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Many modern engineering structures exhibit nonlinear vibration. Characterizing such vibrations efficiently is critical to optimizing designs for reliability and performance. For linear systems, steady-state vibration occurs only at the…
The sampling rate of input and output signals is known to play a critical role in the identification and control of dynamical systems. For slow-sampled continuous-time systems that do not satisfy the Nyquist-Shannon sampling condition for…
The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that…
Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise…
We present a method that formally calculates \emph{exact} frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary…
The bosonisation technique is used to calculate the resonant Raman spectrum of a quantum wire with two electronic sub-bands occupied. Close to resonance, the cross section at frequencies in the region of the inter sub-band transitions shows…
We study the stochastic resonance phenomenon in the overdamped two coupled anharmonic oscillators with Gaussian noise and driven by different external periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth, (iv)…
We consider an oscillator model to describe qualitatively friction force for an atomic force mi-croscope (AFM) tip driven on a surface described by periodic potential. It is shown that average value of the friction force could be controlled…
Resonance based numerical schemes are those in which cancellations in the oscillatory components of the equation are taken advantage of in order to reduce the regularity required of the initial data to achieve a particular order of error…
A new method is introduced to obtain a strong signal by the interference of weak signals in noisy channels. The method is based on the interference of 1/f noise from parallel channels. One realization of stochastic interference is the…
The calibration of modern radio interferometers is a significant challenge, specifically at low frequencies. In this perspective, we propose a novel iterative calibration algorithm, which employs the popular sparse representation framework,…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
Spin noise spectroscopy is a technique to measure magnetization fluctuations, a subject of increasing relevance in ultrafast spintronics. We investigate numerically the equilibrium spin noise of ferro- and antiferromagnets within an…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
The incidence of Alzheimer's disease (AD) and other forms of dementia is increasing in most western countries. For a precise and early diagnosis, several examination modalities exist, among them single-photon emission computed tomography…
We study dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the…
Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion. Of existing methods, mechanical parametric amplification is relatively accessible, but previously thought to be limited to 3dB of squeezing…
We investigate how a constant time delay influences a parametric autoresonant system. This is a nonlinear system driven by a parametrically chirped force with a negative delay-feedback that maintains adiabatic phase locking with the driving…
Spatially selective active noise control (SSANC) hearables aim to attenuate noise from certain directions at the eardrum while preserving desired speech arriving from selected directions. Existing SSANC systems typically assume an accurate…
Atomic force microscopy (AFM) enables high-resolution imaging and quantitative force measurement, which is critical for understanding nanoscale mechanical, chemical, and biological interactions. In dynamic AFM modes, however, interaction…