Random Green's Function Method for Large-Scale Electronic Structure Calculation

We report a linear-scaling random Green's function(rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states and is efficiently calculated by projecting onto Krylov subspace. With the rGF method, the Fermi–Dirac operator can be obtained directly, avoiding the polynomial expansion to Fermi–Dirac function. To demonstrate the applicability, we implement the rGF method with the density-functional tight-binding method. It is shown that the Krylov subspace can maintain at small size for materials with different gaps at zero temperature, including H_(2)O and Si clusters. We find with a simple deflation technique that the rGF self-consistent calculation of H_(2)O clusters at T = 0 K can reach an error of~ 1 me V per H_(2)O molecule in total energy, compared to deterministic calculations. The rGF method provides an effective stochastic method for large-scale electronic structure simulation.

Utility and Application of a Versatile Analytical Method for MMF Calculation in AC Machines

A versatile analytical method(VAM) for calculating the harmonic components of the magnetomotive force(MMF) generated by diverse armature windings in AC machines has been proposed, and the versatility of this method has been established in early literature. However, its practical applications and significance in advancing the analysis of AC machines need further elaboration. This paper aims to complement VAM by augmenting its theory, offering additional insights into its conclusions, as well as demonstrating its utility in assessing armature windings and its application of calculating torque for permanent magnet synchronous machines(PMSM). This work contributes to advancing the analysis of AC machines and underscores the potential for improved design and performance optimization.

Calculating Method for Influence of Material Flow on Energy Consumption in Steel Manufacturing Process

From the viewpoint of systems energy conservation, the influences of material flow on its energy consumption in a steel manufacturing process is an important subject. The quantitative analysis of the relationship between material flow and the energy intensity is useful to save energy in steel industry. Based on the concept of standard material flow diagram, all possible situations of ferric material flow in steel manufacturing process are analyzed. The expressions of the influence of material flow deviated from standard material flow diagram on energy consumption are put forward.

A General Calculating Method of Rotor’s Torsional Stiffness Based on Stiffness Influence Coefficient

In order to develop a general calculating rotor’s torsional stiffness based on stiffness influence coefficient for different rotor assembling, the calculation method of the torsional stiffness influence coefficient of equal thickness disc is researched in this paper at first. Then the torsional stiffness influence coefficient λ of equal thickness disc is fit to a binary curved face and a calculation equation is obtained based on a large quantity of calculating data, which lays the foundation for research on a general calculating method of rotor torsional stiffness. Thirdly a simplified calculation method for equivalent stiffness diameter of stepped equal thickness disc and cone disc in the steam turbine generators is suggested. Finally a general calculating program for calculating rotor’s torsional vibration features is developed, and the torsional vibration features of a verity of steam turbine rotors are calculated for verification. The calculating results show that stiffness influence coefficient λ of equal-thickness disc depends on parameters of B and H, as well as the stiffness influence coefficient λ;and discs with complex structure can be simplified to equal-thickness discs with little error by using the method suggested in this paper;error can be controlled within 1% when equivalent diameter of stiffness is calculated by this method.

Review of Collocation Methods and Applications in Solving Science and Engineering Problems

The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.

Three Dimensional Laser Point Cloud Slicing Method for Calculating Irregular Volume

Volume parameter is the basic content of a spatial body object morphology analysis.However,the challenge lies in the volume calculation of irregular objects.The point cloud slicing method proposed in this study effectively works in calculating the volume of the point cloud of the spatial object obtained through three-dimensional laser scanning(3DLS).In this method,a uniformly spaced sequent slicing process is first conducted in a specific direction on the point cloud of the spatial object obtained through 3DLS.A series of discrete point cloud slices corresponding to the point cloud bodies are then obtained.Subsequently,the outline boundary polygon of the point cloud slicing is searched one by one in accordance with the slicing sequence and areas of the polygon.The point cloud slice is also calculated.Finally,the individual point cloud section volume is calculated through the slicing areas and the adjacent slicing gap.Thus,the total volume of the scanned spatial object can be calculated by summing up the individual volumes.According to the results and analysis of the calculated examples,the slice-based volume-calculating method for the point cloud of irregular objects obtained through 3DLS is correct,concise in process,reliable in results,efficient in calculation methods,and controllable on accuracy.This method comes as a good solution to the volume calculation of irregular objects.

