Dynamical Evolution Of System Research Articles

Relative Occurrence Rate between Hot and Cold Jupiters as an Indicator to Probe Planet Migration

We propose a second-order statistic parameter ε, the relative occurrence rate between hot Jupiters (HJs) and cold Jupiters (CJs) (ε = η HJ/η CJ), to probe the migration of gas giants. Since the planet occurrence rate is the combined outcome of the formation and migration processes, a joint analysis of HJ and CJ frequency may shed light on the dynamical evolution of giant planet systems. We first investigate the behavior of ε as the stellar mass changes observationally. Based on the occurrence rate measurements of HJs (η HJ) from the Transiting Exoplanet Survey Satellite survey and CJs (η CJ) from the California Legacy Survey, we find a tentative trend (97% confidence) that ε drops when the stellar mass rises from 0.8 to 1.4 M ⊙, which can be explained by different giant planet growth and disk migration timescales around different stars. We carry out planetesimal and pebble accretion simulations, both of which can reproduce the results of η HJ, η CJ, and ε. Our findings indicate that the classical core accretion + disk migration model can explain the observed decreasing trend of ε. We propose two ways to increase the significance of the trend and verify the anticorrelation. Future works are required to better constrain ε, especially for M dwarfs and for more massive stars.

On the dynamical evolution of two-planet extrasolar systems orbiting one of the stars of wide binaries separated by less than 3000 au

In recent years several extrasolar planetary systems have been discovered orbiting one of the stars in a wide binary star system. When the separation between the stars is less than 3000 au, the planets in these systems tend to have orbits with low eccentricity. However, when the planetary system has two planets, their orbits can range from moderate to high eccentricities. To understand this bimodal dynamical distribution of the planetary population, we have developed an analytical model to analyse the whole phase space of a hierarchical four body system. We have found that two-planet extrasolar systems in wide binary stars with separations of less than 3000 au are unlikely to be affected by Galactic perturbations. Therefore, the present configuration of these planetary systems could have resulted from other dynamic processes.

On a singular mathematical model for brain lactate kinetics

In this paper, we consider a singular nonlinear differential system that characterizes the intricate dynamics of brain lactate kinetics between cells and capillaries, as described by System (1.1) below. We begin by establishing the existence and uniqueness of nonnegative solutions for our system through the application of Schauder's fixed‐point theorem. Subsequently, we explore the behavior of these solutions as the viscosity term approaches zero, shedding light on the system's dynamic evolution in such scenarios. To provide empirical validation for our theoretical findings, we offer a series of numerical simulations. These simulations not only confirm the results we have obtained but also reinforce prior research, underscoring the model's efficiency in capturing the complexities of the brain's lactate kinetics. Our work contributes not only to the theoretical underpinning of this field but also to its practical implications, making it a valuable resource for both researchers and practitioners seeking to comprehend and manipulate these vital biological processes.

Thermodynamics-Informed Graph Neural Networks

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior with permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics. Several examples are provided in both Eulerian and Lagrangian description in the context of fluid and solid mechanics respectively, achieving relative mean errors of less than 3% in all the tested examples. Two ablation studies are provided based on recent works in both physics-informed and geometric deep learning.

Constructing polynomial libraries for reservoir computing in nonlinear dynamical system forecasting.

Reservoir computing is an effective model for learning and predicting nonlinear and chaotic dynamical systems; however, there remains a challenge in achieving a more dependable evolution for such systems. Based on the foundation of Koopman operator theory, considering the effectiveness of the sparse identification of nonlinear dynamics algorithm to construct candidate nonlinear libraries in the application of nonlinear data, an alternative reservoir computing method is proposed, which creates the linear Hilbert space of the nonlinear system by including nonlinear terms in the optimization process of reservoir computing, allowing for the application of linear optimization. We introduce an implementation that incorporates a polynomial transformation of arbitrary order when fitting the readout matrix. Constructing polynomial libraries with reservoir-state vectors as elements enhances the nonlinear representation of reservoir states and more easily captures the complexity of nonlinear systems. The Lorenz-63 system, the Lorenz-96 system, and the Kuramoto-Sivashinsky equation are used to validate the effectiveness of constructing polynomial libraries for reservoir states in the field of state-evolution prediction of nonlinear and chaotic dynamical systems. This study not only promotes the theoretical study of reservoir computing, but also provides a theoretical and practical method for the prediction of nonlinear and chaotic dynamical system evolution.

