Nonlinear Saturation Research Articles

Effects of plasma nonuniformity on zero frequency zonal structure generation by drift Alfvén wave instabilities in toroidal plasmas

Abstract The effects of plasma nonuniformity on zero frequency zonal structure (ZFZS) excitation by drift Alfvén wave (DAW) instabilities in toroidal plasmas are investigated using nonlinear gyrokinetic theory. The governing equations describing nonlinear interactions among ZFZSs and DAWs are derived, with the contribution of DAW self-beating and radial modulation accounted for on the same footing, and the physics picture contributing to both channels clarified. The obtained equations are then used to derive the nonlinear dispersion relation, which is then applied to investigate ZFZS generation in several scenarios. In particular, it is found that the condition for zonal flow excitation by the kinetic ballooning mode (KBM) could be sensitive to plasma parameters and a more detailed investigation is needed to understand KBM nonlinear saturation, crucial for bulk plasma transport in future reactors.

Femtosecond Mode-Locking and Soliton Molecule Generation Based on GaAs Saturable Absorber

Abstract In the past few years, research on advanced ultrafast photonic devices has maintained great interest throughout the laser community. As a semiconductor material with excellent nonlinear saturation absorption characteristics, GaAs has been used in solid-state and fiber lasers as a mode-locker. However, pulse widths that have been reported in the searchable published literature are all longer and the shortest is also tens of picoseconds. Femtosecond pulse widths, desired for variety of applications, have not yet been reported in GaAs-based pulsed lasers. In this work, we further explore the nonlinear characteristics of GaAs that magnetron sputtered onto the surface of the tapered fiber and its application in the generation of femtosecond laser via effective dispersion optimization and nonlinearity management. With the enhanced interaction between evanescent wave and GaAs nanosheets, mode-locked soliton pulses as short as 830 fs are generated at 4.64 MHz repetition rates. As far as we know, this is the first time that femtosecond-level pulses are generated with a GaAs-based SA. In addition, soliton molecule, including dual-pulse state are also realized under stronger pumping. This work demonstrates that GaAs-based photonic device has good application prospects in effective polymorphous ultrashort pulsed laser generation.

Nonlinear saturation of the ion flow driven ion sound instability in a finite length plasma

The saturation mechanism and nonlinear evolution of the ion sound instability driven by the subsonic ion flow in a finite length plasma are studied by a one-dimensional hybrid model considering kinetic ions and Boltzmann electrons. Three regimes of the instability nonlinear behavior are identified as a function of the frequency of the ion-neutral charge exchange (CX) collision fcoll. In the first (collisionless-alike) regime when the CX frequency is low, the instability is saturated by ions trapping in wave potentials leading to the formation of phase space vortexes (PSVs). One of the PSVs subsequently expands and becomes system long in the steady state. The transition to the second (medium) regime occurs when fcoll≳vp/d, where vp is the PSV expansion velocity and d is the system length. In the second regime, CX collisions convert fraction of beam ions into slow ions that can be trapped in potentials of small scale ion sound eigenmodes fluctuations. The trapping of slow ions results in the formation of a chain of small scale PSVs and the disruption of the establishment of the single system long PSV. In the third (collision-dominated) regime when fcoll≳γ (γ is the instability growth rate), CX collisions transform all beam ions into slow ions and the instability is thereby eliminated.

Para-phenylenediamine Schiff base: highly fluorescent photostable solid-state organic dye

