Dynamic Equations Research Articles

Nonlinear evolution characteristics and seepage mechanical model of fluids in broken rock mass based on the bifurcation theory

With the deep extension of coal mining in China, fault water inrush has become one of the major disasters threatening the safety production of coal mine. Based on the control equations of steady state and non-Darcy seepage in fractured rock mass, the multi-parameter nonlinear dynamic seepage equations of fractured rock mass are established in this paper. Based on the nonlinear dynamics theory, the function of the state variable in the system is derived, and the influence of the gradual change of non-Darcy flow factors on the structural stability of seepage system is studied. The research achievements show that there are three branches in the equilibrium state of the seepage system. Specifically, the stability of the equilibrium state changes abruptly near the limit parameter. The seepage dynamic system of fractured rock mass has the delayed bifurcation, and the coal mine disaster such as fault water inrush occurs easily at the bifurcation point. The research results are of great significance to enrich the theory of fault water inrush in coal mine, and to reveal the disastrous mechanism of fault water inrush and guide its prevention and control technology in coal mine, which can provide the theoretical reference for predicting the water seepage stability in fractured rock mass.

Free vibration analysis of laminated anisotropic doubly-curved shell structures reinforced with three-phase polymer/CNT/fiber material

The present work investigates the vibrational response of laminated anisotropic doubly-curved shell structures reinforced with Carbon Nanotubes (CNTs) short fibers. The fundamental equations are derived from a curvilinear reference system of principal coordinates, employing the Equivalent Single Layer (ESL) methodology. Furthermore, a general variation in laminate thickness is considered. The unknown field variable is described using higher order theories through the unified formulation, taking into account a general interpolation of the unknown variables with Lagrange polynomials across the physical domain. The Hamiltonian Principle is adopted for the derivation of the dynamic equilibrium equations, which arediscretized numerically by using the Generalized Differential Quadrature (GDQ) method. In addition, an efficient isogeometric NURBS-based mapping is adopted for the distortion of the physical domain. The boundary conditions of the differential problem are modelled through a general distribution of linear elastic springs along the lateral surfaces of the three-dimensional doubly-curved solid. The theory is then applied to study the vibrational modes of structures with different curvatures and lamination schemes, taking into account a general distribution of CNTs along the thickness direction. The homogenized properties of CNTs layers are obtained from the Mori-Tanaka procedure, which accounts for the agglomeration effects of the dispersed nanofibers within the matrix. Unlike previous studies focusing on doubly-curved shells reinforced with composite materials and CNTs, the present formulation enables to derive the vibration characteristics of structures made of generally anisotropic materials with general orientations. Furthermore, the calibration of the parameters for the linear elastic springs’ distribution leads to general external constraints within a single element, thus reducing the computational cost of the problem.

Asymptotically safe cosmology with non-canonical scalar field

Abstract We investigate the quantum modified cosmological dynamical equations in a Friedmann-Robertson-Walker universe filled with a barotropic fluid and a general non-canonical scalar field characterized by a Lagrangian similar to k-essence model but with a potential term. Quantum corrections are incorporated by considering the running of gravitational and potential couplings, employing the functional renormalization group approach. Covariant conservation of the non-canonical scalar field and the background barotropic fluid is considered separately, imposing a constraint resulting from the Bianchi identity. This constraint determines the evolution of the cut-off scale with the scale factor and also reveals cosmic fixed points, depending on whether the flow ceases or continues to evolve. We explore how the general non-canonical scalar field parameter affects the different types of cosmic fixed points and how it differs from the canonical case. Furthermore, we establish a bound on the ratio of the RG parameters involving the non-canonical parameter for which the universe may exhibit accelerated expansion for mixed fixed points. This bound indicates the non-canonical scalar field includes larger sets of RG fixed point which may give rise to an accelerated universe.

