Chaotic Evolution Research Articles

Mechanism of the low-frequency wide-band within a nonlinear acoustic metamaterial

In this paper, the formation and broadening mechanism of the low-frequency bandgap are revealed by designing a type of nonlinear acoustic metamaterial (NAM) with gaps. The mechanism of the chaotic evolution through the harmonic coupling for the NAM structure is revealed in detail, which can effectively change spectral characteristics in the bifurcation sequence, and finally, lead to a low frequency and chaos. Then, a low-frequency broadband within the NAM structures with gaps is obtained by the finite element method (FEM) due to the mechanism of chaos. Most importantly, the width of the bandgap can be successfully enlarged by adjusting the small gap, because the energy of the elastic wave can be greatly decreased or redistributed with the system going from periodic motion to doubling bifurcation. This mechanism for achieving a low-frequency bandgap overcomes the shortcomings both in the traditional local resonance with too large additional mass and in the inertial amplification structures with narrow bandgaps. Therefore, this idea of achieving a low-frequency bandgap has great theoretical significance for controlling low-frequency sound waves.

From dawn till disc: Milky Way’s turbulent youth revealed by the APOGEE+Gaia data

ABSTRACT We use accurate estimates of aluminium abundance from the APOGEE Data Release 17 and Gaia Early Data Release 3 astrometry to select a highly pure sample of stars with metallicity −1.5 ≲ [Fe/H] ≲ 0.5 born in-situ in the Milky Way proper. The low-metallicity ([Fe/H] ≲ −1.3) in-situ component we dub Aurora is kinematically hot with an approximately isotropic velocity ellipsoid and a modest net rotation. Aurora stars exhibit large scatter in metallicity and in many element abundance ratios. The median tangential velocity of the in-situ stars increases sharply with metallicity between [Fe/H] = −1.3 and −0.9, the transition that we call the spin-up. The observed and theoretically expected age–metallicity correlations imply that this increase reflects a rapid formation of the MW disc over ≈1–2 Gyr. The transformation of the stellar kinematics as a function of [Fe/H] is accompanied by a qualitative change in chemical abundances: the scatter drops sharply once the Galaxy builds up a disc during later epochs corresponding to [Fe/H] > −0.9. Results of galaxy formation models presented in this and other recent studies strongly indicate that the trends observed in the MW reflect generic processes during the early evolution of progenitors of MW-sized galaxies: a period of chaotic pre-disc evolution, when gas is accreted along cold narrow filaments and when stars are born in irregular configurations, and subsequent rapid disc formation. The latter signals formation of a stable hot gaseous halo around the MW progenitor, which changes the mode of gas accretion and allows development of coherently rotating disc.

Secular chaos in white dwarf planetary systems: origins of metal pollution and short-period planetary companions

ABSTRACT Secular oscillations in multiplanet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This ‘secular chaos’ readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets’ properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-scales spanning several orders of magnitude in a given system. We apply our results to the evolution of planetary systems around white dwarfs (WDs), specifically the tidal disruption and high-eccentricity migration of planetesimals and planets. We find that secular chaos in a planetesimal belt driven by large (≳10 M⊕), distant ($\gtrsim 10 \, \mathrm{au}$) planets can sustain metal accretion on to a WD over Gyr time-scales. We constrain the total mass of planetesimals initially present within the chaotic zone by requiring that the predicted mass delivery rate to the Roche limit be consistent with the observed metal accretion rates of WDs with atmospheric pollution throughout the cooling sequence. Based on the occurrence of long-period exoplanets and exo-asteroid belts, we conclude that secular chaos can be a significant (perhaps dominant) channel for polluting solitary WDs. Secular chaos can also produce short-period planets and planetesimals around WDs in concert with various circularization mechanisms. We discuss prospects for detecting exoplanets driving secular chaos around WDs using direct imaging and microlensing.

