Interaction of Waves, Surface Currents, and Turbulence: the Application of Surface-Following Coordinate Systems

Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, either implicitly or explicitly. In order to calculate the effect of wind forcing on waves and currents, and vice versa, it is necessary to employ a consistent formula- tion of the energy and momentum balance within the airflow, wave field, and water column. It is very advantageous to apply sur- face-following coordinate systems, whereby the steep gradients in mean flow properties near the air-water interface in the cross-interface direction may be resolved over distances which are much smaller than the height of the waves themselves. We may account for the waves explicitly by employing a numerical spectral wave model, and applying a suitable theory of wave–mean flow interaction. If the mean flow is small compared with the wave phase speed, perturbation expansions of the hydrodynamic equations in a Lagrangian or generalized Lagrangian mean framework are useful: for stronger flows, such as for wind blowing over waves, the presence of critical levels where the mean flow velocity is equal to the wave phase speed necessitates the application of more general types of surface-following coordinate system. The interaction of the flow of air and water and associated differences in temperature and the concentration of various substances (such as gas species) gives rise to a complex boundary-layer structure at a wide range of vertical scales, from the sub-millimetre scales of gaseous diffusion, to several tens of metres for the turbulent Ekman layer. The bal- ance of momentum, heat, and mass is also affected significantly by breaking waves, which act to increase the effective area of the surface for mass transfer, and increase turbulent diffusive fluxes via the conversion of wave energy to turbulent kinetic energy.

Efficient object location determination and error analysis based on barycentric coordinates

In this paper,we propose an efficient computational method for converting local coordinates to world coordinates using specially structured coordinate data.The problem in question is the computation of world coordinates of an object throughout a motion,assuming that we only know the changing coordinates of some fixed surrounding reference points in the local coordinate system of the object.The proposed method is based on barycentric coordinates;by taking the aforementioned static positions as the vertices of a polyhedron,we can specify the coordinates of the object in each step with the help of barycentric coordinates.This approach can significantly help us to achieve more accurate results than by using other possible methods.In the paper,we describe the problem and barycentric coordinate-based solution in detail.We then compare the barycentric method with a technique based on transformation matrices,which we also tested for solving our problem.We also present various diagrams that demonstrate the efficiency of our proposed approach in terms of precision and performance.

Aerodynamics of flexible wing in bees' hovering flight

The aerodynamics of 2-dimensional flexible wings in bees＇ normal hovering flight is studied. Four insect flapping flight coordinate systems, including a global system, a bodyfixed system, a rigid wing-fixed system and a flexible wingfixed system, are established to represent the insects＇ position, gesture, wing movement and wing deformation, respectively. Then the transformations among four coordinate systems are studied. It is found that the elliptic coordinate system can improve the computation accuracy and reduce the calculation complexity in a 2-dimensional rigid wing. The computation model of a 2-dimensional flexible wing is established, and the changes of the force, moment, and power are investigated. According to the computation results, the large lift and drag peaks at the beginning and end of the stroke can be explained by the superposition of the rapid translational acceleration, the fast pitching-up rotation and the Magnus effect; and the small force and drag peaks can be explained by the convex flow effect and the concave flow effect. Compared with the pressure force, pressure moment and translational power, the viscous force, viscous moment and rotational power are small and can be ignored.

Necessary and Sufficient Conditions for the Separability and the R-Separability of the Irrotational Stokes Equation and Applications

In the present manuscript, we formulate and prove rigorously, necessary and sufficient conditions for all kinds of separation of variables that a solution of the irrotational Stokes equation may exhibit, in any orthogonal axisymmetric system, namely: simple separation and R-separation. These conditions may serve as a road map for obtaining the corresponding solution space of the irrotational Stokes equation, in any orthogonal axisymmetric coordinate system. Additionally, we investigate how the inversion of the coordinate system, with respect to a sphere, affects the type of separation. Specifically, we prove that if the irrotational Stokes equation separates variables in an axisymmetric coordinate system, then it R-separates variables in the corresponding inverted coordinate system. This is a quite useful outcome since it allows the derivation of solutions for a problem, from the knowledge of the solution of the same problem in the inverted geometry and vice-versa. Furthermore, as an illustration, we derive the eigenfunctions of the irrotational Stokes equation governing the flow past oblate spheroid particles and inverted oblate spheroidal particles.

