Dynamical Evolution Of System Research Articles

Koopman operator for time-dependent reliability analysis

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work, we propose a Koopman operator based approach for time-dependent reliability analysis of nonlinear dynamical systems. Since the Koopman representations can transform any nonlinear dynamical system into a linear dynamical system, the time evolution of dynamical systems can be obtained by Koopman operators seamlessly regardless of the nonlinear or chaotic behavior. Despite the fact that the Koopman theory has been in vogue a long time back, identifying intrinsic coordinates is a challenging task; to address this, we propose an end-to-end deep learning architecture that learns the Koopman observables and then use it for time marching the dynamical response. Unlike purely data-driven approaches, the proposed approach is robust even in the presence of uncertainties; this renders the proposed approach suitable for time-dependent reliability analysis. We propose two architectures; one suitable for time-dependent reliability analysis when the system is subjected to random initial condition and the other suitable when the underlying system have uncertainties in system parameters. The proposed approach is robust and generalizes to unseen environment (out-of-distribution prediction). Efficacy of the proposed approached is illustrated using four numerical examples. Results obtained indicate supremacy of the proposed approach as compared to purely data-driven auto-regressive neural network, long short- term memory network, and DeepONet.

Constraining the overcontact phase in massive binary evolution

Context. Given that mergers are often invoked to explain many exotic phenomena in massive star evolution, understanding the evolutionary phase directly preceding a merger, the overcontact phase, is of crucial importance. Despite this, large uncertainties exist in our understanding of the evolution of massive overcontact binaries. Aims. We aim to provide robust observational constraints on the future dynamical evolution of massive overcontact systems by measuring the rate at which the periods change for a sample of six such objects. Furthermore, we aim to investigate whether the periods of unequal-mass systems show higher rates of change than their equal mass counterparts, as theoretical models predict. Methods. Using archival photometric data from various ground- and space-based missions covering up to ∼40 years, we measure the periods of each system over several smaller time spans. We then fit a linear regression through the measured periods to determine the rate at which the period is changing over the entire data set. Results. We find that all of the stars in our sample have very small period changes and that there does not seem to be a correlation with the mass ratio. This implies that the orbital periods for these systems are stable on the nuclear timescale, and that the unequal-mass systems may not equalize as expected. Conclusions. When comparing our results with population synthesis distributions, we find large discrepancies between the expected mass ratios and period stabilities. We find that these discrepancies can be mitigated to a degree by removing systems with shorter initial periods, suggesting that the observed sample of overcontact systems may originate from binary systems with longer initial orbital periods.

Time series reconstructing using calibrated reservoir computing

Reservoir computing, a new method of machine learning, has recently been used to predict the state evolution of various chaotic dynamic systems. It has significant advantages in terms of training cost and adjusted parameters; however, the prediction length is limited. For classic reservoir computing, the prediction length can only reach five to six Lyapunov times. Here, we modified the method of reservoir computing by adding feedback, continuous or discrete, to “calibrate” the input of the reservoir and then reconstruct the entire dynamic systems. The reconstruction length appreciably increased and the training length obviously decreased. The reconstructing of dynamical systems is studied in detail under this method. The reconstruction can be significantly improved both in length and accuracy. Additionally, we summarized the effect of different kinds of input feedback. The more it interacts with others in dynamical equations, the better the reconstructions. Nonlinear terms can reveal more information than linear terms once the interaction terms are equal. This method has proven effective via several classical chaotic systems. It can be superior to traditional reservoir computing in reconstruction, provides new hints in computing promotion, and may be used in some real applications.

The Promotion Effect of Computer-Aided Technology Combined with RBF Neural Network Algorithm on Art Design

In order to improve the effect of fractal art pattern design, this study combines RBF neural network algorithm to design and evaluate CAD fractal art pattern to improve the effect of fractal art pattern design. Moreover, this study proposes a dynamic weight-based NSC method. Because noise is ubiquitous in reality, the evolution of system dynamics often cannot be carried out strictly according to the iterative rules. In addition, this study shows the changing rules of the competition relationship and the distribution of competitors under the interference of noise. Finally, this study controls the style of the art pattern design in the spatial domain and uses the mask image pattern to disguise the art style. The experimental study shows that the CAD fractal art pattern design system based on the RBF neural network algorithm proposed in this study has a good effect on fractal art pattern design.