Binary Fraction in Galactic Star Clusters: FSR 866, NGC 1960, and STOCK 2

The study of binary stars in different astronomical environments offers insights into the dynamical state of the hosting stellar systems. The binary fraction in fact plays a crucial role in the dynamical evolution of stellar systems, regulating processes like mass segregation and dynamical heating, and in some cases leading to the formation of exotic objects, like, for instance, blue straggler stars. We used two methodologies to estimate the binary fraction in three different-age open star clusters: FSR 866, NGC 1960 (M36), and Stock 2. The first is a photometric approach based on color–magnitude diagram analysis, and the second is a spectroscopic technique that employs radial velocity measurements. We used Gaia DR3 data in tandem with new spectroscopic observations, and employed the Density-Based Spatial Clustering of Applications with Noise algorithm to identify probable cluster members based on proper motion and parallax in 3D space. The new sample of cluster members allows us to provide new estimates of the cluster fundamental parameters. As a by-product, we found two previously undetected, small physical groups of stars in the background of NGC 1960. The resulting binary fractions lie in the range 0.3–0.5 and are in good agreement with those expected theoretically for open clusters.

Integrability and complexity in quantum spin chains

There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexity in practice has remained elusive. We provide a connection of this sort by constructing a specific matrix in terms of the eigenvectors of a given quantum Hamiltonian. The null eigenvalues of this matrix are in one-to-one correspondence with conserved quantities that have simple locality properties (a hallmark of integrability). The typical magnitude of the eigenvalues, on the other hand, controls an explicit bound on Nielsen’s complexity of the quantum evolution operator, defined in terms of the same locality specifications. We demonstrate how this connection works in a few concrete examples of quantum spin chains that possess diverse arrays of highly structured conservation laws mandated by integrability.

Dynamic evolution of gas hydrate systems affected by magmatism and Quaternary mass-transport deposits in the Qiongdongnan Basin, South China Sea, and implications for the global carbon cycle

Methane release from hydrate systems has long been considered as one of the important mechanisms for global carbon cycle perturbations and ocean acidification. Here, a Quaternary active gas hydrate system in Qiongdongnan Basin, South China Sea (SCS), has been analyzed by using seismic, logging while drilling (LWD), and core data. The results show that post-rift magmatism led to the reactivation of a magma diapir, and the faults and fractures related to its emplacement created efficient pathways for deep gas migration. The increase in overburden temperature and circulation of deep thermal fluids, especially in the center of the diapir area, thinned the gas hydrate stability zone (GHSZ). The accumulation of natural gas at the base of GHSZ and the thinning of GHSZ decreased the ability of hydrate bearing sediments to seal free gas and lead to hydraulic fracturing. The free gas entering the GHSZ was buried by mass transport deposits (MTDs) and then formed hydrates due to the overlying compaction and so further sealed the free gas under the GHSZ. This study indicates that two contrasting mechanisms are acting: (1) tectonic activity and magmatism favor the release of deep natural gas which may reach the ocean, (2) MTDs and the overlying compacted sections act as seals, inhibiting the release of such gas to the ocean. This study shows how the seal capacity of MTDs may reduce methane release from deep-seated reservoirs into the ocean. Given their widespread distribution along continental margins, we suggest that the impact of MTDs on vertical fluid flow, and potential consequences for ocean chemistry and the global carbon cycle, might be underestimated.

Energy transfer in N-component nanosystems enhanced by pulse-driven vibronic many-body entanglement

The processing of energy by transfer and redistribution, plays a key role in the evolution of dynamical systems. At the ultrasmall and ultrafast scale of nanosystems, quantum coherence could in principle also play a role and has been reported in many pulse-driven nanosystems (e.g. quantum dots and even the microscopic Light-Harvesting Complex II (LHC-II) aggregate). Typical theoretical analyses cannot easily be scaled to describe these general N-component nanosystems; they do not treat the pulse dynamically; and they approximate memory effects. Here our aim is to shed light on what new physics might arise beyond these approximations. We adopt a purposely minimal model such that the time-dependence of the pulse is included explicitly in the Hamiltonian. This simple model generates complex dynamics: specifically, pulses of intermediate duration generate highly entangled vibronic (i.e. electronic-vibrational) states that spread multiple excitons – and hence energy – maximally within the system. Subsequent pulses can then act on such entangled states to efficiently channel subsequent energy capture. The underlying pulse-generated vibronic entanglement increases in strength and robustness as N increases.

