Properties Of Dynamical Systems Research Articles

From Nash Q-learning to nash-MADDPG: Advancements in multiagent control for multiproduct flexible manufacturing systems

The emergence of flexible manufacturing systems (FMS) capable of processing multiple product types is a result of the growing demand for product customization and personalization. Such multiproduct systems are characterized by a higher level of uncertainty and variability when compared to traditional manufacturing systems. This paper proposes a Nash integrated multiagent deep deterministic policy gradient method (Nash-MADDPG) to control the mobile robots’ assignment in a multiproduct FMS to enable intelligent decision-making, interaction, and dynamic learning capabilities. A mathematical model of a multiproduct FMS from a previous study is described, and system dynamic property is characterized by permanent production loss (PPL). Then, by observing PPL of the system and market demand for each product type, the multi-agent control scheme is developed to assign mobile robots to load/unload various product types at various machines. First, a Nash game is developed among the mobile robots and to improve the cooperation, a collaboration cost is defined. This collaboration cost is then used in the reward function of the multiagent deep deterministic policy gradient (MADDPG) algorithm. Second, the actions are jointly defined based on the action values of MADDPG, and the mobile robots’ strategies in the Nash game, which update the environment to a new state. The performance of the proposed method is verified by comparing it with conventional Nash Q-learning, vanilla MADDPG, Q-learning based single agent reinforcement learning (SARL) and a first-come-first-serve (FCFS) based control. The results demonstrate that the multi-agent control scheme under the proposed Nash-MADDPG is effective in dealing with cooperative FMS environment that involves complicated dynamics and uncertainties.

Fixed Attracting Closed Surfaces in Three and Higher Dimensional Dynamical Systems

Fixed Attracting Closed Surfaces in Three and Higher Dimensional Dynamical Systems

Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges

This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.

Experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics of the “wing model – fuel tank” system

Flexible response of the airframe structural elements under operational loads are one of the main sources of fatigue damage accumulation. It is known that fuel sloshing in tanks can change the dynamic (frequencies and shapes of natural oscillations) and dissipative properties (oscillation damping decrements) of an elastic system, including partially or completely fuelfilled tanks. It is specified that fuel sloshing in tanks due to the additional oscillation energy dissipation of the elastic system can have a significant impact on both the fatigue and aeroelastic characteristics of aircraft structural elements. Theoretical and experimental studies, applicably to the majority of currently operating transport aircraft, have shown that when modeling dynamic phenomena and solving aeroelasticity problems, fuel can be considered conditionally solidified, which actually does not affect the resultant effect. The advent of modern heavy transport aircraft with a high aspect ratio wing and four engines on pylons under the wing has led to a considerable change in the dynamic picture of the aircraft interaction with the environment. The main feature is that, under this arrangement, the first horizontal bending mode of the wing is embedded in the main flexible modes that determine the dynamic response to external effects. In this case, the model of solidified fuel can have a significant impact on the accuracy of predicting dynamic loads and, as a consequence, on the quantitative characteristics of durability and aeroelasticity. The article presents the results of experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics (frequencies of natural oscillations and amplitudes of forced oscillations) of the “wing model – fuel tank” system. The design of the experimental installation and the methodology of conducting experiments are described. During the experiment, the tank was partially filled with liquid or full, and horizontal bending modes of the wing model, for which considering liquid sloshing in the tank is the most relevant, were studied. The tank refueling levels are determined at which the maximum effect of the system oscillation damping is achieved due to energy dissipation under liquid sloshing. The effect of various factors (presence of a top cover, internal structural frame, perforation in the structural frame) on the amplitudes and frequencies of forced oscillations is analyzed.

The role of taxation in an integrated economic-environmental model: a dynamical analysis

AbstractWe propose a model with economic and environmental domains that interact with each other. The economic sphere is described by a Solow growth model, in which productivity is not exogenous but negatively affected by the stock of pollution that stems from the production process. A regulator can charge a tax on production, and the resources collected from taxation are used to reduce pollution. The resulting model consists of a two dimensional discrete dynamical system, and we study the role of taxation from both a static and a dynamical point of view. The focus is on the determination of the conditions under which taxation has a positive effect on the environment and leads to economic growth. Moreover, we show that a suitable environmental policy can allow recovering both local and global stability of the steady states. On the contrary, we show that, if the policy is not adequate, the system can exhibit endogenous oscillating and chaotic behavior and multistability phenomena.