Schiff bases derived from the condensation of primary amines with aldehydes, such as para-phenylenediamine with salicylaldehyde, exhibit unique optical and structural properties ideal for photonic applications. This study synthesizes such a Schiff base, revealing its properties through detailed HNMR1, FTIR, and XRD characterizations. The compound forms a robust π-conjugated structure, showing a fluorescence emission peak at 560 nm and significant absorbance at 380 nm. A spin-coated laser cavity displayed a critical lasing threshold at 1 MW·cm−2, which could be optimized down to 0.6 kW·cm−2. Moreover, the compounds’ acceptor-donor-acceptor configuration raised outstanding nonlinear optical properties, including a substantial two-photon absorption cross-section of 2×10−11 cm ⋅ W−1·GM, enhancing its utility in high-resolution two-photon imaging and advanced photonic applications. Other nonlinear optical characteristics determined during these studies are the saturable absorption-induced nonlinear absorption coefficient (−2×10−11 cm ⋅ W−1), saturation intensity (2.5×1011 W·cm−2), and Kerr-induced nonlinear refractive index (5×10−16 cm2 ⋅ W−1). The combined linear and nonlinear optical properties, supported by sustained emission and minimal photobleaching under intense re-excitation, establish the para-phenylenediamine Schiff base and derivatives as promising materials for high-brightness, photostable organic light emitters, and solid-state lasers.

A Quasilinear Quadratic Tracking Method for Systems With Saturating Actuators

ABSTRACTLinear quadratic tracker (LQT) is usually employed to solve unconstrained tracking problems but falls short when dealing with systems exhibiting actuator saturation. This paper presents a novel quasilinear quadratic tracking method specifically designed to address this scenario. Firstly, the stochastic linearization (SL) approach is utilized to approximate the saturation nonlinearity with equivalent gains and biases using statistical properties of its input, which are thus incorporated into the system model so as to eliminate the nonlinearity. Then, different time scales are applied in the tracking controller and states in order to improve tracking accuracy. In addition, to reduce computational complexity, two algorithms are provided for approximating the equivalent gains and biases, catering to both scalar and vector control signals. Finally, the proposed algorithms are evaluated through numerical examples, demonstrating their effectiveness and superior tracking performances.

Test Mass Capture Control for Drag-Free Satellite Based on State-Dependent Riccati Equation Method

The drag-free satellite plays an important role in the space-based gravitational wave observatory. The capture control of test mass after release is a crucial technology that can affect the success of the mission. The test mass must be released to the center of the electrostatic suspension cage accurately. This paper presents a nonlinear dynamic model of drag-free satellites in Lagrange formalism. A capture control scheme for test mass release phase is proposed based on the state-dependent Riccati equation (SDRE) strategy. To deal with the actuator saturation problem, a nonlinear saturation model is introduced to the dynamics of satellite, while the SDRE strategy is applied to the non-affine system. The effectiveness of the proposed methodology is verified by the numerical simulation for the drag-free satellite.

Instabilities and Pattern Formation in Epidemic Spread Induced by Nonlinear Saturation Effects and Ornstein–Uhlenbeck Noise

Abstract We analytically study the emergence of instabilities and the consequent steady-state pattern formation in a stochastic partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread. The model is characterized by: (1) strongly nonlinear forces representing the infection transmission mechanism and (2) random environmental forces represented by the Ornstein–Uhlenbeck (O–U) stochastic process which better approximates real-world uncertainties. Employing second-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of diffusion-induced instabilities and analyze the effects of O–U noise on these instabilities. We obtain a range of values of the diffusion coefficient and correlation time in parameter space that support the onset of instabilities. Notably, the stability and pattern formation results depend critically on the correlation time of the O–U stochastic process; specifically, we obtain lower values of steady-state infection density for higher correlation times. Also, for lower correlation times the results approach those obtained in the white noise case. The analytical results are valid for lower-order correlation times. In summary, the results provide insights into the onset of noise-induced, and Turing-type instabilities in a stochastic PDE epidemic model in the presence of strongly nonlinear deterministic infection forces and stochastic environmental forces represented by Ornstein–Uhlenbeck noise.

Baroclinic nonlinear saturation and secondary instability of current-undercurrent meanders

Baroclinic nonlinear saturation and secondary instability of current-undercurrent meanders

Dynamic Surface Tracking Control for Nonlinear Constraints

Abstract An adaptive control scheme based on dynamic surface control (DSC), and intelligent control techniques is developed for a 3-DOF helicopter with unknown disturbance and asymmetric saturation. The reconstructed dynamic neural network (NN) is established to compensate for nonlinear terms in real-time. A designed smooth nonlinear sigmoid function is used to model saturation nonlinearity. The combination of dynamic surface control with adaptive intelligent control techniques resolves and improves the tracking and robust performance of the system. The stability and ultimately bound of all signals of the controlled system are demonstrated by theoretical analysis. Numerical results prove the feasibility of the presented control scheme.