Dynamics of asteroid systems post-rotational fission

Asteroid binaries found among the near-Earth objects are believed to have formed from rotational fission. In this paper, we study the dynamical evolution of asteroid systems the moment after fission. The model considers two bodies the moment after a contact binary separates due to rotational fission. Both bodies are modeled as ellipsoids, and the secondary is given an initial rotation angle about its body-fixed y-axis. Moreover, we consider six different cases, three where the density of the secondary varies and three where the shape of the secondary varies. The simulations consider 45 different initial tilt angles of the secondary, each with 37 different mass ratios. We start the dynamical simulations at the moment the contact binary reaches a spin fission limit, and our model ensures that the closest distance between the surfaces of the two bodies is always kept at 1 cm. The forces, torques, and gravitational potential between the two bodies are modeled using a newly developed surface integration scheme, giving exact results for two ellipsoids. We find that more than 80% of the simulations end with the two bodies impacting, and collisions between the bodies are more common when the density of the secondary is lower, or when it becomes more elongated. In comparison with observed data on asteroid pairs, we find that variations in density and shape of the secondary can account for some of the spread seen in the rotation period for observed pairs. Furthermore, the secondary may also reach a spin limit for surface disruption, creating a ternary or multiple system. We find that secondary fission typically occurs within the first five hours after the contact binary separates, and is more common when the secondary is less dense or more elongated.

Chemical effects on the dynamics of organic molecules irradiated with high intensity x rays.

The interaction of a high intensity x-ray pulse with matter causes ionization of the constituent atoms through various atomic processes, and the system eventually goes through a complex structural dynamics. Understanding this whole process is important from the perspective of structure determination of molecules using single particle imaging. XMDYN, which is a classical molecular dynamics-Monte Carlo based hybrid approach, has been successful in simulating the dynamical evolution of various systems under intense irradiation over the past years. The present study aims for extending the XMDYN toolkit to treat chemical bonds using the reactive force field. In order to study its impact, a highly intense x-ray pulse was made to interact with the simplest amino acid, glycine. Different model variants were used to highlight the consequences of charge rearrangement and chemical bonds on the time evolution. The charge-rearrangement-enhanced x-ray ionization of molecules effect is also discussed to address the capability of a classical MD based approach, i.e., XMDYN, to capture such a molecular phenomenon.

Weak nonlinearity for strong non-normality

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of these growth mechanisms and the need for a centre manifold to project the leading-order dynamics. Under the hypothesis of strong non-normality, we take advantage of the fact that small operator perturbations suffice to make the inverse resolvent and the inverse propagator singular, which we encompass in a multiple-scale asymptotic expansion. The methodology is outlined for a generic nonlinear dynamical system, and four application cases highlight common non-normal mechanisms in hydrodynamics: the streamwise convective non-normal amplification in the flow past a backward-facing step, and the Orr and lift-up mechanisms in the plane Poiseuille flow.

4 Boyutlu Modelde Spinör Tipi İnstanton Çözümlerinin Dalgacık Entropisinin İncelenmesi

In recent years, many methods have been proposed in various fields to investigate the properties of orbits of nonlinear dynamical systems. In this study, the characteristics of the orbits of spinor-type instanton solutions in the four-dimensional Gursey model via Heisenberg ansatz is investigated. The orbits of spinor-type instanton solutions are analyzed by Shannon wavelet entropy (WE) method. In order to analyze the regular or irregular states of the orbits of spinor-type instanton solutions, WE spectrum and WE in phase space are studied. It is observed that spinor-type instanton solutions have regular orbits around the fixed point and irregular orbits for other points. According to this study, WE can be used to observe the entropy evolution of nonlinear dynamical systems in phase space.