A Formulation of Spin Dynamics Using Schrodinger Equation

In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.

Energy-saving technologies for construction machinery:a review of electro-hydraulic pump-valve coordinated system

With the rapid development of the global economy,more and more attention has been paid to the energy conservation of construction machinery.The hydraulic system is the key component of construction machinery,and improving its energy utilization rate has become an important means to achieve energy conservation.In conventional valve-controlled or pump-controlled hydraulic systems of construction machinery,controllability and energy-saving performance typically cannot be considered at the same time.The pump-valve coordinated system combines the energy-saving characteristics of the pump-controlled system and the high-precision and high-frequency response of the valve-controlled system,which has the potential to become a primary research direction of electro-hydraulic systems.This review summarizes the recent research progress in energy-saving technologies based on pump-valve coordinated systems.Particularly,we discuss the structures of hydraulic systems in different categories of construction machinery,various control methods of the electro-hydraulic system,novel hydraulic hybrid energy regeneration systems,and key components.In addition,future directions and challenges of the pump-valve coordinated systems are described,such as independent metering system(IMS),common pressure rail(CPR),and hybrid power source(HPS).

Behavioral control task supervisor with memory based on reinforcement learning for human-multi-robot coordination systems

In this study,a novel reinforcement learning task supervisor(RLTS)with memory in a behavioral control framework is proposed for human–multi-robot coordination systems(HMRCSs).Existing HMRCSs suffer from high decision-making time cost and large task tracking errors caused by repeated human intervention,which restricts the autonomy of multi-robot systems(MRSs).Moreover,existing task supervisors in the null-space-based behavioral control(NSBC)framework need to formulate many priority-switching rules manually,which makes it difficult to realize an optimal behavioral priority adjustment strategy in the case of multiple robots and multiple tasks.The proposed RLTS with memory provides a detailed integration of the deep Q-network(DQN)and long short-term memory(LSTM)knowledge base within the NSBC framework,to achieve an optimal behavioral priority adjustment strategy in the presence of task conflict and to reduce the frequency of human intervention.Specifically,the proposed RLTS with memory begins by memorizing human intervention history when the robot systems are not confident in emergencies,and then reloads the history information when encountering the same situation that has been tackled by humans previously.Simulation results demonstrate the effectiveness of the proposed RLTS.Finally,an experiment using a group of mobile robots subject to external noise and disturbances validates the effectiveness of the proposed RLTS with memory in uncertain real-world environments.

Area and shape distortions in open-source discrete global grid systems

A Discrete Global Grid System(DGGS)is a type of spatial reference system that tessellates the globe into many individual,evenly spaced,and well-aligned cells to encode location and,thus,can serve as a basis for data cube construction.This facilitates integration and aggregation of multi-resolution data from various sources to rapidly calculate spatial statistics.We calculated normalized area and compactness for cell geometries from 5 open-source DGGS implementations-Uber H3,Google S2,RiskAware OpenEAGGR,rHEALPix by Landcare Research New Zealand,and DGGRID by Southern Oregon University-to evaluate their suitability for a global-level statistical data cube.We conclude that the rHEALPix and OpenEAGGR and DGGRID ISEA-based DGGS definitions are most suitable for global statistics because they have the strongest guarantee of equal area preservation-where each cell covers almost exactly the same area on the globe.Uber H3 has the smallest shape distortions,but Uber H3 and Google S2 have the largest variations in cell area.However,they provide more mature software library functionalities.DGGRID provides excellent functionality to construct grids with desired geometric properties but as the only implementation does not provide functions for traversal and navigation within a grid after its construction.

