Nonlinear Behavior Research Articles

Numerical study of PPVC modular steel constructions (MSCs) with selected connection strategies under varied earthquake scenarios

Modular steel construction (MSC) represents an innovative approach in civil engineering. Yet, the complexities of its structural response to seismic forces are not fully understood, nor is the practicality concerning its connection systems. Traditional analytical models, often linear and elastic, fail to capture the MSC connection's nuanced, non-linear behaviour under seismic stress. This research embarks on a detailed numerical and parametric analysis of three MSC systems, introducing a novel stiffness coupling spring matrix approach to reflect the connection's behaviour more accurately in seismic conditions. The study analysis identifies MSC1 as demonstrating resilience, with intra and internal inter-module connections experiencing displacement up to 0.719 m and 0.685 m, respectively, under a 7.7Mw Chi-Chi earthquake. Conversely, MSC2, under a 6.7Mw Denali earthquake, highlights an urgent need for design optimisation, with connections displacement up to 0.714 m. MSC3 exhibits superior structural integrity and seismic resilience during a 5.3Mw Kocaeli earthquake, achieving a stiffness peak of 5499.1 N/m and registering minimal displacement of 0.184 m and 0.177 m in intra and internal inter-module connections. Further, a sensitivity analysis incorporating ±10% stiffness variations is crucial in seismic resilience. MSC1 and MSC2 display pronounced sensitivity, particularly MSC1's intra-connection with displacement fluctuations up to 0.789 m and a decrease to −8.273 m. This analysis underscores the imperative for enhanced stiffness in MSC3's external inter-module connections to withstand less severe seismic impact while necessitating increased stiffness for MSC1 and MSC's corner inter-module connections. Maintaining consistent stiffness in module-to-foundation connections is essential for models, notably on MSC1 and MSC2, highlighting the intricate challenge of engineering MSC systems for peak seismic performance.

Efficient and accurate flexible multibody dynamics modeling for complex spacecraft with integrated control applications

This study presents a novel flexible multibody dynamics modeling method tailored to spacecraft with intricate motion features such as multi-axis antenna actuation, robotic manipulations, and space station module rotation. Using a floating base and a tree-topology structure, the model effectively simulates the kinematics and dynamics of large-angle joint rotations and elastic deformations, leveraging the Lagrangian framework and finite element analysis. An advanced augmented proportional–derivative (APD) control scheme is also introduced, incorporating system dynamics for enhanced predictive control, accommodating complex interactions and nonlinear system behaviors. Our modeling approach, compared with the commercial Adams software, shows similar system responses while reducing computation time by about 70%, highlighting its efficiency and accuracy. Moreover, incorporating the APD strategy into our system enhances tracking precision, achieving a 90% reduction in error compared with conventional proportional–derivative controls, underscoring the benefits of combining dynamic modeling with control improvements.

Nonlinear trends in signatures characterizing non-perennial US streams

Stream drying patterns – including duration, timing, and dry-down rates – affect aquatic ecosystems and nutrient exports in non-perennial streams. Because hydrologic processes are often nonlinear, changes in drying may also be nonlinear, but analyses of historical changes in stream drying to date have not characterized the frequency or functional forms of nonlinear change. Understanding the extent of nonlinear change in non-perennial streams is essential for advancing our fundamental knowledge of hydrological processes, aquatic ecosystems, and watershed functioning under a warming climate. This paper uses a polynomial-based trend detection technique (PolyTrend) to analyze the linear and nonlinear trend behaviors of three intermittency signatures (annual no-flow days specifying longer or shorter drying duration, day of first no-flow occurrence specifying timing of stream drying, and days from peak to no-flow specifying dry-down rates) at 540 non-perennial gage stations over 38 years (1980–2017) across the continental United States (CONUS). Additionally, we carried out a breakpoint analysis to characterize the discontinuities in the time series of each intermittency signature. Analysis of annual no-flow days shows that about 37 % of the total streamflow stations are drying for longer each year, whereas about 22 % are wetter for longer than in the past. The day of first no-flow occurrence analysis shows that 10 % of the streams are drying earlier, and 19 % are drying later. On the other hand, analysis of days from peak to no-flow shows that 14 % of streams are drying faster, and 17 % are drying more slowly. For all these metrics, among the significant trends, at least half of the relationships were nonlinear. For annual no-flow days, the breakpoint analysis shows more discontinuities in the second half of the analysis period (1999 to 2017) than in the first half, with more discontinuities in the Southern Great Plains than in other regions. The other two signatures demonstrate less frequent discontinuities in the second half of the analysis period, suggesting decreased nonlinear dynamics in recent years. Nonlinear no-flow duration trends are common in Mediterranean California, and the dry-down rate has increased in recent decades. Our findings indicate that nonlinear change in stream drying is widespread and must be accounted for in watershed planning and management.

