New Invariant Measures to Track Slow Parameter Drifts in Fast Dynamical Systems

Estimates of quantitative characteristics of nonlinear dynamics, e.g., correlation dimension or Lyapunov exponents, require long time series and are sensitive to noise. Other measures (e.g., phase space warping or sensitivity vector fields) are relatively difficult to implement and computationally intensive. In this paper, we propose a new class of features based on Birkhoff Ergodic Theorem, which are fast and easy to calculate. They are robust to noise and do not require large data or computational resources. Application of these metrics in conjunction with the smooth orthogonal decomposition to identify/track slowly changing parameters in nonlinear dynamical systems is demonstrated using both synthetic and experimental data

Dynamic Model for Fatigue Evolution in a Cracked Beam Subjected to Irregular Loading

The coupling of vibration and fatigue crack growth in a simply supported uniform Euler–Bernoulli beam containing a single-edge crack is analyzed. The fatigue crack length is treated as a generalized coordinate in a model for the mechanical system. This coupled model accounts for the interaction between the beam oscillations and the crack propagation dynamics. Nonlinear characteristics of the beam motion are introduced as loading parameters to the fatigue model to match experimentally observed failure dynamics. The method of averaging is utilized both as an analytical and numerical tool to: (1) show that, for cyclic loading, our fatigue model reduces to the Paris\u27 law and (2) compare the predicted fatigue damage accumulation with the experimental data for chaotic and random loadings. A utility of the fatigue model is demonstrated in estimating fatigue life under irregular loadings

Theoretical study of stimulated and spontaneous Hawking effects from an acoustic black hole in a hydrodynamically flowing fluid of light

We propose an experiment to detect and characterize the analog Hawking radiation in an analog model of gravity consisting of a flowing exciton-polariton condensate. Under a suitably designed coherent pump configuration, the condensate features an acoustic event horizon for sound waves that at the semiclassical level is equivalent to an astrophysical black hole horizon. We show that a continuous-wave pump-and-probe spectroscopy experiment allows to measure the analog Hawking temperature from the dependence of the stimulated Hawking effect on the pump-probe detuning. We anticipate the appearance of an emergent resonant cavity for sound waves between the pump beam and the horizon, which results in marked oscillations on top of an overall exponential frequency dependence. We finally analyze the spatial correlation function of density fluctuations and identify the hallmark features of the correlated pairs of Bogoliubov excitations created by the spontaneous Hawking process, as well as novel signatures characterizing the emergent cavity

Optimality conditions in terms of Bouligand generalized differentials for a nonsmooth semilinear elliptic optimal control problem with distributed and boundary control pointwise constraints

We prove a novel optimality condition in terms of Bouligand generalized differentials for a local minimizer of optimal control problems governed by a nonsmooth semilinear elliptic partial differential equation with both distributed and boundary unilateral pointwise control constraints, in which the nonlinear coefficient in the state equation is not differentiable at one point. Therefore, the Bouligand subdifferential of this nonsmooth coefficient in every point consists of one or two elements that will be used to construct the two associated Bouligand generalized derivatives of the control-to-state operator in any admissible control. We also establish the optimality conditions in the form of multiplier existence. There, in addition to the existence of the adjoint state and of the nonnegative multipliers associated with the pointwise constraints as usual, other nonnegative multipliers exist and correspond to the nondifferentiability of the control-to-state mapping. The latter type of optimality conditions shall be applied to the optimal control problems without distributed and boundary pointwise constraints to derive the so-called \emph{strong} stationarity conditions, where the sign of the associated adjoint state does not vary on the level set of the corresponding optimal state at the value of nondifferentiability.Comment: 33 page

Ultra-coherent single photon source

We present a novel type of single photon source in solid state, based on the coherent laser light scattering by a single InAs quantum dot. We demonstrate that the coherence of the emitted single photons is tailored by the resonant excitation with a spectral linewidth below the radiative limit. Our ultra-coherent source opens the way for integrated quantum devices dedicated to the generation of single photons with high degrees of indistinguishability