Modellansatz - English episodes only

Gudrun talks to Anna Geyer. Anna is Assistant professer at TU Delft in the Mathematical Physics group at the Delft Institute of Applied Mathematics. She is interested in the behaviour of solutions to equations which model shallow water waves.

The day before (04.07.2019) Anna gave a talk at the Kick-off meeting for the second funding period of the CRC Wave phenomena at the mathematics faculty in Karlsruhe, where she discussed instability of peaked periodic waves. Therefore, Gudrun asks her about the different models for waves, the meaning of stability and instability, and the mathematical tools used in her field.

For shallow water flows the solitary waves are especially fascinating and interesting. Traveling waves are solutions of the form

u(t,x)=f(x−ct)

representing waves of permanent shape f that propagate at constant speed c. These waves are called solitary waves if they are localized disturbances, that is, if the wave profile f decays at infinity. If the solitary waves retain their shape and speed after interacting with other waves of the same type, we say that the solitary waves are solitons. One can ask the question if a given model equation (sometimes depending on parameters in the equation or the size of the initial conditions) allows for solitary or periodic traveling waves, and secondly whether these waves are stable or unstable. Peaked periodic waves are an interesting phenomenon because at the wave crest (the peak) they are not smooth, a situation which might lead to wave breaking. For which equations are peaked waves solutions? And how stable are they?

Anna answers these questions for the reduced Ostrovsky equation, which serves as model for weakly nonlinear surface and internal waves in a rotating ocean. The reduced Ostrovsky equation is a modification of the Korteweg-de Vries equation, for which the usual linear dispersive term with a third-order derivative is replaced by a linear nonlocal integral term, representing the effect of background rotation. Peaked periodic waves of this equation are known to exist since the late 1970's. Anna presented recent results in which she answers the long standing open question whether these solutions are stable. In particular, she proved linear instability of the peaked periodic waves using semi-group theory and energy estimates. Moreover, she showed that the peaked wave is unique and that the equation does not admit Hölder continuous solutions, which implies that the reduced Ostrovsky equation does not admit cusps. Finally, it turns out that the peaked wave is also spectrally unstable. This is joint work with Dmitry Pelinovsky.

For the stability analysis it is really delicate how to choose the right spaces such that their norms measure the behaviour of the solution. The Camassa-Holm equation allows for solutions with peaks which are stable with respect to certain perturbations and unstable with respect to others, and can model breaking waves.

Anna studied mathematics in Vienna. Adrian Constantin attracted her to the topic of partial differential equations applied to water waves. She worked with him during her PhD which she finished in 2013. Then she worked as Postdoc at the Universitat Autònoma de Barcelona and in Vienna before she accepted a tenure track position in Delft in 2017.

• A. Geyer, D.E. Pelinovsky: Spectral instability of the peaked periodic wave in the reduced Ostrovsky equations, submitted (arXiv)
• A. Geyer, D.E. Pelinovsky: Linear instability and uniqueness of the peaked periodic wave in the reduced Ostrovsky equation, SIAM J. Math. Analysis, 51 (2019) 1188–1208
• A. Geyer, D.E. Pelinovsky: Spectral stability of periodic waves in the generalized reduced Ostrovsky equation, Lett. Math. Phys. 107(7) (2017) 1293–1314
• R. Grimshaw, L. Ostrovsky, V. Shrira, et al.: Long Nonlinear Surface and Internal Gravity Waves in a Rotating Ocean, Surveys in Geophysics (1998) 19: 289.
• A. Constantin, W. Strauss: Stability of peakons, Commun. Pure Appl. Math. 53 (2000) 603–610.
• F. Natali, D.E. Pelinovsky: Instability of H1-stable peakons in the Camassa-Holm equation, submitted (arXiv)

• X. Liao, G. Thäter: Nonhomogenous Fluids, Conversation in the Modellansatz Podcast, Episode 189, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2018.
• M. Lopez-Fernandez, G. Thäter: Convolution Quadrature, Conversation in the Modellansatz Podcast, Episode 133, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2017.
• S. Fliss, G. Thäter: Transparent Boundaries, Conversation in the Modellansatz Podcast episode 075, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.
• F. Sayas, G. Thäter: Acoustic scattering, Conversation in the Modellansatz Podcast episode 058, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.
• E. Zuazua, G. Thäter: Waves Conversation in the Modellansatz Podcast episode 054, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015.

Gudrun talks with Changjing Zhuge. He is a guest in the group of Lennart Hilbert and works at the College of applied sciences and the Beijing Institute for Scientific and Engineering Computing (BISEC) at the Beijing University of Technology.

He is a mathematician who is interested in system biology. In some cases he studies delay differential equations or systems of ordinary differential equations to characterize processes and interactions in the context of cancer research.

