Distribution and dispersion in the Euler-Lagrange random walk

Summary In a new kind of random walk, displaying both Lagrangian and Eulerian statistical properties¹⁾, calculations were made previously of the Eulerian and Lagrangian velocity auto-correlations. Now the characteristic function of particle displacement has been calculated, and possible continuum limit forms for the probability density equation have been deduced. One of these turns out to be the telegraph equation, given by Goldstein²⁾ as the limit of a different kind of random walk. For this case the auto-correlation functions have been determined.This work was supported by the Mechanics Branch, U.S. Office of Naval Research, under contract Nonr 248 (38) and was presented in Session F of the 1959 Annual Meeting of the American Physical Society at New York under the title A Random Walk with both Lagrangian and Eulerian Statistics.Associate Professor of Engineering Research, Ordnance Research Laboratory, The Pennsylvania State University. This work was done as Research Associate, Post-Doctoral Fellow, Mechanical Engineering Department, The Johns Hopkins University.     

CONSTRAINT VIOLATION STABILIZATION OF EULER-LAGRANGE EQUATIONS WITH NON-HOLONOMIC CONSTRAINTS

Two constraint violation stabilization methods are presented to solve the Euler Lagrange equations of motion of a multibody system with nonholonomic constraints. Compared to the previous works, the newly devised methods can deal with more complicated problems such as those with nonholonomic constraints or redundant constraints, and save the computation time. Finally a numerical simulation of a multibody system is conducted by using the methods given in this paper.     

THE PROPERTY OF NONWANDERING OPERATOR

ＴＨＥＰＲＯＰＥＲＴＹＯＦＮＯＮＷＡＮＤＥＲＩＮＧＯＰＥＲＡＴＯＲＴｉａｎＬｉｘｉｎ（田立新）；ＬｕＤｉａｎｃｈｅｎ（卢殿臣）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＰｈｏｎｉｃｓ，ＪｉａｎｇｓｕＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａ...     

The null field approach to two-dimensional elastostatics

The vector basis functions, necessary for solving two-dimensional inclusion problems in an elastic solid under time independent conditions by means of the null field approach (T-matrix method), are obtained as a zero frequency limit of the corresponding basis functions commonly used in elastodynamics. The expansion of the fields appearing in the surface integral representation of the static displacement can thus be achieved, leading to the T-matrix equations of 2d-elastostatics. We specialize the problem to the simple boundary condition case of a single cavity and develop the analytical expressions as much as possible before numerical implementation. A numerical test for the ellipse and some examples for the superellipse, with applied static pressure or shear stress at infinity, are given.     

多体系统Euler-Lagrange方程组的一类新数值分析方法

针对受完整约束的多体系统,首先指出其动力学Euler-Lagrange方程组是高指标(index>2)的微分代数方程组;不同于传统的直接增广法和直接消去法,文中提出了一类将微分代数方程直接视为非线性代数方程组求解的新的数值分析方法;最后,以典型的单摆模型为例给出了新算法与其他方法的比较,结果表明新算法优于BDF方法及违约修正方法。     

用于爆炸流场与结构间相互作用分析的Euler-Lagrange耦合模拟技术

介绍了1种把Eulerian计算过程和Lagrangian计算过程耦合起来的数值技术,编写了计算程序,把爆炸流场作用过程和结构动力学响应过程的计算结合起来,实现了爆炸流场对结构加载和结构动力响应 及对爆炸流场反作用过程的模拟.利用Eulerian过程的流体弹塑性有限差分计算程序MMIC(multi-materials ...     

分数算子描述的黏弹性体力学问题数值方法

讨论由黎曼-刘维尔 (Riemann-Liouville)分数导数描述的黏弹性体力学问题的数 值方法. 该方法利用黎曼-刘维尔分数 导数定义中核函数的特性，并结合被积函数在单步中的逼近以及Newmark型数值法，建立 了分数导数计算公式. 算例表明，该算法具有收敛快、精度高、稳定性好和易于 应用和改进的优点. 在对动态系统的瞬态响应分析和有限元分析格式中，算法都获得了 满意的结果.     

The maximum dissipative extension of Schrödinger operator

In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.     

Euler-Lagrange/DEM simulation of wood gasification in a bubbling fluidized bed reactor

We present an Euler–Lagrange method for the simulation of wood gasification in a bubbling fluidized bed. The gas phase is modeled as a continuum using the 2D Navier–Stokes equations and the solid phase is modeled by a Discrete Element Method(DEM)using a soft-sphere approach for the particle collision dynamic. Turbulence is included via a Large-Eddy approach using the Smagorinsky sub-grid model.The model takes into account detailed gas phase chemistry,zero-dimensional modeling of the pyrolysis and gasification of each individual particle,particle shrinkage,and heat and mass transfer between the gas phase and the particulate phase.We investigate the influence of wood feeding rate and compare exhaust gas compositions and temperature results obtained with the model against experimental data of a laboratory scale bubbling fluidized bed reactor.     

The viscoelastic constitutive differential operator law in terms of the relaxation and retardation spectra

The case of a linear viscoelastic medium is considered. The Carson transforms of the relaxation and retardation functions are expressed in two different ways, taking on the one hand the differential operator form of the constitutive equation, and on the other hand the generalized mechanical models. By identification we deduce general explicit expressions for the constant coefficients of the differential operator law, in terms of the discrete relaxation and retardation spectra.     

Comparison of the standard Euler-Euler and hybrid Euler-Lagrange approaches for modeling particle transport in a pilot-scale circulating fluidized bed

Particle transport phenomena in small-scale circulating fiuidized beds （CFB） can be simulated using the Euler-Euler, discrete element method, and Euler-Lagrange approaches. In this work, a hybrid Euler-Lagrange model known as the dense discrete phase model （DDPM）, which has common roots with the multiphase particle-in-cell model, was applied in simulating particle transport within a mid-sized experimental CFB facility. Implementation of the DDPM into the commercial ANSYS Fluent CFD package is relatively young in comparison with the granular Eulerian model. For that reason, validation of the DDPM approach against experimental data is still required and is addressed in this paper. Additional difficulties encountered in modeling fluidization processes are connected with long calculation times. To reduce times, the complete boiler models are simplified to include just the combustion chamber. Such simplifications introduce errors in the predicted solid distribution in the boiler. To investigate the conse- quences of model reduction, simulations were made using the simplified and complete pilot geometries and compared with experimental data. All simulations were performed using the ANSYSFLUENT 14.0 package. A set of user defined functions were used in the hybrid DDPM and Euler-Euler approaches to recirculate solid particles.     

干涉型光纤陀螺仪零漂建模方法

光纤陀螺仪零漂是衡量光纤陀螺仪精度的重要指标。文中对某光纤陀螺仪的零偏数据进行分析和预处理,采用时间序列分析法建立了AR（2）模型,同时基于BP神经网络建立了预测模型。建模结果分析表明：AR建模方法简单易行,但适用性不如BP网络模型,BP网络模型建模精度高,但算法复杂且收敛速度慢,容易陷入局部极小,因此采用了改进训练方法,改善了BP网络性能。