An evolutionary game and system dynamics approach for the production and consumption of carbon-labeled products-based on a media monitoring perspective

Carbon label is acknowledged as an effective way to combat the problem of global warming. As a powerful way to encourage individuals to adjust their consumption patterns and to promote the development of green consumption, carbon-labeled products are widely developed in China. To reveal the production and consumption process of carbon-labeled products, the present study constructs a tripartite game model consisting of the government, carbon-labeled products manufacturers and consumers based on a media monitoring perspective. The evolutionary stability strategy (ESS) is firstly determined by solving the replication dynamic equations and stability analysis of the equilibrium point, followed by the strategy analysis and sensitivity analysis through numerical simulation. The results show that media supervision can effectively complement and constrain government supervision. In addition, it can promote enterprises to standardize production and enhance consumers' trust and willingness to buy carbon-labeled products. The introduction of media supervision can well realize the ideal equilibrium of "effective government supervision, enterprise compliance and consumer support for purchase".

Angular acceleration estimation and aerodynamic parameter identification based on angular velocity equivalent model

Conventional angular acceleration estimation methods generate non-negligible errors when the control surface rapidly deflects; hence, the estimated angular acceleration cannot be used for aerodynamic parameter identification directly. This paper proposes an angular acceleration estimation method based on angular velocity equivalent model. The angular acceleration of the angular velocity equivalent model, whose angular velocity response is consistent with the flight test data, is used as the estimated angular acceleration. Firstly, the equivalent angular velocity model is established by combining the generic aerodynamic model with the rotational dynamic equations of aircraft. Secondly, the angular velocity data and the control surface deflection data are synchronized. Finally, the angular velocity response of the equivalent model is used as the predictor, and the estimated angular acceleration is obtained by extended Kalman filter. The aerodynamic parameter identification and validation are carried out using the estimated angular acceleration of a large civil aircraft flight test data. The results show that the angular acceleration obtained through the proposed angular acceleration estimation method meets the accuracy requirement of aerodynamic parameter identification.

New Design and Prototype of Two Degrees-of-Freedom Planar Parallel Manipulator for Use in Creating an Infinite 3D Printer

Abstract This paper presents a novel two degrees-of-freedom planar parallel manipulator (PPM) designed for infinite-axis 3D printing, alongside tools for facilitating future design iterations. Unlike traditional gantry-supported designs used in infinite-axis 3D printing, which impose significant mass movement requirements, the examined new design prioritizes reducing overall weight to enhance speed potential at the cost of a reduced work area. In this innovative approach, the PPM effectively reduces weight by decoupling the motion of the hot end from that of the motor. Motors are attached to the frame, controlling a system of pulleys, and connecting arms to drive the hot-end's motion. Due to the length of the arms, the hot end will be unable to fully explore the entire printing plane. Verification of the angled PPM for 3D printing involved developing kinematic and dynamic equations, conducting finite element analysis on critical components, and testing a completed prototype. A metaheuristic optimization method was employed to derive optimal design parameters, focusing on optimizing the arm length of the connectors while maximizing dynamic performance. Considerations included the usable workspace and the angle between the connecting arm and end-effector. The final prototype validated the stability and rigidity of the PPM during movement, indicating its viability for 3D printing. The results presented in this paper demonstrate the capabilities of using an angled PPM in infinite 3D printing, providing fundamental knowledge crucial for future designs involving this innovative mechanism.

LSTM network optimization and task network construction based on heuristic algorithm

This work aims to advance the security management of complex networks to better align with evolving societal needs. The work employs the Ant Colony Optimization algorithm in conjunction with Long Short-Term Memory neural networks to reconstruct and optimize task networks derived from time series data. Additionally, a trend-based noise smoothing scheme is introduced to mitigate data noise effectively. The approach entails a thorough analysis of historical data, followed by applying trend-based noise smoothing, rendering the processed data more scientifically robust. Subsequently, the network reconstruction problem for time series data originating from one-dimensional dynamic equations is addressed using an algorithm based on the principles of Stochastic Gradient Descent (SGD). This algorithm decomposes time series data into smaller samples and yields optimal learning outcomes in conjunction with an adaptive learning rate SGD approach. Experimental results corroborate the remarkable fidelity of the weight matrix reconstructed by this algorithm to the true weight matrix. Moreover, the algorithm exhibits efficient convergence with increasing data volume, manifesting shorter time requirements per iteration while ensuring the attainment of optimal solutions. When the sample size remains constant, the algorithm’s execution time is directly proportional to the square of the number of nodes. Conversely, as the sample size scales, the SGD algorithm capitalizes on the availability of more information, resulting in improved learning outcomes. Notably, when the noise standard deviation is 0.01, models predicated on SGD and the Least-Squares Method (LSM) demonstrate reduced errors compared to instances with a noise standard deviation of 0.1, highlighting the sensitivity of LSM to noise. The proposed methodology offers valuable insights for advancing research in complex network studies.

