The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of ga...The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of gas hydrates,since a large amount of gas is released.Intensive emissions of gases from the earth’s interior are observed on the ocean floor.They are also associated with a large number of subvertical geological structures under the ocean floor,coming to the surface in the formof local ring funnels(pockmarks).Many similar objects have also been found on land.Particular interest in this problemis caused by climate threats associated with the release of greenhouse gases.The movement of gas released fromthe hydrate to the breakthrough channel is similar to the gas inflow to the well(without hydrate),which is usually described by a two-term filtration law.In this work,a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law ofmotion is developed.The systemis split in two blocks by physical processes,taking into account the quadratic correction to the velocity in the filtration law.The first block is responsible for the convective transfer of saturation parameters in the model,water,gas and hydrate saturations are taken into account.The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom,taking into account heat and mass transfer in a porous medium.The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space.For numerical modeling,the support operator method is used,which makes it possible to discretize partial differential equations on irregular grids,which allows taking into account the complex geometry and lithology of the reservoir.A difference scheme based on the support operator method is developed,which,due to the mutually consistent approximation of vector analysis operations(divergence and gradient),allows to take into account the various flux laws between adjacent grid cells,including quadratic corrections to the velocity.Based on the developed numerical algorithms and their program implementations,calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration.The results obtained correspond to the physics of the processes under consideration.展开更多
A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, an...A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model.展开更多
Taking the electroslag remelting with pipe electrode(ESR-PE)and electroslag remelting with solid electrode(ESR-SE)as the research objects,a two-dimensional steady-state mathematical model of coupled electromagnetic fi...Taking the electroslag remelting with pipe electrode(ESR-PE)and electroslag remelting with solid electrode(ESR-SE)as the research objects,a two-dimensional steady-state mathematical model of coupled electromagnetic field equation,energy equation,and flow equation was established.The distribution of its current density,Joule heat,flow field,and temperature field was compared and the difference of their molten metal pool was analyzed.The results show that compared with those of ESR-SE,current density distribution and Joule heating area of ESR-PE are mainly concentrated in the inner and outer wall areas of the electrode tip,while the Joule heat generated in the central area of the slag pool is less.In the ESR-PE,the slag flows from the outside of the electrode to the hollow area of the electrode,which makes the temperature distribution in the slag pool is more uniform.Affected by the Joule heating area and flow field,the heat of ESR-SE is concentrated below the electrode in the slag pool area and it transfers from the center to the periphery.However,in the ESR-PE,the heat is concentrated near the inner and outer walls of the electrode tip,and the heat is transferred from the periphery to the center of the slag pool.The molten metal pool depth of ESR-SE is 0.1188 m and that of ESR-PE is 0.0962 m.Compared with that of ESR-SE,the molten metal pool of ESR-PE is shallower and flatter.展开更多
In the paper a new two-dimensional 'man-WCV'(water cooling vest) mathematical model is developed. This model is of practical use: it can predict transient temperature responses and body temperature distributio...In the paper a new two-dimensional 'man-WCV'(water cooling vest) mathematical model is developed. This model is of practical use: it can predict transient temperature responses and body temperature distribution for a person in a nonuniform hot environment, doing various jobs and dressed in different clothes. In addition, the results calculated from the model can be used to optimize the distribution of the tube-net lined on the WCV and to evaluate an individual thermal conditioning system with cooling water. The results obtained from the model agree well with the author's experimental data.展开更多
A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended i...A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.展开更多
A two-dimensional mathematical model based on the macrohomogeneous theory of porous electrodes was developed for a cylindrical Zn-MnO2 alkaline cell. The model was applied to understand the effect of the length of the...A two-dimensional mathematical model based on the macrohomogeneous theory of porous electrodes was developed for a cylindrical Zn-MnO2 alkaline cell. The model was applied to understand the effect of the length of the anode current collector on the cell performance. Results are presented for the continuous discharge at a high rate of 1A and a moderate rate of 0.2A for a AA-sized cell. With a typical length of an anode current collector at about 70%of the cell height, the analysis showed that an increase in the length of the anode current collector would benefit the lower rate of discharge more than the higher rate of discharge.展开更多
