Nonlinear Saturation Research Articles

Onset of turbulence in rotor–stator cavity flows

Numerous studies have indicated that turbulence typically initiates along the boundary layer of the stationary disk within a rotor–stator cavity. To describe the transition process to turbulence on the stationary side of a closed rotor–stator cavity, a comprehensive approach combining global linear stability analysis with direct numerical simulation was adopted in the present study. The proposed model aligns with that of Yim et al. (J. Fluid Mech., vol. 848, 2018, pp. 631–647), who investigated the stability characteristics of the rotating-disk boundary layer in a rotor–stator cavity. In order to achieve a stable inflow for the stationary-disk boundary layer, we rotate the shroud together with the rotating disk. Through careful global stability analysis, the predominant spiral mode exhibiting the highest instability in the boundary layer of the stationary disk was discerned, corroborating observations from simulations. Initially, the spiral mode undergoes linear amplification, reaches a state of linear saturation and enters the nonlinear regime. Following nonlinear saturation in the flow field, a circular wave mode arises due to the influence of mean flow distortion. As the Reynolds number attained a sufficiently high level, the interplay between the downstream-propagating circular mode and spiral mode amplified disturbances in the boundary layer of the stationary disk, ultimately leading to the development of localised turbulence at the mid-radius of the rotor–stator cavity. Notably, the present study is the first to elucidate the coexistence of laminar–transitional–turbulent flow states in the stationary-disk boundary layer through direct numerical simulations.

Static anti-windup compensator based on BMI optimisation for discrete-time systems with directional change in controls avoidance

In the paper, a design method of a static anti-windup compensator for systems with input saturations is proposed. First, an antiwindup controller is presented for system with cut-off saturations, and, secondly, the design problem of the compensator is presented to be a non-convex optimization problem easily solved using bilinear matrix inequalities formulation. This approach guarantees stability of the closedloop system against saturation nonlinearities and optimizes the robust control performance while the saturation is active.

Disturbance attenuation for neutral descriptor semi‐Markovian jump systems with saturation nonlinearity and time delays

AbstractThis article examines the construction of the tracking control as well as the disturbance attenuation for a class of neutral descriptor semi‐Markovian jump systems involving input time delays. On the basis of Matausek–Micic modified Smith prediction technique, a modified equivalent‐input‐disturbance and multiperiodic modified repetitive controller has been developed for obtaining the required results. In order to reject external disturbances actively, the modified equivalent‐input‐disturbance technique is utilized. To be more explicit, the modification of the Smith predictor block and integration of the transfer function provide accurate estimate, efficient attenuation of external disturbance and proper compensation for input time delays. While constructing the controller gain matrices, the specified matrix inequalities are solved concurrently. At last, the potential and applicability of the framed control law are illustrated through the simulated findings.

Convective Overstability in Radially Global Protoplanetary Disks. I. Pure Gas Dynamics

Protoplanetary disks are prone to several hydrodynamic instabilities. One candidate, convective overstability (COS), can drive radial semiconvection that may influence dust dynamics and planetesimal formation. However, the COS has primarily been studied in local models. This paper investigates the COS near the midplane of radially global disk models. We first conduct a global linear stability analysis, which shows that linear COS modes exist only radially inward of their Lindblad resonance (LR). The fastest-growing modes have LRs near the inner radial domain boundary with effective radial wavelengths that can be a substantial fraction of the disk radius. We then perform axisymmetric global simulations and find that the COS’s nonlinear saturation is similar to previous incompressible shearing box simulations. In particular, we observe the onset of persistent zonal and elevator flows for sufficiently steep radial entropy gradients. In full 3D, nonaxisymmetric global simulations, we find the COS produces large-scale, long-lived vortices, which induce the outward radial transport of angular momentum via the excitation of spiral density waves. The corresponding α-viscosity values of order 10−3 agree well with those found in previous 3D compressible shearing box simulations. However, in global disks, significant modifications to their radial structure are found, including the formation of pressure bumps. Interestingly, the COS typically generates an outward radial mass transport, i.e., decretion. We briefly discuss the possible implications of our results for planetesimal formation and for interpreting dust rings and asymmetries observed in protoplanetary disks.

