Nonlinear Path Research Articles

Application of the Southwell Method to Determine the Critical Load of Compression Rods Made of Nonlinear Materials

Experimental determination of the critical force of a compression bar made of linear material does not pose major problems. The widely used Southwell method is also applicable to bars with cross-sections varying in length. The purpose of the research undertaken was to demonstrate that this method can also be successfully applied to bars made of elastic materials exhibiting nonlinear σ(ε) characteristics. Using analytical relationships for a rod satisfying the assumptions of Euler-Bernoulli theory, F(δ) relationships were derived for a rod with an initial arc imperfection, and Southwell diagrams were constructed on this basis. Nonlinear equilibrium paths F(δ) were also determined numerically using the COSMOS/M program for this purpose. For the pre-assumed different nonlinear characteristics, full confirmation of the validity of the application of the Southwell method for determining the critical force was obtained.

Efficient Nonlinear Model Predictive Path Tracking Control for Autonomous Vehicle: Investigating the Effects of Vehicle Dynamics Stiffness

Motion control is one of the three core modules of autonomous driving, and nonlinear model predictive control (NMPC) has recently attracted widespread attention in the field of motion control. Vehicle dynamics equations, as a widely used model, have a significant impact on the solution efficiency of NMPC due to their stiffness. This paper first theoretically analyzes the limitations on the discretized time step caused by the stiffness of the vehicle dynamics model equations when using existing common numerical methods to solve NMPC, thereby revealing the reasons for the low computational efficiency of NMPC. Then, an A-stable controller based on the finite element orthogonal collocation method is proposed, which greatly expands the stable domain range of the numerical solution process of NMPC, thus achieving the purpose of relaxing the discretized time step restrictions and improving the real-time performance of NMPC. Finally, through CarSim 8.0/Simulink 2021a co-simulation, it is verified that the vehicle dynamics model equations are with great stiffness when the vehicle speed is low, and the proposed controller can enhance the real-time performance of NMPC. As the vehicle speed increases, the stiffness of the vehicle dynamics model equation decreases. In addition to the superior capability in addressing the integration stability issues arising from the stiffness nature of the vehicle dynamics equations, the proposed NMPC controller also demonstrates higher accuracy across a broad range of vehicle speeds.

The asymptotic-numerical method for the post-buckling response of curvilinearly stiffened panels

Abstract In the present work, the asymptotic-numerical method is applied in conjunction with the Ritz method as a powerful mean for analysing the post-buckling response of panels with variable stiffness skin and curvilinear stringers. Main advantage of the proposed approach is the reduced computational time. The Ritz method guarantees an excellent ratio between accuracy and required degrees of freedom; the asymptotic-numerical method requires just one matrix inversion throughout the solution process. Moreover, the complete analytical representation of the non-linear equilibrium path is obtained, as opposed to the point-by-point representation of predictor-corrector algorithms. Several test cases are presented and compared with standard Newton-Raphson computations and commercial finite element simulations. The results show noticeable saving of computational time. For the test cases investigated, the asymptotic-numerical method requires about one third of the time required by a standard Newton-Raphson routine. These results demonstrate that the combination between Ritz and the asymptotic-numerical method is an excellent strategy for investigating the post-buckling response of innovative curvilinearly stiffened panels.

Buckling disappearance via merging/divergence in a nonlinear three-d.o.f. system with linear constitutive law

The phenomenon of buckling disappearance, occurring in a parameter-dependent family of systems admitting a nontrivial fundamental path, is studied. Two different forms of disappearance are detected, namely: (i) the divergence, in which the critical load continuously tends to infinity, and (ii) the merging, in which two critical loads approach each other, coalesce, and then disappear at a finite value of the critical load. It is shown that the two phenomena can be exhibited by the same mechanical system, when a suitable elasto-geometric parameter is varied. More importantly, it is proved that merging continuously changes into divergence when a second parameter is changed. A paradigmatic system is chosen to illustrate the two forms of buckling, i.e., a three degree-of-freedom spherical pendulum, elastically constrained at the ground, loaded by a transverse force and/or a conservative couple, made of two longitudinal potential forces. The springs are taken elastically linear, to stress the fact that divergence not necessarily calls for introducing a nonlinear constitutive law, as also mentioned in literature. Only a linear bifurcation analysis is carried out here, aimed to find the bifurcation points along the nonlinear fundamental path. However, due to the presence of non-negligible prestrains, such a bifurcation problem is governed by nonlinear algebraic equations, whose number of roots cannot be predicted in advance.