Koopman analysis of nonlinear systems with a neural network representation

The observation and study of nonlinear dynamical systems has been gaining popularity over years in different fields. The intrinsic complexity of their dynamics defies many existing tools based on individual orbits, while the Koopman operator governs evolution of functions defined in phase space and is thus focused on ensembles of orbits, which provides an alternative approach to investigate global features of system dynamics prescribed by spectral properties of the operator. However, it is difficult to identify and represent the most relevant eigenfunctions in practice. Here, combined with the Koopman analysis, a neural network is designed to achieve the reconstruction and evolution of complex dynamical systems. By invoking the error minimization, a fundamental set of Koopman eigenfunctions are derived, which may reproduce the input dynamics through a nonlinear transformation provided by the neural network. The corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in.

Rotation-induced granular motion on the secondary component of binary asteroids: Application to the DART impact on Dimorphos

Context. NASA’s Double Asteroid Redirection Test (DART) mission will kinetically impact Dimorphos, the secondary component of the Didymos binary asteroid system, which will excite Dimorphos’s dynamical state and lead to significant libration about the synchronous state and possibly chaotic non-principal axis rotation. Although this particular outcome is human caused, many other secondary components of binary systems are also prone to such exotic spin states. Aims. For a satellite in an excited spin state, the time-varying tidal and rotational environment can lead to significant surface accelerations. Depending on the circumstances, this mechanism may drive granular motion on the surface of the secondary. Methods. We modeled the dynamical evolution of a Didymos-like binary asteroid system using a fully coupled, three-dimensional simulation code. Then, we computed the time-varying gravitational and rotational accelerations felt over the entire surface resulting from the secondary’s perturbed dynamical state. Results. We find that an excited spin and orbit can induce large changes in the effective surface slope, potentially triggering granular motion and surface refreshment. However, for the case of the DART impact, this effect is highly dependent on many unknowns, such as Dimorphos’s detailed shape, bulk density, surface geology, and the momentum transferred. Aside from the Didymos system and the DART mission, this effect also has important implications for binary systems in general.

Dynamic evolution of gas hydrate systems affected by magmatism and Quaternary Mass Transport Deposits in the Qiongdongnan Basin, South China Sea: implications for the global carbon cycle

Dynamic evolution of gas hydrate systems affected by magmatism and Quaternary Mass Transport Deposits in the Qiongdongnan Basin, South China Sea: implications for the global carbon cycle

Dynamic evolution of gas hydrate systems affected by magmatism and Quaternary Mass Transport Deposits in the Qiongdongnan Basin, South China Sea: implications for the global carbon cycle

Dynamic evolution of gas hydrate systems affected by magmatism and Quaternary Mass Transport Deposits in the Qiongdongnan Basin, South China Sea: implications for the global carbon cycle

Dynamic evolution of gas hydrate systems affected by magmatism and Quaternary Mass Transport Deposits in the Qiongdongnan Basin, South China Sea: implications for the global carbon cycle

Dynamic evolution of gas hydrate systems affected by magmatism and Quaternary Mass Transport Deposits in the Qiongdongnan Basin, South China Sea: implications for the global carbon cycle

The dynamic evolution of the Lahendong geothermal system in North-Sulawesi, Indonesia

