Chaotic Transition Research Articles

Public control of coal resources of the United States’ Powder River Basin for a managed decarbonization transition

Abstract The United States (US) has set aggressive targets for reaching a carbon pollution-free power sector by 2035 and a net-zero economy by 2050. Reaching these goals will require both rapid expansion of zero- and negative-carbon infrastructure and a phase-out of unabated fossil fuel infrastructure. New subsidy and regulatory actions focus on eliminating coal emissions at the point of consumption either through carbon capture and storage (CCS) or coal-fired power plant retirement. Yet, these pathways have opposite implications for coal production: CCS is coal intensive, while coal retirement is not. Despite a record of chaotic and harmful transition and significant social scientific research suggesting better outcomes from managed, coordinated decline, these mechanisms rely on uncoordinated private decision making by mine and plant owners. Coal mining has rapidly declined since peak production in 2008. Production has dropped by half; bankruptcies are the norm; and coal mine and power plant host communities have experienced highly disruptive decline as a result of this unmanaged transition. Given this history, we argue the current market-based, plant-driven governance approach could worsen transition challenges, including potentially stranding costly CCS investments. We argue that the US should complement its extensive investments in technology demonstrations with innovative governance demonstrations to facilitate a just energy transition. Specifically, we argue that the Powder River Basin, which is the US’ largest coal basin and consists primarily of federally leased coal, should be brought under public control for managed decline both to meet emissions reduction targets and advance a just energy transition.

Extracting and analyzing the governing model for plastic deformation of metallic glasses

This paper first detects hidden system from plastic deformation of metallic glasses by sparse identification. The extracted model simulates four types of stress-time curves and displays the prediction of serrated events. This interpretation effectively explains various experimental phenomena of repeated yielding. Further, in terms of parametric sensitivity analysis to the model, two parameters are taken as bifurcation parameter, and the analysis of codimension-one and codimension-two bifurcation are carried out to excavate the causes of dynamic transformation, including saddle–node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and cusp bifurcation. Different bifurcation points correspond different types of stress-time curves. The homologous phase diagrams including periodic orbit, unstable orbit and chaotic behavior are presented to show the dynamics diversity of the model. In addition to dynamic analysis, statistical analysis for plasticity values is also applied to excavate the crossover between periodic and chaotic plastic dynamic transitions. Our results provide a novel perspective on the deformation of metallic glasses from the viewpoint of dynamic model and are also important for evaluating the plastic deformation properties of metallic glasses in practical applications.

Introduction | Introduzione

The growth and sharpening of social inequality at both a global and national level is a key theme of the current public and academic debate. This rise in inequality, one of the most significant social facts of the contemporary world, extends beyond the neoliberal era as its permanent legacy: it is also found in the chaotic transition to a historical phase marked first by a return to protectionism and then by the eruption of conflicts in various parts of the world.

Unpredictable tunneling in a retarded bistable potential.

We have studied the rich dynamics of a damped particle inside an external double-well potential under the influence of state-dependent time-delayed feedback. In certain regions of the parameter space, we observe multistability with the existence of two different attractors (limit cycle or strange attractor) with well separated mean Lyapunov energies forming a two-level system. Bifurcation analysis reveals that, as the effects of the time-delay feedback are enhanced, chaotic transitions emerge between the two wells of the double-well potential for the attractor corresponding to the fundamental energy level. By computing the residence time distributions and the scaling laws near the onset of chaotic transitions, we rationalize this apparent tunneling-like effect in terms of the crisis-induced intermittency phenomenon. Further, we investigate the first passage times in this regime and observe the appearance of a Cantor-like fractal set in the initial history space, a characteristic feature of hyperbolic chaotic scattering. The non-integer value of the uncertainty dimension indicates that the residence time inside each well is unpredictable. Finally, we demonstrate the robustness of this tunneling intermittency as a function of the memory parameter by calculating the largest Lyapunov exponent.