NONLINEAR LEARNING PATH: A SYSTEMATIC REVIEW

Students benefit from a nonlinear learning path, also known as a nonsequential learning path, because it allows them to control the pace and sequence of their learning. However, the dynamics of a nonlinear learning path, particularly within an open learning environment like MOOCs, remain underexplored. The current study aims to map out various nonlinear learning paths and explore the potential for personalisation within these environments. Guided by the PRISMA 2020 Statement, we conducted a comprehensive review of 3,418 articles from three databases, focusing on 30 that were relevant to nonlinear learning paths in open learning environments. We discovered that a nonlinear learning path in MOOCs involves path selection, cyclical paths, or skipped paths, all influenced by the design of the MOOC learning materials. In classrooms utilizing an open learning environment, a nonlinear learning path is facilitated by activities such as face-to- face or online discussions, self-study materials, student-created content, project mentoring or coaching, peer feedback, and co-learning activities. Additionally, personalisation, tailored by educators or technology, is key to preventing students from becoming disoriented within these open learning environments. Our findings highlight the importance of promoting nonlinear learning paths in both classrooms and MOOCs, developing learning path recommender systems, and creating supportive MOOC learning materials. Future research should explore students’ perceptions of nonlinear learning paths within an open learning environment, particularly focusing on the integration and impact of MOOC learning materials.

The Changing Ambitions of Workers: Adapting Leadership for Today's Reality

Recent research suggests workers' career ambitions are changing, with fewer aspiring to top executive roles like CEO. This article explores the implications of shifting ambitions for organizational leadership strategies. Research from McKinsey and others finds only 3 in 10 workers today want C-suite careers, down from previous generations where climbing the corporate ladder was standard. Societal factors like economic instability and greater valuation of work-life balance, as well as generational preferences for meaningful work and flexibility over prestige roles, help explain changing priorities. To optimize talent management amid these trends, the author recommends companies realign leadership strategies, talent practices, and culture. Distributed leadership models, non-linear career paths focused on skills development, and culture emphasizing purpose, learning, and well-being can better engage modern workers who prioritize autonomy, growth, and impact over rigid hierarchy. Industry examples demonstrate how redefining success and expanding career definitions can boost retention, diversity, and collaboration.

Anisotropic formability and deformation mechanism of near-α titanium alloy sheet under continuous nonlinear strain paths at high temperature

In the present study, the anisotropic formability and underlying deformation mechanism of near-α TA32 titanium alloy sheet under continuous nonlinear strain paths (CNSPs) at high temperature were investigated in depth. To achieve this goal, a new experimental method combining hot gas bulging with step-combined dies was proposed, and the hot CNSPs of metal sheets can be flexibly and conveniently realized by changing the number and shape of step-combined dies. Based on this method, the anisotropic deformation behavior and forming limits of TA32 sheet under fifteen CNSPs were tested at 800 ℃ with a strain rate of 0.001 s−1. Then, two advanced constitutive models with different scales were embedded into the classical Marciniak-Kuczyński (M-K) theory to predict the forming limits of TA32 sheet under different strain paths: the macro-scale viscoplastic model coupled with Hill48 yield criterion and non-associated flow rule (NAFR) as well as the meso-scale three-dimensional crystal plasticity finite element (CPFE) model coupled with cellular automata (CA). The results demonstrate that the CPFE-CA-MK coupled model exhibits higher accuracy in predicting the forming limits of TA32 sheet under linear and continuous nonlinear strain paths. Especially for the tension-tension strain paths, the CPFE-CA-MK coupled model improves accuracy by at least 3.1 % compared to macro-scale models. Due to the material anisotropy, the initial inclination angle of the groove in the CPFE-CA-MK model is closely related to the strain path and significantly affects the prediction accuracy. Based on the CPFE simulation, the effects of anisotropy and strain path change on the dislocation slip mode of different texture components was analyzed in depth, which provides a theoretical guidance for the optimization of hot forming process of TA32 titanium alloy complex components.

Review on Constitutive Model for Simulation of Weak Rock Mass

Understanding the behavior of weak rock masses is important for predicting the stability of structures under different loading conditions. Traditional models such as the generalized Hoek–Brown and Coulomb weak plane are widely used; however, they often fail to capture the nonlinear and irreversible behavior of weak rock masses. This study offers a comprehensive overview of a critical analysis of constitutive models’ strengths and limitations for simulating weak rock masses. By comparing traditional and advanced novel approaches such as the strength degradation of rock (SDR) masses and continuous damage mechanics (CDM), this investigation shows that the new advanced methods significantly enhance the quality and accuracy of simulations. Moreover, SDR models address the limitations of classical plasticity models by incorporating nonlinear stress paths and irreversible stress changes, while CDM offers detailed insights into microstructural defect progression. These advancements allow for more accurate and practical predictions of long-term stability in geomechanical engineering tailored to specific requirements of each project.

