@article{AbelAhnertKurthsetal.2005,
  author    = {Abel, Markus and Ahnert, Karsten and Kurths, R. and Mandelj, S.},
  title     = {Additive nonparametric reconstruction of dynamical systems from time series},
  issn      = {1063-651X},
  year      = {2005},
  abstract  = {We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential},
  language  = {en}
}
@article{FischerBaderAbel2016,
  author    = {Fischer, Jost Leonhardt and Bader, Rolf and Abel, Markus},
  title     = {Aeroacoustical coupling and synchronization of organ pipes},
  series = {The journal of the Acoustical Society of America},
  volume    = {140},
  journal   = {The journal of the Acoustical Society of America},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0001-4966},
  doi       = {10.1121/1.4964135},
  pages     = {2344 -- 2351},
  year      = {2016},
  abstract  = {A synchronization experiment on two mutual interacting organ pipes is compared with a theoretical model which takes into account the coupling mechanisms by the underlying first principles of fluid mechanics and aeroacoustics. The focus is on the Arnold-tongue, a mathematical object in the parameter space of detuning and coupling strength which quantitatively captures the interaction of the synchronized sound sources. From the experiment, a nonlinearly shaped Arnold-tongue is obtained, describing the coupling of the synchronized pipe-pipe system. This is in contrast to the linear shaped Arnold-tongue found in a preliminary experiment of the coupled system pipe-loudspeaker. To understand the experimental result, a coarse-grained model of two nonlinear coupled self-sustained oscillators is developed. The model, integrated numerically, is in very good agreement with the synchronization experiment for separation distances of the pipes in the far field and in the intermediate field. The methods introduced open the door for a deeper understanding of the fundamental processes of sound generation and the coupling mechanisms on mutual interacting acoustic oscillators. (C) 2016 Acoustical Society of America.},
  language  = {en}
}
@article{KolodnerAbelKurthsetal.1999,
  author    = {Kolodner, P. and Abel, Markus and Kurths, J{\"u}rgen and Voss, Henning U.},
  title     = {Amplitude equations from spatiotemporal binary-fluid convection data},
  year      = {1999},
  language  = {en}
}
@article{KappelAbelGerhard2011,
  author    = {Kappel, Marcel and Abel, Markus and Gerhard, Reimund},
  title     = {Characterization and calibration of piezoelectric polymers in situ measurements of body vibrations},
  series = {Review of scientific instruments : a monthly journal devoted to scientific instruments, apparatus, and techniques},
  volume    = {82},
  journal   = {Review of scientific instruments : a monthly journal devoted to scientific instruments, apparatus, and techniques},
  number    = {7},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0034-6748},
  doi       = {10.1063/1.3607435},
  pages     = {6},
  year      = {2011},
  abstract  = {Piezoelectric polymers are known for their flexibility in applications, mainly due to their bending ability, robustness, and variable sensor geometry. It is an optimal material for minimal-invasive investigations in vibrational systems, e.g., for wood, where acoustical impedance matches particularly well. Many applications may be imagined, e. g., monitoring of buildings, vehicles, machinery, alarm systems, such that our investigations may have a large impact on technology. Longitudinal piezoelectricity converts mechanical vibrations normal to the polymer-film plane into an electrical signal, and the respective piezoelectric coefficient needs to be carefully determined in dependence on the relevant material parameters. In order to evaluate efficiency and durability for piezopolymers, we use polyvinylidene fluoride and measure the piezoelectric coefficient with respect to static pressure, amplitude of the dynamically applied force, and long-term stability. A known problem is the slow relaxation of the material towards equilibrium, if the external pressure changes; here, we demonstrate how to counter this problem with careful calibration. Since our focus is on acoustical measurements, we determine accurately the frequency response curve - for acoustics probably the most important characteristic. Eventually, we show that our piezopolymer transducers can be used as a calibrated acoustical sensors for body vibration measurements on a wooden musical instrument, where it is important to perform minimal-invasive measurements. A comparison with the simultaneously recorded airborne sound yields important insight of the mechanism of sound radiation in comparison with the sound propagating in the material. This is especially important for transient signals, where not only the long-living eigenmodes contribute to the sound radiation. Our analyses support that piezopolymer sensors can be employed as a general tool for the determination of the internal dynamics of vibrating systems.},
  language  = {en}
}
@article{KaiserNoackCordieretal.2014,
  author    = {Kaiser, Eurika and Noack, Bernd R. and Cordier, Laurent and Spohn, Andreas and Segond, Marc and Abel, Markus and Daviller, Guillaume and Osth, Jan and Krajnovic, Sinisa and Niven, Robert K.},
  title     = {Cluster-based reduced-order modelling of a mixing layer},
  series = {Journal of fluid mechanics},
  volume    = {754},
  journal   = {Journal of fluid mechanics},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {0022-1120},
  doi       = {10.1017/jfm.2014.355},
  pages     = {365 -- 414},
  year      = {2014},
  language  = {en}
}
@misc{KaiserNoackCordieretal.2014,
  author    = {Kaiser, Eurika and Noack, Bernd R. and Cordier, Laurent and Spohn, Andreas and Segond, Marc and Abel, Markus and Daviller, Guillaume and Osth, Jan and Krajnovic, Sinisa and Niven, Robert K.},
