TY  - GEN
A1  - Cestnik, Rok
A1  - Abel, Markus
T1  - Erratum: Inferring the dynamics of oscillatory systems using recurrent neural networks (Chaos : an interdisciplinary journal of nonlinear science. - 29 (2019) 063128)
T2  - Chaos : an interdisciplinary journal of nonlinear science
Y1  - 2019
U6  - https://doi.org/10.1063/1.5122803
SN  - 1054-1500
SN  - 1089-7682
VL  - 29
IS  - 8
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Niven, Robert K.
A1  - Abel, Markus
A1  - Schlegel, Michael
A1  - Waldrip, Steven H.
T1  - Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications
JF  - Entropy
N2  - 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.
KW  - maximum entropy analysis
KW  - flow network
KW  - probabilistic inference
Y1  - 2019
U6  - https://doi.org/10.3390/e21080776
SN  - 1099-4300
VL  - 21
IS  - 8
SP  - 776
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Sawicki, Jakub
A1  - Abel, Markus
A1  - Schöll, Eckehard
T1  - Synchronization of organ pipes
JF  - The European physical journal : B, Condensed matter and complex systems
N2  - 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.
Y1  - 2018
U6  - https://doi.org/10.1140/epjb/e2017-80485-8
SN  - 1434-6028
SN  - 1434-6036
VL  - 91
IS  - 2
PB  - Springer
CY  - New York
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 8 : Vorlesung 2009-06-25
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=43
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - THES
A1  - Abel, Markus
T1  - Turbulent flows : transport, analysis and modeling
Y1  - 2005
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Ahnert, Karsten
A1  - Kurths, R.
A1  - Mandelj, S.
T1  - Additive nonparametric reconstruction of dynamical systems from time series
N2  - 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
Y1  - 2005
SN  - 1063-651X
ER  - 
TY  - JOUR
A1  - Abel, Markus
T1  - Nonparametric modeling and spatiotemporal dynamical systems
N2  - 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
Y1  - 2004
SN  - 0218-1274
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Celani, A.
A1  - Ergni, V.
A1  - Vulpiani, A.
T1  - Front speed enhancement in cellular flows
Y1  - 2002
SN  - 1054-1500
ER  - 
TY  - JOUR
A1  - Andersen, K. H.
A1  - Abel, Markus
A1  - Krug, J.
A1  - Ellegaard, L.
A1  - Sondergaard, L. R.
A1  - Udesen, J.
T1  - Pattern dynamics of vortex ripples in sand : nonlinear modeling and experimental validation
N2  - 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.
Y1  - 2002
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/
ER  - 
TY  - JOUR
A1  - Quade, Markus
A1  - Isele, Thomas
A1  - Abel, Markus
T1  - Machine learning control
BT  - explainable and analyzable methods
JF  - Physica : D, Nonlinear phenomena
N2  - 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.
KW  - Explainable AI
KW  - Machine learning control
KW  - Dynamical systems
KW  - Synchronization control
KW  - Genetic programming
Y1  - 2020
U6  - https://doi.org/10.1016/j.physd.2020.132582
SN  - 0167-2789
SN  - 1872-8022
VL  - 412
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Quade, Markus
A1  - Abel, Markus
A1  - Kutz, J. Nathan
A1  - Brunton, Steven L.
T1  - Sparse identification of nonlinear dynamics for rapid model recovery
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - 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.
Y1  - 2018
U6  - https://doi.org/10.1063/1.5027470
SN  - 1054-1500
SN  - 1089-7682
VL  - 28
IS  - 6
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Cestnik, Rok
A1  - Abel, Markus
T1  - Inferring the dynamics of oscillatory systems using recurrent neural networks
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - 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.
Y1  - 2019
U6  - https://doi.org/10.1063/1.5096918
SN  - 1054-1500
SN  - 1089-7682
VL  - 29
IS  - 6
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Gout, Julien
A1  - Quade, Markus
A1  - Shafi, Kamran
A1  - Niven, Robert K.
A1  - Abel, Markus
T1  - Synchronization control of oscillator networks using symbolic regression
JF  - Nonlinear Dynamics
N2  - 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.
KW  - Dynamical systems
KW  - Synchronization control
KW  - Genetic programming
Y1  - 2017
U6  - https://doi.org/10.1007/s11071-017-3925-z
SN  - 0924-090X
SN  - 1573-269X
VL  - 91
IS  - 2
SP  - 1001
EP  - 1021
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - GEN
A1  - Waldrip, Steven H.
A1  - Niven, Robert K.
A1  - Abel, Markus
A1  - Schlegel, Michael
T1  - Consistent maximum entropy representations of pipe flow networks
T2  - AIP conference proceedings
N2  - 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.