Instability from high-order resonant chains in wide-separation massive planet systems

ABSTRACT Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term evolution of model planetary systems, made up of three equal mass giant planets on initially eccentric orbits. The range of separations studied is dominated by secular processes, but intersects chains of high-order mean-motion resonances. Over time-scales of 108 orbits, the secular evolution of the simulated systems is predominantly regular. High-order resonant chains, however, can be a significant source of angular momentum deficit (AMD), leading to instability. Using a time series analysis based on a Hilbert transform, we associate instability with broad islands of chaotic evolution. Previous work has suggested that first-order resonances could modify the AMD of nominally secular systems and facilitate secular chaos. We find that higher order resonances, when present in chains, can have similar impacts.

Orbitally-paced climate change in the early Cambrian and its implications for the history of the Solar System

The early Cambrian was a critical period of Earth history, marked by explosive diversification of metazoans and several profound changes in Earth's surface environments and global climate. A valid temporal framework for the early Cambrian Period and across the major bio-events is poorly constrained, and the key underlying forcings of million-year (Myr) scale sea-level variations in a greenhouse lacking polar ice sheets are still disputed. Here, the high-resolution gamma-ray logs (GR) and Fe/Al records are utilized to conduct cyclostratigraphic analysis of the early Cambrian Stage 2-Stage 3 Qiongzhusi Formation of the Well A borehole in South China. A ∼10.8 Myr-long high-resolution astronomical time scale across Stage 2-Stage 3 is developed by astronomical tuning of gamma-ray logs and Fe/Al series to the stable 405-kyr long-eccentricity cycles. The Myr-scale sea-level fluctuations in the early Cambrian greenhouse are reconstructed through the sedimentary noise modeling of the 405-tuned GR series and agree with sequence stratigraphic interpretations, lithofacies stacking patterns, and depositional environment changes. The antiphase correlation of filtered ∼1.5 Myr cycles of sedimentary noise curves with the ∼1.5 Myr obliquity modulation cycles demonstrates that the variations in land-ocean water exchange linked to changes in poleward moisture and heat transport dominated by ∼1.5 Myr obliquity modulation cycles may be a primary driver for eustasy during non-glacial early Cambrian period. A new resonance state in the early Cambrian Stage 2-Stage 3, manifested by ∼1.5 Myr eccentricity: ∼1.5 Myr obliquity, could be mainly associated with the Earth-Mars secular resonance and constrain the chaotic evolution of the Solar System in deep time. Two independent approaches are employed to reconstruct the history of Earth-Moon system characteristics, including the precession constant, the Earth-Moon distance and the day length. Our results enhance knowledge of the connection of Myr-scale sea-level variations to astronomically induced climate change under greenhouse climate and provide new empirical constraints on the chaotic motion of the Solar System and the evolution of the Earth-Moon System in deep time.

Thermal Processing of Jupiter-family Comets during Their Chaotic Orbital Evolution

Abstract Evidence for cometary activity beyond Jupiter’s and Saturn’s orbits—such as that observed for Centaurs and long-period comets—suggests that the thermal processing of comet nuclei starts long before they enter the inner solar system, where they are typically observed and monitored. Such observations raise questions as to the depth of unprocessed material and whether the activity of Jupiter-family comets (JFCs) can be representative of any primitive material. Here we model the coupled thermal and dynamical evolution of JFCs, from the moment they leave their outer solar system reservoirs until their ejection into interstellar space. We apply a thermal evolution model to a sample of simulated JFCs obtained from dynamical simulations that successfully reproduce the orbital distribution of observed JFCs. We show that due to the stochastic nature of comet trajectories toward the inner solar system, all simulated JFCs undergo multiple heating episodes resulting in significant modifications of their initial volatile contents. A statistical analysis constrains the extent of such processing. We suggest that primordial condensed hypervolatile ices should be entirely lost from the layers that contribute to cometary activity observed today. Our results demonstrate that understanding the orbital (and thus, heating) history of JFCs is essential when putting observations in a broader context.

Coarse-Grained Entanglement and Operator Growth in Anomalous Dynamics.