The Method of Calculating Average Skidding Distance

By analyzing the existing average skidding distance formulac and the shape of the landing area, theauthors put forward that the average skidding distance is the shortest when the ratio of length and width is 1, and the landing collectioll area is in proportion to of average geometrical skidding distance. The new models of calculating average distance are presented.

Calculating method of circle radius using genetic algorithms

Some improved methods of the traditional genetic algorithms were proposed and their application in calculating circle radius was discussed. Simulation shows that real number encoding, simulated annealing and saving the best individual into the next generation can effectively improve the accuracy and speed up the searching for global optimization. It is also shown that improved genetic algorithms can effectively calculate the circle radius and be realized easily using computer.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

Two Methods for Calculating the Size Distribution of Ferritin’s Outer Diameter

Ferritin is a kind of iron-storage protein widely found in animals and plants. The dynamic light scattering (Dynamic Light Scattering) method is used in the laboratory to determine the ferritin size. This paper presents two methods for calculating the outer diameter size distribution of ferritin, both of which assume that ferritin is approximately spherical. The ferritin data file was obtained from the PDB website and was calculated using the coordinate data of the amino acids to which the amino acids belong. The first method is based on the calculation of the sphere center;the second method is based on the method of the farthest distance atom pair. The outer diameter size distribution curves obtained by the two methods are basically consistent with the experimental methods. The paper also compares the calculation results and performance of the two methods. Both methods are versatile and can be used to calculate the size distribution of the globular proteins.

Monte Carlo simulation based thinning and calculating method for noninvasive blood glucose sensing by near-infrared spectroscopy

Previous results show that the floating reference theory(FRT)is an effective tool to reduce the infuence of interference factors on noninvasive blood glucose sensing by near infrared spectros-copy(NIRS).It is the key to measure the floating reference point(FRP)precisely for the application of FRT.Monte Carlo(MC)simulation has been introduced to quantitatively in-vestigate the effects of positioning errors and light source drifts on measuring FRP.In this article,thinning and calculating method(TCM)is proposed to quantify the positioning error.Mean-while,the normalization process(NP)is developed to significantly reduce the error induced by light source drift.The results according to TCM show that 7 purm deviations in positioning can generate about 10.63%relative error in FRP.It is more noticeable that 1%fluctuation in light source intensity may lead to 12.21%relative errors.Gratifyingly,the proposed NP model can effectively reduce the error caused by light source drift.Therefore,the measurement system for FRPs must meet that the positioning error is less than 7 purm,and the light source drift is kept within 1%.Furthermore,an improvement for measurement system is proposed in order to take advantage of the NP model.

A Visual Indoor Localization Method Based on Efficient Image Retrieval

The task of indoor visual localization, utilizing camera visual information for user pose calculation, was a core component of Augmented Reality (AR) and Simultaneous Localization and Mapping (SLAM). Existing indoor localization technologies generally used scene-specific 3D representations or were trained on specific datasets, making it challenging to balance accuracy and cost when applied to new scenes. Addressing this issue, this paper proposed a universal indoor visual localization method based on efficient image retrieval. Initially, a Multi-Layer Perceptron (MLP) was employed to aggregate features from intermediate layers of a convolutional neural network, obtaining a global representation of the image. This approach ensured accurate and rapid retrieval of reference images. Subsequently, a new mechanism using Random Sample Consensus (RANSAC) was designed to resolve relative pose ambiguity caused by the essential matrix decomposition based on the five-point method. Finally, the absolute pose of the queried user image was computed, thereby achieving indoor user pose estimation. The proposed indoor localization method was characterized by its simplicity, flexibility, and excellent cross-scene generalization. Experimental results demonstrated a positioning error of 0.09 m and 2.14° on the 7Scenes dataset, and 0.15 m and 6.37° on the 12Scenes dataset. These results convincingly illustrated the outstanding performance of the proposed indoor localization method.

Method of Calculating the Safety Factor Profile on the HT-7 Tokamak

A method of calculating the safety profile on the HT-7 tokamak has been described in this paper. It is derived from Maxwell's equations, among which we-mainly use .two of them: one is the magnetic field diffusion equation, and the other is Ampere's Law. This method can be also used to evaluate the safety factor on other devices with a circular cross sections. It is helpful to the study of the plasma MHD behavior on the HT-7 tokamak.

Erratum to:“An Approximate Method for Calculating the Fluid Force and Response of A Circular Cylinder at Lock-in” [China Ocean Engineering,22(3),2008,371-384]

Because of my carelessness,Eq.（1）in the paper "An approximate method for calculating the fluid force and response of a circular cylinder at lock-in"(China Ocean Engineering,22（3）,2008,pp.373)should be f’-1.0/U’-5.0=f’;-1.0/5.75f’;-5.0,not f’=U’/5.75. My apology is hereby given.

