Application of the Sediment Mathematical Modelling on Planned Project of Lingdingyang Bay

Based on the combined hydraulic calculation for the eastern network region at the Pearl River estuary and several outlets to the Lingdingyang Bay, the sediment calculation modelling was introduced in the establishment of the sediment mathematical model for Lingdingyang Bay and the eastern region with one and two dimensional flow calculation. Model adjustment and verification were performed in conjunction with field data. The simulated results coincide well with measured data.In addition the model is applied to predict the shore-line planning scheme of Lingdingyang Bay.The theoretical criterion is provided for the shore line plan in the model.And a new mathematical simulated method is put out to research the planning engineering concerned with one-dimensional net rivers and two-dimensional estuary.

MATHEMATICAL MODELLING OF FLOW PHENOMENA IN METAL BATH COVERED WITH MOLTEN SLAG

By use of the two-component LDA and high speed camera,the water model of the flow field in metal bath under molten slag layer has been tested.On the basis of experimental results,the flow boundary conditions of liquid metal at the slag-metal interface of a gas injecting bath were deduced.The flow field and the turbulent parameters of the metal bath covered with slag were solved by the vorticity-stream function method.The results reveal that the flow velocity, turbulent energy and circulating rate of the melt under slag are lower than that of without slagcover.Another one “dead zone” of the lowest turbulent energy is formed in the top layer under cover of slag near the ladle linning.

Mathematical Modelling of Work of Modern Friction-Polymer Shock Absorbers and Determining the Dynamical Force during the Impact

Shock absorbers are main elements into construction of train wagons that secure protection from longitudinal forces which appear during transitional regimes of movement. Besides, development of new constructive solutions for shock absorbers is quite popular development of their working mathematical models. This paper presents modem shock absorber with elastic block made from polymer elements that increase quantity of absorbed energy. This is achieved by increasing the stiffness characteristic of polymer elastic block. The construction is relatively simple and technology used to create the construction is with more or less low price. If there is not enough elastic stiffness of the polymer block, there is a possibility for not meeting the UIC （International Union of Railways） norms for absorbed energy. Therefore, according to the mentioned characteristic, shock absorbers are divided into three groups. The mathematical model presented in this paper allows calculating the necessary elastic characteristic of the polymer block for a short time. Differential equation of movement of the shock absorber elements is presented in this paper. Force change of polymer block for various impact velocities participates in the differential equation of movement where initial velocity V0 and the current meaning of the velocity x are taken into consideration. The presented equation is solved by using program language MATLAB/Simulink by developing a simulation model.

The Development of Mathematical Modelling Activities from Thematic Projects in the Social-Critical Perspective

In this paper, the authors present a modelling activity developed from a thematic project in the models and mathematical modelling class of the professional master＇s degree program in mathematics education at the Federal University of Ouro Preto. The students enrolled in the class chose to study the theme Brazilian Public Politics. After several debates regarding the theme, the students were separated into three groups and each group chose a subtheme to study. The themes were IDH （index of human development）, minimum wage and social security. As an example, a description of the thematic project about the minimum wage in Brazil is presented. The principal results obtained in the study of this theme include a discussion about the potentialities of the theme as a classroom activity in different levels of schooling. As an educational activity, the thematic project demonstrated itself to be greatly relevant, since not only did it provide the learning possibility of mathematics related to the issues studied, but also promoted various discussions regarding the theme, which, in our conception, contributes to the social-critical development of the students. Finally, from the point of view of applied mathematics and mathematics education, the development of a modelling activity from thematic projects showed itself to be a good source of researches.

The Application of a Mathematical Modelling of Drying Kinetics in the Natural Solar Drying of Banana

In this work, a new mathematical modelling of drying kinetics is described. At first, the modelling of the transfer speed （St） of water was performed. Then St was used as basis to state the drying rate model. The drying rate depends not only on drying time, but also on some modelling parameters which are themselves time-dependent. All the modelling parameters are calculated directly from the experimental drying data. Then the theoretical model of the moisture content was stated. Subsequently, the drying kinetics of natural solar drying of plantain banana was studied as illustration. The drying rate was investigated. The comparison with other models encountered in literatures proved that the current theoretical model was decidedly more accurate. Then the modelling of moisture content of banana was performed and the results were compared with the Henderson and Pabis model. The current theoretical modelling provided by far the best fit.