Deep-sea hiatus record reveals orbital pacing by 2.4 Myr eccentricity grand cycles

Astronomical forcing of Earth’s climate is embedded in the rhythms of stratigraphic records, most famously as short-period (104–105 year) Milankovitch cycles. Astronomical grand cycles with periods of millions of years also modulate climate variability but have been detected in relatively few proxy records. Here, we apply spectral analysis to a dataset of Cenozoic deep-sea hiatuses to reveal a ~2.4 Myr eccentricity signal, disrupted by episodes of major tectonic forcing. We propose that maxima in the hiatus cycles correspond to orbitally-forced intensification of deep-water circulation and erosive bottom current activity, linked to eccentricity maxima and peaks in insolation and seasonality. A prominent episode of cyclicity disturbance coincides with the Paleocene-Eocene Thermal Maximum (PETM) at ~56 Myr ago, and correlates with a chaotic orbital transition in the Solar System evident in several astronomical solutions. This hints at a potential intriguing coupling between the PETM and Solar System chaos.

Thermodynamic bifurcations of boiling in solid-state nanopores

Boiling heat transfer is the basis of many commonly used cooling techniques. In cooling of electronic devices, for example, it is desirable to further miniaturize heat exchangers to achieve higher heat transfer, and thus it is necessary to understand boiling phenomena on shorter spatial and temporal scales. This is especially challenging at the nanometer scale because conventional imaging techniques cannot capture the dynamics of nanobubbles, owing to the Abbe diffraction limit. Here in this research, we utilize the nanopore Joule heating system that enables the generation of nanobubbles and simultaneous diagnosis of their nanosecond resolution dynamics using resistive pulse sensing. When a bias voltage is applied across a silicon nitride nanopore immersed in an aqueous salt solution, Joule heat is generated owing to the flow of ionic current. With increasing voltage, the Joule heating intensifies, and the temperature and entropy production in the pore increase. Our sensing results show that nanopore boiling follows the theory of minimum entropy production and attempts to settle to a minimum dissipative state. This results in two boiling bifurcations corresponding to the transition between different boiling states. These characteristics of nanopore boiling are represented by an -shaped boiling curve, experimentally obtained from the Joule heat variation with the applied voltage. A theoretical framework is proposed to model the thermodynamics of nanopore bubbles and estimates the system dissipation, which explains the four arms of the -shaped boiling curve. The present study reveals that the utilization of nanopore boiling as a benchmark platform offers a valuable means for investigating the intricate boiling phenomenon and its correlation with nanoscale bubble dynamics. This would provide much-needed fundamental insights into the chaotic transition boiling regime, which is least understood. Published by the American Physical Society 2024

Reliable chaotic transition in incompressible fluid simulations

Reliable chaotic transition in incompressible fluid simulations

Experimental Observation of Extreme Events in the Shimizu Morioka Oscillator

In this study, we investigate the occurrence of dragon-king extreme events in a three-dimensional autonomous Shimizu–Morioka oscillator. We observe that the bounded chaotic oscillations transition into large amplitude extreme events at a critical value of the system control parameter triggered by an interior crisis. These extreme events exhibit a unique distribution characterized by the probability distribution function. We performed laboratory experiments and conducted rigorous numerical simulations on the Shimizu–Morioka oscillator to validate our findings. The results from both approaches are in excellent agreement and confirm extreme behavior in this autonomous system. Our study represents the first comprehensive investigation of extreme events in the Shimizu–Morioka oscillator, integrating experimental observations and numerical simulations. Also, we observed the dragon-king extreme events in both experimental and numerical studies. These findings enhance our understanding of extreme events and their potential applications in chaos-based dynamical systems, contributing to advancing this field.

Chaotic jam and phase transitions in heterogeneous lattice model integrating the delay characteristics difference with passing effect under autonomous and human-driven vehicles environment

In heterogeneous traffic flow, the response delay of different types' vehicles varies. Accordingly, a heterogeneous lattice model is created for the mixed traffic flows including autonomous vehicles and human-driven vehicles accounting for the delay difference characteristics with the passing effect. The neutral stability condition is acquired from the linear stability analysis, which shows that the stability region of the system significantly decreases with the increase of the passing effect, the proportion of regular vehicles and the reaction time coefficient. The kink-antikink solution of the modified Korteweg-de Vries equation is inferred via nonlinear analysis. The jamming transitions occur between the kink jam and no jam regions with lower passing effect. When the passing effect increases to a critical value, a chaotic jam region appears between the kink jam and no jam regions. And the chaotic jam region further expands with higher passing effect. Moreover, simulation experiments indicate that traffic stability gets better with the delayed time falling down in heterogeneous traffic flow. Also, the impact factors of chaos phenomenon, including the passing effect, the delayed time and proportion of regular vehicles, are investigated in heterogeneous lattice model through Poincaré phase diagram and Lyapunov exponent.

