创生“数尺”:由“具体数学”走向“形式数学”——《认识负数》教学新探

用温度计引入负数教学值得商榷是共识,但离开了温度计后学生理解负数又缺少了直观的支撑。从知识发生、发展的角度切入,以＂＋＂＂-＂作为运算符号与性质符号的统一为抓手展开教学,则少了直观多了演绎,似乎不够完美。创生＂数尺＂引入负数,可帮助学生实现＂由具体数学向形式数学的第一次转折＂。

水平摆倾斜仪“数尺”记录法的可行性

水平摆倾斜仪“数尺”记录法经廿多个台站六年来的使用,取得了良好效益。本文导出其误差公式并进行了精度分析,论证了该法的可行性。

Establishment of size-dependant constitutive model of micro-sheet metal materials

The inherent mechanism of size effect in micro-sheet material behavior of plastic forming was explained by the surface layer model and theory of metal crystal plasticity. A size-dependant constitutive model based on the surface layer model was established by introducing the scale parameters and modifying the classical Hall-Petch equation. The influence of the geometric dimensions and the grain size on the flow behavior of the material was discussed using the new material constitutive model. The results show that, the flow stress decreases while the sheet metal thickness decreases when the grain size keeps constant, and the micro-sheet metal with a larger grain size is more easily to be influenced by the size effects. The material constitutive model established is validated by the stress-strain curve of the micro-sheet metal with different thicknesses derived from the tensile experiments. The rationality of the material model is verified by the fact that the calculation results are consistent with the experimental results.

Soil-structure interaction of unsymmetrical trench installation culvert

The computation of the design load on culverts in the current Chinese General Code for Design of Highway Bridges and Culverts （CGCDHBC）is primarily based on the linear earth pressure theory, which cannot accurately reflect the changes in vertical loads on trench installation culverts. So the changes in vertical earth pressure and soil arching effect in the backfill for an unsymmetrical trench installation culvert are studied based on a full scale experiment and finite element （FE） simulation. The variation laws of foundation pressure and settlement are also analyzed. Meanwhile, the influence of eccentric load induced by an unsymmetrical trench installation on the interaction of a soil- structure system is discussed. Results show that soil arch is formed when the backfill on the culvert reaches a certain height. It can relieve the earth pressure concentration on the crest of the culvert, but it is instable. The earth pressures obtained by full scale experiment and numerical simulation are greater than those calculated by the current CGCDHBC method. The eccentric load effect on the culvert has a significant influence on the stress states and deformation of the soil-structure system.

FLOW CHARACTERISTIC AND HEAT TRANSFER FOR SINGLE PHASE GASEOUS IN SLIP REGIME OF MICROCHANNEL FLOW

Based on analyzing some simulation models of single phase gaseous flow in microchannels （0. 001〈 Kn〈0. 1 ）, a numerical simulation of N-S equations with the slip model is presented. In the simulation, the collocated grid and the SIMPLE scheme are used. Results show that the pressure in the inlet is changed with Knudsen number. The slip speed and the temperature creep are increased with the augment of Knudsen number. The drag force decreases and the resistance of the heat trensfer has a little increase.

Iterative regularization method for image denoising with adaptive scale parameter

In order to decrease the sensitivity of the constant scale parameter, adaptively optimize the scale parameter in the iteration regularization model （IRM） and attain a desirable level of applicability for image denoising, a novel IRM with the adaptive scale parameter is proposed. First, the classic regularization item is modified and the equation of the adaptive scale parameter is deduced. Then, the initial value of the varying scale parameter is obtained by the trend of the number of iterations and the scale parameter sequence vectors. Finally, the novel iterative regularization method is used for image denoising. Numerical experiments show that compared with the IRM with the constant scale parameter, the proposed method with the varying scale parameter can not only reduce the number of iterations when the scale parameter becomes smaller, but also efficiently remove noise when the scale parameter becomes bigger and well preserve the details of images.

Numerical simulation on size effect of copper with nano-scale twins

To understand the tensile deformation of electro-deposited Cu with nano-scale twins, a numerical study was carried out based on a conventional theory of mechanism-based strain gradient plasticity （CMSG）. The concept of twin lamella strengthening zone was used in terms of the cohesive interface model to simulate grain-boundary sliding and separation. The model included a number of material parameters, such as grain size, elastic modulus, plastic strain hardening exponent, initial yield stress, as well as twin lamellar distribution, which may contribute to size effects of twin layers in Cu polycrystalline. The results provide information to understand the mechanical behaviors of Cu with nano-scale growth twins.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

Measuring particle size distribution and total number in the activation chamber of desulfurization system by PIV

Application of particle image velocity (PIV) techniques for measuringparticle size distribution and total number in an activation chamber of desulfurization system isintroduced. Watersheld algorithm is used to choose the suitable initial gray level threshold whichis used to change the gray level images taken by PIV to black and white ones, then every particle inan image is isolated totally. For every isolating particle, its contour is tracked by the edgeenhancement filter function and kept by Freeman s chain code. Based on a set of particle s chincode, its size and size distribution are calculated and sorted. Finally, the experimental data ofcalcium particles and water drops, separately injected into the activation chamber, and the erroranalysis of data are given out.

