@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{NivenAbelSchlegeletal.2019, author = {Niven, Robert K. and Abel, Markus and Schlegel, Michael and Waldrip, Steven H.}, title = {Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications}, series = {Entropy}, volume = {21}, journal = {Entropy}, number = {8}, publisher = {MDPI}, address = {Basel}, issn = {1099-4300}, doi = {10.3390/e21080776}, pages = {776}, year = {2019}, abstract = {The concept of a "flow network"-a set of nodes and links which carries one or more flows-unites many different disciplines, including pipe flow, fluid flow, electrical, chemical reaction, ecological, epidemiological, neurological, communications, transportation, financial, economic and human social networks. This Feature Paper presents a generalized maximum entropy framework to infer the state of a flow network, including its flow rates and other properties, in probabilistic form. In this method, the network uncertainty is represented by a joint probability function over its unknowns, subject to all that is known. This gives a relative entropy function which is maximized, subject to the constraints, to determine the most probable or most representative state of the network. The constraints can include "observable" constraints on various parameters, "physical" constraints such as conservation laws and frictional properties, and "graphical" constraints arising from uncertainty in the network structure itself. Since the method is probabilistic, it enables the prediction of network properties when there is insufficient information to obtain a deterministic solution. The derived framework can incorporate nonlinear constraints or nonlinear interdependencies between variables, at the cost of requiring numerical solution. The theoretical foundations of the method are first presented, followed by its application to a variety of flow networks.}, 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} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 8 : Vorlesung 2009-06-25}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @phdthesis{Abel2005, author = {Abel, Markus}, title = {Turbulent flows : transport, analysis and modeling}, address = {Potsdam}, pages = {Getr. Z{\"a}hlung}, year = {2005}, language = {en} } @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{Abel2004, author = {Abel, Markus}, title = {Nonparametric modeling and spatiotemporal dynamical systems}, issn = {0218-1274}, year = {2004}, abstract = {This article describes how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by means of backfitting or more general algorithms, like the alternating conditional expectation value one. The method is illustrated by numerically generated data. As an application, the example of vortex ripple dynamics, a highly complex fluid-granular system, is treated}, language = {en} } @article{AbelCelaniErgnietal.2002, author = {Abel, Markus and Celani, A. and Ergni, V. and Vulpiani, A.}, title = {Front speed enhancement in cellular flows}, issn = {1054-1500}, year = {2002}, language = {en} } @article{AndersenAbelKrugetal.2002, author = {Andersen, K. H. and Abel, Markus and Krug, J. and Ellegaard, L. and Sondergaard, L. R. and Udesen, J.}, title = {Pattern dynamics of vortex ripples in sand : nonlinear modeling and experimental validation}, year = {2002}, abstract = {Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass transport between neighboring ripples is extracted from experimental runs using a recently proposed method for data analysis, and the predictions of the model are compared to the experiment. An analytic explanation of the wavelength selection mechanism in the model is provided, and the width of the stable band of ripples is measured.}, language = {en} } @article{QuadeIseleAbel2020, author = {Quade, Markus and Isele, Thomas and Abel, Markus}, title = {Machine learning control}, series = {Physica : D, Nonlinear phenomena}, volume = {412}, journal = {Physica : D, Nonlinear phenomena}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2020.132582}, pages = {11}, year = {2020}, abstract = {Recently, the term explainable AI came into discussion as an approach to produce models from artificial intelligence which allow interpretation. For a long time, symbolic regression has been used to produce explainable and mathematically tractable models. In this contribution, we extend previous work on symbolic regression methods to infer the optimal control of a dynamical system given one or several optimization criteria, or cost functions. In earlier publications, network control was achieved by automated machine learning control using genetic programming. Here, we focus on the subsequent path continuation analysis of the mathematical expressions which result from the machine learning model. In particular, we use AUTO to analyze the solution properties of the controlled oscillator system which served as our model. As a result, we show that there is a considerable advantage of explainable symbolic regression models over less accessible neural networks. In particular, the roadmap of future works may be to integrate such analyses into the optimization loop itself to filter out robust solutions by construction.