关联Bernoulli数与Stirling数、Eulerian数的恒等式

自然数的幂和公式可以用Bernoulli数、两类Stirling数和Eulerian数分别表示.这些常数之间一定存在着某种关联,将后两者公式中关于n的组合数用第一类Stirling数的升阶乘定义展开,将所得结果与雅各布·伯努利公式中关于n的各幂次的系数进行比较,得到了关联Bernoulli数和两类Stirling数及Eulerian数的恒等式.

基于mixed Lagrangian/Eulerian方法的轮轨滚动接触特性分析

为了缩短有限元方法显式计算轮轨滚动接触的时间,采用mixed Lagrangian/Eulerian方法建立了轮轨滚动接触有限元模型.应用该模型对轮轨接触区的单元进行细化,计算了列车在启动、运行和制动工况下轮轨的接触特性.计算结果表明:不同工况下,轮轨滚动接触区最大Mises应力、最大接触应力和接触斑面积等法向特性变化幅度均在2%以内,但接触区纵向截面中Mises应力分布及纵向剪切应力分布有较大变化;启动和制动工况下,最大Mises应力和最大纵向剪切应力位置均比自由滚动时更接近于轮轨表面;不同工况下,摩擦力大小和方向发生变化,在列车牵引和制动工况中,摩擦力达到极限时轮轨间出现完全滑动,摩擦力方向与滑动方向相反,且不同速度等级下的纵向摩擦力变化幅度也在2%以内.

云下洗脱-Eulerian模式

在Eulerian模式中,在大气氨浓度大于硝酸的条件下,简要讨论了各种污染物对雨水组成的影响.结果表明,在本文考虑的情况下,氨对SO_2气体洗脱和SO^(2-)形成的影响最大,且能抑制雨水的酸化;过氧化氢的作用略小于氨.气溶胶对雨水SO_4^(2-)浓度的贡献小于气体.云下H_2O_2和O_3氧化能力的大小取决于雨水的pH、降落距离和各自的浓度.在雨水pH高,降落距离短和各自浓度小时,O_3的氧化能力大于H_2O_2,反之则H_2O_2大于O_3.对韶关降水酸化的模拟表明,考虑气体污染物补充机制的Eulerian模式可以较好地模拟现场降水酸化过程.

群体机器人觅食任务Eulerian建模与分析

为了提高觅食任务性能,根据蚂蚁觅食原理引入了觅食概率的概念,机器人按照该概率决定是否离开Home区域,通过改变该概率值来调整环境中机器人的数量。为了研究觅食概率对系统性能的影响,利用Eulerian数学建模方法建立了觅食任务模型,并通过仿真实验分析了觅食概率对系统整体性能的影响。实验结果表明:觅食概率越大,环境中机器人数量越增加,机器人之间的干扰也增加,从而降低系统性能。最后通过实验分析给出了觅食概率与环境中任务数量以及机器人数之间的大致关系。

高温气流内顺/逆流喷雾的Eulerian-Lagrangian数值仿真(英文)

用Eulerian-Lagrangian方法对高温气流内顺/逆流喷雾过程进行了数值仿真。气相方程用Eulerian方法建立,用k-ε模型封闭;液滴相方程用Lagrangian方法建立,采用了随机轨道模型;考虑了气体和液滴间的双向耦合。结果表明,高温气流内喷雾后,气相流场内产生了速度亏损和温度亏损,气体出口压力变化不大,液滴运动决定于气流湍流强度和自身惯性力,液滴在气道内的停留时间决定于液滴运动特性和气流湍流强度;逆流喷雾对气流的影响比顺流喷雾时大。仿真结果与文献结果基本一致。

基于Eulerian模型的空中交通流量控制

通过拓展公路交通中常见的Eulerian模型,研究了一种空中交通流量模型。利用线性二次型最优控制理论,对空中交通流量模型进行了分析研究,实现对特定区域内流量进行控制。最后,用Matlab对系统进行了仿真,结果表明,引入最优控制向量的方法改善了流量波动性大的情况,降低了管制员的工作负荷。

基于level set的Eulerian-Lagrangian耦合方法及其应用

提出了一种基于水平集的Eulerian-Lagrangian耦合方法,其中Lagrangian方法采用相容显式有限元拉氏方法,Eulerian方法采用基于近似Riemann解的有限体积Eulerian方法,多介质界面处理采用新的水平集和Ghost方法计算.给出了若干数值算例,包括激波管问题以及金属和气体的运动界面及其大变形问题,并分别与精确解和相容显式有限元拉氏方法的计算结果进行了对比.数值结果表明,该方法计算结果正确,精度较高,能够准确捕捉物质界面,适用于处理大变形问题.