Chaotic Effect-Based Array Duffing Systems with Improved Nonlinear Restoring Force for Weak Signal Detection in Dynamic MWD.

In the process of dynamic Measurement While Drilling (MWD), the strong vibration and rapid rotation of the Bottom Hole Assembly (BHA) lead to multi-frequency and high-amplitude noise interference in the attitude measurement signal. The weak original signal and extremely low signal-to-noise ratio (SNR) are always the technical difficulties of dynamic MWD. To solve this problem, this paper uses the chaotic effect of the Duffing system, which takes the expression (-x3 + x5) as a nonlinear restoring force to detect the weak characteristic signal of downhole dynamic MWD. First of all, in order to meet the limit condition of the chaotic phase transition of the system output, the frequency value of the characteristic signal is reconstructed and transformed based on the variable scale theory. Then, in order to solve the influence of the initial phase of the characteristic signal on the detection accuracy, a detection model based on the array Duffing system is presented, and a frequency-detection scheme with all-phase coverage is given. Finally, another array Duffing system is designed for the parameter estimation of the characteristic signal. The critical value of chaotic phase transition is determined by adjusting the amplitude of the driving signal of the array Duffing system, and then the amplitude and phase parameters of the characteristic signal are synchronously estimated. The experimental results show that the proposed method can effectively extract the weak characteristic signal within the strong noise, and the SNR of the characteristic signal can be as low as -21 dB. Through the attitude calculation for the extracted characteristic signal, it can be seen that the proposed method can improve the accuracy of the inclination of the drilling tool significantly, which proves the feasibility and effectiveness of the method proposed in this paper.

Phases and Their Transitions Characterizing the Dynamics of Global Terrorism: A Multidimensional Scaling and Visualization Approach

This paper proposes a technique based on unsupervised machine learning to find phases and phase transitions characterizing the dynamics of global terrorism. A dataset of worldwide terrorist incidents, covering the period from 1970 up to 2019 is analyzed. Multidimensional time-series concerning casualties and events are generated from a public domain database and are interpreted as the state of a complex system. The time-series are sliced, and the segments generated are objects that characterize the dynamical process. The objects are compared with each other by means of several distances and classified by means of the multidimensional scaling (MDS) method. The MDS generates loci of objects, where time is displayed as a parametric variable. The obtained portraits are analyzed in terms of the patterns of objects, characterizing the nature of the system dynamics. Complex dynamics are revealed, with periods resembling chaotic behavior, phases and phase transitions. The results demonstrate that the MDS is an effective tool to analyze global terrorism and can be adopted with other complex systems.

Passive dynamics regulates aperiodic transitions in flapping wing systems.

Natural and artificial flapping wing flyers generally do not exhibit chaos or aperiodic dynamic modes, though several experimental and numerical studies with canonical models of flapping foils have reported inevitable chaotic transition at high ranges of dynamic plunge velocity ( ). Here we considered the idealized case of a pitching-plunging flapping foil and numerically investigated the effects of passive pitching dynamics on the fluid forces and dynamical states, and compared it with a fully actuated wing. We found that in comparison to fully actuated foils, aperiodic transition can be avoided even for high when passive oscillations are allowed. Passive pitching modulated the relative foil orientation with respect to the incoming free stream to maintain a lower effective angle-of-attack throughout the stroke and reduced the leading-edge-vortex (LEV) strength. Absence of aperiodic triggers such as flow separation and strong LEVs keep the wake periodic, and chaotic transition is averted. In the presence of fluctuating inflow conditions, passive pitching attenuated the fluid loads experienced by the airfoil thus improving the wing's gust mitigating potential. These findings highlight the favorable properties of passive dynamics in regularizing aerodynamic loads on flapping wing systems and presents viable solutions for artificial flying platforms.