Asymptotics and oscillation for certain higher-order nonlinear dynamic equations on time scales

Asymptotics and oscillation for certain higher-order nonlinear dynamic equations on time scales

Dynamic Height Growth Equations and Site Index-Based Biomass Models for Young Native Species Afforestations in Spain

The expansion of forested areas through afforestation and reforestation is widely recognized as a highly effective natural solution for mitigating climate change. Accurately assessing the potential carbon uptake capacity of newly afforested areas requires modelling tools to estimate biomass stocks, including site index curves and biomass models. Given the unique conditions in terms of tree size, uniform spacing, and tree allometries observed in young afforestations compared to natural stands, specific tools are necessary. In Spain, over 800,000 ha has been afforested with native forest species since 1992, but specific modelling tools for these plantations are lacking. Using data from 370 stem analyses collected across an extensive network of plots in young afforestations, we developed dynamic height growth and site index models for the main native species (five pines and five oaks) commonly used in afforestation in Spain. We compared various nonlinear models, such as ADA (algebraic difference approach) and GADA (generalized algebraic difference approach) expansions. The developed site index models were then used to predict the total biomass stored in the afforestation. Our results underscore the necessity for specific site index models tailored to afforestations, as well as the potential of the established site index in predicting biomass and carbon fixation capacity in these young forests.

A fast solution method for the interaction between the rigid overhead contact system and pantograph on long railway lines

Currently, simulation is an important method for studying the interaction between the pantograph and the rigid overhead contact system (ROCS). However, when solving the ROCS model for long railway line scenarios, the problem of intractable or inefficient computation arises due to the excessively large size of the matrix. To address this issue, this paper proposes a method called: a fast solution method for the interaction between the rigid overhead contact system and pantograph on long railway lines based on a coupled window approach (hereinafter referred to as: CW-RCP). The CW-RCP method utilises coupled windows to simulate the ROCS model, effectively limiting the length of the ROCS involved in each computation. This approach greatly enhances computational efficiency. After deriving the dynamic equations and solving equations of the CW-RCP method in detail, the effectiveness, advantages, and applications of this method are discussed. The results demonstrate that the CW-RCP method can effectively compensate for the computational inefficiencies of traditional methods without compromising computational accuracy.

Evolutionary game analysis on cross-border cooperative R&D of intelligent new energy vehicle industry

PurposeIntelligent new energy vehicles (INEVs) are becoming the competitive hotspot for the automobile industry. The major purpose of this study is to determine how to increase innovation efficiency through knowledge sharing and technology spill between new energy vehicle (NEV) enterprises and technology enterprises. This will help to improve the core competence of the automobile industry in China. Also, it serves as a guide for the growth of other strategic.Design/methodology/approachThe authors construct a tripartite evolutionary game model to study the cross-border cooperative innovation problem. Firstly, the payment matrix of NEV enterprise, technology enterprise and government is established, and the expected revenue of each participant is determined. Then, the replication dynamic equations and evolutionary stability strategies are analyzed. Finally, the theoretical research is validated through numerical simulation.FindingsResults showed that: (1) An optimal range of revenue distribution coefficient exists in the cross-border cooperation. (2) Factors like research and development (R&D) success rate, subsidies, resource and technology complementarity, and vehicles intelligence positively influence the evolution towards cooperative strategies. (3) Factors like technology spillover risk cost inhibit the evolution towards cooperative strategies. To be specific, when the technology spillover risk cost is greater than 2.5, two enterprises are inclined to choose independent R&D, and the government chooses to provide subsidy.Research limitations/implicationsThe research perspective and theoretical analysis are helpful to further explore the cross-border cooperation of the intelligent automobile industry. The findings suggest that the government can optimize the subsidy policy according to the R&D capability and resource allocation of automobile industry. Moreover, measures are needed to reduce the risk of technology spillovers to encourage enterprise to collaborate and innovate. The results can provide reference for enterprises’ strategic choice and government’s policy making.Originality/valueThe INEV industry has become an important development direction of the global automobile industry. However, there is limited research on cross-border cooperation of INEV industry. Hence, authors construct a tripartite evolutionary game model involving NEV enterprise, technology enterprise and the government, and explore the relationship of cooperation and competition among players in the INEV industry, which provides a new perspective for the development of the INEV industry.

