Dynamics Of Physical Systems Research Articles

Multilayer Reservoir Computing Based on Ferroelectric α-In2 Se3 for Hierarchical Information Processing.

Dynamic physical systems such as reservoir computing (RC) architectures show a great prospect in temporal information processing, whereas hierarchical information processing capability is still lacking due to the absence of advanced multilayer reservoir elements. Here, a stackable reservoir system is constructed based on ferroelectric α-In2 Se3 devices with voltage input and output, which is realized by dynamic voltage division between a ferroelectric field-effect transistor and a planar device and therefore allows the reservoirs to cascade, enabling multilayer RC. Fast Fourier transformation analysis shows high-harmonic generation in the first layer as a result of inherent nonlinearity of the reservoir, and progressive low-pass filtering effect is realized where higher-frequency components are progressively filtered in deeper-layer RCs. Time-series prediction and waveform classification tasks are also demonstrated, serving as evidence for the memory capacity and computing capability of the deep reservoir architecture. This work can provide a promising pathway in exploiting emerging 2D materials and dynamics for advanced neuromorphic computing architectures.

Impact of symmetry on ergodic properties of triangular billiards.

Polygonal billiards constitute some of the simplest yet counterintuitive dynamical systems in physics. Even basic features of the dynamics, such as ergodicity of the microcanonical distribution or the decay of correlations have not been settled in general. In this Letter, we will highlight the importance of symmetries of the billiard table for the resulting dynamics. Although typical triangular billiards appear to show correlation decay, symmetric billiards may not even be ergodic with respect to the uniform distribution in phase space.

MODELING MASS-SPRING-DAMPER SYSTEM USING SCILAB

Modeling a system means developing a mathematical representation to simulate certain properties observed in real systems. These systems can range from a car suspension to the most complex robotics. In modern mechanical engineering, it is routine to model a physical dynamic system as a set of differential equations that will later be simulated using a computer. This systems can range from a car suspension to the most complex robotics. Use software for numerical analysis and qualitative analysis of dynamic systems in engineering and applied science education simplifies the analysis and analysis. In this paper, the dynamic behavior of massspring-damper system has been studied by mathematical equations in free software Scilab. Scilab is free and open source software for numerical computation providing a powerful computing environment for engineering and scientific applications. The resulting equations represent a generalization of the classical mass-spring-damper model; the proposed representation can be used to describe a wide variety of systems, which had not been addressed due to the limitations of the classical calculus. Software implementation of the model and calculations are performed in the Scilab environment. The massive use of software generated a great business. Although the reliability and effectiveness of commercial software is undeniable, their cost is not available to most researchers, students, and public universities. This paper clearly shows that Scilab is capable of handling such uncertainties with little effort. It should be noted that this paper is written with the intention of disseminate the ideas of how to use Scilab for teaching theory modelling, dynamic of machine or performing related research works.

Phase Transitions and Bifurcation Points in the Initiation Dynamics of Venture Emergence: A Conceptual Framework

Based on isomorphic considerations, this paper attempts to establish an entrepreneur as complex adaptive system, which is one of the concepts that appear prominently in the field of complexity sciences. The attempt to equate the notion of an entrepreneur with the idea of a complex adaptive system, presupposes recognition of the entrepreneur’s role in adaptive agency. Along with this recognition, comes the convenience of contextualizing the concepts of phase transitions and bifurcation points in terms of venture emergence. The dynamics of these concepts are however more commonly explored within the workings of complex or dynamic physical systems. Yet, the broad applicability of the underlying ideas offers the possibility of identifying similar concepts in biological systems and by extension, the field of entrepreneurial cognition and behavior. Thus, the paper adopts an interdisciplinary approach and employs retroductive reasoning in the assemblage of relevant ideas, sought from diverse literary sources. The outcome is a conceptual framework, which presents certain propositions that offer implication for action.

Certain Operations on Picture Fuzzy Graph with Application

Fuzzy graphs (FGs) can play a useful role in natural and human-made structures, including process dynamics in physical, biological, and social systems. Since issues in everyday life are often uncertain due to inconsistent and ambiguous information, it is extremely difficult for an expert to model those difficulties using an FG. Indeterminate and inconsistent information related to real-valued problems can be studied through a picture of the fuzzy graph (PFG), while the FG does not provide mathematically acceptable information. In this regard, we are interested in reducing the limitations of FGs by introducing some new definitions and results for the PFG. This paper aims to describe and explore a few properties of PFGs, including the maximal product (MP), symmetric difference (SD), rejection (RJ), and residue product (RP). Furthermore, we also discuss the degree and total degree of nodes in a PFG. This study also demonstrates the application of a PFG in digital marketing and social networking.

