Nonlinear Transition Research Articles

A Unified Novel Koopman-Based Model Predictive Control Scheme to Achieve Seamless Stabilization of Nonlinear Dynamic Transitions in Inverter-Based Stochastic Microgrid Clusters

A Unified Novel Koopman-Based Model Predictive Control Scheme to Achieve Seamless Stabilization of Nonlinear Dynamic Transitions in Inverter-Based Stochastic Microgrid Clusters

Disconnected Stationary Solutions in 3D Kolmogorov Flow and Their Relation to Chaotic Dynamics

This paper aims to investigate the nonlinear transition to turbulence in generalized 3D Kolmogorov flow. The difference between this and classical Kolmogorov flow is that the forcing term in the x direction sin(y) is replaced with sin(y)cos(z). This drastically complicates the problem. First, a stability analysis is performed by deriving the analog of the Orr–Sommerfeld equation. It is shown that for infinite stretching, the flow is stable, contrary to classical forcing. Next, a neutral curve is constructed, and the stability of the main solution is analyzed. It is shown that for the cubic domain, the main solution is linearly stable, at least for 0<R≤100. Next, we turn our attention to the numerical investigation of the solutions in the cubic domain. The main feature of this problem is that it is spatially periodic, allowing one to apply a relatively simple pseudo-spectral numerical method for its investigation. We apply the method of deflation to find distinct solutions in the discrete system and the method of arc length continuation to trace the bifurcation solution branches. Such solutions are called disconnected solutions if these are solutions not connected to the branch of the main solution. We investigate the influence of disconnected solutions on the dynamics of the system. It is demonstrated that when disconnected solutions are formed, the nonlinear transition to turbulence is possible, and dangerous initial conditions are these disconnected solutions.

Novel nonlinear wave transitions and interactions for (2+1)-dimensional generalized fifth-order KdV equation

The (2 + 1)-dimensional generalized fifth-order KdV (2GKdV) equation is revisited via combined physical and mathematical methods. By using the Hirota perturbation expansion technique and via setting the nonzero background wave on the multiple soliton solution of the 2GKdV equation, breather waves are constructed, for which some transformed wave conditions are considered that yield abundant novel nonlinear waves including X/Y-Shaped (XS/YS), asymmetric M-Shaped (MS), W-Shaped (WS), Space-Curved (SC) and Oscillation M-Shaped (OMS) solitons. Furthermore, distinct nonlinear wave molecules and interactional structures involving the asymmetric MS, WS, XS/YS, SC solitons, and breathers, lumps are constructed after considering the corresponding existence conditions. The dynamical properties of the nonlinear molecular waves and interactional structures are revealed via analyzing the trajectory equations along with the change of the phase shifts.

The Effects of Loading Angles on the Failure of Cross-Ply Notched Bio-Basalt Composites

A cross-ply basalt V-notched butterfly specimens were subjected to pure tension, combined tension-shear, and shear stress-strain state using a modified Arcan test fixture with loading angles from 0° to 90° with 15° increment. Multiaxial stress and strain states were studied using the principal stress and strain ratio, from which the principal angle was determined and used to represent principal states in the gauge section. The quasi-elastic to non-linear transition stresses were determined for each loading angle. In biaxial stress-strain states and pure shear, the deformation and consequently the shear-induced damage start to accumulate significantly. Also, in biaxial stress-strain states between 15°-75°, the shift from tension-shear to pure shear was observed after the transition to the non-linear part of the stress-strain curve. The digital image correlation (DIC) images and microscopic evaluation show that a large extent of damage is the consequence of the shear deformation after the rotation of 0° clamped fibres, while the 90° fibres maintained their original straight form. In off-axis tests, the principal strain axis rotates towards the weakest material axis even at small off-axis angles. This causes a transition from a tension-shear biaxial state in the linear loading part to shear in the non-linear part, leading to irreversible damage beyond the transition point.

