In March 2018 Gudrun had a day available in London when travelling back from the FENICS workshop in Oxford. She contacted a few people working in mathematics at the University College London (ULC) and asked for their time in order to talk about their research. In the end she brought back three episodes for the podcast. This is the second of these conversations. Gudrun talks to Marta Betcke. Marta is associate professor at the UCL Department of Computer Science, member of Centre for Inverse Problems and Centre for Medical Image Computing. She has been in London since 2009. Before that she was a postdoc in the Department of Mathematics at the University of Manchester working on novel X-ray CT scanners for airport baggage screening. This was her entrance into Photoacoustic tomography (PAT), the topic Gudrun and Marta talk about at length in the episode. PAT is a way to see inside objects without destroying them. It makes images of body interiors. There the contrast is due to optical absorption, while the information is carried to the surface of the tissue by ultrasound. This is like measuring the sound of thunder after lightning. Measurements together with mathematics provide ideas about the inside. The technique combines the best of light and sound since good contrast from optical part - though with low resolution - while ultrasound has good resolution but poor contrast (since not enough absorption is going on). In PAT, the measurements are recorded at the surface of the tissue by an array of ultrasound sensors. Each of that only detects the field over a small volume of space, and the measurement continues only for a finite time. In order to form a PAT image, it is necessary to solve an inverse initial value problem by inferring an initial acoustic pressure distribution from measured acoustic time series. In many practical imaging scenarios it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. Then numerical models of wave propagation can be used within the variational image reconstruction framework to find a regularized least-squares solution of an optimization problem. Assuming homogeneous acoustic properties and the absence of acoustic absorption the measured time series can be related to the initial pressure distribution via the spherical mean Radon transform. Integral geometry can be used to derive direct, explicit inversion formulae for certain sensor geometries, such as e.g. spherical arrays. At the moment PAT is predominantly used in preclinical setting, to image tomours and vasculature in small animals. Breast imaging, endoscopic fetus imaging as well as monitoring of perfusion and drug metabolism are subject of intensive ongoing research. The forward problem is related to the absorption of the light and modeled by the wave equation assuming instanteneous absorption and the resulting thearmal expansion. In our case, an optical ultrasound sensor records acoustic waves over time, i.e. providing time series with desired spacial and temporal resolution. Given complete data, then one can mathematically reverse the time direction and find out the original object. Often it is not possible to collect a complete data due to e.g. single sided access to the object as in breast imaging or underlying dynamics happening on a faster rate than one can collect data. In such situations one can formulate the problem in variational framework using regularisation to compensate for the missing data. In particular in subsampling scenario, one would like to use raytracing methods as they scale linearly with the number of sensors. Marta's group is developing flexible acoustic solvers based on ray tracing discretisation of the Green's formulas. They cannot handle reflections but it is approximately correct to assume this to be true as the soundspeed variation is soft tissue is subtle. These solvers can be deployed alongside with stochastic iterative solvers for efficient solution of the variational formulation. Marta went to school in Poland. She finished her education there in a very selected school and loved math due to a great math teacher (which was also her aunt). She decidede to study Computer Sciences, since there she saw more chances on the job market. When moving to Germany her degree was not accepted, so she had to enrol again. This time for Computer Sciences and Engineering at the Hamburg University of Technology. After that she worked on her PhD in the small group of Heinrich Voss there. She had good computing skills and fit in very well. When she finished there she was married and had to solve a two body problem, which brought the couple to Manchester, where a double position was offered. Now both have a permanent position in London. References M. Betcke e.a.: Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography IEEE Transactions on Medical Imaging 37, 1382 - 1393, 2018. F. Rullan & M. Betcke: Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography archive, 2018. M. Betcke e.a.: On the adjoint operator in photoacoustic tomography Inverse Problems 32, 115012, 2016. doi C. Lutzweiler and D. Razansky: Optoacoustic imaging and tomography - reconstruction approaches and outstanding challenges in image performance and quantification, Sensors 13 7345, 2013. doi: 10.3390/s130607345 Podcasts G. Thäter, K. Page: Embryonic Patterns, Gespräch im Modellansatz Podcast, Folge 161, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. F. Cakoni, G. Thäter: Linear Sampling, Conversation im Modellansatz Podcast, Episode 226, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2019. G. Thäter, R. Aceska: Dynamic Sampling, Gespräch im Modellansatz Podcast, Folge 173, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2018. S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. S. Hollborn: Impedanztomographie. Gespräch mit G. Thäter im Modellansatz Podcast, Folge 68, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. 