Dynamic optimization of nonlinear differential game problems using orthogonal collocation with analytical sensitivities

AbstractThis article presents an effective computational method based on the orthogonal collocation on finite element for nonlinear pursuit‐evasion differential game problems. The original problems are transformed into two dynamic optimization problems at first, so that the difficulty of obtaining the solution is reduced. To improve the convergence rate and the efficiency, the sensitivities describing the influence of control and interval parameters on state are derived through the discretized dynamic equations for the resulting nonlinear programming problem. The convergence speed is introduced to measure the performance in the upper level iteration. The main structure and the algorithm of the method are also given. Two demonstrative differential game problems with different scenarios from practice are studied. Compared with the approach without sensitivity information, the proposed method needs less function evaluations and saves at least 68.4% of the computational time. The research results show the effectiveness of proposed approach.

Observer-based model-free controller for the perturbations estimation and attenuation in robotic plants

The model-free controller is a powerful method because it does not require the knowledge of the robotic plant dynamic equation. Since most of the model-free controllers consider variants of the adaptive or reinforcement learning, one observer-based model-free controller could be a different alternative of interest in the researching community. In this study, an observer-based model-free controller is suggested for the perturbations estimation and attenuation in robotic plants, it contains the model-free observer and the model-free controller. The model-free observer based on the high gain method uses the bounds of the perturbations. The model-free controller based on the sliding mode method uses the bounds of the perturbations and gravity terms. The observer-based model-free controller is applied for the perturbations estimation and attenuation in a cylindrical robotic plant, and a scalar robotic plant.

ON SOME INEQUALITIES FOR EXPONENTIALLY WEIGHTED FRACTIONAL HARDY OPERATORS WITH ∆-INTEGRAL CALCULUS

Dynamic equations, inequalities and operators are the indispensable cornerstones of harmonic analysis and time scale calculus. We know that the topics in question have many applications in different scientific fields. In this paper, some inequalities will be proved for variable exponentially weighted Hardy operators with ∆-integral calculus.

Rigorous justification of the hydrostatic approximation limit of viscous compressible flows

This paper considers the asymptotic limit of small aspect ratio between vertical and horizontal spatial scales for viscous isothermal compressible flows. In particular, it is observed that fast vertical acoustic waves arise and induce an averaging mechanism of the density in the vertical variable, which at the limit leads to the hydrostatic approximation of compressible flows, i.e., the compressible primitive equations of atmospheric dynamics. We justify the hydrostatic approximation for general as well as “well-prepared” initial data. The initial data is called well-prepared when it is close to the hydrostatic balance in a strong topology. Moreover, the convergence rate is calculated in the well-prepared initial data case in terms of the aspect ratio, as the latter goes to zero.

From attentional fluctuations to intentional fluctuations? Monitoring behavior and intraindividual variability in time-based prospective memory.

In sharp contrast to event-based prospective memory (PM), dynamics of (re)allocation of attention between the ongoing and PM tasks have been much less investigated in time-based PM tasks. We propose an in-depth examination of attention allocation in a time-based PM task by jointly analyzing multiple indicators of time-monitoring behavior, net and time-structured intraindividual variability (IIV) in ongoing-task reaction times (OT RTs), and task performance. Results from dynamic structural equation modeling in a lifespan sample of 198 adults (19-86 years) revealed that larger fluctuations in OT RTs (net IIV) predicted poorer OT performance, but fostered a more efficient pattern of time-monitoring behavior (i.e., checking a clock more frequently and strategically, and slowing OT RTs during the PM response window) that, in turn, enhanced PM. Conversely, greater inertia in OT RTs (time-structured IIV) led to fewer clock-checks and poorer PM performance. Focusing attention on time monitoring to enhance PM performance did not detrimentally affect OT accuracy. Instead, participants showed a speed-accuracy tradeoff to optimize both OT and PM accuracies by slowing their OT RTs during the PM response window. This study therefore shows that two concomitant aspects of IIV (net and time-structured IIV) not only predicted time-monitoring behavior, but also OT and PM accuracies differentially, hence advocating for the necessity to consider both aspects of IIV and time monitoring together to better understand attention allocation policies in time-based PM tasks. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A new control method for leader–follower consensus problem of uncertain constrained nonlinear multi-agent systems