Improved bald eagle search algorithm for global optimization and feature selection

The use of metaheuristics is one of the most encouraging methodologies for taking care of real-life problems. Bald eagle search (BES) algorithm is the latest swarm-intelligence metaheuristic algorithm inspired by the intelligent hunting behavior of bald eagles. In recent research works, BES algorithm has performed reasonably well over a wide range of application areas such as chemical engineering, environmental science, physics and astronomy, structural modeling, global optimization, engineering design, energy efficiency, etc. However, it still lacks adequate searching efficiency and has a tendency to stuck in local optima which affects the final outcome. This paper introduces a modified BES (mBES) algorithm that removes the shortcomings of the original BES algorithm by incorporating three improvements; Opposition-based learning (OBL), Chaotic Local Search (CLS), and Transition & Pharsor operators. OBL is embedded in different phases of the standard BES viz. initial population, selecting, searching in space, and swooping phases to update the positions of individual solutions to strengthen exploration, CLS is used to enhance the position of the best agent which will lead to enhancing the positions of all individuals, and Transition & Pharsor operators help to provide sufficient exploration–exploitation trade-off. The efficiency of the mBES algorithm is initially evaluated with 29 CEC2017 and 10 CEC2020 global optimization benchmark functions. In addition, the practicality of the mBES is tested with a real-world feature selection problem and five engineering design problems. Results of the mBES algorithm are compared against a number of classical metaheuristic algorithms using statistical metrics, convergence analysis, box plots, and the Wilcoxon rank sum test. In the case of composite CEC2017 test functions F21-F30, mBES wins against compared algorithms in 70% test cases, whereas for the rest of the test functions, it generates good results in 65% cases. The proposed mBES produces best performance in 55% of the CEC2020 test functions, whereas for the rest of the 45% test cases, it generated competitive results. On the other hand, for five engineering design problems, the mBES is the best among all compared algorithms. In the case of the feature selection problem, the mBES also showed competitiveness with the compared algorithms. Results and observations for all tested optimization problems show the superiority and robustness of the proposed mBES over the baseline metaheuristics. It can be safely concluded that the improvements suggested in the mBES are proved to be effective making it competitive enough to solve a variety of optimization problems.

EXPERIMENTAL INVESTIGATION OF THE TRANSITION BETWEEN LINEAR TO CHAOTIC REGIMES OF SLOSHING

The aim of this paper is to characterize the sloshing regimes in a cylinder and to statistically study the chaotic transition close to the natural frequency. The study was motivated by the lack of experimental data close to the chaotic transition. Using a dedicated shaking table called SHAKESPEARE, a statistical study was performed to exhibit a specific trend close to the transition. The performed tests were compared to the literature and show a slight difference which could be due to a different position of the probes. Close to the transition, a "plateau" in the amplitude of the free surface was observed and characterized using a phase portrait. It shows an elliptical limit cycle dependent on the test conditions. It is especially dependent on the starting point (still or moving water) which was studied in this paper. A later transition position was then observed when applying a frequency at the beginning of the test to break the "still water" assumption.

Reclassification of Mood Disorders with Comorbid Medical Diseases based on Sinai-Ruelle-Bowen/ SRB Entropy Measures

Background: Current classification systems ignore the family histories of patients and psychiatric and medical comorbidity. Methods: We study a new approach of applying spectral clustering to determine distinct bipolar disorder subtypes, which is data whose clusters are of various sizes and densities. We discovered clusters by processing a SRB (Sinai-Ruelle-Bowen) similarity matrix that reflects the proximity of Von Bertalanffy’s functions fitted to phase growth dynamics of EEG (electroencephalography) within a new pipeline architecture. For this purpose, 109 patients diagnosed with bipolar disorder according to DSM-V (Diagnostic and Statistical Manual of Mental Disorders, fifth edition) were evaluated in remission period cross-sectionally. Results: We found three distinct bipolar disorder subtypes with the p-values < 0.001. We exhibit mixing sub-shifts of EEG phase gradients such that there are chaotic phase transitions but higher order phase gradients in a cone basin is always strictly convex. More surprisingly, we show that the SRB entropy measures on some time interval although there exist several equilibrium states each corresponds to equilibrium state. Conclusion: It seems subtypes of the bipolar spectrum were shaped according to seasonality, comorbidity for anxiety disorder and presence of psychotic symptom.

