以“数学化”过程探索学生核心素养培育路径

对核心素养的培养就是要帮助学生养成从数学角度观察现实世界的意识和习惯,形成实事求是的科学态度,养成讲道理、有条理的思维品质,逐步形成理性精神。“数学化”过程就是要让学生经历知识的发生、发展过程,在主动探究的过程中培养学生数学思维,获得研究的方法,积累研究的经验,提高分析问题、解决问题的能力,促进学生的可持续发展。因此,经历数学化过程应成为学生核心素养的培育路径。

Synthesis of Multi-component Mass-exchange Networks

This paper presents a superstructure-based formulation for the synthesis of mass-exchange networks (MENs) considering multiple components. The superstructure is simplified by directly using the mass separation agents (MSA) from their sources, and therefore the automatic synthesis of the multi-component system involved in the MENs can be achieved without choosing a 'key-component' either for the whole process or the mass exchangers. A mathematical model is proposed to carry out the optimization process. The concentrations, flow rates, matches and unit operation displayed in the obtained network constitute the exact representation of the mass exchange process in terms of all species in the system. An example is used to illustrate and demonstrate the application of the proposed method.

Numerical Simulation of Erosion-Corrosion in the Liquid-Solid Two-Phase Flow

Erosion-corrosion of liquid-solid two-phase flow occurring in a pipe with sudden expansion in cross-section is numerically simulated in this paper. The global model for erosion-corrosion process includes three main components: the liquid-solid two-phase flow model, erosion model and corrosion model. The Eulerian-Lagrangian approach is used to simulate liquid-solid two-phase flow, while the stochastic trajectory model was adopted to obtain properties of particle phase. Two-way coupling effect between the fluid and the particle phase is considered in the model. The accuracy of the models is tested by the data in the reference. The comparison shows that the model is basically correct and feasible.

Prediction of Critical Endpoints Based on the PR Equation of State

In the design of chemical processes,such as catalytic cracking of bitumen and heavy oil,the knowledge of phase behavior at the critical endpoint is essential.Based on the PR equation of state,the algorithm developed by Heidemann and Khalil for calculating critical properties was used to compute critical points.An algorithm for determining the equilibrium phase of the critical point using the tangent plane criterion was developed,and was used to calculate the critical endpoints of different mixtures,including non-polar,polar and associating systems.The critical endpoint,representing the type of the phase behavior,was employed to fit the interaction parameter of mixtures in critical state at high pressure.Lines of critical endpoints for ternary mixtures were also determined with the algorithm.

Calculation of Metzner Constant for Double Helical Ribbon Impeller by Computational Fluid Dynamic Method

Using the multiple reference frames （MRF） impeller method, the three-dimensional non-Newtonian flow field generated by a double helical ribbon （DHR） impeller has been simulated. The velocity field calculated by the numerical simulation was similar to the previous studies and the power constant agreed well with the experimental data. Three computational fluid dynamic （CFD） methods, labeled Ⅰ, Ⅱ and Ⅲ, were used to compute the Metzuer constant k5. The results showed that the calculated value from the slop method （method Ⅰ） was consistent with the experimental data. Method Ⅱ, which took the maximal circumference-average shear rate around the impeller as the effective shear rate to compute ks, also showed good agreement with the experiment. However, both methods suffer from the complexity of calculation procedures. A new method （method Ⅲ） was devised in this paper to use the area-weighted average viscosity around the impeller as the effective viscosity for calculating k5. Method Ⅲ showed both good accuracy and ease of use.

Fault Prediction Based on Dynamic Model and Grey Time Series Model in Chemical Processes

This paper combines grey model with time series model and then dynamic model for rapid and in-depth fault prediction in chemical processes. Two combination methods are proposed. In one method, historical data is introduced into the grey time series model to predict future trend of measurement values in chemical process. These predicted measurements are then used in the dynamic model to retrieve the change of fault parameters by model based diagnosis algorithm. In another method, historical data is introduced directly into the dynamic model to retrieve historical fault parameters by model based diagnosis algorithm. These parameters are then predicted by the grey time series model. The two methods are applied to a gravity tank example. The case study demonstrates that the first method is more accurate for fault prediction.

A motion retargeting algorithm based on model simplification

A new motion retargeting algorithm is presented, which adapts me motion capture data to a new character. To make the resulting motion realistic, the physically-based optimization method is adopted. However, the optimization process is difficult to converge to the optimal value because of high complexity of the physical human model. In order to address this problem, an appropriate simplified model automatically determined by a motion analysis technique is utilized, and then motion retargeting with this simplified model as an intermediate agent is implemented. The entire motion retargeting algorithm involves three steps of nonlinearly constrained optimization： forward retargeting, motion scaling and inverse retargeting. Experimental results show the validity of this algorithm.

