Dr. Cordula Reisch

DAAD grant for a research stay

Team

• Principal Investigator
  Cordula Reisch, Technische Universität Braunschweig
• Collaborators
  Cinzia Soresina, University of Graz
  Bao Quoc Tang, University of Graz

Duration

September 2023 to December 2023

Summary

This project falls into within field of mathematical modeling and analysis of partial differential equations, focusing on dynamics, nonlocal effects, pattern formation and bifurcation of models arising from life-science applications like inflammatory processes. Modeling the immune system results in a nonlinear reaction-diffusion system including nonlocal and spatial heterogeneous effects. Those nonlocal terms may lead to a change of the qualitative solution behavior from one stationary point towards another steady state or towards unstable behavior. Nonlocality-driven instabilities are rarely studied in the literature. In this project, I plan to use truncation methods for showing the instability of stationary states depending on the nonlocal term. Furthermore, the stability of the stationary states will be proven for small perturbations. Numerical bifurcation routines will be extended for covering nonlocal terms.

Funding information

This research is funded by the DAAD - Kurzstipendien for Postdocs. 

Simulation and dynamical analysis of wildfire propagation using high resolution computational tools

Team

• Principal Investigator
  Adrián Navas Montilla, Universidad de Zaragoza
• Collaborators
  Pablo Diaz Benito, Universidad de Zaragoza
  Cordula Reisch, Technische Universität Braunschweig
  Ilhan Özgen-Xian, Technische Universität Braunschweig

Duration

August 2023 to September 2026

Summary

Spain is one of the European countries most affected by forest fires. The vulnerability of the Spanish national territory to this problem is increasing because of climate change. According to the latest report of the Intergovernmental Panel on Climate Change (IPCC), temperatures are expected to rise and the weather conducive to wildfires (hot, dry and windy) is becoming more frequent over the next decades. Consequently, forest fires will increase, both in terms of area burned and probability of occurrence. 

Our goal is to develop mathematical and computational tools to analyze and simulate wildfire events, that improve the understanding of the non-linear dynamical processes involved both in the surface propagation and in the atmospheric dynamics of a wildfire. 

The outcome of this research will involve the derivation of new simplified mathematical models for wildfires (including surface-atmosphere interaction), the generation and development of cutting-edge open-source simulation tools, as well as some novel insights on the interplay between the main drivers of the fire spread. We will analyze the conditions for the system to be most susceptible to tipping points due to changes in the external ambient conditions, providing valuable insights for wildfire management and mitigation strategies in a framework of climate change. The scientific results of this research include novel mathematical, numerical and computational tools, e.g. the derivation of novel high-order numerical solvers, which can be of interest to a broad public working on computational fluid dynamics, earth-system modelling, applied mathematics and dynamical system analysis.

Funding information

This research is funded by the Ministerio de Ciencia e Innovación, Spain, under project-nr. PID2022-141051NA-I00.

Interdisciplinary research in ecological, numerical, and mathematical analysis of wildfire hazards

Team

• Principal Investigator
  Cordula Reisch, Technische Universität Braunschweig
• Collaborators
  Ilhan Özgen-Xian, Technische Universität Braunschweig
  Boris Schröder-Esselbach, Technische Universität Braunschweig

Duration

1 April 2023 to 30 November 2023

Summary

Wildfires are large unpredictable fires that occur in natural environments. Many factors contribute to their ignition, spread, and behaviour and as such, the phenomenon is not fully understood. This makes it challenging to develop strategies for managing and preventing wildfires. Our project aims to use mathematical and numerical analysis as well as to follow approaches from theoretical ecology to develop insights into the controls on wildfire propagation and their damage.

Funding information

This research is funded by the Seed Funding Programme of Technische Universität Braunschweig, 2022 Interdisciplinary Collaboration Strengthening Interdisciplinarity - Expanding Research Collaboration.

https://www.tu-braunschweig.de/en/research-services/interdisciplinary-collaboration-matchmaking

Adaptive mesh criteria for highly nonlinear partially saturated concrete

Team

• Principal Investigators
  • Cordula Reisch, Technische Universität Braunschweig
  • Knut Andreas Meyer, Institute of Applied Mechanics, Technische Universität Braunschweig

Duration

1 April 2023 to 30 November 2023

Summary

Numerical simulations help to assess degregation processes in concrete. In this project, we improve simulations for porous media in the interplay between accuracy and computational effort by defining and implementing new criteria for adaptive mesh refinement in the nonlinear partial differential equation.