Two-photon upconversion photoluminescence in CsPbBr3 nanoplates

The utilization of solar energy by light conversion processes in both natural and artificial photosynthesis systems has become a pivotal means of sustaining a consistent power supply for our daily lives and production. In general, these reactions rely on the visible spectra region where the sun produces abundant energy according to the black body's emission. Further expanding the adoption of the near-infrared (NIR) spectral region through upconversion has become an intelligent strategy to improve the entire utilization rate of solar energy. In this work, the two-photon upconversion (TPUC) properties were discovered in CsPbBr3 nanoplates (NPs) emitted at 450 nm, and a sub-gap energy level was observed to serve as the center to facilitate the upconversion process. The excitation threshold for TPUC is drastically lower than that for the two-photon absorption, another nonlinear upconversion path that requires strengthened excitation power. Moreover, a significant negative correlation between the excitation threshold for TPUC in the CsPbBr3 NPs and the exciton binding energy was unveiled, which could be attributed to the enhanced quantum confinement effects. Our work paved the way for a feasible way to expand the utilization of the NIR spectral region in light conversion applications.

System-Level Implementation of a Parallel-Path Hybrid Switched-Capacitor Amplifier with an Embedded Successive Approximation Register for IoT Applications

A system-level implementation of a parallel-path hybrid switched-capacitor amplifier is presented in this paper. The proposed parallel-path amplifier incorporates a gain and slew rate-boosting switching path in parallel with an embedded assisted SAR path, aiming for IoT applications. As an alternative concept to the conventional analog topologies, the proposed amplifier combines nonlinear and linear paths to provide coarse and fine amplifications. In the coarse amplification, a high current is provided through a switching path for a fraction of time, which improves the slew rate and open-loop DC gain without adding significant static current. Moreover, high accuracy is achieved through the embedded assisted SAR path, which provides a resolution of 1/2N. In addition, each extra bit of the embedded SAR path improves the total open-loop DC gain by 6 dB. The theory of operation is performed to study how the switching and assisted SAR paths can enhance the amplifier’s settling error. In addition, an existence trade-off between the coarse amplification error and the capacitive digital-to-analog converter’s number of bits is investigated. The theory and system-level simulation show that the gain and slewing restrictions of the conventional topologies, especially in advanced CMOS technology, can be handled much easier by this parallel combination, where the switching path and assisted SAR path combination provides a high slewing capability and high DC open-loop gain.

Discrete mechanical model for nonlinear dynamical analysis of planar guyed towers considering the unilateral contact of cables

Towers are widely used for power line transmission, wind power plants, TV and radio broadcasting, and telecommunications. To enhance their stability, cables are often employed to anchor these towers to the ground. In this study, we investigate the nonlinear static and dynamic responses of a planar guyed tower in which the unilateral constraints on the cables are considered. A representative discrete mechanical model with two degrees of freedom is developed to simulate the central mast of the tower, and the cables are modeled as unilateral springs with linear stiffness. The nonlinear equilibrium equations are derived using an energy approach that incorporates the dissipative forces, total potential, and kinetic energies into the Euler-Lagrange equations. Unilateral cable contact is directly included in the nonlinear equilibrium equation for the guyed tower, allowing for numerical analysis without the need to evaluate the contact point at each time or load step. Several numerical strategies are employed to obtain nonlinear static equilibrium paths, bifurcation diagrams, phase portraits, and Poincaré sections. Our analyses provide novel results for the influence of unilateral cable contact in nonlinear static and dynamic analysis, evaluating the effects of unilateral contact and prestressing on the results. A parametric analysis reveals that cable contact affects nonlinear oscillations, bifurcation, and stability. Our numerical results indicate that unilateral cable contact introduces less structural stiffness compared to bilateral contact, thereby significantly affecting the static and dynamic stability of a planar guyed tower. This is evidenced by a decrease in the static limit load and alterations in the bifurcation diagrams, where unilateral contact destroys the trivial solutions, leading to periodic and quasi-periodic solutions at low levels of vertical load.

