Nonlinear Region Research Articles

Parameter-by-parameter estimation method for adsorption isotherm in hydrophobic interaction chromatography

Hydrophobic interaction chromatography (HIC) is used as a critical polishing step in the downstream processing of biopharmaceuticals. Normally the process development of HIC is a cumbersome and time-consuming task, and the mechanical models can provide a powerful tool to characterize the process, assist process design and accelerate process development. However, the current estimation of model parameters relies on the inverse method, which lacks an efficient and logical parameter estimation strategy. In this study, a parameter-by-parameter (PbP) method based on the theoretical derivation and simplifying assumptions was proposed to estimate the Mollerup isotherm parameters for HIC. The method involves three key steps: (1) linear regression (LR) to estimate the salt-protein interaction parameter and the equilibrium constant; (2) linear approximation (LA) to estimate the stoichiometric parameter and the maximum binding capacity; and (3) inverse method to estimate the protein-protein interaction parameter and the kinetic coefficient. The results indicated that the LR step should be used for dilution condition (loading factor below 5%), while the LA step should be conducted when the isotherm is in the transition or nonlinear regions. Six numerical experiments were conducted to implement the PbP method. The results demonstrated that the PbP method developed allows for the systematic estimation of HIC parameters one-by-one, effectively reducing the number of parameters required for inverse method estimation from six to two. This helps prevent non-identifiability of structural parameters. The feasibility of the PbP-HIC method was further validated by real-world experiments. Moreover, the PbP method enhances the mechanistic understanding of adsorption behavior of HIC and shows a promising application to other stoichiometric displacement model-derived isotherms.

Trajectory tracking control of autonomous vehicles based on Lagrangian neural network dynamics model

The autonomous vehicles make decisions and plans based on the environmental perception and generate the target command of the control layer. The vehicle dynamics model is an important factor that affects the vehicle control. The dynamic mechanism model has strong interpretability and good stability. However, in extreme conditions, the model accuracy is reduced due to the tire entering the nonlinear region. The data-driven dynamic model achieves high modeling accuracy. However, due to the lack of physical constraints and rationality in the data-driven models, the interpretability and stability of the control is reduced, which in turn increases the unpredictable risk in the driving process. This paper innovatively proposes a deep Lagrangian neural network dynamics model (DeLaN) for autonomous vehicles based on the Lagrangian mechanics and uses a neural network to encode the differential equations. This not only retains the interpretability of the physical model but also makes full use of the learning ability and fitting ability of the neural network to effectively capture the complex dynamic characteristics of the vehicle. To improve the robustness of the control system, this work uses DeLaN as feed-forward control and preview error feedback control to form a closed loop of trajectory tracking control for autonomous vehicles. The experimental results show that the trajectory tracking error of the proposed DeLaN is significantly reduced, the yaw stability and comfort are significantly improved, good longitudinal and lateral cooperative control performance is achieved, and the physical rationality of the neural network is also improved. Therefore, the proposed DeLaN has important engineering application value.

Structural and electrical characteristics of Zr-doped HfO2 (HZO) thin films deposited by atomic layer deposition for RRAM applications

In this study, Zr-doped HfO2 (HZO) based resistive random-access memory (RRAM) device were fabricated. The Hf:Zr (1:1) ratio in the HZO films were controlled by changing the HfO2 and ZrO2 cycle ratio during the atomic layer deposition (ALD) process. Next, we studied the structural and electrical properties of the Au/HZO/TiN RRAM device structure. The RRAM devices exhibits an excellent resistance ratio of the high resistance state (HRS) to the low resistance state (LRS) of ~103 A, and as well as good endurance (300 cycles) and retention (>103 s), respectively. Further, the device showed different conduction mechanism in LRS and HRS modes. The lower biased linear region is dominated by ohmic conductivity, whereas the higher biased nonlinear region is dominated by a space charge limited current conduction. This device is suitable for application in future high-density nonvolatile memory RRAM devices.