Graph neural networks for dynamic modeling of roller bearings

Machine learning has paved the way for the real-time monitoring of complex infrastructure and industrial systems. However, purely data-driven methods have not been able to learn the underlying dynamics and generalize them to operating conditions that have not been covered by the training datasets. Therefore, they have not been able to predict the long-term evolution of the system state of physical systems. Physics-informed neural networks (PINNs) have recently shown promising results in predicting the system state evolution over extended periods of time, owing to the loss terms derived from the underlying partial differential equations governing the dynamics of the systems. However, PINNs have limited generalization ability, i.e., a model trained on one type of boundary condition cannot generalize to other conditions. Moreover, the governing equations used for describing the dynamics of physical systems are an approximation of reality, which can lead to differences between the predictions and the actual roll-out of the trajectory. Recently, graph neural networks (GNNs) have been applied to predict the evolution of system dynamics. Due to the encoded inductive bias, they generalize well to systems with varying configurations and boundary conditions. Message-passing GNN comprises two parts that learn the interaction between nodes: an edge network that takes the translational invariant features between two nodes (for e.g., the distance vector) and generates a message, and a node network that takes the aggregated messages from all the neighboring nodes and produces a new node state. This process is repeated several times until the final node state is decoded as a required output. 
 In the presented work, we propose to apply the framework of GNNs for predicting the dynamics of a rolling element bearing. The computational efficiency and generalizability of such a method enable the scalable use of a real-time digital twin to monitor the health state of a rotating machine. To this end, a GNN is used to mimic a dynamic spring-mass-damper model. Bearings consist of different interacting parts like the inner race, outer race, and multiple rolling elements. This interconnected and interacting architecture of a typical bearing is suitable to be modeled as a graph with nodes representing different components.
 We use the dynamic spring-mass-damper model to generate the training data for the GNN, where bearing components such as rolling elements, and inner and outer raceway are modeled as discrete masses. A Hertzian contact model is used to calculate the forces between these components. We evaluate the learning and generalization capabilities of the proposed GNN framework by testing bearing configurations different from the training configurations and comparing the performance to that of the spring-mass model.

Reservoir computing with error correction: Long-term behaviors of stochastic dynamical systems

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which mimics error modeling to improve traditional Reservoir Computing performance and integrates the virtues of both approaches. With few assumptions about the underlying stochastic dynamical systems, this model-free method successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors. We verify the effectiveness of the proposed framework in several experiments, including the stochastic Van der Pal oscillator, El Niño-Southern Oscillation simplified model, and stochastic Lorenz system. These experiments consist of Markov/non-Markov and stationary/non-stationary stochastic processes, which are defined by linear/nonlinear stochastic differential equations or stochastic delay differential equations. Additionally, we explore the noise-induced tipping phenomenon, relaxation oscillation, stochastic mixed-mode oscillation, and replication of the strange attractor.

Reconstruction, forecasting, and stability of chaotic dynamics from partial data.

The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i) infer the dynamics of unobserved (hidden) chaotic variables (full-state reconstruction); (ii) time forecast the evolution of the full state; and (iii) infer the stability properties of the full state. The tasks are performed with long short-term memory (LSTM) networks, which are trained with observations (data) limited to only part of the state: (i) the low-to-high resolution LSTM (LH-LSTM), which takes partial observations as training input, and requires access to the full system state when computing the loss; and (ii) the physics-informed LSTM (PI-LSTM), which is designed to combine partial observations with the integral formulation of the dynamical system's evolution equations. First, we derive the Jacobian of the LSTMs. Second, we analyze a chaotic partial differential equation, the Kuramoto-Sivashinsky, and the Lorenz-96 system. We show that the proposed networks can forecast the hidden variables, both time-accurately and statistically. The Lyapunov exponents and covariant Lyapunov vectors, which characterize the stability of the chaotic attractors, are correctly inferred from partial observations. Third, the PI-LSTM outperforms the LH-LSTM by successfully reconstructing the hidden chaotic dynamics when the input dimension is smaller or similar to the Kaplan-Yorke dimension of the attractor. The performance is also analyzed against noisy data. This work opens new opportunities for reconstructing the full state, inferring hidden variables, and computing the stability of chaotic systems from partial data.

Dynamical evolution of three-state spin-1 non-Hermitian system with Cayley–Hamilton theorem

In this paper, we study the time evolution of three-states spin-1 non-Hermitian systems. The state vector of the wave function for Schrödinger equation is obtained analytically by using the Cayley–Hamilton theorem. We note that the behavior of the non-Hermitian three-states system corresponds to the Hermitian three-state system. Furthermore, the fluctuation between three-state spin-1 is periodically oscillating when the eigenvalues of the non-Hermitian system are real. Moreover, if the eigenvalues are imaginary, we explore that from our analysis and analytical solution that the probabilities’ amplitudes always grow with time for all physical parameters in the three-state, i.e. including the [Formula: see text]-symmetry non-Hermitian system. It means that the Schrödinger equation becomes the growth exponential.