Funding information

This research is funded by the Seed Funding Programme of Technische Universität Braunschweig, 2022 Interdisciplinary Collaboration Strengthening Interdisciplinarity - Expanding Research Collaboration.

https://www.tu-braunschweig.de/en/research-services/interdisciplinary-collaboration-matchmaking

Workshop "Research challenges in Porous Media at TU Braunschweig" on 16/10/2023

Bachelorarbeiten

• Beschreibung von Waldbränden durch ein höhenabhängiges Kompartmentmodell (Erstprüfer, TU Braunschweig, 2024)
• Einfluss von Modellerweiterungen auf die Lösungen eines Advektion-Diffusion-Reaktion-Modells für Waldbrände (Erstprüfer, TU Braunschweig, 2024)
• Bifurkationsanalyse für dynamische Systeme: Bewertung der Effektivität von Maßnahmen zur Moskito-Bekämpfung (Erstprüfer, TU Braunschweig, 2024)
• Modellierung und Simulation mechatronischer Komponenten des menschlichen Körpers mithilfe von OpenSim  (Erstprüfer, HAWK Göttingen, 2022)
• Erstellung einer Webapplikation zur Kontrolle eines SCADAS XS Messgeräts (Erstprüfer, HAWK Göttingen, 2022)
• Modellgenerierung und - validierung mittels Machine Learning in der Fahrdynamik (Informelle Betreuung, TU Braunschweig, 2021)
• Die Wärmeleitungsgleichung auf gekrümmten Mannigfaltigkeiten und ihre Beziehung zu anisotropen Materialien (Informelle Betreuung, TU Braunschweig, 2019)
• Einbettungssätze im Existenz- und Eindeutigkeitssatz für Reaktions-Diffusions-Gleichungen und ihre Anwendung bei der Modellierung von Leberentzündungen (Informelle Betreuung, TU Braunschweig, 2017)
• Partielle Differentialgleichungen und zelluläre Automaten in der Modellierung von Entzündungsprozessen (Informelle Betreuung, TU Braunschweig, 2017)

Masterarbeiten

• Trennung von Langzeitverhalten und dem Erlernen von Mechanismen mit PINN-Ansätzen (Betreuer, TU Braunschweig, 2024)
• Klassifizierung der Muschelaktivität mittels Künstlicher Intelligenz (Erstprüfer, HAWK Göttingen, 2022)
• Machine Learning techniques for prediction of performance of solar hybrid photovoltaic thermal systems (Erstprüfer, HAWK Göttingen, 2022)
• Planung, Programmierung und virtuelle Inbetriebnahme einer Intralogistikanlage (Erstprüfer, HAWK Göttingen, 2022)
• Performance comparison of CGANs and WGANs for crop disease image synthesis (Zweitprüfer, HAWK Göttingen, 2022)

• Eine praxisnahe mathematische Modellierung der Methanproduktion in einer Biogasanlage (Erstprüfer, Leuphana Universität Lüneburg, 2022)

• Mathematische Modellierung in den Lebenswissenschaften (Wintersemester 2015/16, Übung)
• Funktionentheorie (Sommersemester 2016, 2020, Übung)
• Seminar Funktionentheorie (Wintersemester 2016/17, 2020/21)
• Funktionalanalysis (Wintersemester 2016/17, Übung)
• Seminar Funktionalanalysis (Sommersemester 2017)
• Partielle Differentialgleichungen (Sommersemester 2018, 2021, 2022, Übung)
• Seminar "Partielle Differentialgleichungen" (Sommersemester 2019)
• Mathematische Modellierung (Sommersemester 2017, 2020, 2021, 2022, Übung)
• Ingenieurmathematik V (Wintersemester 2015/16, 2016/17, 2017/18, 2018/19, 2019/20, Übungsbetrieb)
• Wiederholungskurs Ingenieurmathematik V (Sommersemester 2016, 2017, 2018, 2019)
• Modellierung und Numerik von Differentialgleichungen (Sommersemester 2017 [Langemann], 2018 [Löwe], 2019 [Sonar], Übungsbetrieb)
• Ingenieurmathematik A (Analysis 1) (Wintersemester 2020/21)
• Ingenieurmathematik B (Analysis 2 und Gewöhnliche Differentialgleichungen) (Sommersemester 2021)
• CSE - Ordinary Differential Equations (winter term 2020/21)
• CSE - Partial Differential Equations (winter term 2020/21)

• "Partielle Differenzialgleichungen", Master Mathematik, TU Braunschweig, Sommersemester 2024
• "Anwendungsrelevante Ingenieurmathematik", Master Wirtschaftsingenieurwesen, Leuphana Universität Lüneburg, Sommersemester 2020, 2021, 2022, 2024
• "Algorithmen und Datenstrukturen", Bachelor Elektro- und Informationstechnik, HAWK Göttingen (Vertretungsprofessur), Sommersemester 2022
• "Mathematik 3" (Numerik und Statistik), Bachelor-Studiengänge Ingenieurwesen, HAWK Göttingen (Vertretungsprofessur), Wintersemester 2021/22
• "Vertiefte Mathematik" (Vektoranalysis und Funktionalanalysis), Master-Studiengänge Ingenieurwesen, HAWK Göttingen (Vertretungsprofessur), Wintersemester 2021/22
• "Mathematische Modellierung in den Lebenswissenschaften", Master Mathematik, TU Braunschweig, Wintersemester 2019/20