Markus Abel

Open- and closed-loop control of a turbulent mixing layer is experimentally performed in a dedicated large scale, low speed wind-tunnel facility. The flow is manipulated by an array of fluidic micro-valve actuators integrated into the trailing edge of a splitter plate. Sensing is performed using a rake of hot-wire probes downstream of the splitter...

Open-and closed-loop control of a turbulent mixing layer is experimentally performed in a dedicated large scale, low speed wind-tunnel facility. The flow is manipulated by an array of fluidic micro-valve actuators integrated into the trailing edge of a splitter plate. Sensing is performed using a rake of hot-wire probes downstream of the splitter p...

We present the first closed-loop separation control experiment using a novel, model-free strategy based on genetic programming, which we call ‘machine learning control’. The goal is to reduce the recirculation zone of backward-facing step flow at $\mathit{Re}_{h}=1350$ manipulated by a slotted jet and optically sensed by online particle image vel...

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM builds on the pioneering works of Gunzburger's group in cluster analysis (Burkardt et al. 2006) and Eckhardt's group in transition matrix models (Schneider et al. 2007) and constitutes a potential alternative to POD models. This strategy processes a tim...

This study presents a Bayesian maximum a posteriori (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likeliho...

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 opti...

Many inference problems relate to a dynamical system, as represented by d x / d t = f ( x ) , where x ∈ R n is the state vector and f is the (in general nonlinear) system function or model. Since the time of Newton, researchers have pondered the problem of system identification: how should the user accurately and efficiently identify the model f –...

Recently, the term explainable AI became known as an approach to produce models from artificial intelligence which allow interpretation. Since a long time, there are models of symbolic regression in use that are perfectly explainable and mathematically tractable: in this contribution we demonstrate how to use symbolic regression methods to infer th...

The dynamics of an organ pipe's mouth region has been studied by numerical simulations. The investigations presented here were carried out by solving the compressible Navier-Stokes equations under suitable initial and boundary conditions using parts of the open source C++ toolbox OpenFOAM. The focus of the study is on the examination of the velocit...

Over the past century, hydrologists have developed sophisticated methods for the correlation and prediction of streamflow from rainfall data, including protocols for hyetograph and hydrograph separation, and deconvolu-tion to determine the unit hydrograph. Very recently, some researchers have advocated an alternative approach in which the hydrologi...

Recently, many researchers have developed sparse regression methods for the identification of a dynamical system from its time-series data. We demonstrate that these methods fall within the framework of Bayesian inverse methods. Indeed, the Bayesian maximum a posteriori method, using Gaussian likelihood and prior functions, is equivalent to Tikhono...

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 generalize...

Recently, many researchers have developed sparse regression methods for the identification of a dynamical system from its time-series data. We demonstrate that these methods fall within the framework of Bayesian inverse methods. Indeed, the Bayesian maximum a posteriori method, using Gaussian likelihood and prior functions, is equivalent to Tikhono...

We present Glyph – a Python package for genetic programming based symbolic regression. Glyph is designed for usage in numerical simulations as well as real world experiments. For experimentalists, glyph-remote provides a separation of tasks: a ZeroMQ interface splits the genetic programming optimization task from the evaluation of an experimental (...

This study examines MaxEnt methods for probabilistic inference of the state of flow networks, including pipe flow, electrical and transport networks, subject to physical laws and observed moments. While these typically assume networks of invariant graph structure, we here consider higher-level MaxEnt schemes, in which the network structure constitu...

We present Glyph - a Python package for genetic programming based symbolic regression. Glyph is designed for usage let by numerical simulations let by real world experiments. For experimentalists, glyph-remote provides a separation of tasks: a ZeroMQ interface splits the genetic programming optimization task from the evaluation of an experimental (...

Big data has 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 learni...

Big data has 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 learni...

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 th...

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...

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 occurrin...

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 occurrin...

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 de...

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...

Using a 128 microphone array, the sound source distribution of musical wind instruments from their blowing and finger holes are measured. The Japanese \emph{shakuhachi} flute, the Chinese \emph{dizi} transverse flute, the Balinese \emph{suling} bamboo flute and flue organ pipes are investigated. The sound radiation is measured by a rectangular micr...

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...

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 quan...

We examine Bayesian cyclic networks , here defined as complete directed graphs in which the nodes, representing the domains of discrete or continuous variables, are connected by directed edges representing conditional probabilities between all pairs of variables. The prior probabilities associated with each domain are also included as probabilistic...

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 t...

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-Bénard convection with varying aspect ratio. Addition...

A maximum entropy (MaxEnt) method is developed to predict mean external and internal flow rates and mean pressure gradients (potential differences) in hydraulic pipe networks, without or with sufficient constraints to enable a closed-form solution. This substantially extends existing methods for the analysis of flow networks (e.g., Hardy Cross), ap...

