The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, de...

In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive co...

A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This equivalence enables us to write down the complete set of eigenfunctions. We find the exact constants of motion and a linear W1+∞ algebra associated with this model....

There exist some modular mechanical systems that exhibit inherent synchronization capabilities. Among these, arrays of pendula connected to the same moving platform, under particular conditions are analyzed in this work, tend approach synchronous in-phase or antiphase motion. Such an appealing behavior can be replicated within electronic circuits equipped with multiple power converters achieve ...

We investigate the performance of a linear electromechanical oscillator as an energy harvester of finite-bandwidth random vibrations. We derive exact analytical expressions for the net electrical power and the efficiency of the conversion of the power supplied by the noise into electrical power for arbitrary colored noise. We apply our results to the important case of exponentially correlated n...