Multiphysics Modeling Investigation of Wellbore Storage Effect and Non‐Darcy Flow

AbstractThis study presents a comprehensive investigation of wellbore storage effects and non‐Darcy flow in pumping well systems using a multiphysics numerical model. The model incorporates the Reynolds‐averaged Navier‐Stokes equations coupled with a moving free surface to simulate the flow field and drawdown in the wellbore. Hydraulic behavior of the system, including well and aquifer drawdown, pumped water ratio, aquifer flow nonlinearity, and wellbore flow field, is analyzed and compared with simplified 1‐D models. This study highlights the presence of a vortex in the wellbore flow field induced by large Reynolds number and the uneven stress distribution at the screen. This vortex influences the wellbore drawdown and introduces 2‐D flow in the surrounding aquifer, which further contributes to the longer travel paths for groundwater particles and increased hydraulic pressure consumption. The results show that non‐Darcy flow, coupled with wellbore storage effects, leads to higher drawdown in the pumping well compared to Darcy flow cases. The aquifer drawdown exhibits a similar temporal pattern but with decreasing deviation at larger distances due to the cone of depression. The pumped water ratio indicates the challenge of supplying outflow at the intake from aquifer storage, with nonlinear flow resulting in a smaller ratio compared to linear cases. A nonlinearity ratio is defined to illustrate the expansion of nonlinear flow regions over time, their convergence to a predictable quasi‐steady‐state shape, which is influenced by the Forchheimer parameter, and the gradual transition to Darcy flow away from the wellbore.

Convex-based lightweight feature descriptor for Augmented Reality Tracking.

Feature description is a critical task in Augmented Reality Tracking. This article introduces a Convex Based Feature Descriptor (CBFD) system designed to withstand rotation, lighting, and blur variations while remaining computationally efficient. We have developed two filters capable of computing pixel intensity variations, followed by the covariance matrix of the polynomial to describe the features. The superiority of CBFD is validated through precision, recall, computation time, and feature location distance. Additionally, we provide a solution to determine the optimal block size for describing nonlinear regions, thereby enhancing resolution. The results demonstrate that CBFD achieves a average precision of 0.97 for the test image, outperforming Superpoint, Directional Intensified Tertiary Filtering (DITF), Binary Robust Independent Elementary Features (BRIEF), Binary Robust Invariant Scalable Keypoints (BRISK), Speeded Up Robust Features (SURF), and Scale Invariant Feature Transform (SIFT), which achieve scores of 0.95, 0.92, 0.72, 0.66, 0.63 and 0.50 respectively. Noteworthy is CBFD's recall value of 0.87 representing at the maximum of a 13.6% improvement over Superpoint, DITF, BRIEF, BRISK, SURF, and SIFT. Furthermore, the matching score for the test image is 0.975. The computation time for CBFD is 2.8 ms, which is at least 6.7% lower than that of other algorithms. Finally, the plot of location feature distance illustrates that CBFD exhibits minimal distance compared to DITF and Histogram of Oriented Gradients (HOG). These results highlight the speed and robustness of CBFD across various transformations.

A nonlinear contraction channel design inspired by typical mathematical curves: Boosting net power and water discharge of PEM fuel cells

The next-generation fuel cell needs to fit high current density operating conditions, necessitating improved flow fields with superior capabilities in mass transfer and drainage. This study introduces four innovative nonlinear contraction channels aimed at enhancing net power and mitigating waterflooding under high current density. This design draws inspiration from classical mathematical curves, which can provide targeted mass transfer enhancement contingent upon species distribution. Multiple quantitative indicators are employed to evaluate the efficacy of nonlinear structures in cross-scale mass transfer, drainage, temperature uniformity, and power consumption. Numerical results indicate that the exponential-like curve channel exhibits notably superior overall performance. Its nonlinear contraction region induces purge airflow at the tail of channel, facilitating drainage and boosting the local mass transfer flux in oxygen-starved region by 48.75%. The utilization of nonlinear contraction structures alters the diffusion-convection distribution mechanism and increases the convective mass transfer proportion. Under conditions of high current density, there is a noticeable rise in the Peclet number. Considering the pumping power loss, the hyperbolic tangent, quarter-ellipse, parabolic, and exponential-like curve flow channels can enhance the net power by 3.10%, 6.82%, 8.57%, and 10.04% over straight channels. Additionally, the exponential-like curve channel enhances temperature uniformity in the catalyst layer under rated working conditions, whereas the hyperbolic tangent flow channel demonstrates superior uniformity in higher current density.