Robust flexible spacecraft attitude tracking under measurement errors, actuator nonlinearities, and faults

Reliable spacecraft attitude maneuver is one of the core research areas of the space industry due to the need for sustainable space exploration and advancements in the space technology. The paper presents an observer-based adaptive backstepping (OB-ABST) fault-tolerant control scheme for a flexible spacecraft attitude tracking under the effect of state measurement errors, inertial uncertainties, external disturbances, multiple actuator faults, and input nonlinear saturation (INS) while suppressing vibrations due to flexible modes. Initially, we design an adaptive backstepping controller to mitigate the system’s unwanted nonlinearities and observers to get estimates of the attitude dynamics in a recursive design framework. Later, the control structure incorporates a simple actuator saturation compensator to tackle input torque saturation in the system. The critical feature of the proposed OB-ABST control structure is to ensure precise attitude-tracking maneuvers and vibration suppression without intelligent materials such as shape memory alloys (SMA) and piezoelectric material (PZT). Lyapunov stability analysis proves practical finite-time convergence of the system state errors, observation errors, and actuator saturation compensators. Moreover, we provide specific conditions to tune design parameters. Finally, comparative simulation experiments validate the control performance of the proposed controller in the presence of multiple challenges.

Non-Hermitian mode management in periodically modulated waveguide amplifiers

We propose an efficient mode management scheme in active nonlinear multimode fibers based on non-Hermitian potentials in the longitudinal direction with an antisymmetric transverse profile. The proposal takes advantage of the nonlinear saturation toward particular mode configurations, which can be tuned by the non-Hermitian potential. We demonstrate flexible control of the beam profile within the parameter space of the applied potential with various possibilities, such as improving the beam quality by condensing photons to the lowest order Hermite mode, exciting higher order modes, or engineering a desired mode profile as a combination of modes. The effect is also analytically predicted using a mode-expansion approach, showing good agreement with the full model calculations based on the complex Ginzburg–Landau equation. This study was performed for 1D planar guiding structures, yet the results can be extended to 2D fibers and could be very useful in applications of fiber amplifiers and lasers.

Two-Phase Incompressible Flow with Dynamic Capillary Pressure in a Heterogeneous Porous Media

We prove the existence of weak solutions of a two-incompressible immiscible wetting and non-wetting fluids phase flow model in porous media with dynamic capillary pressure. This model is a coupled system which includes a nonlinear parabolic saturation equation and an elliptic pressure–velocity equation. In the regularized case, the existence and uniqueness of the weak solution are obtained. We let the regularization parameter be η→0 to prove the existence of weak solutions.

Coupled modes analysis of stimulated Brillouin scattering in the regimes of nonlinear ion acoustic waves

The nonlinear saturation of stimulated Brillouin scattering (SBS) in long scale length plasmas is studied in detail through coupled mode equations. Our model incorporates harmonic and subharmonic generation of ion acoustic waves (IAWs), as well as nonlinear Landau damping and the nonlinear frequency shift of IAWs induced by particle trapping. Numerical simulations are carried out across various IAW wavenumbers (k a λ De ) and electron-ion temperature ratios (Z i T e /T i ) within different SBS instability regimes. The results demonstrate that our model can distinguish the importance of each effect contributing to the nonlinear behavior in SBS under different plasma conditions. Furthermore, we examine the scaling of SBS reflectivity with laser intensity under conditions relevant to inertial confinement fusion.

