数感分析:数学解题思路的分析方法——以2020年高考试题为例

数感是数学核心素养的核心成分.数感分析有利于发现解题的思路或结论.数感的产生依赖于丰富的经验、敏锐的眼光、灵活的思维.因此,数学解题是培养数感的重要资源.

Numerical Analysis of Steady Smoldering of Biomass Rods

Understanding the steady mechanism of biomass smoldering plays a great role in the utilization of smoldering technology.In this study numerical analysis of steady smoldering of biomass rods was performed.A two-dimensional(2D)steady model taking into account both char oxidation and pyrolysis was developed on the basis of a calculated propagation velocity according to empirical correlation.The model was validated against the smoldering experiment of biomass rods under natural conditions,and the maximum error was smaller than 31%.Parameter sensitivity analysis found that propagation velocity decreases significantly while oxidation area and pyrolysis zone increase significantly with the increasing diameter of rod fuel.

Numerical modeling of the 2D time-domain transient electromagnetic secondary field of the line source of the current excitation

To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of the line source based on the DuFort- Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force （Emf）, and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the fiat layered model with high precision--the maximum relative error is less than 0.01% between our method and the analytical method--and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.

Parametric analysis on buffeting performance of a long-span high-speed railway suspension bridge

The buffeting performance of kilometer-level high-speed railway suspension bridges has a great impact on the smooth operation of high-speed trains.To investigate the buffeting performance of the structure significantly different from traditional suspension bridges,the first long-span high-speed railway suspension bridge,Wufengshan Yangtze River Bridge(WYRB),is taken as a numerical example to demonstrate the effects of structural parameters and wind field parameters on the buffeting responses.Based on the design information,the spatial finite element model(FEM)of WYRB is established before testing its accuracy.The fluctuating wind fields are simulated via both classical and stochastic wave based spectral representation method(SRM).Finite element method is further taken to analyze the parametric sensitivity on wind induced buffeting responses in time domain.The results show that the vertical displacement is more sensitive to the changing dead load than the lateral and torsional ones.The larger stiffness of the main girder and the lower sag-to-span ratio are both helpful to reduce the buffeting responses.Wind spectrum and coherence function are key influencing factors to the responses so setting proper wind field parameters are essential in the wind-resistant design stage.The analytical results can provide references for wind resistance analysis and selection of structural and fluctuating wind field parameters for similar long-span high-speed railway suspension bridges.

Parameter sensitivities analysis for classical flutter speed of a horizontal axis wind turbine blade

The parameter sensitivities affecting the flutter speed of the NREL （National Renewable Energy Laboratory） 5-MW baseline HAWT （horizontal axis wind turbine） blades are analyzed. An aeroelastic model, which comprises an aerodynamic part to calculate the aerodynamic loads and a structural part to determine the structural dynamic responses, is established to describe the classical flutter of the blades. For the aerodynamic part, Theodorsen unsteady aerodynamics model is used. For the structural part, Lagrange’s equation is employed. The flutter speed is determined by introducing “V–g” method to the aeroelastic model, which converts the issue of classical flutter speed determination into an eigenvalue problem. Furthermore, the time domain aeroelastic response of the wind turbine blade section is obtained with employing Runge-Kutta method. The results show that four cases （i.e., reducing the blade torsional stiffness, moving the center of gravity or the elastic axis towards the trailing edge of the section, and placing the turbine in high air density area） will decrease the flutter speed. Therefore, the judicious selection of the four parameters （the torsional stiffness, the chordwise position of the center of gravity, the elastic axis position and air density） can increase the relative inflow speed at the blade section associated with the onset of flutter.

A Preliminary Global Analysis of Remotely Sensed Radiation Characteristics of Ground Features:Ⅱ. Result Discussion

Based on the L,B and V statistics of the 106 ground feature groups or the 769 ground feature class units in the world presented in the part I of the paper,the distribution of the world ground features on the axes of L,B and V,in the planes of L-B,L-V and B-V and in the space of L-B-V was discussed.And the typical numerical characteristics of the various ground features were also summarized.