Parametric Resonance Control of Flexible Manipulator Based on Saturation and Quadratic Nonlinearity Enhancement

Parametric Resonance Control of Flexible Manipulator Based on Saturation and Quadratic Nonlinearity Enhancement

Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0

Ground state solitons for periodic Schrödinger lattice systems with saturable nonlinearities and spectrum 0

The ratio of alanine aminotransferase to high-density lipoprotein cholesterol is positively correlated with the insulin resistance in American adults: a population-based cohort study.

Previous studies have demonstrated a correlation between the ratio of alanine aminotransferase to high-density lipoprotein cholesterol (ALT/HDL-C) in the serum and the risk of diabetes. However, no existing study has investigated the association between insulin resistance (IR) and ALT/HDL-C. Therefore, this study aims to explore the association between ALT/HDL-C and IR in American adults. A total of 7,599 adults selected from the National Health and Nutrition Examination Survey (NHANES) in 2013 to 2020 were studied. IR was assessed based on the homeostatic model assessment of insulin resistance (HOMA-IR). And the association between IR and ALT/HDL-C was assessed through multiple logistic regression, generalized smooth curve fitting and subgroup analyses. Multiple logistic regression analysis indicated a significant correlation between IR and ALT/HDL-C, with odds ratios (OR) of 1.04 (95% CI = 1.02-1.05) in males and 1.04 (95% CI = 1.02-1.07) in females. A non-linear association and saturation effect between ALT/HDL-C and IR risk were identified, with an inverted L shaped curve and an inflection point at 33.62. The area under the ROC curve (AUC) of ALT/HDL-C was significantly larger (AUC = 0.725 for males and 0.696 for females, all p < 0.01) compared with the use of ALT, HDL-C, AST and AST/ALT. Subgroup analysis showed a significantly higher independent association in obese individuals and individuals aged ≥50 years (All P interaction <0.05). Elevated ALT/HDL-C demonstrates a significant correlation with IR, which can be used as a potential indicator of IR in American adults.

Nonlinear disturbance observer-based finite-time prescribed performance control for MSVs with input saturation

ABSTRACT A finite-time prescribed performance control scheme based on an improved nonlinear disturbance observer is proposed for tracking the trajectory of marine surface vessels (MSVs) under the disturbance of the marine environment. The objective of this paper is to design a nonlinear disturbance observer based on state estimation error feedback that accurately estimates and compensates for the unknown disturbance problem. An adaptive law is applied to estimate the upper bound of its error, removing the requirement of a priori knowledge of the unknown lumped disturbance upper bound. This paper also introduces a non-logarithmic performance function in order to efficiently solve the problem of considering both transient and steady state MSVs performance simultaneously. In addition, the adaptive dynamic system is introduced to overcome the adverse effects caused by nonlinear saturation factors for the input-constrained problem. With this control strategy, the system output error converges to a pre-defined region within a finite amount of time and meets the prescribed performance requirements. Finally, simulation and comparison verify the control scheme's effectiveness and superiority.

Central obesity may affect bone development in adolescents: association between abdominal obesity index ABSI and adolescent bone mineral density

PurposePrevious studies have suggested that obesity defined by body mass index(BMI) is a protective factor for bone mineral density(BMD), but have overlooked the potential influence of different types of obesity. This study aims to evaluate the correlation between abdominal obesity index A Body Shape Index(ABSI) and adolescent bone density, and analyze the relationship between abdominal obesity and bone metabolism.MethodsA total of 1557 adolescent participants were included in NHANES from 2007 to 2018. Calculate the ABSI using a specific formula that takes into account waist circumference and BMI. A weighted multiple linear regression model is used to evaluate the linear correlation between ABSI and BMD. Forest plots are used to analyze the correlations between subgroups, and cubic splines are limited to evaluate the nonlinear correlations and saturation effects between ABSI and BMD.ResultsAfter adjusting for confounding factors, there was a significant linear correlation (P < 0.01) between ABSI and femoral BMD, both as a continuous variable and an ordered categorical variable. The restrictive cubic spline curve indicates a significant nonlinear correlation and saturation effect between adolescent ABSI and BMD.ConclusionResearch has shown a significant negative correlation between ABSI and BMD at the four detection sites of the femur, and this correlation may vary slightly due to age, race, family income, and different detection sites. The research results indicate that compared to overall body weight, fat distribution and content may be more closely related to bone metabolism.