Constrained H∞ control with gain switching for a nonlinear active suspension system matching non-pneumatic wheel

In this study, a constrained H ∞ controller with gain switching is put forward for the active suspension system to improve the overall performance of vehicles equipped with non-pneumatic wheels, considering the nonlinearity of wheel stiffness, actuator saturation, and output constraints. Firstly, a quarter-vehicle model incorporating active suspension and non-pneumatic wheel (NPW) is established experimentally. Secondly, the system model is linearized using Taylor series expansion and linear fractional transformation (LFT). A constrained H ∞ control strategy and a gain switching method based on road classification are proposed, taking into account the parameter uncertainty in linearization process and the variation of performance demands under different road conditions. Then, an L ∞ state observer is designed for the required system state, and the road roughness classifier based on grey wolf optimization (GWO) and probabilistic neural network (PNN) is developed to obtain the necessary road information. A bench test is finally performed using the reconstructed actual road as input. The test results validate the effectiveness and superiority of the proposed control strategy.

Correlation between ratio of fasting blood glucose to high density lipoprotein cholesterol in serum and non-alcoholic fatty liver disease in American adults: a population based analysis.

Based on previous research, elevated fasting blood glucose (FBG) and decreased high-density lipoprotein cholesterol (HDL-C) levels are associated with non-alcoholic fatty liver disease (NAFLD). It is hypothesized that the prevalence of NAFLD may be proportional to the FBG-to-HDL-C ratio (GHR). In this study, 3,842 participants from the National Health and Nutrition Examination Survey (NHANES) (2013-2020) were investigated. Liver steatosis was assessed using vibration-controlled transient elastography (VCTE). NAFLD was defined as controlled attenuation parameter (CAP) ≥288 dB/m. After adjusting for race, gender, age, diabetes, BMI, moderate activities, uric acid, albumin, ALT, GGT, ALP, total bilirubin and creatinine, multiple logistic regression analysis indicated a positive correlation between GHR and the prevalence of NAFLD (OR = 1.22, 95% CI = 1.17-1.28). Additionally, multiple linear regression analysis showed a positive correlation between GHR and the severity of liver steatosis according to CA p-values (β = 4.97, 95% CI: 4.28, 5.66). According to the subgroup analysis, the correlation was stronger in other race, participants at the age <50 years old and those with non-diabetes. In this study, a non-linear relationship and saturation effect between GHR and the prevalence of NAFLD was also revealed, characterized by an inverted L-shaped curve, with an inflection point of 7.443. Finally, the receiver operating characteristic (ROC) analysis suggested that the area under the curve (AUC) of GHR (AUC = 0.731) significantly exceeded that of FBG and HDL-C. Elevated GHR levels are independently associated with the severity of liver steatosis and the increased prevalence of NAFLD in American adults.

Adaptive neural network dynamic surface optimal saturation control for single‐phase grid‐connected photovoltaic systems

AbstractAn adaptive neural network (NN) based optimal saturation control scheme is investigated for single‐phase grid‐connected photovoltaic (PV) systems by incorporating dynamic surface control (DSC) and adaptive dynamic programming (ADP) based on the backstepping control design framework. For each backstepping step, a critic‐actor architecture is constructed via reinforcement learning (RL), and the PV system is optimized according to the cost function in the architecture. Due to the nonlinearity, it is difficult to solve the Hamilton–Jacobi–Bellman (HJB) equation. The neural networks (NNs) are employed to approximate the solution of the HJB equation such that the optimal virtual control and the actual controller are obtained. By considering control input symmetric saturation nonlinearity link, constraints on pulse width modulation (PWM) are ensured. On this basis, the combination of backstepping control design and dynamic surface technique is used to overcome the shortcomings of “differential explosion” and simplify calculations. Based on the Lyapunov method, the stability analysis proves that all signals of the closed‐loop PV systems are semiglobally uniformly ultimately bounded (SGUUB). Simulation experiments and comparative results are given to verify the efficacy of the studied control strategy.