Approximation to NLAR(p) with Wavelet Neural Networks

Recently, wavelet neural networks have become a popular tool for non-linear functional approximation. Wavelet neural networks, which basis functions are orthonormal scalling functions, are more suitable in approximating to function. Based on it, approximating to NLAR(p) with wavelet neural networks is studied.

Fractal Characteristics of Aerosols Deposition in the Fiber Surface

To study the effects of particle motion mechanism and size distribution on fractal dimension of dust cake structure,the process of aerosol particles deposition in fibrous filtration medium was simulated on basis of Diffusion-Limited Aggregation(DLA)improving model.In this study,effects of inertia movement and diffusion movement on particles deposition would be considered.In the mean while,ratio of inertia movement to diffusion movement was defined as Pe number.The results show that surface curve of dust cake becomes irregular with Pe reducing and fractal dimension of dust cake surface increased with Pe increasing.The more greater particles dispersion,the more greater dust cake porosity,the more uneven the distribution.The porosity,formed by Polydisperse dust particles,is less than that formed by monodisperse particles.Stronger particle diffusion movement,more uniform the dust cakes was.

Investigation on Zener-Hollomon parameter in the warm-hot deformation behavior of 20CrMnTi

The warm-hot deformation behavior of 20CrMnTi steel was studied with hot compression tests at temperature range of 1123-1273 K and strain rate of 0.1-20 s^-1. The activation energy for warm-hot deformation is 426.064 KJ/mol. The influences of Zener-Hollomon parameter, strain and grain size imposing on the flow stress were analyzed in the temperature range of warm-hot forging. Creep theory and mathematical theory of statistics were used to obtain mathematical models of flow stress. The research and results provide scientific basis for controlling microstructure of forging process through Zener-Hollomon parameter.

Multi-scale and multi-component digital core construction and elastic property simulation

The conventional digital core models are usually small in size and have difficulty in representing the complex structures of heterogeneous rocks;Therefore,the parameters of simulated rock physics are difficult to be referenced.In this study,we propose a feasible simulation method for obtaining multi-scale and multi-component digital cores based on three types of sandstone samples.In the proposed method,the plug and subplug samples are scanned via micro-computed tomography at different resolutions.Furthermore,the images are precisely registered using the proposed hybrid image registration method.In case of high-resolution images,the traditional segmentation method is used to segment the cores into pores and minerals.Subsequently,we established the relations between the gray values and the porosity/mineral content in case of the low-resolution images based on the registered domains and the relation curves were applied to the segmentation of the low-resolution images.The core images constitute the multi-scale and multi-component digital core models after segmentation.Further,the elastic properties of the three samples were simulated at both fine and coarse scales based on the multi-scale and multi-component digital core models,and four component models were considered.The results show that the multi-scale and multi-component digital core models can overcome the representative limits of the conventional digital core models and accurately characterize pores and minerals at different scales.The numerical results of the elastic modulus are more representative at large scales,and considerably reliable results can be obtained by appropriately considering the minerals.

Using Satellite Data to Analyze the Initiation and Evolution of Deep Convective Clouds

In this study, two deep convective cloud cases were analyzed in detail to study their initiation and evolution. In both cases, all deep convective clouds were positioned at the rear of the cold front cloud bands and propagated backward. Satellite data showed that prior to initiation of the deep convective clouds, thermodynamic and moist conditions were favorable for their formation. In the morning, a deep convective cloud at the rear of cold front cloud band propagated backward, the outflow boundary of which created favorable conditions for initiation. An additional deep convective cloud cluster moved in from the west and interacted with the outflow boundary to develop a mesoscale convective system(MCS) with large, ellipse-shaped deep convective clouds that brought strong rainfall. The initiation and evolution of these clouds are shown clearly in satellite data and provide significant information for nowcasting and short-term forecasting.

Parameter optimization for improved aerodynamic performance of louver-type wind barrier for train-bridge system

To improve the safety of trains running in an undesirable wind environment,a novel louver-type wind barrier is proposed and further studied in this research using a scaled wind tunnel simulation with 1:40 scale models.Based on the aerodynamic performance of the train-bridge system,the parameters of the louver-type wind barrier are optimized.Compared to the case without a wind barrier,it is apparent that the wind barrier improves the running safety of trains,since the maximum reduction of the moment coefficient of the train reaches 58%using the louver-type wind barrier,larger than that achieved with conventional wind barriers(fence-type and grid-type).A louver-type wind barrier has more blade layers,and the rotation angle of the adjustable blade of the louver-type wind barrier is 90–180°(which induces the flow towards the deck surface),which is more favorable for the aerodynamic performance of the train.Comparing the 60°,90°and 120°wind fairings of the louver-type wind barrier blade,the blunt fairing is disadvantageous to the operational safety of the train.