The Reconstruction Technique of Multi-Product Production and MINLP Mathematical Modelling

Low efficiency, negative impacts on the environment and non-profitable operations are the main shortcomings of out-dated industrial processes. Such systems can be reconstructed and improved in the direction of multi-product operations. The study of this article focuses on the development of a method for multi-product operations by reconstructing out-dated industrial processes. This article contains the theory of a developed method that enables the updating of existing process units and integrated systems on the basis of reconstruction scenarios and pathways. The goals of the set out method are: 1) to maintain the existing process units and chemical plants to a greater extent, 2) to enable the potential for finding new process alternatives and technological solutions, 3) to provide a streamlined operation for all subsystems and total systems, 4) to promote environmental and social responsibilities, and 5) to apply the concept of the presented reconstruction method to non-profitable industrial processes. In regard to multi-product operations, a conceptual model is a suitable tool for the reconstruction of industrial processes. It connects several software tools and so enables quick decision-making between process alternatives. A reconstruction method provides foresight into the possible improvements to existing industrial processes. In comparison with the indirect synthesis of DME (simple reconstruction pathway), the lower operating costs from the direct synthesis of DME (complex reconstruction pathway) were confirmed.

Mathematical modelling and numerical optimization of particle heating process in copper flash furnace

A mathematical model of the particle heating process in the reaction shaft of flash smelting furnace was established and the calculation was performed.The results indicate that radiation plays a significant role in the heat transfer process within the first 0.6 m in the upper part of the reaction shaft,whilst the convection is dominant in the area below 0.6 m for the particle heating.In order to accelerate the particle ignition,it is necessary to enhance the convection,thus to speed up the particle heating.A high-speed preheated oxygen jet technology was then suggested to replace the nature gas combustion in the flash furnace,aiming to create a lateral disturbance in the gaseous phase around the particles,so as to achieve a slip velocity between the two phases and a high convective heat transfer coefficient.Numerical simulation was carried out for the cases with the high-speed oxygen jet and the normal nature gas burners.The results show that with the high-speed jet technology,particles are heated up more rapidly and ignited much earlier,especially within the area of the radial range of R=0.3−0.6 m.As a result,a more efficient smelting process can be achieved under the same operational condition.

A continuous and high-efficiency process to separate coal bed methane with porous ZIF-8 slurry:Experimental study and mathematical modelling

Coal bed methane has been considered as an important energy resource.One major difficulty of purifying coal bed methane comes from the similar physical properties of CH_4 and N_2.The ZIF-8/water-glycol slurry was used as a medium to separate coal bed methane by fluidifying the solid adsorbent material.The sorption equilibrium experiment of binary mixture(CH_4/N_2)and slurry was conducted.The selectivity of CH_4 to N_2 is within the range of 2-6,which proved the feasibility of the slurry separation method.The modified Langmuir equation was used to describe the gas-slurry phase equilibrium behavior,and the calculated results were in good agreement with the experimental data.A continuous absorption-adsorption and desorption process on the separation of CH_4/N_2 in slurry is proposed and its mathematical model is also developed.Sensitivity analysis is conducted to determine the operation conditions and the energy performance of the proposed process was also evaluated.Feed gas contains 30 mol%of methane and the methane concentration in product gas is 95.46 mol%with the methane recovery ratio of 90.74%.The total energy consumption for per unit volume of product gas is determined as 1.846 kWh Nm^(-3).Experimental results and process simulation provide basic data for the design and operation of pilot and industrial plant.

Mathematical Modelling of Particle Movement Ahead of the Solid-liquid Interface in Continuous Casting

Whether the particle will be trapped by the solid-liquid interface or not is dependent on its moving behavior ahead of the interface, so a mathematical model has been developed to investigate the movement of the particle ahead of the solid-liquid interface. Based on the theory for the boundary layer, the fluid velocity field near the solid-liquid interface was obtained, and the trajectories of particles were calculated by the equations of motion for particles. In this model, the drag force, the added mass force, the buoyance force, the gravitational force, the Saffman force and the Basset history force are considered. The results show that the behavior of the particle ahead of the solid-liquid interface is affected by the physical property of the particle and fluid flow. And in the continuous casting process, if it moves in the stream directed upward or downward near vertical solid-liquid interface or in the horizontal flow under the solid-liquid interface, the particle with the diameter from 5 um to 60um can reach the solid-liquid interface. But if it moves in horizontal flow above the solid-liquid interface, only the particle with the diameter from 5 um to 10 um can reach the solid-liquid interface.

Mathematical modelling of translational motion of rail-guided cart with suspended payload

In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart,driven by a travel mechanism,is modelled as a discrete six degrees of freedom (DOF) dynamic system. The hoisting mechanism for lowering and lifting the payload is considered and is included in the dynamic model as one DOF system. Differential equations of motion of the cart elements are derived using Lagrangian dynamics and are solved for a set of real-life constant parameters of the cart. A two-sided interaction was observed between the swinging payload and the travel mechanism. Results for kinematical and force parameters of the system are obtained. A verification of the proposed model was conducted.

