Generalization of the Second Order Vector Potential Formulation for Arbitrary Non-Orthogonal Curvilinear Coordinates Systems from the Covariant Form of Maxwell's Equations

A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.

Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

Stochastic programming based coordinated expansion planning of generation,transmission,demand side resources,and energy storage considering the DC transmission system

With the increasing penetration of wind and solar energies,the accompanying uncertainty that propagates in the system places higher requirements on the expansion planning of power systems.A source-grid-load-storage coordinated expansion planning model based on stochastic programming was proposed to suppress the impact of wind and solar energy fluctuations.Multiple types of system components,including demand response service entities,converter stations,DC transmission systems,cascade hydropower stations,and other traditional components,have been extensively modeled.Moreover,energy storage systems are considered to improve the accommodation level of renewable energy and alleviate the influence of intermittence.Demand-response service entities from the load side are used to reduce and move the demand during peak load periods.The uncertainties in wind,solar energy,and loads were simulated using stochastic programming.Finally,the effectiveness of the proposed model is verified through numerical simulations.

Coupling Coordination Analysis of Cropland Intensification and Agroecosystem Services:Evidence from Loess Plateau in Shaanxi Province,China

One of the greatest challenges in the agroecosystem is to improve cropland intensification while preserving agroecosystem services.While many studies have investigated the effect of cropland intensification on agroecosystem service,the interactive coupling and coordination among these factors remain largely unexplored.In view of this,this study performed a case study of the Loess Plateau in Shaanxi Province,China and constructed comprehensive evaluation models to quantify the cropland intensification and agroecosystem service in this area.Balance analysis and the coupling coordination degree model were used to evaluate the interactive relationship between cropland intensification and agroecosystem service,and statistical analysis and spatial autocorrelation were used to analyze the spatial characteristics and potential mechanism of the coupling coordination.Results show that both the cropland intensification and agroecosystem service in the study area were relatively low yet gradually increased from 2000 to 2020.Agroecosystem service lag was identified as the dominant unbalanced development type.Improving the supply capacity of agroecosystem services plays a key role in the balanced development of cropland in the Loess Plateau.The coupling coordination degree between cropland intensification and agroecosystem service ranges from basic coordination to serious incoordination.Therefore,cropland intensification practices in the area should be optimized to enhance this coordination degree.An upward trend was also observed in the coupling coordination degree from2000 to 2020.The withdrawal of marginal cropland in the Grain for Green program is one of the most important reasons for this trend,especially for the northern region.Around 83.6%of the high-high clusters are concentrated in the southern region of the Loess Plateau,whereas 70.5%of the low-low clusters are distributed in the northern region.These clustering characteristics are mainly attributed to the environmental suitability of these areas for agriculture and their degree of economic development.

A coordinated operation method of wind-PV-hydrogenstorage multi-agent energy system

Wind-photovoltaic(PV)-hydrogen-storage multi-agent energy systems are expected to play an important role in promoting renewable power utilization and decarbonization.In this study,a coordinated operation method was proposed for a wind-PVhydrogen-storage multi-agent energy system.First,a coordinated operation model was formulated for each agent considering peer-to-peer power trading.Second,a coordinated operation interactive framework for a multi-agent energy system was proposed based on the theory of the alternating direction method of multipliers.Third,a distributed interactive algorithm was proposed to protect the privacy of each agent and solve coordinated operation strategies.Finally,the effectiveness of the proposed coordinated operation method was tested on multi-agent energy systems with different structures,and the operational revenues of the wind power,PV,hydrogen,and energy storage agents of the proposed coordinated operation model were improved by approximately 59.19%,233.28%,16.75%,and 145.56%,respectively,compared with the independent operation model.

