Dynamic Equations Research Articles

A cyber–physical system prospect theoretic game through a VANET lens

AbstractIn this paper, the problem of attack mitigation in an intelligent transportation network or vehicular network is considered as a game. The player’s perception of uncertainty and decision making is studied under a subjective prospect theoretic (PT) model and an objective expected utility theory (EUT) model. A game where each player chooses one of two strategies with certain probabilities is analysed. The case where subjective players bias their choices of the probabilities using the Prelec weighting function is considered and compared with the EUT based decisions and the effect of the framing effect function and . The corresponding Nash equilibria (NE) are derived and found through the replicator dynamic equation. Under the Prelec function, the results agree with the previously published results that the defender is biased more into defending the more important road side units. However, under both the function and the framing effect, the players' behaviour does not depend on the loss penalty parameter, and the Prelec function dominates the framing effect. For small values, the players make conservative decisions compared to higher values regardless of the effect of the framing function. For high values the players are more certain in their decisions than the EUT players.

An Analytical Framework for Global Dynamic Modeling of Flexible Variable Topology Mechanisms

The coupling of topology transition with flexible deformation and rigid motion presents significant challenges in the dynamic modeling of flexible variable topology mechanisms. Existing dynamics models are mostly special-purpose models for their particular cases and thus struggle to completely depict the general topology transition characteristics. To address this gap, this paper proposes an analytical framework for the global dynamic modeling of flexible variable topology mechanisms, focusing on general cases. Initially, the flexible variable topology mechanisms are rigorously defined by the ordered triples and the general topology transition approaches are presented. A novel concept, the “basic flexible kinematic chain set”, is suggested, which can easily transform into the topology of each submechanism by slightly extending. Based on this concept, basic and conditional constraints are established. The continuous dynamic modeling method for each topology is developed using Jourdain’s principle and the Lagrange multiplier method. Additionally, three classes of constraints related to topology transition are identified, and their equations are formulated, elucidating the topology transition nature. Compatibility equations are proposed to define the new coordinate system for describing the deformation of flexible components after the topology transition. An impact dynamic equation is established to describe abrupt velocity change. Integrating compatibility and impact equations, a discontinuous dynamic modeling method for topology transition is developed. Finally, a flexible variable topology mechanism example is studied, and simulations and experiments are conducted to validate the proposed framework. This analytical framework is general-purpose and efficient, guiding the global dynamic modeling of various flexible variable topology mechanisms and the development of sophisticated control techniques.

Trajectory tracking of a quadrotor using model predictive and backstepping control with anti-disturbance compensation subjected to variations in the center of gravity

The trajectory tracking control of a quadrotor unmanned aerial vehicle is done in this paper in the presence of changes in the center of gravity due to the variations of a connected load mass and its position, external disturbances, and parametric uncertainties. At first, dynamic equations are obtained using Newton–Euler relations, and then a two-loop control architecture is designed for the trajectory tracking task. Backstepping and model predictive control are used in the inner and outer loops, respectively. An extended disturbance observer is adopted to improve disturbance rejection capabilities in both loops. For the six-degrees-of-freedom unmanned aerial vehicle, the effects of time-varying mass, which leads to the change in the moment of inertia and center of gravity of the system, together with external disturbances and parametric uncertainties are taken into account. It is possible to mount an arbitrary number of different point masses at arbitrary positions on the unmanned aerial vehicle. The proposed control scheme is evaluated using simulation in the presence of uncertainties and external disturbances. According to the simulation results, the developed control scheme can achieve stable flight under different conditions.

