Biography
Biography: Elena Tobisch
Abstract
Description of the universe in the scientific paradigm is based on conceptions of action and reaction. The main question then is, what sort of reaction should be expected to this or that action. Intuitively we expect bigger reaction to bigger action, and this is mostly the case. However, there exists a remarkable exception-the phenomenon of resonance first described by Galileo Galilei in 1638: “one can confer motion upon even a heavy pendulum which is at rest by simply blowing against it; by repeating these blasts with a frequency which is the same as that of the pendulum one can impart considerable motion”. Nowadays resonance is generally regarded as a red thread which runs through almost every branch of physics; without resonance we wouldn't have radio, television, music, etc. Horrible destructions due to the occurrence of resonance in a particular system are also well known. The demand for a good mathematical description allowing to predict the appearance of a resonance and to deduce its quantitative characteristics, is obvious. Linear resonances are easily treatable by the linear Fourier analysis while for the description of nonlinear resonances a new branch of the mathematical physics has been recently developed (a book of speaker): “Nonlinear Resonance Analysis”, with its own theory, computational methods, applications and open questions. In this lecture I shall demonstrate how nonlinear resonance analysis can be applied to a number of real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments.