Linear vs. Non-linear Behaviour in Ion Irradiation Nanostructuring of Nickel and Silicon Surfaces

Spontaneous nanometre-scale quasi-periodic ripple-like structures are formed at the surface of polycrystalline Ni films and Si(111) single crystal wafers by irradiation with a broad Ar+ ion beam at room temperature and studied with Atomic Force Microscopy as a function of fluence. The development of these structures can be reproduced by numerical solution of a continuum equation describing the evolution of surface morphology under ion irradiation, using realistic coefficients derived from material properties. In particular, we demonstrate that differences observed in pattern formation on the two surfaces under the conditions studied, such as wavelength stability and exponential growth of interface width for the Ni surfaces compared with wavelength coarsening and interface width saturation on Si(111), can be understood in terms of a cross-over between linear and non-linear behaviours.

Highly distinctive linear and nonlinear rheological behaviors of mucin-based protein solutions as simulated normal and asthmatic human airway mucus

Mucus on the human airway surface normally provides a fluid barrier to trap and remove inhaled hazardous particulates such as viruses and bacteria, a physiological function known as mucus clearance. This function, however, can fail if the mucus has abnormal rheological properties, as in the case of certain lung diseases such as asthma. Despite its importance, airway mucus rheology has not been well studied so far, largely because of its complex nature and limited availability. Therefore, in this study, we prepared mucin-based protein solutions as simulated normal and asthmatic airway mucus (NM and AM, respectively) and subsequently studied them in both linear and nonlinear rheological conditions using either conventional steady-state or large amplitude oscillatory shear experiments together with nonlinear multi-mode Giesekus model analysis. We also examined the microscopic structure of the simulated airway mucus by optical or atomic force microscopy. We found that both NM and AM exhibited typical nonlinear rheological behaviors of protein solutions. However, as compared to NM, AM was much more solid-like, and the viscosity, yield stress, and dynamic modulus were more than ten times that of NM. These differences in macroscopic rheological behaviors between NM and AM could be attributed to their different microstructures. Taken together, this study provides evidence that airway mucus may dramatically change its rheological behaviors with changing chemical composition and microstructure as occurring in diseased conditions such as AM. Thus, the presented rheological assessment and modeling analysis, together with the microscopic characterization of simulated airway mucus, may have important values for better understanding the critical roles of mucus rheology in the determination of the mucus clearance function in health and disease as well as the development of pulmonary drug delivery systems.

Opposition-based manta ray foraging algorithm for global optimization and its application to optimize nonlinear type-2 fuzzy logic control