We experimentally perform open and closed-loop control of a separating turbulent boundary layer downstream from a sharp edge ramp. The turbulent boundary layer just above the separation point has a Reynolds number $Re_{\theta}\approx 3\,500$ based on momentum thickness. The goal of the control is to mitigate separation and early re-attachment. The...

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. Th...

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. Th...

We present the toolbox ClimateLearn to tackle problems in climate prediction using machine learning techniques and climate network analysis. The package allows basic operations of data mining, i.e. reading, merging, and cleaning data, and running machine learning algorithms such as multilayer artificial neural networks and symbolic regression with...

The concept of a flow network - a set of nodes connected by flow paths - encompasses many different disciplines, including electrical, pipe flow, transportation, chemical reaction, ecological, epidemiological, economic and human social networks. Over the past two years, we have developed a maximum entropy (MaxEnt) method to infer the stationary sta...

We present a novel experimental setup to investigate two-dimensional thermal convection in a freestanding thin liquid film. We develop a setup for the reproducible generation of freestanding thin liquid films. Such films can be produced in a controlled way on the scale of 5 to 1000 nanometers. Our primary goal is to investigate the statistics of re...

A Maximum Entropy (MaxEnt) method is developed to infer mean external and internal flow rates and mean pressure gradients (potential differences) in hydraulic pipe networks, without or with sufficient constraints to render the system deterministic. The proposed method substantially extends existing methods for the analysis of flow networks (e.g. Ha...

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...

Thin liquid films are nanoscopic elements of foams, emulsions and suspensions, and form a paradigm for nanochannel transport that eventually test the limits of hydrodynamic descriptions. Here we use classical dynamical systems characteristics to study the complex interplay of thermal convection, interface and gravitational forces which yields turbu...

Turbulent shear flows have triggered fundamental research in nonlinear dynamics, like transition scenarios, pattern formation and dynamical modeling. In particular, the control of nonlinear dynamics is subject of research since decades. In this publication, actuated turbulent shear flows serve as test-bed for a nonlinear feedback control strategy w...

We present a generalised MaxEnt method to infer the stationary state of a flow network, subject to “observable” constraints on expectations of various parameters, as well as “physical” constraints arising from frictional properties (resistance functions) and conservation laws (Kirchhoff laws). The method invokes an entropy defined over all uncertai...

A maximum entropy (MaxEnt) method is developed to infer the state of a pipe flow network, for situations in which there is insufficient information to form a closed equation set. This approach substantially extends existing deterministic methods for the analysis of engineered flow networks (e.g. Newton's method or the Hardy Cross scheme). The...

Cluster-based reduced-order modelling (CROM) builds on the pioneering works of Gunzburger's group in cluster analysis [1] and Eckhardt's group in transition matrix models [2] and constitutes a potential alternative to reduced-order models based on a proper-orthogonal decomposition (POD). This strategy frames a time-resolved sequence of fl...

This study examines a generalised maximum entropy (MaxEnt) analysis of a flow network, involving flow rates and potential differences on the network, connected by resistance functions. The analysis gives a generic derivation based on an explicit form of the resistance functions. Accounting for the constraints also leads to an extended form of Gibb...

A novel framework for closed-loop control of turbulent flows is tested in an experimental mixing layer flow. This framework, called Machine Learning Control (MLC), provides a model-free method of searching for the best control law (see talk of B.~R.\ Noack). Here, MLC is benchmarked against classical open-loop actuation of the mixing layer. Result...

Synchronization of musical instruments has raised attention due to the important implications on sound production in musical instruments and technological applications. In this contribution, we show new results on the interaction of two coupled organ pipes: we present a new experiment where the pipes were positioned in a plane with varying distance...

We present results on the coupling mechanisms in wind-driven, self-sustained acoustic oscillators. Such systems are found in engineering applications, as gas burners, and—more beautiful—in musical instruments. As a result, we find that coupling and oscillators are nonlinear in character, which can lead to synchronization. We demonstrate our ideas u...

A novel framework for closed-loop control of turbulent flows is tested in an experimental mixing layer flow. This framework, called Machine Learning Control (MLC), provides a model-free method of searching for the best function, to be used as a control law in closed-loop flow control. MLC is based on genetic programming, a function optimization met...

We propose a novel closed-loop control strategy of turbulent flows using machine learning methods in a model-free manner. This strategy, called Machine Learning Control (MLC), allows -- for the first time -- to detect and exploit all enabling nonlinear actuation mechanisms in an un-supervised automatic manner. In this communication, we focus on M...

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 osc...

We propose a general model-free strategy for feedback control design of turbulent flows. This strategy called 'machine learning control' (MLC) is capable of exploiting nonlinear mechanisms in a systematic unsupervised manner. It relies on an evolutionary algorithm that is used to evolve an ensemble of feedback control laws until minimization of a t...

Wind-driven sound generation is a source of anger and pleasure, depending on the situation: airframe and car noise, or combustion noise are some of the most disturbing environmental pollutions, whereas musical instruments are sources of joy. We present an experiment on two coupled sound sources -organ pipes- together with a theoretical model which...