Mathematical Modelling of Carbonitride Precipitation during Hot Working in Nb Microalloyed Steels

Based on thermodynamics and kinetics, precipitation behavior of microalloyed steels was analyzed. Deformation greatly promotes isothermal carbonitride precipitation and makes C-curve shift leftwards. The position and shape of C-curve also depend on the content of Nb and N. C-curve shifts leftwards a little when N content increases and the nose temperature is raised with increasing Nb content. Deformation shortened precipitation start time during continuous cooling, raised precipitation start temperature, accelerated precipitation kinetics of carbonitrides. With decreasing the finishing temperature and coiling temperature, the precipitates volume fraction increases and strength increment is raised during hot rolling. The simulated results are in agreement with experiment results.

Reducing the Range of Cancer Risk on BI-RADS 4 Subcategories via Mathematical Modelling

Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.

Experimental Research and Mathematical Modelling for Coal Reburning in Furnace

Reburning technology is one of the most cost-effective NOx reduction strategies for coal combustion systems. In this paper, a nitric oxide submodel incorporated into a comprehensive coal combustion model was developed for predicting NOx reduction in a 93 kW laboratory-scale coal combustion furnace by reburning. This NO submodel, including reburning mechanism, requires the solution of only two transport equations to model the behavior of NO reduction in the reburning process. A number of experiments have been performed in the same furnace, and the experimental data obtained from the optimized reburn configuration was used to validate the model. Measurements and predictions both show above 50% reduction of NO emissions for the optimized reburning process. Profile comparisons show that the predicted temperature and oxygen concentration match well with the measurements, and the general trend of predicted NO concentration is very similar to that measured. The results of this study show that the present nitric oxide submodel depicts quite well the observed behaviour of NO annihilation in the reburning process. It is expected that this usable and computationally economic model represents a useful tool to simulate the gaseous fuel reburning process for the researchers concerned with practical combustors.

Mathematical Modelling of Cutting Force as the Most Reliable Information Bearer on Cutting Tools Wearing Phenomenon

Being one of their prominent exploitative characteristics, cutting tools durability depends on the character, intensity and the speed of wearing. Identification of tool wearing is of great significance for the purpose of avoiding sooner or later replacement of tools. The parameters of tool wearing can be measured by out-process and in-process-measuring systems. Given the extremely limiting role of the former in modern production lines, development of the latter （the indirect measuring systems） has gained prominence, The basis of indirect measuring systems comprises a set of various signals originating from the units of the system under treatment which stand in certain correlations with the wearing parameters. The paper presents mathematical models of axial force designed on the basis of experimental research in drilling tempered steel by twist drills made of high-speed steel manufactured by powder metallurgy.

Mathematical modelling on diffusion and control of COVIDe19

In this paper,we develop a mathematical model for the spread and control of the coronavirus disease.An outbreak of COVID-19 has led to more than one million confirmed cases as of April 3rd,2020.Understanding the early spread dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas.Combining a mathematical model of severe COVID-19 spread with four datasets from within and outside of Wuhan,China;it is estimated how spread in Wuhan varied between January and February 2020.It is used these estimates to assess the potential for sustained human-to-human spread to occur in locations outside Wuhan if disease holders were introduced.It is combined SEIR framework model with data on cases of COVID-19 in China and International cases that originated in Wuhan to estimate how spread had varied over time during January and February 2020.Based on these estimates,it is calculated the probability that freshly introduced cases might produce outbreaks in other regions.Also,it is calculated approximately the median day by day basic reproduction number in Wuhan,refused from 2$45(95%CI:1.16-4.87)one week before travel restrictions were introduced on Jan 23rd,2020,to 1.05(0.42-2.40)one week after.Based on our estimates of,presumptuous SARS approximating disparity,it is computed that in locations with a similar spread potential to Wuhan in near the beginning of January,some time ago there are at least four independently set up cases,there is a more than fifty percent chance the infection will found within those inhabitants.COVID-19 spreading probably refused in Wuhan during delayed January 2020,corresponding with the prologue of voyage control channels.As more cases arrive in international locations with similar spread potential to Wuhan,before these organize measures,it is likely many chains of spread will fail to create initially but might lead to innovative outbreaks ultimately.

Mathematical modelling for Zoonotic Visceral Leishmaniasis dynamics:A new analysis considering updated parameters and notified human Brazilian data