Interval Type-2 Fuzzy Logic Control (IT2FLC) possesses a high control ability in a way that it can optimally handle the presence of uncertainty in a system dynamic. However, the design of such a control scheme is a challenging task due to its complex structure and nonlinear behavior. A Manta Ray Foraging Optimization (MRFO) is a promising algorithm that can be applied to optimize the control design. However, MRFO still suffers the local optima problem due to unbalance exploration-exploitation of the MRFO agents and hence limiting the performance of the desired control. In this paper, Standard, Quasi, Super, and Quasi-Reflected opposition strategies are integrated into the MRFO structure. Each strategy enhances the exploration-exploitation capability and offers different approaches of varying agent’s step size relative to the algorithm’s iteration. The proposed opposition-based MRFO (OMRFO) algorithms are applied to optimize the IT2FLC control design for a laboratory-scaled inverted pendulum system. Moreover, as the algorithms are also promising strategies to other problems, they are applied to solve 50D of 30 IEEE CEC14 benchmark functions representing problems with different features. Performance analysis of the algorithms is statistically conducted using Wilcoxon sign rank and Friedman tests. The result shows that the performance of MRFO and Quasi-Reflected-OMRFO are equal, while all other OMRFO variants show a significant improvement and better rank over the MRFO. The Super and Quasi OMRFO-IT2FLC schemes acquired the best responses for the cart and pendulum, respectively.

Multiscale computational modelling of nano-silica reinforced cement paste: Bridging microstructure and mechanical performance

This study presents a systematic model to optimise nano-silica utilisation in cement paste and predict its nonlinear behaviour. The model integrates a hydration model, which calculates the dissolution rate of each clinker mineral, with a thermodynamic model that simulates the hydration reaction and interaction between hydrates and nano-silica. The investigation considered different replacement levels of nano-silica (2 and 4% by weight of cement) to analyse the phase assemblages and porosity of nano-silica reinforced cement paste. The reaction between nano-silica and the hydrate (portlandite) was meticulously accounted for by incorporating the formation of calcium-silica-hydrate (C-S-H) with a realistic transition from jennite-type C-S-H (Si/Ca ratio of 0.58) to tobermorite C-S-H (Si/Ca ratio of 0.67). The coupled model was validated against the experimental results obtained from thermogravimetric analysis, X-ray diffraction, and scanning electron microscopy, ensuring its reliability. Subsequently, the model was used to compute the volume fractions of various phases including hydrates, unhydrated clinkers, pores, and unreacted nano-silica. A representative volume element (RVE) was formulated for the cement pastes with and without nano-silica using MATLAB. The RVE was further evaluated through finite element analysis using COMSOL Multiphysics, enabling the computation of homogenised material properties such as compressive strength, and this aligned well with experimental findings. In summary, the proposed systematic model provides a realistic prediction of the nonlinear behaviour of cement pastes with different nano-silica replacement levels. Its applicability extends to the optimisation of cement-based composites for diverse engineering applications.

Nonlinear spreading behavior across multi-platform social media universe.

Understanding how harmful content (mis/disinformation, hate, etc.) manages to spread among online communities within and across social media platforms represents an urgent societal challenge. We develop a non-linear dynamical model for such viral spreading, which accounts for the fact that online communities dynamically interconnect across multiple social media platforms. Our mean-field theory (Effective Medium Theory) compares well to detailed numerical simulations and provides a specific analytic condition for the onset of outbreaks (i.e., system-wide spreading). Even if the infection rate is significantly lower than the recovery rate, it predicts system-wide spreading if online communities create links between them at high rates and the loss of such links (e.g., due to moderator pressure) is low. Policymakers should, therefore, account for these multi-community dynamics when shaping policies against system-wide spreading.

Effect of temperature on ferroelastic and creep behavior of LaCoO3

The study investigates the time-dependent deformation of LaCoO3 under constant uniaxial compressive stresses at various temperatures ranging from room temperature to 880 °C. Through the acquisition of stress-strain curves at different temperatures, it has been observed that LaCoO3 exhibits non-linear ferroelastic behavior. The stiffness of LaCoO3 increases with temperature, up to 600 °C, after which it starts to decrease at higher temperatures. Furthermore, negative creep occurs at lower temperatures, whereas positive creep is observed at temperatures exceeding 600 °C. This can be attributed to transitioning from a ferroelastic creep at low temperatures to a combination of ferroelastic and high-temperature conventional creep at temperatures above 600 °C. The magnitude of both negative and positive creep is proportional to the temperature. The structural stability of LaCoO3 under creep loading at all temperatures has been assessed by comparing pre-test and post-test X-ray diffraction analyses, which showed the texture formation after testing.