The inbuilt delays originate e.g. from the modeling of hematopoietic stem cell populations. Hematopoietic stem cells give rise to other blood cells. Chemotherapy is frequently accompanied by unwished for side effects to the blood cell production due to the character of the drugs used. Often the production of white blood cells is hindered, which is called neutropenia. In an effort to circumvent that, together with chemotherapy, one treats the patient with granulocyte colony stimulating factor (G-CSF).

To examine the effects of the typical periodic chemotherapy in generating neutropenia, and the corresponding response of this system to given to G-CSF Changjing and his colleagues studied relatively simple but physiologically realistic mathematical models for the hematopoietic stem cells. And these models are potential for modeling of other stem-like biosystems such as cancers.

The delay in the system is related to the platelet maturation time and the differentiation rate from hematopoietic stem cells into the platelet cell.

Changjing did his Bachelor in Mathematics at the Beijing University of Technology (2008) and continued with a PhD-program in Mathematics at the Zhou-Peiyuan Center for Applied Mathematics, Tsinghua University, China. He finished his PhD in 2014. During his time as PhD student he also worked for one year in Michael C Mackey's Lab at the Centre for Applied Mathematics in Bioscience and Medicine of the McGill University in Montreal (Canada).

• C. Zhuge, M.C. Mackey, J. Lei: Origins of oscillation patterns in cyclical thrombocytopeniaJournal of Theoretical Biology 462,432-445, 2019.
• C. Zhuge, X. Sun, J. Lei: On positive solutions and the Omega limit set for a class of delay differential equations. Discrete and Continuous Dynamical Systems - Series B, 18(9), 2487~2503, 2013.
• C. Zhuge, M.C. Mackey, J. Lei: Neutrophil dynamics in response to chemotherapy and G-CSF Journal of Theoretical Biology 293, 111-120 2012.

• L. Hilbert, G. Thäter: Zellkerne, Gespräch im Modellansatz Podcast, Folge 206, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2019.
• M. Gonciarz, G. Thäter: Portrait of Science, Gespräch im Modellansatz Podcast, Folge 197, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2019.
• G. Thäter, K. Page: Embryonic Patterns, Gespräch im Modellansatz Podcast, Folge 161, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.
• L. Adlung, G. Thäter, S. Ritterbusch: Systembiologie, Gespräch im Modellansatz Podcast, Folge 39, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2016.
• Omega Tau-Podcast 072: Forschung in der Zellbiologie, 2011.
• J. Schmoranze, I. Wessolowski: Beim Herrn der Mikroskope – AMBIO Core Facility, Sciencekompass Podcast, Episode 009 B, 2017.

In June 2019 Gudrun talked with Serena Carelli. Serena is member of the Research Training Group (RTG) Simet, which is based in Karlsruhe, Ulm and Offenburg. It started its work in 2017 and Gudrun is associated postdoc therein. The aim of that graduate school is to work on the better understanding of Lithium-ion batteries. For that it covers all scales, namley from micro (particles), meso (electrodes as pairs) to macro (cell) and involves scientists from chemistry, chemical engineering, material sciences, electro engineering, physics and mathematics. The group covers the experimental side as well as modeling and computer simulations.

Serena is one of the PhD-students of the program. She is based in Offenburg in the group of Wolfgang Bessler (the deputy speaker of the RTG). Her research focusses on End-of-life prediction of a lithium-ion battery cell by studying the mechanistic ageing models of the graphite electrode among other things.

Mathematical modelling and numerical simulation have become standard techniques in Li-ion battery research and development, with the purpose of studying the issues of batteries, including performance and ageing, and consequently increasing the model-based predictability of life expectancy. Serena and others work on an electrochemical model of a graphite-based lithium-ion cell that includes combined ageing mechanisms:

1. Electrochemical formation of the solid electrolyte interphase (SEI) at the anode,
2. breaking of the SEI due to mechanical stress from volume changes of the graphite particles, causing accelerated SEI growth,
3. gas formation and dry-out of the electrodes,
4. percolation theory for describing the loss of contact of graphite particles to the liquid electrolyte,
5. formation of reversible and irreversible Li plating.

The electrochemistry is coupled to a multi-scale heat and mass transport model based on a pseudo-3D approach.

A time-upscaling methodology is developed that allows to simulate large time spans (thousands of operating hours). The combined modeling and simulation framework is able to predict calendaric and cyclic ageing up to the end of life of the battery cells. The results show a qualitative agreement with ageing behavior known from experimental literature.

Serena has a Bachelor in Chemistry and a Master's in Forensic Chemistry from the University of Torino. She worked in Spain, the Politécnico de Torino and in Greece (there she was Marie Curie fellow at the Foundation for Research and Technology - Hellas) before she decided to spend time in Australia and India.