Modellansatz - English episodes only

Photoacoustic Tomography

This is the third of three conversation recorded during the Conference on mathematics of wave phenomena 23-27 July 2018 in Karlsruhe. Gudrun is in conversation with Anne-Sophie Bonnet-BenDhia from ENSTA in Paris about transmission properties in perturbed waveguides. The spectral theory is essential to study wave phenomena. For instance, everybody has experimented with resonating frequencies in a bathtube filled with water. These resonant eigenfrequencies are eigenvalues of some operator which models the flow behaviour of the water. Eigenvalue problems are better known for matrices. For wave problems, we have to study eigenvalue problems in infinite dimension. Like the eigenvalues for a finite dimensional matrix the Spectral theory gives access to intrinisic properties of the operator and the corresponding wave phenomena. Anne-Sophie is interested in waveguides. For example, optical fibres can guide optical waves while wind instruments are guides for acoustic waves. Electromagnetic waveguides also have important applications. A practical objective is to optimize the transmission in a waveguide, even if there are some perturbations inside. It is known that for certain frequencies, there is no reflection by the perturbations but it is not apriori clear how to find these frequencies. Anne-Sophie uses complex analysis for that. The idea is to complexify the (originally real) coordinates by analytic extension. It is a classic idea for resonances that she adapts to the problem of transmission. This mathematical method of complex scaling is linked to the method of perfectly matched layers in numerics. It is used to solve problems set in unbounded domains on a computer by finite elements. Thanks to the complex scaling, she can solve a problem in a bounded domain, which reproduces the same behaviour as in the infinite domain. Finally, Anne-Sophie is able to get numerically a complex spectrum of frequencies, related to the quality of the transmission in a perturbed waveguide. The imaginary part of the complex quantity gives an indication of the quality of the transmission in the waveguide. The closer to the real axis the better the transmission. References A-S. Bonnet-BenDhia, L. Chesnel and V. Pagneux:Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem Proceedings of the Royal Society A, 2018, doi 10.1098/rspa.2018.0050 A-S. Bonnet-BenDhia: Mathematical and numerical treatment of plasmonic waves at corners of metals and metamaterials Emerging Topics in Optics, IMA, Minneapolis, 2017 A-S. Bonnet-BenDhia, L. Chesnel and S. Nazarov: Perfect transmission invisibility for waveguides with sound hard walls Journal de Mathématiques Pures et Appliquées, 2017, doi 10.1016/j.matpur.2017.07.020 A.-S. Bonnet-BenDhia e.a.: A method to build non-scattering perturbations of two-dimensional acoustic waveguides Math. meth. appl. sci., vol. 40, pp. 335–349, 2015 doi 10.1002/mma.3447 Podcasts S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. 