Data-driven probability density forecast for stochastic dynamical systems

In this paper, a data-driven non-parametric approach is presented for forecasting the probability density evolution of stochastic dynamical systems. The method is based on stochastic Koopman operator and extended dynamic mode decomposition (EDMD). To approximate the finite-dimensional eigendecomposition of the stochastic Koopman operator, EDMD is applied to the training data set sampled from the stationary distribution of the underlying stochastic dynamical system. The family of the Koopman operators form a semigroup, which is generated by the infinitesimal generator of the stochastic dynamical system. A significant connection between the generator and Fokker-Planck operator is leveraged to construct an orthonormal basis of a weighted Hilbert space, enabling a spectral decomposition of the probability density function to be performed in this space. This approach is a data-driven method and used to predict the probability density evolution and real-time moment estimation. In the limit of the large number of snapshots and observables, the data-driven probability density approximation converges to the Galerkin projection of the semigroup solution of Fokker-Planck equation on a basis adapted to an invariant measure. This method shares similarities with diffusion forecasting but is capable of producing more accurate probability density forecasts than diffusion forecasting. A few numerical examples are presented to illustrate the performance of the proposed data-driven probability density forecast.

An Evaluation of Non-Gaussian Data Assimilation Methods in Moist Convective Regimes

Abstract Obtaining a faithful probabilistic depiction of moist convection is complicated by unknown errors in subgrid-scale physical parameterization schemes, invalid assumptions made by data assimilation (DA) techniques, and high system dimensionality. As an initial step toward untangling sources of uncertainty in convective weather regimes, we evaluate a novel Bayesian data assimilation methodology based on particle filtering within a WRF ensemble analysis and forecasting system. Unlike most geophysical DA methods, the particle filter (PF) represents prior and posterior error distributions nonparametrically rather than assuming a Gaussian distribution and can accept any type of likelihood function. This approach is known to reduce bias introduced by Gaussian approximations in low-dimensional and idealized contexts. The form of PF used in this research adopts a dimension-reduction strategy, making it affordable for typical weather applications. The present study examines posterior ensemble members and forecasts for select severe weather events between 2019 and 2020, comparing results from the PF with those from an ensemble Kalman filter (EnKF). We find that assimilating with a PF produces posterior quantities for microphysical variables that are more consistent with model climatology than comparable quantities from an EnKF, which we attribute to a reduction in DA bias. These differences are significant enough to impact the dynamic evolution of convective systems via cold pool strength and propagation, with impacts to forecast verification scores depending on the particular microphysics scheme. Our findings have broad implications for future approaches to the selection of physical parameterization schemes and parameter estimation within preexisting data assimilation frameworks. Significance Statement The accurate prediction of severe storms using numerical weather models depends on effective parameterization schemes for small-scale processes and the assimilation of incomplete observational data in a manner that faithfully represents the probabilistic state of the atmosphere. Current generation methods for data assimilation typically assume a standard form for the error distributions of relevant quantities, which can introduce bias that not only hinders numerical prediction, but that can also confound the characterization of errors from the model itself. The current study performs data assimilation using a novel method that does not make such assumptions and explores characteristics of resulting model fields and forecasts that might make such a method useful for improving model parameterization schemes.

Reduced-order modeling of geometrically nonlinear rotating structures using the direct parametrisation of invariant manifolds

The direct parametrisation method for invariant manifolds is a nonlinear reduction technique which derives nonlinear mappings and reduced-order dynamics that describe the evolution of dynamical systems along a low-dimensional invariant-based span of the phase space. It can be directly applied to finite element problems. When the development is performed using an arbitrary order asymptotic expansion, it provides an efficient reduced-order modeling strategy for geometrically nonlinear structures. It is here applied to the case of rotating structures featuring centrifugal effect. A rotating cantilever beam with large amplitude vibrations is first selected in order to highlight the main features of the method. Numerical results show that the method provides accurate reduced-order models (ROMs) for any rotation speed and vibration amplitude of interest with a single master mode, thus offering remarkable reduction in the computational burden. The hardening/softening transition of the fundamental flexural mode with increasing rotation speed is then investigated in detail and a ROM parametrised with respect to rotation speed and forcing frequencies is detailed. The method is then applied to a twisted plate model representative of a fan blade, showing how the technique can handle more complex structures. Hardening/softening transition is also investigated as well as interpolation of ROMs, highlighting the efficacy of the method.