• Serena's Linked in site
• A. Latz & J. Zausch: Thermodynamic consistent transport theory of Li-ion batteries, Journal of Power Sources 196 3296--3302, 2011.
• T. Seger: Elliptic-Parabolic Systems with Applications to Lithium-Ion Battery Models, Doktorarbeit Universität Konstanz, 2013.
• M. Kespe & H. Nirschl: Numerical simulation of lithium-ion battery performance considering electrode microstructure, International Journal of Energy Research 39 2062-2074, 2015.
• J.-M. Tarascon & M. Armand: Issues and challenges facing rechargeable lithium batteries, Nature 414 359-367, 2001.
• W.G. Bessler: Elektrische Energiespeicherung mit Batterien und Brennstoffzellen, Forschung im Fokus, Hochschule Offenburg (2018).

• A. Jossen: Batterien, Gespräch mit Markus Völter im Omega Tau Podcast, Folge 222, 2016.
• J. Holthaus: Batterien für morgen und übermorgen, KIT.Audio Podcast, Folge 2, 2016.
• D. Breitenbach, U. Gebhardt, S. Gaedtke: Elektrochemie, Laser, Radio, Proton Podcast, Folge 15, 2016.
• M. Maier: Akkumulatoren, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 123, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.
• V. Auinger: Optimale Akkuladung, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 160, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.

Gudrun met Magdalena Gonciarz in Dresden. They sat down in a very quiet Coffeeshop in Dreikönigskirche and talked about their experiences as scientists giving science an image. Magda started Portrait of science in 2016 with two objectives: to show that science is a process with many contributors at all carreer levels and to have a get-away from a demanding PhD-project, to express her creativity and have tangible results.

The person who pointed Gudrun in Magda's direction is Lennart Hilbert, a former co-worker of Magda in Dresden who is now working at KIT on Computational Architectures in the Cell Nucleus (he will be a podcast guest very soon).

On the Portrait of Science page one can find photographs of people from Dresden's Life Science campus. Apart from the photographs, one can also find their stories. How and why did they become scientists? What do they do, what are they passionate about? Magda invites us: "Forget the tubes and Erlenmeyer flasks. Science is only as good as the people who do it. So sit back, scroll down and get to know them looking through the lens of Magdalena Gonciarz. Have you ever wondered what kind of people scientists are? Would you like to know what are they working on? What drives and motivates them - spending days in the basement without the sun? Portrait of Science project aims at uncovering more about people who contribute to science at all levels - Research Group Leaders, Postdocs, PhD Students, Staff Scientists and Technicians. All of them are vital for progress of scientific research and all of them are passionate people with their own motivations."

When she started the Portrait of Science project, Magda challenged herself to take more pictures. She wanted to show the real people behind science and their personality. This was a creative task, quite different from her work as scientist - done with comparably little time. On top of taking the pictures, interviewees were asked to fill out a questionaire to accompany the story told by the photographs. Surprisingly, the stories told by her co-workers turned out to be quite inspiring. The stories told have shown the passion and the diverse motivations. People mentioned their failures as well. There were stories about accidents and their crucial role in carreers, about coincidence of finding a fascinating book or the right mentor - even as far back as in early childhood sometimes. Sharing ups and downs and the experience that there is a light at the end of the tunnel was a story she needed and which was worth to be shared. Knowing how hard scientific work can be, and how multiple friends and colleagues struggled more than she herself, Magda still strongly feels that it is useful to show that this is not a private and unique experience, but probably a part of the life of every scientist. This struggle can be overcome with time, effort, and help.

Magda comes from Poland. During her Master's studies, she had an opportunity to do a research placement at the University of Virginia. During that time she felt welcomed as part of a scientific community in which she wanted to stay. It was a natural decision to proceed with a PhD. She applied to the very prestigious Dresden International Graduate School for Biomedicine and Bioengineering and joined the biological research on proteins and their modifications in the lab of Jörg Mansfeld. After finishing her project, she decided to leave academia. Since 2018 she works for a learning and training agency CAST PHARMA and is involved in producing e-Learning solutions for pharmaceutical companies.

Magda also talked a bit about her PhD research. As we all know, genes code for proteins. However, one protein can exist in multiple different forms with multiple varying functions. A protein can be post-translationallly modified, i.e., modified after it is created in order to e.g., be relocated, have different interaction partners or become activated or destroyed in a manner of minutes. Recently, modern methods such as mass spectrometry, made it possible to see the multitude of post-translationally modified forms of proteins and allowed further research with the use of biochemistry or imaging techniques to gain insight into functions of these modifications, e.g., at different stages of the cell life.

Gudrun and Magda also talked about the challenge to make a broader audience understand what the particular research topic is all about. It is hard to refer to things we cannot see. It is often easier for people with more translatable research to connect it to various diseases, e.g., cancer but still creates a challenge for those working with more basic issues such as developmental biology.

What Magda took from her time in academia is much more than her results and her part in the basic research story. She feels that curiosity and quick learning skills are her superpowers. She is able to become familiar with any topic in a short amount of time. She can manage multiple parts of a project. Also she learned resilience and how to deal with challenges and failures on a daily basis, which can prove to be helpful in all areas of life.
At the moment, she is still making plans whether to continue the Portrait of Science in the future, maybe in a changed format.