PNA Nonlinearity and ENSO Transition Asymmetry Weaken PMM before La Niña Onset

Abstract The Pacific meridional mode (PMM) is one of the dominant coupled modes in the northeastern tropical Pacific (NETP), characterized by strip-like sea surface temperature (SST) anomalies spanning from Baja California to the central equatorial Pacific. While the majority of the El Niño events follow a positive PMM, only a few La Niña events are preceded by a negative PMM. Such an asymmetric activity of PMM before the onset of El Niño–Southern Oscillation (ENSO) was previously attributed to the inherent nonlinear response of the wind–evaporation–SST (WES) feedback to trade winds in the NETP. Through data analysis and coupled model experiments, we pointed out that PMM is in fact a highly symmetric phenomenon, and the asymmetry of PMM before the ENSO onset thus must be associated with ENSO. On the one hand, the nonlinear response of deep convection over the equator to symmetric ENSO forcing in the central equatorial Pacific permits a stronger Pacific–North America (PNA) pattern in El Niño years than in La Niña years. On the other hand, since the majority of La Niña events are preceded by a sharp decay of an El Niño, the warm equatorial SST anomalies associated with the preceding El Niño provide another source to trigger PNA before the La Niña onset. The two mechanisms modulate the trade winds and heat fluxes in NETP more heavily before the La Niña onset than the El Niño onset and equally contribute to PMM asymmetry before the ENSO onset.

Nonlinear soliton spiral induces coupled multimode dynamics in multi-stable dissipative metamaterials

With the robust and self-trapped properties, recent advances about soliton dynamics in multi-stable mechanical metamaterials have led to many innovative techniques from signal processing to robotics. This work proposes a multi-stable mechanical metamaterial driven by nonlinear dissipative solitons, in which the coupling and decoupling of multiple locomotion modes can be achieved. Based on a cylinder network with asymmetric energy landscape, the uniform field model of Landau theory is developed. During the theoretical calculation, the analytical solutions of several dissipative solitons are derived, which allow multiple special behaviors of solitary waves, such as wave velocity gaps, directional propagation and spiral phase transition. By incorporating such effects into robotic designs, a variety of complex movements can be achieved by a single structure, including hopping, rolling, rotating, swinging, bending and translational components. In particular, as excitation positions change, the mechanical metamaterial can flexibly switch multiple locomotion modes without changing configurations, e.g., spinning and spin-less, straight and oblique as well as coupled multimode movements. This work wishes to provide some new inspirations for the applications of nonlinear elastic wave metamaterials and phase transition theory in robotics.

Experimental investigation on the mode transition characteristics of a phase-change thermofluidic oscillator with external loads

Phase-change thermofluidic oscillator has drawn significant attention thanks to its low operating temperature, which is beneficial for recovering low-grade heat. The vapor–liquid coupling oscillation in the thermofluidic oscillator leads to complex non-linear mode transition phenomenon that affects the steady operation. In this work, the mode transition characteristics of a thermofluidic oscillator with external loads (i.e., a needle valve and a load reservoir) are experimentally investigated through bifurcation analysis. A low-order van der Pol model is employed to examine the effect of acoustic resistance on mode transition. Experimental results demonstrate that modifying the valve opening and load volume under a constant temperature difference can trigger bifurcation, resulting in high-frequency limit cycle, low-frequency limit cycle and quasi-periodic modes. The non-linear features of each mode are revealed through phase space and Poincaré section, with Neimark-Sacker bifurcation, second bifurcation and inverse Neimark-Sacker bifurcation observed. Steady-state performance of oscillator is then characterized under different oscillation modes. The maximum pressure amplitudes measured are 11.54 kPa during the high-frequency oscillation and 1.35 kPa during the low-frequency oscillation, while the maximum displacement amplitudes obtained are 45.5 mm during the high-frequency oscillation and 91.4 mm during the low-frequency oscillation. The oscillation modes can be adjusted by external load to maximize output performance. This study offers comprehensive guidelines for constructing phase-change thermofluidic oscillators.

