@phdthesis{Abel2005,
  author    = {Abel, Markus},
  title     = {Turbulent flows : transport, analysis and modeling},
  address   = {Potsdam},
  pages     = {Getr. Z{\"a}hlung},
  year      = {2005},
  language  = {en}
}
@article{StraubeAbelPikovskij2004,
  author    = {Straube, Arthur V. and Abel, Markus and Pikovskij, Arkadij},
  title     = {Temporal chaos versus spatial mixing in reaction-advection-diffusion systems},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time- independent flows and equal Peclet numbers of different components, is demonstrated to work accurately for time- dependent flows and different Peclet numbers},
  language  = {en}
}
@article{AbelBergweilerGerhard2006,
  author    = {Abel, Markus and Bergweiler, Steffen and Gerhard, Reimund},
  title     = {Synchronization of organ pipes : experimental observations and modeling},
  issn      = {0001-4966},
  doi       = {10.1121/1.217044},
  year      = {2006},
  abstract  = {We report measurements on the synchronization properties of organ pipes. First, we investigate influence of an external acoustical signal from a loudspeaker on the sound of an organ pipe. Second, the mutual influence of two pipes with different pitch is analyzed. In analogy to the externally driven, or mutually coupled self-sustained oscillators, one observes a frequency locking, which can be explained by synchronization theory. Further, we measure the dependence of the frequency of the signals emitted by two mutually detuned pipes with varying distance between the pipes. The spectrum shows a broad '' hump '' structure, not found for coupled oscillators. This indicates a complex coupling of the two organ pipes leading to nonlinear beat phenomena.},
  language  = {en}
}
@article{SawickiAbelSchoell2018,
  author    = {Sawicki, Jakub and Abel, Markus and Sch{\"o}ll, Eckehard},
  title     = {Synchronization of organ pipes},
  series = {The European physical journal : B, Condensed matter and complex systems},
  volume    = {91},
  journal   = {The European physical journal : B, Condensed matter and complex systems},
  number    = {2},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2017-80485-8},
  pages     = {9},
  year      = {2018},
  abstract  = {We investigate synchronization of coupled organ pipes. Synchronization and reflection in the organ lead to undesired weakening of the sound in special cases. Recent experiments have shown that sound interaction is highly complex and nonlinear, however, we show that two delay-coupled Van-der-Pol oscillators appear to be a good model for the occurring dynamical phenomena. Here the coupling is realized as distance-dependent, or time-delayed, equivalently. Analytically, we investigate the synchronization frequency and bifurcation scenarios which occur at the boundaries of the Arnold tongues. We successfully compare our results to experimental data.},
  language  = {en}
}
@article{GoutQuadeShafietal.2017,
  author    = {Gout, Julien and Quade, Markus and Shafi, Kamran and Niven, Robert K. and Abel, Markus},
  title     = {Synchronization control of oscillator networks using symbolic regression},
  series = {Nonlinear Dynamics},
  volume    = {91},
  journal   = {Nonlinear Dynamics},
  number    = {2},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0924-090X},
  doi       = {10.1007/s11071-017-3925-z},
  pages     = {1001 -- 1021},
  year      = {2017},
  abstract  = {Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far-reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice versa. The genetic programming-based controller allows learning optimal control functions in an interpretable symbolic form. The effectiveness of the proposed approach is demonstrated in controlling synchronization in coupled oscillator systems linked in networks of increasing order complexity, ranging from a simple coupled oscillator system to a hierarchical network of coupled oscillators. The results show that the proposed method can learn highly effective and interpretable control functions for such systems.},
  language  = {en}
}
@article{QuadeAbelKutzetal.2018,
  author    = {Quade, Markus and Abel, Markus and Kutz, J. Nathan and Brunton, Steven L.},
  title     = {Sparse identification of nonlinear dynamics for rapid model recovery},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {28},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {6},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5027470},
  pages     = {10},
  year      = {2018},
  abstract  = {Big data have become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt changes must be rapidly characterized based on limited, incomplete, and noisy data. Many leading automated learning techniques rely on unrealistically large data sets, and it is unclear how to leverage prior knowledge effectively to re-identify a model after an abrupt change. In this work, we propose a conceptual framework to recover parsimonious models of a system in response to abrupt changes in the low-data limit. First, the abrupt change is detected by comparing the estimated Lyapunov time of the data with the model prediction. Next, we apply the sparse identification of nonlinear dynamics (SINDy) regression to update a previously identified model with the fewest changes, either by addition, deletion, or modification of existing model terms. We demonstrate this sparse model recovery on several examples for abrupt system change detection in periodic and chaotic dynamical systems. Our examples show that sparse updates to a previously identified model perform better with less data, have lower runtime complexity, and are less sensitive to noise than identifying an entirely new model. The proposed abrupt-SINDy architecture provides a new paradigm for the rapid and efficient recovery of a system model after abrupt changes.},
  language  = {en}
}
@article{StefanakisAbelBergner2015,
  author    = {Stefanakis, Nikolaos and Abel, Markus and Bergner, Andre},
  title     = {Sound Synthesis Based on Ordinary Differential Equations},