A novel control approach for discrete-time 2D Roesser systems under input saturation and intrinsic nonlinearity: A region of stability investigation

This paper presents the control system design for the nonlinear discrete-time Roesser systems under saturated control input. A deficiency in the existing literature has been addressed in this study for the control of two-dimensional (2D) systems. A generalized boundary condition analysis is presented in the form of tractable invariant sets for the derivation of region of stability to design a suitable state feedback control. A mechanism for the evaluation of controller parameters is presented by considering the generalized structure of 2D Lyapunov function. The work has been extended when external disturbances are present in the 2D systems, and a robust design condition by accounting the perturbations as well as the input saturation has been established. In comparison to the existing works, a control system design for 2D Roesser systems under input saturation and intrinsic nonlinearity by application of a generalized Lyapunov function has been revealed. Furthermore, a tractable 2D region of stability for the local control of the 2D systems is achieved, rather than the conventional global controllers. Furthermore, a method has also been studied for obtainment of the controller gain matrix through convex optimization regarding the complete structure of the 2D Lyapunov function. Simulation results are provided for the stabilization of an unstable nonlinear 2D system under input saturation.

Association between the triglyceride–glucose index and serum soluble Klotho in middle-aged and older adults from NHANES 2007–2016

Klotho, an anti-aging protein, is believed to participate in metabolic diseases and play a potential protective role by regulating insulin sensitivity. This study aimed to explore the relationship between the triglyceride-glucose (TyG) index (a simple marker of insulin resistance) and serum soluble Klotho (S-Klotho) levels. The cross-sectional study comprised 5237 adults aged 40–79 years who participated in the National Health and Nutrition Examination Surveys (NHANES) 2007–2016. The TyG index was calculated as ln [fasting triglycerides (mg/dL) × fasting glucose (mg/dL)/2]. The serum levels of S-Klotho were measured by enzyme-linked immunosorbent assay. The association between the TyG index and S-Klotho levels was investigated by multiple linear regression models, smoothed curve fitting, segmented linear regression models, subgroup analyses, and interaction tests. The TyG index was inversely associated with serum S-Klotho level after full adjustment (β = − 45.11, 95% CI (− 79.53, − 10.69), P = 0.011). Furthermore, we also found a non-linear correlation and saturation phenomenon between the TyG index and serum S-Klotho levels, with a turning point of 9.56. In addition, a significant interaction effect of sex was found between the two (P for interaction < 0.001), with a more pronounced association observed in females. Further studies are required to explore the mechanisms and verify the correlation.

Synchronization under saturable nonlinearity.

In this theoretical work, we introduce a nonlinear gain saturation law representative of the experimentally observed properties manifested by phenomena ranging from aeroacoustic shear layers in self-sustained cavity oscillations to flame heat release rate in thermoacoustic instabilities. Furthermore, this type of saturable gain may be relevant for a wider class of physical systems, such as active laser media in photonics. The nonlinearity discussed herein governs the fullscale behavior of a self-oscillator exhibiting linear loss under large amplitude perturbations, in contrast to the cubic damping and linear gain of the Van der Pol model. A distinctive characteristic of the proposed equation is the simple, well behaved gain term in the slow timescale dynamics.

Periodic event-triggered adaptive neural control of USVs under replay attacks

This work aims to address the control issue of unmanned surface vehicles (USVs) under replay attacks, where the influence of internal/external uncertainties and actuator’s physical constraints are taken into account. In the control design, a hyperbolic tangent function is used to replace the actuator saturation nonlinearity. To solve the design problem of mismatched unknown time-varying control gain caused by replay attacks, the single-parameter-learning technique is introduced, which avoids the operation of estimating for the unknown gain directly. To compensate for the effect of lumped uncertainties including attacks, unknown dynamics and external disturbances, the adaptive neural network with the finite covering principle is involved in the kinematic and dynamic channels, respectively. Furthermore, to reduce the update rate of actuator and alleviate the actuator wear, a periodic event-triggering mechanism (PETM) is established in the controller-actuator (C-A) channel. Finally, a periodic event-triggered (PET) adaptive neural tracking control solution for USVs under replay attacks is proposed, and it is verified that the control solution can force the trajectory of USVs to follow the reference trajectory even if there exists the effect of replay attacks. In addition, all signals in the closed-loop control system of USVs under replay attacks are bounded, and simulation and comparison results demonstrate the effectiveness of the control strategy.