Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations

The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time.

Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.

The Effect of Cultural Differences between China and Occident in English Reading Comprehension

With the development of society, English is pushed to be a significant position as a tool of communication. In English learning, the differences between Chinese culture and Occidental culture bring a lot of difficulties in English reading comprehension. And the effect mainly represents in vocabulary, grammar system, language background. This paper analyzes the effect from the three aspects to help Chinese English learners understand the effect better and give them some enlightenment in English reading comprehension.

Effects of Different Seed Stem Sizes on the Changes of Available Elements in Rhizosphere Soil of Fritillaria thunbergii Miq.

[Objectives]This study was conducted to screen suitable seed stems of Fritillaria thunbergii Miq.from different provenances and to provide a theoretical basis for the high-yielding and high-efficiency cultivation of F.thunbergii Miq.introduced to different places.[Methods]F.thunbergii Miq.from four different provenances including Zhejiang,Nantong and Chongqing were introduced and cultivated in Wanzhou of Chongqing.The contents of available Zn,Fe,Mn,Cu,Mo,N,P,K,Ca and Mg in rhizosphere soil of F.thunbergii Miq.during five growing stages were determined after selecting different stem sizes for field cultivation.[Results]Small stems of Pan an and Ningbo provenances(SSG3,121-160/kg)and middle stems of Nantong and Fengjie provenances(SSG2,81-120/kg)showed higher soil availability.[Conclusions]In the process of introduction and cultivation of F.thunbergii Miq.,high yield and high efficiency can be achieved by selecting smaller seed stems of F.thunbergii Miq.

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.

An analysis of Liver and Kidney pathogenesis and treatment based on the theory of interpromotion and restraint of the five elements

The interpromotion and restraint of the five elements is the self-regulation mechanism of the five elements system under normal conditions.For the human viscera,by comparing the images,deducing and classifying the attributes of things,the human viscera are connected with the five elements,and it is concluded that the Liver belongs to Wood and the Kidney belongs to Water.According to the law of mutual generation and restriction between the five elements,the pathogenic causes,pathogenesis and relationship with other viscera of the Liver and Kidney can be known,so as to establish corresponding treatment methods,such as"Nourishing Water and protecting Wood"(providing Kidney for the growth of Liver method),"Golden Water symbiosis"(generation between the Lung and Kidney),"Cultivating soil and generating gold"(warming the Kidney and benefited Spleen method),Supporting lung to suppress Liver,purging heart Fire to nourish renal Water method,etc.It is of referential significance for the treatment of Liver and Kidney diseases in the diagnosis and treatment of traditional Chinese medicine.

Comparative Study on Mineral Elements in the Roots of Rheum tanguticum from Qinghai-Plateau

In the present paper,the authors analysed 10 mineral elements in the roots of Rheum tanguticum collected from 30 different habitats.The mean concentration values of the 10 elements decreased as follows: Ca>Mg>K>Fe>Mn>Cr>Zn>Ni>Cu>Se. Ca,Mg,K and Fe were abundant in this herb.Most elements varied over a wide range depending on the different habitats.The mineral element data were evaluated by principal component analysis to reveal the distribution pattern of elements in root.Four principal components(K-Ca factor,Cu factor,Mg factor and Zn-Se factor) of plant elements were selected.The authors' study provided a new scientific foundation for further studies and general application of this Chinese herb.

The starting mechanism and movement process of the coseismic rockslide: A case study of the Laoyingyan rockslide induced by the “5.12” Wenchuan earthquake

The"5.12"Wenchuan earthquake in 2008 triggered a large number of co-seismic landslides.The rear boundary or cracks of co-seismic landslide are generally located at the steep free surface of thin or thick mountains.Dynamic process of this kind of landslides could be divided into two parts:the seismic dynamic response of the slope and the movement process of rock mass.Taking the Laoyingyan rockslide as an example,the amplification effect was studied by single-degree-of-freedom system analysis method.Besides,the dynamic process of landslide under seismic loading was simulated by the finite difference method(FDM)and discrete element method(DEM).The amplification coefficient of the rockslide to seismic wave is 1.25.The results show that the critical sliding surface of the Laoyingyan rockslide was formed at the 23 th seconds under the action of seismic wave.At the same time,tension failure occurred at the rear edge of the sliding mass and shear failure occurred at the front edge.The maximum displacement was 0.81 m and the initial velocity was 2.78 m/s.During the initiation process of the rockslide,the rock mass firstly broke down along the joints which are along the dip of the rock stratum,and then collapsed bodily along the secondary structural planes.In the process of movement,the maximum velocity of rock mass was 38.24 m/s.After that,the rock mass underwent multiple collisions,including contact,deceleration to 0 and speed recovery after rebound.Finally,due to the constant loss of energy,the rocks stopped and accumulated loosely at the foot of the slope.The longest distance of movement was about 494 m.Besides,the smaller the damping ratio,the farther the rock mass moved.Compared with the results without considering the amplification factor,the movement distance of landslide by considering the amplification factor was more accurate.The study of the Laoyingyan rockslide is helpful to strengthen our field identification of potential co-seismic rockslides.At the same time,understanding its movement and accumulation process can help us better predict the hazard scope of the co-seismic rockslides,and provide a reference for the design of treatment projects.

A Computational Study with Finite Element Method and Finite Difference Method for 2D Elliptic Partial Differential Equations

In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results.

A streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations

A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.

