3D Numerical Simulation of Overbank Flow in Non-Orthogonal Curvilinear Coordinates

The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow.

Study on the SVPWM algorithm of N-level inverter in the context of non-orthogonal coordinates

In this paper,the authors propose a new space vector pulse width modulation(SVPWM)algorithm based on non-orthogonal coordinates for N-level inverters.First,it is pointed out that classicalαβcoordinates-based SVPWM has many shortcomings because of improper coordinate choice.Then,a non-orthogonal coordinates-based SVPWM is proposed to solve these problems.The proposed algorithm can easily identify which sector the reference space vector falls in and conduct simple operations to find the duty cycle of each vector.Finally,it is verified that the proposed SVPWM is actually a pulse−width modulation(PWM)technology based on line voltages.

Numerical model of flow and pollutant transportation in non-orthogonal curvilinear coordinates

The planar 2D k-ε double equations' turbulence model was adopted and transformed into non-orthogonal curvilinear coordinates. The concentration convection-diffusion was introduced to planar 2D SIMPLEC algorithm of flow in non-orthogonal curvilinear coordinates. The numerical model of pollutant transportation in non-orthogonal curvilinear coordinates was constructed. The model was applied to simulate the flow and pollutant concentration fields. In the testing concentration field, two optimal operations of contamination discharging both along bank and in the centerline at the first bend of the meandering channel were adopted. Comparison with available data showed the model developed was successful, was valuable to engineering application.

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.

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.

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.

Enhanced hyperspectral imagery representation via diffusion geometric coordinates

The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high- dimensional spectral measurements are organized by the affinity graph where each node in this graph only connects to its local neighbors and each edge in this graph represents local similarity information. By normalizing the affinity graph appropriately, the diffusion operator of the underlying hyperspectral imagery is well-defined, which means that the Markov random walk can be simulated on the hyperspectral imagery. Therefore, the diffusion geometric coordinates, derived from the eigenfunctions and the associated eigenvalues of the diffusion operator, can capture the intrinsic geometric information of the hyperspectral imagery well, which gives more enhanced representation results than traditional linear methods, such as principal component analysis based methods. For large-scale full scene hyperspectral imagery, by exploiting the backbone approach, the computation complexity and the memory requirements are acceptable. Experiments also show that selecting suitable symmetrization normalization techniques while forming the diffusion operator is important to hyperspectral imagery representation.

Numerical Modeling of the Hyperbolic Mild-Slope Equation in Curvilinear Coordinates

The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However, its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines, such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates, the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by the ADI method with space-staggered grids. The numerical predictions in curvilinear co- ordinates show good agreemenl with the data obtained in three typical physical expedments, which demonstrates that the present model can be used to simulate wave propagation, for normal incidence and oblique incidence, in domains with complicated topography and boundary conditions.

Analysis of Non-Orthogonal Multiple Access for 5G

The major challenge faced by the fifth generation(5G) mobile network is higher spectral efficiency and massive connectivity,i.e.,the target spectrum efficiency is 3 times over 4G,and the target connection density is one million devices per square kilometer.These requirements are difficult to be satisfied with orthogonal multiple access(OMA) schemes.Non-orthogonal multiple access(NOMA) has thus been proposed as a promising candidate to address some of the challenges for 5G.In this paper,a comprehensive survey of different candidate NOMA schemes for 5G is presented,where the usage scenarios of5 G and the application requirements for NOMA are firstly discussed.A general framework of NOMA scheme is established and the features of typical NOMA schemes are analyzed and compared.We focus on the recent progress and challenge of NOMA in standardization of international telecommunication union(ITU),and 3rd generation partnership project(3GPP).In addition,prototype development and future research directions are also provided respectively.

An Oceanic General Circulation Model in Pressure Coordinates

A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-sigma coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approximations. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum. equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations.

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.

Development of practical postprocessor for 5-axis machine tool with non-orthogonal rotary axes

In order to develop a practical postprocessor for 5-axis machine tool,the general equations of numerically controlled(NC) data for 5-axis configurations with non-orthogonal rotary axes were exactly expressed by the inverse kinematics,and a windows-based postprocessor written with Visual Basic was developed according to the proposed algorithm.The developed postprocessor is a general system suitable for all kinds of 5-axis machines with orthogonal and non-orthogonal rotary axes.Through implementation of the developed postprocessor and verification by a cutting simulation and machining experiment,the effectiveness of the proposed algorithm is confirmed.Compatibility is improved by allowing exchange of data formats such as rotational total center position(RTCP) controlled NC data,vector post NC data,and program object file(POF) cutter location(CL) data,and convenience is increased by adding the function of work-piece origin offset.Consequently,a practical post-processor for 5-axis machining is developed.

