Nonlinear Saturation Effects Research Articles

Exclusive vector meson photoproduction at high energies using the discrete BFKL approach

A phenomenological study of the exclusive vector meson photoproduction within the discrete BFKL approach is performed. We estimate the BFKL amplitude in terms of a discrete set of eigenfunctions and use the HERA [Formula: see text] data to constrain the free parameters of the model. As a consequence, we derive a parameter free prediction of the energy dependence of the exclusive vector meson cross section. We demonstrate that the HERA and LHCb data for the exclusive [Formula: see text] and [Formula: see text] photoproduction are quite well describe in a large energy range. However, the model overestimates the precise LHCb data for the smallest values of [Formula: see text], which can be interpreted as an indication of the onset of nonlinear (saturation) effects in the QCD dynamics.

Improved Online Optimization-Based Optimal Tracking Control Method for Induction Motor Drives

An online optimization-based optimal tracking control method to control IM drives in the entire speed and torque ranges is proposed in this article. The main feature of the proposed method is considering the nonlinear core saturation effects in generating the optimal reference currents in MTPA, field-weakening, and maximum torque per voltage (MTPV) regions. Constrained optimization problems are formulated and solved using Lagrange multipliers method to derive improved nonlinear MTPA and MTPV optimality conditions. Unlike most of the existing loss minimization methods in the literature, using optimal reference point look-up tables is avoided in the proposed method. Moreover, the effects of stator resistive drops, dc-link voltage variations, and inverter nonlinear voltage drop, which are usually neglected in the literature, are considered in generating optimal reference currents. A new straightforward and well-structured optimal reference point calculation scheme is proposed by dividing the operating plane of IM into four regions. The optimal reference currents in each region are then generated by solving the corresponding optimization problem. The smooth operation and transition of the proposed control method between MTPA and field-weakening regions are verified using simulations. The effectiveness of the proposed method is experimentally validated on a 4.7-kW, 4-pole, three-phase induction motor drive.

Infrared renormalon contributions in gluon TMD at small-x

The nonperturbative uncertainties from the infrared renormalons in the (color dipole) gluon distribution is estimated. It is shown that non-linear saturation effects at small-x shift the first IR pole at the Borel plane from 2/β2 to 1/β2. As a consequence the estimated uncertainty is found to be O(ΛQCD2) instead of O(ΛQCD4). It is however accompanied by a soft suppression term which results further suppression of the nonperturbative infrared renormalon contribution at small x.

Novel auxiliary saturation compensation design for neuroadaptive NTSM tracking control of high speed trains with actuator saturation

In this paper, a novel auxiliary saturation compensation system is constructed to eliminate the negative effect of asymmetric nonlinear actuator saturation (ANAS). Two chatter-free neuroadaptive sliding mode tracking control strategies are proposed by combining nonsingular terminal sliding mode (NTSM) control technique with radial basis function neural network (RBFNN) for high speed trains for resp., the actuator saturation-free and ANAS saturation cases. These two control strategies are used to guarantee that the closed-loop signals are bounded and the steady-state tracking errors converge to a residual around zero. The common assumption that the initial velocities of the train and the desired trajectory are zero, is removed in this paper. In addition, the computationally inexpensive strategy contains an optimized NN adaptation mechanism where only one parameter requires online updating no matter how many neurons are chosen. Finally, numerical examples are provided to demonstrate the validity of the proposed control strategies.

Forms, Importance, and Ineffability of Factor Interactions to Define Personality Disorders.

The emergent interpersonal syndrome (EIS) approach conceptualizes personality disorders as the interaction among their constituent traits to predict important criterion variables. We detail the difficulties we have experienced finding such interactive predictors in our empirical work on psychopathy, even when using uncorrelated traits that maximize power. Rather than explaining a large absolute proportion of variance in interpersonal outcomes, EIS interactions might explain small amounts of variance relative to the main effects of each trait. Indeed, these interactions may necessitate samples of almost 1,000 observations for 80% power and a false positive rate of .05. EIS models must describe which specific traits' interactions constitute a particular EIS, as effect sizes appear to diminish as higher-order trait interactions are analyzed. Considering whether EIS interactions are ordinal with non-crossing slopes or disordinal with crossing slopes, or entail nonlinear threshold or saturation effects may help researchers design studies, sampling strategies, and analyses to model their expected effects efficiently.