Revisit of electron temperature effect on stimulated Brillouin scattering in homogenous plasma

Stimulated Brillouin scattering (SBS) has complex dependence on the plasma electron temperature via the Landau damping, particle trapping, and consequent nonlinear frequency shift. It is found from our numerical simulation that the SBS reflectivity in its saturation stage tends to increase with the plasma electron temperature within a certain range, although the linear growth rate of SBS normally reduces with the increasing electron temperature. This is because the phase velocity of an ion acoustic wave (IAW) increases with the electron temperature, which tends to reduce the Landau damping of the IAWs and hence reduce ion trapping. In the nonlinear saturation stage, ion trapping will modify the ion distribution function and induce a negative frequency shift in the IAW. This nonlinear frequency shift will break the three-wave coupling, thereby causing saturation of the SBS. With further increase in the electron temperature, however, electron trapping will dominate over ion trapping, which induces a positive frequency shift in the IAW and can lead to the SBS saturation as well. As a result, the SBS reflectivity first increases and then decreases with increase in the electron temperature. At around the peak of the SBS reflectivity, the positive frequency shift of IAW induced by electron trapping roughly offsets the negative frequency shift induced by ion trapping.

Numerical study of the influence of electron inertial effects and electron dynamics on tearing mode instability

The tearing mode instabilities were numerically studied in two distinct models: the finite electron inertial magnetohydrodynamics (MHD) and the electron MHD (EMHD). The finite electron inertial MHD model employed a modified Hall-MHD model that incorporated the electron inertial effects in the generalized Ohm’s Law. On the other hand, the electron dynamics were described by the EMHD model. It is found that both electron inertial effects and electron dynamics significantly influence the linear and nonlinear growth of tearing mode instabilities, with electron dynamics playing a more dominant role. The dependence of the linear growth rate of tearing modes on the electron inertial length de was investigated. The results show that electron inertial effects enhance the growth rate but resemble the behavior of resistivity η. Whereas, in the EMHD model, electron inertia plays a dominant role in tearing mode instabilities. Additionally, a study on the nonlinear saturation of (2,1) tearing modes was conducted, demonstrating consistency with relevant analytical theories. The study indicates that, in both models, the magnetic island exhibits faster growth and achieves a larger saturated island width as de increases.

Association between the arm circumference and non-alcoholic fatty liver disease in American children and adolescence: a population-based analysis.

The arm circumference (AC) has been used as an important tool to access the risk of non-alcoholic fatty liver disease (NAFLD) in adults. However, the association between AC and NAFLD in children and adolescence remains unclear. This study aims to explore the relationship between AC and NAFLD in American children and adolescence. 2017-2020 National Health and Nutrition Examination Survey (NHANES) was used to carry out the cross-sectional study. The association between AC and the risk of NAFLD, and liver steatosis was analyzed using weighted multivariable logistic regression and multivariate linear regression. Additionally, a two-part linear regression model was used to identify threshold effects in this study. Subgroup analysis, interaction tests and receiver operating characteristic (ROC) curve analysis were also carried out. A total of 1,559 children and adolescence aged 12-18 years old were included, and the prevalence of NAFLD was 27.3%. AC was positively correlated with the risk of NAFLD (OR = 1.25, 95% CI: 1.19, 1.32) and liver steatosis (β = 4.41, 95% CI: 3.72, 5.09). Subgroup analysis stratified by age and race showed a consistent positive correlation. A non-linear relationship and saturation effect between AC and NAFLD risk were identified, with an S shaped curve and an inflection point at 34.5 cm. Area under the ROC of AC to NAFLD was 0.812, with the sensitivity of 67.6%, the specificity of 83.8% and the cutoff value of 31.7 cm. Our study shows that AC is independently correlated with an increased risk of NAFLD and the severity of liver steatosis in American children and adolescence.