Are remittances an opportunity or a threat to sustainable environmental quality in India? Evidence from nonlinear smooth transition models

Are remittances an opportunity or a threat to sustainable environmental quality in India? Evidence from nonlinear smooth transition models

Stress-strain modelling of circular concrete-filled FRP–steel composite tube columns under axial compression load

Concrete filled-circular steel tube (CFCST) columns, when externally confined with carbon or glass fiber-reinforced polymers (FRP) sheets and subjected to axial load, exhibit improved strength and ductility compared to unconfined cases. The mechanical properties of the confinement materials are crucial in determining the stress-strain relationship of the confined concrete. This study presents an in-depth analysis of the stress-strain behavior of FRP-confined CFST columns, based on data from 252 specimens. It examines a range of factors, including various infill concrete grades from 14.15 to 140.39 MPa, two types of carbon steel outer tubes with yield strengths (fy) from 226 to 466.5 MPa, and two types of FRP (CFRP and GFRP) with tensile strengths from 1260 to 4900 MPa. The complete axial stress-strain curve is divided into four phases according to a mathematical expression by Wu and Wei (2015): the elastic phase, nonlinear transition phase, linear softening phase, and residual phase. New formulas for ultimate stress, based on confinement stress, were proposed by Hassanin et al. (2023), while the ultimate strain was calculated using the classical formula by Richart et al. Peak stress and strain were determined through statistical linear regression analysis using SPSS software, based on 252 experimental data points and involved using a combined factor of steel contribution (Elsfco) and FRP contribution (Elffco). Eight specimens were specifically used to validate the models through Finite Element Method (FEM) simulations. The accuracy of the predicted analysis results was also assessed by comparing them to existing models. The evaluation showed that the models successfully simulated the complete stress-strain curve of FRP-wrapped CFST columns under axial load, producing satisfactory results. These four models provide reliable results for calculating ultimate stress, ultimate strain, peak stress, peak strain, and the complete stress-strain behavior of these columns.

Force, inertia and motion from Aristotle to nowadays didactics

This study delves into the historical development of the core principles of dynamics, namely the interplay between forces and motion. We explore the intricate and nonlinear transition from the Aristotelian framework, which held sway for eighteen centuries, to the Newtonian paradigm. We posit that the complexity of this transition largely stems from what we perceive as an inadequate understanding of force. Our focus lies particularly on the seminal contributions of Galileo and the subsequent remarkable advancements made by Newton. However, we also note that, somewhat surprisingly, the transition does not conclude with Newton himself. What is commonly known as Newtonian dynamics in modern textbooks diverges significantly from the original theory outlined in the Principia, and we endeavour to elucidate these disparities. In the concluding sections, we scrutinise the implications of these concepts for contemporary teaching methodologies. Specifically, we delve into various interpretations of the Principle of Inertia, the Second Law, and their interrelationship, pinpointing what we perceive as weak points in current didactic approaches and proffering some suggestions for effectively imparting these concepts.

A local and hierarchical Koopman spectral analysis of fluid dynamics

AbstractA local and hierarchical Koopman spectral analysis is proposed to extend Koopman spectral analysis typically used in a linear system or an ergodic process to its application in general nonlinear dynamics. The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness. A proliferation rule is identified to derive high‐order eigenvalues and eigenfunctions from lower‐order ones, thus various spectral patterns may be generated through recursive proliferations. The locally linear map around each state constructs base local Koopman eigenvalues and eigenfunctions from an algebraic eigenvalue problem, and high‐order ones are generated via the proliferation rule to express the systematic nonlinearity. The aforementioned hierarchy simplifies the Koopman spectral analysis and is verified by studying the development of Kármán vortex streets. The triangular chain and the lattice distribution of Koopman eigenvalues confirm the critical role of the proliferation rule and the hierarchy structure of Koopman eigenvalues. The local spectral analysis on the transition process shows that the periodic flow forms as the growth rates of the critical Koopman modes reduce to zero, and meanwhile, the Koopman modes at the same frequency superpose on each other to form the well‐known Fourier or Floquet modes, where the latter are the enhanced nonlinear motions due to the alignment of Koopman eigenvalues with the critical ones.

