Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS

In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].

Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials

The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional problems.In order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this article.In the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy.Besides,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain.The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy.For instance,the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.

Multiscale Finite Element Method for Coupling Analysis of Heterogeneous Magneto-Electro-Elastic Structures in Thermal Environment

Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.

Optimization of the Dressing Parameters in Cylindrical Grinding Based on a Generalized Utility Function

The existing studies, concerning the dressing process, focus on the major influence of the dressing conditions on the grinding response variables. However, the choice of the dressing conditions is often made, based on the experience of the qualified staff or using data from reference books. The optimal dressing parameters, which are only valid for the particular methods and dressing and grinding conditions, are also used. The paper presents a methodology for optimization of the dressing parameters in cylindrical grinding. The generalized utility function has been chosen as an optimization parameter. It is a complex indicator determining the economic, dynamic and manufacturing characteristics of the grinding process. The developed methodology is implemented for the dressing of aluminium oxide grinding wheels by using experimental diamond roller dressers with different grit sizes made of medium- and high-strength synthetic diamonds type AC32 and AC80. To solve the optimization problem, a model of the generalized utility function is created which reflects the complex impact of dressing parameters. The model is built based on the results from the conducted complex study and modeling of the grinding wheel lifetime, cutting ability, production rate and cutting forces during grinding. They are closely related to the dressing conditions （dressing speed ratio, radial in-feed of the diamond roller dresser and dress-out time）, the diamond roller dresser grit size/grinding wheel grit size ratio, the type of synthetic diamonds and the direction of dressing. Some dressing parameters are determined for which the generalized utility fimction has a maximum and which guarantee an optimum combination of the following： the lifetime and cutting ability of the abrasive wheels, the tangential cutting force magnitude and the production rate of the grinding process. The results obtained prove the possibility of control and optimization of grinding by selecting particular dressing parameters.

Performance driven expression mapping based on segmented examples

We present a method that combines performance-driven method with segmented 3D blendshape models to animate a face. First we prepare key sample examples and corresponding key target examples. Next we segment the whole face into two regions, for each region we reduce dimensionality of source examples using PAC into abstract space which is defined by truncated PCA eigen- vectors. Then for each example we fix the cardinal base function, which can determine the weight of the target example. Finally, in the animation stage we compute the weight of each example for each frame and add the weighted displacement vectors of each re- gion on the general face model.

Improvement of Cardiac Function by Dry Weight Optimization Based on Interdialysis Inferior Vena Caval Diameter (1)

In hemodialysis (HD) patients, the diameter of the inferior vena cava (IVC) serves for evaluation of the amount of body fluid.

The Numerical Integration of Discrete Functions on a Triangular Element

With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.

Signal Separation and Instantaneous Frequency Estimation Based on Multi-scale Chirplet Sparse Signal Decomposition

An approach based on multi-scale ehirplet sparse signal decomposition is proposed to separate the malti-component polynomial phase signals, and estimate their instantaneous frequencies. In this paper, we have generated a family of multi-scale chirplet functions which provide good local correlations of chirps over shorter time interval. At every decomposition stage, we build the so-called family of chirplets and our idea is to use a structured algorithm which exploits information in the family to chain chirplets together adaptively as to form the polyncmial phase signal component whose correlation with the current residue signal is largest. Simultaueously, the polynomial instantaneous frequency is estimated by connecting the linear frequency of the chirplet functions adopted in the current separation. Simulation experiment demonstrated that this method can separate the camponents of the multi-component polynamial phase signals effectively even in the low signal-to-noise ratio condition, and estimate its instantaneous frequency accurately.

Ab Initio Calculation of Dielectric Function in Wurtzite GaN Based on Walter's Model

The wavelength-dependent and frequency-dependent dielectric function of wurtzite-GaN is cMculated totally from fundamental parameters such as the lattice constant using Waiter＇s ab initio model. The errors occurring in the cMculation are carefully reduced by/inear interpolation of energy data. The Kramers-Kronig transform of the real part of greater range is obtained by extrapolation of the reM part. The calculation is time-consuming but meaningful The long-wave results are similar to the experimental data of the photon and are useful for related investigation of properties of wide-gap semiconductors such as electron scattering like the Auger recombination and impact ionization.

Function and Design Idea of UHVDC Test Base

The function of the UHVDC test base of the State Grid Corporation of China (SGCC) is oriented to serve UHVDC power transmission and substation projects, especially power transmission from West China to East China, and to promote localization of UHVDC transmission and substation equipment. In essentials, this test base consists of UHVDC test transmission line, corona cage, outdoor test site, UHV test hall, pollution and environment laboratory, electromagnetic environment simulation test site, insulator laboratory, arrester laboratory and live equipment test field. This paper introduces the function and design idea of the test base, presents the main performance parameters of the above-mentioned test facilities, and summarizes the matters of concern when siting and planning.

On solitary waves.Part 2 A unified perturbation theory for higher-order waves

A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n） （the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.

Predictive functional control （PFC） and its application in chlorinated polyethylene process

The main principle and the characteristic of Predictive Functional Control (PFC) strategy are presented in this paper and the corresponding control system aid design software APC-PFC is also introduced. For a chlorinated polyethylene (CPE) process, a design scheme of cascade predictive functional control system is described and the control performance is improved obviously.