This paper investigates ruin,capital injection,and dividends for a two-dimensional risk model.The model posits that surplus levels of insurance companies are governed by a perturbed composite Poisson risk model.This m...This paper investigates ruin,capital injection,and dividends for a two-dimensional risk model.The model posits that surplus levels of insurance companies are governed by a perturbed composite Poisson risk model.This model introduces a dependence between the two surplus levels,present in both the associated perturbations and the claims resulting from common shocks.Critical levels of capital injection and dividends are established for each of the two risks.The surplus levels are observed discretely at fixed intervals,guiding decisions on capital injection,dividends,and ruin at these junctures.This study employs a two-dimensional Fourier cosine series expansion method to approximate the finite time expected discounted operating cost until ruin.The ensuing approximation error is also quantified.The validity and accuracy of the method are corroborated through numerical examples.Furthermore,the research delves into the optimal capital allocation problem.展开更多
In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment a...In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment among teaching,learning,and assessment.To counter these challenges,we propose an Inquiry-Construction Double-Helix model that uses a domain-specific knowledge graph as its cognitive spine.The model interweaves two mutually reinforcing strands-student-driven inquiry and systematic knowledge construction-into a double-helix trajectory analogous to DNA replication.The Inquiry Strand is launched by authentic,situation-based tasks that shepherd students through the complete cycle:question→hypothesis→verification→reflection.The Construction Strand simultaneously externalizes,restructures,and internalizes core disciplinary concepts via visual,hierarchical knowledge graphs.Within the flow of a lesson,the two strands alternately dominate and scaffold each other,securing the co-development of conceptual understanding,procedural fluency,and mathematical literacy.Empirical evidence demonstrates that this model significantly enhances students’systematic knowledge integration,problem-solving transfer ability,and core mathematical competencies,offering a replicable and operable teaching paradigm and practical pathway for deepening high school mathematics classroom reform.展开更多
Vehicle electrification,an important method for reducing carbon emissions from road transport,has been promoted globally.In this study,we analyze how individuals adapt to this transition in transportation and its subs...Vehicle electrification,an important method for reducing carbon emissions from road transport,has been promoted globally.In this study,we analyze how individuals adapt to this transition in transportation and its subsequent impact on urban structure.Considering the varying travel costs associated with electric and fuel vehicles,we analyze the dynamic choices of households concerning house locations and vehicle types in a two-dimensional monocentric city.A spatial equilibrium is developed to model the interactions between urban density,vehicle age and vehicle type.An agent-based microeconomic residential choice model dynamically coupled with a house rent market is developed to analyze household choices of home locations and vehicle energy types,considering vehicle ages and competition for public charging piles.Key findings from our proposed models show that the proportion of electric vehicles(EVs)peaks at over 50%by the end of the first scrappage period,accompanied by more than a 40%increase in commuting distance and time compared to the scenario with only fuel vehicles.Simulation experiments on a theoretical grid indicate that heterogeneity-induced residential segregation can lead to urban sprawl and congestion.Furthermore,households with EVs tend to be located farther from the city center,and an increase in EV ownership contributes to urban expansion.Our study provides insights into how individuals adapt to EV transitions and the resulting impacts on home locations and land use changes.It offers a novel perspective on the dynamic interactions between EV adoption and urban development.展开更多
Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies i...Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.展开更多
Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.Thi...Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.展开更多
The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternat...The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternative/renewable sources.One of the economicalways to get energy is through the utilization of solar ponds.In this study,a mathematical model of a salt gradient solar pond under the Islamabad climatic conditions has been analyzed for the first time.The model uses a one-dimensional finite difference explicit method for optimization of different zone thicknesses.The model depicts that NCZ(Non-Convective Zone)thickness has a significant effect on LCZ(Lower Convective Zone)temperature and should be kept less than 1.7mfor the optimal temperature.It is also observed that for long-termoperation of a solar pond,heat should be extracted by keeping the mass flowrate of 17.3 kg/m^(2)/day.Themodel also suggests that when the bottom reflectivity is about 0.3,then only 24%of the radiation is absorbed in the pond.展开更多