Power Amplifier Optimization for M2M Node using DPD and Hybrid DFT-s-OFDM with CFR

Power Amplifiers (PAs) play a vital role in mobile communication. However, their inherent nonlinearity can lead to issues such as unwanted radiation, interference with neighboring channels, and distortion within the desired frequency range. To address these problems, PAs are typically operated at a lower power level than their saturation point, sacrificing power efficiency to improve Error Vector Magnitude (EVM) performance. Consequently, more than 70-80% of the DC power is wasted as heat. This inefficiency necessitates the exploration of techniques to enhance PA efficiency while maintaining acceptable linearity and performance. Digital Pre-Distortion (DPD) is a useful technique to linearize PAs. DPD allows affordable nonlinear PAs to function with minimal distortion in their nonlinear operating regions. This results in amplified signals with increased power output and improved power efficiency. Using nonlinear functions, the output signal of the PA can be linearized, mitigate distortions, and be effectively optimized. When using various operating channels and varying time, temperature, and PA nonlinearity, the DPD must adjust. In order to increase the power efficiency of 5G systems, DPD-enabled systems are inculcating with adaptive DFT-s-OFDM employed 5G physical layer along with the Crest Factor Reduction (CFR) algorithm.

New Region of Nonlinearity in the IV-Curve of SFS φ0 JJ under Radiation

New Region of Nonlinearity in the IV-Curve of SFS φ0 JJ under Radiation

Multi-Parameter Practical Stability Region Analysis of Wind Power System Based on Limit Cycle Amplitude Tracing

The existing division of system stability region does not fully consider the influence of nonlinear characteristics of the system. To address the challenge that it is difficult to inscribe the stability region of wind power grid-connected systems accurately and quantitatively, this paper proposes a nonlinear system multi-parameter practical stability region analysis method based on limit cycle amplitude tracking. Firstly, the nonlinear dynamic model of multi-machine system with doubly fed induction generator (DFIG) is established, and the bifurcation diagram of the system is obtained by nonlinear analysis of the model. Then, the limit cycle-parameter diagram is obtained by tracking the limit cycle of the Hopf bifurcation point of the system, and the problem of how the system oscillation evolves with the change of operating parameters is analyzed. Afterwards, the single parameter practical stability region of the nonlinear system is obtained by combining the system equilibrium manifold. Finally, the multi-parameter practical stability region of the nonlinear system is obtained by the three-dimensional bifurcation map with the system time delay, DFIG output active power and reactive load as the bifurcation parameters. The division of the stability region has important guiding significance for the parameter adjustment in the actual operation of the system.

A standardized approach to identify nonlinearity in fighter jet noise during ground run-ups

High-intensity military sources (explosions, gunfire, fighter jet noise. . . ) fall out of the scope of linearity-based commercial software and international standards. On top of its intrinsic complexity (high temperature supersonic jet, shocks, turbulent eddies, etc), fighter jet engine noise bears additional challenges: turbulent surrounding flow, airframe interference, directionality and tonal components typical of rotating equipment. The absence of a suitable metric to determine the boundary of the nonlinear propagation region can lead to costly mispredictions in the exposure levels for noise abatement procedures and the personnel's safety. The derivative skewness of the time domain signal used as an indicator of spectral reshaping proved effective in setting a threshold to the generation of acoustic nonlinearity for seven firearms. Its application to aircraft noise is here discussed, in order to verify the claim of persistence of nonlinear behaviour at large distances and set the foundations for a common framework contemplating the peculiarities of each military noise source. The experimental data was collected during a series of static ground run-ups of an F-16 military jet aircraft. The results from five engine regimes and two propagation paths are compared with the findings from firearms, existing literature and the solution of a nonlinear acoustic propagation solver.