Formalization of bond graph using higher-order-logic theorem proving

Bond graph is a unified graphical approach for describing the dynamics of complex engineering and physical systems and is widely adopted in a variety of domains, such as, electrical, mechanical, medical, thermal and fluid mechanics. Traditionally, these dynamics are analyzed using paper-and-pencil proof methods and computer-based techniques. However, both of these techniques suffer from their inherent limitations, such as human-error proneness, approximations of results and enormous computational requirements. Thus, these techniques cannot be trusted for performing the bond graph based dynamical analysis of systems from the safety-critical domains like robotics and medicine. Formal methods, in particular, higher-order-logic theorem proving, can overcome the shortcomings of these traditional methods and provide an accurate analysis of these systems. It has been widely used for analyzing the dynamics of engineering and physical systems. In this paper, we propose to use higher-order-logic theorem proving for performing the bond graph based analysis of the physical systems. In particular, we provide formalization of bond graph, which mainly includes functions that allow conversion of a bond graph to its corresponding mathematical model (state–space model) and the verification of its various properties, such as, stability. To illustrate the practical effectiveness of our proposed approach, we present the formal stability analysis of a prosthetic mechatronic hand using HOL Light theorem prover. Moreover, to help non-experts in HOL, we encode our formally verified stability theorems in MATLAB to perform the stability analysis of an anthropomorphic prosthetic mechatronic hand.

On the Semi-Local Convergence of an Ostrowski-Type Method for Solving Equations

Symmetries play a crucial role in the dynamics of physical systems. As an example, microworld and quantum physics problems are modeled on principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Then, these equations can be solved using iterative methods. In this article, an Ostrowski-type method for solving equations in Banach space is extended. This is achieved by finding a stricter set than before containing the iterates. The convergence analysis becomes finer. Due to the general nature of our technique, it can be utilized to enlarge the utilization of other methods. Examples finish the paper.

Analysis of physical health risk dynamic evaluation system based on sports network technology

The people are the pillar of national construction and the driving force of social sustainable development. Therefore, people must develop morality, intelligence and body in an all-round way. The physical health risk assessment is of great significance to the improvement of the physical health of the public. Based on the sports network technology, this paper improves the traditional human posture recognition algorithm, and combines machine learning to construct the human body dynamic feature recognition method. Moreover, this paper combines actual needs to construct a physical health risk dynamic evaluation system based on sports network technology, which can recognize sports through pose recognition and combine dynamic monitoring technology to detect daily diet and living habits. In addition, this paper constructs the network structure of this paper system and designs its functional modules according to actual needs. Finally, this paper designs experiments to verify the performance of the model constructed in this paper. The research shows that the system constructed in this paper meets actual needs and can provide theoretical references for subsequent related research.

Optimization of Influencing Factors in Tidal Current Data Assimilation Modeling in Macro Tidal Estuary, Gyeonggi Bay, South Korea

Gu, B.-H.; Woo, S.-B., and Kim, S., 2021. Optimization of influencing factors in tidal current data assimilation modeling in macro tidal estuary, Gyeonggi Bay, South Korea. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 66–70. Coconut Creek (Florida), ISSN 0749-0208. The study investigates the effect of the model prediction accuracy improvement using data assimilation technique in macro-tidal estuary, such as the Gyeonggi Bay (GGB), South Korea. The observation data used in this study is a tidal current measurement from Acoustic Doppler Current Profiler (ADCP) mooring device. GGB is located at the middle west coast of South Korea, and it is semi-closed estuary that has a tidal range over 6.8 m. To take the irregularity of coastline into account, this study utilized the Finite Volume Coastal Ocean Model (FVCOM), which has the flexible advantage of grid resolution by using unstructured triangular grid system. When applying data assimilation into the coastal model, various parameters, such as scaling factors and correlation lengths are needed to be adjusted to find out the best performance. Total 25 cases used in Taylor diagram showed that different influencing factors are required to be optimized at each observation location. It means that parameters in data assimilation depend on the physical dynamic system via complicated geometry. The optimized parameters not only increase by the tidal range but also it is offset by the effect of river discharge. The horizontal influence range of data assimilation with all observed locations becomes even less than the result applying only one location. It is estimated that the phenomena occurred due to strong tidal currents and interference between the range of influence. The sensitivity of data assimilation parameters in tidally dominated coastal area indicates that a systematic way of choosing the most optimized site-specific parameters are required in macro tidal area.