Nitrogen Loss from Pluto’s Birth to the Present Day via Atmospheric Escape, Photochemical Destruction, and Impact Erosion

We estimate the loss of nitrogen from Pluto over its lifetime, including the giant planet instability period, which we term the “Wild Years.” We analyze the orbital migration of 53 simulated Plutinos, which are Kuiper Belt Objects (KBOs) captured into 3:2 mean-motion resonance with Neptune during the instability. This orbital migration brought the Plutinos from 20 to 30 au to their present-day orbits near 40 au along a nonlinear path that includes orbits with semimajor axes from 10 to 100 au. We model the thermal history that results from this migration and estimate the volatile loss rates due to the ever-changing thermal environment. Due to the early Sun’s enhanced ultraviolet radiation, the photochemical destruction rate during the Wild Years was a factor of 100 higher than the present-day rate, but this only results in a loss of ∼10 m global equivalent layer (GEL). The enhanced Jeans escape rate varies wildly with time, and a net loss of ∼100 cm GEL is predicted. Additionally, we model the impact history during the migration and find that impacts are a net source, not loss, of N2, contributing ∼100 cm GEL. The 100 cm GEL is 0.1% of the amount of N2 in Sputnik Planitia. We therefore conclude that Pluto did not lose an excessive amount of volatiles during the Wild Years, and its primordial volatile inventory can be approximated as its present-day inventory. However, significant fractions of this small total loss of N2 occurred during the Wild Years, so estimates made using present-day rates will be underestimates.

Complex-Path: Effective and Efficient Node Ranking with Paths in Billion-Scale Heterogeneous Graphs

Node ranking in heterogeneous graphs, which quantifies the relative importance of nodes, can often be improved by incorporating information from relevant paths. Graph database and heterogeneous graph neural network (HGNN) are two main approaches to better solve this problem. Graph databases support efficient path queries for flexible path types but require manual design to combine results for node ranking. Conversely, current HGNNs can automatically integrate semantic information from multiple linear path types for accurate node ranking. However, our experiments show that they fail to outperform a multi-layer perceptron model that utilizes features extracted from multiple nonlinear conditional paths, which can be handled by graph databases. Therefore, we aim to enable HGNN to take advantage of these path types for better performance. However, HGNNs require a generalized path schema to define the structure of input paths, and incorporating each additional path type will significantly increase the required system memory and sampling time for HGNNs. To address these limitations, we introduce CompNode, a novel framework based on a new unified path schema definition called Complex-path, which is used to describe all the required path types, including nonlinear conditional path types. Then, we design a pre-aggregation method to reduce the required system memory and sampling time by pre-aggregating the same type of complex-path. Furthermore, we develop a model that combines semantic information from all aggregated complex-paths for accurate node ranking. Real-world experiments on identifying top potential high-value customers show CompNode outperforms state-of-the-art HGNNs by 20% in average precision and the previously deployed graph database method by 252% in success rate.

Photogrammetry of the Deep Seafloor from Archived Unmanned Submersible Exploration Dives

Large amounts of video images have been collected for decades by scientific and governmental organizations in deep (>1000 m) water using manned and unmanned submersibles and towed cameras. The collected images were analyzed individually or were mosaiced in small areas with great effort. Here, we provide a workflow for utilizing modern photogrammetry to construct virtual geological outcrops hundreds or thousands of meters in length from these archived video images. The photogrammetry further allows quantitative measurements of these outcrops, which were previously unavailable. Although photogrammetry had been carried out in recent years in the deep sea, it had been limited to small areas with pre-defined overlapping dive paths. Here, we propose a workflow for constructing virtual outcrops from archived exploration dives, which addresses the complicating factors posed by single non-linear and variable-speed vehicle paths. These factors include poor navigation, variable lighting, differential color attenuation due to variable distance from the seafloor, and variable camera orientation with respect to the vehicle. In particular, the lack of accurate navigation necessitates reliance on image quality and the establishment of pseudo-ground-control points to build the photogrammetry model. Our workflow offers an inexpensive method for analyzing deep-sea geological environments from existing video images, particularly when coupled with rock samples.

Constitutive description of distortional hardening in a TWIP steel: Addressing differential hardening under nonlinear strain paths

The present study aims to describe the in-plane differential hardening behaviour of the twinning induced plasticity sheet metal TWIP980 under various stress states, including uniaxial tension, plane strain tension, and pure shear, particularly focusing on non-proportional loading conditions. The true stress–strain curves for each stress states were inversely obtained from their corresponding load–displacement curves and modeled using a differential hardening model that can accommodate all three stress states simultaneously on plastic work (density) contours. For non-proportional loading tests, oversize specimens were initially stretched under uniaxial tension up to a 10% pre-strain along the rolling, diagonal, and transverse directions, respectively. Subsequently, the three stress states were applied to subsize specimens cut from the deformed oversize specimens along the rolling direction. To describe the hardening behaviours during non-proportional loading, a homogeneous anisotropic hardening model was adopted and calibrated using two-step uniaxial tension tests. Subsequently, the differential hardening model was successfully incorporated into the homogeneous anisotropic hardening model to describe both the differential hardening and the strain path change-induced hardening behaviours under the two-step loadings, i.e., uniaxial tension to pure shear and uniaxial tension to plane strain tension. Both experimental and simulation results underscore the necessity to consider differential hardening under non-proportional loading conditions.