Effect of Shear History on Solid-Liquid Transition of Particulate Gel Fuels.

Investigating the structural evolution of particulate gels is a very challenging task due to their vulnerability and true flow characteristics. In this work, deeper insight into the rheological properties of gel fuels filled with fumed silica (FS) and aluminum microparticles (Al MPs) was gained by changing shear procedures. Firstly, the flow curves were found to no longer follow the monotonic power law and exhibited subtle thixotropic responses. As the shear rate increased, the gel structure underwent a transition from local shear to bulk shear in the nonlinear region after yielding. This finding reveals the prevalence of nonideal local shear in industry. Secondly, the time-dependent rheological responses demonstrated that the strength spectrum of gel fuels depends on the applied shear rate, with stress relaxation more easily observed at lower shear rates. Those results involved the structural disruption, recovery, and equilibrium of particulate gels from two scales of shear rate and shear time.

Tunable microwave frequency comb generation via periodic relaxation oscillation in directly modulated laser

In this paper, a novel and simple generation scheme based on a directly modulated laser (DML) is proposed for tunable microwave frequency combs (MFCs). When the input modulated RF power is intentionally controlled to be sufficiently high to drive the DML into its nonlinear operating region periodically, relaxation oscillations will be excited in the same period. The modulated light from the DML is subsequently detected by a photodetector, and a special kind of microwave signal source can be optically produced and shows up in the form of MFC in the frequency domain. In the proof-of-concept experiment, tunable MFCs are demonstrated with the bandwidth of more than 25 GHz, the comb spacing of 0.5 ∼ 3 GHz, and the flatness of less than ± 2 dB with the frequency from 3 GHz to 18 GHz. The bandwidth of the generated MFC is in accordance with the relaxation oscillation frequency of the DML. The comb spacing is strictly equal to the frequency of the modulated RF signal and thus flexibly adjustable. The carrier-to-noise ratio can be up to 48 dB, and the single-sideband phase noise is measured to be lower than − 90 dBc/Hz@1 kHz for MFCs with comb spacings of 0.7 ∼ 3 GHz.

Mechanism and Development of Thermo-Rheological Properties of Asphalts Modified by Reactive Polymer Systems.

The new class of reactive polymers is designed to modify asphalt through chemical reactions with asphalt components. The complexity of such systems and the long experience with thermoplastic elastomers as well as with some other "classical" modifiers, and to a degree that our present testing methods and even specifications revolve around these materials, might obscure the fact that we are dealing with rather different modification systems and possibly with new emerging asphalt paving technologies. Our present work attempted to compare two different reactive polymer systems with the "classical" system which uses thermoplastic elastomer. The impact of reactive polymer systems on asphalt was studied through material properties manifested by specification tests and through the development of thermo-rheological properties in linear and non-linear viscoelastic regions. As expected, the behavior of reactive polymeric systems with different chemistries also differed among themselves. The available results showed that the reactive groups of polymers react with polar components of asphalt leading to higher stiffness at elevated pavement temperatures and differing impact on low temperature properties. The data point to a significantly improved resistance to plastic deformation of pavement in the case of reactive polymers, despite the fact that elastic recovery-based specification tests failed to identify this improvement.

