Based on the paraxial wave equation, this study extends the theory of small-scale self-focusing (SSSF) from coherent beams to spatially partially coherent beams (PCBs) and derives a general theoretical equation that reveals the underlying physics of the reduction in the B-integral of spatially PCBs. From the analysis of the simulations, the formula for the modulational instability (MI) gain coefficient of the SSSF of spatially PCBs is obtained by introducing a decrease factor into the formula of the MI gain coefficient of the SSSF of coherent beams. This decrease can be equated to a drop in the injected light intensity or an increase in the critical power. According to this formula, the reference value of the spatial coherence of spatially PCBs is given, offering guidance to overcome the output power limitation of the high-power laser driver due to SSSF.

This paper introduces the generalized additive mixed model (GAMM) and the quantile generalized additive mixed model (QGAMM) through reanalyses of bilinguals’ lexical decision data from Dijkstra et al. (2010) and Miwa et al. (2014). We illustrate how regression splines can be used to test for nonlinear effects of cross-language similarity in form as well as for controlling experimental trial effects. We further illustrate the tensor product smooth for a nonlinear interaction between cross-language semantic similarity and word frequency. Finally, we show how the QGAMM helps clarify whether the effect of a particular predictor is constant across distributions of RTs.

In the present work, the ankle rehabilitation robot (ARR) dynamic model that implements a new series of connection control strategies is introduced. The dynamic models are presented in this regard. This model analyzes the robot LuGre friction model and the nonlinear disturbance model. To improve the ARR system’s rapidity and robustness, a composite 2-degree of freedom (2-DOF) internal model control (IMC) controller is presented. The control performance of the compound 2-DOF IMC controller is simulated and analyzed in the present work. The simulation shows that the composite 2-DOF IMC controller has high following performance. For practical testing purposes, 1-DOF passive training and predetermined trajectory following have been completed for different swing amplitudes and frequencies. Moreover, the thrust and tension torque of the robotic dynamic and static loading characteristics are studied in active control mode. The experimental results show the effectiveness of passive training of the given trajectory and impedance training active control strategy. This paper gives the specific functions of ARR.

A fully discrete A-ϕ finite element scheme for a nonlinear model of type-II superconductors is proposed and analyzed. The nonlinearity is due to a field dependent conductivity with the regularized power-law form. The challenge of this model is the error estimate for the nonlinear term under the time derivative. Applying the backward Euler method in time discretisation, the well-posedness of the approximation problem is given based on the theory of monotone operators. The fully discrete system is derived by standard finite element method. The error estimate is suboptimal in time and space.

I revisit the popular concern over a nonlinearity or threshold in the relationship between public debt and growth employing long time series data from up to 27 countries. My empirical approach recognizes that standard time series arguments for long-run equilibrium relations between integrated variables (cointegration) break down in nonlinear specifications such as those predominantly applied in the existing debt–growth literature. Adopting the novel cosummability approach, my analysis overcomes these difficulties to find no evidence for a systematic long-run relationship between debt and growth in the bivariate and economic theory-based multivariate specifications popular in this literature.

This paper develops a model positing a nonlinear relationship between public investment and growth. The model is then applied to a panel of African countries, using nonlinear estimating procedures. The growth-maximizing level of public investment is estimated at about 10% of GDP, based on System GMM estimation. The paper further runs simulations, obtaining the constant optimal public investment share that maximizes the sum of discounted consumption as between 8.1% and 9.6% of GDP. Compared with the observed end-of-panel mean value of no more than 7.26%, these estimates suggest that there has been significant public underinvestment in Africa.

This paper applies smooth transition regressions to incorporate nonlinearity into the impact of trading volume on exchange rate volatility, the so-called mixture distribution hypothesis (MDH). Linking this analysis to the Tobin tax debate, we provide the first empirical corroboration that such a tax may be effective in limiting speculation and reducing exchange rate volatility, especially in turbulent times. Our study points to two main results. First, we show that nonlinearities should be taken into account to explain the MDH. When volatility, spreads, and volume are simultaneously high, the relationship between trading volume and volatility tends to grow stronger and thus the MDH holds in turbulent periods. Second, on the assumption of constant trading volume elasticity, a Tobin tax would have been stabilizing and effective in the 2008 crisis.

