on the SM production cross section (sigma(H)) for values of the Higgs boson mass (m_H) in the range from 110 to 200 GeV. These limits are the most stringent for m_H > 130 GeV and are 1.29 above the predicted value of sigma(H) for mH = 165 GeV.We present a search for standard model (SM) Higgs boson production using pp̅ collision data at √s=1.96  TeV, collected with the CDF II detector and corresponding to an integrated luminosity of 4.8  fb-1. We search for Higgs bosons produced in all processes with a significant production rate and decaying to two W bosons. We find no evidence for SM Higgs boson production and place upper limits at the 95% confidence level on the SM production cross section (σH) for values of the Higgs boson mass (mH) in the range from 110 to 200 GeV. These limits are the most stringent for mH>130  GeV and are 1.29 above the predicted value of σH for mH=165  GeV.Peer reviewe