}, 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{CestnikAbel2019, author = {Cestnik, Rok and Abel, Markus}, title = {Inferring the dynamics of oscillatory systems using recurrent neural networks}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {29}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {6}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5096918}, pages = {9}, year = {2019}, abstract = {We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor but in its vicinity as well. For this, we consider systems perturbed by an external force. This allows us to not merely predict the time evolution of the system but also study its dynamical properties, such as bifurcations, dynamical response curves, characteristic exponents, etc. It is shown that they can be effectively estimated even in some regions of the state space where no input data were given. We consider several different oscillatory examples, including self-sustained, excitatory, time-delay, and chaotic systems. Furthermore, with a statistical analysis, we assess the amount of training data required for effective inference for two common recurrent neural network cells, the long short-term memory and the gated recurrent unit. Published under license by AIP Publishing.}, 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} } @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{WaldripNivenAbeletal.2017, author = {Waldrip, Steven H. and Niven, Robert K. and Abel, Markus and Schlegel, Michael}, title = {Maximum entropy analysis of transport 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 = {10.1063/1.4985364}, pages = {8}, year = {2017}, abstract = {The maximum entropy method is used to derive an alternative gravity model for a transport network. The proposed method builds on previous methods which assign the discrete value of a maximum entropy distribution to equal the traffic flow rate. The proposed method however, uses a distribution to represent each flow rate. The proposed method is shown to be able to handle uncertainty in a more elegant way and give similar results to traditional methods. It is able to incorporate more of the observed data through the entropy function, prior distribution and integration limits potentially allowing better inferences to be made.}, language = {en} } @article{VossBuennerAbel1998, author = {Voss, Henning U. and B{\"u}nner, M. J. and Abel, Markus}, title = {Identification of continuous, spatiotemporal systems}, year = {1998}, language = {en} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 9 : Vorlesung 2009-07-02}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 7 : Vorlesung 2009-06-18}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 6 : Vorlesung 2009-06-11}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @article{AbelSpicci1998, author = {Abel, Markus and Spicci, M.}, title = {Nonlinear localization periodic solutions in a coupled map lattice}, year = {1998}, abstract = {We prove the existence of nonlinear localized time-periodic solutions in a chain of symplectic mappings with nearest neighbour coupling. This is a class of systems whose behaviour can be seen as representation of a lattice of pendula. The effect of discrete time changes the mathematical as well as the numerical procedures. Applying the discrete version of Floquet theory eases and clarifies the procedure of proving the existence of the localized time-periodic solutions. As an extension of the concept of rotobreathers one can produce solutions which rotate at every site of the lattice. To consider these we use a general definition of localization.}, language = {en} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 10 : Vorlesung 2009-07-09}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @article{AbelStojkovicBreuer2006, author = {Abel, Markus and Stojkovic, Dragan and Breuer, Michael}, title = {Nonlinear stochastic estimation of wall models for LES}, issn = {0142-727X}, doi = {10.1016/j.heatfluidflow.2005.10.011}, year = {2006}, abstract = {A key technology for large eddy simulation (LES) of complex flows is an appropriate wall modeling strategy. In this paper we apply for the first time a fully nonparametric procedure for the estimation of generalized additive models (GAM) by conditional statistics. As a database, we use DNS and wall-resolved LES data of plane channel flow for Reynolds numbers, Re = 2800, 4000 (DNS) and 10,935, 22,776 (LES). The statistical method applied is a quantitative tool for the identification of important model terms, allowing for an identification of some of the near-wall physics. The results are given as nonparametric functions which cannot be attained by other methods. We investigated a generalized model which includes Schumann's and Piomelli et al.'s model. A strong influence of the pressure gradient in the viscous sublayer is found; for larger wall distances the spanwise pressure gradient even dominates the tau(w,zy). component. The first a posteriori LES results are given.}, language = {en} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 2 : Vorlesung 2009-04-23}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 3 : Vorlesung 2009-04-23}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 4 : Vorlesung 2009-04-23}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 5 : Vorlesung 2009-06-04}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 1 : Vorlesung 2009-04-23}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @phdthesis{Abel1998, author = {Abel, Markus}, title = {Localization in driven nonlinear lattices}, address = {Potsdam}, pages = {100 S. : graph. Darst.}, year = {1998}, 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{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} } @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{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{WaldripNivenAbeletal.2016, author = {Waldrip, S. H. and Niven, R. K. and Abel, Markus and Schlegel, M.}, title = {Maximum Entropy Analysis of Hydraulic Pipe Flow Networks}, series = {Journal of hydraulic engineering}, volume = {142}, journal = {Journal of hydraulic engineering}, publisher = {American Society of Civil Engineers}, address = {Reston}, issn = {0733-9429}, doi = {10.1061/(ASCE)HY.1943-7900.0001126}, pages = {332 -- 347}, year = {2016}, language = {en} } @article{QuadeAbelShafietal.2016, author = {Quade, Markus and Abel, Markus and Shafi, Kamran and Niven, Robert K. and Noack, Bernd R.