Improving the specific,technical,economic,and environmental characteristics of piston engines(ICE)operating on alternative gaseous fuels is a pressing task for the energy and mechanical engineering industries.The aim ...Improving the specific,technical,economic,and environmental characteristics of piston engines(ICE)operating on alternative gaseous fuels is a pressing task for the energy and mechanical engineering industries.The aim of the study was to optimize the parameters of the ICE working cycle after replacing the base fuel(propane-butane blend)with syngas from wood sawdust to improve its technical and economic performance based on mathematical modeling.The modeling results were verified through experimental studies(differences for key parameters did not exceed 4.0%).The object of the study was an electric generator based on a single-cylinder spark ignition engine with a power of 1 kW.The article describes the main approaches to creating a mathematical model of the engine working cycle,a test bench for modeling verification,physicochemical properties of the base fuel(propane-butane blend),and laboratory syngas.It was shown that replacing the fuel from a propane-butane blend to laboratory syngas caused a decrease in engine efficiency to 33%(the efficiency of the base ICE was 0.179 vs.the efficiency of 0.119 for the converted ICE for the 0.59 kW power mode).Engine efficiency was chosen as the key criterion for optimizing the working cycle.As a result of optimization,the efficiency of the converted syngas engine was 6.1%higher than that of the base engine running on the propane-butane blend,and the power drop did not exceed 8.0%.Thus,careful fine-tuning of the working cycle parameters allows increasing the technical and economic characteristics of the syngas engine to the level of ICEs running on traditional types of fuel.展开更多
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...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.展开更多
The mathematical model of 4He quantum interferometer gyroscope is presented. The model includes the driven equation, the current equation and the position equation. Therefore, it can sufficiently describe the gyro- sc...The mathematical model of 4He quantum interferometer gyroscope is presented. The model includes the driven equation, the current equation and the position equation. Therefore, it can sufficiently describe the gyro- scope system. The driven equation shows the thermally driven gyroscope can work for a long time but the pres- sure driven one cannot. From the current equation, the superfluid currents passing through the weak link contain the AC currents which show the rotation flux, and other currents caused by drive. As shown in the position equa- tion, the displacement of diaphragm is the only detectable parameter in the gyroscope system. The model is tested by the simulations based on experimental parameters, and can be used to research performance of the gyroscope and analyse the gyroscope error.展开更多
The most prospective method for certain structural failures and damages that cannot employ redundancy is self-repairing techniques, to ensure especially the maximum flight safety. Based on the characters of self-repai...The most prospective method for certain structural failures and damages that cannot employ redundancy is self-repairing techniques, to ensure especially the maximum flight safety. Based on the characters of self-repairing aircraft, this paper states some basic assumptions of the self-repairing aircraft, and puts forward some special new conceptions concerning the self-repairing aircraft: control input, operating input, command input, repair input and operating and control factor as well as their relationships. Thus it provides a simple and reliable mathematical model structure for the research on the self-repairing control of the aircraft.展开更多
Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect th...Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.展开更多
Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad...Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.展开更多
In the chemical vapor deposition（CVD） process of C/C composites,the dynamics and mechanism of precursor gas flowing behavior were analyzed mathematically,in which the precursor gas was infiltrated by the pressure di...In the chemical vapor deposition（CVD） process of C/C composites,the dynamics and mechanism of precursor gas flowing behavior were analyzed mathematically,in which the precursor gas was infiltrated by the pressure difference of the gas flowing through felt.Differential equations were educed which characterized the relations among the pressure inside the felt,the pressure outside the felt of the precursor gas and the porosity of the felt as a function of CVD duration.The gas residence time during the infiltration process through the felt was obtained from the differential equations.The numerical verification is in good agreement with the practical process,indicating the good reliability of the current mathematical model.展开更多
According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas...According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance（fast,） streamline method is employed to solve this model as an alternative to traditional finite（difference） （methods.） Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method （BEM）, an explicit total variation diminishing （TVD） method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less（information） need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an（effective） tool for early stage screening and reservoir dynamic management of the CO2（miscible） oil field.展开更多
基金the framework of the state assignment of Keldysh Institute of Applied Mathematics of RAS(Project No.125020701776-0)the Ministry of Education and Science of Russia for IO RAS(Project No.FMWE-2024-0018).