Waveguides

In den nächsten Wochen bis zum 20.2.2020 möchte Anna Hein, Studentin der Wissenschaftskommunikation am KIT, eine Studie im Rahmen ihrer Masterarbeit über den Podcast Modellansatz durchführen. Dazu möchte sie gerne einige Interviews mit Ihnen, den Hörerinnen und Hörern des Podcast Modellansatz führen, um herauszufinden, wer den Podcast hört und wie und wofür er genutzt wird. Die Interviews werden anonymisiert und werden jeweils circa 15 Minuten in Anspruch nehmen. Für die Teilnahme an der Studie können Sie sich bis zum 20.2.2020 unter der Emailadresse studie.modellansatz@web.de bei Anna Hein melden. Wir würden uns sehr freuen, wenn sich viele Interessenten melden würden. In the coming weeks until February 20, 2020, Anna Hein, student of science communication at KIT, intends to conduct a study on the Modellansatz Podcast within her master's thesis. For this purpose, she would like to conduct some interviews with you, the listeners of the Modellansatz Podcast, to find out who listens to the podcast and how and for what purpose it is used. The interviews will be anonymous and will take about 15 minutes each. To participate in the study, you can register with Anna Hein until 20.2.2020 at studie.modellansatz@web.de . We would be very pleased if many interested parties would contact us. This is the second of three conversation recorded Conference on mathematics of wave phenomena 23-27 July 2018 in Karlsruhe. Gudrun is in conversation with Mariana Haragus about Benard-Rayleigh problems. On the one hand this is a much studied model problem in Partial Differential Equations. There it has connections to different fields of research due to the different ways to derive and read the stability properties and to work with nonlinearity. On the other hand it is a model for various applications where we observe an interplay between boyancy and gravity and for pattern formation in general. An everyday application is the following: If one puts a pan with a layer of oil on the hot oven (in order to heat it up) one observes different flow patterns over time. In the beginning it is easy to see that the oil is at rest and not moving at all. But if one waits long enough the still layer breaks up into small cells which makes it more difficult to see the bottom clearly. This is due to the fact that the oil starts to move in circular patterns in these cells. For the problem this means that the system has more than one solutions and depending on physical parameters one solution is stable (and observed in real life) while the others are unstable. In our example the temperature difference between bottom and top of the oil gets bigger as the pan is heating up. For a while the viscosity and the weight of the oil keep it still. But if the temperature difference is too big it is easier to redistribute the different temperature levels with the help of convection of the oil. The question for engineers as well as mathematicians is to find the point where these convection cells evolve in theory in order to keep processes on either side of this switch. In theory (not for real oil because it would start to burn) for even bigger temperature differences the original cells would break up into even smaller cells to make the exchange of energy faster. In 1903 Benard did experiments similar to the one described in the conversation which fascinated a lot of his colleagues at the time. The equations where derived a bit later and already in 1916 Lord Rayleigh found the 'switch', which nowadays is called the critical Rayleigh number. Its size depends on the thickness of the configuration, the viscositiy of the fluid, the gravity force and the temperature difference. Only in the 1980th it became clear that Benards' experiments and Rayleigh's analysis did not really cover the same problem since in the experiment the upper boundary is a free boundary to the surrounding air while Rayleigh considered fixed boundaries. And this changes the size of the critical Rayleigh number. For each person doing experiments it is also an observation that the shape of the container with small perturbations in the ideal shape changes the convection patterns. Maria does study the dynamics of nonlinear waves and patterns. This means she is interested in understanding processes which change over time. Her main questions are: Existence of observed waves as solutions of the equations The stability of certain types of solutions How is the interaction of different waves She treats her problems with the theory of dynamical systems and bifurcations. The simplest tools go back to Poincaré when understanding ordinary differential equations. One could consider the partial differential equations to be the evolution in an infinite dimensional phase space. Here, in the 1980s, Klaus Kirchgässner had a few crucial ideas how to construct special solutions to nonlinear partial differential equations. It is possible to investigate waterwave problems which are dispersive equations as well as flow problems which are dissipative. Together with her colleagues in Besancon she is also very keen to match experiments for optical waves with her mathematical analysis. There Mariana is working with a variant of the Nonlinear Schrödinger equation called Lugiato-Lefever Equation. It has many different solutions, e.g. periodic solutions and solitons. Since 2002 Mariana has been Professor in Besancon (University of Franche-Comté, France). Before that she studied and worked in a lot of different places, namely in Bordeaux, Stuttgart, Bucharest, Nice, and Timisoara. References V.A. Getling: Rayleigh-Bénard Convection Structures and Dynamics, Advanced Series in Nonlinear Dynamics, Volume 11, World Scientific, Oxford (1998) P. H. Rabinowitz: Existence and nonuniqueness of rectangular solutions of the Bénard problem. Arch. Rational Mech. Anal. (1968) 29: 32. M. Haragus and G. Iooss: Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems. Universitext. Springer-Verlag London, Ltd., London; EDP Sciences, Les Ulis, 2011. Newell, Alan C. Solitons in mathematics and physics. CBMS-NSF Regional Conference Series in Applied Mathematics, 48. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1985. Y. K. Chembo, D. Gomila, M. Tlidi, C. R. Menyuk: Topical Issue: Theory and Applications of the Lugiato-Lefever Equation. Eur. Phys. J. D 71 (2017). Podcasts S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. 