Bending performance and failure mechanisms of composite sandwich structures with 3D printed hybrid triply periodic minimal surface cores

In this paper, a novel hybrid triply periodic minimal surface (TPMS) core with a nonlinear transition region was designed by combining two types of TPMS (Diamond and Schwarz P) structures using the sigmoid function. The width of the transition region was precisely regulated by adjusting the gradient control parameter r in the sigmoid function. Composite sandwich structures (CSS) were fabricated by bonding two carbon fiber reinforced polymer (CFRP) face sheets to a 3D printed polylactic acid (PLA) core. The bending performance and failure mechanisms of the CSSs with the hybrid TPMS cores were analyzed through three-point bending tests and finite element analysis (FEA). The results indicate that as r increases, the transition region of the hybrid TPMS cores becomes narrower, leading to a gradual decrease in bending strength, bending stiffness, and core shear stress. The failure process of the CSSs in the experiment aligns well with the FEA results. Through comparative analysis of the stiffness-to-weight and strength-to-weight ratios of the CSSs with the native TPMS cores, the hybrid TPMS cores with a wider transition region enhance the structural efficiency of the CSSs, while those with a narrower transition region negatively impact the performance of the CSSs.

A fast adaptive spatio-temporal fusion method to enhanced Fit-FC.

Space-time fusion is an economical and efficient way to solve "space-time contradiction". Among all kinds of space-time fusion methods, Fit-FC space-time fusion method based on weight Function is widely used. However, this method is based on the linear model to depict the phase change, but the phase change in the real scene is complicated, and the linear model is difficult to accurately capture the phase change, resulting in the spectral distortion of the fusion image. In addition, pixel-by-pixel scanning with moving Windows leads to inefficiency issues, limiting its use in large-scale and long-term tasks. To overcome these limitations, this paper developed a simple and fast adaptive remote sensing image Spatio-Temporal fusion method based on Fit-FC, called Adapt Lasso-Fit-FC (AL-FF). Firstly, the sparse characteristics of time phase change between images are explored, and a time phase change estimation model based on sparse regression is constructed, which overcomes the fuzzy problem of fusion image caused by the failure of linear regression to capture complex nonlinear time phase transition in the weighted Function method, making the algorithm better at capturing details. Secondly, an adaptive window selection Function is established to overcome the problem of manually setting parameters on different data sets, improve the convenience of the algorithm and robustness of the application on different data sets, and make the algorithm simpler and more efficient. Finally, the improved AL-FF algorithm is compared with other algorithms to verify the performance improvement. Compared with the current advanced Spatio-Temporal fusion methods, AL-FF algorithm has stronger detail capture ability and can generate more accurate fusion results. In addition, the computational efficiency is significantly improved, and the efficiency is increased by more than 20 times compared with the current mainstream method.

Transition delay in a Mach 6 boundary layer using steady blowing and suction strips

Direct numerical simulations (DNS) were carried out to investigate flow control for transition delay using steady blowing/suction strips at the wall of a flared cone at Mach 6 and zero angle of attack. For the numerical investigations of the transition control strategy, the flared cone geometry and the flow conditions of the experiments in the Boeing/Air Force Office of Scientific Research (AFOSR) Mach 6 Quiet Tunnel (BAM6QT) at Purdue University were chosen. For the DNS, transition was initiated by introducing random disturbances at the inflow of the computational domain, emulating ‘natural’ transition in wind-tunnel experiments caused by free-stream noise. In both wind-tunnel experiments and numerical simulations, streamwise ‘hot’ streaks were found on the surface of the flared cone, which are caused by a nonlinear interaction of an axisymmetric second-mode wave and a pair of oblique waves of the same frequency (‘fundamental resonance’). The objective of the flow control strategy proposed here is to delay the transition onset, and thus mitigate the negative consequences associated with the nonlinear transition stages, i.e. the development of hot streaks and large wall-pressure amplitudes that were observed in experiments and DNS. Our previous so-called ‘controlled’ transition simulations have shown that flow control using steady blowing and suction strips can lead to a significant delay of the hot streak development on the surface of the flared cone. The simulation results presented in this paper show that this flow control strategy remains effective, even in a natural transition scenario characterized by broadband disturbances.

