The research and networking activities of MB2 have the goal to provide a growing interdisciplinary exchange platform for differential equation models, their analytical and numerical treatment as well as their simulation. Numerous small and large scale projects are contributing to MB 2 ranging from a large DFG-funded collaborative research center (CRC 1173 Wave Phenomena: Analysis and Numerics) and research training groups (RTG 2218: Simulation of Mechano-Electro-Thermal Processes in Lithium-Ion Batteries, RTG 2450: Tailored Scale-Bridging Approaches to Computational Nanoscience) to small seed-funded projects involving individual researchers. Each of the projects provides an example of a successful collaboration between mathematicians and applied scientists. The projects are characterized by formulating a common differential equation model of the underlying real-world problem which is then mathematically analyzed by using analytical and numerical tools. The findings are used e.g., to predict material or fluid behaviour, to refine models, to calibrate laboratory equipment, to construct innovative telecommunication technologies, to fabricate optimized components and to simulate outcomes of experiments which are too costly to run in reality.

Example projects cover chip-scale loss-optimized optical waveguides and photonic wire bonds coupling electronic and optical components,  tailor-made frequency combs in optical micro-resonators for telecommunication applications, simulation of performance and aging of cell-stacked lithium-ion batteries, electrophysiological dynamical models of the human heart, Lattice-Bolzmann methods for fluid flows of rough surfaces, particle-fuid-flows and turbulent flows.

MB 2 is running regular topical meetings where members give short presentations (5 minutes, 3 slides) of their current research and address questions like:

• How does our problem/model look like?
• What is our ansatz?
• For which questions do we need answers?
• What kind of cooperation do we seek?

The next topical meeting will be held with the title "Anything related to COVID-19". Its goal is to provide a quick and easily organizable overview on our contributions to the scientific evaluations of different aspects of the pandemic, e.g., aerosol simulation, pandemic differential equation models, teaching basics of mathematical biology to undergraduates, science communication etc.

In the future, MB 2 aims to enhance the collaborations between its members by specifically addressing young researchers on student, PhD, junior research group leader and tenure track professor level since we believe that in particular early-career researchers will make a significant difference in the development of interdisciplinary research.