A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available

An Optomechanical Oscillator on a Silicon Chip

The recent observation on radiation-pressure-driven self-sustained oscillation in high-Q optical microresonators has created new possibilities for development of photonic devices that benefit from unique functionalities offered by these “optomechanical oscillators” (OMOs). Here, we review the physics, fundamental characteristics, and potential applications of OMOs using the silica microtoroidal OMO as an example

Modeling for Active Control of Combustion and Thermally Driven Oscillations

Organized oscillations excited and sustained by high densities of energy release in combustion chambers have long caused serious problems in development of propulsion systems. The amplitudes often become sufficiently large to cause unacceptable structural vibrations. Because the oscillations are self-excited, they reach limiting amplitudes (limit cycles) only because of the action of nonlinear processes. Traditionally, satisfactory behavior has been achieved through a combination of trial-and-error design and testing, with control always involving passive means: geometrical modifications, changes of propellant composition, or devices to enhance dissipation of acoustic energy. Active control has been applied only to small-scale laboratory devices, but the limited success suggests the possibility of serious applications to full-scale propulsion systems. Realization of that potential rests on further experimental work, combined with deeper understanding of the mechanisms causing the oscillations and of the physical behavior of the systems. Effective design of active control systems will require faithful modeling of the relevant processes over broad frequency ranges covering the spectra of natural modes. This paper will cover the general character of the linear and nonlinear behavior of combustion systems, with special attention to acoustics and the mechanisms of excitation. The discussion is intended to supplement the paper by Doyle et al. concerned primarily with controls issues and the observed behavior of simple laboratory devices

Dynamic aperture limitation in e+e−e^+e^- colliders due to synchrotron radiation in quadrupoles

In a lepton storage ring of very high energy (e.g. in the $e^+e^-$ Higgs factory) synchrotron radiation from quadrupoles constrains transverse dynamic aperture even in the absence of any magnetic nonlinearities. This was observed in tracking for LEP and the Future Circular $e^+e^-$ Collider (FCC-ee). Here we describe a new mechanism of instability created by modulation of the particle energy at the double betatron frequency by synchrotron radiation in the quadrupoles. Energy modulation varies transverse focusing strength at the same frequency and creates a parametric resonance of the betatron oscillations with unusual properties. It occurs at arbitrary betatron frequency (the resonant detuning is always zero) and the magnitude of the parameter modulation of the betatron oscillation (strength of the resonance driving term) depends on the oscillation amplitude. Equilibrium between the radiation damping and the resonant excitation gives the boundary of the stable motion. Starting from 6d equations of motion we derive and solve the relevant differential equation describing the resonance, and show good agreement between analytical results and numerical simulation

Oscillation threshold of a clarinet model: a numerical continuation approach

This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach

Orbital angular momentum exchange in an optical parametric oscillator

We present a study of orbital angular momentum transfer from pump to down-converted beams in a type-II Optical Parametric Oscillator. Cavity and anisotropy effects are investigated and demostrated to play a central role in the transverse mode dynamics. While the idler beam can oscillate in a Laguerre-Gauss mode, the crystal birefringence induces an astigmatic effect in the signal beam that prevents the resonance of such mode.Comment: 10 pages, 8 figures, regular articl