Nonlinear waves and transitions mechanisms for (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation

In this paper, state transition waves are investigated in a (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation by analyzing characteristic lines. Firstly, the N-soliton solutions are given by using the Hirota bilinear method. The breather and lump waves are constructed by applying complex conjugation limits and the long-wave limit method to the parameters. In addition, the transition condition of breather and lump wave are obtained by using characteristic line analysis. The state transition waves consist of quasi-anti-dark soliton, M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, W-shaped soliton, and quasi-periodic wave soliton. Through analysis, when solitary wave and periodic wave components undergo nonlinear superposition, it leads to the formation of breather waves and transformed wave structures. It can be used to explain the deformable collisions of transformation waves after collision. Furthermore, the time-varying property of transformed waves are studied using characteristic line analysis. Based on the high-order breather solutions, the interactions involving breathers, state transition waves, and solitons are exhibited. Finally, the dynamics of these hybrid solutions are analyzed through symbolic computations and graphical representations.

Investigations on structural and opto-electrical characterization of Ag-TCNQ (metal-organic frameworks) as complex thin films for potential device applications

The silver- (7, 7, 8, 8-tetracyanoquinodimethane (Ag-TCNQ) organometallic complex was synthesized chemically as a nano-powder and thereafter deposited as a thin film by thermal evaporation. The monoclinic, needle-like, polycrystalline structure of the Ag-TCNQ complex was analyzed employing x-ray diffraction (XRD) and a scanning electron microscope (SEM). Whereas their chemical structure and stability were explored using Fourier transformation infrared (FTIR) techniques. The findings imply a charge transfer of degree −0.5 between TCNQ° and TCNQ−, as revealed by the shift of the bands of the C≡N stretching and the (C═C-H) bond positioned at 2198 and 824 cm−1, respectively. As well as the optical properties of Ag-TCNQ thin film were studied using spectrophotometric measuring in the wavelength ranging 200 to 2500 nm. The measurement of transmittance and reflectance spectra were employed to calculate the refractive index (n), dielectric constant, absorption index (k), surface and volume energy loss functions, and optical conductivity. In the normal dispersion zone, optical characteristics such free charge carrier concentration, infinity dielectric constant (ε ∞), lattice dielectric constant (ε L), oscillator energy (Eo), and dispersion energy (Ed) were estimated. Furthermore, the optoelectronic nonlinear optical features and electronic transitions for the Ag-TCNQ thin film were assessed. Finally, these findings are promising milestones on the path to providing convincing evidence for the synthesis of stoichiometric thermally stable Ag-TCNQ thin film by conventional thermal evaporation technique that is potential to be utilized in optoelectronic devices applications.

Effect of Embedded g-C3N4 Nanosheets on the Hydration and Thermal Response Behavior of Cross-Linked Thermoresponsive Copolymer Films.

The effect of embedded graphitic carbon nitride (g-C3N4) nanosheets on hydration and thermal response behavior of cross-linked thermoresponsive poly(di(ethylene glycol) methyl ether methacrylate-co-oligo(ethylene glycol) methyl ether methacrylate), abbreviated as P(MA-co-MA300), thin films is probed by white light interferometry. Compared with that of the cross-linked pure P(MA-co-MA300) films, the surface roughness of the cross-linked hybrid films is slightly increased, which is caused by the minor aggregation of g-C3N4 nanosheets during the spin-coating process. After exposure to a water vapor atmosphere, both cross-linked pure and hybrid films can absorb water and swell. However, the introduction of g-C3N4 not only induces a larger hydration extent but also triggers a nonlinear transition behavior upon heating. This prominent difference might be related to the residual hydrophilic groups (-NH2 and N-H) on the surface of g-C3N4 nanosheets, which enhance the interaction and absorption capability for water molecules in the hybrid films. Upon further increasing the amount of embedded g-C3N4 nanosheets in films, more hydrogen bonds are formed and a larger hydration extent of films is observed. To break all of the hydrogen bonds in films, a higher transition temperature (TT) is required. The observed hydration and transition behaviors of hybrid films can be used to design hydrogel-based films for hydrogen evolution or wastewater treatment.