Pattern Formation

 In den nächsten Wochen bis zum 20.2.2020 möchte Anna Hein, Studentin der Wissenschaftskommunikation am KIT, eine Studie im Rahmen ihrer Masterarbeit über den Podcast Modellansatz durchführen. Dazu möchte sie gerne einige Interviews mit Ihnen, den Hörerinnen und Hörern des Podcast Modellansatz führen, um herauszufinden, wer den Podcast hört und wie und wofür er genutzt wird. Die Interviews werden anonymisiert und werden jeweils circa 15 Minuten in Anspruch nehmen. Für die Teilnahme an der Studie können Sie sich bis zum 20.2.2020 unter der Emailadresse studie.modellansatz@web.de bei Anna Hein melden. Wir würden uns sehr freuen, wenn sich viele Interessenten melden würden. In the coming weeks until February 20, 2020, Anna Hein, student of science communication at KIT, intends to conduct a study on the Modellansatz Podcast within her master's thesis. For this purpose, she would like to conduct some interviews with you, the listeners of the Modellansatz Podcast, to find out who listens to the podcast and how and for what purpose it is used. The interviews will be anonymous and will take about 15 minutes each. To participate in the study, you can register with Anna Hein until 20.2.2020 at studie.modellansatz@web.de . We would be very pleased if many interested parties would contact us. This is the first of three conversation recorded Conference on mathematics of wave phenomena 23-27 July 2018 in Karlsruhe. Gudrun talked to Fioralba Cakoni about the Linear Sampling Method and Scattering. The linear sampling method is a method to reconstruct the shape of an obstacle without a priori knowledge of either the physical properties or the number of disconnected components of the scatterer. The principal problem is to detect objects inside an object without seeing it with our eyes. So we send waves of a certain frequency range into an object and then measure the response on the surface of the body. The waves can be absorbed, reflected and scattered inside the body. From this answer we would like to detect if there is something like a tumor inside the body and if yes where. Or to be more precise what is the shape of the tumor. Since the problem is non-linear and ill posed this is a difficult question and needs severyl mathematical steps on the analytical as well as the numerical side. In 1996 Colton and Kirsch (reference below) proposed a new method for the obstacle reconstruction problem in inverse scattering which is today known as the linear sampling method. It is a method to solve the above stated problem, which scientists call an inverse scattering problem. The method of linear sampling combines the answers to lots of frequencies but stays linear. So the problem in itself is not approximated but the interpretation of the response is. The central idea is to invert a bounded operator which is constructed with the help of the integral over the boundary of the body. Fioralba got her Diploma (honor’s program) and her Master's in Mathematics at the University of Tirana. For her Ph.D. she worked with George Dassios from the University of Patras but stayed at the University of Tirana. After that she worked with Wolfgang Wendland at the University of Stuttgart as Alexander von Humboldt Research Fellow. During her second year in Stuttgart she got a position at the University of Delaware in Newark. Since 2015 she has been Professor at Rutgers University. She works at the Campus in Piscataway near New Brunswick (New Jersey). References F. Cakoni, D. Colton and H. Haddar, Inverse Scattering Theory and Transmission Eigenvalues, CBMS-NSF Regional Conference Series in Applied Mathematics, 88, SIAM Publications, 2016. F. Cakoni, D. Colton, A Qualitative Approach to Inverse Scattering Theory, Springer, Applied Mathematical Series, Vol. 188, 2014. T. Arens: Why linear sampling works, Inverse Problems 20 163-173, 2003. https://doi.org/10.1088/0266-5611/20/1/010 A. Kirsch: Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems 14 1489-512, 1998 D. Colton, A. Kirsch: A simple method for solving inverse scattering problems in the resonance region, Inverse Problems 12 383-93, 1996. Podcasts S. Fliss, G. Thäter: Transparent Boundaries. Conversation in the Modellansatz Podcast episode 75, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. M. Kray, G. Thäter: Splitting Waves. Conversation in the Modellansatz Podcast episode 62, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. F. Sayas, G. Thäter: Acoustic scattering. Conversation in the Modellansatz Podcast episode 58, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2015. 