• A. Leßmöllmann: Wissenschaftskommunikation, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 130, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.
• C. Rojas-Molian: Rage of the Blackboard, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 121, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.

Gudrun Talks to Sema Coşkun who at the moment of the conversation in 2018 is a Post Doc researcher at the University Kaiserslautern in the group of financial mathematics. She constructs models for the behaviour of energy markets.

In short the conversation covers the questions

• How are classical markets modelled?
• In which way are energy markets different and need new ideas?

The seminal work of Black and Scholes (1973) established the modern financial theory. In a Black-Scholes setting, it is assumed that the stock price follows a Geometric Brownian Motion with a constant drift and constant volatility. The stochastic differential equation for the stock price process has an explicit solution. Therefore, it is possible to obtain the price of a European call option in a closed-form formula. Nevertheless, there exist drawbacks of the Black-Scholes assumptions. The most criticized aspect is the constant volatility assumption. It is considered an oversimplification. Several improved models have been introduced to overcome those drawbacks. One significant example of such new models is the Heston stochastic volatility model (Heston, 1993). In this model, volatility is indirectly modeled by a separate mean reverting stochastic process, namely. the Cox-Ingersoll-Ross (CIR) process. The CIR process captures the dynamics of the volatility process well. However, it is not easy to obtain option prices in the Heston model since the model has more complicated dynamics compared to the Black-Scholes model.

In financial mathematics, one can use several methods to deal with these problems. In general, various stochastic processes are used to model the behavior of financial phenomena. One can then employ purely stochastic approaches by using the tools from stochastic calculus or probabilistic approaches by using the tools from probability theory. On the other hand, it is also possible to use Partial Differential Equations (the PDE approach). The correspondence between the stochastic problem and its related PDE representation is established by the help of Feynman-Kac theorem. Also in their original paper, Black and Scholes transferred the stochastic representation of the problem into its corresponding PDE, the heat equation. After solving the heat equation, they transformed the solution back into the relevant option price. As a third type of methods, one can employ numerical methods such as Monte Carlo methods.

Monte Carlo methods are especially useful to compute the expected value of a random variable. Roughly speaking, instead of examining the probabilistic evolution of this random variable, we focus on the possible outcomes of it. One generates random numbers with the same distribution as the random variable and then we simulate possible outcomes by using those random numbers. Then we replace the expected value of the random variable by taking the arithmetic average of the possible outcomes obtained by the Monte Carlo simulation. The idea of Monte Carlo is simple. However, it takes its strength from two essential theorems, namely Kolmogorov’s strong law of large numbers which ensures convergence of the estimates and the central limit theorem, which refers to the error distribution of our estimates.

Electricity markets exhibit certain properties which we do not observe in other markets. Those properties are mainly due to the unique characteristics of the production and consumption of electricity. Most importantly one cannot physically store electricity. This leads to several differences compared to other financial markets. For example, we observe spikes in electricity prices. Spikes refer to sudden upward or downward jumps which are followed by a fast reversion to the mean level. Therefore, electricity prices show extreme variability compared to other commodities or stocks.

For example, in stock markets we observe a moderate volatility level ranging between 1% and 1.5%, commodities like crude oil or natural gas have relatively high volatilities ranging between 1.5% and 4% and finally the electricity energy has up to 50% volatility (Weron, 2000). Moreover, electricity prices show strong seasonality which is related to day to day and month to month variations in the electricity consumption. In other words, electricity consumption varies depending on the day of the week and month of the year. Another important property of the electricity prices is that they follow a mean reverting process. Thus, the Ornstein-Uhlenbeck (OU) process which has a Gaussian distribution is widely used to model electricity prices. In order to incorporate the spike behavior of the electricity prices, a jump or a Levy component is merged into the OU process. These models are known as generalized OU processes (Barndorff-Nielsen & Shephard, 2001; Benth, Kallsen & Meyer-Brandis, 2007). There exist several models to capture those properties of electricity prices. For example, structural models which are based on the equilibrium of supply and demand (Barlow, 2002), Markov jump diffusion models which combine the OU process with pure jump diffusions (Geman & Roncoroni, 2006), regime-switching models which aim to distinguish the base and spike regimes of the electricity prices and finally the multi-factor models which have a deterministic component for seasonality, a mean reverting process for the base signal and a jump or Levy process for spikes (Meyer-Brandis & Tankov, 2008).