Extended multiscale finite element method for mechanical analysis of heterogeneous materials

An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.

Development of slope mass rating system using K-means and fuzzy c-means clustering algorithms

Classification systems such as Slope Mass Rating(SMR) are currently being used to undertake slope stability analysis. In SMR classification system, data is allocated to certain classes based on linguistic and experience-based criteria. In order to eliminate linguistic criteria resulted from experience-based judgments and account for uncertainties in determining class boundaries developed by SMR system,the system classification results were corrected using two clustering algorithms, namely K-means and fuzzy c-means(FCM), for the ratings obtained via continuous and discrete functions. By applying clustering algorithms in SMR classification system, no in-advance experience-based judgment was made on the number of extracted classes in this system, and it was only after all steps of the clustering algorithms were accomplished that new classification scheme was proposed for SMR system under different failure modes based on the ratings obtained via continuous and discrete functions. The results of this study showed that, engineers can achieve more reliable and objective evaluations over slope stability by using SMR system based on the ratings calculated via continuous and discrete functions.

Characterisation of the plasma density with two artificial neural network models

This paper establishes two artificial neural network models by using a multi layer perceptron algorithm and radial based function algorithm in order to predict the plasma density in a plasma system. In this model, the input layer is composed of five neurons： the radial position, the axial position, the gas pressure, the microwave power and the magnet coil current. The output layer is the target output neuron： the plasma density. The accuracy of prediction is tested with the experimental data obtained by the Langmuir probe. The effectiveness of two artificial neural network models are demonstrated, the results show good agreements with corresponding experimental data. The ability of the artificial neural network model to predict the plasma density accurately in an electron cyclotron resonance-plasma enhanced chemical vapour deposition system can be concluded, and the radial based function is more suitable than the multi layer perceptron in this work.

3D image reconstruction with controllable spatial filtering based on correlation of multiple periodic functions in computational integral imaging

We propose a novel method of slice image reconstruction with controllable spatial filtering by using the correlation of periodic delta-function arrays （PDFAs） with elemental images in computational integral imaging. The multiple PDFAs, whose spatial periods correspond to object＇s depths with the elemental image array （EIA）, can generate a set of spatially filtered EIAs for multiple object depths compared with the conventional method for the depth of a single object. We analyze a controllable spatial filtering effect by the proposed method. To show the feasibility of the proposed method, we carry out preliminary experiments for multiple objects and present the results.

Modeling of Transient Thermal Conditions in Cutting

The thermal conditions like the temperature distribution and the heat fluxes during metal cutting have a major influence on the machinability, the tool lifetime, the metallurgical structure and thus the functionality of the work piece. This in particular applies for manufacturing processes like milling, drilling and turning for high-value turbomachinery components like impellers, combustion engines and compressors of the aerospace and automotive industry as well as energy generation, which play a major role in modern societies. However, numerous analytical and experimental efforts have been conducted in order to understand the thermal conditions in metal cutting, yet many questions still prevail. Most models are based on a stationary point of view and do not include time dependent effects like in intensity and distribution varying heat sources, varying engagement conditions and progressive tool wear. In order to cover such transient physics an analytical approach based on Green＇s functions for the solution of the partial differential equations of unsteady heat conduction in solids is used to model entire transient temperature fields. The validation of the model is carried out in orthogonal cutting experiments not only punctually but also for entire temperature fields. For these experiments an integrated measurement of prevailing cutting force and temperature fields in the tool and the chip by means of high-speed thermography were applied. The thermal images were analyzed with regard to thermodynamic energy balancing in order to derive the heat partition between tool, chips and workpiece. The thus calculated heat flow into the tool was subsequently used in order to analytically model the transient volumetric temperature fields in the tool. The described methodology enables the modeling of the transient thermal state in the cutting zone and particular in the tool, which is directly linked to phenomena like tool wear and workpiece surface modifications.

Application of aluminosilicate clay mineral-based composites in photocatalysis

Aluminosilicate clay mineral(ACM)is a kind of typical raw materials that used widely in manufacturing industry owing to the abundant reserve and low-cost exploring.In past two decades,in-depth understanding on unique layered structure and abundant surface proper-ties endows ACM in the emerging research and application fields.In field of solar-chemical energy conversion,ACM has been widely used to support various semiconductor photocata-lysts,forming the composites and achieving efficient conversion of reactants under sunlight irradiation.To date,classic ACM such as kaolinite and montmorillonite,loaded with semi-conductor photocatalysts has been widely applied in photocatalysis.This review summaries the recent works on ACM-based composites in photocatalysis.Focusing on the properties of surface and layered structure,we elucidate the different features in the composition with various functional photocatalysts on two typical kinds of ACM,i.e.,type 1∶1 and type 2∶1.Not only large surface area and active surface hydroxyl group assist the substrate adsorption,but also the layered structure provides more space to enlarge the application of ACM-based photocatalysts.Besides,we overview the modifications on ACM from both external surface and the inter-layer space that make the formation of composites more efficiently and boost the photo-chemical process.This review could inspire more upcoming design and synthesis for ACM-based photocatalysts,leading this kind of economic and eco-friendly materials for more practical application in the future.