A novel approach to data analysis for lithium-ion batteries using higher-order spectral analysis

The usage of lithium-ion batteries has become widespread across various applications, such as electronic devices, electric vehicles, and integrated renewable energy systems. Hence, there is a pressing need to enhance analytical techniques to optimize their performance and prolong their operational lifespan. This study introduces an innovative methodology that utilizes higher-order spectral analysis (HOSA) for evaluating data collected from lithium-ion batteries. The objective is to capture the inherent nonlinear and non-stationary behaviors displayed by battery data. The proposed approach mainly uses Bispectrum and Bicoherence to establish hypothesis tests for nonlinearity and non-Gaussianity of data. Through a customized algorithm, the higher-order spectrum of these refined data is calculated, uncovering intricate characteristics that may go unnoticed by conventional analytical methods. These findings have a wide range of potential applications, including battery modeling, fault detection, state-of-charge estimation, state-of-health estimation and the enhancement of battery performance. Finally, an experiment is conducted to validate the effectiveness of the method.

Propagation of solitary wave solutions to (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation arise in mathematical physics and stability analysis

This innovative study simulates the (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) equation, which has anomalous applications in the field of mathematical physics. The current research has two basic pillars. Firstly, numerous novel soliton solutions are synthesised in distinct formats, such as dark, bright, periodic, combo, W-shape, mixed trigonometric, exponential, and rational, based on the modified sardar sub-equation (MSSE) method and the improved F-expansion method. Secondly, the stability analysis of the selected model is manifested to study modulation instability (MI) gain. Furthermore, for the physical demonstration of the acquired solutions in 3D and 2D, contour and density plots are depicted. The discovered results have a distinctive feature that has not been developed before and indicate a good balance between the nonlinear physical components. Also, the resulting structure of the acquired results can enrich the nonlinear dynamical behaviours of the given system and may be useful in many domains, such as mathematical physics and fluid dynamics, as well as demonstrate that the approaches used are effective and worthy of validation.

Nonlinear static solution of suspension bridge formulated from a surrogate model with secant stiffness of suspension cables

Explicit analytical solution may offer great convenience for the design and parametric study of suspension bridges. However, the nonlinear behavior of suspension cable exacerbates the difficulty of such theoretical derivation. Adopting secant stiffness is an effective way to deal with the nonlinearity of the cable, but the crux is how to find its deformed state under external loading. The strategy of this study is primarily targeted at a typically arranged three-span suspension bridge. It starts from formulating the basic form of nonlinear stiffness of suspension cables by setting the elastic stiffness and geometric stiffness in series, then a surrogate model is accordingly established with the nonlinear springs to replace the mid-span and side-span cables. The deformed state of the surrogate model subjected to the specified external load cases will be found by restricting and releasing its tower tops, and thus the analytical formula of the secant stiffness can be obtained. Consequently, the nonlinear static solution of suspension bridge, including force and deformation changes in the cables and towers, can be explicitly expressed with the secant stiffness. The general solution procedure can also be extended to multi-span suspension bridges. Finally, the nonlinear static solution is verified by numerical examples of a three-span suspension bridge and a four-span suspension bridge. The parametric analysis reveals that the nonlinearity of suspension bridge will become significant as the side-span to mid-span ratio increases, or when the side-span cables are hung with hangers.