The German electricity market is one of the largest in Europe. The energy strategy of Germany follows the objective to phase out the nuclear power plants by 2021 and gradually introduce renewable energy ressources. For electricity production, the share of renewable ressources will increase up to 80% by 2050. The introduction of renewable ressources brings also some challenges for electricity trading. For example, the forecast errors regarding the electricity production might cause high risk for market participants. However, the developed market structure of Germany is designed to reduce this risk as much as possible. There are two main electricity spot price markets where the market participants can trade electricity. The first one is the day-ahead market in which the trading takes place around noon on the day before the delivery. In this market, the trades are based on auctions. The second one is the intraday market in which the trading starts at 3pm on the day before the delivery and continues up until 30 minutes before the delivery. Intraday market allows continuous trading of electricity which indeed helps the market participants to adjust their positions more precisely in the market by reducing the forecast errors.

• S. Coskun and R. Korn: Pricing Barrier Options in the Heston Model Using the Heath-Platen estimator. Monte Carlo Methods and Applications. 24 (1) 29-42, 2018.
• S. Coskun: Application of the Heath–Platen Estimator in Pricing Barrier and Bond Options. PhD thesis, Department of Mathematics, University of Kaiserslautern, Germany, 2017.
• S. Desmettre and R. Korn: 10 Computationally challenging problems in Finance. FPGA Based Accelerators for Financial Applications, Springer, Heidelberg, 1–32, 2015.
• F. Black and M. Scholes: The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3):637-654, 1973.
• S.L. Heston: A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6(2):327–343, 1993.
• R. Korn, E. Korn and G. Kroisandt: Monte Carlo Methods and Models in Finance and Insurance. Chapman & Hall/CRC Financ. Math. Ser., CRC Press, Boca Raton, 2010.
• P. Glasserman, Monte Carlo Methods in Financial Engineering. Stochastic Modelling and Applied Probability, Appl. Math. (New York) 53, Springer, New York, 2004.
• M.T. Barlow: A diffusion model for electricity prices. Mathematical Finance, 12(4):287-298, 2002.
• O.E. Barndorff-Nielsen and N. Shephard: Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society B, 63(2):167-241, 2001.
• H. Geman and A. Roncoroni: Understanding the fine structure of electricity prices. The Journal of Business, 79(3):1225-1261, 2006.
• T. Meyer-Brandis and P. Tankov: Multi-factor jump-diffusion models of electricity prices. International Journal of Theoretical and Applied Finance, 11(5):503-528, 2008.
• R. Weron: Energy price risk management. Physica A, 285(1-2):127–134, 2000.

• G. Thäter, M. Hofmanová: Turbulence, conversation in the Modellansatz Podcast, episode 155, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2018. http://modellansatz.de/turbulence
• G. Thäter, M. J. Amtenbrink: Wasserstofftankstellen, Gespräch im Modellansatz Podcast, Folge 163, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. http://modellansatz.de/wasserstofftankstellen
• S. Ajuvo, S. Ritterbusch: Finanzen damalsTM, Gespräch im Modellansatz Podcast, Folge 97, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2016. http://modellansatz.de/finanzen-damalstm
• K. Cindric, G. Thäter: Kaufverhalten, Gespräch im Modellansatz Podcast, Folge 45, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. http://modellansatz.de/kaufverhalten
• V. Riess, G. Thäter: Gasspeicher, Gespräch im Modellansatz Podcast, Folge 23, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. http://modellansatz.de/gasspeicher
• F. Schueth, T. Pritlove: Energieforschung, Episode 12 im Forschergeist Podcast, Stifterverband/Metaebene, 2015. https://forschergeist.de/podcast/fg012-energieforschung/

In this episode Gudrun talks with her new colleague Xian Liao. In November 2018 Xian has been appointed as Junior Professor (with tenure track) at the KIT-Faculty of Mathematics. She belongs to the Institute of Analysis and works in the group Nonlinear Partial Differential Equations.

She is very much interested in Dispersive Partial Differential Equations. These equations model, e.g., the behaviour of waves. For that it is a topic very much in the center of the CRC 1173 - Wave phenomena at our faculty.

Her mathematical interest was always to better understand the solutions of partial differential equations. But she arrived at dispersive equations through several steps in her carreer. Originally she studied inhomogeneous incompressible fluids. This can for example mean that the fluid is a mixture of materials with different viscosities. If we have a look at the Navier-Stokes equations for materials like water or oil, one main assumption therein is, that the viscosity is a material constant. Nevertheless, the equations modelling their flows are already nonlinear and there are a few serious open questions. Studying flows of inhomogneous materials brings in further difficulties since there occur more and more complex nonlinearities in the equations.

It is necessary to develop a frame in which one can characterise the central properties of the solutions and the flow. It turned out that for example finding and working with quantities which remain conserved in the dynamics of the process is a good guiding line - even if the physical meaning of the conserved quantitiy is not always clear. Coming from classical theory we know that it makes a lot of sense to have a look at the conservation of mass, energy and momentum, which translate to conserved quantities as combinations of velocity, its derivatives, pressure and density. Pressure and density are not independent in these simplified models but are independent in the models Xiao studies. In the complex world of inhomogeneous equations we lose the direct concept to translate between physics and mathematics but carry over the knowledge that scale invarance and conservation are central properties of the model.