<i>Supereulerian Digraph</i>Strong Products

A vertex cycle cover of a digraph H is a collection C = {C1, C2, …, Ck} of directed cycles in H such that these directed cycles together cover all vertices in H and such that the arc sets of these directed cycles induce a connected subdigraph of H. A subdigraph F of a digraph D is a circulation if for every vertex in F, the indegree of v equals its out degree, and a spanning circulation if F is a cycle factor. Define f (D) to be the smallest cardinality of a vertex cycle cover of the digraph obtained from D by contracting all arcs in F, among all circulations F of D. Adigraph D is supereulerian if D has a spanning connected circulation. In [International Journal of Engineering Science Invention, 8 (2019) 12-19], it is proved that if D1 and D2 are nontrivial strong digraphs such that D1 is supereulerian and D2 has a cycle vertex cover C’ with |C’| ≤ |V (D1)|, then the Cartesian product D1 and D2 is also supereulerian. In this paper, we prove that for strong digraphs D1 and D2, if for some cycle factor F1 of D1, the digraph formed from D1 by contracting arcs in F1 is hamiltonian with f (D2) not bigger than |V (D1)|, then the strong product D1 and D2 is supereulerian.

ENUMERATING ROOTED EULERIAN PLANAR MAPS

This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.

基于Eulerian法计算多颗粒冷喷涂Ti-6Al-4V涂层的孔隙率和残余应力

冷喷涂涂层具有喷涂温度低、沉积效率高和结合强度高等特性,在航空航天等工业领域具有广阔的应用前景,但关于喷涂参数对涂层孔隙率和残余应力影响的研究较少.考虑送粉速度和涂层厚度的影响,建立不同颗粒密度和数量的随机分布颗粒冲击模型,采用Eulerian法模拟TC4(Ti-Al-4V)涂层的孔隙率和残余应力分布规律.结果表明,此方法能够很好地预测颗粒的沉积行为,揭示颗粒的原位夯实致密化效应,获得冷喷涂涂层的孔隙率和残余应力分布规律.颗粒密度减小,孔隙率略有降低;颗粒数量增加,孔隙率减小;当颗粒温度在一定范围(523~823K)时,孔隙率随温度上升呈线性降低.同时,不同颗粒密度和数量的模型获得的残余应力分布规律相似.计算结果可为冷喷涂涂层在航空航天等工业领域中的应用提供理论和数据支持.

Thermophoresis effects on gas-particle phases flow behaviors in entrained flow coal gasifier using Eulerian model

A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles are thoroughly investigated. The thermophoresis is due to the gas temperature gradient caused by absorpted heat of coal char gasification. This work, firstly, calculates the gas temperature gradient and thermophoretic force at1100 °C,1200 °C,1300 °C and 1400 °C wall temperatures. Then, the changes of particle volume fraction and velocity in the gasifier are studied in the simulation with thermophoresis or not. The results indicate that considering the particle thermophoresis has some effects on the calculation of particle volume fraction in the gasifier, especially at wall temperature of 1400 °C, and the maximum particle volume fraction variance ratio reaches up to 1.38% on wall surface of the gasifier. These effects are mainly caused by large gas temperature gradient along the radial direction of the gasifier. For the particle velocity, the changes are small but can be observable along radial direction of the gasifier, which has good agreement with the distributions of radial gas temperature gradient and thermophoretic force. These changes above may have certain effects on gasification reaction rates in this Eulerian model. So the change of gasification reaction rates in the simulation with thermophoresis or not is studied finally.

NUMERICAL SIMULATION OF WET STEAM CONDENSING FLOW WITH AN EULERIAN/EULERIAN MODEL

Wet steam condensing flow in low-pressure steam turbine leads to efficiencylosses and blade erosions. In order to investigate this problem by numerical approach, anEulerian/Eulerian model has been developed, in which the wet steam is regarded as mixture comprisingtwo coupled systems: the vapor phase and the liquid phase. These two systems are both described byconservation equations. High resolution TVD scheme is employed to capture condensing phenomena inwet steam flow. This model has been validated by numerical simulations of condensing flows in 1D and2D nozzles. Compared with experimental data, a good agreement is observed. This Eulerian/Eulerianmodel can be extended to 3D calculation of condensing flow.