Y1  - 2017
SN  - 978-0-7354-1527-0
U6  - https://doi.org/10.1063/1.4985365
SN  - 0094-243X
VL  - 1853
IS  - 1
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - GEN
A1  - Waldrip, Steven H.
A1  - Niven, Robert K.
A1  - Abel, Markus
A1  - Schlegel, Michael
T1  - Maximum entropy analysis of transport networks
T2  - AIP conference proceedings
N2  - 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.
Y1  - 2017
SN  - 978-0-7354-1527-0
U6  - https://doi.org/10.1063/1.4985364
SN  - 0094-243X
VL  - 1853
IS  - 1
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Voss, Henning U.
A1  - Bünner, M. J.
A1  - Abel, Markus
T1  - Identification of continuous, spatiotemporal systems
Y1  - 1998
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/PRE57-2820.pdf
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 9 : Vorlesung 2009-07-02
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=44
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 7 : Vorlesung 2009-06-18
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=42
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 6 : Vorlesung 2009-06-11
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=41
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Spicci, M.
T1  - Nonlinear localization periodic solutions in a coupled map lattice
N2  - 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.
Y1  - 1998
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/PhD119-22.ps.gz
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 10 : Vorlesung 2009-07-09
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=45
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Stojkovic, Dragan
A1  - Breuer, Michael
T1  - Nonlinear stochastic estimation of wall models for LES
N2  - 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.
Y1  - 2006
UR  - http://www.sciencedirect.com/science/journal/0142727X
U6  - https://doi.org/10.1016/j.heatfluidflow.2005.10.011
SN  - 0142-727X
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 2 : Vorlesung 2009-04-23
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=33#32
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 3 : Vorlesung 2009-04-23
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=33#33
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 4 : Vorlesung 2009-04-23
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=33#34
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 5 : Vorlesung 2009-06-04
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=33#36
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Abel, Markus
A1  - Holschneider, Matthias
T1  - Modellierung und Datenbankanalyse komplexer Systeme Teil 1 : Vorlesung 2009-04-23
N2  - 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 Ökonomie findet. Die Ausbildung von Verständnis 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 Komplexität auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und eingeübt. Auf der methodischen Seite werden lineare und nichtlineare Ansätze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Schätzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexitätsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexität durch Wechselwirkung diskutiert - sowohl für diskrete als auch für ausgedehnte Systeme. Die beiden Ansätze werden durch Systemanalyse jeweils passender Beispiele vereint.
Y1  - 2009
UR  - http://info.ub.uni-potsdam.de/multimedia/show_projekt.php?projekt_id=33#31
PB  - Univ.-Bibl.
CY  - Potsdam
ER  - 
TY  - THES
A1  - Abel, Markus
T1  - Localization in driven nonlinear lattices
Y1  - 1998
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Stefanakis, Nikolaos
A1  - Abel, Markus
A1  - Bergner, Andre
T1  - Sound Synthesis Based on Ordinary Differential Equations
JF  - Computer music journal
N2  - 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.
Y1  - 2015
U6  - https://doi.org/10.1162/COMJ_a_00314
SN  - 0148-9267
SN  - 1531-5169
VL  - 39
IS  - 3
SP  - 46
EP  - 58
PB  - MIT Press
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Ahnert, Karsten
A1  - Abel, Markus
A1  - Kollosche, Matthias
A1  - Jorgensen, Per Jorgen
A1  - Kofod, Guggi
T1  - Soft capacitors for wave energy harvesting
JF  - Journal of materials chemistry
N2  - 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.
Y1  - 2011
U6  - https://doi.org/10.1039/c1jm12454d
SN  - 0959-9428
SN  - 1364-5501
VL  - 21
IS  - 38
SP  - 14492
EP  - 14497
PB  - Royal Society of Chemistry
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Kaiser, Eurika
A1  - Noack, Bernd R.
A1  - Cordier, Laurent
A1  - Spohn, Andreas
A1  - Segond, Marc
A1  - Abel, Markus
A1  - Daviller, Guillaume
A1  - Osth, Jan
A1  - Krajnovic, Sinisa
A1  - Niven, Robert K.
T1  - Cluster-based reduced-order modelling of a mixing layer
JF  - Journal of fluid mechanics
KW  - low-dimensional models
KW  - nonlinear dynamical systems
KW  - shear layers
Y1  - 2014
U6  - https://doi.org/10.1017/jfm.2014.355
SN  - 0022-1120
SN  - 1469-7645
VL  - 754
SP  - 365
EP  - 414
PB  - Cambridge Univ. Press
CY  - New York
ER  - 
TY  - JOUR
A1  - Winkler, Michael
A1  - Abel, Markus
T1  - Small- and large-scale characterization and mixing properties in a thermally driven thin liquid film
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - 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.