The design of Adaptive Fuzzy Sliding-Mode Control (AFSMC) is discussed in this study for the distributed leader–follower consensus problem of nonlinear uncertain multi-agent systems with input and state constraints. Avoiding the critical circumstances related to the violation of input and state constraints is an important issue in the design of consensus control systems. The limitations of existing adaptive consensus controllers developed for full-state constrained systems motivated the present novel method without restrictive structural assumptions. To convert the original problem to an unconstrained consensus control problem, the proposed control system uses a barrier function-based state transformation method and the input-state linearization methodology. As a result, each agent’s adaptive fuzzy sliding-mode control input, which consists of a fuzzy system and a robust term, is constructed based on the derived representation of the system dynamics. The fuzzy system is used to approximate the dynamic equations of the agent, its neighbors, and maybe the leader in each local feedback control law structure, and the robust term is designed to compensate for the fuzzy approximation error. The magnitudes of the robust terms and the output vectors of the fuzzy systems are also determined using the proposed adaptation laws. The second Lyapunov theorem and Barbalat’s lemma are used to verify the closed-loop system’s asymptotic stability. The effectuality of the proposed methodology is confirmed by numerical simulations for several Autonomous Underwater Vehicles (AUVs). Simulation results show that by means of the proposed AFSMC, the leader–follower consensus is achieved without state constraint violation and performance degradation.

Modelling and dynamic characterisation of a double-pendulum overhead crane carrying a distributed-mass payload

In industries, cranes are commonly used for transportation of a distributed-mass payload (DMP). However, analysis of the dynamic characteristics of such a system is limited since most of the research work considered a point-mass payload. This paper presents modelling and analysis of dynamic characteristics of a double-pendulum overhead crane carrying a DMP with and without payload hoisting. Nonlinear dynamic models representing the crane in both scenarios are derived. The effects of varying cable lengths, and carrying different payload masses and lengths on the dynamics of hook and payload oscillations are also studied. Simulations are performed to observe the dynamic characteristics of the crane under several conditions, and experiments are carried out to validate the theory and simulation results, and to assess the accuracy of the derived nonlinear dynamic equations. The results demonstrate that the payload oscillation is significantly affected by changes in the cable lengths and DMP parameters. In addition, satisfactory agreements between simulation and experimental results are achieved, which indicate validity of the nonlinear models and good compliance with the theory. It is envisaged that the dynamic characteristic analyses of the crane can be beneficial in designing efficient controllers, especially in suppressing DMP oscillation.

Accurately estimating the scanning angle of an electrostatic MEMS mirror with a novel damping model

A novel damping model to accurately analyze the scanning angle of electrostatic microelectromechanical system (MEMS) mirrors is proposed in this article. The computational fluid dynamic (CFD) simulations are used to calculate the aerodynamic moment of the MEMS mirror oscillating in air. The simulation results demonstrate the linear dependence of the equivalent damping coefficient of the MEMS mirror on the oscillation amplitude and frequency. Then the equivalent damping expression of the MEMS mirror is established. The damping model is applied to the dynamic equation of the MEMS mirror for numerical solution. The frequency responses of the electrostatic MEMS mirror under square wave excitation with different voltage amplitudes and duty cycles are obtained. The measurement results provide good accuracy verification for numerical results. This verifies the accuracy of the proposed damping model, which can be used to accurately estimate the scanning angle in the design and parameter optimization process of electrostatic MEMS mirrors.

Impulsive fractional dynamic equation with non-local initial condition on time scales

In this manuscript we investigate the existence and uniqueness of an im-pulsive fractional dynamic equation on time scales involving non-local initial condition with help of Caputo nabla derivative. The existency is based on the Scheafer’s fixed point theorem along with the Arzela-Ascoli theorem and Banach contraction theorem. The comparison of the Caputo nabla derivative and Riemann-Liouvile nabla derivative of fractional order are also discussed in the context of time scale.