A mathematical introduction to complex dynamical systems

This work proposes an investigation of the theory of dynamic systems, focusing on the analysis of entropy in its classical and topological manifestations. Initially, the fundamental concepts of dynamical systems theory are presented, with an emphasis on topological dynamical systems (TDS). Next, definitions of discrete topological entropy and its relationship to dynamical systems are discussed, followed by the introduction of topological entropy pressure as a weighted form of topological entropy. Subsequently, some applications of topological entropy in dynamic systems are examined, highlighting its role in the analysis of chaotic systems and in ergodic theory. Furthermore, we present a new theory, called Topological Ergodic Entropy Theory (TEET), which offers an innovative approach to the analysis of ergodic dynamical systems. Finally, the Ergodic Theory of Turbulent Flow (ETTF) is introduced, exploring the relationship between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. The results presented contribute to a deeper understanding of the complexity of dynamical systems and their applications in various areas of mathematics and physics. The investigation of topological entropy and its applications in dynamical systems offers new insights into the chaotic and stochastic behavior of these systems, while the introduction of new theories, such as ETTF, provides a new perspective for the analysis and modeling of turbulent phenomena.

Port-Hamiltonian discontinuous Galerkin finite element methods

Abstract A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical systems that have a nonzero energy flow through the boundaries. In this paper, we propose a novel framework for discontinuous Galerkin (DG) discretizations of pH-systems. Linking DG methods with pH-systems gives rise to compatible structure preserving semidiscrete finite element discretizations along with flexibility in terms of geometry and function spaces of the variables involved. Moreover, the port-Hamiltonian formulation makes boundary ports explicit, which makes the choice of structure and power preserving numerical fluxes easier. We state the Discontinuous Finite Element Stokes–Dirac structure with a power preserving coupling between elements, which provides the mathematical framework for a large class of pH discontinuous Galerkin discretizations. We also provide an a priori error analysis for the port-Hamiltonian discontinuous Galerkin Finite Element Method (pH-DGFEM). The port-Hamiltonian discontinuous Galerkin finite element method is demonstrated for the scalar wave equation showing optimal rates of convergence.

A flexible, reusable and adjustable high-performance energy absorption system inspired by interlocking suture structures

Energy absorption systems play a very important role in impact protection under complex load conditions. However, traditional protective structures cannot adjust the mechanical properties on demand to accommodate variable load characteristics once manufactured. Therefore, inspired by the superior compression resistance of the diabolical ironclad beetle, a modular energy absorption system is developed by combining the efficient mechanical properties of thin-walled tubes and the robust connectivity of interlocking suture structures, which can be easily assembled from only bio-inspired tubes without external constraints. FEM simulations were performed to systematically investigate the static and dynamic mechanical properties of the developed system, and its crushing performance was demonstrated experimentally. Additionally, the influence of geometric parameters on the mechanical properties of the system has been investigated, and the insensitivity of secondary geometrical parameters and assembly defects has been verified, which shows that the system has a certain safety margin to avoid catastrophic accidents caused by fabrication defects. Moreover, the system exhibits excellent reusability under multi-impact load environments and its energy absorption capacity does not degrade after the primary impact. Furthermore, the system exhibits good designability thanks to the discrete modular structures, its mechanical properties can be tuned by stiffness design without affecting the energy absorption capacity, and its specific energy absorption can be effectively improved by lightweight design. This study provides a novel design strategy for the protection system applied in multiple complex environments.

Dynamics of the atom-polyatomic molecule conversion with quantum decoherence

Based on the mean-field approximation and the two-mode Bose–Hubbard model, we investigate the dynamical properties of atom-polyatomic molecule conversion systems under dissipation and dephasing. For such a many-body system problem, we partition phase space based on the states of fixed points, study the movement of fixed points and the transition to attractors in an open system. Additionally, for all the atoms that constitute a molecule, depending on whether the species of these atoms are identical or not, we introduce the innovative concepts of unbiased and biased systems. We discover that in biased conversion systems under particle losses, the evolution trajectories are distributed on a three-dimensional Bloch sphere with an internal structure. There exists a significant difference from the two-dimensional Hilbert space of an unbiased system. Finally, we discuss the sweeping rate of the time-varying magnetic field applied externally to the conversion system, and analyze a feasible scheme for the quantum coherent synthesis of triatomic molecules.