NEW DELAY-DEPENDENT STABILITY CRITERIA AND ROBUST CONTROL OF NONLINEAR TIME-DELAY SYSTEMS

This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.

Improved Approaches Toward Analysis of Electromagnetic Processes in Electrodynamical Devices Based on the Theory of Electromagnetic Field

In the course of designing and developing different-purpose electrodynamical devices,electromagnetic processes in movable and immovable media need to be calculated simultaneously.The solution for such tasks based on the electromagnetic field theory is associated with the emergence of significant theoretical and practical difficulties.The problems that arise during the calculation of electromagnetic processes in movable and immovable media of electrodynamical devices using the electromagnetic field theory are examined in this study.Improved approaches toward the calculation of electromagnetic processes in electrodynamical devices using Maxwell’s equations are suggested.Notably,calculating electromagnetic processes in movable and immovable media using Maxwell’s equations necessitates consideration of the systems of coordinates where the electromagnetic phenomena are analyzed.Theoretically substantiated methods of calculating electromagnetic processes in movable and immovable media based on the principles of electromagnetic field theory are proposed.The methods consider the systems of coordinates where the analysis of electromagnetic phenomena is conducted.The effectiveness of the suggested methods for example in calculating electromagnetic processes in movable and immovable media of the turbogenerator is illustrated.

NUMERICAL SOLUTION FOR UNSTEADY 2－D FLOW USING THE TRANSFORMED SHALLOW WATER EQUATIONS

This paper is concerned with the numerical solution of two-dimensional flow.The technique of boundary-fitted coordinate systems is used to overcome the difficulties resulting from the complicated shape of natural river boundaries; the method of fractional steps is used to solve the partial differential equations in the transformed plane; and the technique of moving boundary is used to deal with the river bed exposed to water surface. Comparison between computed and experimental data shows a satisfactory agreement.

AN APPROACH TO THE STUDY OF TRANSVERSE MIXING IN NATURAL RIVERS

A numerical model of transverse mixing in natural rivers has been presented by using the body-fitted coordinate systems,which is capable of describing the complex flow and mixing characteristics of rivers.To study the validity and to illustrate the applicability of this model,field measurement date in the Gan River near Nanchang have been used to compare the numerical results.

ON THE HIGH PRECISION ADAPTIVE OPEN BOUNDARY CONDITIONS FOR TRANSIENT WAVES

The adaptive open boundary conditions (AOBC) designed by Chen and Zou for transient waves overcome the limitation of the existing open boundary conditions (OBC) and can be used for the cases of waves with arbitrary incident angles. In this paper a new family of AOBC has been designed on the basis of the AOBC with first order mentioned above. In comparing with all other OBC with the same order, this new family of AOBC has the highest precision. It can be generalized into 3D problems without difficulty and its forms in different curvilinear coordinate systems can be got very easily. The distinguished advantages above mentioned of the AOBC will be discussed in this paper.

EASE-DGGS:a hybrid discrete global grid system for Earth sciences

Although we live in an era of unprecedented quantities and access to data,deriving actionable information from raw data is a hard problem.Earth observation systems(EOS)have experienced rapid growth and uptake in recent decades,and the rate at which we obtain remotely sensed images is increasing.While significant effort and attention has been devoted to designing systems that deliver analytics ready imagery faster,less attention has been devoted to developing analytical frameworks that enable EOS to be seamlessly integrated with other data for quantitative analysis.Discrete global grid systems(DGGS)have been proposed as one potential solution that addresses the challenge of geospatial data integration and interoperability.Here,we propose the systematic extension of EASE-Grid in order to provide DGGS-like characteristics for EOS data sets.We describe the extensions as well as present implementation as an application programming interface(API),which forms part of the University of Minnesota’s GEMS(Genetic x Environment x Management x Socioeconomic)Informatics Center’s API portfolio.