Structured time-delay models for dynamical systems with connections to Frenet-Serret frame.

Time-delay embedding and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it has been shown that models identified by dynamic mode decomposition on time-delay coordinates provide linear representations of strongly nonlinear systems, in the so-called Hankel alternative view of Koopman (HAVOK) approach. Curiously, the resulting linear model has a matrix representation that is approximately antisymmetric and tridiagonal; for chaotic systems, there is an additional forcing term in the last component. In this paper, we establish a new theoretical connection between HAVOK and the Frenet–Serret frame from differential geometry, and also develop an improved algorithm to identify more stable and accurate models from less data. In particular, we show that the sub- and super-diagonal entries of the linear model correspond to the intrinsic curvatures in the Frenet–Serret frame. Based on this connection, we modify the algorithm to promote this antisymmetric structure, even in the noisy, low-data limit. We demonstrate this improved modelling procedure on data from several nonlinear synthetic and real-world examples.

Variational integrator graph networks for learning energy-conserving dynamical systems.

Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long-term dynamics of complex physical systems from noisy data. Despite this success, there has only been a limited study on how to optimally combine physics priors to improve predictive performance. To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments. As such, we are able to systematically investigate all possible combinations of inductive biases of which existing methods are a natural subset. Using this framework we introduce variational integrator graph networks-a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order symplectic variational integrators, and graph neural networks. We demonstrate, across an extensive ablation, that the proposed unifying framework outperforms existing methods, for data-efficient learning and in predictive accuracy, across both single- and many-body problems studied in the recent literature. We empirically show that the improvements arise because high-order variational integrators combined with a potential energy constraint induce coupled learning of generalized position and momentum updates which can be formalized via the partitioned Runge-Kutta method.

Port-Hamiltonian neural networks for learning explicit time-dependent dynamical systems.

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known a priori. Despite this success, many real world dynamical systems are nonautonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such nonautonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

Dynamics of a power hacksaw mechanism, contact interaction with the workpiece, and material removal

ABSTRACT During the metal cutting process, dynamics of a mechanism influence the cutting phenomenon at the contact interface while the contact interaction also has its reciprocal effect on the mechanism. Modeling the dynamics and the contact interaction between the cutting tool and workpiece, causing material removal, is a complex and challenging task. The mechanism of a machine involves a number of interconnected rigid bodies that interact with each other dynamically. Modeling dynamics of such mechanisms is necessary from the point of view of design and analysis. In this paper, the multibond graph approach has been used fxor modeling the dynamics of a power hacksaw machine. The power hacksaw machine is quite commonly used for cutting materials in industries. This graphical approach offers scope for analysis of causality, which is an important aspect of physical systems, and its application, a feature not offered by the energy-based formulations, such as the Euler-Lagrange’s method and Hamilton’s method. These energy-based formulations, commonly used for modeling dynamics of physical systems, also tend to be too mathematically inclined. MATLAB coding for simulation has been done directly from the multibond graph model without explicitly deriving system equations. The simulation results have been presented, analyzed, and discussed.

Memory properties of electromigrated Au nanogaps to realize reservoir computing

The reservoir computing (RC) scheme, which employs the inherent computational capabilities of dynamical systems, is a key technology to implement artificial intelligence systems physically. Ensuring the nonlinear expansion of input data through the dynamics of physical systems is a necessary aspect of RC. Previously, we developed artificial synapses of Au nanogaps by using the “activation” technique, which allowed the implementation of synaptic functions such as short-term plasticity, long-term plasticity, and spike-timing-dependent plasticity. The activation technique is an electromigration-based method to control the tunnel resistance of nanogaps. In this study, the memory property of the Au nanogap, using activation for RC, was evaluated via short-term memory (STM) and parity check (PC) tasks. More specifically, memory capacity was introduced to evaluate the performance of the Au nanogap, defined as the sum of squares of the correlation between the outputs of RC and the teacher for delay D = 1 to 6. By utilizing the simple dynamics of short-term plasticity, the memory capacities of the STM and PC tasks were found to be 1.07 and 0.90, respectively, when 10 virtual nodes were used. This demonstrates that the dynamic process of the activation technique enables the Au nanogap-based reservoir to process information directly in the temporal domain. The experimental results can facilitate the development of compact devices to realize physical RC.

State evolution formula and stability analysis of a paraxial optical system.