Immersion in Complex Dynamical Systems with Ergodicity

This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion progresses to explore discrete topological entropy and its significance within dynamical systems, culminating in the introduction of topological entropy pressure as a nuanced form of this concept. The study then investigates various applications of topological entropy within dynamic systems, emphasizing its utility in understanding chaotic systems and its role in ergodic theory. A novel theory, termed Topological Ergodic Entropy Theory (TEET), is presented, offering a fresh perspective on the analysis of ergodic dynamical systems. Furthermore, the work introduces the Ergodic Theory of Turbulent Flow (ETTF), which probes the interplay between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. Through these explorations, the findings contribute significantly to the comprehension of the intricate nature of dynamical systems and their diverse applications across mathematics and physics. By scrutinizing topological entropy and its implications in dynamical systems, this research offers novel insights into the chaotic and stochastic behaviors exhibited by these systems. Additionally, the introduction of pioneering theories like ETTF opens up new avenues for understanding and modeling turbulent phenomena, thereby enriching our understanding of complex dynamical processes.

A sub-100 nm thickness flat jet for extreme ultraviolet to soft X-ray absorption spectroscopy.

Experimental characterization of the structural, electronic and dynamic properties of dilute systems in aqueous solvents, such as nanoparticles, molecules and proteins, are nowadays an open challenge. X-ray absorption spectroscopy (XAS) is probably one of the most established approaches to this aim as it is element-specific. However, typical dilute systems of interest are often composed of light elements that require extreme-ultraviolet to soft X-ray photons. In this spectral regime, water and other solvents are rather opaque, thus demanding radical reduction of the solvent volume and removal of the liquid to minimize background absorption. Here, we present an experimental endstation designed to operate a liquid flat jet of sub-micrometre thickness in a vacuum environment compatible with extreme ultraviolet/soft XAS measurements in transmission geometry. The apparatus developed can be easily connected to synchrotron and free-electron-laser user-facility beamlines dedicated to XAS experiments. The conditions for stable generation and control of the liquid flat jet are analyzed and discussed. Preliminary soft XAS measurements on some test solutions are shown.

Transmission Electron Microscopy and Dynamic Light Scattering-Fundamental Perspective

Transmission Electron Microscopy (TEM) and Dynamic Light Scattering (DLS) are fundamental tools in nanotechnology and materials science, providing information about the structural and dynamic properties of nanomaterials and colloidal systems. This review provides a thorough examination of TEM and DLS, beginning with a discussion of their fundamental principles. It discusses the interaction of electron beams in TEM and the dynamics of scattered light in DLS, followed by an examination of instrumentation and experimental setups, including recent advances for increased resolution and sensitivity. The article then discusses the numerous applications of TEM and DLS in nanomaterial characterization. It includes analyses of nanoparticle size, shape, morphology, and distribution, as well as research into colloidal system dynamics such as nanoparticle aggregation, diffusion, and stability. The review concludes with a forward-looking perspective on emerging trends and future directions in nanomaterial characterization. It emphasizes the potential of TEM and DLS to overcome current challenges and advance our understanding of nanoscale phenomena. Overall, this comprehensive review provides researchers and practitioners with a solid understanding of the TEM and DLS principles, methodologies, and applications, as well as valuable fundamental insights.

Some Results on Shadowing and Local Entropy Properties of Dynamical Systems

Some Results on Shadowing and Local Entropy Properties of Dynamical Systems

Wave propagation in finite discrete chains unravelled by virtual measurement of dispersion properties

AbstractTravelling waves in circuit chains are studied to measure continuous dispersion. A lock‐in frequency meter (LIF) is suitable for precisely determining k for each set of waves in finite alternate LC chains, where LIF has been proven to be more accurate than the fast Fourier transform. In addition to the –k measurement, the wave impedance spectrum of the travelling wave can be measured simultaneously, for investigating the dispersion and splitting of pulse propagation. The measured dispersion is validated to be consistent with the derived theoretical equations. The result provides an independent way to precisely obtain dynamical system properties for chains composed of non‐ideal components, such as resistors for researching non‐Hermitian behaviour under dissipation. Systematical mapping of relative deviation dependence of wave dispersion measurement with LIF on different chain length and component variation is studied, indicating boundaries of 1%, 0.1%, and 0.01% precision for guidance of experiments.

