In this CRC colloquium, organized by N.N., we're happy to welcome:

- Ana Djurdjevac
Mesoscopic nonlinear SPDE models of particle systems

Abstract:

Interacting particle systems provide flexible and powerful models that are useful in many application areas such as sociology (agents), molecular dynamics

(proteins) etc. However, particle systems with large numbers of particles are very complex and difficult to handle, both analytically and computationally. One of the common strategies is to derive effective equations that describe the time evolution of the empirical particle density.

The main idea of the presentation is to derive and study continuum models for the mesoscopic behavior of particles systems. Contrary to recent work in the field (Fehrman, Gess and others), we are interested in finite size effects and will not consider the infinite particle limit. This approach is also considered in the fluctuating hydrodynamics and we will comment on some of the similarities of the problems. More precisely, we will introduce nonlinear and non-Gaussian models that provide a more faithful representation of the evolution of the empirical density of a given particle system than the usual linear Gaussian perturbations around the hydrodynamic limit models.

In particular, we want to study the well-posedness of these nonlinear SPDE models and to control the weak error of the SPDE approximation with particular control of the initial condition. A prototypical example that we will consider is the formal identification of a finite system of diffusions with the singular Dean Kawasaki SPDE. This is the joint work with H. Kremp and N. Perkowski and is the part of the project C10 with SFB 1114. Furthermore, we will discuss the application of these type of equations in the feedback-loop opinion dynamics, which is a joint work with Jonas Köppl and N. Dj. Conrad.

- Claudia Schillings
Continuous time limit and convergence analysis of ensemble Kalman inversion

Abstract:

The ideas from the Ensemble Kalman Filter introduced by Evensen in 1994 can be adapted to inverse problems by introducing artifical dynamics. In this talk, we will discuss an analysis of the EnKF based on the continuous time scaling limits, which allows to derive estimates on the long-time behavior of the EnKF and, hence, provides insights into the convergence properties of the algorithm.

- Marita Thomas
On a porous-media model for reactive fluid-rock interaction

Abstract:

We discuss the thermodynamical structure of models for reactive two-phase flows and their connection to a porous-media model for reactive fluid-rock interaction used in Geosciences. For this, we make use of the thermodynamical modeling framework of GENERIC (General Equation of Non-Equilibrium Reversible Irreversible Coupling). Mathematical properties of the porous media model are discussed and first results on its mathematical analysis are presented. This is joint work in progress within CRC 1114-project C09 in collaboration with A. Zafferi, D. Peschka, K., Huber, J. Vrijmoed, and T. John.