It is interesting to characterize how the complex system develops with a change of properties. To have a simple idea - if it is more developing in the direction of fast flowing air or slow flowing almost solid material. One number which helps to see what types of waves one has to expect is the Mach number. It helps to seperate sound waves from fluid waves. A mathematical/physical question then is to understand the process of letting the Mach number go to zero in the model. It is not that complicated to make this work in the formulae. But the hard work is done in proving that the solutions to the family of systems of PDEs with lower and lower Mach number really tend to the solutions of the derived limit system. For example in order to measure if solutions are similar to each other (i.e. they get nearer and nearer to each other) one needs to find the norms which measure the right properties.

Xian was Undergraduate & Master student at the Nanjing University in China from 2004 to 2009, where she was working with Prof. Huicheng Yin on Partial Differential Equations. She succeeded in getting the scholarship from China Scholarship Council and did her PhD within the laboratory LAMA (with Prof. Raphaël Danchin on zero-Mach number system). She was member of the University Paris-Est but followed many master courses in the programs of other Parisian universities as well.

In 2013 she spent 8 months at the Charles University in Prague as Postdoc within the research project MORE. There she collaborated with Prof. Eduard Feireisl and Prof. Josef Málek on understanding non-Newtonian fluids better.

After that period she returned to China and worked two years at the Academy of Mathematics & Systems Science as Postdoc within the research center NCMIS. With Prof. Ping Zhang she was working on density patch problems. Before her appointment here in Karlsruhe she already returned to Europe. 2016-2018 she was Postdoc at the University Bonn within the CRC 1060. She was mainly working with Prof. Herbert Koch on Gross-Pitaevskii equations - a special topic within dispersive equations.

• Short Interview with the CRC 1173 Wave phenomena
• X. Liao, R. Danchin: On the wellposedness of the full low-Mach number limit system in general Besov spaces. Commun. Contemp. Math.: 14(3), 1250022, 2012.
• X. Liao: A global existence result for a zero Mach number system. J. Math. Fluid Mech.: 16(1), 77-103, 2014.
• X. Liao, E. Feireisl and J. Málek: Global weak solutions to a class of non-Newtonian compressible fluids. Math. Methods Appl. Sci.: 38(16), 3482-3494, 2015.
• X. Liao: On the strong solutions of the nonhomogeneous incompressible Navier-Stokes equations in a thin domain. Differential Integral Equations: 29, 167-182, 2016.
• X. Liao, P. Zhang: Global regularities of 2-D density patches for viscous inhomogeneous incompressible flow with general density: high regularity case, 2016.

Gudrun talks to Carlos Mauricio Rojas La Rotta. They use a Skype connection since Carlos is in Berlin and Gudrun in Karlsruhe.

Carlos is an electrical engineer from Colombia. His first degree is from Pontifcia Universidad Javeriana in Bogotá. For five years now he has been working at Schneider Electric in Berlin. In September 2018 Gudrun met Carlos at the EUREF-Campus in Berlin for discussing the work of Claire Harvey on her Master's thesis. The schedule on that day was very full but Gudrun and Carlos decided to have a Podcast conversation later.

Carlos came to Germany as a car enthusiast. Then he got excited about the possibilities of photovoltaic energy production. For that from 2005-2007 he studied in the Carl von Ossietzky Universität in Oldenburg in the PPRE Master course Renewable Energies. When he graduated within a group of about 20 master students they found a world ready for their knowledge. Carlos worked in various topics and in different parts of Germany in the field of renewable energies. Now, at Schneider he has the unique situation, that he can combine all his interests. He develops the most modern cars, which are driving with renewable energy. In the course of his work he is also back at his original love: working with electronics, protocols and data.

The work on the EUREF-Campus in Berlin started about 8-10 years ago with more questions than clear ideas. Schneider Electric is a big company with about 150.000 employees all over the world. They deal in all types of software and hardware devices for energy delivery. But the topic for Berlin was completely new: It was a test case how to construct energy sustainable districts.

They started out investing in e-mobility with renewable energy and making their own offices a smart building. It is a source of a lot of data telling the story how energy is produced and consumed. At the moment they collect 1GB data per day in the office building on about 12.000 measure points into database and build this as a benchmark to compare it to other scenarios. The next step now is also to find ways to optimize these processes with limited computational possibilities.

This is done with open source code on their own interface and at the moment it can optimize in the micro smart grid on the Campus. For example with 40 charging points for e-cars - consumption is planned according to production of energy. On Campus traditional batteries are used to buffer the energy, and also a bus now works on the Campus which can be discharged and is loaded without a cable!

One can say: Carlos is working in a big experiment. This does not only cover a lot of new technical solutions. The Energiewende is more than putting photovoltaic and wind power out. We as a society have to change and plan differently - especially concerning mobility.