A METHOD FOR CALCULATING TRANSIENT FUNCTIONS OF EQUIVALENT DETERMINISTIC INPUT

In the present paper the analytical formulas for calculating the equivalent deterministictransients for multivariable cross correlated random processes are developed.The formulaspermit the determination of the Root-mean-square of the responses of a lineartime-invariant system to stationary multiple random inputs in the time domain.The methodis applicable in the study of flight of airplanes in atmospheric turbulence and is also usefulfor general engineering applications of stochastc processes control.

ON THE LIMIT CASE OF THE STEP-REDUCTION METHOD FOR CALCULATING NON-UNIFORM BEAM WITH VARIOUS SECTIONS

In this paper, the step reduction method is discussed, which was advanced by Prof. Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not in the pure mathematics sense but in the mechanics sense.

Equivalent Method of Integrated Power Generation System of Wind, Photovoltaic and Energy Storage in Power Flow Calculation and Transient Simulation

针对工程实际开展风光储联合发电系统在潮流计算和机电暂态仿真中的等值方法研究，旨在为大容量风光储联合发电系统的并网仿真分析奠定基础。将潮流计算的等值分为单元机组和集电系统2部分来研究。单元机组等值采用根据不同控制模式选取不同节点类型的方法，针对集电系统等值提出基于损耗不变原则的方法。等值模型和详细模型的算例结果表明，潮流计算等值方法具有较好的精度。在机电暂态仿真动态等值中，基于实际工程计算的最严重工况分析原则，提出运行在满出力点的单机“倍乘”等值模型，为工程计算中的风光储联合发电系统动态等值提供了一种解决方案。

An integrated computational method for calculating dynamic thermal bridges of building facades in tropical countries

Identifying thermal bridges on building façades has been a great challenge for architects,especially during the conceptual design stage.This is not only due to the complexity of parameters when calculating thermal bridges,but also lack of feature integration between building energy simulation(BES)tools and the actual building conditions.For example,existing BES tools predominantly calculate thermal bridges only in steady state without considering the temperature dynamic behaviour of building outdoors.Consequently,relevant features such as thermal delay,decrement factor,and operative temperature are often neglected,and this can lead to miscalculation of energy consumption.This study then proposes an integrated method to calculate dynamic thermal bridges under transient conditions by incorporating field observations and computational simulations of thermal bridges.More specifically,the proposed method employs several measurement tools such as HOBO data logger to record the actual conditions of indoor and outdoor room temperature and thermal cameras to identify the surface temperature of selected building junctions.The actual datasets are then integrated with the simulation workflow developed in BES tools.This study ultimately enables architects not only to identify potential thermal bridges on existing building façades but also to support material and geometric exploration in early design phase.

A Flexible-Segment-Model-Based Dynamics Calculation Method for Free Hanging Marine Risers in Re-Entry

In re-entry, the drilling riser hanging to the holding vessel takes on a free hanging state, waiting to be moved from the initial random position to the wellhead. For the re-entry, dynamics calculation is often done to predict the riser motion or evaluate the structural safety. A dynamics calculation method based on Flexible Segment Model （FSM） is proposed for free hanging marine risers. In FSM, a riser is discretized into a series of flexible segments. For each flexible segment, its deflection feature and external forces are analyzed independently. For the whole riser, the nonlinear governing equations are listed according to the moment equilibrium at nodes. For the solution of the nonlinear equations, a linearization iteration scheme is provided in the paper. Owing to its flexibility, each segment can match a long part of the riser body, which enables that good results can be obtained even with a small number of segments. Moreover, the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points. The FSM-based dynamics calculation is timesaving and stable, so suitable for the shape prediction or real-time control of free hanging marine risers.

Application of Two-dimensional Viscous CE/SE Method in Calculation of Two-phase Detonation

The method of two-dimensional viscous space-time conservation element and solution element (CE/SE) can be used to calculate the gas-liquid two-phase interior flow field in pulse detonation engine (PDE). In this paper, the evolution of the detonation wave and the distribution of its physical parameters were analyzed. The numerical results show that the change of axial velocity of gas is the same as that of detonation pressure. The larger the liquid droplet radius is, the longer the time to get stable detonation wave is. The calculated results coincide with the experimented results better.