Study on the Correlation Between Chlorophyll Maximum and Remote Sensing Data

Based on the in situ optical measurements in the Bohai Sea of China, which belongs to a typical case-2 water area, we studied the characteristics of DCM (deep chlorophyll maximum) such as its spatial distribution, vertical profile, etc. We found that when the depth of the chlorophyll maximum is comparatively small, even in turbid coastal water regions, there is always a good correlation between the concentrations of chlorophyll maximum and the satellite-received signals in blue-green spectral bands; the correlation is even better than that between the surface chlorophyll concentrations and the satellite-received signals. The strong correlation existing even in turbid coastal water regions indicates that an ocean color model to retrieve the concentration of DCM can be constructed for coastal waters if a comprehensive knowledge of the vertical distribution of chlorophyll concentration in the Bohai Sea of China is available.

Sensitivity Analysis of Thermal Equilibrium Parameters of MIKE 11 Model:A Case Study of Wuxikou Reservoir in Jiangxi Province of China

Sensitivity analysis of thermal equilibrium parameters in the reservoir module of MIKE 11 model was conducted for the Wuxikou Reservoir in Jiangxi Province of China in order to apply the module to the environmental impact assessment to accurately predict water temperature of reservoirs.Results showed that radiation parameter A and evaporation-first parameter were much more sensitive than other parameters.The values of the radiation parameter A ranged from 0.10 to 0.34.The values of evaporation-first parameter varied from 0 to 10.The sensitivity of solar absorption parameters was less than that of evaporation parameter,of which light attenuation values ranged from 0.5 to 0.7,and this parameter would not impact model results if it was more than 2.Constants in Beer's law ranged from 0.2 to 0.7.Radiation parameter B was not more sensitive than evaporation parameter and its reasonable range was higher than 0.48.The fitting curves showed consistent changing tendency for these parameters within the reasonable ranges.Additionally,all the thermal equilibrium parameters had much more important effects on surface water temperature than deep water temperature.Moreover,if no observed data could be obtained,the local empirical value would be used to input to the MIKE 11 model to simulate the changes in the discharged outflow-water temperature qualitatively.

Similarity theory for the physical simulation of natural gas hydrate reservoir development

In order to apply physical simulation results to natural gas hydrate reservoir parameters to provide a theoretical framework for the design of a development plan,an analytical equation method was used to obtain the similarity criteria of natural gas hydrate reservoir development by physical simulation,based on a mathematical model of natural gas hydrate development.Given the approach of numerical simulation,a sensitivity analysis for all parameters was carried out,which specifically demonstrated that initial temperature is the most important parameter.Parameters of thermal conductivity coefficients are not necessary for conducting the NGH dissociation process,which will fundamentally simplify the design and establishment of the model.The analysis provides a sound theoretical basis and design principles for particular similarity.

Landslide stability for Shuitianba in the Three Gorges area

According to the data of preliminary survey, the authors established a landslide geological model,on the basis of analyses on the sensitivity of landslide, tried to simulate and calculate the landslide stability of Shuitianba with the method of transfer coefficient when it is under different strength parameters, and study the landslide mechanism. The results show that it is sensitive to the effects of shear strength parameters of sliding zone and groundwater level on landslide stability safety coefficient, which provides reliable basis for calculation of landslide stability.

Sensitivity analysis of geomechanical parameters affecting a wellbore stability

Wellbore stability analysis is a growing concern in oil industries. There are many parameters affecting the stability of a wellbore including geomechanical properties (e.g., elastic modulus, uni-axial compressive strength (UCS) and cohesion) and acting forces (e.g., field stresses and mud pressure). Accurate determination of these parameters is time-consuming, expensive and sometimes even impossible. This work offers a systematic sensitivity analysis to quantify the amount of each parameter’s effect on the stability of a wellbore. Maximum wellbore wall displacement is used as a stability factor to study the stability of a wellbore. A 3D finite difference method with Mohr model is used for the numerical modeling. The numerical model is verified against an analytical solution. A dimensionless sensitivity factor is developed in order to compare the results of various parameters in the sensitivity analysis. The results show a different order of importance of parameters based on rock strength. The most sensitive properties for a weak rock are the maximum horizontal stress, internal friction angle and formation pressure, respectively, while for a strong rock, the most sensitive parameters are the maximum horizontal stress, mud pressure and pore pressure, respectively. The amount of error in wellbore stability analysis inflicted by the error in estimation of each parameter was also derived.