Linear Sampling

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 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. References 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) Related Podcasts 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. 

Peaked Waves

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). References 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.Podcasts 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.

Cancer Research

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: Electrochemical formation of the solid electrolyte interphase (SEI) at the anode, breaking of the SEI due to mechanical stress from volume changes of the graphite particles, causing accelerated SEI growth, gas formation and dry-out of the electrodes, percolation theory for describing the loss of contact of graphite particles to the liquid electrolyte, 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. References 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). Podcasts 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. 

Batteries

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. Podcasts 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.

Portrait of Science

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. References 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. Podcasts 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/

Energy Markets

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

Inno2Grid

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. References 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. Podcasts 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. 

Micro Grids

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. References 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. Podcasts 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.

Electric Vehicles on the Grid

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. Simulation around Burj Khalifa using SimScale References 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. Related Podcasts 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.

SimScale

In the last two semesters Gudrun has taught the courses Advanced Mathematics I and II for Mechanical Engineers. This is a mandatory lecture for the International mechanical engineering students at KIT in their first year of the Bachelor program. This program is organized by the Carl Benz School of Engineering. Beside the study courses, the school also provides common housing for students coming to Karlsruhe from all over the world. The general structure and topics of the first year in Advanced Mathematics were already discussed in our episode 146 Advanced Mathematics with Jonathan Rollin. This time Gudrun invited two students from her course to have the student's perspective, talking about mathematics, life, and everything. Yueyang Cai grew up mostly in China. In 2015, the work of her mother led Yueyang to Stuttgart. While looking for opportunities to study a technical subject in Germany the English speaking program in Karlsruhe somehow suggested itself. After one year she is sure to have made the right decision. The second student in the conversation is Siddhant Dhanrajani. His family is Indian but lives in Dubai. For that he got his education in Dubai in an Indian community follwowing the Indian educational system (CBSE). He had never heard of the Engineering program in Karlsruhe but found it through thourough research. He is really amazed at how such an excellent study program and such an excellent university as the KIT are not better known for their value in the world. In the conversation both students talk about their education in their respective countries, their hopes and plans for the study course mechanical engineering and their experiences in the first year here in Karlsruhe. It is very interesting to see how the different ways to teach mathematics, namely, either as a toolbox full of recipes (which the students get well-trained in) or secondly as a way to approach problems in a context of a mathematical education contribute to an experience to be well-equipped to work creative and with a lot of potential as an engineer. Though the students finished only the first year in a three years course they already work towards applications and necessary certificates for their possible master program after finishing the course in Karlsruhe. Related Podcasts G. Thäter, J. Rollin: Advanced Mathematics, Conversation in the Modellansatz Podcast, Episode 146, Department of Mathematics, Karlsruhe Institute for Technology (KIT), 2017. F. Hettlich, G. Thäter: Höhere Mathematik, Gespräch im Modellansatz Podcast, Folge 34, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2014.

