A4.2025: Multiscale rheological inverse problems and active processes in cells
Collaborating PIs: Andreas Janshoff, Sarah Köster, Tim Salditt, Peter Sollich
Overarching research question: How can rheological data for active matter be evaluated in a stable way with respect to noise?
Many mechanical properties of active matter, cells or biological tissue cannot be measured directly. We thus have to draw conclusions on such properties from indirect measurements, i.e., from their impact on observable quantities. Mathematically, such problems are called inverse problems. Since measured data are usually corrupted by noise, we have to develop solution techniques that are stable with respect to noisy data. The goal of this project is to formulate, analyze, and solve inverse problems arising in rheological experiments on multiple scales. This requires techniques from numerical mathematics, functional analysis and partial differential equations as well as a good understanding of physical modeling. We work closely with our collaborators from experimental and theoretical physics regarding appropriate modeling and measurement data to develop suitable mathematical methods for the analysis and stable reconstruction techniques of the inverse problems. We focus on viscoelastic properties of active matter and, on a larger scale, of migrating cells.
Core field: theoretical physics/mathematics
PhD training objectives: inverse problems in cell physics (ill-posedness, regularization techniques); modelling (rheology, active processes); understanding of the data generation process and experimental techniques; implementation of algorithms.