Cooperative maximum adhesion tracking control for multi-motor electric locomotives

PurposeThis study aims to propose a cooperative adhesion control method for trains with multiple motors electric locomotives. The method is intended to optimize the output torque of each motor, maximize the utilization of train adhesion within the total torque command, reduce the train skidding/sliding phenomenon and achieve optimal adhesion utilization for each axle, thus realizing the optimal allocation of the multi-motor electric locomotives.Design/methodology/approachIn this study, a model predictive control (MPC)-based cooperative maximum adhesion tracking control method for multi-motor electric locomotives is presented. Firstly, train traction system with multiple motors is constructed in accordance with Newton’s second law. These equations include the train dynamics equations, the axle dynamics equations, and the wheel-rail adhesion coefficient equations. Then, a new MPC-based multi-axle adhesion co-optimization method is put forward. This method calculates the optimal output torque through real-time iteration based on the known reference slip speed to achieve multi-axle co-optimization under different circumstances.FindingsThis paper presents a MPC system designed for the cooperative control of multi-axle adhesion. The results indicate that the proposed control system is able to optimize the adhesion of multiple axles under numerous different conditions and achieve the optimal power distribution based on the reduction of train skidding/sliding.Originality/valueThis study presents a novel cooperative adhesion tracking control scheme. It is designed for multi-motor electric locomotives, which has rarely been studied before. And simulations are carried out in different conditions, including variable surfaces and motor failing.

Nonassociative gauge gravity theories with R-flux star products and Batalin–Vilkovisky quantization in algebraic quantum field theory

Abstract Nonassociative modifications of general relativity, GR, and quantum gravity, QG, models naturally arise as star product and R-flux deformations considered in string/ M-theory. Such nonassociative and noncommutative geometric and quantum information theories were formulated on phase spaces defined as cotangent Lorentz bundles enabled with nonassociative symmetric and nonsymmetric metrics and nonlinear and linear connection structures. We outline the analytic methods and proofs that corresponding geometric flow evolution and dynamical field equations can be decoupled and integrated in certain general off-diagonal forms. New classes of solutions describing nonassociative black holes, wormholes, and locally anisotropic cosmological configurations are constructed using such methods. We develop the Batalin-Vilkovisky, BV, formalism for quantizing modified gravity theories, MGTs, involving twisted star products and semi-classical models of nonassociative gauge gravity with de Sitter/affine/ Poincar'{e} double structure groups. Such theories can be projected on Lorentz spacetime manifolds in certain forms equivalent to GR or MGTs with torsion generalizations etc. We study the properties of the classical and quantum BV operators for nonassociative phase spaces and nonassociative gauge gravity. Recent results and methods from algebraic QFT are generalized to involve nonassociative star product deformations of the anomalous master Ward identity. Such constructions are elaborated in a nonassociative BV perspective and for developing non-perturbative methods in QG.

Daily reciprocal relationships between affect, physical activity, and sleep in middle and later life.

The daily dynamics among affect, physical activity, and sleep are often explored by taking a unidirectional approach. Yet, obtaining a comprehensive understanding of the reciprocal dynamics among affect and health behaviors is crucial for promoting daily well-being. This study examined the reciprocal associations among affect, physical activity, and sleep in daily life in a U.S. national sample of mid- and later-life adults. The study sample included 1,171 participants (mean age = 62.61 years, SD = 10.26 years, 57% female, 82% White) with 9,033 daily interview days from the daily diary project of the third wave of the Midlife in the United States study (MIDUS III). Participants reported their daily experiences across eight consecutive days. Using a dynamic structural equation modeling, we examined day-to-day autoregressive and cross-lagged associations among positive and negative affect, physical activity, and sleep. Results revealed that higher positive affect predicted a greater likelihood of engaging in moderate-to-vigorous physical activity (MVPA) and better sleep quality the following day. Higher sleep quality predicted increased positive affect, reduced negative affect, and a greater likelihood of MVPA engagement the next day. Longer sleep duration predicted lower negative affect the following day. However, MVPA engagement predicted subsequent higher negative affect. Findings underscore the importance of simultaneously considering affect, physical activity, and sleep in studying their day-to-day dynamics, and the protective role of positive affect and sleep quality in daily life. Maintaining high positive affect and managing sleep quality may be important intervention targets for enhancing daily well-being.