Quantitative investigation on micro-parameters of cemented paste backfill and its sensitivity analysis

The mechanical properties of cemented paste backfill(CPB) depend heavily on its pore structural characteristics and micro-structural changes. In order to explore the variation mechanisms of macro-mechanical characteristics and micro-structure of CPB. CPB specimens with different mass concentrations prepared from the full tailings of Xianglushan Tungsten Ore were micro-tests. Moreover, acquired pore digital images were processed by using the pores(particles) and cracks analysis system(PCAS), and a sensitivity analysis was performed. The results show that as the mass concentration of CPB increases from 70% to 78%, the porosity, the average pore area and the number of pores drop overall, leading to a decline in the pores opening degree and enhancing the mechanical characteristics. As the mass concentration of CPB increases, the trend of fractal dimension, probability entropy and roundness is reduced, constant and increased, which can result in an enhancement of the uniformity, an unchanged directionality and more round pores. According to the definition of sensitivity, the sensitivities of various micro-parameters were calculated and can be ranked as porosity > average pore area > number of pores > roundness > fractal dimension > probability entropy.

Structural-acoustic coupling characteristics of honeycomb sandwich plate based on parameter sensitivity analysis

The structural-acoustic coupling model for isotropic thin elastic plate was extended to honeycomb sandwich plate(HSP) by applying Green function method.Then an equivalent circuit model of the weakly-strongly coupled system was proposed.Based on that,the estimation formulae of the coupled eigenfrequency were derived.The accuracy of the theoretical predictions was checked against experimental data,with good agreement achieved.Finally,the effects of HSP design parameters on the system coupling degree,the acoustic cavity eigenfrequency,and sound pressure response were analyzed.The results show that mechanical and acoustical characteristics of HSP can be improved by increasing the thickness of face sheet and reducing the mass density of material.

Unprecedented Retreat in a 50-Year Observational Record for Petermann Glacier, North Greenland

Petermann Glacier is a marine-terminating outlet glacier that had a 70 km-long floating ice tongue prior to a ～ 270 km2 calving event that was observed from satellite sensors in August 2010,shortening the ice tongue by ～ 27 km.Further,in July 2012,another 10 km was lost through calving.In order to understand these events in perspective,here the authors perform a long-term data analysis of Petermann Glacier calving-front variability and ice velocity for each year in the 1990s-2000s,supplemented by available observations from the previous three decades.Five major （on the order of 100 krm2） calving events are identified,with ～ 153 km2 calved from 1959 to 1961,～ 168 km2 in 1991,～ 71 km2 in 2001,～ 270 km2 in 2010,and ～ 130 km2 in 2012-as well as ～ 31 k m2 calved in 2008.The increased frequency of major calving events in recent years has left the front terminus position retreated nearly 25 km beyond the range of observed in previous decades.In contrast,stable ice-dynamics are suggested from ice-velocity measurements made each year between 1993-2012,which are on average 1063 m yr-1,with limited interannual variability and no significant trend; moreover,there is no apparent relationship between ice-velocity variability and calving events.The degree to which the massive calving events in 2010 and 2012 represent natural episodic variability or a response to atmospheric and/or oceanic changes remains speculative; however,melt-induced weakening of the floating ice tongue in recent years is strongly suggested.

Sensitivity analysis on globularized fraction of α lamellae in titanium alloys

The sensitivity analysis functions on globularized fraction ofαlamellae were established using a physically-based microstructure model and gradient method.These functions were applied to the sensitivity analysis on globularized fraction ofαlamellae in TC17 alloy.The material constants in these functions are determined using the genetic algorithm-based objective optimization technique.The globularized fraction ofαlamellae during isothermal compression of TC17 alloy was quantitatively analyzed based on scanning electron microscopy(SEM)observation.The results show thatαlamellae mostly change to equiaxedαgrains at a deformation temperature of 1083 K,a strain rate of 0.01 s^-1 and a strain of 1.2.The globularized fraction decreases with increasing strain rate because lower strain rate provides enough time for the spheroidization.The effect of deformation temperature on the globularized fraction is controlled by the strain rate.And,the predicted derivations of globularized fraction with respect to processing parameters show good agreement with the experimental values.

