The effect of finite response–time in coupled dynamical systems

The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ?=?0) case. The critical coupling strength at which synchronization sets in is found to increase with τ. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization.     

Green and fast DSL via joint processing of multiple lines and time–frequency packed modulation

In this paper, strategies to enhance the performance, in terms of available data-rate per user, energy efficiency, and spectral efficiency, of current digital subscriber lines (DSL) are proposed. In particular, a system wherein a group of copper wires is jointly processed at both ends of the communication link is considered. For such a scenario, a resource allocation scheme aimed at energy efficiency maximization is proposed, and, moreover, time–frequency packed modulation schemes are investigated for increased spectral efficiency. Results show that a joint processing of even a limited number of wires at both ends of the communication links brings remarkable performance improvements with respect to the case of individual point-to-point DSL connections; moreover, the considered solution does represent a viable means to increase, in the short term, the data-rate of the wired access network, without an intensive (and expensive) deployment of optical links.     

Stochastic feedback,nonlinear families of Markov processes,and nonlinear Fokker–Planck equations

We discuss two fundamental aspects of Fokker–Planck equations that are nonlinear with respect to probability densities. First, we show that evolution equations of this kind describe processes involving stochastic feedback and interpret stochastic feedback processes in terms of hitchhiker processes and path integral solutions. Second, we demonstrate that nonlinear Fokker–Planck equations can be interpreted as linear Fokker–Planck equations describing nonlinear families of Markov diffusion processes. We exploit this finding in order to derive complete hierarchies of probability densities from nonlinear Fokker–Planck equations.     

Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.     

The von Neumann representation as a joint time–frequency parameterization for polarization-shaped femtosecond laser pulses

We generalize the joint time–frequency von Neumann representation of femtosecond laser pulses for usage with time-dependent polarization states. The electric field is expanded in terms of Gaussian-shaped transform-limited subpulses located on a discrete time–frequency lattice, each with a specific polarization state. This formalism provides an intuitive picture for the time- and frequency-dependent polarization state. It can also serve as a basis for polarization pulse shaping. As an illustration, we define pulses for which polarization parameters (ellipticity and orientation) are given directly in time–frequency phase space. This approach has applications in quantum control and other areas for which time- and frequency-dependent light polarization is relevant.     

On the recovery of moving source characteristics using time–frequency approach

Four time–frequency analysis techniques, namely the short-time Fourier transform, the wavelet transform, the polynomial phase estimation and the Chirplet transform, are used in the present study to recover the moving speed, the sound frequency and the strength of a point source moving with a subsonic speed relevant to those of the road vehicles. Their performances in the presence of background random noises are tested in detail. The instant of the highest rate of change of the Doppler frequency is used as the time reference in the parameter recovery process. Results suggest that the performances of short-time Fourier transform and the wavelet transform, especially the former, are not satisfactory when compared to those of the other two methods even when the signal-to-noise ratio is reasonably high. The Chirplet transform gives a performance which is the least affected by the signal-to-noise ratio, while the accuracy of the polynomial phase estimation is the best among the four methods tested.     

X-ray fluorescence analysis of Ni–Fe–Mn/Cr systems

We have developed a procedure for x-ray fluorescence determination of the constituent composition and thickness of two-layer Ni–Fe–Mn/Cr films deposited on Polikor, an aluminum oxide ceramic. We have calculated correction coefficients taking into account interelement interference effects in this system. We have experimentally determined the density of the materials making up the composition of the films. We have established and present the metrological characteristics of the procedure developed.     

Fokker–Planck equation analysis of randomly excited nonlinear energy harvester

The probability structure of the response and energy harvested from a nonlinear oscillator subjected to white noise excitation is investigated by solution of the corresponding Fokker–Planck (FP) equation. The nonlinear oscillator is the classical double well potential Duffing oscillator corresponding to the first mode vibration of a cantilever beam suspended between permanent magnets and with bonded piezoelectric patches for purposes of energy harvesting. The FP equation of the coupled electromechanical system of equations is derived. The finite element method is used to solve the FP equation giving the joint probability density functions of the response as well as the voltage generated from the piezoelectric patches. The FE method is also applied to the nonlinear inductive energy harvester of Daqaq and the results are compared. The mean square response and voltage are obtained for different white noise intensities. The effects of the system parameters on the mean square voltage are studied. It is observed that the energy harvested can be enhanced by suitable choice of the excitation intensity and the parameters. The results of the FP approach agree very well with Monte Carlo Simulation (MCS) results.     

Evolutionary (frequency/time) spectral analysis of the response of vehicles moving on rough ground by using “covariance equivalent” modelling

In a number of physical problems such as the motion of vehicles travelling over rough ground or the noise emanating from a moving source, non-stationarity is induced by a non-linear time dilation (due to velocity variations or Doppler effects) of the source or excitation process so that the resulting process is “frequency modulated”. This is true even if the underlying process is homogeneous in another domain. Hitherto it has not been possible to apply the frequency/time analysis due to Priestley [1] to this class of problem but here, by introducing the concept termed “covariance equivalence” by the authors, this method can be seen to apply. An example of a vehicle moving with variable velocity on a rough surface is considered.     

Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis

Investigating long-range correlation by the Hurst exponent, H$H$, is crucial in the study of time series. Recently, empirical-mode-decomposition-based arbitrary-order Hilbert spectral analysis (EMD-HSA) has been proposed to numerically obtain without proof a scaling relationship, generated from the amplitude–frequency distribution, related to H$H$. We propose a formalism to empirically study EMD-HSA, to deduce its scaling exponent ξ(q)$\xi \left(q\right)$ from the perspective of EMD-based arbitrary-order Hilbert marginal spectrum (EMD-HMS), and to numerically compare the results with the expected H$H$. EMD-HSA and EMD-HMS experiments show that, by incompletely removing (quasi-)periodic trends, the sunspot series should have an H$H$ value around 0.12.     

Transient analysis of nonlinear Euler–Bernoulli micro-beam with thermoelastic damping,via nonlinear normal modes

In this paper an Euler–Bernoulli model has been used for vibration analysis of micro-beams with large transverse deflection. Thermoelastic damping is considered to be the dominant damping mechanism and introduced as imaginary stiffness into the equation of motion by evaluating temperature profile as a function of lateral displacement. The obtained equation of motion is analyzed in the case of pure single mode motion by two methods; nonlinear normal mode theory and the Galerkin procedure. In contrast with the Galerkin procedure, nonlinear normal mode analysis introduces a nonconventional nonlinear damping term in modal oscillator which results in strong damping in case of large amplitude vibrations. Evaluated modal oscillators are solved using harmonic balance method and tackling damping terms introduced as an imaginary stiffness is discussed. It has been shown also that nonlinear modal analysis of micro-beam with thermoelastic damping predicts parameters such as inverse quality factor, and frequency shift, to have an extrema point at certain amplitude during transient response due to the mentioned nonlinear damping term; and the effect of system?s characteristics on this critical amplitude has also been discussed.     

Numerical analysis of absorption–amplification response in an optical fiber

We investigated the transient and steady-state processes of a probe field in an optical fiber. It is found that the nonlinear processes can be easily controlled via the coherent field and incoherent pumping field. The underlying mechanisms are much more practical than those in atomic systems, which may provide some possibilities for technological applications in optical-fiber communication.     

Dose response and kinetic analysis of thermoluminescence of Li–Zn fluoroborate glass

The intention of this study is to explore the thermoluminescence properties of beta-irradiated Li–Zn fluoroborate glass. The glow-curve corresponding to 10?Gy shows two peaks when measured at 1°C/s. The dose response of the glass to beta irradiation was investigated. The trapping level parameters such as activation energy, frequency factor and order of kinetics associated with the observed glow-peak were determined using different methods. The thermoluminescence is affected by thermal quenching. A possible mechanism for the thermoluminescence is described.     

Analytical treatments of the space–time fractional coupled nonlinear Schrödinger equations

Under investigation in this work is a (\(2+1\))-dimensional the space–time fractional coupled nonlinear Schrödinger equations, which describes the amplitudes of circularly-polarized waves in a nonlinear optical fiber. With the aid of conformable fractional derivative and the fractional wave transformation, we derive the analytical soliton solutions in the form of rational soliton, periodic soliton, hyperbolic soliton solutions by four integration method, namely, the extended trial equation method, the \(\exp (-\,\Omega (\eta ))\)-expansion method and the improved \(\tan (\phi (\eta )/2)\)-expansion method and semi-inverse variational principle method. Based on the the extended trial equation method, we derive the several types of solutions including singular, kink-singular, bright, solitary wave, compacton and elliptic function solutions. Under certain condition, the 1-soliton, bright, singular solutions are driven by semi-inverse variational principle method. Based on the analytical methods, we find that the solutions give birth to the dark solitons, the bright solitons, combine dark-singular, kink, kink-singular solutions with fractional order for nonlinear fractional partial differential equations arise in nonlinear optics.     

Fast nonlinear optical mechanism of photoconversion in systems of lyotropic ionic liquid crystals–viologen impurities

We study a new nonlinear optical mechanism of reversible photoconversion between excited dimers and cation radicals, the reduction products of electrochromic molecules (viologens), in lyotropic ionic liquid crystals of metal alkanoates. The results of the theoretical study are compared with experimental data obtained from dynamic holographic recordings as well as nonlinear absorption measurements. The estimated value of the photoconversion probability is higher than the probability of non-radiative relaxation of excited molecules. The value of the cubic nonlinearity is χ ^(3)?～?4?·?10^?7?esu for colored cells of these materials.     

The efficient computation of the nonlinear dynamic response of a foil–air bearing rotor system

The foil–air bearing (FAB) enables the emergence of oil-free turbomachinery. However, its potential to introduce undesirable nonlinear effects necessitates a reliable means for calculating the dynamic response. The computational burden has hitherto been alleviated by simplifications that compromised the true nature of the dynamic interaction between the rotor, air film and foil structure, introducing the potential for significant error. The overall novel contribution of this research is the development of efficient algorithms for the simultaneous solution of the state equations. The equations are extracted using two alternative transformations: (i) Finite Difference (FD); and (ii) a novel arbitrary-order Galerkin Reduction (GR) which does not use a grid, considerably reducing the number of state variables. A vectorized formulation facilitates the solution in two alternative ways: (i) in the time domain for arbitrary response via implicit integration using readily available routines; and (ii) in the frequency domain for the direct computation of self-excited periodic response via a novel Harmonic Balance (HB) method. GR and FD are cross-verified by time domain simulations which confirm that GR significantly reduces the computation time. Simulations also cross-verify the time and frequency domain solutions applied to the reference FD model and demonstrate the unique ability of HB to correctly accommodate structural damping.