文摘The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of gas hydrates,since a large amount of gas is released.Intensive emissions of gases from the earth’s interior are observed on the ocean floor.They are also associated with a large number of subvertical geological structures under the ocean floor,coming to the surface in the formof local ring funnels(pockmarks).Many similar objects have also been found on land.Particular interest in this problemis caused by climate threats associated with the release of greenhouse gases.The movement of gas released fromthe hydrate to the breakthrough channel is similar to the gas inflow to the well(without hydrate),which is usually described by a two-term filtration law.In this work,a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law ofmotion is developed.The systemis split in two blocks by physical processes,taking into account the quadratic correction to the velocity in the filtration law.The first block is responsible for the convective transfer of saturation parameters in the model,water,gas and hydrate saturations are taken into account.The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom,taking into account heat and mass transfer in a porous medium.The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space.For numerical modeling,the support operator method is used,which makes it possible to discretize partial differential equations on irregular grids,which allows taking into account the complex geometry and lithology of the reservoir.A difference scheme based on the support operator method is developed,which,due to the mutually consistent approximation of vector analysis operations(divergence and gradient),allows to take into account the various flux laws between adjacent grid cells,including quadratic corrections to the velocity.Based on the developed numerical algorithms and their program implementations,calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration.The results obtained correspond to the physics of the processes under consideration.
文摘A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model.
基金The authors gratefully express their appreciation to Natural Science Foundation of China(No.51974153,No.U1960203)the Joint Fund of State key Laboratory of Marine Engineering and University of Science and Technology Liaoning(SKLMEA-USTLN-201901,SKLMEA-USTL-201707)the China Scholarship Council(201908210457).
文摘Taking the electroslag remelting with pipe electrode(ESR-PE)and electroslag remelting with solid electrode(ESR-SE)as the research objects,a two-dimensional steady-state mathematical model of coupled electromagnetic field equation,energy equation,and flow equation was established.The distribution of its current density,Joule heat,flow field,and temperature field was compared and the difference of their molten metal pool was analyzed.The results show that compared with those of ESR-SE,current density distribution and Joule heating area of ESR-PE are mainly concentrated in the inner and outer wall areas of the electrode tip,while the Joule heat generated in the central area of the slag pool is less.In the ESR-PE,the slag flows from the outside of the electrode to the hollow area of the electrode,which makes the temperature distribution in the slag pool is more uniform.Affected by the Joule heating area and flow field,the heat of ESR-SE is concentrated below the electrode in the slag pool area and it transfers from the center to the periphery.However,in the ESR-PE,the heat is concentrated near the inner and outer walls of the electrode tip,and the heat is transferred from the periphery to the center of the slag pool.The molten metal pool depth of ESR-SE is 0.1188 m and that of ESR-PE is 0.0962 m.Compared with that of ESR-SE,the molten metal pool of ESR-PE is shallower and flatter.
文摘In the paper a new two-dimensional 'man-WCV'(water cooling vest) mathematical model is developed. This model is of practical use: it can predict transient temperature responses and body temperature distribution for a person in a nonuniform hot environment, doing various jobs and dressed in different clothes. In addition, the results calculated from the model can be used to optimize the distribution of the tube-net lined on the WCV and to evaluate an individual thermal conditioning system with cooling water. The results obtained from the model agree well with the author's experimental data.
基金supported by the National Natural Science Foundation of China (No. 10772051)the ScienceFoundation for the Excellent Youth Scholars of Higher Education of Shanghai (No. 571215)the Research Fund for the Doctoral Program of University of Shanghai for Science and Technology(No. 10D214)
文摘A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.
文摘A two-dimensional mathematical model based on the macrohomogeneous theory of porous electrodes was developed for a cylindrical Zn-MnO2 alkaline cell. The model was applied to understand the effect of the length of the anode current collector on the cell performance. Results are presented for the continuous discharge at a high rate of 1A and a moderate rate of 0.2A for a AA-sized cell. With a typical length of an anode current collector at about 70%of the cell height, the analysis showed that an increase in the length of the anode current collector would benefit the lower rate of discharge more than the higher rate of discharge.
