@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{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{VossBuennerAbel1998, author = {Voss, Henning U. and B{\"u}nner, M. J. and Abel, Markus}, title = {Identification of continuous, spatiotemporal systems}, year = {1998}, 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{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} } @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{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{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} }