This study uses an integrated approach to characterize the dynamic evolution of the power-producing high-enthalpy geothermal system of Lahendong, North-Sulawesi, Indonesia. Lahendong has two primary reservoirs, the southern and the northern, which have been utilised for electricity production for more than twenty years. The main focus of this study is the characterisation of heat and mass flows in the system with respect to geological structures and permeability distribution. Also, it delineates how the geothermal system has evolved and the spatial variation of the response resulting from prolonged utilization of the reservoirs. This research implemented geological structure analysis on recent surface fault mapping and pre-existing fault studies from literature. Further, the study analysed well data comprising well pressure, enthalpy, drilling program reviews and tracer tests. Hydrochemical investigation compiled new and old surface and subsurface hydrochemical evolution in both the temporal and spatial domain. The results confirm several fault trends in the study area: NE-SW and NW-SE are the major striking directions, while E-W and N-S are less dominant. The most apparent trends are NE-SW striking strike-slip faults, NW-SE thrust faults and N-S and E-W striking normal faults. The faults compartmentalize the reservoir. A comparison of the southern and the northern reservoir shows that the southern one is more controlled by faults; both reservoirs rely on fractures as permeability provider and are controlled by shallow hydrogeology, as derived from the integrated analysis of transient well data. Geochemical analysis shows that the reservoir fluids have generally a higher eelectrical conductivity and are closer to fluid-rock equilibrium, probably due to boiling, compared to spring waters. Spring waters have generally become more acidic, which is an expected result of reservoir boiling and increased steam input to near-surface waters. The spatial distribution of changes shows a permeability evolution over time and also the role of structural permeability in response to changing reservoir conditions. Observing and recording reservoir data is highly important to understand the reservoir response to production and ensure the long-term sustainability of the system. Additionally, the data is critical for making a major difference in the reservoir management strategy.

Metamorphic dynamical quantum phase transition in double-quench processes at finite temperatures

By deriving a general framework and analyzing concrete examples, we demonstrate a class of dynamical quantum phase transitions (DQPTs) in one-dimensional two-band systems going through double-quench processes. When this type of DQPT occurs, the Loschmidt amplitude vanishes and the rate function remains singular after the second quench, meaning the final state continually has no overlap with the initial state. This type of DQPT is named metamorphic DQPT to differentiate it from ordinary DQPTs that only exhibit zero Loschmidt amplitude and singular rate function at discrete time points. The metamorphic DQPTs occur at zero as well as finite temperatures. Our examples of the Su-Schrieffer-Heeger (SSH) model and Kitaev chain illustrate the conditions and behavior of the metamorphic DQPT. Since ordinary DQPTs have been experimentally realized in many systems, similar setups with double quenches will demonstrate the metamorphic DQPT. Our findings thus provide additional controls of dynamical evolution of quantum systems.

Geologically constrained astronomical solutions for the Cenozoic era

Astronomical solutions provide insight into the Solar System's dynamical evolution and are indispensable tools in cyclostratigraphy and astrochronology. Constructing an absolute, fully calibrated astronomical time scale (ATS) has hitherto been hindered beyond ∼50 Ma because orbital calculations disagree before that age due to solar system chaos. We have recently developed a new approach that allows extending the fully calibrated astronomical time scale to ∼58 Ma. Here, we present geologic data and new astronomical solutions, extending our approach across the Paleocene epoch (∼66 to ∼56 Ma). New astronomical solutions were generated using numerical solar system integrations following our earlier work, which now provides geologically constrained astronomical solutions for the Cenozoic era (66-0 Ma). The orbital solutions are available to 300 Ma — we caution, however, that the time interval 300-66 Ma is unconstrained due to dynamical chaos in the solar system. We have tested the sensitivity of our new solutions to various parameters, including numerical stepsize, solar quadrupole moment, number of asteroids included, initial positions, and tidal dissipation. We demonstrate that our new solutions yield improved agreement with the geologic record across the Paleocene epoch, compared to previously available astronomical solutions for that period. Furthermore, we discuss implications of our results for solar system chaos and resonance transitions. We have also obtained K/T boundary (KTB) ages based on our new solutions, which suggest slightly younger KTB ages than those inferred from most recent 40Ar/39Ar radiometric dating.

SU(3)-transformation-based inverse engineering for fast population transfer in three-level systems

We propose a scheme to inverse engineer the Hamiltonian of any general driven three-level system by employing a SU(3) transformation. For special cases, the scheme is then introduced to explore nonadiabatic dynamic evolution of systems with two-photon resonance. We demonstrate that, by selecting the control parameters with explicit function forms, both the ideal process and the practical evolution driving with the truncation of pulses, systematic error and decaying can implement fast population transfer with high fidelity. Moreover, the nonadiabatic passages are not reconstructed by the superadiabatic approach.