Intrinsic resonance in gyrotron using non-resonant RF structure

Gyromonotrons are typically believed to rely on the convective interaction between the co-propagating beam and wave, with the extended energy-exchanging process stemming from the external feedback. However, numerous studies focusing on both transverse electric (TE) mode and transverse magnetic (TM) mode gyrotrons have consistently shown that beam–wave interactions in weak-feedback systems or even in uniform tubes without any structural feedback can yield a theoretical beam efficiency of more than 30% with major forward-wave output during near-cutoff operation, which is the typical operating condition for gyromonotrons. These intriguing findings raise questions about the actual feedback mechanism of gyromonotrons. In this article, comparative studies on the linear and nonlinear behaviors of uniform-tube gyrotron are investigated. The forward and backward waves are observed to co-generate and exhibit similar characteristics of ultra-slow group velocity under near-cutoff operation. This situation allows the as-generated forward wave to modulate the fresh beam, establishing a new backward-wave-like internal feedback loop. Additionally, the quasi-degenerate nature of the bi-directional propagating waves ensures their intrinsic in-phase relationship. The consequent constructive interference enables the uniform tube to function as a high-Q resonator. These findings are found to be independent of the choices of TE or TM modes, providing valuable insights into the underlying interaction mechanism of gyrotron devices.

Mitigation of the Brighter-fatter Effect in the LSST Camera

Thick, fully depleted charge-coupled devices are known to exhibit nonlinear behavior at high signal levels due to the dynamic behavior of charges collecting in the potential wells of pixels, called the brighter-fatter effect (BFE). The effect results in distorted images of bright calibration stars, creating a flux-dependent point-spread function that if left unmitigated, could make up a large fraction of the error budget in Stage IV weak-lensing (WL) surveys such as the Legacy Survey of Space and Time (LSST). In this paper, we analyze image measurements of flat fields and artificial stars taken at different illumination levels with the LSST Camera (LSSTCam) at SLAC National Accelerator Laboratory in order to quantify this effect in the LSSTCam before and after a previously introduced correction technique. We observe that the BFE evolves anisotropically as a function of flux due to higher-order BFEs, which violates the fundamental assumption of this correction method. We then introduce a new method based on a physically motivated model to account for these higher-order terms in the correction, and then we test the modified correction on both data sets. We find that the new method corrects the effect in flat fields better than it corrects the effect in artificial stars, which we suggest is the result of sub-pixel physics not included in this correction model. We use these results to define a new metric for the full-well capacity of our sensors and advise image processing strategies to further limit the impact of the effect on LSST WL science pathways.

Bio inspired heuristic computing scheme for the human liver nonlinear model

In this research, a bio-inspired heuristic computing approach has been developed to solve the nonlinear behavior of the human liver, which is categorized into the liver and blood. The solutions of the human liver model are presented by using the stochastic computation procedure based on the artificial neural network (ANN) along with the optimization of genetic algorithm (GA) and interior-point (IP). A fitness function is designed through the differential form of the nonlinear human liver model and then optimized by using the hybrid competency of GAIP scheme. The correctness and exactness of the proposed approach are observed through the overlapping of the obtained (GAIP) and reference (Adams scheme) solutions, while the calculated absolute error values in good order enhance the worth of the proposed solver. The log-sigmoid transfer function together with ten numbers of neurons is executed to perform the solutions of the human liver nonlinear model. Furthermore, the statistical approaches have been applied in order to observe the reliability of the designed approach for solving the nonlinear human liver model.

Computational Validation and Assessment of Large Amplitude Transverse Gust Physics

Rotary-wing vehicles, in particular smaller, lighter unmanned and urban air vehicles in urban and shipboard settings, will operate in low-speed flight conditions that are dominated by strong transient aerodynamics. Understanding the physics of these transient aerodynamics, specifically large amplitude transverse gusts and the resulting vehicle response, is crucial to the successful development and certification of safe air vehicles that operate in these environments. A high-fidelity computational study, including validation with experiments, explores sharp-edged or step transverse gusts where the gust velocity induces nonlinear behavior caused by flow separation. The behavior of the maximum lift and leading edge vortex behavior with the gust ratio is presented. Gust responses are observed to depart from Küssner’s theory when the leading edge vortex first forms as a distinct feature and breaks away from the wing, resulting in flow nonlinearities. Traditional linear indicial admittance techniques are shown to no longer be valid to predict gust responses when the gust velocity approaches the vehicle flight speed.