Schneider Electric just started an expansion phase to the whole campus, which has a size of 5.5 ha and 2500 people working there. More than 100 charging point for e-cars will be available very soon.

• C. Harvey, G. Thäter: Micro Grids, Gespräch im Modellansatz Podcast, Folge 186, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.

Gudrun talks with the Scotish engineer Claire Harvey. After already having finished a Master's degree in Product design engineering at the University of Glasgow for the last two years Claire has been a student of the Energy Technologies (ENTECH) Master program. This is an international and interdisciplinary program under the label of the European Institute of Innovation and Technology (EIT) inbetween a number of European technical universities. She spent her first year in Lisbon at Instituto Superior Técnico (IST) and the second master year at the Karlsruhe Institute of Technology (KIT). Gudrun had the role of her supervisor at KIT while she worked on her Master's thesis at the EUREF Campus in Berlin for the Startup inno2grid.

Her study courses prepared her for very diverse work in the sector of renewable energy. Her decision to work with inno2grid in Berlin was based on the fact, that it would help to pave the way towards better solutions for planning micro grids and sustainable districts. Also, she wanted to see an actual micro grid at work. The office building of Schneider Electric, where the Startup inno2grid has its rooms is an experiment delivering data of energy production and consumption while being a usual office building. We will hear more about that in the episode with Carlos Mauricio Rojas La Rotta soon.

Micro grids are small scale electrical grid systems where self-sufficient supply is achieved. Therefore, the integration of micro grid design within district planning processes should be developed efficiently. In the planning process of districts with decentralised energy systems, unique and customised design of micro grids is usually required to meet local technical, economical and environmental needs. From a technical standpoint, a detailed understanding of factors such as load use, generation potential and site constraints are needed to correctly and most efficiently design and implement the network. The presence of many different actors and stakeholders contribute to the complexity of the planning process, where varying levels of technical experience and disparate methods of working across teams is commonplace.

Large quantities of digital information are required across the whole life-cycle of a planning project, not just to do with energetic planning but also for asset management and monitoring after a micro grid has been implemented. In the design of micro grids, large amounts of data must be gathered, there are initial optimization objectives to be met, and simulating control strategies of a district which are adapted to customer requirements is a critical step. Linking these processes - being able to assemble data as well as communicate the results and interactions of different "layers" of a project to stakeholders are challenges that arise as more cross-sector projects are carried out, with the growing interest in smart grid implementation.

Claire's thesis explores tools to assist the planning process for micro grids on the district scale. Using geographical information system (GIS) software, results relating to the energetic planning of a district is linked to geo-referenced data. Layers related to energy planning are implemented - calculating useful parameters and connecting to a database where different stakeholders within a project can contribute. Resource potential, electrical/thermal demand and supply system dimensioning can be calculated, which is beneficial for clients and decision makers to visualize digital information related to a project. Within the open source program QGIS, spatial analysis and optimizations relating to the design of an energy system are performed. As the time dimension is a key part in the planning of the energy supply system of a micro grid, the data is linked to a Python simulation environment where dynamic analysis can be performed, and the results are fed back in to the QGIS project.

• T. Benz et al.: Der Zellulare Ansatz. VDE, Energietechnische Gesellschaft, Frankfurt, Germany, 2015.
• A. Halu et al.: Data-driven modeling of solar-powered urban microgrids. Science Advances 2 (1). DOI:10.1126/sciadv.1500700, 2016.
• M. Giudice and E. Patti: BIM and GIS for District Modelling Politecnico di Torino, Turin, Italy, 2014.
• QGIS
• Ch. Nytsch-Geusen et al.: Sustainable and energy-efficient redevelopment of city quarters - Analytical and planning tools for energy assessment and rehabilitation of urban districts. Universität der Künste, Berlin, 2015.

• Z. Ahamed, G. Thäter: Electric Vehicles on the Grid, Gespräch im Modellansatz Podcast, Folge 183, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.
• G. Thäter, M. J. Amtenbrink: Wasserstofftankstellen, Gespräch im Modellansatz Podcast, Folge 163, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.
• G. Thäter, B. Pousinho: Weather Generator, Gespräch im Modellansatz Podcast, Folge 148, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.

Gudrun talks to Zaheer Ahamed about the influence of an increasing number of Electric vehicles (EV) to the electrical grid. Zaheer just finished the ENTECH Master's program. He started it with his first year at the Karlsruhe Institute for Technology (KIT) and continued in Uppsala University for the second year.

Gudrun was part of the grading process of Zaheer's master thesis "Estimating Balancing Capacities of Electric Vehicles on the German and Swedish grids in 2030".

The rising awareness of pollution from transport is leading to innovations within the transport sector. At the moment EVs are the leading technology. With many countries Germany and Sweden joined the so-called EV30@30 campaign, aiming for 30% of new vehicles sales to be electric by 2030. These ambitions alongside an ever increasing capacity of variable renewable energy sources (RES) in our power systems, pose a concerning challenge for Transmission systems operators (TSO) to maintain proper power system operation. Imbalances between supply and demand are undesirable in any electrical power system and with the rising popularity of EVs and RES such events are only expected to continue or increase.

