Mathematical modeling and simulations of stress mitigation by coating polycrystalline particles in lithium-ion batteries

A chemo-mechanical model is developed to investigate the effects on the stress development of the coating of polycrystalline Ni-rich LiNixMnyCo_(z)O_(2)(x≥0.8)(NMC)particles with poly(3,4-ethylenedioxythiophene)(PEDOT).The simulation results show that the coating of primary NMC particles significantly reduces the stress generation by efficiently accommodating the volume change associated with the lithium diffusion,and the coating layer plays roles both as a cushion against the volume change and a channel for the lithium transport,promoting the lithium distribution across the secondary particles more homogeneously.Besides,the lower stiffness,higher ionic conductivity,and larger thickness of the coating layer improve the stress mitigation.This paper provides a mathematical framework for calculating the chemo-mechanical responses of anisotropic electrode materials and fundamental insights into how the coating of NMC active particles mitigates stress levels.

Molecular simulation study of the microstructures and properties of pyridinium ionic liquid[HPy][BF_(4)]mixed with acetonitrile

The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently.

Using Monte Carlo Simulation Technology to Improve Intuitive Effect of Teaching Probability and Mathematical Statistics Course

With the illustration of a specific problem, this paper demonstrates that using Monte Carlo Simulation technology will improve intuitive effect of teaching Probability and Mathematical Statistics course, and save instructors' effort as well.And it is estimated that Monte Carlo Simulation technology will be one of the major teaching methods for Probability and Mathematical Statistics course in the future.

Mathematical Model and Simulation of Harmful Invasive Plant Control

Plant invasion refers to the phenomenon that some plants grow too fast due to they are far away from the original living environment or predators, affecting the local environment. With the development of tourism and trade, the harm caused by invasive plants will be more and more serious. Therefore, it is necessary to ex- plore an effective method for controlling plant invasion through qualitative and quan- titative research. In this paper, the models were established for the early and late harmful plant invasion control. The huge computation was completed by the com- puter programming to obtain the optimal solutions of the models. The real meaning of the optimal solution was further discussed. Through numerical simulations and discussion, it could be concluded that the quantitative research on the invasive plant control had a certain application value.

Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas

A three-phase reactor mathematical model was set up to simulate and design a three-phase bubble column reactor for direct synthesis of dimethyl ether （DME） from syngas, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction. On the basis of this model, the influences of the size and reaction conditions of a 100000 t/a DME reactor on capacity were investigated. The optimized size of the 10000 t/a DME synthesis reactor was proposed as follows： diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger （Ф 38×2 mm）, and inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Reaction temperature and pressure were important factors influencing the reaction conversion for different size reactors. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature were proposed to achieve a higher production capacity of DME. The best ratio of fresh syngas for DME synthesis was 2.04.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, effiux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch （ABU） should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch （PBU） is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

Mathematical model for the thermal process of controlled cooling of wires and its numerical simulation

The mathematical model for the thermal process of billets rolling has beenestablished, including transporting in air and temperature-holding cover, descaling withhigh-pressure water, and the process of rolling and cooling in water box. The calculated data by themodel have been compared with the measured data and the results show that the model is right andcreditable. Based on the model, the main thermal characters of rolling line have been simulated andthe influence of all the parameters on the temperature of rolling has been analyzed.

Numerical Simulation of a Mathematical Model for Dry/Wet-Spun Nascent Hollow Fiber Membrane

In an effort to find the effect of mass transfer, surface tension and drag forces on the velocity distribution, the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method). The effect of mass transfer on velocity distribution based on the complicated function (G(Cs h)) was presented and the effects of a complicated function were studied in two cases: in the first case, G(Cs h) was constant; in the second, G(Cs h) was variable. The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region. One empirical equation was used to describe this change and the predicted values had a better agreement with the experimental values. To verify the model hypotheses, hollow fiber membranes were spun from 20∶80 polybenzimidazole/polyetherimide dopes with 25.6 wt% solid in N, N-dimethylacetamide (DMAc) using water as the external and internal coagulants. Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes, it is found that the model calculated values were in a good agreement with the experimental values.

Mathematical simulation and observation of ground subsidence basin in coal mining area

Based on a great amount of practically observational data and by computer simulation, a formula for estimating the ground subsidence caused by coal mining was derived. Meanwhile, an empirical mathematical model for ground subsidence basin in coal mining was given.

