Abstract
Escape from a potential well due to an external excitation is a classical problem, relevant in many branches of physics, chemistry and engineering. The classical approach, known since the early 40s, considers the escape under the effect of white noise and is widely applied in the theory of chemical reactions. The current presentation addresses the opposite case from the viewpoint of the excitation spectrum – the escape from a potential well under narrow-band forcing. The setting itself is ubiquitous and exhibits certain typical quantitative features known for a long time. However, only recently a mathematical approach capable to cope with the transient character of the process and the strong nonlinearity, and to predict/explain these typical features has been devised. One reveals a profound resonant underlying mechanism of the efficient (or most dangerous) escape. Appropriate reduced-order models allow predicting the dependence of the escape threshold on the forcing frequency, as well as the safe basins in the space of initial conditions. Increase of the dimensionality leads to substantial complications in the escape dynamics. Even for simple energy-preserving 2DOF models, one reveals a plethora of possible resonant and non-resonant escape mechanisms. For some of these mechanisms, it is also possible to develop efficient reduced – order models allowing deep exploration of the escape patterns.
About the Speaker
Born in Kharkov, Ukraine in 1969. Received the MSc degree in applied mathematics and physics from Moscow Institute of Physics and Technology in 1992, PhD (1995) and Doctor of Sciences (2000) degrees in mathematical and physical sciences - in the Institute of Chemical Physics in Moscow. Since 2003 with Faculty of Mechanical Engineering, Technion - Israel Institute of Technology in Haifa. Currently - chaired professor, in 2019-2022 – Dean of the Faculty. Authored more than 230 scientific papers and multiple monographs, presented numerous plenary and invited talks at major scientific conferences in the field and at professional courses.
Host: Professor Alex Vakakis