Non-Orthogonal Multiple Access in Cell-Free Massive MIMO Networks

In this paper, we investigate the downlink performance of cell-free massive multi-input multi-output non-orthogonal multiple access(CF-m MIMO-NOMA) system with conjugate beamforming precoder and compare against the orthogonal multiple access(OMA) counterpart. A novel achievable closed-form spectral efficiency(SE) expression is derived, which characterizes the effects of the channel estimation error, pilot contamination, imperfect successive interference cancellation(SIC) operation, and power optimization technique. Then, motivated by the closedform result, a sum-SE maximization algorithm with the sequential convex approximation(SCA) is proposed, subject to each AP power constraint and SIC power constraint. Numerical experiments indicate that the proposed sum-SE maximization algorithms have a fast converge rate, within about five iterations. In addition, compared with the full power control(FPC) scheme, our algorithms can significantly improve the achievable sum-SE. Moreover, NOMA outperforms OMA in many respects in the presence of the proposed algorithms.

Outage Performance of Non-Orthogonal Multiple Access Based Unmanned Aerial Vehicles Satellite Networks

With rapid development of unmanned aerial vehicles(UAVs), more and more UAVs access satellite networks for data transmission. To improve the spectral efficiency, non-orthogonal multiple access(NOMA) is adopted to integrate UAVs into the satellite network, where multiple satellites cooperatively serve the UAVs and mobile terminal using the Ku-band and above. Taking into account the rain fading and the fading correlation, the outage performance is first analytically obtained for fixed power allocation and then efficiently calculated by the proposed power allocation algorithm to guarantee the user fairness. Simulation results verify the outage performance analysis and show the performance improvement of the proposed power allocation scheme.

A Survey: Several Technologies of Non-Orthogonal Transmission for 5G

One key advantage of 4G OFDM system is the relatively simple receiver implementation due to the orthogonal resource allocation.However,from sum-capacity and spectral efficiency points of view,orthogonal systems are never the achieving schemes.With the rapid development of mobile communication systems,a novel concept of non-orthogonal transmission for 5G mobile communications has attracted researches all around the world.In this trend,many new multiple access schemes and waveform modulation technologies were proposed.In this paper,some promising ones of them were discussed which include Non-orthogonal Multiple Access(NOMA),Sparse Code Multiple Access(SCMA),Multi-user Shared Access(MUSA),Pattern Division Multiple Access(PDMA)and some main new waveforms including Filter-bank based Multicarrier(FBMC),Universal Filtered Multi-Carrier(UFMC),Generalized Frequency Division Multiplexing(GFDM).By analyzing and comparing features of these technologies,a research direction of guiding on future 5G multiple access and waveform are given.

Numerical Simulation of Wave-Induced Currents Combined with Parabolic Mild-Slope Equation in Curvilinear Coordinates

Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results.

A reconstructed edge-based smoothed DSG element based on global coordinates for analysis of Reissner–Mindlin plates

A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner-Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices, which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner-Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.

Frameworks of Non-Orthogonal Multiple Access Techniques in Cognitive Radio Communication Systems

Recently,the increasing demand of radio spectrum for the next generation communication systems due to the explosive growth of applications appetite for bandwidths has led to the problem of spectrum scarcity.The potential approaches among the proposed solutions to resolve this issue are well explored cognitive radio(CR)technology and recently introduced non-orthogonal multiple access(NOMA)techniques.Both the techniques are employed for efficient spectrum utilization and assure the significant improvement in the spectral efficiency.Further,the significant improvement in spectral efficiency can be achieved by combining both the techniques.Since the CR is well-explored technique as compared to that of the NOMA in the field of communication,therefore it is worth and wise to implement this technique over the CR.In this article,we have presented the frameworks of NOMA implementation over CR as well as the feasibility of proposed frameworks.Further,the differences between proposed CR-NOMA and conventional CR frameworks are discussed.Finally,the potential issues regarding the implementation of CR-NOMA are explored.

Practical non-orthogonal decoy state quantum key distribution with heralded single photon source

Recently the performance of the quantum key distribution （QKD） is substantially improved by the decoy state method and the non-orthogonal encoding protocol, separately. In this paper, a practical non-orthogonal decoy state protocol with a heralded single photon source （HSPS） for QKD is presented. The protocol is based on 4 states with different intensities. i.e. one signal state and three decoy states. The signal state is for generating keys; the decoy states are for detecting the eavesdropping and estimating the fraction of single-photon and two-photon pulses. We have discussed three cases of this protocol, i.e. the general case, the optimal case and the special case. Moreover, the final key rate over transmission distance is simulated. For the low dark count of the HSPS and the utilization of the two-photon pulses, our protocol has a higher key rate and a longer transmission distance than any other decoy state protocol.

Symbol Error Rate Performance Analysis of Non-Orthogonal Multiple Access for Visible Light Communications

Non-orthogonal multiple access(NOMA) is considered as one of promising radio access techniques for visible light communications(VLC) in next-generation wireless communications systems.In order to provide theoretical support for designing VLC-NOMA,we derive its analytic expressions for the symbol error rate(SER).Specifically,NOMA is first incorporated with appropriate VLC to establish a VLC-NOMA framework.Afterwards,mathematical expressions of the SER for the VLC-NOMA are developed.Moreover,numerical results are provided carefully to demonstrate that the proposed VLC-NOMA scheme outperforms than state-of-the-art orthogonal frequency division multiple access(OFDMA) one in terms of SER performance.Finally,relationships between the SER performance and the number of users,power allocation coefficient and semi-angle are well investigated,which can give us a scientific guide to devise the VLC-NOMA system for achieving better SER performance.