Blind instrument response function identification from fluorescence decays

Time-resolved fluorescence spectroscopy plays a crucial role when studying dynamic properties of complex photochemical systems. Nevertheless, the analysis of measured time decays and the extraction of exponential lifetimes often requires either the experimental assessment or the modeling of the instrument response function (IRF). However, the intrinsic nature of the IRF in the measurement process, which may vary across measurements due to chemical and instrumental factors, jeopardizes the results obtained by reconvolution approaches. In this paper, we introduce a novel methodology, called blind instrument response function identification (BIRFI), which enables the direct estimation of the IRF from the collected data. It capitalizes on the properties of single exponential signals to transform a deconvolution problem into a well-posed system identification problem. To delve into the specifics, we provide a step-by-step description of the BIRFI method and a protocol for its application to fluorescence decays. The performance of BIRFI is evaluated using simulated and time-correlated single-photon counting data. Our results demonstrate that the BIRFI methodology allows an accurate recovery of the IRF, yielding comparable or even superior results compared with those obtained with experimental IRFs when they are used for reconvolution by parametric model fitting.

Relational Quantum Mechanics, quantum relativism, and the iteration of relativity

The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations.

NMR Relaxation of Gas Adsorbed in Microporous Material.

NMR relaxometry has been widely applied to characterize fluid confined in porous media because of its versatility, chemical selectivity, and noninvasive nature. Here we extend its usage to gas adsorbed in microporous materials by establishing a new quantitative model based on the molecular level NMR relaxation mechanism revealed by the molecular simulation of a prototypical adsorption system, CH4 adsorbed in ZIF-8. The model enables new NMR relaxometry-based characterization methods for thermodynamic, dynamic, and structural properties of adsorption systems, as demonstrated and validated by the experiments where the adsorption capacity and self-diffusivity of H2, CH4, and small alcohols adsorbed in ZIF-8 are deduced from the NMR relaxation data. The findings can serve for a better understanding of the composition-structure-properties relationships of a wide range of adsorption systems which is essential for the development and application of new functional microporous materials.

High-order nonstandard finite difference methods preserving dynamical properties of one-dimensional dynamical systems

High-order nonstandard finite difference methods preserving dynamical properties of one-dimensional dynamical systems

Quantum model in the context of six-level atom and deformed Lie algebra: Entanglement and statistical properties

In this work, we study the interplay between an atomic system with six levels configured in a cascade-type and one-mode fields in the framework of the f-coherent states. We explore the considered system dynamic properties under the effects of field nonlinearity and the number of photon transitions. In particular, we consider the quantum coherence, atomic upper level-occupation probability, and atom–field entanglement of a system when the effect of deformation is considered. Moreover, we analyze the dynamic of the Mandel parameter as a quantifier of the statistical properties of the field in the presence of deformation when the field is initially in coherent states.

Why is economics the only discipline with so many curves going up and down? There is an alternative

Even the most rudimentary training from Economics 101 starts with demand curves going down and supply curves going up. They are so ‘natural’ that they sound even more obvious than the Euclidian postulates in mathematics. But are they? What do they actually mean? Start with “demand curves”. Are they hypothetical ‘psychological constructs’ on individual preferences? Propositions on aggregation over them? Reduced forms of actual dynamic proposition of time profiles of prices and demanded quantities? Similar considerations apply to “supply curves” The point here, drawing upon the chapter by Kirman and Dosi, in Dosi (Dosi, Foundations of Complex Evolving Economies Innovation, Organization and Industrial Dynamics, Oxford University Press, 2023), is that the forest of demand and supply curves is basically there to populate the analysis with double axiomatic notions of equilibria, both ‘in the head’ of individual agents, and in environments in which they operate. Supply and demand “curves”, I am arguing, are one of the three major methodological stumbling blocks on the way of progress in economics, the other related ones being ‘utility functions’ and ‘production functions’. There is an alternative: represent markets and industries how they actually works, and model them both via fully fledged Agent Based Models and via lower dimensional dynamical systems.