Analyzing the Dynamics and Friction Forces on Spheres in Fluid Flows: Applications Across Engineering and Sports Science

This study explores the dynamics and friction forces of spherical objects in fluid flows, emphasizing their applications across engineering and sports science. By examining key theoretical concepts such as drag coefficient, Reynolds number, and fluid dynamics equations, the research highlights how these principles influence the motion of spheres in various fluid environments. The analysis encompasses computational fluid dynamics (CFD) and experimental approaches, addressing applications in ocean, aerospace, and vehicle engineering, as well as sports science. The findings demonstrate the critical role of understanding drag and friction characteristics in optimizing designs, improving performance, and driving technological innovation. Challenges such as multi-scale phenomena, nonlinear dynamics, and measurement techniques are identified, suggesting future research directions to refine theoretical models and enhance practical applications. The study not only advances the theoretical understanding of fluid dynamics but also provides essential insights for engineering optimization and sports performance enhancement.

New Studies for Dynamic Programming and Fractional Differential Equations in Partial Modular b-Metric Spaces

This study explores innovative insights into the realms of dynamic programming and fractional differential equations, situated explicitly within the framework of partial modular b-metric spaces enriched with a binary relation R, proposing a novel definition for a generalized ℷC-type Suzuki R-contraction specific to these spaces. By doing so, we pave the way for a range of relation-theoretical common fixed-point theorems, highlighting the versatility of our approach. To illustrate the practical relevance of our findings, we present a compelling example. Ultimately, this work aims to enrich the existing academic discourse and stimulate further research and practical applications within the field.

Dynamic problem of a power-law graded half-plane and an associated carleman problem for two functions

Summary A steady state plane problem of an inhomogeneous half-plane subjected to a load running along the boundary at subsonic speed is analyzed. The Lame coefficients and the density of the half-plane are assumed to be power functions of depth. The model is different from the standard static model have been used in contact mechanics since the Sixties and originated from the 1964 Rostovtsev exact solution of the Flamant problem of a power-law graded half-plane. To solve the governing dynamic equations with variable coefficients written in terms of the displacements, we propose a method that, by means of the Fourier and Mellin transforms, maps the model problem into a Carleman boundary value problem for two meromorphic functions in a strip with two shifts or, equivalently, to a system of two difference equations of the second order with variable coefficients. By partial factorization the Carleman problem is recast as a system of four singular integral equations on a segment with a fixed singularity and highly oscillating coefficients. A numerical method for its solution is proposed and tested. Numerical results for the displacement and stress fields are presented and discussed.

Multibody elastodynamic modeling of parallel manipulators based on the Lagrangian equations without Lagrangian multipliers

Due to the complexity of the multi constraint and multi closed-loop of parallel mechanisms (PMs), their dynamic equations require additional Lagrangian multipliers and constraint equations, which is unfavorable for solving the dynamic equations. In this paper, a multibody elastodynamic modeling of PMs based on the Lagrangian equations is proposed to fix this issue. First, we decompose the closed-loop PMs into open-loop ones by cutting open at the joints, and we propose the subassembly element that considers the flexible links and joints to avoid the singularity of the traditional constraint equations. Second, we extract the nonsingular independent coordinates for these nodes that are constrained by joints and rigid element through multi-point constraint theory and singularity analysis, and then summarized to establish the global independent generalized displacement coordinates (IGDCs). Third, we formulate the Lagrangian equations through the global IGDCs by closing the open-loop of the mechanism. The Guyuan, improved reduction system, subspace iteration method, and precision integration method are respectively presented to analyze the natural frequencies and dynamic response of the mechanism. The proposed method is computationally efficient because the computation concerning the Lagrangian multipliers are not required. Finally, the 3PRRR PM is presented to implement the proposed method.

Existence and Uniqueness of Solutions for Fractional Dynamic Equations with Impulse Effects

Abstract The aim of the study is to establish sufficient conditions to ensure the existence and uniqueness of solutions for nonlinear Riemann-Liouville fractional dynamic equations under impulse effects. The current state of the literature reveals a visible gap in the investigation of the existence-uniqueness aspects of such equations, and this research makes a significant contribution to filling this gap. To highlight the practical implications of our results, we present an illustrative example that exemplifies the applicability of the established conditions.

