Abstract Flexure oscillators are promising time bases, thanks to their high quality factor and monolithic design compatible with microfabrication. In mechanical watchmaking, they could advantageously replace the traditional balance hairspring oscillator, leading improvements in timekeeping accuracy, autonomy, assembly. As MEMS oscillators, performance can rival that of well-established quartz o...

We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show...

Optical excitation plays an important role in the actuation of higher flexural and torsional modes of nanoelectromechanical oscillators. We show that optical fields are extremely efficient for excitation, direct control and measurement of in-plane motion of cantilever-type nanomechanical oscillators. As a model system, 200 nm and 250 nm thick single crystal silicon cantilevers with dissimilar l...

Vibrational transitions contain some of the richest fingerprints of molecules and materials, providing considerable physicochemical information. Vibrational transitions can be characterized by different spectroscopies, and alternatively by several imaging techniques enabling to reach sub-microscopic spatial resolution. In a quest to always push forward the detection limit and to lower the numbe...

The BN -type Calogero-Sutherland-Moser system in one-dimension is shown to be equivalent to a set of decoupled oscillators by a similarity transformation. This result is used to show the connection of the AN and BN type models and explain the degeneracy structure of the later. We identify the commuting constants of motion and the generators of a linear W∞ algebra associated with the BN system. ...

Optoelectronic oscillators (OEOs) are hybrid RF-photonic devices that promise to be environmentally robust high-frequency RF sources with very low phase noise. Previously, we showed that Rayleigh-scattering-induced noise in optical fibers coupled with amplitude-to-phase noise conversion in photodetectors and amplifiers leads to fiber-length-dependent noise in OEOs. In this work, we report on tw...

We develop an algebraic approach for finding the eigenfunctions of a large class of few and many-body Hamiltonians, in one and higher dimensions, having linear spectra. The method presented enables one to exactly map these interacting Hamiltonians to decoupled oscillators, thereby, giving a precise correspondence between the oscillator eigenspace and the wavefunctions of these quantum systems. ...

A single bunch of charged particles in a storage ring is a system of 10-10 coupled non-linear oscillators with radiative energy loss and compensated by the accelerating cavity. A stable collective mode in such system was induced and observed in the SPEAR storage ring using a turn-by-turn phase space monitor. New possibilities of using this mode as a tool to experimentally study non-linear dynam...

Oscillatory instability at the Hopf bifurcation is a dynamical phenomenon that has been suggested to characterize active non-linear processes observed in the auditory system. Networks of oscillators poised near Hopf bifurcation points and tuned to tonotopically distributed frequencies have been used as models of auditory processing at various levels, but systematic investigation of the dynamica...

We study the scaling properties of energy spreading in disordered strongly nonlinear Hamiltonian lattices. Such lattices consist of nonlinearly coupled local linear or nonlinear oscillators, and demonstrate a rather slow, subdiffusive spreading of initially localized wave packets. We use a fractional nonlinear diffusion equation as a heuristic model of this process, and confirm that the scaling...