Design and Research of Dynamic Evolution System in Football Tactics Under Computational Intelligence

With the rapid development of computer vision, it has been widely used in football. Aiming at the problems of incomplete collection of information, poor operability of system, and bad practical application in the field of football match, an analysis system of football tactics is designed in this paper. Combining the requirements of functions and performance, the analysis system is divided into management of basic information, collection of tactical information, detection of passing pattern, inquiry of tactical information, and visual display, which puts forward the method of the detection of passing pattern based on model. Through the intelligent design, the visual display of the information of athlete, team, competition, tactics, and passing pattern is realized under computational intelligence, which has certain practical value in application.

Entanglement, Complexity, and Causal Asymmetry in Quantum Theories

It is often claimed that one cannot locate a notion of causation in fundamental physical theories. The reason most commonly given is that the dynamics of those theories do not support any distinction between the past and the future, and this vitiates any attempt to locate a notion of causal asymmetry -- and thus of causation -- in fundamental physical theories. I argue that this is incorrect: the ubiquitous generation of entanglement between quantum systems grounds a relevant asymmetry in the dynamical evolution of quantum systems. I show that by exploiting a connection between the amount of entanglement in a quantum state and the algorithmic complexity of that state, one can use recently developed tools for causal inference to identify a causal asymmetry -- and a notion of causation -- in the dynamical evolution of quantum systems. https://doi.org/10.1007/s10701-022-00562-0

Tidally excited oscillations in MACHO 80.7443.1718: Changing amplitudes and frequencies, high-frequency tidally excited mode, and a decrease in the orbital period

Context. Eccentric ellipsoidal variables (also known as heartbeat stars) is a class of eccentric binaries in which proximity effects, and tidal distortion due to time-dependent tidal potential in particular, lead to measurable photometric variability close to the periastron passage. Varying tidal potential may also give rise to tidally excited oscillations (TEOs), which are forced eigenmodes with frequencies close to the integer multiples of the orbital frequency. TEOs may play an important role in the dynamical evolution of massive eccentric systems. Aims. Our study is aimed at detecting TEOs and characterising the long-term behaviour of their amplitudes and frequencies in the extreme-amplitude heartbeat star MACHO 80.7443.1718, consisting of a blue supergiant and a late O-type massive dwarf. Methods. We used two seasons of Transiting Exoplanet Survey Satellite (TESS) observations of the target to obtain new 30-min cadence photometry by means of the difference image analysis of TESS full-frame images. In order to extend the analysis to longer timescales, we supplemented the TESS data with 30-year long ground-based photometry of the target. Both TESS and ground-based photometry are carefully analysed by means of Fourier techniques in order to detect TEOs, examine the long-term stability of their amplitudes and frequencies, and characterise other types of variability in the system. Results. We confirm the detection of the known n = 23, 25, and 41 TEOs and announce the detection of two new TEOs, with n = 24 and 230, in the photometry of MACHO 80.7443.1718. Amplitudes of all TEOs were found to vary on a timescale of years or months. For n = 25, the TEO amplitude and frequency changes are related, which may indicate that the main cause of the amplitude drop in this TEO in TESS observations is the change in its frequency and increase in its detuning parameter. The light curve of the n = 230 TEO is strongly non-sinusoidal. Its high frequency may indicate that the oscillation is a strange mode. Stochastic variability observed in the target fits the behaviour observed in massive stars well and independently confirms that the primary is an evolved star. We also find that the orbital period of the system decreases at a rate of about 11 s (yr)−1. This can be explained by several phenomena: a significant mass loss, mass transfer between components, tidal dissipation, and the presence of a tertiary in the system. All of these phenomena may contribute to the observed changes. Conclusions. The discovery of variable amplitudes and frequencies of TEOs prompts for similar studies in other eccentric elliptical variables with TEOs. Long-term photometric monitoring of these targets is also desirable. The results we obtained pose a challenge for theory. In particular, it needs to be explained why n = 230 TEO is excited. In a general context, studies on the long-term behaviour of TEOs may help to explain the role of TEOs in the dynamical evolution of massive eccentric systems.