In two-dimensional Floquet systems, many-body localized dynamics in the bulk may give rise to a chaotic evolution at the one-dimensional edges that is characterized by a nonzero chiral topological index. Such anomalous dynamics is qualitatively different from local-Hamiltonian evolution. Here we show how the presence of a nonzero index affects entanglement generation and the spreading of local operators, focusing on the coarse-grained description of generic systems. We tackle this problem by analyzing exactly solvable models of random quantum cellular automata (QCA) that generalize random circuits. We find that a nonzero index leads to asymmetric butterfly velocities with different diffusive broadening of the light cones and to a modification of the order relations between the butterfly and entanglement velocities. We propose that these results can be understood via a generalization of the recently introduced entanglement membrane theory, by allowing for a spacetime entropy current, which in the case of a generic QCA is fixed by the index. We work out the implications of this current on the entanglement "membrane tension" and show that the results for random QCA are recovered by identifying the topological index with a background velocity for the coarse-grained entanglement dynamics.

The main perturbing objects on the orbits of (616) Prometheus and (617) Pandora

ABSTRACT The dynamical evolution of the Prometheus and Pandora pair of satellites is chaotic, with a short 3.3 yr Lyapunov time. It is known that the anti-alignment of the apses line of Prometheus and Pandora, which occurs every 6.2 yr, is a critical configuration that amplifies their chaotic dynamical evolution. However, the mutual interaction between Prometheus and Pandora is not enough to explain the longitudinal lags observed by the Hubble Space Telescope. The main goal of the current work is to identify the main contributors to the chaotic dynamical evolution of the Prometheus–Pandora pair beyond themselves. Therefore, in this work, we first explore the sensibility of this dynamical system to understand it numerically and then build numerical experiments to reach our goals. We identify that almost all major satellites of the Saturn system play a significant role in the evolution of Prometheus’s and Pandora’s orbits.

Transient Electromagnetic Inversion: An ICDE-Trained Kernel Principal Component OSELM Approach

The traditional extreme learning machine (ELM) inversion of transient electromagnetic method (TEM) based on random initial weights is known to be inept for its low-computational efficiency and poor generalization performance. To solve these problems, a kernel principal component online sequential extreme learning machine (KPCOSELM) trained by an improved chaotic differential evolution (ICDE) method is proposed. An additional kernel principal component (KPC) layer is used, which reduces the dimension of TEM data and enhances the computational efficiency of online sequential extreme learning machine (OSELM). Moreover, a novel ICDE algorithm is presented for improving the learning ability and generalization performance of OSELM inversion. In the proposed ICDE, the tent chaotic sequence is adopted to enhance the global exploitation ability, and a constraint factor is added to ensure better convergence. The feasibility and effectiveness of the proposed inversion method are evaluated via four groups of experiments. The inversion results of the synthetic and field examples show that the proposed approach outperformed other methods in terms of computational efficiency and prediction accuracy, and realized satisfactory performance in TEM inversion, which provides a new strategy for the application of neural networks in TEM inversion.

The Chaotic History of the Retrograde Multi-planet System in K2-290A Driven by Distant Stars

Abstract The equator of star K2-290A was recently found to be inclined by 124° ± 6° relative to the orbits of both its known transiting planets. The presence of a companion star B at ∼100 au suggested that the birth protoplanetary disk could have tilted, thus providing an explanation for the peculiar retrograde state of this multi-planet system. In this work, we show that a primordial misalignment is not required and that the observed retrograde state is a natural consequence of the chaotic stellar obliquity evolution driven by a wider-orbit companion C at ≳2000 au long after the disk disperses. The star C drives eccentricity and/or inclination oscillations on the inner binary orbit, leading to widespread chaos from the periodic resonance passages between the stellar spin and planetary secular modes. Based on a population synthesis study, we find that the observed stellar obliquity is reached in ∼40%–70% of the systems, making this mechanism a robust outcome of the secular dynamics, regardless of the spin-down history of the central star. This work highlights the unusual role that very distant companions can have on the orbits of close-in planets and the host star’s spin evolution, connecting four orders of magnitude in distance scale over billions of orbits. We finally comment on the application to other exoplanet systems, including multi-planet systems in wide binaries.