Y1  - 2015
U6  - https://doi.org/10.1103/PhysRevE.92.063002
SN  - 1539-3755
SN  - 1550-2376
VL  - 92
IS  - 6
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Fischer, Jost Leonhardt
A1  - Bader, Rolf
A1  - Abel, Markus
T1  - Aeroacoustical coupling and synchronization of organ pipes
JF  - The journal of the Acoustical Society of America
N2  - 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.
Y1  - 2016
U6  - https://doi.org/10.1121/1.4964135
SN  - 0001-4966
SN  - 1520-8524
VL  - 140
SP  - 2344
EP  - 2351
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Waldrip, S. H.
A1  - Niven, R. K.
A1  - Abel, Markus
A1  - Schlegel, M.
T1  - Maximum Entropy Analysis of Hydraulic Pipe Flow Networks
JF  - Journal of hydraulic engineering
KW  - Maximum entropy method
KW  - Water distribution systems
KW  - Hydraulic networks
KW  - Pipe networks
KW  - Hydraulic models
KW  - Non-linear analysis
KW  - Probability
Y1  - 2016
U6  - https://doi.org/10.1061/(ASCE)HY.1943-7900.0001126
SN  - 0733-9429
SN  - 1943-7900
VL  - 142
SP  - 332
EP  - 347
PB  - American Society of Civil Engineers
CY  - Reston
ER  - 
TY  - JOUR
A1  - Quade, Markus
A1  - Abel, Markus
A1  - Shafi, Kamran
A1  - Niven, Robert K.
A1  - Noack, Bernd R.
T1  - Prediction of dynamical systems by symbolic regression
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - 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.
Y1  - 2016
U6  - https://doi.org/10.1103/PhysRevE.94.012214
SN  - 2470-0045
SN  - 2470-0053
VL  - 94
PB  - American Society for Pharmacology and Experimental Therapeutics
CY  - Bethesda
ER  - 
TY  - JOUR
A1  - Winkler, Michael
A1  - Abel, Markus
T1  - Optimized setup for two-dimensional convection experiments in thin liquid films
JF  - Review of scientific instruments : a monthly journal devoted to scientific instruments, apparatus, and techniques
N2  - 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.
Y1  - 2016
U6  - https://doi.org/10.1063/1.4950871
SN  - 0034-6748
SN  - 1089-7623
VL  - 87
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Parezanovic, Vladimir
A1  - Cordier, Laurent
A1  - Spohn, Andreas
A1  - Duriez, Thomas
A1  - Noack, Bernd R.
A1  - Bonnet, Jean-Paul
A1  - Segond, Marc
A1  - Abel, Markus
A1  - Brunton, Steven L.
T1  - Frequency selection by feedback control in a turbulent shear flow
JF  - Journal of fluid mechanics
N2  - 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.
KW  - free shear layers
KW  - instability control
KW  - turbulence control
Y1  - 2016
U6  - https://doi.org/10.1017/jfm.2016.261
SN  - 0022-1120
SN  - 1469-7645
VL  - 797
SP  - 247
EP  - 283
PB  - Cambridge Univ. Press
CY  - New York
ER  - 
TY  - JOUR
A1  - Parezanovic, Vladimir
A1  - Laurentie, Jean-Charles
A1  - Fourment, Carine
A1  - Delville, Joel
A1  - Bonnet, Jean-Paul
A1  - Spohn, Andreas
A1  - Duriez, Thomas
A1  - Cordier, Laurent
A1  - Noack, Bernd R.
A1  - Abel, Markus
A1  - Segond, Marc
A1  - Shaqarin, Tamir
A1  - Brunton, Steven L.
T1  - Mixing layer manipulation experiment from open-loop forcing to closed-loop machine learning control
JF  - Flow, turbulence and combustion : an international journal published in association with ERCOFTAC
KW  - Shear flow
KW  - Turbulence
KW  - Active flow control
KW  - Extremum seeking
KW  - POD
KW  - Machine learning
KW  - Genetic programming
Y1  - 2015
U6  - https://doi.org/10.1007/s10494-014-9581-1
SN  - 1386-6184
SN  - 1573-1987
VL  - 94
IS  - 1
SP  - 155
EP  - 173
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Celani, A.
A1  - Vergeni, D.
A1  - Vulpiani, A.
