Below you find an interactive list of all my publications, which can be filtered by keywords, year, publication type and coauthors. There are also static lists of my books/book-chapters as well as journal-, conference-, and submitted publications.

## 2020 |

Borsche, Raul; Kocoglu, Damla; Trenn, Stephan A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Journal Article Mathematics of Control, Signals, and Systems (MCSS), 32 , pp. 455-487, 2020, (Open Access). Abstract | Links | BibTeX | Tags: DAEs, delay, networks, open-access, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs @article{BorsKoco20, title = {A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs}, author = {Raul Borsche and Damla Kocoglu and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2020/11/23-MCSS2020.pdf, Paper}, doi = {10.1007/s00498-020-00267-7}, year = {2020}, date = {2020-11-18}, journal = {Mathematics of Control, Signals, and Systems (MCSS)}, volume = {32}, pages = {455-487}, abstract = {A distributional solution framework is developed for systems con- sisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.}, note = {Open Access}, keywords = {DAEs, delay, networks, open-access, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs}, pubstate = {published}, tppubtype = {article} } A distributional solution framework is developed for systems con- sisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions. |

## 2018 |

Kausar, Rukhsana; Trenn, Stephan Water hammer modeling for water networks via hyperbolic PDEs and switched DAEs Inproceedings Klingenberg, Christian; Westdickenberg, Michael (Ed.): Theory, Numerics and Applications of Hyperbolic Problems II, pp. 123-135, Springer, Cham, 2018, ISBN: 978-3-319-91548-7, (Presented at XVI International Conference on Hyperbolic Problems (HYPO2016), Aachen). Abstract | Links | BibTeX | Tags: application, DAEs, nonlinear, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems @inproceedings{KausTren18, title = {Water hammer modeling for water networks via hyperbolic PDEs and switched DAEs}, author = {Rukhsana Kausar and Stephan Trenn}, editor = {Christian Klingenberg and Michael Westdickenberg}, url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT170418.pdf, Preprint}, doi = {10.1007/978-3-319-91548-7_9}, isbn = {978-3-319-91548-7}, year = {2018}, date = {2018-06-27}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems II}, pages = {123-135}, publisher = {Springer}, address = {Cham}, abstract = {In water distribution network instantaneous changes in valve and pump settings introduce jumps and sometimes impulses. In particular, a particular impulsive phenomenon which occurs due to sudden closing of valve is the so called water hammer. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). We observed that under some suitable assumptions the PDEs usually used to describe water flows can be simplified to differential algebraic equations (DAEs). The idea is to model water hammer phenomenon in the switched DAEs framework due to its special feature of studying such impulsive effects. To compare these two modeling techniques, a system of hyperbolic PDE model and the switched DAE model for a simple set up consisting of two reservoirs, six pipes and three valve is presented. The aim of this contribution is to present results of both models as motivation for the claim that a switched DAE modeling framework is suitable for describing a water hammer.}, note = {Presented at XVI International Conference on Hyperbolic Problems (HYPO2016), Aachen}, keywords = {application, DAEs, nonlinear, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } In water distribution network instantaneous changes in valve and pump settings introduce jumps and sometimes impulses. In particular, a particular impulsive phenomenon which occurs due to sudden closing of valve is the so called water hammer. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). We observed that under some suitable assumptions the PDEs usually used to describe water flows can be simplified to differential algebraic equations (DAEs). The idea is to model water hammer phenomenon in the switched DAEs framework due to its special feature of studying such impulsive effects. To compare these two modeling techniques, a system of hyperbolic PDE model and the switched DAE model for a simple set up consisting of two reservoirs, six pipes and three valve is presented. The aim of this contribution is to present results of both models as motivation for the claim that a switched DAE modeling framework is suitable for describing a water hammer. |

## 2017 |

Kall, Jochen; Kausar, Rukhsana; Trenn, Stephan Modeling water hammers via PDEs and switched DAEs with numerical justification Inproceedings Proc. 20th IFAC World Congress 2017, pp. 5349 - 5354, Toulouse, France, 2017, ISSN: 2405-8963. Abstract | Links | BibTeX | Tags: application, DAEs, nonlinear, PDEs, solution-theory, switched-DAEs, switched-systems @inproceedings{KallKaus17, title = {Modeling water hammers via PDEs and switched DAEs with numerical justification}, author = {Jochen Kall and Rukhsana Kausar and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KKT170324.pdf, Preprint}, doi = {10.1016/j.ifacol.2017.08.927}, issn = {2405-8963}, year = {2017}, date = {2017-03-23}, booktitle = {Proc. 20th IFAC World Congress 2017}, journal = {IFAC-PapersOnLine}, volume = {50}, number = {1}, pages = {5349 - 5354}, address = {Toulouse, France}, abstract = {In water distribution networks instantaneous changes in valve and pump settings may introduces jumps and peaks in the pressure. In particular, a well known phenomenon in response to the sudden closing of a valve is the so called water hammer, which (if not taken into account properly) may destroy parts of the water network. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). After discussing this PDE model we propose a simplified model using switched differential-algebraic equations (DAEs). Switched DAEs are known to be able to produce infinite peaks in response to sudden structural changes. These peaks (in the mathematical form of Dirac impulses) can easily be predicted and may allow for a simpler analysis of complex water networks in the future. As a first step toward that goal, we verify the novel modeling approach by comparing these two modeling techniques numerically for a simple set up consisting of two reservoirs, a pipe and a valve.}, keywords = {application, DAEs, nonlinear, PDEs, solution-theory, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } In water distribution networks instantaneous changes in valve and pump settings may introduces jumps and peaks in the pressure. In particular, a well known phenomenon in response to the sudden closing of a valve is the so called water hammer, which (if not taken into account properly) may destroy parts of the water network. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). After discussing this PDE model we propose a simplified model using switched differential-algebraic equations (DAEs). Switched DAEs are known to be able to produce infinite peaks in response to sudden structural changes. These peaks (in the mathematical form of Dirac impulses) can easily be predicted and may allow for a simpler analysis of complex water networks in the future. As a first step toward that goal, we verify the novel modeling approach by comparing these two modeling techniques numerically for a simple set up consisting of two reservoirs, a pipe and a valve. |