Nonlinear Risk Spillover Path Between China’s Carbon Market, China’s New Energy Market, and the International Crude Oil Futures Market

Nonlinear Risk Spillover Path Between China’s Carbon Market, China’s New Energy Market, and the International Crude Oil Futures Market

Boosted Fourier nonlinear filter and boosted even mirror Fourier nonlinear filter for active control of machinery noises

To overcome the limitations of the Fourier nonlinear filter and even mirror Fourier nonlinear filter-based adaptive algorithms for active noise control, this paper introduces boosted Fourier nonlinear filter and boosted even mirror Fourier nonlinear filter algorithms. Weight updating equations for the proposed algorithms are derived. Their performance is compared with Fourier nonlinear filter and even mirror Fourier nonlinear filter. Experimentally recorded bandsawand compressor noises are utilized for the analysis. The analysis is carried out for (a) linear primary and linear secondary paths, and (b) nonlinear primary path and linear secondary path. Visual inspection of residual noises after control and dB values of residual noises are utilized to understand the performance of the developed algorithms.

On nonlinear buckling of microshells

Investigation of the geometrical nonlinear action of doubly curved shell panels (DCSPs) in micro scale is the main target of this paper. The proposed microshell panels (MSPs) are assumed to be made of an auxetic honeycomb core (AHOC), leading to negative magnitudes of Poisson's ratio, covered by two nanocomposite enriched coating layers (NCECLs). To conduct the size-dependent nonlinear analysis and achieve the corresponding nonlinear equilibrium path (EQP) of the proposed MSPs, the nonlocal strain gradient theory (NLSGT) is utilized. The governing equations containing the equilibrium and compatibility nonlinear partial differential equations in terms of the deformation components are analytically solved based on the Galerkin technique for different types of simply-supported panels. The achieved results of the present solution exhibit the fact that nonlocal and material length scale parameters significantly affect the EQP of the proposed MSPs especially at their post-buckling stage during their snap-through instability. By solving several numerical examples, the effects of various parameters on the size-dependent EQP of the proposed MSPs are investigated. The results indicate that the influences of size-dependency are significantly affected by the curvature and also boundary conditions of the microshells.

MinActionPath2: path generation between different conformations of large macromolecular assemblies by action minimization.

Recent progress in solving macromolecular structures and assemblies by cryogenic electron microscopy techniques enables sampling of their conformations in different states that are relevant to their biological function. Knowing the transition path between these conformations would provide new avenues for drug discovery. While the experimental study of transition paths is intrinsically difficult, in-silico methods can be used to generate an initial guess for those paths. The Elastic Network Model (ENM), along with a coarse-grained representation (CG) of the structures are among the most popular models to explore such possible paths. Here we propose an update to our software platform MinActionPath that generates non-linear transition paths based on ENM and CG models, using action minimization to solve the equations of motion. The new website enables the study of large structures such as ribosomes or entire virus envelopes. It provides direct visualization of the trajectories along with quantitative analyses of their behaviors at http://dynstr.pasteur.fr/servers/minactionpath/minactionpath2_submission.

A one-dimensional augmented Shallow Water Equations system for channels of arbitrary cross-section

This work provides a new formulation of the one-dimensional augmented Shallow Water Equations system for open channels and rivers with arbitrarily shaped cross sections, suitable for numerical integration when discontinuous geometry is encountered. The additional variable considered can be the bottom elevation, a reference width, a shape coefficient, or a vector containing these or other geometric parameters. The appropriate numerical method, which is well suited to coupling with the mathematical one, is a path-conservative method, capable of reconstructing the behaviour of physical and geometrical variables at the cell boundaries, where the discrete solution of hyperbolic systems of equations is discontinuous. A nonlinear path suitable for the shallow water context is adopted. The resulting model is shown to be well-balanced and accurate to the second order and is further validated against analytical solutions related to channels with power-law cross-sections, specifically for dam break patterns over a variable-width channel and the run-up dynamics of long water waves over sloping bays.