Numerical simulation of chemical vapor deposition reaction in polysilicon reduction furnace

Three-dimensional model of chemical vapor deposition reaction in polysilicon reduction furnace was established by considering mass, momentum and energy transfer simultaneously. Then, CFD software was used to simulate the flow, heat transfer and chemical reaction process in reduction furnace and to analyze the change law of deposition characteristic along with the H_2 mole fraction, silicon rod height and silicon rod diameter. The results show that with the increase of H_2 mole fraction, silicon growth rate increases firstly and then decreases. On the contrary, SiHCl_3 conversion rate and unit energy consumption decrease firstly and then increase. Silicon production rate increases constantly. The optimal H_2 mole fraction is 0.8-0.85. With the growth of silicon rod height, Si HCl3 conversion rate, silicon production rate and silicon growth rate increase, while unit energy consumption decreases. In terms of chemical reaction, the higher the silicon rod is, the better the performance is. In the view of the top-heavy situation, the actual silicon rod height is limited to be below 3 m. With the increase of silicon rod diameter, silicon growth rate decreases firstly and then increases. Besides, SiHCl_3 conversion rate and silicon production rate increase, while unit energy consumption first decreases sharply, then becomes steady. In practice, the bigger silicon rod diameter is more suitable. The optimal silicon rod diameter must be over 120 mm.

Branch Processes of Vortex Filaments and Hopf Invariant Constraint on Scroll Wave

In this paper, by making use of Duan＇s topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z（x, t）. [t is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes （splitting, merging, or encountering） during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the ＂exclusion principle＂ in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the ＂exclusion principle＂ is also protected by topology.

Soft sensor of chemical processes with large numbers of input parameters using auto-associative hierarchical neural network

To explore the problems of monitoring chemical processes with large numbers of input parameters, a method based on Auto-associative Hierarchical Neural Network(AHNN) is proposed. AHNN focuses on dealing with datasets in high-dimension. AHNNs consist of two parts: groups of subnets based on well trained Autoassociative Neural Networks(AANNs) and a main net. The subnets play an important role on the performance of AHNN. A simple but effective method of designing the subnets is developed in this paper. In this method,the subnets are designed according to the classification of the data attributes. For getting the classification, an effective method called Extension Data Attributes Classification(EDAC) is adopted. Soft sensor using AHNN based on EDAC(EDAC-AHNN) is introduced. As a case study, the production data of Purified Terephthalic Acid(PTA) solvent system are selected to examine the proposed model. The results of the EDAC-AHNN model are compared with the experimental data extracted from the literature, which shows the efficiency of the proposed model.

An Investigation of Stimulating the Autoclave Curing Process of Resin Matrix/Fiber Reinforced Composite Material, Ⅰ: Process model

A mathematical model is made which describes the curing process of composites constructed from continuous fiber-reinforced, thermosetting resin matrix prepreg materials, and the consolidation of the composite is developed. The model provides the variation of temperature distribution, the cure reaction process in the resin, the resin flow and fibers stress inside the composite, and the void variation and the residual stress distribution. It can be used to illustrate the mechanism of curing process and optimize the cure cycle of composite material in order to ensure the quality of a product.

A Mathematical Model to Study the Effect of Pore Sizes Distribution on Densification Process in Ceramic Compacts

In this research the effect of pore size distribution on densification process during sintering of ceramic compacts is studied by assuming a Gaussian distribution of the pore sizes and depending on a mathematical model that was developed in a previous research in describing the densification process.

Capillary Phase-Transition and Self-Diffusion of Ethylene in the Slit Carbon Pores

The grand canonical Monte Carlo (GCMC), the canonical Monte Carlo by using equal probability perturbation, and the molecular dynamics (MD) methods were used to study the capillary phase-transition (capillary condensation and evaporation) and self-diffusion for a simple Lennard-Jones model of ethylene confined in slit carbon pores of 2.109 nm at temperatures between 141.26 K and 201.80 K. The critical point of capillary phase-transition was extrapolated by the critical power law and the law of rectilinear diameter from the capillary phase-transition data in the near critical region. The effects of temperature and fluid density on the parallel self-diffusion coefficients of ethylene molecules confined in the slit carbon pores were examined. The results showed that the parallel selfdiffusion coefficients in the capillary phase transition area strongly depended on the fluids local densities in the slit carbon pores.

Comparison on Non-isothermal Oxidation between Spent Catalytic Cracking Catalysts and Coal

Oxidation of coke deposited on spent catalytic cracking catalysts was compared with that of coal and coal char via the non-isothermal oxidation means, i.e. the thermal-gravimetric analysis （TGA） and the differential thermal analysis （DTA）. Oxidation kinetic parameters were further investigated by model-fitting methods. The test results showed that the oxidation of spent catalysts was a quite mild process, while coal and coal char experienced sharp weight loss during oxidation. The temperature for commencement and termination of oxidation increased in the following order： coal〈coal char〈spent catalysts, and the oxidation of the three tested materials displayed a self-catalytic nature, with their largest oxidation rate appearing at a weight percent of 24.96%, 34.21% and 57.93%, respectively. The oxidation of spent catalysts obeyed a random nucleation model for the first-order reaction, with Ea=206.13 kJ/mol and lgA=10.10, and the oxidation of coal could be a diffusion-controlled reaction mechanism, with Ea=161.61 kJ/mol and lgA=7.74, while the oxidation of coal char also obeyed a random nucleation model for the first-order reaction, with Ea= 149.36 k J/mol and lgA=7.89.