基金supported by the Shihezi University High-Level Talents Research Startup Project(Project No.RCZK202521)the National Natural Science Foundation of China(Grant Nos.12271066,11871121,12171405)+1 种基金the Chongqing Natural Science Foundation Joint Fund for Innovation and Development Project(Project No.CSTB2024NSCQLZX0085)the Chongqing Normal University Foundation(Grant No.23XLB018).
文摘This paper investigates ruin,capital injection,and dividends for a two-dimensional risk model.The model posits that surplus levels of insurance companies are governed by a perturbed composite Poisson risk model.This model introduces a dependence between the two surplus levels,present in both the associated perturbations and the claims resulting from common shocks.Critical levels of capital injection and dividends are established for each of the two risks.The surplus levels are observed discretely at fixed intervals,guiding decisions on capital injection,dividends,and ruin at these junctures.This study employs a two-dimensional Fourier cosine series expansion method to approximate the finite time expected discounted operating cost until ruin.The ensuing approximation error is also quantified.The validity and accuracy of the method are corroborated through numerical examples.Furthermore,the research delves into the optimal capital allocation problem.
文摘In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment among teaching,learning,and assessment.To counter these challenges,we propose an Inquiry-Construction Double-Helix model that uses a domain-specific knowledge graph as its cognitive spine.The model interweaves two mutually reinforcing strands-student-driven inquiry and systematic knowledge construction-into a double-helix trajectory analogous to DNA replication.The Inquiry Strand is launched by authentic,situation-based tasks that shepherd students through the complete cycle:question→hypothesis→verification→reflection.The Construction Strand simultaneously externalizes,restructures,and internalizes core disciplinary concepts via visual,hierarchical knowledge graphs.Within the flow of a lesson,the two strands alternately dominate and scaffold each other,securing the co-development of conceptual understanding,procedural fluency,and mathematical literacy.Empirical evidence demonstrates that this model significantly enhances students’systematic knowledge integration,problem-solving transfer ability,and core mathematical competencies,offering a replicable and operable teaching paradigm and practical pathway for deepening high school mathematics classroom reform.
基金supported by National Natural Science Foundation of China(72288101,72361137002,and 72101018)the Dutch Research Council(NWO Grant 482.22.01).
文摘Vehicle electrification,an important method for reducing carbon emissions from road transport,has been promoted globally.In this study,we analyze how individuals adapt to this transition in transportation and its subsequent impact on urban structure.Considering the varying travel costs associated with electric and fuel vehicles,we analyze the dynamic choices of households concerning house locations and vehicle types in a two-dimensional monocentric city.A spatial equilibrium is developed to model the interactions between urban density,vehicle age and vehicle type.An agent-based microeconomic residential choice model dynamically coupled with a house rent market is developed to analyze household choices of home locations and vehicle energy types,considering vehicle ages and competition for public charging piles.Key findings from our proposed models show that the proportion of electric vehicles(EVs)peaks at over 50%by the end of the first scrappage period,accompanied by more than a 40%increase in commuting distance and time compared to the scenario with only fuel vehicles.Simulation experiments on a theoretical grid indicate that heterogeneity-induced residential segregation can lead to urban sprawl and congestion.Furthermore,households with EVs tend to be located farther from the city center,and an increase in EV ownership contributes to urban expansion.Our study provides insights into how individuals adapt to EV transitions and the resulting impacts on home locations and land use changes.It offers a novel perspective on the dynamic interactions between EV adoption and urban development.
文摘Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
文摘Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.
文摘The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternative/renewable sources.One of the economicalways to get energy is through the utilization of solar ponds.In this study,a mathematical model of a salt gradient solar pond under the Islamabad climatic conditions has been analyzed for the first time.The model uses a one-dimensional finite difference explicit method for optimization of different zone thicknesses.The model depicts that NCZ(Non-Convective Zone)thickness has a significant effect on LCZ(Lower Convective Zone)temperature and should be kept less than 1.7mfor the optimal temperature.It is also observed that for long-termoperation of a solar pond,heat should be extracted by keeping the mass flowrate of 17.3 kg/m^(2)/day.Themodel also suggests that when the bottom reflectivity is about 0.3,then only 24%of the radiation is absorbed in the pond.
