Engineering Seminars Test Calendar 2.10

Abstract 

Two-degree-of-freedom system in external potential well is a simple benchmark for exploration of interaction between internal and external transient dynamics. Two simple physical realizations of such systems are a pair of coupled particles in one-dimensional well or more generic case of a single particle in two-dimensional well. We explore two main dynamical settings: escape, when the system starts inside the well, and scattering, when the system starts outside the well. As for more specific model of coupled particles in the single – DOF well, there exists an unexpected asymmetry between the capture and the escape dynamics. The escape dynamics is almost completely governed by asymptotic regimes of strong and weak coupling for a family of different benchmark potential wells; the resonant phenomena are hardly observable. The scattering processes are very different – the possible outcomes are multiple (transition/reflection or also trapping, if the damping is present) and resonant phenomena profoundly reveal themselves. In the space of initial conditions/parameters one observes both regions of integrity (well-predictable scattering outcome) and erosion (sensitive dependence of the outcome on the conditions). Asymptotic methods help to reveal the transition to sensitivity. In more generic 2DOF settings one readily observes the resonance phenomena both for escape and scattering settings. Among multiple interesting phenomena, one can mention dynamics in the vicinity of integrable cases. We can demonstrate that proximity to integrable cases strongly affects the structure of the safety basins and critical excitation level for the escape transitions.  

About the Speaker 

Born in Kharkov, Ukraine in 1969. Received an 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. Authored more than 250 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