Active energy transport and the role of symmetry breaking in microscopic power grids

We study the transfer of energy through a network of coupled oscillators, which represents a minimalmicroscopic power grid connecting multiple active quantum machines. We evaluate the resulting energy currentsin the macroscopic, thermal, and quantum regime and describe how transport is affected by the competitionbetween coherent and incoherent processes and nonlinear saturation effects. Specifically, we show that thetransfer of energy through such networks is strongly influenced by a nonequilibrium phase transition between anoise-dominated and a coherent transport regime. This transition is associated with the formation and breakingof spatial symmetries and is identified as a generic feature of active networks. Therefore, these findings haveimportant practical consequences for the distribution of energy over coherent microwave, optical, or phononicchannels, in particular close to or at the quantum limit

Boundary robust adaptive anti-saturation control of vibrating flexible riser systems

In this paper, we address the vibration abatement problem of a flexible riser system preceded by nonlinear input saturation characteristic and uncertainties of the system. By virtue of Lyapunov theory, auxiliary system and robust control strategy, a boundary robust adaptive anti-saturation control is developed to restrain the vibration, remove the nonlinear input saturation effects and compensate for the uncertainties of system parameters and boundary disturbance. Applying the rigorous analysis without simplifying or discretizing the partial differential equation dynamics, the controlled system is ensured to be uniformly bounded stable with the designed control law. In the end, simulation results are presented for control performance verification.

Bubble shape oscillations of finite amplitude

Shape oscillations arising from the spherical instability of an oscillating bubble can be sustained in a stationary acoustic field. Describing such a steady state requires that nonlinear saturation effects are accounted for to counteract the natural exponential growth of the instability. In this paper, we analyse the establishment of finite-amplitude bubble shape oscillations as a consequence of nonlinear interactions between spherical and non-spherical modes. The set of coupled dynamical equations describing the volume pulsation and the shape oscillations is solved using a perturbation technique based on the Krylov–Bogoliubov method of averaging. A set of first-order differential equations governing the slowly varying amplitudes and phases of the different modes allows us to reproduce the exponential growth and subsequent nonlinear saturation of the most unstable, parametrically excited, shape mode. Solving these equations for steady-state conditions leads to analytical expressions of the modal amplitudes and derivations of the conditionally stable and absolutely stable thresholds for shape oscillations. The analysis of the solutions reveals the existence of a hysteretic behaviour, indicating that bubble shape oscillations could be sustained for acoustic pressures below the classical parametric threshold.

Controlling Fluctuated Chaotic Power Systems With Compensation of Input Saturation: Application to Electric Direct Current Machines

It is shown that brushless direct current (DC) motors (BLDCMs), which have found many useful applications in motion control areas, display chaotic behaviors. To avoid undesirable inherent oscillations of such DC motors, a control strategy should be adopted in the applications. So, the control problem of applied chaotic power systems is taken into account in this paper. Some important aspects of the design and implementation are considered to reach a suitable controller for the applications. In this regard, it is assumed that the system is fluctuated by unknown uncertainties and environmental noises. Additionally, a part of the system dynamics is supposed to be unknown in advance and the effects of nonlinear input saturation are fully taken into account. Then, a one input nonsmooth adaptive sliding mode controller is realized to handle the aforementioned issues. The proposed controller does not require any knowledge about the bounds of the system uncertainties and external fluctuations as well as about the parameters of the input saturation. The finite time convergence and robustness of the driven control scheme are mathematically proved and numerically illustrated using matlab simulations for DC motors.

High-energy evolution to three loops

The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to the equation in planar mathcal{N} = 4 super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the threeloop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in crosssection calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.

Direct saturation-corrected chemical exchange saturation transfer MRI of glioma: Simplified decoupling of amide proton transfer and nuclear overhauser effect contrasts.

Chemical exchange saturation transfer (CEST) MRI has shown promise in tissue characterization in diseases like stroke and tumor. However, in vivo CEST imaging such as amide proton transfer (APT) MRI is challenging because of concomitant factors such as direct water saturation, macromolecular magnetization transfer, and nuclear overhauser effect (NOE), which lead to a complex contrast in the commonly used asymmetry analysis (MTRasym). Here, we propose a direct saturation-corrected CEST (DISC-CEST) analysis for simplified decoupling and quantification of in vivo CEST effects. CEST MRI and relaxation measurements were carried out on a classical 2-pool creatine-gel CEST phantom and normal rat brains (N = 6) and a rat model of glioma (N = 8) at 4.7T. The proposed DISC-CEST quantification was carried out and compared with conventional MTRasym and the original three-offset method. We demonstrated that the DISC-CEST contrast in the phantom had much stronger correlation with MTRasym than the three-offset method, which showed substantial underestimation. In normal rat brains, the DISC-CEST approach revealed significantly stronger APT effect in gray matter and higher NOE effect in white matter. Furthermore, the APT and NOE maps derived from DISC-CEST showed significantly higher APT effect in the tumors than contralateral normal tissue but no apparent difference in NOE. The proposed DISC-CEST method, by correction of nonlinear direct water saturation effect, serves as a promising alternative to both the commonly used MTRasym and the simplistic three-offset analyses. It provides simple yet reliable in vivo CEST quantification such as APT and NOE mapping in brain tumor, which is promising for clinical translation. Magn Reson Med 78:2307-2314, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Probing saturation physics in the Real Compton Scattering at ultraperipheral pPb collisions