  series = {Computer music journal},
  volume    = {39},
  journal   = {Computer music journal},
  number    = {3},
  publisher = {MIT Press},
  address   = {Cambridge},
  issn      = {0148-9267},
  doi       = {10.1162/COMJ_a_00314},
  pages     = {46 -- 58},
  year      = {2015},
  abstract  = {Ordinary differential equations (ODEs) have been studied for centuries as a means to model complex dynamical processes from the real world. Nevertheless, their application to sound synthesis has not yet been fully exploited. In this article we present a systematic approach to sound synthesis based on first-order complex and real ODEs. Using simple time-dependent and nonlinear terms, we illustrate the mapping between ODE coefficients and physically meaningful control parameters such as pitch, pitch bend, decay rate, and attack time. We reveal the connection between nonlinear coupling terms and frequency modulation, and we discuss the implications of this scheme in connection with nonlinear synthesis. The ability to excite a first-order complex ODE with an external input signal is also examined; stochastic or impulsive signals that are physically or synthetically produced can be presented as input to the system, offering additional synthesis possibilities, such as those found in excitation/filter synthesis and filter-based modal synthesis.},
  language  = {en}
}
@article{AhnertAbelKolloscheetal.2011,
  author    = {Ahnert, Karsten and Abel, Markus and Kollosche, Matthias and Jorgensen, Per Jorgen and Kofod, Guggi},
  title     = {Soft capacitors for wave energy harvesting},
  series = {Journal of materials chemistry},
  volume    = {21},
  journal   = {Journal of materials chemistry},
  number    = {38},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {0959-9428},
  doi       = {10.1039/c1jm12454d},
  pages     = {14492 -- 14497},
  year      = {2011},
  abstract  = {Wave energy harvesting could be a substantial renewable energy source without impact on the global climate and ecology, yet practical attempts have struggled with the problems of wear and catastrophic failure. An innovative technology for ocean wave energy harvesting was recently proposed, based on the use of soft capacitors. This study presents a realistic theoretical and numerical model for the quantitative characterization of this harvesting method. Parameter regions with optimal behavior are found, and novel material descriptors are determined, which dramatically simplify analysis. The characteristics of currently available materials are evaluated, and found to merit a very conservative estimate of 10 years for raw material cost recovery.},
  language  = {en}
}
@article{WinklerAbel2015,
  author    = {Winkler, Michael and Abel, Markus},
  title     = {Small- and large-scale characterization and mixing properties in a thermally driven thin liquid film},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {92},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {6},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.92.063002},
  pages     = {10},
  year      = {2015},
  abstract  = {We study aqueous, freestanding, thin films stabilized by a surfactant with respect to mixing and dynamical systems properties. With this special setup, a two-dimensional fluid can be realized experimentally. The physics of the system involves a complex interplay of thermal convection and interface and gravitational forces. Methodologically, we characterize the system using two classical dynamical systems properties: Lyapunov exponents and entropies. Our experimental setup produces convection with two stable eddies by applying a temperature gradient in one spot that yields weakly turbulent mixing. From dynamical systems theory, one expects a relation of entropies, Lyapunov exponents, a prediction with little experimental support. We can confirm the corresponding statements experimentally, on different scales using different methods. On the small scale the motion and deformation of fluid filaments of equal size (color imaging velocimetry) are used to compute Lyapunov exponents. On the large scale, entropy is computed by tracking the left-right motion of the center fluid jet at the separatrix between the two convection rolls. We thus combine here dynamical systems methods with a concrete application of mixing in a nanoscale freestanding thin film.},
  language  = {en}
}
@article{WaldripNivenAbeletal.2017,
  author    = {Waldrip, S. H. and Niven, Robert K. and Abel, Markus and Schlegel, M.},
  title     = {Reduced-Parameter Method for Maximum Entropy Analysis of Hydraulic Pipe Flow Networks},
  series = {Journal of hydraulic engineering},
  volume    = {144},
  journal   = {Journal of hydraulic engineering},
  number    = {2},
  publisher = {American Society of Civil Engineers},
  address   = {Reston},
  issn      = {0733-9429},
  doi       = {10.1061/(ASCE)HY.1943-7900.0001379},
  pages     = {10},
  year      = {2017},
  abstract  = {A maximum entropy (MaxEnt) method is developed to predict flow rates or pressure gradients in hydraulic pipe networks without sufficient information to give a closed-form (deterministic) solution. This methodology substantially extends existing deterministic flow network analysis methods. It builds on the MaxEnt framework previously developed by the authors. This study uses a continuous relative entropy defined on a reduced parameter set, here based on the external flow rates. This formulation ensures consistency between different representations of the same network. The relative entropy is maximized subject to observable constraints on the mean values of a subset of flow rates or potential differences, the frictional properties of each pipe, and physical constraints arising from Kirchhoff's first and second laws. The new method is demonstrated by application to a simple one-loop network and a 1,123-node, 1,140-pipe water distribution network in the suburb of Torrens, Australian Capital Territory, Australia.},
  language  = {en}
}