Prediction of Machine Tool's Motion Accuracy Deterioration Based on Chaotic Evolution of Thermal Error

Prediction of Machine Tool's Motion Accuracy Deterioration Based on Chaotic Evolution of Thermal Error

An exponential chaotic differential evolution algorithm for optimizing bridge maintenance plans

Bridges are one of the fundamental infrastructure assets that are vital for economic growth and public welfare. Over the past few decades, the numbers of deteriorating bridges have drastically escalated raising concerns for serviceable, safe and functional transportation networks. This state of affairs poses a paramount challenge especially when coupled with the need to address social and environmental constraints. Accordingly, this current research paper proposes an automated three-component model for bridge maintenance optimization at both project and network levels. The first component aims at identifying the physical characteristics of the tackled bridge inventory. The second component encompasses designing a multi-objective optimization model to determine the optimal set of maintenance plans through four principal objective functions. These functions comprise maximization of performance condition of bridge elements, minimization of agency and user costs, minimization of duration of traffic disruption and minimization of environmental impact. In the multi-objective optimization model, an exponential chaotic differential evolution (ECDE) algorithm is introduced in an attempt to circumvent the drawbacks of convergence speed and search behavior of classical meta-heuristics. The third component combines criteria importance through inter-criteria correlation (CRITIC), complex proportional assessment (COPRAS) and grey relational analysis (GRA) to select the most optimum maintenance plan for each study period. Comparison results revealed that ECDE-based Sinusoidal algorithm managed to improve the performance diagnostics of classical meta-heuristics by values ranged from 49.2% to 73.1% over the multi-year maintenance plans. The results of benchmark test functions exemplified that ECDE-based Sinusoidal algorithm performed better than genetic and differential evolution algorithms by 114.2% and 79.5%, respectively. The developed integrated model is expected to assist infrastructure managers in executing optimized and sustainable maintenance budget plans within various planning scenarios.

A revisit to the past plague epidemic (India) versus the present COVID-19 pandemic: fractional-order chaotic models and fuzzy logic control.

India is one of the worst hit regions by the second wave of COVID-19 pandemic and ‘Black fungus’ epidemic. This paper revisits the Bombay Plague epidemic of India and presents six fractional-order models (FOMs) of the epidemic based on observational data. The models reveal chaotic dispersion and interactive coupling between multiple species of rodents. Suitable controllers based on fuzzy logic concept are designed to stabilise chaos to an infection-free equilibrium as well as to synchronise a chaotic trajectory with a regular non-chaotic one so that the unpredictability dies out. An FOM of COVID-19 is also proposed that displays chaotic propagation similar to the plague models. The index of memory and heredity that characterise FOMs are found to be crucial parameters in understanding the progression of the epidemics, capture the behaviour of transmission more accurately and reveal enriched complex dynamics of periodic to chaotic evolution, which otherwise remain unobserved in the integral models. The theoretical analyses successfully validated by numerical simulations signify that the results of the past Plague epidemic can be a pathway to identify infected regions with the closest scenarios for the present second wave of Covid-19, forecast the course of the outbreak, and adopt necessary control measures to eliminate chaotic transmission of the pandemic.