Carrying Capacity and Coupling Coordination of Water and Land Resources Systems in Arid and Semi-arid Areas: A Case Study of Yulin City, China

Quantitatively assessing the carrying capacity of water and land resources systems in arid and semi-arid areas is crucial for achieving the 2030 Sustainable Development Goals.In this work,taking Yulin City in China as a case study and employing the Criteria Importance Through Intercriteria Correlation(CRITIC)method,a modified model of coupling degree was developed to evaluate the car-rying capacity of water and land resources systems endowment and utilization,as well as their coupling coordination degree from 2013 to 2020.Our findings indicate that the water and land resources of Yulin are diminishing due to declines in agriculture,higher industrial water use,and wetland shrinkage.However,reallocating domestic water for ecological sustainability and reducing sloping farmland can mitigate this trend of decline.Temporally,as the coupling coordination between water and land resources system endowment in Yulin continuously improved,the coupling coordination between water and land resources system utilization first decreased and then in-creased with 2016 as the turning point.Spatially,the carrying capacity of water and land resources systems,the coupling coordination degree between water and land resources system endowment,and the coupling coordination degree between water and land resources system utilization in Yulin exhibited the same pattern of being higher in the six northern counties than in the six southern counties.Improving the water resources endowment is vital for the highly efficient use of water and land resources.

Coupling and coordination relationship of tourism inclusive green growth system:Evidence from Shandong Province

Sustainable growth is a prerequisite for high-quality development,and inclusive green growth is regarded as an important way to realize sustainable growth.This paper constructs a tourism inclusive green growth index(IGGI)system based on the 2018 Asian Development Bank IGGI.Using Shandong Province from 2017 to 2019,the entropy weight method is utilized to explore the degree of coupling and coordination among the subsystems of tourism inclusive green growth.The study shows that:(1)the tourism IGGI continues to grow;(2)in the tourism inclusive green growth system,the social equity subsystem shows a trend of steady improvement;and(3)in the system,there is a slight discordance between the economic growth subsystem and the environmental sustainability subsystem.The study aims to provide the scientific basis for the high-quality development of tourism and theoretical support for the field of tourism and environmental sustainability.

UAV-assisted cooperative offloading energy efficiency system for mobile edge computing

Reliable communication and intensive computing power cannot be provided effectively by temporary hot spots in disaster areas and complex terrain ground infrastructure.Mitigating this has greatly developed the application and integration of UAV and Mobile Edge Computing(MEC)to the Internet of Things(loT).However,problems such as multi-user and huge data flow in large areas,which contradict the reality that a single UAV is constrained by limited computing power,still exist.Due to allowing UAV collaboration to accomplish complex tasks,cooperative task offloading between multiple UAVs must meet the interdependence of tasks and realize parallel processing,which reduces the computing power consumption and endurance pressure of terminals.Considering the computing requirements of the user terminal,delay constraint of a computing task,energy constraint,and safe distance of UAV,we constructed a UAV-Assisted cooperative offloading energy efficiency system for mobile edge computing to minimize user terminal energy consumption.However,the resulting optimization problem is originally nonconvex and thus,difficult to solve optimally.To tackle this problem,we developed an energy efficiency optimization algorithm using Block Coordinate Descent(BCD)that decomposes the problem into three convex subproblems.Furthermore,we jointly optimized the number of local computing tasks,number of computing offloaded tasks,trajectories of UAV,and offloading matching relationship between multi-UAVs and multiuser terminals.Simulation results show that the proposed approach is suitable for different channel conditions and significantly saves the user terminal energy consumption compared with other benchmark schemes.

A Remark on the Affine Coordinates for KdV Tau-Functions

We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.

Optimal Operation Strategy of Electricity-Hydrogen Regional Energy System under Carbon-Electricity Market Trading

Given the“double carbon”objective and the drive toward low-carbon power,investigating the integration and interaction within the carbon-electricity market can enhance renewable energy utilization and facilitate energy conservation and emission reduction endeavors.However,further research is necessary to explore operational optimization methods for establishing a regional energy system using Power-to-Hydrogen(P2H)technology,focusing on participating in combined carbon-electricity market transactions.This study introduces an innovative Electro-Hydrogen Regional Energy System(EHRES)in this context.This system integrates renewable energy sources,a P2H system,cogeneration units,and energy storage devices.The core purpose of this integration is to optimize renewable energy utilization and minimize carbon emissions.This study aims to formulate an optimal operational strategy for EHRES,enabling its dynamic engagement in carbon-electricity market transactions.The initial phase entails establishing the technological framework of the electricity-hydrogen coupling system integrated with P2H.Subsequently,an analysis is conducted to examine the operational mode of EHRES as it participates in carbon-electricity market transactions.Additionally,the system scheduling model includes a stepped carbon trading price mechanism,considering the combined heat and power generation characteristics of the Hydrogen Fuel Cell(HFC).This facilitates the establishment of an optimal operational model for EHRES,aiming to minimize the overall operating cost.The simulation example illustrates that the coordinated operation of EHRES in carbon-electricity market transactions holds the potential to improve renewable energy utilization and reduce the overall system cost.This result carries significant implications for attaining advantages in both low-carbon and economic aspects.