Sulfur Distribution and Transport Studies in East Asia Using Eulerian Model

A three-dimensional regional Eulenan model of sulfur deposition and transport is developed.Processes treated in the model include emission,transport,diffusion,gas-phase and aqueous-phase chemical process,dry deposition,ramout and washout of sulfur.A 'looking up table' method is provided to deal with the gas-phase chemical process including sulfur transfer Dry-depositon velocity considers the influence of underlying surface,wind,degree of stability by parameterization Model calculated values reasonably agrees with observation.Distribution of sulfur deposition and transport in East Asia are also analyzed in this paper Some amount of sulfur emission of different countries transport across boundaries,but the main origin of sulfur deposition in each country in East Asia is from itself.Furthermore.some transport paths on different layers and outlet or inlet zones are found.According to sulfur balance and budget we concluded that sulfur outlets are bigger than inlets across boundary and emissions are more than deposition in most places of East Asia

Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method

n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.

A hybrid Lagrangian-Eulerian numerical model for sea-ice dynamics

A hybrid Lagrangian - Eulerian （HLE） method is developed for sea ice dynamics, which combines the high computational efficiency of finite difference method （FDM） with the high numerical accuracy of smoothed particle hydrodynamics （SPH）. In this HLE model, the sea ice cover is represented by a group of Lagrangian ice particles with their own thicknesses and concentrations. These ice variables are interpolated to the Eularian gird nodes using the Gaussian interpolation function. The FDM is used to determine the ice velocities at Eulerian grid nodes, and the velocities of Lagrangian ice particles are interpolated from these grid velocities with the Gaussian function also. The thicknesses and concentrations of ice particles are determined based on their new locations. With the HLE numerical model, the ice ridging process in a rectangular basin is simulated, and the simulated results are validated with the analytical solution. This method is also applied to the simulation of sea ice dynamics in a vortex wind field. At last, this HLE model is applied to the Bohai Sea, and the simulated concentration, thickness and velocity match the satellite images and the field observed data well.

ON THE NUMBER OF EULERIAN PLANAR MAPS

This paper presents the number of combinatorially distinct rooted Eulerian planar maps with the number of non-root-vertices and the number of non-root-faces as two parameters. The parametric expressions for determining the number in tha loopless Eulerian case are also obtained.

Efficient modeling of cable-pulley system with friction based on arbitrary-Lagrangian-Eulerian approach

In conventional modeling of a cable-pulley system, the cable must be finely meshed with Lagrangian elements for valid contact detections with pulleys, leading to extremely low efficiency. The sliding joint method based on the arbitrary-Lagrangian- Eulerian （ALE） formulation still lacks an efficient cable element, and in particular, modeling of friction between a sliding joint and the cable has not been studied. This paper presents efficient multi-body modeling of a cable-pulley system with friction. A variable- length cable element with a node movable along the cable, which is described with ALE, is developed to mesh the cable. A transitional cable element is then proposed to model the contact part of the cable by fixing its two nodes to the two corresponding locations of the pulley. Friction of the cable-pulley is derived as a simple law of tension decay and embedded in the multi-body system modeling. It is simplified as a generalized friction force acting only on the arc-length coordinate. This approach can use a rough mesh on the cable, and is free of contact detections, thus significantly saving computation time. Several examples are presented to validate the proposed method, and show its effectiveness in real engineering applications.

COUNTING ROOTED NEAR-4-REGULAR EULERIAN MAPSON SOME SURFACES

In this article the rooted planar near-4-regular Eulerian trails are enum erated and an explicit form ula for such m aps is presented. Further, the rooted near-4-regular Eulerian m aps on the torus are counted in an exact w ay.

Particulate flow modelling in a spiral separator by using the Eulerian multi-fluid VOF approach

The Euler-Euler model is less effective in capturing the free surface of flow film in the spiral separator,and thus a Eulerian multi-fluid volume of fluid(VOF)model was first proposed to describe the particulate flow in spiral separators.In order to improve the applicability of the model in the high solid concentration system,the Bagnold effect was incorporated into the modelling framework.The capability of the proposed model in terms of predicting the flow film shape in a LD9 spiral separator was evaluated via comparison with measured flow film thicknesses reported in literature.Results showed that sharp air–water and air-pulp interfaces can be obtained using the proposed model,and the shapes of the predicted flow films before and after particle addition were reasonably consistent with the observations reported in literature.Furthermore,the experimental and numerical simulation of the separation of quartz and hematite were performed in a laboratory-scale spiral separator.When the Bagnold lift force model was considered,predictions of the grade of iron and solid concentration by mass for different trough lengths were more consistent with experimental data.In the initial development stage,the quartz particles at the bottom of the flow layer were more possible to be lifted due to the Bagnold force.Thus,a better predicted vertical stratification between quartz and hematite particles was obtained,which provided favorable conditions for subsequent radial segregation.

Hybrid N-order Lagrangian Interpolation Eulerian-Lagrangian Method for Salinity Calculation

The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.