In man as well as in animals, diurnal rhythms are based on endogenous, periodic processes which can be considered self-sustained oscillations in a technical sense2). Evidence for this is given by the observation that, underconstant conditions, the rhythm continues a) undamped and b) with a frequency which deviates from that of the earth's rotation6). It is this deviation of the free-running 'ci...

Title of dissertation: NOISE-INFLUENCED DYNAMICS OF NONLINEAR OSCILLATORS J. Edmon Perkins, Doctor of Philosophy, 2015 Dissertation directed by: Professor Balakumar Balachandran Department of Mechanical Engineering Noise is usually considered detrimental to the performance of a system and the effects of noise are usually mitigated through design and/or control. In this dissertation, noise-influ...

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, ...

Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It ...

We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the framework of nonlinear coherent states theory. Using the deformed algebra, we construct a quantum field theory in confined space. In particular, we find that...

A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel ̄lter is described. The Bessel unit plays the role of \three-in-one": a delay line, an ampli ̄er and a ̄lter. Results of hardware experiments and numerical simulation are presented. Depending on the parameters of the nonlinear unit the oscillator operates either in a one-scroll or two-scroll mode. Two pos...

Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility c...