Properties Of Dynamical Systems Research Articles

Kylin-V: An open-source package calculating the dynamic and spectroscopic properties of large systems.

Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples.

Investigation of structural, electrical, dynamical, optical, and thermoelectric properties of Sr-doped Mg2Si systems using first-principles calculations

Investigation of structural, electrical, dynamical, optical, and thermoelectric properties of Sr-doped Mg2Si systems using first-principles calculations

Proposal and Evaluation of Vertical Vibration Theory of Air Caster

Urbanization and human development have increased the exposure of seismic risk. Therefore, engineers need to develop new and more efficient technologies to protect people and objects from the disastrous consequences of earthquakes. Air casters have gained attention and have been utilized in the past decade as effective seismic vibration control devices. Although such active isolation systems perform well in mitigating horizontal input vibrations, they might cause excessive rocking motions, if not designed properly. This fact emphasizes the importance of exploring the vertical dynamic properties of air isolation systems. To gain such an understanding, this research examines and proposes a formula for the vertical stiffness and damping of air caster systems. Theoretical solutions to the vertical stiffness and damping of such systems have been explored. Computer simulations considering fluid-structure interaction have also been performed to understand the dynamic behavior of the supporting air layer. Results have been compared to validate the proposed dynamic quantities within the considered simulation range. It is also concluded that the instantaneous air layer thickness, representing the air chamber pressure, and the bearing inlet flow rate are the key factors in determining the dynamic properties of the air layer. It is concluded that to evaluate the performance of the air caster seismic isolation device and increase the probability that the qualified seismic isolation performance will be exhibited, it is necessary to investigate which parameters are greatly involved in the viscous damping coefficient and the spring constant of amass-spring-damper system equivalent to the air caster isolation system.

Level statistics of the one-dimensional dimerized Hubbard model

The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi–Hubbard model with dimerized hopping amplitude and find that after taking into account translation, reflection, spin and η pairing symmetries to isolate irreducible blocks of the Hamiltonian, the level spacings in the limit of large system sizes follow the distribution expected for hermitian random matrices from the Gaussian orthogonal ensemble. We show this by analyzing the distribution of the ratios of consecutive level spacings in this system, its cumulative distribution and quantify the deviations of the distributions using their mean, standard deviation and skewness.

Existence and stability of a quasi-periodic two-dimensional motion of a self-propelled particle

AbstractThe mechanism of self-propelled particle motion has attracted much interest in mathematical and physical understanding of the locomotion of living organisms. In a top-down approach, simple time-evolution equations are suitable for qualitatively analyzing the transition between the different types of solutions and the influence of the intrinsic symmetry of systems despite failing to quantitatively reproduce the phenomena. We aim to rigorously show the existence of the rotational, oscillatory, and quasi-periodic solutions and determine their stabilities regarding a canonical equation proposed by Koyano et al. (J Chem Phys 143(1):014117, 2015) for a self-propelled particle confined by a parabolic potential. In the proof, the original equation is reduced to a lower dimensional dynamical system by applying Fenichel’s theorem on the persistence of normally hyperbolic invariant manifolds and the averaging method. Furthermore, the averaged system is identified with essentially a one-dimensional equation because the original equation is O(2)-symmetric.

Complex dynamical behaviors of a honeybee-mite model in parameter plane

The honeybee has a significant impact on ecosystem stability, biodiversity conservation, and pollinating crops. However, during the past few years, there has been a sharp reduction in both the honeybee population and their colonies. It has been found that the parasitic mite Varroa destructor and its interactions with certain viruses are responsible for the decline in honeybee colonies around the world, which in turn immensely affects the economic growth of a country. To investigate how the dynamics of a system is influenced by the growth of honeybees and the parasitism of mites, we study a nonlinear honeybee-mite population model in a discrete-time setup. We observe that an increase in the value of the queen’s egg-laying rate drives the system towards chaos. However, chaos can be controlled as well if the parasite attachment effect is increased. The intrinsic dynamical properties of the proposed system are investigated with the simultaneous variation of the queen’s egg-laying rate and the mite’s parasite attachment effect by constructing several largest Lyapunov exponent and isoperiodic diagrams. The investigation reveals the existence of several periodic structures in the quasiperiodic and chaotic regimes of the parameter plane, including Arnold tongues, saddle area, spring area, connected shrimp-shaped structure, and connected saddle area. We also find the appearance of a novel ‘jellyfish’-shaped periodic structure. One of the most fascinating findings of this study is the appearance of Arnold tongues along the inner boundary region of another Arnold tongue. In addition, this work also reveals different types of multistability, e.g., the coexistence of two, three, and even four attractors. What’s more interesting is that the current analysis unveils the coexistence of five attractors as well, more specifically, four different periodic attractors coexist with the trivial fixed point attractor, which is quite rare in ecological systems. The structures of the basins of these coexisting attractors are either smooth or very complex in nature. Furthermore, the present study also discloses the fact that variation in the initial condition of the system can significantly change the appearance of the periodic structures in the parameter plane.

Spectro-photometry of Phobos simulants: I. Detectability of hydrated minerals and organic bands

Previous Mars Reconnaissance Orbiter and Mars Express observations of Phobos and Deimos, the moons of Mars, have improved our understanding of these small bodies. However, their formation and composition remain poorly constrained. Physical and spectral properties suggest that Phobos may be a weakly thermal-altered captured asteroid but the dynamical properties of the martian system suggest a formation by giant collision similar to the Earth moon. In 2027, the JAXA’s MMX mission aims to address these outstanding questions.We undertook measurements with a new simulant called OPPS (Observatory of Paris Phobos Simulant) which closely matches Phobos reflectance spectra from the visible to the mid-infrared wavelength range. The simulant was synthesized using a mixture of olivine, saponite, anthracite, and coal.Since observation geometry strongly influences the photometry and spectra of the light reflected from planetary surfaces, we evaluated the parameters obtained by modeling the phase curves – obtained through laboratory measurements – of two different Phobos simulants (UTPS-TB and OPPS) using Hapke IMSA model. Our results show that the photometric properties of Phobos simulants are not fully consistent with those of carbonaceous chondrites and martian meteorites. We also investigated the detection of volatiles/organic compounds and hydrated minerals, as the presence of such components is expected on Phobos in the hypothesis of a captured primitive asteroid. To investigate their detectability, we examined the variability of the 3.28μm and 3.42μm absorption bands related to aliphatic/aromatic carbon (as a proxy of organic material), as well as the 2.7μm O-H feature in a Phobos laboratory spectroscopic simulant. The results indicate that a significant amount of organic compounds is required for the detection of C-H bands at 3.4μm. The bands at 3.28 and 3.42μm are faint (less than 2%) when ∼3 wt% of organic compounds are present in the simulant and are likely undetectable by the MIRS spectrometer onboard the MMX mission. When the concentration of aliphatic and aromatic compounds is increased to 6 wt%, a positive detection starts to become more plausible using remote sensing infrared spectroscopy. In contrast, the 2.7μm absorption band, due to hydrated minerals, is much deeper and easier to detect than C-H organic features at the same concentration levels. The feature is still clearly detectable even when the simulant contains only 3 vol.% of phyllosilicates, corresponding to 0.7 wt% OH groups.Posing limits on detectability of some possible key components of Phobos surface will be pivotal to prepare and interpret future observations of the MIRS spectrometer as well as TENGOO and OROCHI cameras onboard MMX mission.

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.