THE EFFECT OF DRAINAGE ON CHEMICALELEMENTS CONTENT OF MARSH

This paper takes marsh in the Sanjiang Plain as an example in order to research the effect of draining on the chemical elements in marsh. The Sanjiang Ecological Test Station of Mire and Uetland serves as the resarch base. The authors selected soil samples in the Sanjiang Plain (the top and the end of the drain, marsh soil and degeneration marsh soil), mainly analyzed contents of main ions (HCO 3 ? , Cl?, SO 4 2? and NO 3 ? ), main heavy metals (Fe, Mn, Zn and Cu), nutritive elements (N, P, K), organic matter and pH value. By testing these samples as above, the paper initially researches the effect on chemical elements content by draining by the means of the contrast of chemical elements contents between marsh soil and degenerative marsh soil and different characteristics of marsh soil elements. Results show that a lot of chemical elements had been lost because of draining.

MODELING OF CONTROLLED THERMO-MECHANICAL PROCESSING OF TUBES FOR ENHANCED MANUFACTURING AND PERFORMANCE

An integrated mathematical model to simulate seamless tube rolling processes has been developed at The Timken Company. The model is capable of simulating the thermal, deformation and microstructure evolution in the piercing, elongating and reducing/sizing and the austenite decomposition in the mill annealing and cooling operations. Finite difference schemes are employed to model cooling, reducing/sizing and stretch reducing, and finite-element schemes are employed to simulate piercing and elongating. The model predicts the thermal history, deformation, rolling load, torque, recrystallization and grain growth in hot tube rolling, austenite decomposition in cooling or annealing, and the final structure-properties. In this paper mathematical models which are employed to describe the thermal, deformation and microstructure evolution along with the modeling results are presented. The developed 'tube rolling mill in the computer' provides a powerful tool for engineers for product and process development, process control, process optimization and quality control.

Simulation of the water level influence on the difference within the water-tube tiltmeter in Shuangyang Lake

This article analyzes the relationship between the water level and the water-tube tilting in Shuangyang lake,based on the differential deformation features reflected by the NS and EW components of the water-tube tiltmeter.The results show a good spatiotemporal consistency between the variation of water level and the NS tilt component,which is considered to be affected by the magnitude and duration of the water level variation in Shuangyang Lake.The article uses Landsat remote sensing image data to extract the water boundary of Shuan-gyang Lake,and takes advantage of the finite element numerical simulation method to build three-dimensional models for different geological structural conditions of the Shuangyang seismostation.The simulation results show that when the underground medium is granite,the effect of water level variation on the vertical displacement of the surface is non-directional.With a 50-m soil layer in Model 2,the simulated NS tilt variation is equivalent to the actual observed water-tube tiltmeter NS component when the water level variation is 0.44 m and 0.8m.When the variation of water level reaches 2.0m,the simulation result of the NS component is 79.6 ms,which is slightly larger than the observed result of 60.32 ms.However,the simulation results show that the variation of the EW component is significantly smaller than that of the NS one.Due to the fact that the Shuan-gyang lake is long in the NS direction and short in the EW direction,the existence of the soil layer tends to generate ground deformation along the NS direction in the vicinity of the lake after the increase of water level,thereby resulting in the difference of the ground deformation in the two directions.

DIFFERENCE SCHEME AND NUMERICAL SIMULATION BASED ON MIXED FINITE ELEMENT METHOD FOR NATURAL CONVECTION PROBLEM

The non_stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non_stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.

Finite Element Solution of a Problem for Gravity Gyroscopic Equation in the Time Domain

To solve the equation for gravity-gyroscopic waves in a rectangular domain, the distinguished algorithm for the solution of the Cauchy problem for a second-order transient equation is proposed. This algorithm is developed by using the time-varying finite element method. The space derivatives in the gravity-gyroscopic wave equation are approximated with finite differences. The stability and accuracy of the method are estimated. The procedure for the implementation of the method is developed. The calculations were performed for determining the steady-state modes of fluctuations of the solutions of the gravity-gyroscopic wave equation depending on the problem parameters.

The dimension split element-free Galerkin method for three-dimensional potential problems

This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Studies of Cultural Differences between English and Chinese Address Terms

English and Chinese address terms have apparent differences,which are caused by their own different social and cultural backgrounds and reflect different cultural implications between the east and the west. To understand the eastern and western culture better,it's necessary to make a comparison between them.

A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

Improvement of prediction model for work roll thermal contour in hot strip mill

Though high accuracy of the thermal contour was obtained while adopting finite element method,it could not meet the real-time requirement.One-dimensional finite difference method could realize real-time control in the case of neglecting both the circumferential and radical heat exchange,but the over-simplified modes resulted in poor accuracy.And two-dimensional full explicit difference was also limited in practical application since its time step was restricted to keep the model stable.Consequently,a new method of alternating direction finite difference was introduced and discussed in the model's stability,calculating speed and precision.Specific work roll after one real rolling unit was researched,The result shows that error of temperature on work roll surface between measured and calculated values is within 5 ℃.The influence of rolling rhythm and strip width on thermal crown was also studied.The conclusion is verified theoretically and practically that it can maintain absolutely stable and meet the online requirement.

Remaining Useful Life Prediction of Rolling Element Bearings Based on Different Degradation Stages and Particle Filter

A method is proposed to improve the accuracy of remaining useful life prediction for rolling element bearings,based on a state space model(SSM)with different degradation stages and a particle filter.The model is improved by a method based on the Paris formula and the Foreman formula allowing the establishment of different degradation stages.The remaining useful life of rolling element bearings can be predicted by the adjusted model with inputs of physical data and operating status information.The late operating trend is predicted by the use of the particle filter algorithm.The rolling bearing full life experimental data validate the proposed method.Further,the prediction result is compared with the single SSM and the Gamma model,and the results indicate that the predicted accuracy of the proposed method is higher with better practicability.