Integrated Dynamic Analysis of Thin-Walled Beams: Coupled Bidirectional Bending, Torsion, and Axial Vibrations Under Axial Loads

This paper proposes a beam model integrating the Timoshenko beam theory with Vlasov beam theory to capture the coupled behavior of bidirectional bending, torsion, and axial vibration in thin-walled beams subjected to axial loads. Our model incorporates the effects of shear deformation, rotational inertia, and axial loads, offering a comprehensive approach to complex dynamic behaviors. By utilizing Hamilton’s principle, we derived a complete set of coupled dynamic equations and boundary conditions. The highlight of this model is its capacity to accurately predict the dynamic response of thin-walled beams under multifaceted loading conditions, surpassing traditional models by integrating coupled axial vibrations. This research significantly advances the understanding of the dynamic behavior of thin-walled beams, providing a precise analytical tool for structural design and safety assessment. The robustness and accuracy of the proposed model were validated through extensive theoretical analysis and empirical validation, equipping engineers with critical insights to optimize the design of engineering structures subjected to complex dynamic loads.

Simulating groundwater flow and contaminant transport

This study presents a comprehensive simulation of groundwater flow and contaminant transport using advanced numerical modeling techniques. The research focuses on understanding the complex interactions between groundwater movement and pollutant dispersion across various geological settings. By applying the governing equations of fluid dynamics and solute transport, the model incorporates essential parameters such as hydraulic conductivity, porosity, and dispersivity, enabling the accurate prediction of contaminant behavior over time. Simulations were carried out under a range of scenarios to assess the effects of differing recharge rates and contaminant source configurations on groundwater quality. The results provide critical insights into the mechanisms governing contaminant migration, highlighting the importance of soil properties, boundary conditions, and flow dynamics in influencing transport behavior. Moreover, the study demonstrates how variations in geological features and pollutant sources can significantly alter contaminant dispersal patterns. This work contributes to the development of robust groundwater management strategies and emphasizes the role of simulation tools in assessing environmental risks tied to groundwater contamination.

Affect dynamics and depressive symptomatology: Revisiting the inertia-instability paradox.

The inertia-instability paradox poses an intriguing question in depression research: How can the affective experiences of depressed individuals demonstrate both resistance to change and fluctuation? Prior studies examining this paradox have faced limitations, including small sample sizes, analytic approaches prone to biased parameter estimates, and inconsistent results. Using data from 842 adults (Mage = 54.31, SD = 13.25, age range: 18-88; 58.2% female) collected over 56 consecutive days, we applied dynamic structural equation modeling to quantify individualized indices of mean levels, variability, instability, and inertia of negative affect. When adjusting for shared variances among affect dynamic measures, depressive symptoms were uniquely associated with both higher mean levels and inertia of negative affect. However, neither variability nor instability demonstrated unique links to depressive symptoms after accounting for the mean and inertia. Findings indicate that greater predictability in day-to-day negative affect is an important dynamic feature of depression. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Study on the dynamic characteristics of double row self-aligning roller bearings with surface faults

Purpose The aim of this study is to establish the nonlinear dynamics equations of roller bearings with surface faults on outer raceway, inner raceway and rolling elements to analyze the dynamic characteristics of the double row self-aligning roller bearings, and provided theoretical basis for bearing fault diagnosis and life prediction. Design/methodology/approach First, based on the momentum theorem, the formulas for quantitative calculation of impact load were established, when roller was in contact with the fault of the inner or outer raceway. Then, the fault position piecewise functions and the load-carrying zone piecewise functions were established. Based on these, the nonlinear dynamic equations of double row self-aligning roller bearings are established, and Matlab is used to simulate the faulty bearings at different positions, sizes and rotational speeds. Finally, the vibration test of the fault bearings are completed, and the correctness of the nonlinear dynamic equations of the rolling bearing are verified. Findings The simulation and test results show that: the impact load increased with the increasing rotate speed and fault size, and the larger the fault size, the longer the impact load existed and the shorter vice versa. Originality/value The nonlinear dynamic equation of double row self-aligning roller bearings is established, which provides a theoretical basis for bearing faults diagnosis and fatigue life prediction.