Brazil is one of the highest endemic countries for Zoonotic Visceral Leishmaniasis:according to the Brazilian Ministry of Health,the annual number of new human cases and deaths due to this disease has been increasing for the last 20 years.In addition,regarding the Americas,the specific relationship between canine and human for Visceral Leishmaniasis dynamics is still not well understood.In this work we propose a new model for Zoonotic Visceral Leishmaniasis,based on the models previously published by Burattini et al.(1998)and Ribas et al.(2013).Herein,we modeled the disease dynamics using a modified set of differential equations from those two authors,considering the same assumptions(inclusion of human,dog and sandfly populations,all constants over time).From this set of equations we were able to calculate the basic reproduction number R 0 and to analyze the stability and sensitivity of the system to the parameters variability.As main result,when the stability of the system is reached,the normalized reporting human cases rate is estimated in 9.12E-08/day.This estimation is very close to the 2015 report from Araçatuba city,5.69E-08/day.We also observed from stability and sensitivity analysis that the activity of sandfly population is critical to introduction and maintenance of Zoonotic Visceral Leishmaniasis in the population.In addition,the importance of dog as source of infection concentrates on latent dog,since it does not show clinical symptoms and signs and,therefore,has a great contribution to disease dissemination.As conclusion,considering the presently ethical issues regarding to elimination of positive dog in Brazil and the highly sensitivity of disease dynamics on sandfly population,we recommend that the sandfly population control should be prioritized.

Mathematical and Numerical Modelling of Copper Tube Extrusion after Optimizing Geometrical and Operating Parameters

This study aimed to optimize cross-sectional area of the extruder and the flow rate of the material through the extruder. Extrusion process was first modelized using the continuum mechanics method before being simulated with the commercial software LS-DYNA using the Johnson-Cook model based on the finite element method after optimization of the factors with simplex algorithm. The study was carried out on a connecting rod: diameter of 145 mm, cross-section of 1.65 m2, length of 0.25 m, volume of 0.41 m3 and a mass of 37 kg. Optimum parameters obtained were temperature of 850℃, flow rate of 0.237 m/s, die diameter of 19.2 mm, pin diameter of 14 mm, extrusion strength of 565.6 kN and press pressure of 245 GPa. From these factors, a blank was obtained with external and internal diameters of 19.2 and 14 mm respectively over a length of 28 m with a thickness of 2.6 mm. Simulation using LS-DYNA software resulted in a difference in values of 7.4% between optimization and simulation when the difference of 2.4% was found between modelling and simulation. These values make the process optimal for industrial application to improve the extrusion requirements of copper tubes.

Research on the Mechanism of Impedance Matching for Underwater Acoustic Transmitter based on Mathematical Modelling and Corresponding Balance Transformer

With the progress of power transmission technology, it is necessary for researchers to conduct related research on impedance matching. In this paper, we conduct research on the mechanism of impedance matching for underwater acoustic transmitter based on mathematical modelling and corresponding balance transformer. To realize underwater acoustic signal of wide band and high power emission, in addition to need the bandwidth performance good transducer array yuan, to a large extent also depends on a good matching between the transducer and amplifier. The result shows the feasibility and robustness of our designed system.

A framework for dynamic modelling of railway track switches considering the switch blades,actuators and control systems

The main contribution of this paper is the development and demonstration of a novel methodology that can be followed to develop a simulation twin of a railway track switch system to test the functionality in a digital environment.This is important because,globally,railway track switches are used to allow trains to change routes;they are a key part of all railway networks.However,because track switches are single points of failure and safety-critical,their inability to operate correctly can cause significant delays and concomitant costs.In order to better understand the dynamic behaviour of switches during operation,this paper has developed a full simulation twin of a complete track switch system.The approach fuses finite element for the rail bending and motion,with physics-based models of the electromechanical actuator system and the control system.Hence,it provides researchers and engineers the opportunity to explore and understand the design space around the dynamic operation of new switches and switch machines before they are built.This is useful for looking at the modification or monitoring of existing switches,and it becomes even more important when new switch concepts are being considered and evaluated.The simulation is capable of running in real time or faster meaning designs can be iterated and checked interactively.The paper describes the modelling approach,demonstrates the methodology by developing the system model for a novel“REPOINT”switch system,and evaluates the system level performance against the dynamic performance requirements for the switch.In the context of that case study,it is found that the proposed new actuation system as designed can meet(and exceed)the system performance requirements,and that the fault tolerance built into the actuation ensures continued operation after a single actuator failure.

MATHEMATICAL MODELLING OF DEGRADATION AND FLUVIAL PROCESS DOWNSTREAM RESERVOIRS

To research into the problem of degradation and fluvial process downstream reservoirs and its influence on flood control and navigation, a 1-D mathematical model of degradation and fluvial process downstream the reservoir was established in this paper. The non-equilibrium transport of non-uniform suspended load, the non-uniform bedload transport and bed material sorting were considered in the model. Some techniques were suggested for some problems in calculation, such as the effective suspended load carrying capacity of the different reaches of bed materials, the coefficient of suspended load carrying capacity, the recovering coefficient of carrying capacity, the mixed layer thickness, the bedload transport width, bifurcation and confluence of main and branch channel, and the distribution of deposition and erosion along the cross section, etc. The model was tested by the data of degradation downstream the Danjiangkou reservoir on the Hanjiang River and the data of degradation downstream the Gezhouba Project on the Yangtze River.