By analyzing the phase vector evolution of a paraxial optical system (POS) with a variational background refractive index, we obtain a continuous dynamic equation, called state evolution formula (SEF), which simultaneously gives the phase vector transformation and ray trajectory inside and outside the optical elements. Compared with ray transfer matrix method, this phase-vector equation is universal in treating problems about propagation and stability of paraxial rays, since it extends the linear and discrete matrix equation to a differential equation. It takes a consistent form for both continuous and discontinuous cases without considering the special rays, even the input and output states present a nonlinear relation. Based on the SEF, we further propose a rigorous criterion about whether a continuous and non-periodic POS is stable. This formula provides a reference model for the theoretical analysis of ray dynamics in geometric and physical optical systems.

Real-time optimal quantum control of mechanical motion at room temperature.

The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2,3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5-7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56±0.02quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.

Modeling of Time-Delayed Distributed Cyber-Physical Power Systems for Small-Signal Stability Analysis

Compared with a power system under centralized control, a power system under fully distributed control has stronger interdependence between its physical side and cyber side. Such a system is a typical cyber-physical system (CPS). The time delay problem is one of the most critical issues in the application of distributed control for power systems. First, a distributed information flow model is established considering multiple sources of time delay, especially the communication delay between neighboring agents. Second, combining the dynamics of physical power systems, a general model of time-delayed CPS under fully distributed control is proposed, especially for inverter-based microgrids. Third, the stability of the time-delayed CPS is analyzed based on the proposed model with a critical eigenvalue tracking algorithm. A real-world microgrid with DGs under fully distributed frequency control is tested for small-signal stability analysis. The findings show that the stability of the distributed CPS with multiple sources of time delay depends on not only the absolute value of time delays but also the coordination of time delays and that the delay merging property in centralized mode is not relevant in a distributed CPS. The accuracy of the model and the obtained stability margin are verified by Simulink simulations.

Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences

Symmetries are important in studying the dynamics of physical systems which in turn are converted to solve equations. Jarratt’s method and its variants have been used extensively for this purpose. That is why in the present study, a unified local convergence analysis is developed of higher order Jarratt-type schemes for equations given on Banach space. Such schemes have been studied on the multidimensional Euclidean space provided that high order derivatives (not appearing on the schemes) exist. In addition, no errors estimates or results on the uniqueness of the solution that can be computed are given. These problems restrict the applicability of the methods. We address all these problems by using the first order derivative (appearing only on the schemes). Hence, the region of applicability of existing schemes is enlarged. Our technique can be used on other methods due to its generality. Numerical experiments from chemistry and other disciplines of applied sciences complete this study.

A Class of Novel Mann-Type Subgradient Extragradient Algorithms for Solving Quasimonotone Variational Inequalities

Symmetries play an important role in the dynamics of physical systems. As an example, quantum physics and microworld are the basis of symmetry principles. These problems are reduced to solving inequalities in general. That is why in this article, we study the numerical approximation of solutions to variational inequality problems involving quasimonotone operators in an infinite-dimensional real Hilbert space. We prove that the iterative sequences generated by the proposed iterative schemes for solving variational inequalities with quasimonotone mapping converge strongly to some solution. The main advantage of the proposed iterative schemes is that they use a monotone and non-monotone step size rule based on operator knowledge rather than a Lipschitz constant or some line search method. We present a number of numerical experiments for the proposed algorithms.

Modeling Data Flows with Network Calculus in Cyber-Physical Systems: Enabling Feature Analysis for Anomaly Detection Applications

The electric grid is becoming increasingly cyber-physical with the addition of smart technologies, new communication interfaces, and automated grid-support functions. Because of this, it is no longer sufficient to only study the physical system dynamics, but the cyber system must also be monitored as well to examine cyber-physical interactions and effects on the overall system. To address this gap for both operational and security needs, cyber-physical situational awareness is needed to monitor the system to detect any faults or malicious activity. Techniques and models to understand the physical system (the power system operation) exist, but methods to study the cyber system are needed, which can assist in understanding how the network traffic and changes to network conditions affect applications such as data analysis, intrusion detection systems (IDS), and anomaly detection. In this paper, we examine and develop models of data flows in communication networks of cyber-physical systems (CPSs) and explore how network calculus can be utilized to develop those models for CPSs, with a focus on anomaly and intrusion detection. This provides a foundation for methods to examine how changes to behavior in the CPS can be modeled and for investigating cyber effects in CPSs in anomaly detection applications.