An optimization-based equilibrium measure describing fixed points of non-equilibrium dynamics: application to the edge of chaos

Understanding neural dynamics is a central topic in machine learning, non-linear physics, and neuroscience. However, the dynamics are non-linear, stochastic and particularly non-gradient, i.e., the driving force cannot be written as the gradient of a potential. These features make analytic studies very challenging. The common tool is the path integral approach or dynamical mean-field theory. Still, the drawback is that one has to solve the integro-differential or dynamical mean-field equations, which is computationally expensive and has no closed-form solutions in general. From the associated Fokker–Planck equation, the steady-state solution is generally unknown. Here, we treat searching for the fixed points as an optimization problem, and construct an approximate potential related to the speed of the dynamics, and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics. Only in the zero temperature limit, can the distribution of the original fixed points be achieved. The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure. Within this framework, the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method, which leads naturally to order parameters for the non-equilibrium steady states. Our theory reproduces the well-known result of edge-of-chaos. Furthermore, the order parameters characterizing the continuous transition are derived, and the order parameters are explained as fluctuations and responses of the steady states. Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.

A bird wing-inspired low-frequency double pendulum piezoelectric energy harvester with stoppers-assisted bending vibration

A bird wing-inspired low-frequency double pendulum piezoelectric energy harvester with stoppers-assisted bending vibration

Nonlinear Vibrations of Wind Towers with Variable Cross Section and Elastic Foundation Under Base Excitation

In this work, the nonlinear vibrations of coupled tower-nacelle-blade system, considering variable cross section and elastic foundation, subjected to base excitation (harmonic and seisme) are studied. For this, the nonlinear Euler-Bernoulli beam theory is applied to model the tower and nacelle and the elastic base is described as a Winkler model, considering contact problem. The Rayleigh-Ritz method together with Hamilton principle are applied to obtain the set of nonlinear dynamic equilibrium equations which are, in turn, solved with the fourth order Runge-Kutta method. Numerical results show the strong influence of parameters and base excitation on the natural frequencies, on the resonance curves and on bifurcation diagrams.

Optimization analysis of carrier-track collision in braiding process

Abstract The relationship between the speed of the driver plate and the collision of the spindle and the track is studied in this work. It is theoretically analyzed that the spindle will collide with the track in different degrees in the process of motion, and the impact is more intense due to the vibration of the mechanism. First, the dynamic equation of the spindle-track model is established. Then, fireworks algorithm is used to optimize the speed of the driver plate, to reduce the collision and impact times of the spindle on the track, so as to reduce the severe collision times between the spindle and the track, resulting in the wear of mechanical parts and affecting the braiding effect. Finally, it is concluded that the number of collisions increases sharply with the increase in recovery coefficient when the random disturbance is not considered; second, the number of collisions decreases with the appropriate increase in friction coefficient when the random disturbance is not considered; and third, the number of collisions increases sharply with the increase in random disturbance.

A novel analytical tool for complex propagation processes in networks: High-order dynamic equation.

Controlling the spread of epidemics in complex networks has always been an important research problem in the field of network science and has been widely studied by many scholars so far. One of the key problems in the transmission process of epidemics in complex networks is the transmission mechanism. At present, the transmission mechanism in complex networks can be divided into simple transmission and complex transmission. Simple transmission has been widely studied and the theory is relatively mature, while complex transmission still has many questions to answer. In fact, in the complex transmission process, the higher-order structure of the network plays a very important role, which can affect the transmission speed, final scale, and transmission path of the epidemic by strengthening the mechanism. However, due to the lack of complex dynamic analysis tools, the measurement of influence on propagation is still at the low-dimensional node level. Therefore, in this paper, we propose a set of closed dynamic higher-order structure equations to gain insight into the complex propagation process in the network, which breaks the inherent thinking and enables us to reexamine the complex dynamic behavior more clearly from the higher-order level rather than just from the node level, opening up a new way to analyze the higher-order interaction on the dynamic network. We apply the proposed high-order dynamic equations to a complex susceptible-infection-recovery epidemiological model on two real and synthetic networks, and extensive numerical simulation results demonstrate the effectiveness of the proposed approach. Our research results help to deepen the understanding of the relationship between complex propagation mechanisms and higher-order structures and develop a complete set of complex dynamic analysis tools that can be extended to higher-order forms to help in-depth understanding of the propagation rules and mechanisms in complex propagation processes, providing an important theoretical basis for predicting, analyzing, and controlling complex propagation processes.