07.10.2024–30.09.2027
FWF ESPRIT project
Principal investigator: Claudia RAITHEL (E101-01-3)

IIn the FWF ESPRIT Project “Effective Large-Scale Models for Random Diffusive Systems” we are interested in the mathematical study and approximation of systems exhibiting scale separation, meaning that there is a measurable distinction between the scale of microscopic structures and a relevant macroscale of interest. Since such systems are ubiquitous throughout nature, they are of fundamental interest in Applied Mathematics. In the project, which commenced in October 2024 and is led by Dr. Claudia Raithel and mentored by Prof. E. Davoli, two different types of scale separation are considered: a separation of length scales as well as one in terms of the number of particles in an interacting particle system. In the first part of the project we are interested in approximating the physical properties of a material sample with random heterogeneities that are much smaller than the size of the sample. In the second part of the project our goal is to justify the approximation of certain stochastic particle systems describing interacting subpopulations in the mesoscopic regime of 'large but finite' particle numbers via equations of ‘fluctuating hydrodynamics’ -i.e., in terms of suitable highly singular SPDEs.