We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with finite number of actuators (multiple inputs) and sensors (multiple outputs). The control law maps outputs into inpu...

We present recent results on the synchronization (Mitnahme Effect) of organ pipes. Previous work has focused on the detailed measurement and reconstruction of the driving of an organ pipe by a loudspeaker. As a result the full Arnold tongue was measured and reconstructed and a synchronization could be found down to a fraction of 1/500 of the sound...

Thin liquid films serve as the paradigms of atmospheric convection, thermal convection in the Earth's mantle or turbulence in magnetohydrodynamics, thereby connecting with typical systems exhibiting turbulent mixing. In addition, recent research on colloids, interfaces and nanofluids led to advances in the development of micro-mixers (lab-on-a-chip...

We show first results on the dynamics of ultrathin regions, black film (BF) –bubbles, in a two-dimensional thermal convection experiment with already very thin aqueous films. The formation of such stable regions in thin films is a new feature which makes it possible to study the collision dynamics of BF-bubbles in detail. This is of high interest d...

Turbulent flows are ubiquitous in nature and technology. Turbulent flows govern the transport of particulate matter in nature. For example, in atmospheric flows turbulence impacts the dynamics of aerosols, droplets, spores and of the living world by either chemo-attractant transport or transport of the insects themselves. In marine flows examples i...

Films are nanoscopic elements of foams, emulsions and suspensions, and form a paradigm for nanochannel transport that eventually tests the limits of hydrodynamic descriptions. Here, we study the collapse of a freestanding film to its equilibrium. The generation of nanoscale films usually is a slow linear process; using thermal forcing we find unpre...

We present experimental results on flows on very thin, nanometer--scale membranes. More specific we observe an enormous speed-up of the thinning of a film with surfactants towards its equilibrium of a few nanometers when we drive it thermally by cooling locally on a spot in the upper third of the film. Interesting and beautiful to watch by itself,...

This fluid dynamics video demonstrates an experiment on superfast thinning of a freestanding thin aqueous film. The production of such films is of fundamental interest for interfacial sciences and the applications in nanoscience. The stable phase of the film is of the order $5-50\,nm$; nevertheless thermal convection can be established which change...

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., mo...

Wave energy harvesting could be a substantial renewable energy source without impact on the global climate and ecology, yet practical attempts have struggle d with 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 rea...

The grand piano is one of the most important instruments in western music. Its functioning and details are investigated and understood to a reasonable level, however, differences between manufacturers exist which are hard to explain. To add a new piece of understanding, we decided to investigate the effect of ribs mounted on a soundboard. Apart fro...

Development of efficient business process models and determination of their characteristic properties are subject of intense interdisciplinary research. Here, we consider a business process model as a directed graph. Its nodes correspond to the units identified by the modeler and the link direction indicates the causal dependencies between units. I...

The sound radiated by a turbulent jet is not only interesting as a research topic by itself, but also highly relevant for many applications in nature and engineering. In this contribution, we outline a procedure to find a dynamical system from acoustical data. This approach should be considered in the context of reduced order modeling. Basically, w...

Sound generation and interaction are highly complex, nonlinear, and self-organized. Nearly 150 years ago Rayleigh raised the following problem: two nearby organ pipes of different fundamental frequencies sound together almost inaudibly with identical pitch. This effect is now understood qualitatively by modern synchronization theory M. Abel et al....

Sound generation and -interaction is highly complex, nonlinear and self-organized. Already 150 years ago Lord Rayleigh raised the following problem: Two nearby organ pipes of different fundamental frequencies sound together almost inaudibly with identical pitch. This effect is now understood qualitatively by modern synchronization theory (M. Abel e...

In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial or ordinary differential equations. Usually, one does not take care for accuracy of the resulting estimates of...

We report results on the synchronization of two organ pipes positioned side by side. Special attention is put on the synchronization of the higher harmonics. As possible explanation, classical theory provides the amplitude death as explanation for the reduction to almost silence of two coupled organ pipes. With our measurements we exclude this scen...

Wall models are the key technology making possible the application of large eddy simulation to flows of engineering interest. In this paper, a new approach to the development of wall models is presented, which, in contrast to classical wall models, relies on a strong physical background and therefore is considered to be able to predict separated fl...

From measurements on organ pipes, it has been known for a long time that the so‐called Mitnahme Effekt can lead to a mutual influence of organ pipes by each other. The same holds for external driving of pipes by acoustical sources of well‐defined frequencies. A locking of two differently tuned pipes to a single frequency, or to the frequency of the...

Zum Vol. I von: Computer science meets automation: 52. IWK, Internationales Wissenschaftliches Kolloquium ; proceedings ; 10 - 13 September 2007 Zum Vol. II von: Computer science meets automation: 52. IWK, Internationales Wissenschaftliches Kolloquium ; proceedings ; 10 - 13 September 2007