Nonlinear Dynamics in Distributed Systems

We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a systematic way using Van Kanpen's expansion method for Markov processes. We present some results for both stationary and time-dependent states. Our approach allows the effect of fluctuations to be explored, particularly in finite systems where such processes assume increasing importance.Comment: Two parts: 8 pages LaTeX file and 5 (uuencoded) figures in Postscript forma

On Artifacts in Nonlinear Dynamics

Nonlinear oscillations are of permanent interest in the field of dynamics of mechanical and mechatronical systems. There exist several well-known semi-analytical methods like Harmonic Balance, perturbation analysis or multiple scales for such problems. We reconsider in our presentation the method of Harmonic Balance but add some additional steps in order to avoid artifacts and get information about the stability. The classical method of Harmonic Balance is therefore added by an error criterion, which considers the neglected terms. Looking on this error for increasing ansatz orders, it can be decided whether a solution exists or is an artifact of the method. For the low error solutions, a stability analysis is performed. As example, an extended Duffing oscillator with additional nonlinear damping and excitation is considered showing regions of separated island solutions. Also a nonlinear piezo-beam energy harvesting system is investigated. The described method enables to calculate solutions in a rapid manner with comparable low effort, to get an overview over regular responses of nonlinear systems.DFG, 253161314, Untersuchung des nichtlinearen dynamischen Verhaltens von stochastisch erregten Energy Harvesting Systemen mittels Lösung der Fokker-Planck-Gleichun

Optomechanics

We review recent progress in the field of optomechanics, where one studies the effects of radiation on mechanical motion. The paradigmatic example is an optical cavity with a movable mirror, where the radiation pressure can induce cooling, amplification and nonlinear dynamics of the mirror.Comment: 12 pages, 4 figures, submitted to the proceedings of the NATO Advanced Research Workshop 'Recent Advances in Nonlinear Dynamics and Complex System Physics', Tashkent, Uzbekistan, 200