Financial fragility, regime change, and monetary policy in an open economy – A model and empirical application to emerging market countries

July 20, 2023 (Revised April 15, 2024) The experiences of the 1997–98 Asian Financial Crisis and the 2008–09 Global Financial Crisis encouraged economists to develop new open-economy dynamic finance-macro models. Such models allow for nonlinearities -- to study the effects of contractionary currency devaluation -- in contrast to models of expansionary currency devaluation. The generic dynamic model of the finance-macro link in this paper includes the dynamics of the inflation rates, output gap, and financial variables (credit flows, risk premia, and exchange rates). The theoretical model with nonlinearities shows that there can be resilient or non-resilient outcomes of the dynamics. The level of resilience is however dependent on some empirical vulnerabilities. Relevant empirics show the risk premium is related not only to domestic real macro and financial variables, but also to the exchange rate and the foreign currency reserves. Econometrically, this paper explores the regime-dependent interaction of the output gap and financial variables in a two-regime non-linear Logistic Vector Smooth Transition Auto-Regressive (LVSTAR) model with a logistic-type transition function. This empirical study reveals that the financial variables of emerging economies show regime-dependent responses to external shocks. Therefore, a positive shock to the risk premia in a negative output gap regime entails an exchange rate depreciation, and accelerating contractions. Overall, however, a diversity of EM economies are examined in terms of their response to external shocks and their resilience levels. This research also has implications for international portfolio holdings.

Topological boundary modes in nonlinear dynamics with chiral symmetry

Particle-hole symmetry and chiral symmetry play a pivotal role in multiple areas of physics, yet they remain unstudied in systems with nonlinear interactions whose nonlinear normal modes do not exhibit U(1) -gauge symmetry. In this work, we establish particle-hole symmetry and chiral symmetry in such systems. Chiral symmetry ensures the quantization of the Berry phase of nonlinear normal modes and categorizes the topological phases of nonlinear dynamics. We show topologically protected static boundary modes in chiral-symmetric nonlinear systems. Furthermore, we demonstrate amplitude-induced nonlinear topological phase transition in chiral-symmetric nonlinear dynamics. Our theoretical framework extends particle-hole and chiral symmetries to nonlinear dynamics, whose nonlinear modes do not necessarily yield U(1) -gauge symmetry.

Doomed Worlds. I. No New Evidence for Orbital Decay in a Long-term Survey of 43 Ultrahot Jupiters

Ultrahot Jupiters (UHJs) are likely doomed by tidal forces to undergo orbital decay and eventual disruption by their stars, but the timescale over which this process unfolds is unknown. We present results from a long-term project to monitor UHJ transits. We recovered WASP-12 b’s orbital decay rate of Ṗ=−29.8±1.6 ms yr−1, in agreement with prior work. Five other systems initially had promising nonlinear transit ephemerides. However, a closer examination of two—WASP-19 b and CoRoT-2 b, both with prior tentative detections—revealed several independent errors with the literature timing data; after correction, neither planet shows signs of orbital decay. Meanwhile, a potential decreasing period for TrES-1 b, Ṗ=−16±5 ms yr−1, corresponds to a tidal quality factor Q⋆′=160 and likely does not result from orbital decay if driven by dissipation within the host star. Nominal period increases in two systems, WASP-121 b and WASP-46 b, rest on a small handful of points. Only 1/43 planets (WASP-12 b) in our sample is experiencing detectable orbital decay. For nearly half (20/42), we can rule out Ṗ as high as observed for WASP-12 b. Thus, while many UHJs could still be experiencing rapid decay that we cannot yet detect, a sizable subpopulation of UHJs are decaying at least an order of magnitude more slowly than WASP-12 b. Our reanalysis of Kepler-1658 b with no new data finds that it remains a promising orbital decay candidate. Finally, we recommend that the scientific community take steps to avoid spurious detections through better management of the multi-decade-spanning data sets needed to search for and study planetary orbital decay.