One‐Step Generation of Energy‐Time‐Polarization‐Hyper‐Entangled W‐Class Triphotons: Nonlinear and Linear Optical Responses

AbstractNonclassical multiphoton have attracted extensive attention to serve as entangled resources for quantum information technology. Here, the continuous‐mode hyper‐entangled W‐class triphotons are theoretically generated through spontaneous six‐wave mixing (SSWM) in 85Rb. In nonlinear optical response, Zeeman sub‐states are high‐dimensionally quantized by polarized dressing. High‐dimensional entanglement is structured via atomic non‐Hermitian nature. Through linear optical response, the temporal correlations are shaped via diverse polarized dressing. SSWM‐based triphoton is a genuine triphoton possessing non‐Gaussian tripartite entanglement. The high production rate is due to co‐action of three strong input fields, electromagnetically induced transparency (EIT) protection, and slow light effect. Non‐Hermitian nature endows the system with sensitive adjustability around exceptional points (EP). Eventually, the results demonstrate multiple SSWMs causing oscillations with multiple periods in three‐photon temporal correlations for the nonlinear region, build a high‐dimensional three‐body entangled quantum network and transform multifarious profiles of the three‐photon temporal correlations for the linear region. Especially, both high‐dimensional and hyper entanglements are obtained, contributing to high quantum information capacity. Further, the system is switched among multiple states when non‐Hermitian nature is manipulated by polarized dressing. The research opens a broad prospect for generating the hyper‐entangled multiphoton with potential application in adjustable quantum networks of high information capacity.

Design and verification of a backward wave oscillation suppression circuit for the Ka-band gyrotron travelling-wave tube.

Backward wave oscillation seriously degrades the stability of gyrotron travelling-wave tubes (gyro-TWTs), especially during high average/continuous wave operation. To solve this problem, a selective mode suppression structure (SMSS) based on the mode coupling principle is proposed and applied in the nonlinear beam-wave interaction region to suppress the parasitic TE11 mode. It is capable of obtaining a high power and improving the tube stability. Simulation results demonstrate that the SMSS can raise the starting current from 10 to 18A and the starting pitch factor from 1.2 to 1.6. Based on this proposed circuit, a Ka-band TE01 mode gyro-TWT was designed, and the particle-in-cell simulation shows that it can achieve a saturated output power of over 150 kW from 29.7 to 31.7GHz with a velocity spread of 2.2%. For verification, a SMSS is manufactured and cold tested. The measurement of S-parameters reveals that it can effectively suppress the parasitic TE11 mode.

A novel Woodbury solution method for nonlinear seismic response analysis of large‐scale structures

AbstractThe Woodbury formula is an efficient tool in mathematics to calculate low‐rank perturbation problems and has been applied to improve the computational efficiency of nonlinear seismic response analysis (NSRA) of structures with local nonlinearity. Using the Woodbury formula for NSRA can avoid the time‐consuming recalculation and factorization of the large‐dimensional global stiffness matrix of a structure by only solving a small‐dimensional Schur complement system representing local nonlinearity per iteration. Because the dimension of the Schur complement matrix is determined by the inelastic degree of freedom (IDOF) number, which represents the scale of local nonlinear regions, a small IDOF number is helpful for achieving the high‐efficiency advantage of the Woodbury formula. However, when performing NSRA for large‐scale structures, the IDOF number is usually relatively large, which contradicts the efficiency requirement of the Woodbury formula. To solve this problem and extend the advantage of the Woodbury formula to the NSRA of large‐scale structures, this paper first proposes a two‐stage IDOF number reduction method by eliminating the IDOFs that have insignificant effects on the results, and consequently, a variant Woodbury formula is derived. Because only the principal component in the Schur complement matrix is retained, the dimension of this matrix and the cost for factorizing it can be reduced significantly without losing accuracy, thus greatly improving the efficiency of the proposed method. Moreover, to reduce the additional computational time introduced by the IDOF number reduction procedure and to further improve the computational performance of the proposed method, an OpenMP parallel computational strategy is incorporated. Finally, the validity of the proposed method is verified by implementing incremental dynamic analysis for a large‐scale reinforced concrete structure.