Fortunately, with the recent development of Vehicle to grid (V2G) concepts as well as extensive studies into the load-shifting potential of EVs, EVs presents an interesting solution for power system balancing distributed energy storage system. Zaheer's study showed that EV are capable of balancing the grid for approximately 60% of the time providing 55-60% of the total balancing energy required. However, the operation also took heavy toll on the EV’s battery performance as it could potentially reduce its life to a 1/7th of its original lifetime.

• Commission Regulation (EU) 2017/1485 of 2 August 2017 on establishing a guideline on electricity transmission system operation, 2017.
• S. Weitemeyer e.a.: Integration of Renewable Energy Sources in future power systems: The role of storage. Renewable Energy, 75 pp.14-20, 2015.
• D.M.Greenwood e.a.: Frequency response services designed for energy storage. Applied Energy, 203 pp.115-127, 2017.
• Eurostat Database
• J. Schäuble e.a.: Generating electric vehicle load profiles from empirical data of three EV fleets in Southwest Germany. Journal of Cleaner Production, 150 pp.253-266, 2017.

• Volker Quaschning, Tim Pritlove: Energiewende, Forschergeist 053, Stifterverband / Metaebene, 2018.
• V. Auinger, G. Thäter: Optimale Akkuladung, Gespräch im Modellansatz Podcast, Folge 160, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. http://modellansatz.de/optimale-akkuladung
• M. Lösch, S. Ritterbusch: Smart Meter Gateway, Gespräch im Modellansatz Podcast, Folge 135, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017. http://modellansatz.de/smart-meter
• M. Maier, G. Thäter: Akkumulatoren, Gespräch im Modellansatz Podcast, Folge 123, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017. http://modellansatz.de/akkumulatoren
• D. Schumann, M. Voelter: Elektromobilität, Omega Tau Podcast 163, Makus Völter und Nora Ludewig, 2015.
• J. Dickmann, S. Ritterbusch: Pumpspeicherkraftwerke, Gespräch im Modellansatz Podcast, Folge 5, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2013.

Gudrun talks to Jousef Murad about the computing platform SimScale. Jousef is currently studying mechanical engineering at the Karlsruhe Institute of Technology (KIT) and focuses on turbulence modelling and computational mechanics in his Master's studies. He first learned about the existence of SimScale early in the year 2015 and started as a FEA (finite element analysis) simulation assistant in November 2016. Meanwhile he switched to Community Management and now is Community and Academic Program Manager at the company being responsible for user requests and Formula student teams all over the world. Formula student is a name for design competitions for teams of students constructing racing cars.

SimScale is a cloud-based platform that gives instant access to computational fluid dynamics (CFD) and finite element analysis (FEA) simulation technology, helping engineers and designers to easily test performance, optimize durability or improve efficiency of their design. SimScale is accessible from a standard web browser and from any computer, eliminating the hurdles that accompany traditional simulation tools: high installation costs, licensing fees, deployment of high-performance computing hardware, and required updates and maintenance.

Via the platform, several state-of-the-art open solvers are made available like,e.g., OpenFOAM and Meshing with SnappyHexMesh. More information about the packages being used can be found at https://www.simscale.com/open-source/ .

On top of having easier access to open source software, the connected user forum is very active and helps everybody to enter the field even as a person without experience.

Founded in 2012 in Munich (Germany), nowadays SimScale is an integral part of the design validation process for many companies worldwide and individual users. It is mainly used by product designers and engineers working in Architecture, Engineering & Construction or Heating, Ventilation & Air-Conditioning. Also in the Electronics, Consumer Goods and Packaging and Containers industries SimScale is useful for testing and optimizing designs in the early development stages.

SimScale offers pricing plans that can be customized, from independent professionals to SMEs and multinational companies. The Community plan makes it possible to use SimScale for free, with 3000 core hours/year using up to 16 cloud computing cores.

• Turbulence models on the English Wikipedia
• S. Pope: Turbulent Flows. Cambridge University Press, 2000.
• P. Sagaut, C. Cambon: Homogeneous Turbulence Dynamics. Cambridge University Press, 2008.

• G. Thäter, M. Hofmanová: Turbulence, Gespräch im Modellansatz Podcast, Folge 155, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018.
• N. Vercauteren, S. Ritterbusch: Lokale Turbulenzen, Gespräch im Modellansatz Podcast, Folge 144, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2017.
• P. Allinger, N. Stockelkamp, G. Thäter: Strukturoptimierung, Gespräch im Modellansatz Podcast, Folge 53, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015.
• B.Valsler, D. Ansell: The Science of Turbulence, The Naked Scientists Podcast, 2010.