The Real Compton Scattering in ultraperipheral pPb collisions at RHIC and LHC energies is investigated and predictions for the squared transverse momentum (t) and rapidity (Y) distributions are presented. The scattering amplitude is assumed to be given by the sum of the Reggeon and Pomeron contributions and the Pomeron one is described by the Color Dipole formalism taking into account the non-linear (saturation) effects in the QCD dynamics. We demonstrate that the behavior of the cross sections at large-t and/or Y is dominated by the Pomeron contribution and is strongly affected by the non-linear effects present in the QCD dynamics. These results indicate that a future experimental analysis of this process can be useful to probe the QCD dynamics at high energies.

Unveiling saturation effects from nuclear structure function measurements at the EIC

We analyze the possibility of extracting a clear signal of non-linear parton saturation effects from future measurements of nuclear structure functions at the Electron–Ion Collider (EIC), in the small-x region. Our approach consists in generating pseudodata for electron-gold collisions, using the running-coupling Balitsky–Kovchegov evolution equation, and in assessing the compatibility of these saturated pseudodata with existing sets of nuclear parton distribution functions (nPDFs), extrapolated if necessary. The level of disagreement between the two is quantified by applying a Bayesian reweighting technique. This allows to infer the parton distributions needed in order to describe the pseudodata, which we find quite different from the actual distributions, especially for sea quarks and gluons. This tension suggests that, should saturation effects impact the future nuclear structure function data as predicted, a successful refitting of the nPDFs may not be achievable, which would unambiguously signal the presence of non-linear effects.

X mode Doppler reflectometry k-spectral measurements in ASDEX Upgrade: experiments and simulations

The perpendicular density fluctuation spectrum in the tokamak ASDEX Upgrade was measured with Doppler reflectometry. In this paper, extensive plasma turbulence and microwave propagation simulations with the gene gyro-kinetic code and the ipf-fd3d full-wave code were undertaken to explain the observed spectral shape. It was shown that in this case the X-mode polarisation suffers both from a large nonlinear saturation effect at low-to-intermediate probed wavenumbers, and a super-linear enhancement effect at large wavenumbers. With these effects, we were able to explain the observed discrepancies between the gene perpendicular wavenumber spectra and the Doppler reflectometry derived wavenumber spectra. While the agreement is not perfect, the simulations give guidance on how to interpret X-mode Doppler reflectometry spectra.

Anderson localization and saturable nonlinearity in one-dimensional disordered lattices

We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the stationary discrete non-linear Schrödinger equation in the fixed input case, the disorder-averaged logarithmic transmittance and the localization length are calculated in a numerically precise manner. The localization length is found to be a non-monotonic function of the incident wave intensity, acquiring a minimum value at a certain finite intensity, due to saturation effects. For low incident intensities where the saturation effect is ineffective, the enhancement of localization due to Kerr-type nonlinearity occurs in a way similar to the case without saturation. For sufficiently high incident intensities, we find that the localization length is an increasing function of the incident wave intensity, which implies that localization is suppressed for stronger input intensities, and ultimately approaches a saturation value. This feature is associated with the fact that the non-linear system is reduced to an effectively linear one, when either the incident wave intensity or the saturation parameter is sufficiently large. The non-linear saturation effect is found to be stronger and more pronounced when the energy of the incident wave is larger. We also calculate the variance of the inverse localization length and find that it also shows a non-monotonic behaviour.

Longitudinal mode selection in a delay-line homogeneously broadened oscillator with a fast saturable amplifier.