Multiplet cascade in a semiconductor laser with optoelectronic feedback

We report experimentally and theoretically a dynamical scenario involving the formation of pulse multiplet structures, i.e., configurations of two, three, and more pulses per round trip, in a semiconductor laser with positive optoelectronic feedback. The delayed feedback loop includes a cascade of two band-limited amplifiers with nonlinear saturation of sigmoid type. The multiplets appear subcritically in the vicinity of the lasing threshold, resembling gain-switched operation, and evolve with the injection current.

Adjusting exceptional points using saturable nonlinearities

We study the impact of saturable nonlinearity on the presence and location of exceptional points in a non-Hermitian dimer system. The inclusion of the saturable nonlinearity leads to the emergence of multiple eigenvalues, exceeding the typical two found in the linear counterpart. To identify the exceptional points, we calculate the nonlinear eigenvalues both from a polynomial equation for the defined population imbalance and through a fully numerical method. Our results reveal that exceptional points can be precisely located by adjusting the non-equal saturable nonlinearities in the detuning space.

Adaptive finite‐time recoil control of deepwater drilling riser systems with nonlinear forces and saturation input using switched event‐triggered scheme

AbstractThis article investigates the finite‐time recoil control problem of deepwater drilling riser systems with nonlinear friction force, tension force and saturation input. For the friction force, a new approximation model based on radial basis function neural networks is presented, which not only can ensure a better approximation effect than the sine‐function type and exponential‐polynomial‐function type computational models, but also can be easily used for control design. Different from the existing linear optimal control methods, a neural‐network‐based adaptive backstepping control method is proposed to deal with the nonlinear friction and tension forces, which can achieve better recoil control responses. An auxiliary system combining with the change of coordinates is employed to compensate the saturation input effect. To prolong the average release interval of control input while preserving satisfied control performance, a new switched event‐triggered control (ETC) scheme is developed, in which the triggering conditions are switched between the fixed and relative thresholds based on the strength of control signal. With the event‐triggered controller, the practical finite‐time stability condition of recoil control system is derived and the Zeno behavior is avoided. Numerical results are given to show the advantages of the proposed methods in handling the model nonlinearities, finite‐time stability and ETC performance of riser‐tension systems.

Ultra low-power multistability in [formula omitted]-symmetric periodic structures with saturable coupling, gain and loss

The present work investigates the switching dynamics of conventional fiber Bragg gratings (FBGs) with saturable coupling and parity-time (PT)-symmetric fiber Bragg gratings (PTFBGs) with saturable coupling (SC) and saturable gain-loss (SGL) in the presence of Kerr nonlinearity (KNL) [model - I] and saturable nonlinearity (SNL) [model - II]. Both system models can generate distinct optical multistability (OM) and bistability (OB) curves, including S-shaped, ramp-like, and mixed OM curves in both unbroken and broken PT-symmetric regimes. The impact of each control parameter on controlling switching intensities, hysteresis width, and the number of stable states is thoroughly examined for both of these system models. The direction of right light incidence enables a significant reduction in the switching intensities to below 100 W/cm2, the lowest critical power ever reported in the literature of PTFBGs, thanks to the concept of both saturable coupling, gain and loss.