Glycolytic Wave Patterns in a Simple Reaction‐diffusion System with Inhomogeneous Influx: Dynamic Transitions

An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in open spatial reactor and will provide a knowledge about the dynamics that shape and control biological information processing and related phenomena.

Mapping the Chaotic Transitions of the Lorenz Equations With Unsupervised Machine Learning

Abstract Prior work has explored utilizing machine learning for the Lorenz system in the time domain. In this work, we have focused on applications of machine learning for predicting the onset of chaotic transitions in the Lorenz system. Our methods included the development of a robust numerical solution to the Lorenz equations using a fourth order Runge–Kutta method. We solved the Lorenz equations for a large range of Raleigh ratios from 1 to 1000. We calculated the power spectral density, various descriptive statistics, and a cluster analysis using unsupervised machine learning. To identify behaviors and regions in the data, we utilize unsupervised learning as it is designed to assist in recognizing patterns without being told or trained by prior knowledge. We confirmed the performance of the machine learning system's ability to identify chaotic transitions independent of expert selection of Raleigh ratio ranges. The system correctly identifies the transitional behaviors described in prior mathematical work. The results indicate that the power spectral density is very important for the clustering. We also found that examining machine learning clusters by dimension (x, y, and z) was important to understand many of the facets of the chaotic transitions. The results provide a visual mapping of the regions where chaotic transitions may occur based on variations in the Prandtl number and geometry constant. Unsupervised machine learning may be used as a tool to characterize the transition regions for these geometries, providing new lenses for the heat transfer community.

Novel memristor and memristor-based applications

This special issue presents 25 papers regarding memristor systems and their applications. Part of the manuscripts are about memristor-based neural systems, and the systems show rich dynamics. Multistability in memristive systems has aroused much interest, and nonlinear behaviors, such as hidden attractors, extreme multistability, and transient chaotic transition, are observed. There are also two works investigating controllers of fractional-order memristor chaotic systems and several for circuit implementation of memristor chaotic systems. As new research, discrete memristor chaotic maps are reported and show potential application value in the future. Finally, there are two papers about the application of memristive chaotic systems to image encryption fields, indicating that memristive chaotic systems can be used in the information security field.

Route to chaos in a branching model of neural network dynamics

Simplified models are a necessary steppingstone for understanding collective neural network dynamics, in particular the transitions between different kinds of behavior, whose universality can be captured by such models, without prejudice. One such model, the cortical branching model (CBM), has previously been used to characterize part of the universal behavior of neural network dynamics and also led to the discovery of a second, chaotic transition which has not yet been fully characterized. Here, we study the properties of this chaotic transition, that occurs in the mean-field approximation to the kin=1 CBM by focusing on the constraints the model imposes on initial conditions, parameters, and the imprint thereof on the Lyapunov spectrum. Although the model seems similar to the Hénon map, we find that the Hénon map cannot be recovered using orthogonal transformations to decouple the dynamics. Fundamental differences between the two, namely that the CBM is defined on a compact space and features a non-constant Jacobian, indicate that the CBM maps, more generally, represent a class of generalized Hénon maps which has yet to be fully understood.

Peratic phase transition by bulk-to-surface response

The study of dynamical phase transitions has been attracting considerable research efforts in the last decade. One theme of present interest is to search for exotic scenarios beyond the framework of equilibrium phase transitions. Here, we establish a duality between many-body dynamics and static Hamiltonian ground states for both classical and quantum systems. We construct frustration free Hamiltonians whose ground state phase transitions have rigorous duality to chaotic transitions in dynamical systems. By this duality, we show the corresponding ground state phase transitions are characterized by bulk-to-surface response, which are then dubbed "peratic" meaning defined by response to the boundary. For the classical system, we show how the time-like dimension emerges in the static ground states. For the quantum system, the ground state is a superposition of geometrical lines on a two dimensional array, which encode the dynamical Floquet evolution history of one dimensional disordered spin chains. Our prediction of peratic phase transition has direct consequences in quantum simulation platforms such as Rydberg atoms and superconducting qubits, as well as anisotropic spin glass materials. The discovery would shed light on the unification of dynamical phase transitions with equilibrium systems.