Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

An efficient method for train-track-substructure dynamic interaction analysis by implicit-explicit integration and multi-time-step solution

In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solution method(abbreviated as mI-nE-MTS method).The TTS system is divided into train-track subsystem and substruc-ture subsystem.Considering that the root cause of low effi-ciency of obtaining TTS solution lies in solving the alge-braic equation of the substructures,the high-efficient Zhai method,an explicit integration scheme,can be introduced to avoid matrix inversion process.The train-track system is solved by implicitly Park method.Moreover,it is known that the requirement of time step size differs for different sub-systems,integration methods and structural frequency response characteristics.A multi-time-step solution is pro-posed,in which time step size for the train-track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand,namely the time spent for m implicit integral steps is equal to n explicit integral steps,i.e.,mI=nE as mentioned above.The numeri-cal examples show the accuracy,efficiency,and engineering practicality of the proposed method.

Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems

We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation.

The Effectiveness of Explicit Vocabulary Instruction on Productive Vocabulary Learning in Writing Among Intermediate School Learners in Saudi Arabia

This study aimed to identify the effectiveness of explicit vocabulary instruction on productive vocabulary learning in writing among intermediate school learners in Saudi Arabia,verify the existence of any statistically significant differences at the significance level of 0.01 between the mean scores of the post-test of the control group and the experimental group in the vocabulary test,and verify the existence of any statistically significant differences at the significance level of 0.01 between the mean scores of the pre-and post-test of the experimental group in the vocabulary test in favor of the post-test.The study community consisted of all intermediate school students in the Kingdom of Saudi Arabia,while the study sample included 30 students.The experimental method was adopted to identify the effectiveness of explicit vocabulary instruction on productive vocabulary learning in writing and the achievement test was used as the study tool.The study reached many results including there were no statistically significant differences at the significance level of 0.01 between the mean scores of the post-test of the control group and the experimental group in the vocabulary test and there were no statistically significant differences at the significance level of 0.01 between the mean scores of the pre-and post-test of the experimental group in the vocabulary test in favor of the post-test.According to these results,some recommendations and proposals were made including training English teachers at the intermediate school level in the Kingdom of Saudi Arabia,on explicit vocabulary instruction and conducting future researches on the trends of English teachers at the intermediate school level,in the Kingdom of Saudi Arabia,regarding the adoption of explicit vocabulary instruction while teaching the English language.

A Case Study of the Explicit and Implicit Teaching:Based on a Senior High Grammar Course

More researchers have been attempting to clarify some appropriate approaches in teaching and learning grammar especially in the implicit or explicit way. I would attempt to find out some hints in the grammar course offered by a senior teacher of a senior high in order to provide some ideas and inspirations toward future teaching and researches.

基于ABAQUS/Explicit的桩腿耦合缓冲器准静态分析

桩腿耦合缓冲器在应用中主要起减小撞击力和限制上下结构相对位移的作用。在设计时,必须考虑到橡胶材料的大变形、橡胶-钢的接触和摩擦问题,它具有几何、材料和边界的三种非线性。通过结构非线性有限元软件ABAQUS/Explicit建立了桩腿耦合缓冲器的三维体单元模型,用基于中心差分法的准静态法,对其在水平和垂直两种工况下的准静力变形过程进行了数值仿真,从能量、接触、刚度与吸能以及应力应变等各方面对计算结果及其合理性进行了分析,并针对现有结构尺寸提出了改进建议。分析表明使用准静态分析方法是可行的,对桩腿耦合缓冲器的优化设计具有一定参考价值。

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering-Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.

On k-Error Linear Complexity of Some Explicit Nonlinear Pseudorandom Sequences

Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol＇s, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.

Explicit Grammar Instruction in L2 Learners'Writing Development:Effective or Ineffective?

It has long been in dispute about whether explicit grammar teaching is more effective in second language learning or implicit grammar teaching is.However,there are more than one factor to take into consideration while discussing which way is better for L2 learners.This short essay aims at depicting three respects concerning grammar teaching,namely learning context,language learners'beliefs and needs,and grammar instruction.When educators and practitioners try to adopt grammar instruction either implicitly or explicitly in L2 learners'writing development,they probably need to consider the above three factors and to find out the best way to produce more effective teaching results among their students.

Evaluation of Forecast Performance of an Economical Explicit Time Integration Scheme in a Limited Area Model over Indian Region

An economical explicit scheme of time integration is implemented in a regional model over Indian region to achieve computational economy. The model is also integrated by explicit Leap-Frog Scheme. The performance of economical explicit scheme is evaluated by comparing the forecast results with those produced by leap-frog scheme. The results show that the economical explicit scheme produces more or less similar forecasts as compared to those produced with leap-frog scheme. However, application of the economical explicit scheme saves substantial amount of computer time. The scheme is found nearly four times economical as compared to explicit leap-frog scheme.

Implicit Learning and Explicit Learning in Second Language Vocabulary Acquisition

Implicit and explicit learning strategies of SL vocabulary acquisition are summarized based on precious studies and experiments. It is concluded that implicit learning strategies dolittlehelpto SL vocabulary acquisition, but explicit learning strategies play a very important part in SL vocabulary acquisition. Besides, an assumption is proposed: the more obvious explicit learning is in vocabulary acquisition, the more words learners can acquire. It is hoped that this research has certain implications for SL learners and teaching.