  title     = {Cluster-based reduced-order modelling of a mixing layer},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {605},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41611},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416113},
  pages     = {365 -- 414},
  year      = {2014},
  abstract  = {We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt, Gunzburger \& Lee, Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337-355) and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider, Eckhardt \& Vollmer, Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e. g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.},
  language  = {en}
}
@misc{WaldripNivenAbeletal.2017,
  author    = {Waldrip, Steven H. and Niven, Robert K. and Abel, Markus and Schlegel, Michael},
  title     = {Consistent maximum entropy representations of pipe flow networks},
  series = {AIP conference proceedings},
  volume    = {1853},
  journal   = {AIP conference proceedings},
  number    = {1},
  publisher = {American Institute of Physics},
  address   = {Melville},
  isbn      = {978-0-7354-1527-0},
  issn      = {0094-243X},
  doi       = {10.1063/1.4985365},
  year      = {2017},
  abstract  = {The maximum entropy method is used to predict flows on water distribution networks. This analysis extends the water distribution network formulation of Waldrip et al. (2016) Journal of Hydraulic Engineering (ASCE), by the use of a continuous relative entropy defined on a reduced parameter set. This reduction in the parameters that the entropy is defined over ensures consistency between different representations of the same network. The performance of the proposed reduced parameter method is demonstrated with a one-loop network case study.},
  language  = {en}
}
@misc{CestnikAbel2019,
  author    = {Cestnik, Rok and Abel, Markus},
  title     = {Erratum: Inferring the dynamics of oscillatory systems using recurrent neural networks (Chaos : an interdisciplinary journal of nonlinear science. - 29 (2019) 063128)},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {29},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {8},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5122803},
  pages     = {1},
  year      = {2019},
  language  = {en}
}
@article{ParezanovicCordierSpohnetal.2016,
  author    = {Parezanovic, Vladimir and Cordier, Laurent and Spohn, Andreas and Duriez, Thomas and Noack, Bernd R. and Bonnet, Jean-Paul and Segond, Marc and Abel, Markus and Brunton, Steven L.},
  title     = {Frequency selection by feedback control in a turbulent shear flow},
  series = {Journal of fluid mechanics},
  volume    = {797},
  journal   = {Journal of fluid mechanics},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {0022-1120},
  doi       = {10.1017/jfm.2016.261},
  pages     = {247 -- 283},
  year      = {2016},
  abstract  = {Many previous studies have shown that the turbulent mixing layer under periodic forcing tends to adopt a lock-on state, where the major portion of the fluctuations in the flow are synchronized at the forcing frequency. The goal of this experimental study is to apply closed-loop control in order to provoke the lock-on state, using information from the flow itself. We aim to determine the range of frequencies for which the closed-loop control can establish the lock-on, and what mechanisms are contributing to the selection of a feedback frequency. In order to expand the solution space for optimal closed-loop control laws, we use the genetic programming control (CPC) framework. The best closed-loop control laws obtained by CPC are analysed along with the associated physical mechanisms in the mixing layer flow. The resulting closed-loop control significantly outperforms open-loop forcing in terms of robustness to changes in the free-stream velocities. In addition, the selection of feedback frequencies is not locked to the most amplified local mode, but rather a range of frequencies around it.},
  language  = {en}
}
@misc{ParezanovićCordierSpohnetal.2016,
  author    = {Parezanović, Vladimir and Cordier, Laurent and Spohn, Andreas and Duriez, Thomas and Noack, Bernd R. and Bonnet, Jean-Paul and Segond, Marc and Abel, Markus and Brunton, Steven L.},
  title     = {Frequency selection by feedback control in a turbulent shear flow},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {572},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41369},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413693},
  pages     = {37},
  year      = {2016},
  abstract  = {Many previous studies have shown that the turbulent mixing layer under periodic forcing tends to adopt a lock-on state, where the major portion of the fluctuations in the flow are synchronized at the forcing frequency. The goal of this experimental study is to apply closed-loop control in order to provoke the lock-on state, using information from the flow itself. We aim to determine the range of frequencies for which the closed-loop control can establish the lock-on, and what mechanisms are contributing to the selection of a feedback frequency. In order to expand the solution space for optimal closed-loop control laws, we use the genetic programming control (CPC) framework. The best closed-loop control laws obtained by CPC are analysed along with the associated physical mechanisms in the mixing layer flow. The resulting closed-loop control significantly outperforms open-loop forcing in terms of robustness to changes in the free-stream velocities. In addition, the selection of feedback frequencies is not locked to the most amplified local mode, but rather a range of frequencies around it.},
  language  = {en}
}