基金the Ministry of Science and Higher Education of the Russian Federation(Ural Federal University Program of Development within the Priority-2030 Program)is gratefully acknowledged.
文摘Improving the specific,technical,economic,and environmental characteristics of piston engines(ICE)operating on alternative gaseous fuels is a pressing task for the energy and mechanical engineering industries.The aim of the study was to optimize the parameters of the ICE working cycle after replacing the base fuel(propane-butane blend)with syngas from wood sawdust to improve its technical and economic performance based on mathematical modeling.The modeling results were verified through experimental studies(differences for key parameters did not exceed 4.0%).The object of the study was an electric generator based on a single-cylinder spark ignition engine with a power of 1 kW.The article describes the main approaches to creating a mathematical model of the engine working cycle,a test bench for modeling verification,physicochemical properties of the base fuel(propane-butane blend),and laboratory syngas.It was shown that replacing the fuel from a propane-butane blend to laboratory syngas caused a decrease in engine efficiency to 33%(the efficiency of the base ICE was 0.179 vs.the efficiency of 0.119 for the converted ICE for the 0.59 kW power mode).Engine efficiency was chosen as the key criterion for optimizing the working cycle.As a result of optimization,the efficiency of the converted syngas engine was 6.1%higher than that of the base engine running on the propane-butane blend,and the power drop did not exceed 8.0%.Thus,careful fine-tuning of the working cycle parameters allows increasing the technical and economic characteristics of the syngas engine to the level of ICEs running on traditional types of fuel.
文摘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.
基金Supported by the National Natural Science Foundation of China(61074162)the Ph.D.Program Foundation of Ministry of Education of China(200802870011)~~
文摘The mathematical model of 4He quantum interferometer gyroscope is presented. The model includes the driven equation, the current equation and the position equation. Therefore, it can sufficiently describe the gyro- scope system. The driven equation shows the thermally driven gyroscope can work for a long time but the pres- sure driven one cannot. From the current equation, the superfluid currents passing through the weak link contain the AC currents which show the rotation flux, and other currents caused by drive. As shown in the position equa- tion, the displacement of diaphragm is the only detectable parameter in the gyroscope system. The model is tested by the simulations based on experimental parameters, and can be used to research performance of the gyroscope and analyse the gyroscope error.
文摘The most prospective method for certain structural failures and damages that cannot employ redundancy is self-repairing techniques, to ensure especially the maximum flight safety. Based on the characters of self-repairing aircraft, this paper states some basic assumptions of the self-repairing aircraft, and puts forward some special new conceptions concerning the self-repairing aircraft: control input, operating input, command input, repair input and operating and control factor as well as their relationships. Thus it provides a simple and reliable mathematical model structure for the research on the self-repairing control of the aircraft.
文摘Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.
文摘Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.
基金Projects (50702078,50874123) supported by the National Natural Science Foundation of ChinaProject (2009AA03Z536) supported by the National High-tech Research and Development Program of China+1 种基金Project (2011CB606306) supported by the National Research Program of ChinaProject supported by the Program for New Century Excellent Talents in University of China
文摘In the chemical vapor deposition（CVD） process of C/C composites,the dynamics and mechanism of precursor gas flowing behavior were analyzed mathematically,in which the precursor gas was infiltrated by the pressure difference of the gas flowing through felt.Differential equations were educed which characterized the relations among the pressure inside the felt,the pressure outside the felt of the precursor gas and the porosity of the felt as a function of CVD duration.The gas residence time during the infiltration process through the felt was obtained from the differential equations.The numerical verification is in good agreement with the practical process,indicating the good reliability of the current mathematical model.
文摘According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance（fast,） streamline method is employed to solve this model as an alternative to traditional finite（difference） （methods.） Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method （BEM）, an explicit total variation diminishing （TVD） method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less（information） need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an（effective） tool for early stage screening and reservoir dynamic management of the CO2（miscible） oil field.
