Prof. N. Sri Namachchivaya (University of Waterloo)
Friday, July 5, 2019 - 14:00
Humboldt-Universität zu Berlin, Erwin-Schrödinger-Zentrum
Rudower Chaussee 26, 12489 Berlin, Konferenzraum, Erdgeschoss
Institut für Mathematik, Humboldt-Universität zu Berlin,
Richard von Mises-Lecture
I will present a general overview of several engineered and natural systems with uncertain mathematical models, the multidisciplinary methods (that encompass the area of random dynamical systems) required for their analysis, and relevant results. The first part of this talk focuses on developing methods to unravel complex interactions between noise and nonlinearities using a mix of multidisciplinary approaches from theory, modeling, and simulation. Practical applications of these research results are beginning to appear across the entire spectrum of mechanics. I will examine the flutter characteristics of an airfoil in turbulent flow. Turbulence is a common factor in airplane accidents, for example loss of in-flight control associated with wind gusts, which can cause substantial damage to the aircraft and injuries to crew and passengers. The analysis is performed close to the critical value of the bifurcation parameter (the free-stream airspeed) that induces flutter in a two-dimensional airfoil. The second part of the talk focuses on the challenges in data assimilation that arise from the interactions between uncertainties, nonlinearities, and observations. I will present rigorous reduced-order data assimilation techniques for high dimensional multi-scale problems. In particular, I will outline how scaling interacts with filtering via stochastic averaging. Finally, I will present a new particle filtering algorithm that combines stochastic homogenization with filtering theory, where importance sampling and control methods are used as a basic and flexible tool for the construction of the proposal density inherent in particle filtering.
submitted by Sabine Bergmann (bergmann@math.hu-berlin.de, 2093 5811)