Suppression of Torque Ripple in Switched Reluctance Motors Which is Based on Synchronization Technology

The double salient pole structure of Switched Reluctance Motor (SRM) makes its electromagnetic field exist nonlinear saturation characteristics, resulting in its large torque pulsation in operation, so it is difficult to achieve speed regulation smoothly by traditional control methods. In view of this problem, a sliding mode control strategy which is based on synchronous transmission technology was proposed.Firstly, the basic structure of switched reluctance motor was analyzed, and the mathematical model of mechanical motion of switched reluctance motor was established. Secondly, an improved sliding mode controller which is based on synchronous signal transmission technology was designed by analyzing the reason of large torque ripple of switched reluctance motor, and the stability of the system was proved. Finally, simulation is used to verify the effectiveness of the control strategy.Compared with the traditional PID (Proportional Integral Differential) control algorithm, this control technology not only suppresses the SRM torque ripple effectively , but also makes the sliding mode controller output the precise target electromagnetic torque quickly by increasing the control variables. The results of research indicate that this design can not only restrain the torque ripple effectively, but also adjust the convergence speed and overshoot of the controller by adjusting the design parameters.

Adaptive neural bounded formation tracking control of multiple autonomous surface vessels subject to actuator saturation and faults

This paper introduces an adaptive neural bounded formation tracking control strategy for a fleet of autonomous surface vessels with actuator saturation nonlinearity and faults. To begin with, by using the error transformation technique, the proposed algorithm derives the controller only based on the relative distance and angles measured by local sensor, which can avoid the requirement for supplementary leader-related information. Secondly, by employing neural networks (NNs) and auxiliary dynamic system, the system uncertainty and actuator saturation nonlinearity are handled, and a NNs-based bounded control law is derived. In addition, in order to solve actuator faults such as loss of validity, hard over faults and bias faults, the fault-tolerant adaptive law is introduced to compensate the weight matrix of the neural network and the upper bound of the fault parameters, instead of dealing with each individual matrix element. This can significantly decrease the computational workload of the algorithm, facilitating its practical implementation in engineering applications. Finally, it is demonstrated that all signals of the closed-loop system are semi-globally ultimately uniformly bounded. The performance and superiority of this control strategy are validated through numerical examples in various scenarios.

Superradiant pulse saturation in a Free Electron Laser

A study is made of the saturation mechanism of a single superradiant ‘spike’ of radiation in a Free Electron Laser. A one-dimensional (1D) computer model is developed using the Puffin, un-averaged FEL simulation code, which allows sub-radiation wavelength evolution of both the spike radiation field and the electron dynamics to be modelled until the highly non-linear saturation process of the spike is observed. Animations of the process from the start to the end of the interaction are available. The resultant saturated spike duration is at the sub-wavelength scale and has a broad spectrum. The electrons passing through the spike can both lose and gain energy many times greater than that of the ‘normal’ non-pulsed FEL interaction. A saturation mechanism is proposed and tested via a simple analysis of the 1D FEL equations. The scaling results of the analysis are seen to be in good agreement with the numerical results. A simple model of three dimensional diffraction effects of the radiation is applied to the results of the 1D simulations. This greatly reduces longer wavelengths of the power spectrum, which are seen to be emitted mainly after the electrons have propagated through the spike, and is seen to be in qualitative agreement with recent experimental results.

Resonant decay of kinetic Alfvén waves and implication on spectral cascading

A general equation describing the resonant nonlinear mode-coupling among kinetic Alfvén waves (KAWs) is derived using nonlinear gyrokinetic theory, which can be applied to study the potentially strong spectral energy transfer of KAWs. As a first application, the parametric decay of a pump KAW into two sideband KAWs is studied, with particular emphasis on cascading in the perpendicular wavenumber. It is found that, for the “co-propagating” cases with all three KAWs propagating in the same direction along the equilibrium magnetic field line, it exhibits a dual cascading character in the perpendicular wavenumber space; while for the “counter-propagating” cases with one sideband propagating in the opposite direction with respect to the pump wave, it instead, can exhibit both dual and inverse cascading behaviors. Furthermore, the implications of these findings on shear Alfvén waves regarding instability, nonlinear saturation, and charged particle transport in fusion plasmas are also discussed.