Dynamic explicit FE modeling of hot ring rolling process

A new FE modeling method of hot ring rolling was presented by solving key technologies such as contact and heat boundary conditions,motion control over guide rolls,and mass scaling.The method has the following features:1)the elastic-plastic dynamic explicit approach instead of the static implicit approach is adopted to solve the process so as to greatly improve computational efficiency without sacrificing computational accuracy;2)the coupled thermal-mechanical effect is considered as opposed to the conventional isothermal assumption,which is more practical;3)in contrast to the simplified 2D or local 3D ring model,the full 3D ring is modeled to simulate the process.Based on the FE modeling method,two cases of hot plain ring rolling are simulated in the FEA software ABAQUS/Explicit.The simulation results are compared with the experimental measurements and the good agreement between them is observed regarding the material flow and the temperature distribution of the ring.

基于ABAQUS/Explicit的铣削加工物理仿真技术研究

为预测铣削力,在ABAQUS/Explicit平台上建立了铣削加工物理仿真模型,以高速侧铣加工铝合金7050-T7451槽腔为例,仿真了铣削力,并与实验结果进行了对比。结果表明仿真铣削力与实际铣削力误差最大为20.89%,认为仿真模型可以代替大量的切削实验来获得不同加工参数和刀具参数下的铣削力。

OPTIMIZATION OF AUTOBODY PANEL STAMPING PROCESS BASED ON DYNAMIC EXPLICIT FINITE ELEMENT METHOD

Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this paper, for the sake of illustrating in detail how dynamic explicit finite element method is applied to the numerical simulation of the autobody panel forming process,an example of optimization of stamping process pain meters of an inner door panel is presented. Using dynamic explicit finite element code Ls-DYNA3D, the inner door panel has been optimized by adapting pa- rameters such as the initial blank geometry and position, blank-holder forces and the location of drawbeads, and satisfied results are obtained.

An explicit finite element－finite difference method for analyzing the effect of visco－elastic local topography on the earthquake motion

An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability.

A CLASS OF EXPLICIT FORWARD TIME-DIFFERENCE SQUARE CONSERVATIVE SCHEMES

In the present paper, a class of explicit forward time-difference schemes are established from a geometric view with strict analytical deductions. This class includes the schemes with a constant time interval and with adjustable time intervals, which is proved to be effective and remarkably time-saving in numerical tests and applications.

Parallelized Implementation of the Finite Particle Method for Explicit Dynamics in GPU

As a novel kind of particle method for explicit dynamics,the finite particle method(FPM)does not require the formation or solution of global matrices,and the evaluations of the element equivalent forces and particle displacements are decoupled in nature,thus making this method suitable for parallelization.The FPM also requires an acceleration strategy to overcome the heavy computational burden of its explicit framework for time-dependent dynamic analysis.To this end,a GPU-accelerated parallel strategy for the FPM is proposed in this paper.By taking advantage of the independence of each step of the FPM workflow,a generic parallelized computational framework for multiple types of analysis is established.Using the Compute Unified Device Architecture(CUDA),the GPU implementations of the main tasks of the FPM,such as evaluating and assembling the element equivalent forces and solving the kinematic equations for particles,are elaborated through careful thread management and memory optimization.Performance tests show that speedup ratios of 8,25 and 48 are achieved for beams,hexahedral solids and triangular shells,respectively.For examples consisting of explicit dynamic analyses of shells and solids,comparisons with Abaqus using 1 to 8 CPU cores validate the accuracy of the results and demonstrate a maximum speed improvement of a factor of 11.2.

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.

MULTIPLE ELECTRONIC CONTROL UNITS CALIBRATION SYSTEM BASED ON EXPLICIT CALIBRATION PROTOCOL AND J1939 PROTOCOL

The rising number of electronic control units （ECUs） in vehicles and the decreasing time to market have led to the need for advanced methods of calibration. A multi-ECU calibration system was developed based on the explicit calibration protocol （XCP） and J1939 communication protocol to satisfy the need of calibrating multiple ECUs simultaneously. The messages in the controller area network （CAN） are defined in the J1939 protocol. Each CAN node can get its own calibration messages and information from other ECUs, and block other messages by qualifying the CAN messages with priority, source or destination address. The data field of the calibration message is designed with the XCP, with CAN acting as the transport layer. The calibration sessions are setup with the event-triggered XCP driver in the master node and the responding XCP driver in the slave nodes. Mirroring calibration variables from ROM to RAM enables the user to calibrate ECUs online. The application example shows that the multi-ECU calibration system can calibrate multiple ECUs simultaneously, and the main program can also accomplish its calculation and send commands to the actuators in time. By the multi-ECU calibration system, the calibration effort and time can be reduced and the variables in ECU can get a better match with the variables of other ECUs.

DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS

In this paper, we study a differential-difference equation associated with discrete 3 × 3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-difference equation is given. In order to solve the differential-difference equation, a systematic algebraic algorithm is given. As an application, explicit soliton solutions of the differential-difference equation are given.