Homogeneously broadened delay-line oscillators such as lasers or optoelectronic oscillators (OEOs) can potentially oscillate in a large number of cavity modes that are supported by their amplifier bandwidth. In a continuous wave operating mode, the oscillating mode is selected between one or few cavity modes that experience the highest small-signal gain. In this manuscript, we show that the oscillation mode of a homogeneously broadened oscillator can be selected from a large number of modes in a frequency region that can be broader than the full width at half maximum of the effective cavity filter. The mode is selected by a short-time injection of an external signal into the oscillator. After the external signal is turned off, the oscillation is maintained in the selected mode even if this mode has a significantly lower small-signal gain than that of other cavity modes. The stability of the oscillation is obtained due to nonlinear saturation effect in the oscillator amplifier. We demonstrate, experimentally and theoretically, mode selection in a long cavity OEO. We could select any desired mode between 400 cavity modes while maintaining ultra-low phase noise in the selected mode and in the non-oscillating modes. No mode-hopping was observed during our maximum measurement duration of about 24 hours.

Shock formation and nonlinear saturation effects in the ultrasound field of a diagnostic curvilinear probe.

Newer imaging and therapeutic ultrasound technologies may benefit from in situ pressure levels higher than conventional diagnostic ultrasound. One example is the recently developed use of ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe has been used to deliver the acoustic pushing pulses. The probe is a curvilinear array comprising 128 elements equally spaced along a convex cylindrical surface. The effectiveness of the treatment can be increased by using higher transducer output to provide a stronger pushing force; however nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the three-dimensional Westervelt equation with the boundary condition set to match low power measurements of the acoustic pressure field. Nonlinear focal waveforms simulated for different numbers of operating elements of the array at several output power levels were compared to fiber-optic hydrophone measurements and were found to be in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of a diagnostic imaging probe.

Transverse-momentum-dependent gluon distributions from JIMWLK evolution

Transverse-momentum-dependent (TMD) gluon distributions have different operator definitions, depending on the process under consideration. We study that aspect of TMD factorization in the small-x limit, for the various unpolarized TMD gluon distributions encountered in the literature. To do this, we consider di-jet production in hadronic collisions, since this process allows to be exhaustive with respect to the possible operator definitions, and is suitable to be investigated at small x. Indeed, for forward and nearly back-to-back jets, one can apply both the TMD factorization and Color Glass Condensate (CGC) approaches to compute the di-jet cross-section, and compare the results. Doing so, we show that both descriptions coincide, and we show how to express the various TMD gluon distributions in terms of CGC correlators of Wilson lines, while keeping Nc finite. We then proceed to evaluate them by solving the JIMWLK equation numerically. We obtain that at large transverse momentum, the process dependence essentially disappears, while at small transverse momentum, non-linear saturation effects impact the various TMD gluon distributions in very different ways. We notice the presence of a geometric scaling regime for all the TMD gluon distributions studied: the "dipole" one, the Weizs\"acker-Williams one, and the six others involved in forward di-jet production.

Preliminary Design and Optimization of Toroidally Wound Limited Angle Servo Motor Based on a Generalized Magnetic Circuit Model

This paper proposes a new generalized equivalent magnetic circuit model for the preliminary design of a toroidally wound limited angle servo motor. In the model, the magnetic networks are formulated as a function of the pole number and geometric dimensions. Nonlinear saturation effect of the ferromagnetic material is also taken into consideration. A multi-objective optimization function involving the torque requirement, the mass, the time constant, and the magnetic saturations of ferromagnetic material is introduced. Based on the proposed model, six design cases with different objectives have been carried by the particle swarm optimization method. The comparisons of different optimization cases demonstrate the effectiveness and computation efficiency of the proposed method, and hence its suitability in preliminary design. Moreover, the generalized model can be readily applied in the other electromagnetic modeling.

-symmetry breaking in the steady state of microscopic gain–loss systems

The phenomenon of (parity- and time-reversal) symmetry breaking is conventionally associated with a change in the complex mode spectrum of a non-Hermitian system that marks a transition from a purely oscillatory to an exponentially amplified dynamical regime. In this work we describe a new type of -symmetry breaking, which occurs in the steady-state energy distribution of open systems with balanced gain and loss. In particular, we show that the combination of nonlinear saturation effects and the presence of thermal or quantum noise in actual experiments results in unexpected behavior that differs significantly from the usual dynamical picture. We observe additional phases with preserved or ‘weakly’ broken -symmetry, and an unconventional transition from a high-noise thermal state to a low-amplitude lasing state with broken symmetry and strongly reduced fluctuations. We illustrate these effects here for the specific example of coupled mechanical resonators with optically induced loss and gain, but the described mechanisms will be essential for a general understanding of the steady-state properties of actual -symmetric systems operated at low amplitudes or close to the quantum regime.