Linear stability analysis (LSA) is applied to the mean flow of an oscillating round jet with the aim of investigating the robustness and accuracy of mean flow stability wave models. The jet’s axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry (PIV) and decomposed into a mean and periodic part utilizing proper orthogonal decomposition (POD). Local LSA is applied to the measured mean flow adopting a weakly non-parallel flow approach. The resulting global perturbation field is carefully compared with the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{>}40\, \%$), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

This paper describes a digital signal processing (DSP) method for achieving “ideal” amplification, maximizing both the average output signal power and power-added-efficiency for any signal waveform and any power amplifier (PA) transfer characteristic. Detailed algorithms are described for optimally accomplishing peak reduction (PR), predistortion (PD) linearization, and integration of these DSP techniques with envelope tracking PAs. Hardware characterization results validate the theories of PD and PR operation.

Using international data, this paper explores whether the efficient market hypothesis for real stock prices is supported for different panels. The stationarity of a real stock price has important implications for modeling and forecasting financial activities. On a global scale, we implement the recently developed nonlinear heterogeneous panel unit root test, which allows us to account for possible nonlinearity and cross-section dependence and to identify how many and which countries of the panel contain a unit root. The primary conclusion is that the stationarity of real stock prices varies between regions and levels of economic development. Overall, our empirical results illustrate that real stock prices in these countries are a mixture of stationary (integrated of order zero) and nonstationary (integrated of order one) processes.

This paper estimates time-varying forward-looking monetary policy reaction functions for the central banks of France, Germany, Italy, and the United Kingdom. We utilize the framework developed by Kim [Economics Letters 91 (2006) 21–26] and Kim and Nelson [Journal of Monetary Economics (2006) 1949–1966] to deal with the issue of endogeneity in a time varying–parameter model. Our results find substantial time variation in the conduct of monetary policy in these four countries, which cannot be adequately captured by the conventional fixed-coefficient approach. Our findings suggest that there was a significant decline in the Bank of France's and the Bank of Italy's response to the German interest rate in 1992, and it coincided with the breakdown of the exchange rate management system in Europe. Our results suggest that the Bank of England was slower than the Bundesbank to increase its response to expected inflation, as its response to inflation became more than one-for-one only in the early 1980s.

Acceleration processes at astrophysical collisionless shocks are reviewed with a special emphasis on the importance of in situ observations of heliospheric shocks. Topics to be included are nonlinear reaction of shock acceleration process, effect of neutral particles, and electron acceleration.

A simple fluorescence microscopy technique is developed and presented to investigate heterogeneities in emission intensity and quenching responses of luminescence sensors and to measure diffusion and permeation coefficients of oxygen in polymers. Most luminescence oxygen sensors do not follow linearity of the Stern-Volmer (SV) equation due to heterogeneity of luminophore in the polymer matrix. To circumvent this limitation, inverted fluorescence microscopy is utilized in this work to investigate the SV response of the sensors at the micron scale. It was found that intensity is higher in regions where the luminophore is aggregated, but the response is poorer to oxygen concentration. In contrast, the nearly homogeneous regions exhibit linearity with high SV constants. In these diffusion experiments, oxygen concentration was measured by luminescence changes in regions with high SV constants and good linearity. Two diffusion experiments were performed—termed film-on-sensor and accumulation-in-volume techniques. A new Fick's law based quasi-steady-state diffusion model was developed and combined with the SV equation to obtain effective permeation coefficients for the accumulation-in-volume technique. Using these experimental techniques, oxygen diffusion properties in free-standing Teflon polymer films, cast silicon elastomers, and cast polydimethylsiloxane films containing different weight percentages of zeolite were determined with good precision.