Feasibility analysis of deep steep riser based on co-rotational coordinate method

DSR (Deep steep riser) is a new riser structure that reduces the ultra-high-tension load caused by the riser self-weight. In this paper, the mechanical behavior of DSR under different buoyancy module configurations and different ocean currents is studied. The finite element model of DSR is established based on co-rotational coordinate method. The model is solved by arc length method. The accuracy of the numerical method is verified by Abaqus software. Then, the effects of buoyancy module length and buoyancy factor on DSR are analyzed. Finally, the influence of different current incidence angles and velocities on DSR is evaluated. The results show that the DSR model based on the co-rotational coordinate method can effectively simulate the nonlinear behavior of large deformation of DSR. The method is simple, flexible and computationally efficient. This method can quickly improve the efficiency of numerical calculation in static analysis of deepwater riser. And DSR is feasible under certain conditions.

Nonlinear vibrations of cracked microbeams based on modified couple stress theory

In this study, nonlinear vibrations of cracked microbeams have been investigated. The micro size characteristics of the beam have been involved in the model by utilizing the modified couple stress theory. Longitudinal elongation of the microbeam during transverse vibrations have been considered to capture the nonlinear behavior. To model the crack, a torsional spring has been introduced at the crack location and the spring constant corresponds to the severity of the crack. Approximate solutions have been obtained by using the method of multiple scales, a perturbation technique. The results have been validated by comparing them with existing literature and have been presented in terms of both crack severity and micro scale properties. The effects of the crack have been examined on various aspects, including natural frequency, nonlinear frequency-response curves and nonlinear frequency responses. These effects have been investigated with respect to parameters such as crack severity, crack location, amplitude of excitation, slenderness of the beam, all under differing boundary conditions. The predicted results reveal that as the crack severity increases, both natural frequency and nonlinear frequency decrease. Furthermore, the modified couple stress theory predicts an increase in natural frequencies as the size scale of the microbeams reduces. The frequency-response curves with varying crack severity and crack locations have indicated the significant effects of the presence of the crack in microbeams.

Multiscale nonlinear analysis of 3D orthogonal woven C/SiC composites based on the CT reconstruction

AbstractDue to the effects of manufacturing process, there are lots of distributed voids in the interior area of three‐dimensional (3D) woven C/SiC composites, leading to the difficulties in predictions of damage evolution and ultimate strength. In this work, the mesoscale geometry of 3D woven C/SiC composites is reconstructed based on the high‐resolution CT scanning, considering the yarn path, yarn profile, and void content. The CT‐based reconstructed model agrees well with the experimental observations. Then, the constitutive laws of mesoscale constituents and macroscale structure are established and implemented numerically by the user‐defined material subroutine UMAT. Finally, the established constitutive laws are applied for the reconstructed model, and the mesoscale and macroscale nonlinear progressive damage behavior of 3D woven C/SiC composite structures are predicted using the hierarchical multiscale method, which are also validated by the experiments. The established CT‐based multiscale computational scheme would be a potential tool for performance evaluation and design of composites.

Study of Metal Chalcogenide Material for Optical and Electrical Properties

Abstract: Metal chalcogenide materials offer a complex tapestry of optical and electrical properties that engage researchers from a variety of disciplines, making their study an important area of study in materials science. This abstract light up the dual nature of these materials and their possible uses by exploring the complex interactions that exist between structure, composition, and functioning. The search for new materials with customised optical responses has focused attention on the optical characteristics of metal chalcogenides recently. Optoelectronic device improvements are made possible by the versatile platform provided by the bandgap engineering in these compounds for altering light-matter interactions. A thorough understanding of metal chalcogenides' optical properties is provided by examining their absorption and emission spectra, quantum yield, and nonlinear optical behaviours. This knowledge is essential for the creation of sensors, photodetectors, and light-emitting gadgets of the future.