Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biology and numerical methods for ODEs

We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with basic knowledge in dynamical systems and numerical methods for ordinary differential equations, we explore a model from mathematical biology where numerical methods fail badly due to catastrophic floating point errors. We analyze the reasons for this behavior by studying the steady states of the model and use the theory of invariants to develop an alternative model that is suited for numerical simulations. Our story intends to motivate combining analytical and numerical knowledge, even in cases where the world looks fine at first sight. We have set up an online repository containing an interactive notebook with all numerical experiments to make this study fully reproducible and useful for classroom teaching.Comment: 17 pages, 10 figure

Longterm existence of solutions of a reaction diffusion system with non-local terms modeling an immune response

This paper shows the global existence and boundedness of solutions of a reaction diffusion system modeling liver infections. Non-local effects in the dynamics between the virus and the cells of the immune system lead to an integro-partial differential equation with homogeneous Neumann boundary conditions. Depending on the chosen model parameters, the system shows two types of solutions which are interpreted as different infection courses. Apart from solutions decaying to zero, there are solutions with a tendency towards a stationary and spatially inhomogeneous state. By proving the boundedness of the solution in the $L^1(\Omega)$- and the $L^2(\Omega)$-norms, it is possible to show the global boundedness of the solution. The proof uses the opposite mechanisms in the reaction terms. The gained rough estimates for showing the boundedness in the $L^1(\Omega)$- and the $L^2(\Omega)$-norms are compared numerically with the norms of the solutions.Comment: 19 pages, 7 figure

Quantenkryptographie als Thema für den Physikunterricht - Vorstellung einer Masterarbeit

Quantenkryptographie ist ein modernes Forschungsgebiet der Physik, welches einen motivierenden Kontext für die Grundkonzepte der Quantenphysik bieten kann. Im Rahmen einer Masterarbeit wurde eine Unterrichtseinheit zur Quantenkryptographie mit Photonen erstellt und an einem Physikkurs der 11. Jahrgangsstufe getestet. Wir stellen die Unterrichtsmaterialien sowie die Ergebnisse von Interviews und Fragebögen vor

Quantenkryptographie als Thema für den Physikunterricht - Vorstellung einer Masterarbeit

Quantenkryptographie ist ein modernes Forschungsgebiet der Physik, welches einen motivierenden Kontext für die Grundkonzepte der Quantenphysik bieten kann. Im Rahmen einer Masterarbeit wurde eine Unterrichtseinheit zur Quantenkryptographie mit Photonen erstellt und an einem Physikkurs der 11. Jahrgangsstufe getestet. Wir stellen die Unterrichtsmaterialien sowie die Ergebnisse von Interviews und Fragebögen vor

Modelling health impacts of hepatitis – model selection and treatment plans

Hepatitis B and C are viruses causing liver infections and resulting in grave secondary diseases. While there are different treatments for chronic liver infections, the process of evolving chronic diseases is still not fully understood. This paper presents an economic-inspired model for the overall health of an infected organism. The health model is based on the results of a reaction diffusion model for describing the space-dependent dynamics of virus and T cells during a liver infection. The different treatments affect the parameters of the reaction diffusion model and influence therefore the well-being of the infected person during an infection. The health model is selected in a detailed process out of a class of possible models. The presented work provides a foundation for an optimal control problem for finding the best treatment strategy

Longterm existence of solutions of a reaction diffusion system with non-local terms modeling an immune response: An interpretation-orientated proof

This paper shows the global existence and boundedness of solutions of a reaction diffusion system modeling liver infections. The existence proof is presented step by step and the focus lies on the interpretation of intermediate results in the context of liver infections which is modeled. Non-local effects in the dynamics between the virus and the immune system cells coming from the immune response in the lymphs lead to an integro-partial differential equation. While existence theorems for parabolic partial differential equations are textbook examples in the field, the additional integral term requires new approaches to proving the global existence of a solution. This allows to set up an existence proof with a focus on interpretation leading to more insight in the system and in the modeling perspective at the same time. We show the boundedness of the solution in the L1 (Omega)- and the L2(Omega)-norms, and use these results to prove the global existence and boundedness of the solution. A core element of the proof is the handling of oppositely acting mechanisms in the reaction term, which occur in all population dynamics models and which results in reaction terms with opposite monotonicity behavior. In the context of modeling liver infections, the boundedness in the L(unendlich)(Omega)-norm has practical relevance: Large immune responses lead to strong inflammations of the liver tissue. Strong inflammations negatively impact the health of an infected person and lead to grave secondary diseases. The gained rough estimates are compared with numerical tests

Hybrid environments for universities. A shared commitment to campus innovation and sustainability

This publication is the result of an international and interdisciplinary expert summit at Technische Universität Berlin, in March 2020. The aim of the expert meeting was to collaboratively write and publish a book, within five days, on the central question: Which organizational structures and processes at universities support a strategic as well as innovative campus development? As experts with an interdisciplinary background including the social sciences, public real estate, urban planning, architecture and landscape architecture, we could examine the question from a holistic perspective and gain new insights. The resulting manifesto states necessary steps and strategies to create innovative and sustainable hybrid environments for universities. It addresses all decision makers – executives, practitioners and contributors alike – as all of us face the challenge of limited resources and needing to do more with less. (DIPF/Orig.

Four perspectives of landscape architectural thinking

Gedruckt erschienen im Universitätsverlag der TU Berlin, ISBN 978-3-7983-2914-0Was ist gute Landschaftsarchitektur? – Undine Giseke, Norbert Kühn, Cordula Loidl-Reisch und Jürgen Weidinger antworten in Auseinandersetzung mit den Konzepten Urbaner Metabolismus, Designing Urban Nature, Alltagstauglichkeit und Atmosphäre. Mit den Konzepten soll etwas verstanden und sollen zugleich Impulse für das Entwerfen gegeben werden. Das kennzeichnet eine besondere Form der Reflexion, die hier als landschaftsarchitektonisches Denken bezeichnet wird.What is good landscape architecture? — Undine Giseke, Norbert Kühn, Cordula Loidl-Reisch, and Jürgen Weidinger provide answers to this question, examining the concepts of urban metabolism, designing urban nature, suitability for daily use, and atmosphere. Their articles seek to bring clarity and provide inspiration for design work. This characterizes a special form of reflection that is referred to here as landscape-architectural thinking

From Social Spaces to Training Fields: Changes in Design Theory of the Children’s Public Sphere in Hungary in the First Half of the 20th Century

The first half of the 20th century brought turbulent changes into the political and social scene of Hungary. Within a few decades the country shifted from being a partner in the Austro-Hungarian Monarchy, to the short-lived Hungarian Soviet Republic, thereafter, the creation of the independent Kingdom of Hungary, which, after the WW2 ultimately became the People’s Republic of Hungary. These changes strongly affected the main ideologies of all fields of life in the country, including architectural, landscape architectural and educational theory and practice. This paper discusses evolving Hungarian ideas about designing places for children in the international context of education. It follows the changing concepts of play space, from designing for physical education and health, to the idea of training soldiers for an approaching war. By tracing the intricate links between these ideas and the history of Hungary during the period between the turn of the 20th century and the beginning of WW2, the paper argues that the interwoven nature of design theory and the socio-political context of children’s spaces is key in understanding their development