T1  - Front propagation in laminar flows
N2  - 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 <i>V<sub><i>f</sub> depends on the typical flow velocity <i>U as<sup> </sup>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<sup> </sup><i>V<sub><i>f</sub>~<i>U, whereas for cellular flows we observe <i>V<sub><i>f</ sub>~<i>U<sup>1/4</sup> for fast advection and <i>V<sub><i>f</sub>~<i>U<sup>3/4</sup> for slow advection.
Y1  - 2001
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/PRE64-46307-1.pdf
ER  - 
TY  - JOUR
A1  - Kolodner, P.
A1  - Abel, Markus
A1  - Kurths, Jürgen
A1  - Voss, Henning U.
T1  - Amplitude equations from spatiotemporal binary-fluid convection data
Y1  - 1999
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/PRL83-3422.pdf
ER  - 
TY  - GEN
A1  - Parezanović, Vladimir
A1  - Cordier, Laurent
A1  - Spohn, Andreas
A1  - Duriez, Thomas
A1  - Noack, Bernd R.
A1  - Bonnet, Jean-Paul
A1  - Segond, Marc
A1  - Abel, Markus
A1  - Brunton, Steven L.
T1  - Frequency selection by feedback control in a turbulent shear flow
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 572 
KW  - free shear layers
KW  - instability control
KW  - turbulence control
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413693
SN  - 1866-8372
IS  - 572
ER  - 
TY  - GEN
A1  - Kaiser, Eurika
A1  - Noack, Bernd R.
A1  - Cordier, Laurent
A1  - Spohn, Andreas
A1  - Segond, Marc
A1  - Abel, Markus
A1  - Daviller, Guillaume
A1  - Osth, Jan
A1  - Krajnovic, Sinisa
A1  - Niven, Robert K.
T1  - Cluster-based reduced-order modelling of a mixing layer
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - 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.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 605 
KW  - low-dimensional models
KW  - nonlinear dynamical systems
KW  - shear layers
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-416113
SN  - 1866-8372
IS  - 605
SP  - 365
EP  - 414
ER  - 
TY  - JOUR
A1  - Waldrip, S. H.
A1  - Niven, Robert K.
A1  - Abel, Markus
A1  - Schlegel, M.
T1  - Reduced-Parameter Method for Maximum Entropy Analysis of Hydraulic Pipe Flow Networks
JF  - Journal of hydraulic engineering
N2  - 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.
KW  - Maximum entropy method
KW  - Water distribution systems
KW  - Hydraulic networks
KW  - Pipe networks
KW  - Hydraulic models
KW  - Nonlinear analysis
KW  - Probability
Y1  - 2017
U6  - https://doi.org/10.1061/(ASCE)HY.1943-7900.0001379
SN  - 0733-9429
SN  - 1943-7900
VL  - 144
IS  - 2
PB  - American Society of Civil Engineers
CY  - Reston
ER  - 
TY  - JOUR
A1  - Straube, Arthur V.
A1  - Abel, Markus
A1  - Pikovskij, Arkadij
T1  - Temporal chaos versus spatial mixing in reaction-advection-diffusion systems
N2  - 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
Y1  - 2004
SN  - 0031-9007
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Flach, S.
A1  - Pikovskij, Arkadij
T1  - Localisation in a coupled standard map lattice
N2  - 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
Y1  - 1998
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/PhD119-4.ps.gz
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Flach, S.
A1  - Pikovskij, Arkadij
T1  - Localization in a coupled standard map lattice
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Pikovskij, Arkadij
T1  - Parametric excitation of breathers in a nonlinear lattice
N2  - 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.
Y1  - 1997
UR  - http://www.stat.physik.uni-potsdam.de/~markus/papers/par.ps.gz
ER  - 
TY  - JOUR
A1  - Abel, Markus
A1  - Bergweiler, Steffen
A1  - Gerhard, Reimund
T1  - Synchronization of organ pipes : experimental observations and modeling
N2  - 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.
Y1  - 2006
UR  - http://scitation.aip.org/jasa/
U6  - https://doi.org/10.1121/1.217044
SN  - 0001-4966
ER  - 
TY  - JOUR
A1  - Kappel, Marcel
A1  - Abel, Markus
A1  - Gerhard, Reimund
T1  - Characterization and calibration of piezoelectric polymers in situ measurements of body vibrations
JF  - Review of scientific instruments : a monthly journal devoted to scientific instruments, apparatus, and techniques
N2  - 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.
KW  - acoustic transducers
KW  - calibration
KW  - durability
KW  - electric sensing devices
KW  - piezoelectricity
KW  - polymers
Y1  - 2011
U6  - https://doi.org/10.1063/1.3607435
SN  - 0034-6748
VL  - 82
IS  - 7
PB  - American Institute of Physics
CY  - Melville
ER  -