Learning to Correct Climate Projection Biases

AbstractThe fidelity of climate projections is often undermined by biases in climate models due to their simplification or misrepresentation of unresolved climate processes. While various bias correction methods have been developed to post‐process model outputs to match observations, existing approaches usually focus on limited, low‐order statistics, or break either the spatiotemporal consistency of the target variable, or its dependency upon model resolved dynamics. We develop a Regularized Adversarial Domain Adaptation (RADA) methodology to overcome these deficiencies, and enhance efficient identification and correction of climate model biases. Instead of pre‐assuming the spatiotemporal characteristics of model biases, we apply discriminative neural networks to distinguish historical climate simulation samples and observation samples. The evidences based on which the discriminative neural networks make distinctions are applied to train the domain adaptation neural networks to bias correct climate simulations. We regularize the domain adaptation neural networks using cycle‐consistent statistical and dynamical constraints. An application to daily precipitation projection over the contiguous United States shows that our methodology can correct all the considered moments of daily precipitation at approximately resolution, ensures spatiotemporal consistency and inter‐field correlations, and can discriminate between different dynamical conditions. Our methodology offers a powerful tool for disentangling model parameterization biases from their interactions with the chaotic evolution of climate dynamics, opening a novel avenue toward big‐data enhanced climate predictions.

Q-switching bifurcation dynamics of passively mode-locked lasers.

We model Q-switched pulses in passively mode-locked lasers using the cubic-quintic complex Ginzburg-Landau equation (CGLE). We show that a wide set of parameters of this equation leads to Q-switched pulses of triangular shape that consist of a periodic sequence of evolving dissipative solitons. Bifurcation diagrams demonstrating various transformations of these pulses are calculated in terms of five major parameters of the CGLE. The diagrams show period doubling transformations as well as the transition to a chaotic evolution of the Q-switched pulses.

Simulations shed insight on COVID-19 transmission on a public transportation system

High-fidelity simulations of airflow in an urban bus offer a unique opportunity to peer into the chaotic evolution and spatial distribution of infectious aerosols.

Sparse nonlinear models of chaotic electroconvection.

Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh–Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.

Wake instabilities of a pre-swirl stator pump-jet propulsor

The wake of a pump-jet propulsor (PJP) with a pre-swirl stator is investigated using stress-blended eddy simulations. The flow field is analyzed in detail through a systematic comparison of the wake morphology under different loading conditions, allowing the destabilization process and the mechanism of wake instabilities to be inspected. To further examine the evolution of the vortices, as well as their interaction and destabilization, the pressure fluctuations and spectra of turbulent kinetic energy are considered. The mean loads are in good agreement with experimental results. The PJP flow field has a complex vortical system, the evolution of which determines the wake instabilities. The tip clearance leakage vortex first exhibits short-wave instabilities, and the destabilization process then accelerates under the effects of duct shed vortices, which promote the generation of secondary vortices. The secondary vortices further enhance the destabilization process and lead to chaotic evolution. The stator blade root vortices are strongly affected by the rotor blade root vortices, causing an exchange of vorticity that depends on the relative intensity of the two sets of root vortices. The instability of the hub vortices is apparently related to the upstream vortices. The correlation between the tip clearance leakage vortices and the instability of hub vortices is very weak.

Constraints on the spatial variation of Planck constant

Inspired by recently published researches, we present two protocols for setting an upper limit to the claimed variation of hbar upon the position. The protocols, both within today state of art, involve the use of two delayed laser pulses driving an atom. The distinct positions of the laboratory, due to the Earth motion, affects hbar and hence the atomic dynamics. The first protocol measures the difference in population of the atomic ground state while the second one the red-shift of the harmonics emitted by the atom in the two moments of the experiment. The protocols improve the reported upper limit of varDelta hbar /hbar . The theory shows that hbar (varvec{r}) induces a chaotic evolution to the atom. This form of Chaos is generated by a variation of a physical parameter and is one example of Parametric Chaos.

Chaotic behavior of quantum cascade lasers at ignition

The ignition of Quantum Cascade Lasers can occur from a state of oscillating field domains. Here, the interplay between lasing and the kinetics of traveling domain boundaries provides complex oscillation scenarios. We analyze our numerical findings in detail for a device operating at terahertz frequencies and manifest chaotic evolution by positive Lyapunov exponents. This shows that these important devices can exhibit chaotic behavior even without periodic driving, which needs to be taken into account in their design.