Mathematical Modeling,Field Calibration and Numerical Simulation of Low-Speed Mixed Traffic Flow in Cities

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MATHEMATICAL MODELS OF NITROGEN CONCENTRATION PROFILE OF ION NITRIDED LAYERS AND COMPUTER SIMULATION

The mathematical models of the kinetics of the layer growth at different ion nitriding condi- tions of armco iron.steels 45,40Cr,42CrMo and 38CrMoAl have been established.Based on these models the expression of nitrogen concentration profile of ion nitrided layers have been deduced with profile simulating method.They are C_=C_(min)^+(P_4)/(ξ_1-x)+(P_5)/(ξ_(10)~2)(ξ_1-x)~2 C_(γ′)=C_(min)^(γ′)+(P_1)/(ξ_(21))(ξ_2-x)+(P_2)/(ξ_(21)~2)(ξ_2-x)~2 C_α=C_(min)~α+(C_(33))/(C_(33))/(ξ_(32))(ξ_3-x)~3 Using these models,the kinetics of layer growth and the nitrogen concentration profile of ion nitrided layers were sinulated on Apple-Ⅱ computer.Results show that the simulated curves coincide quite well with the experimental data.

Mathematical simulation of direct reduction process in zinc-bearing pellets

A one-dimensional unsteady mathematical model was established to describe direct reduction in a composite pellet made of metallurgical dust. The model considered heat transfer, mass transfer, and chemical reactions including iron oxide reductions, zinc oxide reduction and carbon gasification, and it was numerically solved by the tridiagonal matrix algorithm （TDMA）. In order to verify the model, an experiment was performed, in which the profiles of temperature and zinc removal rate were measured during the reduction process. Results calculated by the mathematical model were in fairly good agreement with experimental data. Finally, the effects of furnace temperature, pellet size, and carbon content were investigated by model calculations. It is found that the pellet temperature curve can be divided into four parts according to heating rate. Also, the zinc removal rate increases with the increase of furnace temperature and the decrease of pellet size, and carbon content in the pellet has little influence on the zinc removal rate.

Mathematic simulation of heat transfer and operating optimization in alumina rotary kiln

Based on the analysis of material motion in the axial direction, heat transfer and mass transport processes in a rotary kiln, and combining with pulverized coal combustion, material pyrogenation, cooling of furnace wall finally, and heat transfer and mass transport equations, the combined heat transfer mathematical model for alumina rotary kiln was built up. According to the in-site real operation parameters, the heat transfer mathematical model was solved numerically for an alumina rotary kiln to predict the temperature profiles of gas and material in the axial direction. The results show that as the excess air coefficient reduces from 1.38 to 1.20, the temperature of the sintering zone increases and the length decreases. However, as the excess air coefficient reduces from 1.20 to 1.10, the temperature of the sintering zone decreases and the length increases. When the mixed coal amount at the end of kiln is reduced from 68.6 kg/t to 62.0 kg/t and the burned coal amount at the head of kiln correspondingly increases from 155.3 kg/t to 161.9 kg/t, the sintering zone temperature increases and the length reduces. The suitable excess air coefficient and mixed coal amount at the end of kiln are recommended for the rotary kiln operation optimization.

Dynamic Monitoring of Plant Cover and Soil Erosion Using Remote Sensing, Mathematical Modeling, Computer Simulation and GIS Techniques

Dynamic monitoring of plant cover and soil erosion often uses remote sensing data, especially for estimating the plant cover rate (vegetation coverage) by vegetation index. However, the latter is influenced by atmospheric effects and methods for correcting them are still imperfect and disputed. This research supposed and practiced an indirect, fast, and operational method to conduct atmospheric correction of images for getting comparable vegetation index values in different times. It tries to find a variable free from atmospheric effects, e.g., the mean vegetation coverage value of the whole study area, as a basis to reduce atmospheric correction parameters by establishing mathematical models and conducting simulation calculations. Using these parameters, the images can be atmospherically corrected. And then, the vegetation index and corresponding vegetation coverage values for all pixels, the vegetation coverage maps and coverage grade maps for different years were calculated, i.e., the plant cover monitoring was realized. Using the vegetation coverage grade maps and the ground slope grade map from a DEM to generate soil erosion grade maps for different years, the soil erosion monitoring was also realized. The results show that in the study area the vegetation coverage was the lowest in 1976, much better in 1989, but a bit worse again in 2001. Towards the soil erosion, it had been mitigated continuously from 1976 to 1989 and then to 2001. It is interesting that a little decrease of vegetation coverage from 1989 to 2001 did not lead to increase of soil erosion. The reason is that the decrease of vegetation coverage was chiefly caused by urbanization and thus mainly occurred in very gentle terrains, where soil erosion was naturally slight. The results clearly indicate the details of plant cover and soil erosion change in 25 years and also offer a scientific foundation for plant and soil conservation.