Piezoresistive behavior in cement-based sensors: Nonlinear modeling and preliminary application

Self-sensing cement sensors detect stress/strain by measuring the fractional change in electrical resistivity. However, neglecting the nonlinear portion of the FCR-stress/strain curves may limit monitoring range. Existing functional models lack versatility and physical meanings of parameters. A new model based on Ramberg-Osgood relation, incorporating the gauge factor, fractional change in resistance, and strain was proposed to cover linear and nonlinear regions. To validate the model, compression and tension cement sensors made of ultra-high toughness cementitious composite and multi-walled carbon nanotubes were tested. Results from various types of cement-based sensors validated the model's versatility. A four-point bending test on a C70 steel-reinforced concrete beam with an embedded cement sensor confirmed the feasibility of the proposed functional model.

Wheat Flour Quality Assessment by Fundamental Non-Linear Rheological Methods: A Critical Review.

Wheat quality assessment involves physical, physicochemical, chemical, and sensory characterization of wheat kernels and the resulting wheat flour, dough, and bread. The physical tests conducted on wheat flour dough are mostly based on empirical methods. Empirical methods have been useful in industry and research to relate wheat flour quality to baking performance. However, these methods have the disadvantage of providing data in arbitrary units, which makes the fundamental interpretation of results difficult. Therefore, this review focuses on the use of fundamental rheological methods to determine wheat flour quality in terms of processing performance. During the transition from wheat flour to bread, wheat flour dough is mostly exposed to large deformations, and the quality of wheat flour determines its response to these large deformations and its baking quality. For this reason, this review only focuses on the application of fundamental rheological tests that are conducted in the non-linear viscoelastic region where wheat flour dough experiences large deformations.

Effects of vacancy concentration on the edge dislocation motion in copper by atomic simulations

Nonequilibirum vacancy concentration widely appears in crystals under many extreme loading conditions, but receives relatively few attentions. In this work, we systematically explore the influence of a serial of different vacancy concentrations on the edge dislocation motion in copper using molecular dynamics (MD) simulations. Our result shows that the vacancy would hinder the dislocation motion, but the mechanism depends on the detailed dislocation motion regions. In thermally activated region, its influence is mainly reflected by modifying the dynamic and static threshold stresses required for edge dislocation initiation and continuous motion. In the linear region, the hindering mechanism is gradually transformed from phonon damping to vacancy pinning with the increasing vacancy concentration. In contrasts, the dislocation structure is almost unchanged under different vacancy concentrations in the non-linear region. Under high applied stress, high vacancy concentration will cause the dislocation velocity to jump back and forth between transonic and subsonic velocities more frequently. It has been attributed to the reactions between the dislocation and vacancies. The latter may result in dislocation local constriction and climbing. Moreover, a mobility equation suitable for describing edge dislocations at different non-equilibrium vacancy concentrations is proposed, which fits the MD results well. Finally, the roles of the nonequilibirum vacancy concentration on the edge dislocation motion is interpreted using the degrading elastic property and stacking fault energy.

Modeling of Linear-Nonlinear Behavior in Electrical Contacts With Interaction Interference

The reliability of electrical contacts is important to the quality of signal transmission. In this letter, an equivalent circuit model is proposed to illustrate the linear-nonlinear interaction effect in coaxial connectors. The linear region is simplified to a cascade system composed of impedance matching and impedance mismatch networks, while the nonlinear region is equivalent to a contact impedance network coupling a module defined by nonlinear I-V relation. By tuning values of each component in the presented circuit, the effect of linear and nonlinear elements on scattering characteristics and passive intermodulation (PIM) are observed. The S-parameters are sensitive to linear network with equivalent inductance and capacitance, but the PIM behavior is affected by both nonlinear resistance and linear resistance which are temperature and frequency dependent. Connectors with designed contact resistance are tested separately in different frequency band and environmental temperature, verifying the proposed model in predicting scattering performance and PIM behavior.