A theoretical model for the estimation of maximum impact force from a rockfall based on contact theory

Rockfall poses a great threat to buildings and personal security. To understand the dynamic characteristics of rockfalls is a prerequisite for disaster prevention and assessment. Models for rockfalls in different forms are established based on the theory of rigid body motion. The equivalent velocity considering the rotational effect is determined by the energy ratio. Besides, considering plastic deformation and nonlinear hardening, the maximum impact force is estimated based on the Hertz contact theory. Then, a case study is carried out to illustrate the applicability of the model and sensitive analyses on some affecting parameters are also made. Calculation results show that the maximum impact force increases with the increasing of incident velocity, angle and slope gradient reflected by the changing of energy ratio. Moreover, the model for the estimation of maximum impact force is validated by two different scales of experiments and compared with other theoretical models. Simulated maximum impact forces agree well with the experiments.

Analysis of photonic crystal fiber sensor character

The special character of a PCF which is used as a gas or liquid sensor is discussed. The field distribution is analyzed when the solid core PCF is injected with different medium that has different relative dielectric constant （or refractive index）. And the experiential formulas of the relation between refractive index of some kinds of liquid and their concentration are given, in order to measure the concentration of the relative liquid. At the same time, the effect of propagation constant on PCF sensor character is also discussed. Furthermore, the photonic medium relative dielectric constant, when it is injected with . band-gap （PBG） of PCF （PBG-PCF） is calculated at different different medium. That is the principle basis for this kind of PCF sensors.

Numerical analysis of 3D spot continual induction hardening on curved surface of AISI 1045 steel

In order to investigate and predict the material properties of curved surface AISI 1045 steel component during spot continual induction hardening(SCIH),a 3D model for curved surface workpieces which coupled electromagnetic,temperature and phase transformation fields was built by finite element software ANSYS.A small size inductor and magnetizer were used in this model,which can move along the top surface of workpiece flexibly.The effect of inductor moving velocity and workpiece radius on temperature field was analyzed and the heating delay phenomenon was found through comparing the simulated results.The temperature field results indicate that the heating delay phenomenon is more obvious under high inductor moving velocity condition.This trend becomes more obvious if the workpiece radius becomes larger.The predictions of microstructure and micro-hardness distribution were also carried out via this model.The predicted results show that the inductor moving velocity is the dominated factor for the distribution of 100% martensite region and phase transformation region.The influencing factor of workpiece radius on 100% martensite region and phase transformation region distribution is obvious under relatively high inductor moving velocity but inconspicuous under relatively low inductor moving velocity.

SPH-FEM simulations of microwave-treated basalt strength

Microwave precondition has been highlighted as a promising technology for softening the rock mass prior to rock breakage by machine to reduce drill bit/cutter wear as well as inverse production rate.To numerically explore the effect of numerical parameters on rock static strength simulation,and determine the numerical mechanical parameters of microwave-treated basalts for future drilling and cutting simulations,numerical models of uniaxial compression strength(UCS)and Brazilian tensile strength(BTS)were established with the coupling of smoothed particle hydrodynamics and finite element method(SPH-FEM).To eliminate the large rock strength errors caused by microwave-induced damage,the cohesion and internal friction angle of microwave-treated basalt specimens with the same microwave treatment parameters were calibrated based on a linear Mohr-Coulomb theory.Based on parametric sensitivity analysis of SPH simulation of UCS and BTS,experimental UCS and BTS values were simultaneously captured according to the same set of calibrated cohesion and internal friction angle data,and the UCS modeling results are in good agreement with experimental tests.Furthermore,the effect of microwave irradiation parameter on the basalt mechanical behaviors was evaluated.

P25 Scoring Method for the Assessment of R/C Buildings

An effective rapid assessment technique, called ＂P25 Scoring Method＂, has been developed and tested on 26 different case studies recently, in order to predict the collapse vulnerability of the R/C buildings. After a short description of the approach, the study presents the sensitivity study of the method to the selected structural parameters by considering incremental deviation of the final scores from the base model. Further, the methodology was applied to an additional 100 damaged buildings in order to check the reliability of the method and some necessary modifications have been applied to the algorithm after considering this larger database. The evaluation of the results has been interpreted as a beneficial guidance for local authorities. The risk bands are defined according to the final scores and the effect of changing the band-width has also been studied through a safe but an economical procedure. A satisfactory correlation of the method with real damage states is obtained and a ready-to-use methodology has been introduced for future studies.