Mechanical Engineering

Gudrun met the USA-based mathematician Roza Aceska from Macedonia in Turin at the Conference MicroLocal and Time-Frequency Analysis 2018. The topic of the recorded conversation is dynamical sampling. The situation which Roza and other mathematician study is: There is a process which develops over time which in principle is well understood. In mathematical terms this means we know the equation which governs our model of the process or in other words we know the family of evolution operators. Often this is a partial differential equation which accounts for changes in time and in 1, 2 or 3 spatial variables. This means, if we know the initial situation (i.e. the initial conditions in mathematical terms), we can numerically calculate good approximations for the instances the process will have at all places and at all times in the future. But in general when observing a process life is not that well sorted. Instead we might know the principal equation but only through (maybe only a few) measurements we can find information about the initial condition or material constants for the process. This leads to two questions: How many measurements are necessary in order to obtain the full information (i.e. to have exact knowledge)? Are there possibilities to choose the time and the spatial situation of a measurement so clever as to gain as much as possible new information from any measurement? These are mathematical questions which are answered through studying the equations. The science of sampling started in the 1940s with Claude Shannon who found fundamental limits of signal processing. He developed a precise framework - the so-called information theory. Sampling and reconstruction theory is important because it serves as a bridge between the modern digital world and the analog world of continuous functions. It is surprising to see how many applications rely on taking samples in order to understand processes. A few examples in our everyday life are: Audio signal processing (electrical signals representing sound of speech or music), image processing, and wireless communication. But also seismology or genomics can only develop models by taking very intelligent sample measurements, or, in other words, by making the most scientific sense out of available measurements. The new development in dynamical sampling is, that in following a process over time it might by possible to find good options to gain valuable information about the process at different time instances, as well as different spatial locations. In practice, increasing the number of spatially used sensors is more expensive (or even impossible) than increasing the temporal sampling density. These issues are overcome by a spatio-temporal sampling framework in evolution processes. The idea is to use a reduced number of sensors with each being activated more frequently. Roza refers to a paper by Enrique Zuazua in which he and his co-author study the heat equation and construct a series of later-time measurements at a single location throughout the underlying process. The heat equation is prototypical and one can use similar ideas in a more general setting. This is one topic on which Roza and her co-workers succeeded and want to proceed further. After Roza graduated with a Ph.D. in Mathematics at the University of Vienna she worked as Assistant Professor at the University Ss Cyril and Methodius in Skopje (Macedonia), and after that at the Vanderbilt University in Nashville (Tennessee). Nowadays she is a faculty member of Ball State University in Muncie (Indiana). References Overview on sampling theory and applications: M. Unser: Sampling-50 years after Shannon Proceedings of the IEEE 88 (4) 569 - 587, 2000. Dynamical sampling in shift-invariant spaces: R. Aceska e.a.: Dynamical Sampling in Shift-Invariant Spaces 2014 (Version at Archive} Dynamical sampling: R. Aceska, A. Petrosyan, S. Tang: Dynamical sampling of two-dimensional temporally-varying signals International Conference on Sampling Theory and Applications (SampTA), DOI:10.1109/SAMPTA.2015.7148929, 2015. DeVore, Ronald, and Enrique Zuazua: Recovery of an initial temperature from discrete sampling, Mathematical Models and Methods in Applied Sciences 24.12 (2014): 2487-2501, 2014. Evolution operators involved in dynamical sampling: S. Tang: System identification in dynamical sampling, Advances in Computational Mathematics 43 (3) 555–580, 2017. On Bessel systems, bases and frames in the dynamical sampling setup: A.Aldroubi e.a.:lterative actions of normal operators Journal of Functional Analysis 272 (3), 1121-1146, 2017. Related Podcasts G. Thäter, E. Zuazua: Waves, Conversation in Modellansatz Podcast Episode 054, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. 

Dynamical Sampling

On closer inspection, we find science and especially mathematics throughout our everyday lives, from the tap to automatic speed regulation on motorways, in medical technology or on our mobile phone. What the researchers, graduates and academic teachers in Karlsruhe puzzle about, you experience firsthand in our podcast "The modeling approach".

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Modellansatz - English episodes only

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