Influence of Fine Sediment on the Fluidity of Debris Flows

Debris flows include a great diversity of grain sizes with inherent features such as inverse grading, particle size segregation, and liquefaction of fine sediment. The liquefaction of fine sediment affects the fluidity of debris flows, although the behavior and influence of fine sediment in debris flows have not been examined sufficiently. This study used flume tests to detect the effect of fine sediment on the fluidity of laboratory debris flows consisting of particles with various diameters. From the experiments, the greatest sediment concentration and flow depth were observed in the debris flows mixed with fine sediment indicating increased flow resistance. The experimental friction coefficient was then compared with the theoretical friction coefficient derived by substituting the experimental values into the constitutive equations for debris flow. The theoretical friction coefficient was obtained from two models with different fine-sediment treatments： assuming that all of the fine sediments were solid particles or that the particles consisted of a fluid phase involving pore water liquefaction. From the comparison of the friction coefficients, a fully liquefaction state was detected for the fine particle mixture. When the mixing ratio and particle size of the fine sediment were different, some other eases were considered to be in a partially liquefied transition state. These results imply that the liquefaction of fine sediment in debris flows was induced not only by the geometric conditions such as particle sizes, but also by the flow conditions.

Fermionic Zero Modes in Gauge and Gravity Backgrounds on a Sphere

In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere axe discussed and some simple fermionic zero modes are obtained.

Mesh Size Effect in Numerical Simulation of Blast Wave Propagation and Interaction with Structures

Numerical method is popular in analysing the blast wave propagation and interaction with structures.However,because of the extremely short duration of blast wave and energy trans-mission between different grids,the numerical results are sensitive to the finite element mesh size.Previous numerical simulations show that a mesh size acceptable to one blast scenario might not be proper for another case,even though the difference between the two scenarios is very small,indicating a simple numerical mesh size convergence test might not be enough to guarantee accu-rate numerical results.Therefore,both coarse mesh and fine mesh were used in different blast scenarios to investigate the mesh size effect on numerical results of blast wave propagation and interaction with structures.Based on the numerical results and their comparison with field test re-sults and the design charts in TM5-1300,a numerical modification method was proposed to correct the influence of the mesh size on the simulated results.It can be easily used to improve the accu-racy of the numerical results of blast wave propagation and blast loads on structures.

Seasonal variation of the Taiwan Warm Current Water and its underlying mechanism

Based on the historical observed data and the modeling results,this paper investigated the seasonal variations in the Taiwan Warm Current Water(TWCW)using a cluster analysis method and examined the contributions of the Kuroshio onshore intrusion and the Taiwan Strait Warm Current(TSWC)to the TWCW on seasonal time scales.The TWCW has obviously seasonal variation in its horizontal distribution,T-S characteristics and volume.The volume of TWCW is maximum(13746 km^3)in winter and minimum(11397 km^3)in autumn.As to the contributions to the TWCW,the TSWC is greatest in summer and smallest in winter,while the Kuroshio onshore intrusion northeast of Taiwan Island is strongest in winter and weakest in summer.By comparison,the Kuroshio onshore intrusion make greater contributions to the Taiwan Warm Current Surface Water(TWCSW)than the TSWC for most of the year,except for in the summertime(from June to August),while the Kuroshio Subsurface Water(KSSW)dominate the Taiwan Warm Current Deep Water(TWCDW).The analysis results demonstrate that the local monsoon winds is the dominant factor controlling the seasonal variation in the TWCW volume via Ekman dynamics,while the surface heat fl ux can play a secondary role via the joint ef fect of baroclinicity and relief.

Experimental study on dimension-form effect for compressive strength of coal

The uniaxial compression tests of cylinder standard specimens and different dimension cube specimens of No.13 coal seam of Jianxin Colliery were carried out using MTS, and the basic mechanics parameters of Jianxin Colliery 13 coal were studied. The dimension-form effect of uniaxial compression strength was analyzed. The exponent formula σc=6.928＋130.269 8 exp（-0.105 95D）of dimension effect was fitted. While the side length of specimen reaches 80 mm, its unaxial strength tends to a stable value which is called to be the strength of coal mass. Studies indicates that since the cube specimen suffered more shake than the cylinder one during machining and processing and the stress is centralized at four corners of cube during compressive experiment, the coal strength of standard cylinder specimen is higher than that of cube one.