Designing a Protection Scheme in Micro-Grid Systems with DG Using Central Protection Unite and Multiple Setting Group Protection Relays

Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this continuous changes in generation condition, the fault current level in network will be affected, this changes in fault current level will affect in the coordination between protection relays and to keep the coordination at right way, an adaptive protection system is required that can adaptive its setting according to generation changes, the fault current level in each case is evaluated using ETAP software, and the required relay setting in each case is also evaluated using Grey Wolf Optimizer (GWO) algorithm, and to select suitable setting which required in each condition, to select the active setting group of protection relay according to generation capacity, central protection unite can be used, and to improve protection stability and minimizing relays tripping time, a proposed method for selecting suitable backup relay is used, which leads to decrease relays tripping time and increase system stability, output settings for relays in all cases achieved our constrains.

Lie Symmetries and Conserved Quantities of Holonomic Systems with Remainder Coordinates

Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.

Sensitivity Analysis Approach to Multibody Systems Described by Natural Coordinates

The classical natural coordinate modeling method which removes the Euler angles and Euler parameters from the governing equations is particularly suitable for the sensitivity analysis and optimization of multibody systems. However, the formulation has so many principles in choosing the generalized coordinates that it hinders the implementation of modeling automation, A first order direct sensitivity analysis approach to multibody systems formulated with novel natural coordinates is presented. Firstly, a new selection method for natural coordinate is developed. The method introduces 12 coordinates to describe the position and orientation of a spatial object. On the basis of the proposed natural coordinates, rigid constraint conditions, the basic constraint elements as well as the initial conditions for the governing equations are derived. Considering the characteristics of the governing equations, the newly proposed generalized-ct integration method is used and the corresponding algorithm flowchart is discussed. The objective function, the detailed analysis process of first order direct sensitivity analysis and related solving strategy are provided based on the previous modeling system Finally, in order to verify the validity and accuracy of the method presented, the sensitivity analysis of a planar spinner-slider mechanism and a spatial crank-slider mechanism are conducted. The test results agree well with that of the finite difference method, and the maximum absolute deviation of the results is less than 3%. The proposed approach is not only convenient for automatic modeling, but also helpful for the reduction of the complexity of sensitivity analysis, which provides a practical and effective way to obtain sensitivity for the optimization problems of multibody systems.

Generalized Lutzky Conserved Quantities of Holonomic Systems with Remainder Coordinates Subjected to Unilateral Constraints

This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The differential equations of motion of the system are established, and the definition of Lie symmetry for the system is given. The conditions under which a Lie symmetry can directly lead up to a generalized Lutzky conserved quantity and the form of the new conserved quantity are obtained, and an example is given to illustrate the application of the results.

Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.

Application of canonical coordinates for solving single-freedom constraint mechanical systems

This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.

A Comprehensive Evaluation Framework of Water-Energy-Food System Coupling Coordination in the Yellow River Basin,China