Integrating systems thinking and flexibility in infrastructure management

Infrastructure systems are subjected to demands imposed by extreme natural events and increasing socioeconomic pressures. The latter are derived, for example, from a rise in the export of goods and services, and population growth, which is also associated with problems such as access to housing and basic sanitation. According to the World Risk Report 2016, inadequate infrastructure increases the frequency of losses to life and property, as well as the risk that an extreme natural event might become a disaster. Thus, frequently, traditional infrastructure systems design and management have fail to meet the stakeholders’ expectations. The main problems emerge from decisions based on the assumption that systems are static, instead of changing continuously, and on uncertainty management. This paper presents, first, a conceptual proposal that combines systems thinking and flexibility as the main pillars to facilitate systems to respond and change over time. Systems thinking recognizes the dynamic evolution of systems and helps understand how processes and subprocesses interact at different levels (i.e., hierarchical arrangement of processes). Flexibility, which is the ability of a system to respond or change, is crucial to managing better risks and varying demands, thus fostering resilience to disasters and climate change. Incorporating flexibility in the development of infrastructure contributes to enhancing the management of planned or unplanned events, taking advantage of investment/business opportunities, reducing possible cost overruns, and handling the perceptions and interests of stakeholders. Based on the conceptual framework, the second part of the paper presents a proposal to integrate these concepts into a physical and financial infrastructure model. The outcome of this model is a set of management policies that render the actions that best reflect the interest of stakeholders. The conceptual ideas and the proposed model are illustrated with two examples showing the value of integrating systems thinking and flexibility in infrastructure management over time.

Multi-stage dynamic evolution of green financial system from the perspective of bilateral moral hazard

In order to improve the regulatory efficiency of the government in the construction process of the green financial system, the multi-stage dynamic evolution game model of green financial system from the perspective of bilateral moral risk is constructed and analyzed. It is found that cost-controllable and profitable collaborative innovation are the fundamental to realize the sustainable cooperation of green innovation between financial institutions and carbon emission enterprises. The introduction of reward and punishment mechanism and transfer payment mechanism for government is conducive to promoting the willingness of financial institutions and carbon emission enterprises to cooperate in green innovation. However, with the increase of appeal willingness of carbon emission enterprises and the cost reduction of appeal, although the risk of illegal arbitrage of financial institutions can be curbed to a certain extent, there is a risk of deterioration in the collaborative relationship between financial institutions and carbon emission enterprises.

The complexity of the urban system: Profiles based on current literature and gaps with Sustainable Development Goals

AbstractThe realization of sustainable development goals (SDGs) is not only the independent progress of each goal but, more importantly, to combat undesirable interactions, conflicts, and impacts, which can exactly reflect in system analysis. Cities, as the main body of development and policy implementation, the system perspectives of which provide an integrated way across the full extension. Narrowing the gaps between urban system research and SDGs helps ensure their realization with the lowest cost and highest efficiency. Therefore, this article first collects literature from the Web of Science Core Collection, eliminating out‐of‐scope articles and integrating citing and cited references. Then, this article profiles the final 59 urban system studies on three levels (coupling evaluation, internal element interactions, and dynamic system evolution). Finally, the gaps between the research and SDGs are discussed. Based on the results, the four aspects should be addressed to narrow the gaps: (1) Give full play to the advantages of system methods on the urban scale. (2) Give full play to the bridge role of research among various urban stakeholders. (3) Give full play to experience sharing toward sustainable urban development to avoid futile attempts. (4) Give full play to the language media role of data in policy goals, scientific research, urban needs, and other aspects.

Dissipative Capture of Planets into First-order Mean-motion Resonances

The emergence of orbital resonances among planets is a natural consequence of the early dynamical evolution of planetary systems. While it is well established that convergent migration is necessary for mean-motion commensurabilities to emerge, recent numerical experiments have shown that the existing adiabatic theory of resonant capture provides an incomplete description of the relevant physics, leading to an erroneous mass scaling in the regime of strong dissipation. In this work, we develop a new model for resonance capture that self-consistently accounts for migration and circularization of planetary orbits, and derive an analytic criterion based upon stability analysis that describes the conditions necessary for the formation of mean-motion resonances. We subsequently test our results against numerical simulations and find satisfactory agreement. Our results elucidate the critical role played by adiabaticity and resonant stability in shaping the orbital architectures of planetary systems during the nebular epoch, and provide a valuable tool for understanding their primordial dynamical evolution.