A case study of how the availability of tools controls the progress of science.

• Thematic program: Models in Plasmas, Earth and Space Science (2024/2025)

Abstract: The spontaneous emergence of tissue patterns is often attributed to biochemical reaction-diffusion systems. Strictly biochemical mechanism modelled through the LALI-type Gierer-Meinhardt-Turing system are a hallmark of Mathematical Biology and have been identified as drivers of pattern formation in a series of experimental systems. In Hydra spheroids, however, a purely biochemical model for self-organization remains elusive. In this talk, we present a general overview of mathematical models for pattern formation including LALI models, and then introduce a mechanochemical realisation of this concept based on a positive feedback loop between morphogen concentration and and tissue stretching. We briefly discuss the resulting minimal mathematical model for mechanochemical pattern formation in a closed elastic shell represents regenerating Hydra epithelial spheroids. Linear stability analysis of the 1D-version of the model and 3D simulations illustrate how mechanical forces drive axis formation and predict the organizer's location under various perturbations.

• Thematic program: Mathematics – Magnetism - Materials (2024/2025)
• Event: Workshop on "Computational Micromagnetism" (2025)

The investigation of ultra-fast magnetization processes is crucial in spin dynamics due to their potential use in future generations of nanomagnetic and spintronic devices. Recently, experimental demonstration (Neeraj et al, Nat. Phys 17, 245 2021) of the presence of inertial effects in magnetization dynamics predicted several years ago (Ciornei et al., PRB 83, 020410, 2011) was achieved by direct detection of spin nutation in ferromagnets at terahertz frequencies. From a theoretical perspective, inertial magnetization dynamics can be modelled by augmenting the classical Landau-Lifshitz-Gilbert (LLG) precessional dynamics with a torque term that considers angular momentum relaxation proportional to the second time-derivative of magnetization, leading to a higher-order dynamical system governed by the inertial LLG equation (iLLG). In this presentation, we first derive and discuss the qualitative properties of the iLLG dynamics that profoundly differs from the classical LLG despite including remarkably similar conservation properties. Then, we develop analytical theory for inertial exchange spin-wave propagation in infinite thin-films. Finally, we propose and validate a couple of time-integration schemes for iLLG dynamics that allow to realize accurate and efficient inertial micromagnetic simulations.

• Thematic program: Mathematics – Magnetism - Materials (2024/2025)
• Event: Workshop on "Computational Micromagnetism" (2025)