Discussion on Art Design Education in Colleges and Universities in Digital

At present, the reform of colleges and universities in our country is in full swing. In the course of teaching design of art in colleges and universities, it is necessary to change the teaching mode in time to adapt to the new teaching development environment. In the era of digital development, we need to give full attention to the optimization of art design teaching in colleges and universities, and run new teaching techniques. This paper mainly analyzes the advantages and importance of the digital art design in colleges and universities, and then discusses the application of digital technology in the art design teaching and the concrete teaching optimiTatiun strategy in detail. Hoping to through this theoretical research, contribute to the improvement of the quality of art design teaching.

Numerical Modeling of Pulverized Coal Combustion at Thermal Power Plant Boilers

The paper deals with development and application the numerical model for solution of processes at combustion chamber of the thermal power plant boiler. Mathematical simulation is based on solution of physical and chemical processes occuring at burning pulverized coal in the furnace model. Three-dimensional flows, heat and mass transfer, chemical kinetics of the processes, effects of thermal radiation are considered. Obtained results give quantitative information on velocity distributions, temperature and concentration profiles of the components, the amount of combustion products including harmful substances. The numerical model becomes a tool for investigation and design of combustion chambers with high-efficiency and reliable operation of boiler at thermal power plants.

Mathematical Modeling of Heat Transfer Processes of Coal Waste Combustion in a Chamber of Automated Energy Generating Complex

The automated energy generating complex allows obtaining heat energy from waste coal-water slurry fuel （WCF） that is a mixture of fine coal particles from coal enrichment wastes with water. The mixture is blown into the swirl chamber under the pressure through the special sprayers. The received heat energy is used in different ways. One of the important issues is to estimate the heat losses through the walls of this chamber. In this paper we solved the boundary problem of mathematical physics to estimate the temperature fields in the walls of the swirl chamber. The obtained solution allows us to estimate the heat losses through the waUs of the swid chamber. The task of the mathematical physics has been solved by a numerical finite-difference method. The method for solving this prob- lem can be used in the calculation of temperature fields and evaluation of heat losses in other thermal power units.

Turbulence and mixing in a freshwater-influenced tidal bay: Observations and numerical modeling

In situ observations and numerical simulations of turbulence are essential to understanding vertical mixing processes and their dynamical controls on both physical and biogeochemical processes in coastal embayments. Using in situ data collected by bottom-mounted acoustic Doppler current profilers(ADCPs) and a free-falling microstructure profiler, as well as numerical simulations with a second-moment turbulence closure model, we studied turbulence and mixing in the Xiamen Bay, a freshwater-influenced tidal bay located at the west coast of the Taiwan Strait. Dynamically, the bay is driven predominantly by the M2 tide, and it is under a significant influence of the freshwater discharged from the Jiulong River. It is found that turbulence quantities such as the production and dissipation rates of the turbulent kinetic energy(TKE) were all subject to significant tidal variations, with a pronounced ebb-flood asymmetry. Turbulence was stronger during flood than ebb. During the flooding period, the whole water column was nearly well mixed with the depth-averaged TKE production rate and vertical eddy viscosity being up to 5?10?6 W kg?1 and 2?10?2 m2 s?1, respectively. In contrast, during the ebb strong turbulence was confined only to a 5?8 m thick bottom boundary layer, where turbulence intensity generally decreases with distance from the seafloor. Diagnosis of the potential energy anomaly showed that the ebb-flood asymmetry in turbulent dissipation and mixing was due mainly to tidal straining process as a result of the interaction between vertically shared tidal currents and horizontal density gradients. The role of vertical mixing in generating the asymmetry was secondary. A direct comparison of the modeled and observed turbulence quantities confirmed the applicability of the second-moment turbulence closure scheme in modeling turbulent processes in this weakly stratified tidally energetic environment, but also pointed out the necessity of further refinements of the model.

Chemical Versus Thermal Folding of Graphene Edges

Using molecular dynamics （MD） simulations, we have investigated the kinetics of the graphene edge folding process. The lower limit of the energy barrier is found to be -380 meV/A （or about 800 meV per edge atom） and -50 meV/A （or about 120 meV per edge atom） for folding the edges of intrinsic clean single-layer graphene （SLG） and double-layer graphene （DLG）, respectively. However, the edge folding barriers can be substantially reduced by imbalanced chemical adsorption, such as of H atoms, on the two sides of graphene along the edges. Our studies indicate that thermal folding is not feasible at room temperature （RT） for clean SLG and DLG edges and is feasible at high temperature only for DLG edges, whereas chemical folding （with adsorbates） of both SLG and DLG edges can be spontaneous at RT. These findings suggest that the folded edge structures of suspended graphene observed in some experiments are possibly due to the presence of adsorbates at the edges.