Mathematical Simulation on Oxidation of Ilmenite in Fluidized Bed

An unsteady-state mathematical model describing the behaviors of gas and solid during the oxidation of ilmenite in a fluidized bed was developed on the basis of the two-phase theory of a fluidized-bed reactor. The longitudinal distribution of the concentration of gaseous species and that of the unreacted ratio of solid material in both bubble phase and emulsion phase as well as their variation with reaction time were determined by means of mathematical simulation with kinetic parameters measured experimentally, furthermore, the reaction behavior of particles with different size in a multiparticle system was also analyzed, and finally, the potential way for increasing the reactor efficiency was put forward.

Numerical simulation of inhibiting effects on solid tumour cells in anti-angiogenic therapy: application of coupled mathematical model of angiogenesis with tumour growth

To investigate the inhibiting effects of the anti-angiogenic factor andostatin and the anti-angiogenic drug endostatin on turnout angiogenesis and turnout cells, a coupled mathematical model of tumor angiogenesis with tumour growth and blood perfusion is developed. Simulation results show that angiostatin and endostatin can improve the abnormal microenvironment inside the tumour tissue by effectively inhibiting the process of tumor angiogenesis and decreasing tumour cells. The present model can be used as a valid theoretical method in the investigation of the tumour anti-angiogenic therapy.

Mathematical Simulation of Cleat Porosity in Coal Reservoir

Cleat system of coal reservoir is one of the main migrating passage of coalbed methane (CBM). The development of cleat system has important influence on both the preservation of CBM in geological history and surface CBM exploitation. The relationship among cleat porosity, net confine pressure, rock mechanics, coal seam’s occurrence and other factors of coal reservoir is established and simulated based on the energy conservation law. The result indicates that the net confine pressure and buried depth of coalbed are the major control factors of cleat porosity. The extensive stress and abnormal high reservoir pressure can make cleats open thus increase tbe cleat porosity; while the overburden pressure and compressive stress make cleats close and decrease the cleat porosity. The influence of occurrence (dip and dip angle) of coalbed on cleat porosity depends on the change of the above mentioned factors. It is also affected by rock mechanics parameters to some extent, while water-gas saturation and reservoir temperature have little effect on cleat porosity. The above conclusions are of great significance in geological exploration and surface exploitation region determination of CBM.

Mathematical modeling and simulation of the interface region of a tri-layer composite material,brass-steel-brass,produced by cold rolling

The object of this study was to find the optimum conditions for the production of a sandwich composite from the sheets of brass-steel-brass. The experimental data obtained during the production process were used to validate the simulation program, which was written to establish the relation between the interface morphology and the thickness reduction amount of the composite. For this purpose, two surfaces of a steel sheet were first prepared by scratching brushing before inserting it between two brass sheets with smooth surfaces. Three sheets were then subjected to a cold rolling process for producing a tri-layer composite with various thick- nesses. The sheet interface after rolling was studied by different techniques, and the bonding strength for each rolling condition was determined by peeling test. Moreover, a relation between interfacial bonding strength and thickness reduction was found. The simulation results were compared with the experimental data and the available theoretical models to modify the original simulation program with high application efficiency used for predicting the behavior of the interface under different pressures.

Mathematical Simulation of Dynamic Heat Transfer in a Human-Clothing-Environment System

A mathematical model has been developed to describe the dynamic heat transfer in the clothing microclimate under transient wear conditions. This model is solved numerically by the implicit finite difference method. If the physical activity and ambient conditions are specified, the model can predict the thermoregulatory response of the body. Experimental measurements with garments made of fibers with different levels of hygroscopicity are compared with predictions by the model. There is good agreement between prediction and experiment for the temperature of the clothing microclimate.

Mathematical simulations of the galvanic coupling intra-body communication by using the transfer function method

The galvanic coupling intra-body communication （IBC） was mathematically simulated based on the proposed transfer function. Firstly, a galvanic coupling IBC circuit model was developed and the corresponding parameters were discussed. Secondly, the transfer function of the galvanic coupling IBC was derived and proposed. Finally, the signal attenuation characteristics of the galvanic coupling IBC were measured along different signal transmission paths of actual human bodies, while the corresponding mathematical simulations based on the proposed transfer function were carried out. Our investigation showed that the mathematical simulation results coincided with the measured results over the frequency range of 100kHz to 5MHz, which indicated that the proposed transfer function could be useful for theoretical analysis and application of the galvanic coupling IBC.