For mankind’s survival and development,water,energy,and food(WEF)are essential material guarantees.In China,however,the spatial distribution of WEF is seriously unbalanced and mismatched.Here,a collaborative governance mechanism that aims at nexus security needs to be urgently established.In this paper,the Yellow River Basin in China with a representative WEF system,was selected as a case.Firstly,a comprehensive framework for WEF coupling coordination was constructed,and the relationship and mechanism between them were analyzed theoretically.Then,we investigated the spatiotemporal characteristics and driving mechanisms of the coupling coordination degree(CCD)with a composite evaluation method,coupling coordination degree model,spatial statistical analysis,and multiscale geographic weighted regression.Finally,policy implications were discussed to promote the coordinated development of the WEF system.The results showed that:1)WEF subsystems showed a significant imbalance of spatial pattern and diversity in temporal changes;2)the CCD for the WEF system varied little and remained at moderate coordination.Areas with moderate coordination have increased,while areas with superior coordination and mild disorder have decreased.In addition,the spatial clustering phenomenon of the CCD was significant and showed obvious characteristics of polarization;and 3)the action of each factor is self-differentiated and regionally variable.For different factors,GDP per capita was of particular importance,which contributed most to the regional development’s coupling coordination.For different regions,GDP per capita,average yearly precipitation,population density,and urbanization rate exhibited differences in geographical gradients in an east-west direction.The conclusion can provide references for regional resource allocation and sustainable development by enhancing WEF system utilization efficiency.

A Preliminary Study on the Theory of Polar Coordinates Digital Photogrammetry and the Coordinate System of Spatial Information

The development of new aeronautics and astronautics technologies has been constrained by strict mathematical rules for data processing among the diverse methods used to obtain spatial information.The acquisition of spatial information has been affected by various choices including the applied technologies(e.g.,push broom sensors),techniques(e.g.,zoom imaging),and equipment settings(e.g.,swing angle,aerial platform attitude,camera angle)in terms of the convergence,efficiency,and accuracy of the data.Based on the principle of the bionic machine parallax angle and pyramidal projection of the aerial space platform to the surface,this study explored solutions for high-resolution image sparsity,ill-conditioned singularity,and non-convergence by building a set of mathematical models to process the polar coordinates of the parallax angular vector.This study also formed a polar information theory for initial spatial information.This method improved the ranges of accuracy,efficiency,and anti-interference in close-range photogrammetry and the free net bundle adjustment model by several orders of magnitude.The open source code was made globally available more than 3 years ago,and has received positive reactions.The method’s effectiveness was verified using aerophotogrammetry and absolute network adjustment model experiments,and its performance was better than that of the Cartesian coordinate processing method.Finally,the higher-order solution characteristics of various applications and spaceflight platforms were provided,which are expected to provide a foundation for construction of a new polar coordinate system for aerospace multi-scale all-attitude spatial information acquisition,organization,management,storage,processing,and application.

Tracking Control of Multi-Agent Systems Using a Networked Predictive PID Tracking Scheme

With the rapid development of network technology and control technology,a networked multi-agent control system is a key direction of modern industrial control systems,such as industrial Internet systems.This paper studies the tracking control problem of networked multi-agent systems with communication constraints,where each agent has no information on the dynamics of other agents except their outputs.A networked predictive proportional integral derivative(PPID)tracking scheme is proposed to achieve the desired tracking performance,compensate actively for communication delays,and simplify implementation in a distributed manner.This scheme combines the past,present and predictive information of neighbour agents to form a tracking error signal for each agent,and applies the proportional,integral,and derivative of the agent tracking error signal to control each individual agent.The criteria of the stability and output tracking consensus of multi-agent systems with the networked PPID tracking scheme are derived through detailed analysis on the closed-loop systems.The effectiveness of the networked PPID tracking scheme is illustrated via an example.

Evaluation of the coordinated development of China’s forest resources-economy-environment system

Forests provide enormous ecological, economic, and social benefits, as such forest development should be ori‐ented toward resource-economy-environment harmonization. This paper constructs a comprehensive evalua‐tion index system and uses the coupled coordination degree model to measure the coordinated development level of China’ s forest resources-economy-environment system. The results show that, across 2006‒2020, the level of coupled coordinated development of China’ s forest resources-economy-environment composite system fluctuates in an upward trend, thus gradually developing from an initial imbalance to a high degree of coordi‐nation;the level of coordinated development of each subsystem of the forest resources, economy, and environ‐ment also shows an upward trend. The factors influencing the coordinated development of the forest resource economy-environment system are, in order, the government’ s financial capacity, market environment, scien‐tific and technological innovation capacity, level of economic development, and strength of policy implemen‐tation. Therefore, this paper proposes some measures to improve the coordinated development.