}, title = {Prediction of dynamical systems by symbolic regression}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {94}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Society for Pharmacology and Experimental Therapeutics}, address = {Bethesda}, issn = {2470-0045}, doi = {10.1103/PhysRevE.94.012214}, pages = {15}, year = {2016}, abstract = {We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.}, language = {en} } @article{WinklerAbel2016, author = {Winkler, Michael and Abel, Markus}, title = {Optimized setup for two-dimensional convection experiments in thin liquid films}, series = {Review of scientific instruments : a monthly journal devoted to scientific instruments, apparatus, and techniques}, volume = {87}, journal = {Review of scientific instruments : a monthly journal devoted to scientific instruments, apparatus, and techniques}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0034-6748}, doi = {10.1063/1.4950871}, pages = {11}, year = {2016}, abstract = {We present a novel experimental setup to investigate two-dimensional thermal convection in a freestanding thin liquid film. Such films can be produced in a controlled way on the scale of 5-1000 nm. Our primary goal is to investigate convection patterns and the statistics of reversals in Rayleigh-Benard convection with varying aspect ratio. Additionally, questions regarding the physics of liquid films under controlled conditions can be investigated, like surface forces, or stability under varying thermodynamical parameters. The film is suspended in a frame which can be adjusted in height and width to span an aspect ratio range of Gamma = 0.16-10. The top and bottom frame elements can be set to specific temperature within T = 15 degrees C to 55 degrees C. A thickness to area ratio of approximately 108 enables only two-dimensional fluid motion in the time scales relevant for turbulent motion. The chemical composition of the film is well-defined and optimized for film stability and reproducibility and in combination with carefully controlled ambient parameters allows the comparison to existing experimental and numerical data. Published by AIP Publishing.}, 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} } @article{ParezanovicLaurentieFourmentetal.2015, author = {Parezanovic, Vladimir and Laurentie, Jean-Charles and Fourment, Carine and Delville, Joel and Bonnet, Jean-Paul and Spohn, Andreas and Duriez, Thomas and Cordier, Laurent and Noack, Bernd R. and Abel, Markus and Segond, Marc and Shaqarin, Tamir and Brunton, Steven L.}, title = {Mixing layer manipulation experiment from open-loop forcing to closed-loop machine learning control}, series = {Flow, turbulence and combustion : an international journal published in association with ERCOFTAC}, volume = {94}, journal = {Flow, turbulence and combustion : an international journal published in association with ERCOFTAC}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {1386-6184}, doi = {10.1007/s10494-014-9581-1}, pages = {155 -- 173}, year = {2015}, language = {en} } @article{AbelCelaniVergenietal.2001, author = {Abel, Markus and Celani, A. and Vergeni, D. and Vulpiani, A.}, title = {Front propagation in laminar flows}, year = {2001}, abstract = {The Problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius type are considered under the assumption of no feedback of the concentration on the velocity. Numerical simulations of advection-reaction-diffusion equations have been performed by an algorithm based on discrete-time maps. The results show a generic enhancement of the speed of front propagation by the underlying flow. For small molecular diffusivity, the front speed Vf depends on the typical flow velocity U as a power law with an exponent depending on the topological properties of the flow, and on the ratio of reactive and advective time scales. For open-streamline flows we find always Vf~U, whereas for cellular flows we observe Vf~U1/4 for fast advection and Vf~U3/4 for slow advection.}, 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} } @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} } @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} } @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} } @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{AbelFlachPikovskij1998, author = {Abel, Markus and Flach, S. and Pikovskij, Arkadij}, title = {Localisation in a coupled standard map lattice}, year = {1998}, abstract = {We study spatially localized excitations in a lattice of coupled standard maps. Time-periodic solutions (breathers) exist in a range of coupling that is shown to shrink as the period grows to infinity, thus excluding the possibility of time-quasiperiodic breathers. The evolution of initially localized chaotic and quasiperiodic states in a lattice is studied numerically. Chaos is demonstrated to spread}, language = {en} } @article{AbelFlachPikovskij1998, author = {Abel, Markus and Flach, S. and Pikovskij, Arkadij}, title = {Localization in a coupled standard map lattice}, year = {1998}, language = {en} } @article{AbelPikovskij1997, author = {Abel, Markus and Pikovskij, Arkadij}, title = {Parametric excitation of breathers in a nonlinear lattice}, year = {1997}, abstract = {We investigate localized periodic solutions (breathers) in a lattice of parametrically driven, nonlinear dissipative oscillators. These breathers are demonstrated to be exponentially localized, with two characteristic localization lengths. The crossover between the two lengths is shown to be related to the transition in the phase of the lattice oscillations.}, 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{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} }