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.

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.

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.

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.